Daily Papers

Domain Generalization (DG) is a critical area that focuses on developing models capable of performing well on data from unseen distributions, which is essential for real-world applications. Existing approaches primarily concentrate on learning domain-invariant features, which assume that a model robust to variations in the source domains will generalize well to unseen target domains. However, these approaches neglect a deeper analysis at the parameter level, which makes the model hard to explicitly differentiate between parameters sensitive to domain shifts and those robust, potentially hindering its overall ability to generalize. In order to address these limitations, we first build a covariance-based parameter sensitivity analysis framework to quantify the sensitivity of each parameter in a model to domain shifts. By computing the covariance of parameter gradients across multiple source domains, we can identify parameters that are more susceptible to domain variations, which serves as our theoretical foundation. Based on this, we propose Domain-Sensitive Parameter Regularization (DSP-Reg), a principled framework that guides model optimization by a soft regularization technique that encourages the model to rely more on domain-invariant parameters while suppressing those that are domain-specific. This approach provides a more granular control over the model's learning process, leading to improved robustness and generalization to unseen domains. Extensive experiments on benchmarks, such as PACS, VLCS, OfficeHome, and DomainNet, demonstrate that DSP-Reg outperforms state-of-the-art approaches, achieving an average accuracy of 66.7\% and surpassing all baselines.

Domain adaptation framework of GANs has achieved great progress in recent years as a main successful approach of training contemporary GANs in the case of very limited training data. In this work, we significantly improve this framework by proposing an extremely compact parameter space for fine-tuning the generator. We introduce a novel domain-modulation technique that allows to optimize only 6 thousand-dimensional vector instead of 30 million weights of StyleGAN2 to adapt to a target domain. We apply this parameterization to the state-of-art domain adaptation methods and show that it has almost the same expressiveness as the full parameter space. Additionally, we propose a new regularization loss that considerably enhances the diversity of the fine-tuned generator. Inspired by the reduction in the size of the optimizing parameter space we consider the problem of multi-domain adaptation of GANs, i.e. setting when the same model can adapt to several domains depending on the input query. We propose the HyperDomainNet that is a hypernetwork that predicts our parameterization given the target domain. We empirically confirm that it can successfully learn a number of domains at once and may even generalize to unseen domains. Source code can be found at https://github.com/MACderRu/HyperDomainNet

The objective of domain generalization (DG) is to enhance the transferability of the model learned from a source domain to unobserved domains. To prevent overfitting to a specific domain, Sharpness-Aware Minimization (SAM) reduces source domain's loss sharpness. Although SAM variants have delivered significant improvements in DG, we highlight that there's still potential for improvement in generalizing to unknown domains through the exploration on data space. This paper introduces an objective rooted in both parameter and data perturbed regions for domain generalization, coined Unknown Domain Inconsistency Minimization (UDIM). UDIM reduces the loss landscape inconsistency between source domain and unknown domains. As unknown domains are inaccessible, these domains are empirically crafted by perturbing instances from the source domain dataset. In particular, by aligning the loss landscape acquired in the source domain to the loss landscape of perturbed domains, we expect to achieve generalization grounded on these flat minima for the unknown domains. Theoretically, we validate that merging SAM optimization with the UDIM objective establishes an upper bound for the true objective of the DG task. In an empirical aspect, UDIM consistently outperforms SAM variants across multiple DG benchmark datasets. Notably, UDIM shows statistically significant improvements in scenarios with more restrictive domain information, underscoring UDIM's generalization capability in unseen domains. Our code is available at https://github.com/SJShin-AI/UDIM.

This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer. Specifically, we propose treating the element-wise contributions to the final results as the rationale for making a decision and representing the rationale for each sample as a matrix. For a well-generalized model, we suggest the rationale matrices for samples belonging to the same category should be similar, indicating the model relies on domain-invariant clues to make decisions, thereby ensuring robust results. To implement this idea, we introduce a rationale invariance loss as a simple regularization technique, requiring only a few lines of code. Our experiments demonstrate that the proposed approach achieves competitive results across various datasets, despite its simplicity. Code is available at https://github.com/liangchen527/RIDG.

Neural networks are known to be data hungry and domain sensitive, but it is nearly impossible to obtain large quantities of labeled data for every domain we are interested in. This necessitates the use of domain adaptation strategies. One common strategy encourages generalization by aligning the global distribution statistics between source and target domains, but one drawback is that the statistics of different domains or tasks are inherently divergent, and smoothing over these differences can lead to sub-optimal performance. In this paper, we propose the framework of {\it Domain Differential Adaptation (DDA)}, where instead of smoothing over these differences we embrace them, directly modeling the difference between domains using models in a related task. We then use these learned domain differentials to adapt models for the target task accordingly. Experimental results on domain adaptation for neural machine translation demonstrate the effectiveness of this strategy, achieving consistent improvements over other alternative adaptation strategies in multiple experimental settings.

When training large flexible models, practitioners often rely on grid search to select hyperparameters that control over-fitting. This grid search has several disadvantages: the search is computationally expensive, requires carving out a validation set that reduces the available data for training, and requires users to specify candidate values. In this paper, we propose an alternative: directly learning regularization hyperparameters on the full training set via the evidence lower bound ("ELBo") objective from variational methods. For deep neural networks with millions of parameters, we recommend a modified ELBo that upweights the influence of the data likelihood relative to the prior. Our proposed technique overcomes all three disadvantages of grid search. In a case study on transfer learning of image classifiers, we show how our method reduces the 88+ hour grid search of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.

Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the simple case of a one-dimensional (scalar) hyperparameter. This leaves the practically important, multi-dimensional hyperparameter tuning setting unresolved. We address this open question by establishing the first general framework for establishing generalization guarantees for tuning multi-dimensional hyperparameters in data-driven settings. Our approach strengthens the generalization guarantee framework for semi-algebraic function classes by exploiting tools from real algebraic geometry, yielding sharper, more broadly applicable guarantees. For completeness, we also instantiate the first lower bound for this general setting. We further extend the analysis to hyperparameter tuning using the validation loss under minimal assumptions, and derive improved bounds when additional structure is available. Finally, we demonstrate the scope of the framework with new learnability results, including data-driven weighted group lasso and weighted fused lasso.

Domain-specific embedding models have shown promise for applications that require specialized semantic understanding, such as coding agents and financial retrieval systems, often achieving higher performance gains than general models. However, state-of-the-art embedding models are typically based on LLMs, which contain billions of parameters, making deployment challenging in resource-constrained environments. Model compression through pruning offers a promising solution, but existing pruning methods treat all parameters uniformly, failing to distinguish between general semantic representations and domain-specific patterns, leading to suboptimal pruning decisions. Thus, we propose GAPrune, a pruning framework that addresses this challenge by considering both domain importance and preserving general linguistic foundation. Our method uses Fisher Information to measure importance and general-domain gradient alignment to assess parameter behavior, then combines these signals using our Domain Alignment Importance (DAI) scoring. Lower DAI scores indicate that the parameter is either less important for the domain task or creates conflicts between domain and general objectives. Experiments on two domain benchmarks, FinMTEB and ChemTEB, show that GAPrune maintains performance within 2.5% of dense models in one-shot pruning at 50% sparsity, while outperforming all baselines. With retraining in 100 steps, GAPrune achieves +4.51% improvement on FinMTEB and +1.73% on ChemTEB, demonstrating that our pruning strategy not only preserves but enhances domain-specific capabilities. Our findings demonstrate that principled pruning strategies can achieve model compression and enhanced domain specialization, providing the research community with a new approach for development.

Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping between the data input space and the loss value. We specify the level of regularity by requiring that the loss of the network satisfies an elliptic operator over the data domain. To do this, we modify the usual empirical risk minimization objective such that we instead minimize a new objective that satisfies an elliptic operator over points within the domain. This allows us to use existing theory on elliptic operators to anticipate the behavior of the error for points outside the training set. We propose a tractable computational method that approximates the behavior of the elliptic operator while being computationally efficient. Finally, we analyze the properties of the proposed regularization to understand the performance on common problems of distribution shift and group imbalance. Numerical experiments confirm the utility of the proposed regularization technique.

Recent domain generalization (DG) approaches typically use the hypothesis learned on source domains for inference on the unseen target domain. However, such a hypothesis can be arbitrarily far from the optimal one for the target domain, induced by a gap termed ``adaptivity gap''. Without exploiting the domain information from the unseen test samples, adaptivity gap estimation and minimization are intractable, which hinders us to robustify a model to any unknown distribution. In this paper, we first establish a generalization bound that explicitly considers the adaptivity gap. Our bound motivates two strategies to reduce the gap: the first one is ensembling multiple classifiers to enrich the hypothesis space, then we propose effective gap estimation methods for guiding the selection of a better hypothesis for the target. The other method is minimizing the gap directly by adapting model parameters using online target samples. We thus propose Domain-specific Risk Minimization (DRM). During training, DRM models the distributions of different source domains separately; for inference, DRM performs online model steering using the source hypothesis for each arriving target sample. Extensive experiments demonstrate the effectiveness of the proposed DRM for domain generalization with the following advantages: 1) it significantly outperforms competitive baselines on different distributional shift settings; 2) it achieves either comparable or superior accuracies on all source domains compared to vanilla empirical risk minimization; 3) it remains simple and efficient during training, and 4) it is complementary to invariant learning approaches.

Vision Foundation Models (VFMs) excel in generalization due to large-scale pretraining, but fine-tuning them for Domain Generalized Semantic Segmentation (DGSS) while maintaining this ability remains challenging. Existing approaches either selectively fine-tune parameters or freeze the VFMs and update only the adapters, both of which may underutilize the VFMs' full potential in DGSS tasks. We observe that domain-sensitive parameters in VFMs, arising from task and distribution differences, can hinder generalization. To address this, we propose FisherTune, a robust fine-tuning method guided by the Domain-Related Fisher Information Matrix (DR-FIM). DR-FIM measures parameter sensitivity across tasks and domains, enabling selective updates that preserve generalization and enhance DGSS adaptability. FisherTune incorporates variational inference to stabilize DR-FIM estimation, treating parameters as Gaussian-distributed variables and leveraging pre-trained priors. Extensive experiments show that FisherTune achieves superior cross-domain segmentation while maintaining generalization, outperforming selective-parameter and adapter-based methods.

Domain generalization (DG) aims to tackle the distribution shift between training domains and unknown target domains. Generating new domains is one of the most effective approaches, yet its performance gain depends on the distribution discrepancy between the generated and target domains. Distributionally robust optimization is promising to tackle distribution discrepancy by exploring domains in an uncertainty set. However, the uncertainty set may be overwhelmingly large, leading to low-confidence prediction in DG. It is because a large uncertainty set could introduce domains containing semantically different factors from training domains. To address this issue, we propose to perform a moderately distributional exploration (MODE) for domain generalization. Specifically, MODE performs distribution exploration in an uncertainty subset that shares the same semantic factors with the training domains. We show that MODE can endow models with provable generalization performance on unknown target domains. The experimental results show that MODE achieves competitive performance compared to state-of-the-art baselines.

In this paper, we propose a framework for efficient Source-Free Domain Adaptation (SFDA) in the context of time-series, focusing on enhancing both parameter efficiency and data-sample utilization. Our approach introduces an improved paradigm for source-model preparation and target-side adaptation, aiming to enhance training efficiency during target adaptation. Specifically, we reparameterize the source model's weights in a Tucker-style decomposed manner, factorizing the model into a compact form during the source model preparation phase. During target-side adaptation, only a subset of these decomposed factors is fine-tuned, leading to significant improvements in training efficiency. We demonstrate using PAC Bayesian analysis that this selective fine-tuning strategy implicitly regularizes the adaptation process by constraining the model's learning capacity. Furthermore, this re-parameterization reduces the overall model size and enhances inference efficiency, making the approach particularly well suited for resource-constrained devices. Additionally, we demonstrate that our framework is compatible with various SFDA methods and achieves significant computational efficiency, reducing the number of fine-tuned parameters and inference overhead in terms of MACs by over 90% while maintaining model performance.

We introduce Domain-specific Masks for Generalization, a model for improving both in-domain and out-of-domain generalization performance. For domain generalization, the goal is to learn from a set of source domains to produce a single model that will best generalize to an unseen target domain. As such, many prior approaches focus on learning representations which persist across all source domains with the assumption that these domain agnostic representations will generalize well. However, often individual domains contain characteristics which are unique and when leveraged can significantly aid in-domain recognition performance. To produce a model which best generalizes to both seen and unseen domains, we propose learning domain specific masks. The masks are encouraged to learn a balance of domain-invariant and domain-specific features, thus enabling a model which can benefit from the predictive power of specialized features while retaining the universal applicability of domain-invariant features. We demonstrate competitive performance compared to naive baselines and state-of-the-art methods on both PACS and DomainNet.

Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different distance measurements between source and target domains but fail to consider the optimization property of the learned model. As empirically shown in recent work, the sharpness of learned minima influences OOD generalization. To bridge this gap between optimization and OOD generalization, we study the effect of sharpness on how a model tolerates data change in domain shift which is usually captured by "robustness" in generalization. In this paper, we give a rigorous connection between sharpness and robustness, which gives better OOD guarantees for robust algorithms. It also provides a theoretical backing for "flat minima leads to better OOD generalization". Overall, we propose a sharpness-based OOD generalization bound by taking robustness into consideration, resulting in a tighter bound than non-robust guarantees. Our findings are supported by the experiments on a ridge regression model, as well as the experiments on deep learning classification tasks.

The goal of domain generalization algorithms is to predict well on distributions different from those seen during training. While a myriad of domain generalization algorithms exist, inconsistencies in experimental conditions -- datasets, architectures, and model selection criteria -- render fair and realistic comparisons difficult. In this paper, we are interested in understanding how useful domain generalization algorithms are in realistic settings. As a first step, we realize that model selection is non-trivial for domain generalization tasks. Contrary to prior work, we argue that domain generalization algorithms without a model selection strategy should be regarded as incomplete. Next, we implement DomainBed, a testbed for domain generalization including seven multi-domain datasets, nine baseline algorithms, and three model selection criteria. We conduct extensive experiments using DomainBed and find that, when carefully implemented, empirical risk minimization shows state-of-the-art performance across all datasets. Looking forward, we hope that the release of DomainBed, along with contributions from fellow researchers, will streamline reproducible and rigorous research in domain generalization.

Domain Generalization aims to develop models that can generalize to novel and unseen data distributions. In this work, we study how model architectures and pre-training objectives impact feature richness and propose a method to effectively leverage them for domain generalization. Specifically, given a pre-trained feature space, we first discover latent domain structures, referred to as pseudo-domains, that capture domain-specific variations in an unsupervised manner. Next, we augment existing classifiers with these complementary pseudo-domain representations making them more amenable to diverse unseen test domains. We analyze how different pre-training feature spaces differ in the domain-specific variances they capture. Our empirical studies reveal that features from diffusion models excel at separating domains in the absence of explicit domain labels and capture nuanced domain-specific information. On 5 datasets, we show that our very simple framework improves generalization to unseen domains by a maximum test accuracy improvement of over 4% compared to the standard baseline Empirical Risk Minimization (ERM). Crucially, our method outperforms most algorithms that access domain labels during training.

Large language models (LLMs) are commonly trained on multi-domain datasets, where domain sampling strategies significantly impact model performance due to varying domain importance across downstream tasks. Existing approaches for optimizing domain-level sampling strategies struggle with maintaining intra-domain consistency and accurately measuring domain impact. In this paper, we present Domain Impact-aware Data Sampling (DIDS). To ensure intra-domain consistency, a gradient clustering algorithm is proposed to group training data based on their learning effects, where a proxy language model and dimensionality reduction are employed to reduce computational overhead. To accurately measure domain impact, we develop a Fisher Information Matrix (FIM) guided metric that quantifies how domain-specific parameter updates affect the model's output distributions on downstream tasks, with theoretical guarantees. Furthermore, to determine optimal sampling ratios, DIDS combines both the FIM-guided domain impact assessment and loss learning trajectories that indicate domain-specific potential, while accounting for diminishing marginal returns. Extensive experiments demonstrate that DIDS achieves 3.4% higher average performance while maintaining comparable training efficiency.

Neural operators have become increasingly popular in solving partial differential equations (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the data-hungry nature of operator learning inevitably poses a bottleneck for their widespread applications. At the core of the challenge lies the absence of transferability of neural operators to new geometries. To tackle this issue, we propose operator learning with domain decomposition, a local-to-global framework to solve PDEs on arbitrary geometries. Under this framework, we devise an iterative scheme Schwarz Neural Inference (SNI). This scheme allows for partitioning of the problem domain into smaller subdomains, on which local problems can be solved with neural operators, and stitching local solutions to construct a global solution. Additionally, we provide a theoretical analysis of the convergence rate and error bound. We conduct extensive experiments on several representative PDEs with diverse boundary conditions and achieve remarkable geometry generalization compared to alternative methods. These analysis and experiments demonstrate the proposed framework's potential in addressing challenges related to geometry generalization and data efficiency.

Democratization of machine learning requires architectures that automatically adapt to new problems. Neural Differential Equations (NDEs) have emerged as a popular modeling framework by removing the need for ML practitioners to choose the number of layers in a recurrent model. While we can control the computational cost by choosing the number of layers in standard architectures, in NDEs the number of neural network evaluations for a forward pass can depend on the number of steps of the adaptive ODE solver. But, can we force the NDE to learn the version with the least steps while not increasing the training cost? Current strategies to overcome slow prediction require high order automatic differentiation, leading to significantly higher training time. We describe a novel regularization method that uses the internal cost heuristics of adaptive differential equation solvers combined with discrete adjoint sensitivities to guide the training process towards learning NDEs that are easier to solve. This approach opens up the blackbox numerical analysis behind the differential equation solver's algorithm and directly uses its local error estimates and stiffness heuristics as cheap and accurate cost estimates. We incorporate our method without any change in the underlying NDE framework and show that our method extends beyond Ordinary Differential Equations to accommodate Neural Stochastic Differential Equations. We demonstrate how our approach can halve the prediction time and, unlike other methods which can increase the training time by an order of magnitude, we demonstrate similar reduction in training times. Together this showcases how the knowledge embedded within state-of-the-art equation solvers can be used to enhance machine learning.

Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L2-regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs).

Domain generalization (DG) aims to avoid the performance degradation of the model when the distribution shift between the limited training data and unseen test data occurs. Recently, foundation models with enormous parameters have been pre-trained with huge datasets, demonstrating strong generalization ability and showing promising direction for solving the DG problem. However, fully Fine-Tuning (FT) the foundation models results in unsatisfactory out-of-distribution accuracy due to the destroyed pre-trained generalized features. Recently, Parameter-Efficient Fine-Tuning (PEFT) alleviates the above problem by fine-tuning a small portion of the model parameters while keeping the rest frozen, which achieves better generalization performance compared to FT. Nevertheless, PEFT still suffers from the issue of overfitting to the training domains. To address the above issue, we propose Parameter-Efficient Group with Orthogonal regularization (PEGO) for vision transformers, which effectively preserves the generalization ability of the pre-trained network and learns more diverse knowledge compared with conventional PEFT. Specifically, we inject a group of trainable Low-Rank Adaptation (LoRA) modules into the pre-trained model and propose an orthogonal regularization loss to enhance the generalization ability of the model. Our framework achieves SOTA performance on five DG benchmarks, while only requiring training a small number of parameters without adding additional testing cost.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder varphi^* that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder Phi^*_tau. We prove that non-commutativity steers the optimization towards Phi^*_tau instead of varphi^*, bringing the H-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning Phi^*_tau, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over 2%, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.

Distribution shift presents a significant challenge in machine learning, where models often underperform during the test stage when faced with a different distribution than the one they were trained on. This paper focuses on domain shifts, which occur when the model is applied to new domains that are different from the ones it was trained on, and propose a new approach called D^3G. Unlike previous methods that aim to learn a single model that is domain invariant, D^3G leverages domain similarities based on domain metadata to learn domain-specific models. Concretely, D^3G learns a set of training-domain-specific functions during the training stage and reweights them based on domain relations during the test stage. These domain relations can be directly obtained and learned from domain metadata. Under mild assumptions, we theoretically prove that using domain relations to reweight training-domain-specific functions achieves stronger out-of-domain generalization compared to the conventional averaging approach. Empirically, we evaluate the effectiveness of D^3G using real-world datasets for tasks such as temperature regression, land use classification, and molecule-protein binding affinity prediction. Our results show that D^3G consistently outperforms state-of-the-art methods.

Domain generalization (DG) aims to adapt a model using one or multiple source domains to ensure robust performance in unseen target domains. Recently, Parameter-Efficient Fine-Tuning (PEFT) of foundation models has shown promising results in the context of DG problem. Nevertheless, existing PEFT methods still struggle to strike a balance between preserving generalizable components of the pre-trained model and learning task-specific features. To gain insights into the distribution of generalizable components, we begin by analyzing the pre-trained weights through the lens of singular value decomposition. Building on these insights, we introduce Singular Value Decomposed Minor Components Adaptation (SoMA), an approach that selectively tunes minor singular components while keeping the residual parts frozen. SoMA effectively retains the generalization ability of the pre-trained model while efficiently acquiring task-specific skills. Moreover, we freeze domain-generalizable blocks and employ an annealing weight decay strategy, thereby achieving an optimal balance in the delicate trade-off between generalizability and discriminability. SoMA attains state-of-the-art results on multiple benchmarks that span both domain generalized semantic segmentation to domain generalized object detection. In addition, our methods introduce no additional inference overhead or regularization loss, maintain compatibility with any backbone or head, and are designed to be versatile, allowing easy integration into a wide range of tasks.

Recovering a latent potential from observed flow on a directed graph (a discrete Poisson problem with Dirichlet boundaries) is ill-posed, and the standard fix backfires: ridge regularization shrinks toward a gauge-meaningless origin, collapsing and reversing the recovered ordering (+0.81to-0.42 rank correlation against a planted ground truth). The gauge-invariant graph Dirichlet energy removes the hazard and delivers parameter-insensitivity: the estimate is stable across four orders of magnitude in λ, whereas ridge inverts the ordering for every λ>0. We prove the reduced solve is SPD and preserves dynamic range exactly where ridge collapses it, and localize absorbing boundaries from flow alone via a Poisson residual. The H^1 seminorm is classical; what is new is the gauge diagnosis, the parameter-insensitivity it buys, and an ablation showing the result is robust to the extraction method. On three public clickstream corpora the gauge-invariant estimate retains 28--41% of the interior dynamic range while ridge collapses to as little as 0.2%. The same gauge invariance carries into graph neural networks -- neutralizing the constant mode per layer prevents the oversmoothing that collapses a deep directed GCN -- linking this classical inverse problem to a central question in graph learning.

The phenomenon of adversarial examples illustrates one of the most basic vulnerabilities of deep neural networks. Among the variety of techniques introduced to surmount this inherent weakness, adversarial training has emerged as the most effective strategy for learning robust models. Typically, this is achieved by balancing robust and natural objectives. In this work, we aim to further optimize the trade-off between robust and standard accuracy by enforcing a domain-invariant feature representation. We present a new adversarial training method, Domain Invariant Adversarial Learning (DIAL), which learns a feature representation that is both robust and domain invariant. DIAL uses a variant of Domain Adversarial Neural Network (DANN) on the natural domain and its corresponding adversarial domain. In the case where the source domain consists of natural examples and the target domain is the adversarially perturbed examples, our method learns a feature representation constrained not to discriminate between the natural and adversarial examples, and can therefore achieve a more robust representation. DIAL is a generic and modular technique that can be easily incorporated into any adversarial training method. Our experiments indicate that incorporating DIAL in the adversarial training process improves both robustness and standard accuracy.

Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty gets exacerbated when employing regularizers involving a large number of hyperparameters. To overcome this challenge, bilevel learning can be employed to learn such parameters from data. However, neither exact function values nor exact gradients with respect to the hyperparameters are attainable, necessitating methods that only rely on inexact evaluation of such quantities. State-of-the-art inexact gradient-based methods a priori select a sequence of the required accuracies and cannot identify an appropriate step size since the Lipschitz constant of the hypergradient is unknown. In this work, we propose an algorithm with backtracking line search that only relies on inexact function evaluations and hypergradients and show convergence to a stationary point. Furthermore, the proposed algorithm determines the required accuracy dynamically rather than manually selected before running it. Our numerical experiments demonstrate the efficiency and feasibility of our approach for hyperparameter estimation on a range of relevant problems in imaging and data science such as total variation and field of experts denoising and multinomial logistic regression. Particularly, the results show that the algorithm is robust to its own hyperparameters such as the initial accuracies and step size.

The Invariant Risk Minimization (IRM) principle was first proposed by Arjovsky et al. [2019] to address the domain generalization problem by leveraging data heterogeneity from differing experimental conditions. Specifically, IRM seeks to find a data representation under which an optimal classifier remains invariant across all domains. Despite the conceptual appeal of IRM, the effectiveness of the originally proposed invariance penalty has recently been brought into question. In particular, there exists counterexamples for which that invariance penalty can be arbitrarily small for non-invariant data representations. We propose an alternative invariance penalty by revisiting the Gramian matrix of the data representation. We discuss the role of its eigenvalues in the relationship between the risk and the invariance penalty, and demonstrate that it is ill-conditioned for said counterexamples. The proposed approach is guaranteed to recover an invariant representation for linear settings under mild non-degeneracy conditions. Its effectiveness is substantiated by experiments on DomainBed and InvarianceUnitTest, two extensive test beds for domain generalization.

We introduce a transfer learning framework for regression that leverages heterogeneous source domains to improve predictive performance in a data-scarce target domain. Our approach fits a conditional generative model to each source domain and calibrates a shared linear combination of the generated responses via conditional quantile matching at the observed target covariates. The calibration aligns the conditional response distributions while accommodating simultaneous shifts in both the covariate and conditional response distributions. The calibrated responses then serve as pseudo-labels to augment the target data for a broad class of downstream learning tasks. Theoretically, we derive an excess risk bound for an empirical risk minimizer (ERM) trained on the augmented data, separating the benefit of an enlarged training sample from errors due to density ratio estimation, source generator estimation, conditional calibration, and irreducible transfer bias. Empirically, simulations and real-data applications show that the proposed method can improve target-domain prediction when the transfer bias is small.

Domain generalization (DG) aims to learn a robust model from source domains that generalize well on unseen target domains. Recent studies focus on generating novel domain samples or features to diversify distributions complementary to source domains. Yet, these approaches can hardly deal with the restriction that the samples synthesized from various domains can cause semantic distortion. In this paper, we propose an online one-stage Cross Contrasting Feature Perturbation (CCFP) framework to simulate domain shift by generating perturbed features in the latent space while regularizing the model prediction against domain shift. Different from the previous fixed synthesizing strategy, we design modules with learnable feature perturbations and semantic consistency constraints. In contrast to prior work, our method does not use any generative-based models or domain labels. We conduct extensive experiments on a standard DomainBed benchmark with a strict evaluation protocol for a fair comparison. Comprehensive experiments show that our method outperforms the previous state-of-the-art, and quantitative analyses illustrate that our approach can alleviate the domain shift problem in out-of-distribution (OOD) scenarios.

Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we propose an algorithm for the optimization of continuous hyperparameters using inexact gradient information. An advantage of this method is that hyperparameters can be updated before model parameters have fully converged. We also give sufficient conditions for the global convergence of this method, based on regularity conditions of the involved functions and summability of errors. Finally, we validate the empirical performance of this method on the estimation of regularization constants of L2-regularized logistic regression and kernel Ridge regression. Empirical benchmarks indicate that our approach is highly competitive with respect to state of the art methods.

We tackle the challenging problem of source-free unsupervised domain adaptation (SFUDA) for 3D semantic segmentation. It amounts to performing domain adaptation on an unlabeled target domain without any access to source data; the available information is a model trained to achieve good performance on the source domain. A common issue with existing SFUDA approaches is that performance degrades after some training time, which is a by product of an under-constrained and ill-posed problem. We discuss two strategies to alleviate this issue. First, we propose a sensible way to regularize the learning problem. Second, we introduce a novel criterion based on agreement with a reference model. It is used (1) to stop the training when appropriate and (2) as validator to select hyperparameters without any knowledge on the target domain. Our contributions are easy to implement and readily amenable for all SFUDA methods, ensuring stable improvements over all baselines. We validate our findings on various 3D lidar settings, achieving state-of-the-art performance. The project repository (with code) is: github.com/valeoai/TTYD.

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

Offline optimization is an important task in numerous material engineering domains where online experimentation to collect data is too expensive and needs to be replaced by an in silico maximization of a surrogate of the black-box function. Although such a surrogate can be learned from offline data, its prediction might not be reliable outside the offline data regime, which happens when the surrogate has narrow prediction margin and is (therefore) sensitive to small perturbations of its parameterization. This raises the following questions: (1) how to regulate the sensitivity of a surrogate model; and (2) whether conditioning an offline optimizer with such less sensitive surrogate will lead to better optimization performance. To address these questions, we develop an optimizable sensitivity measurement for the surrogate model, which then inspires a sensitivity-informed regularizer that is applicable to a wide range of offline optimizers. This development is both orthogonal and synergistic to prior research on offline optimization, which is demonstrated in our extensive experiment benchmark.

A key challenge in Domain Generalization (DG) is preventing overfitting to source domains, which can be mitigated by finding flatter minima in the loss landscape. In this work, we propose Quantization-aware Training for Domain Generalization (QT-DoG) and demonstrate that weight quantization effectively leads to flatter minima in the loss landscape, thereby enhancing domain generalization. Unlike traditional quantization methods focused on model compression, QT-DoG exploits quantization as an implicit regularizer by inducing noise in model weights, guiding the optimization process toward flatter minima that are less sensitive to perturbations and overfitting. We provide both an analytical perspective and empirical evidence demonstrating that quantization inherently encourages flatter minima, leading to better generalization across domains. Moreover, with the benefit of reducing the model size through quantization, we demonstrate that an ensemble of multiple quantized models further yields superior accuracy than the state-of-the-art DG approaches with no computational or memory overheads. Code is released at: https://saqibjaved1.github.io/QT_DoG/.

In the field of object detection, domain generalisation (DG) aims to ensure robust performance across diverse and unseen target domains by learning the robust domain-invariant features corresponding to the objects of interest across multiple source domains. While there are many approaches established for performing DG for the task of classification, there has been a very little focus on object detection. In this paper, we propose a domain penalisation (DP) framework for the task of object detection, where the data is assumed to be sampled from multiple source domains and tested on completely unseen test domains. We assign penalisation weights to each domain, with the values updated based on the detection networks performance on the respective source domains. By prioritising the domains that needs more attention, our approach effectively balances the training process. We evaluate our solution on the GWHD 2021 dataset, a component of the WiLDS benchmark and we compare against ERM and GroupDRO as these are primarily loss function based. Our extensive experimental results reveals that the proposed approach improves the accuracy by 0.3 percent and 0.5 percent on validation and test out-of-distribution (OOD) sets, respectively for FasterRCNN. We also compare the performance of our approach on FCOS detector and show that our approach improves the baseline OOD performance over the existing approaches by 1.3 percent and 1.4 percent on validation and test sets, respectively. This study underscores the potential of performance based domain penalisation in enhancing the generalisation ability of object detection models across diverse environments.

Large Language Models (LLMs) exhibit strong general language capabilities. However, fine-tuning these models on domain-specific tasks often leads to catastrophic forgetting, where the model overwrites or loses essential knowledge acquired during pretraining. This phenomenon significantly limits the broader applicability of LLMs. To address this challenge, we propose a novel approach to compute the element-wise importance of model parameters crucial for preserving general knowledge during fine-tuning. Our method utilizes a dual-objective optimization strategy: (1) regularization loss based on element-wise parameter importance, which constrains the updates to parameters crucial for general knowledge; (2) cross-entropy loss to adapt to domain-specific tasks. Additionally, we introduce layer-wise coefficients to account for the varying contributions of different layers, dynamically balancing the dual-objective optimization. Extensive experiments on scientific, medical, and physical tasks using GPT-J and LLaMA-3 demonstrate that our approach mitigates catastrophic forgetting while enhancing model adaptability. Compared to previous methods, our solution is approximately 20 times faster and requires only 10-15% of the storage, highlighting the practical efficiency. The code will be released.

Machine learning models fail to perform when facing out-of-distribution (OOD) domains, a challenging task known as domain generalization (DG). In this work, we develop a novel DG training strategy, we call PGrad, to learn a robust gradient direction, improving models' generalization ability on unseen domains. The proposed gradient aggregates the principal directions of a sampled roll-out optimization trajectory that measures the training dynamics across all training domains. PGrad's gradient design forces the DG training to ignore domain-dependent noise signals and updates all training domains with a robust direction covering main components of parameter dynamics. We further improve PGrad via bijection-based computational refinement and directional plus length-based calibrations. Our theoretical proof connects PGrad to the spectral analysis of Hessian in training neural networks. Experiments on DomainBed and WILDS benchmarks demonstrate that our approach effectively enables robust DG optimization and leads to smoothly decreased loss curves. Empirically, PGrad achieves competitive results across seven datasets, demonstrating its efficacy across both synthetic and real-world distributional shifts. Code is available at https://github.com/QData/PGrad.

We introduce a novel class of regularization functions, called Cauchy-Schwarz (CS) regularizers, which can be designed to induce a wide range of properties in solution vectors of optimization problems. To demonstrate the versatility of CS regularizers, we derive regularization functions that promote discrete-valued vectors, eigenvectors of a given matrix, and orthogonal matrices. The resulting CS regularizers are simple, differentiable, and can be free of spurious stationary points, making them suitable for gradient-based solvers and large-scale optimization problems. In addition, CS regularizers automatically adapt to the appropriate scale, which is, for example, beneficial when discretizing the weights of neural networks. To demonstrate the efficacy of CS regularizers, we provide results for solving underdetermined systems of linear equations and weight quantization in neural networks. Furthermore, we discuss specializations, variations, and generalizations, which lead to an even broader class of new and possibly more powerful regularizers.

Ad-hoc instruction fine-tuning of large language models (LLMs) is widely adopted for domain-specific adaptation. While domain-specific supervised fine-tuning (SFT) is effective and efficient, it often weakens cross-domain generalization and struggles with noisy training data. To address these challenges, we propose DONOD, a lightweight model-intrinsic data pruning method. Our approach evaluates data using two model-parameter-based metrics: Delta of Norm (DON), which captures the cumulative influence on model weights, and Norm of Delta (NOD), which quantifies weight instability. Moreover, by employing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm, we effectively filter noisy, unlearnable, and generalization-harming samples without relying on auxiliary models during the SFT process. Experiments on mathematical tasks demonstrate that data selected by DONOD achieve superior fine-tuning efficiency and improved robustness against noisy data. By filtering out 70% of the full dataset, we improve target-domain accuracy by 14.90% and cross-domain accuracy by 5.67%. Meanwhile, our selected data present superior cross-architecture generalization. Data pruned by smaller models (e.g., Llama 3.1-8B) generalize effectively on larger models (e.g., Llama 2-13B). Compared to existing related methodologies, DONOD demonstrates comparable or superior performance while remaining dataset-agnostic, enabling broader applicability.

This study addresses the challenge of noise in training datasets for Direct Preference Optimization (DPO), a method for aligning Large Language Models (LLMs) with human preferences. We categorize noise into pointwise noise, which includes low-quality data points, and pairwise noise, which encompasses erroneous data pair associations that affect preference rankings. Utilizing Distributionally Robust Optimization (DRO), we enhance DPO's resilience to these types of noise. Our theoretical insights reveal that DPO inherently embeds DRO principles, conferring robustness to pointwise noise, with the regularization coefficient beta playing a critical role in its noise resistance. Extending this framework, we introduce Distributionally Robustifying DPO (Dr. DPO), which integrates pairwise robustness by optimizing against worst-case pairwise scenarios. The novel hyperparameter beta' in Dr. DPO allows for fine-tuned control over data pair reliability, providing a strategic balance between exploration and exploitation in noisy training environments. Empirical evaluations demonstrate that Dr. DPO substantially improves the quality of generated text and response accuracy in preference datasets, showcasing enhanced performance in both noisy and noise-free settings. The code is available at https://github.com/junkangwu/Dr_DPO.

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained optimization, called Disentanglement-constrained Domain Generalization (DDG). We relax this non-trivial constrained optimization problem to a tractable form with finite-dimensional parameterization and empirical approximation. Then a theoretical analysis of the extent to which the above transformations deviates from the original problem is provided. Based on the transformation, we propose a primal-dual algorithm for joint representation disentanglement and domain generalization. In contrast to traditional approaches based on domain adversarial training and domain labels, DDG jointly learns semantic and variation encoders for disentanglement, enabling flexible manipulation and augmentation on training data. DDG aims to learn intrinsic representations of semantic concepts that are invariant to nuisance factors and generalizable across domains. Comprehensive experiments on popular benchmarks show that DDG can achieve competitive OOD performance and uncover interpretable salient structures within data.

Vision-Language Models (VLMs) exhibit remarkable zero-shot generalization, yet they often encode unwanted or hazardous stylistic domains such as idealized textbook diagrams in medical AI or cartoon vehicles in autonomous driving. Approximate Domain Unlearning (ADU) aims to selectively erase a model's recognition of a target visual domain while preserving accuracy on the remaining domains. However, existing ADU methods operate under a flawed closed-vocabulary assumption: they evaluate unlearning solely on the specific object classes seen during the unlearning fine-tuning phase. Consequently, these methods do not unlearn the domain itself; they merely overfit to seen class-domain pairs, leaving the domain easily recognizable for unseen classes and providing a false sense of removal. We argue that true domain erasure must be class-agnostic. To address this, we formalize Open-Vocabulary Domain Unlearning (OVDU), a rigorous protocol that mandates domain forgetting must transfer to held-out classes. To solve the OVDU challenge, we propose a surgical parameter-editing framework. First, a Fisher Information mask isolates domain-sensitive weights, mathematically protecting foundational zero-shot generalization. Second, our Targeted Manifold Scattering (TMS) objective uses preference-based mining to locally scatter the forget domain's stylistic geometry. Evaluated across PACS, OfficeHome, and DomainNet, our method vastly improves open-vocabulary generalization over existing baselines. Crucially, it delivers exceptional sample efficiency, outperforming peak 8-shot baseline results with only 4 shots.

As opaque predictive models increasingly impact many areas of modern life, interest in quantifying the importance of a given input variable for making a specific prediction has grown. Recently, there has been a proliferation of model-agnostic methods to measure variable importance (VI) that analyze the difference in predictive power between a full model trained on all variables and a reduced model that excludes the variable(s) of interest. A bottleneck common to these methods is the estimation of the reduced model for each variable (or subset of variables), which is an expensive process that often does not come with theoretical guarantees. In this work, we propose a fast and flexible method for approximating the reduced model with important inferential guarantees. We replace the need for fully retraining a wide neural network by a linearization initialized at the full model parameters. By adding a ridge-like penalty to make the problem convex, we prove that when the ridge penalty parameter is sufficiently large, our method estimates the variable importance measure with an error rate of O(1{n}) where n is the number of training samples. We also show that our estimator is asymptotically normal, enabling us to provide confidence bounds for the VI estimates. We demonstrate through simulations that our method is fast and accurate under several data-generating regimes, and we demonstrate its real-world applicability on a seasonal climate forecasting example.

Parameter regularization or allocation methods are effective in overcoming catastrophic forgetting in lifelong learning. However, they solve all tasks in a sequence uniformly and ignore the differences in the learning difficulty of different tasks. So parameter regularization methods face significant forgetting when learning a new task very different from learned tasks, and parameter allocation methods face unnecessary parameter overhead when learning simple tasks. In this paper, we propose the Parameter Allocation & Regularization (PAR), which adaptively select an appropriate strategy for each task from parameter allocation and regularization based on its learning difficulty. A task is easy for a model that has learned tasks related to it and vice versa. We propose a divergence estimation method based on the Nearest-Prototype distance to measure the task relatedness using only features of the new task. Moreover, we propose a time-efficient relatedness-aware sampling-based architecture search strategy to reduce the parameter overhead for allocation. Experimental results on multiple benchmarks demonstrate that, compared with SOTAs, our method is scalable and significantly reduces the model's redundancy while improving the model's performance. Further qualitative analysis indicates that PAR obtains reasonable task-relatedness.

Domain adaptation (DA) aims to transfer knowledge from a fully labeled source to a scarcely labeled or totally unlabeled target under domain shift. Recently, semi-supervised learning-based (SSL) techniques that leverage pseudo labeling have been increasingly used in DA. Despite the competitive performance, these pseudo labeling methods rely heavily on the source domain to generate pseudo labels for the target domain and therefore still suffer considerably from source data bias. Moreover, class distribution bias in the target domain is also often ignored in the pseudo label generation and thus leading to further deterioration of performance. In this paper, we propose GeT that learns a non-bias target embedding distribution with high quality pseudo labels. Specifically, we formulate an online target generative classifier to induce the target distribution into distinctive Gaussian components weighted by their class priors to mitigate source data bias and enhance target class discriminability. We further propose a structure similarity regularization framework to alleviate target class distribution bias and further improve target class discriminability. Experimental results show that our proposed GeT is effective and achieves consistent improvements under various DA settings with and without class distribution bias. Our code is available at: https://lulusindazc.github.io/getproject/.

Domain generalization (DG) methods aim to achieve generalizability to an unseen target domain by using only training data from the source domains. Although a variety of DG methods have been proposed, a recent study shows that under a fair evaluation protocol, called DomainBed, the simple empirical risk minimization (ERM) approach works comparable to or even outperforms previous methods. Unfortunately, simply solving ERM on a complex, non-convex loss function can easily lead to sub-optimal generalizability by seeking sharp minima. In this paper, we theoretically show that finding flat minima results in a smaller domain generalization gap. We also propose a simple yet effective method, named Stochastic Weight Averaging Densely (SWAD), to find flat minima. SWAD finds flatter minima and suffers less from overfitting than does the vanilla SWA by a dense and overfit-aware stochastic weight sampling strategy. SWAD shows state-of-the-art performances on five DG benchmarks, namely PACS, VLCS, OfficeHome, TerraIncognita, and DomainNet, with consistent and large margins of +1.6% averagely on out-of-domain accuracy. We also compare SWAD with conventional generalization methods, such as data augmentation and consistency regularization methods, to verify that the remarkable performance improvements are originated from by seeking flat minima, not from better in-domain generalizability. Last but not least, SWAD is readily adaptable to existing DG methods without modification; the combination of SWAD and an existing DG method further improves DG performances. Source code is available at https://github.com/khanrc/swad.

LOBSTER (LOss-Based SensiTivity rEgulaRization) is a method for training neural networks having a sparse topology. Let the sensitivity of a network parameter be the variation of the loss function with respect to the variation of the parameter. Parameters with low sensitivity, i.e. having little impact on the loss when perturbed, are shrunk and then pruned to sparsify the network. Our method allows to train a network from scratch, i.e. without preliminary learning or rewinding. Experiments on multiple architectures and datasets show competitive compression ratios with minimal computational overhead.

The key of the out-of-distribution (OOD) generalization is to generalize invariance from training domains to target domains. The variance risk extrapolation (V-REx) is a practical OOD method, which depends on a domain-level regularization but lacks theoretical verifications about its motivation and utility. This article provides theoretical insights into V-REx by studying a variance-based regularizer. We propose Risk Variance Penalization (RVP), which slightly changes the regularization of V-REx but addresses the theory concerns about V-REx. We provide theoretical explanations and a theory-inspired tuning scheme for the regularization parameter of RVP. Our results point out that RVP discovers a robust predictor. Finally, we experimentally show that the proposed regularizer can find an invariant predictor under certain conditions.

Hyperparameter tuning almost always means search: fit the model at every value on a grid, score each by cross-validation, and keep the winner. For spline regression that search is unnecessary. The optimal resolution can be solved for in closed form, to the accuracy an exhaustive search reaches, at a fraction of the compute. Three ingredients make this possible: classical approximation theory pins the squared bias to a known power of the resolution G, exactly the Kolmogorov n-width of the smoothness class; the basis dimension is an explicit polynomial in G; and leave-one-out error follows from a single fit via the PRESS identity. Balancing the two known curves gives the minimizer analytically. We extend this calculus to many coordinates by replacing ambient input dimension with interaction order, the number of active low-order components in an ANOVA decomposition, yielding a scaling law in which the optimal resolution and error are power functions of the effective density (sample size per active component), with input dimension absent from the exponent. The law becomes an algorithm. KORE (Kolmogorov-optimal Order-aware Resolution Estimation) fits two pilot resolutions, solves a leverage-calibrated 2x2 system for the bias and noise scales, and evaluates the closed-form plug-in resolution with a tiny leave-one-out certificate: about a dozen fits instead of a full grid sweep, with a consistency guarantee as the sample grows. Across additive and sparse pairwise targets up to 80 input dimensions, KORE matches exhaustive 3-fold cross-validation and the full classical ladder (GCV, Mallows' Cp, AIC, BIC) while fitting roughly 8x fewer models; on 36 real tabular datasets it ranks first among 21 methods in accuracy per unit of compute, ahead of tuned boosters and kernel machines. When complexity lives in low interaction order, solving for the resolution beats searching for it.

Deep neural networks (DNNs) often underperform in real-world, dynamic settings where data distributions change over time. Domain Incremental Learning (DIL) offers a solution by enabling continual model adaptation, with Parameter-Isolation DIL (PIDIL) emerging as a promising paradigm to reduce knowledge conflicts. However, existing PIDIL methods struggle with parameter selection accuracy, especially as the number of domains and corresponding classes grows. To address this, we propose SOYO, a lightweight framework that improves domain selection in PIDIL. SOYO introduces a Gaussian Mixture Compressor (GMC) and Domain Feature Resampler (DFR) to store and balance prior domain data efficiently, while a Multi-level Domain Feature Fusion Network (MDFN) enhances domain feature extraction. Our framework supports multiple Parameter-Efficient Fine-Tuning (PEFT) methods and is validated across tasks such as image classification, object detection, and speech enhancement. Experimental results on six benchmarks demonstrate SOYO's consistent superiority over existing baselines, showcasing its robustness and adaptability in complex, evolving environments. The codes will be released in https://github.com/qwangcv/SOYO.

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific parameterization for second-order optimization that promotes feature learning in a stable manner even if the network width increases significantly. Inspired by a maximal update parameterization, we consider a one-step update of the gradient and reveal the appropriate scales of hyperparameters including random initialization, learning rates, and damping terms. Our approach covers two major second-order optimization algorithms, K-FAC and Shampoo, and we demonstrate that our parameterization achieves higher generalization performance in feature learning. In particular, it enables us to transfer the hyperparameters across models with different widths.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

Fine-tuning pre-trained models has been ubiquitously proven to be effective in a wide range of NLP tasks. However, fine-tuning the whole model is parameter inefficient as it always yields an entirely new model for each task. Currently, many research works propose to only fine-tune a small portion of the parameters while keeping most of the parameters shared across different tasks. These methods achieve surprisingly good performance and are shown to be more stable than their corresponding fully fine-tuned counterparts. However, such kind of methods is still not well understood. Some natural questions arise: How does the parameter sparsity lead to promising performance? Why is the model more stable than the fully fine-tuned models? How to choose the tunable parameters? In this paper, we first categorize the existing methods into random approaches, rule-based approaches, and projection-based approaches based on how they choose which parameters to tune. Then, we show that all of the methods are actually sparse fine-tuned models and conduct a novel theoretical analysis of them. We indicate that the sparsity is actually imposing a regularization on the original model by controlling the upper bound of the stability. Such stability leads to better generalization capability which has been empirically observed in a lot of recent research works. Despite the effectiveness of sparsity grounded by our theory, it still remains an open problem of how to choose the tunable parameters. To better choose the tunable parameters, we propose a novel Second-order Approximation Method (SAM) which approximates the original problem with an analytically solvable optimization function. The tunable parameters are determined by directly optimizing the approximation function. The experimental results show that our proposed SAM model outperforms many strong baseline models and it also verifies our theoretical analysis.

Aiming to generalize the label knowledge from a source domain with continuous outputs to an unlabeled target domain, Domain Adaptation Regression (DAR) is developed for complex practical learning problems. However, due to the continuity problem in regression, existing conditional distribution alignment theory and methods with discrete prior, which are proven to be effective in classification settings, are no longer applicable. In this work, focusing on the feasibility problems in DAR, we establish the sufficiency theory for the regression model, which shows the generalization error can be sufficiently dominated by the cross-domain conditional discrepancy. Further, to characterize conditional discrepancy with continuous conditioning variable, a novel Conditional Operator Discrepancy (COD) is proposed, which admits the metric property on conditional distributions via the kernel embedding theory. Finally, to minimize the discrepancy, a COD-based conditional invariant representation learning model is proposed, and the reformulation is derived to show that reasonable modifications on moment statistics can further improve the discriminability of the adaptation model. Extensive experiments on standard DAR datasets verify the validity of theoretical results and the superiority over SOTA DAR methods.

Domain adaptation (DA) attempts to transfer the knowledge from a labeled source domain to an unlabeled target domain that follows different distribution from the source. To achieve this, DA methods include a source classification objective to extract the source knowledge and a domain alignment objective to diminish the domain shift, ensuring knowledge transfer. Typically, former DA methods adopt some weight hyper-parameters to linearly combine the training objectives to form an overall objective. However, the gradient directions of these objectives may conflict with each other due to domain shift. Under such circumstances, the linear optimization scheme might decrease the overall objective value at the expense of damaging one of the training objectives, leading to restricted solutions. In this paper, we rethink the optimization scheme for DA from a gradient-based perspective. We propose a Pareto Domain Adaptation (ParetoDA) approach to control the overall optimization direction, aiming to cooperatively optimize all training objectives. Specifically, to reach a desirable solution on the target domain, we design a surrogate loss mimicking target classification. To improve target-prediction accuracy to support the mimicking, we propose a target-prediction refining mechanism which exploits domain labels via Bayes' theorem. On the other hand, since prior knowledge of weighting schemes for objectives is often unavailable to guide optimization to approach the optimal solution on the target domain, we propose a dynamic preference mechanism to dynamically guide our cooperative optimization by the gradient of the surrogate loss on a held-out unlabeled target dataset. Extensive experiments on image classification and semantic segmentation benchmarks demonstrate the effectiveness of ParetoDA

Large Language Model-based Dense Retrieval (LLM-DR) optimizes over numerous heterogeneous fine-tuning collections from different domains. However, the discussion about its training data distribution is still minimal. Previous studies rely on empirically assigned dataset choices or sampling ratios, which inevitably leads to sub-optimal retrieval performances. In this paper, we propose a new task-level Distributionally Robust Optimization (tDRO) algorithm for LLM-DR fine-tuning, targeted at improving the universal domain generalization ability by end-to-end reweighting the data distribution of each task. The tDRO parameterizes the domain weights and updates them with scaled domain gradients. The optimized weights are then transferred to the LLM-DR fine-tuning to train more robust retrievers. Experiments show optimal improvements in large-scale retrieval benchmarks and reduce up to 30% dataset usage after applying our optimization algorithm with a series of different-sized LLM-DR models.

Language model performance depends strongly on the mixture of domains in the pretraining data corpus. Popular data mixing methods select these domain weights by training many small proxy models on random mixes and then fitting a regression model to predict performance from the mix. We recognize this practice as a domain attribution problem, where the regression measures each domain's contribution to the target metric. Through this lens, the standard Dirichlet sampling of proxy data mixes is a poor regression design that requires tuning and cannot support a linear fit for hundreds of domains. Building on classical optimal experimental design, we introduce LinMix, which samples mixes at the vertices of the capped simplex so that each domain is at its cap or absent. This hyperparameter-free vertex sampling decorrelates domain effects, enabling an interpretable linear model whose coefficients are the domain attributions. The optimal mix given by LinMix provably keeps only domains with positive attribution values and requires no search over candidate mixes. We further establish the optimality of vertex sampling, and prove that Dirichlet sampling inflates the attribution error when its mixes concentrate around the prior data mix. Pretraining experiments with 1B-parameter OLMo2 and 4B Qwen3.5 language models show that LinMix outperforms Dirichlet-based data mixing across reasoning, code, and math benchmarks, with relative gains of 46% on MBPP and 14% on GSM8K. At 288 fine-grained domains, only vertex sampling supports a linear fit, and LinMix improves benchmark accuracy by 11% on average over the best nonlinear baseline.

Diffusion models excel in generating images that closely resemble their training data but are also susceptible to data memorization, raising privacy, ethical, and legal concerns, particularly in sensitive domains such as medical imaging. We hypothesize that this memorization stems from the overparameterization of deep models and propose that regularizing model capacity during fine-tuning can mitigate this issue. Firstly, we empirically show that regulating the model capacity via Parameter-efficient fine-tuning (PEFT) mitigates memorization to some extent, however, it further requires the identification of the exact parameter subsets to be fine-tuned for high-quality generation. To identify these subsets, we introduce a bi-level optimization framework, MemControl, that automates parameter selection using memorization and generation quality metrics as rewards during fine-tuning. The parameter subsets discovered through MemControl achieve a superior tradeoff between generation quality and memorization. For the task of medical image generation, our approach outperforms existing state-of-the-art memorization mitigation strategies by fine-tuning as few as 0.019% of model parameters. Moreover, we demonstrate that the discovered parameter subsets are transferable to non-medical domains. Our framework is scalable to large datasets, agnostic to reward functions, and can be integrated with existing approaches for further memorization mitigation. To the best of our knowledge, this is the first study to empirically evaluate memorization in medical images and propose a targeted yet universal mitigation strategy. The code is available at https://github.com/Raman1121/Diffusion_Memorization_HPO.

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

Hyperparameter tuning can dramatically impact training stability and final performance of large-scale models. Recent works on neural network parameterisations, such as μP, have enabled transfer of optimal global hyperparameters across model sizes. These works propose an empirical practice of search for optimal global base hyperparameters at a small model size, and transfer to a large size. We extend these works in two key ways. To handle scaling along most important scaling axes, we propose the Complete^{(d)} Parameterisation that unifies scaling in width and depth -- using an adaptation of CompleteP -- as well as in batch-size and training duration. Secondly, with our parameterisation, we investigate per-module hyperparameter optimisation and transfer. We characterise the empirical challenges of navigating the high-dimensional hyperparameter landscape, and propose practical guidelines for tackling this optimisation problem. We demonstrate that, with the right parameterisation, hyperparameter transfer holds even in the per-module hyperparameter regime. Our study covers an extensive range of optimisation hyperparameters of modern models: learning rates, AdamW parameters, weight decay, initialisation scales, and residual block multipliers. Our experiments demonstrate significant training speed improvements in Large Language Models with the transferred per-module hyperparameters.

A plethora of sentence embedding models makes it challenging to choose one, especially for domains such as telecom, rich with specialized vocabulary. We evaluate multiple embeddings obtained from publicly available models and their domain-adapted variants, on both point retrieval accuracies as well as their (95\%) confidence intervals. We establish a systematic method to obtain thresholds for similarity scores for different embeddings. We observe that fine-tuning improves mean bootstrapped accuracies as well as tightens confidence intervals. The pre-training combined with fine-tuning makes confidence intervals even tighter. To understand these variations, we analyse and report significant correlations between the distributional overlap between top-K, correct and random sentence similarities with retrieval accuracies and similarity thresholds. Following current literature, we analyze if retrieval accuracy variations can be attributed to isotropy of embeddings. Our conclusions are that isotropy of embeddings (as measured by two independent state-of-the-art isotropy metric definitions) cannot be attributed to better retrieval performance. However, domain adaptation which improves retrieval accuracies also improves isotropy. We establish that domain adaptation moves domain specific embeddings further away from general domain embeddings.

The mixture proportions of pretraining data domains (e.g., Wikipedia, books, web text) greatly affect language model (LM) performance. In this paper, we propose Domain Reweighting with Minimax Optimization (DoReMi), which first trains a small proxy model using group distributionally robust optimization (Group DRO) over domains to produce domain weights (mixture proportions) without knowledge of downstream tasks. We then resample a dataset with these domain weights and train a larger, full-sized model. In our experiments, we use DoReMi on a 280M-parameter proxy model to find domain weights for training an 8B-parameter model (30x larger) more efficiently. On The Pile, DoReMi improves perplexity across all domains, even when it downweights a domain. DoReMi improves average few-shot downstream accuracy by 6.5% over a baseline model trained using The Pile's default domain weights and reaches the baseline accuracy with 2.6x fewer training steps. On the GLaM dataset, DoReMi, which has no knowledge of downstream tasks, even matches the performance of using domain weights tuned on downstream tasks.

Large Language Models (LLMs) have exhibited remarkable proficiency across a wide array of NLP tasks. However, the escalation in model size also engenders substantial deployment costs. While few efforts have explored model pruning techniques to reduce the size of LLMs, they mainly center on general or task-specific weights. This leads to suboptimal performance due to lacking specificity on the target domain or generality on different tasks when applied to domain-specific challenges. This work introduces an innovative unstructured dual-pruning methodology, D-Pruner, for domain-specific compression on LLM. It extracts a compressed, domain-specific, and task-agnostic LLM by identifying LLM weights that are pivotal for general capabilities, like linguistic capability and multi-task solving, and domain-specific knowledge. More specifically, we first assess general weight importance by quantifying the error incurred upon their removal with the help of an open-domain calibration dataset. Then, we utilize this general weight importance to refine the training loss, so that it preserves generality when fitting into a specific domain. Moreover, by efficiently approximating weight importance with the refined training loss on a domain-specific calibration dataset, we obtain a pruned model emphasizing generality and specificity. Our comprehensive experiments across various tasks in healthcare and legal domains show the effectiveness of D-Pruner in domain-specific compression. Our code is available at https://github.com/psunlpgroup/D-Pruner.

Although pre-trained language models have exhibited great flexibility and versatility with prompt-based few-shot learning, they suffer from the extensive parameter size and limited applicability for inference. Recent studies have suggested that PLMs be used as dataset generators and a tiny task-specific model be trained to achieve efficient inference. However, their applicability to various domains is limited because they tend to generate domain-specific datasets. In this work, we propose a novel approach to universal domain generalization that generates a dataset regardless of the target domain. This allows for generalization of the tiny task model to any domain that shares the label space, thus enhancing the real-world applicability of the dataset generation paradigm. Our experiments indicate that the proposed method accomplishes generalizability across various domains while using a parameter set that is orders of magnitude smaller than PLMs.

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which recently received a lot of attention is described by the notion of invariance. In this work we provide a causal perspective and new algorithm for learning invariant representations. Empirically we show that this algorithm works well on a diverse set of tasks and in particular we observe state-of-the-art performance on domain generalization, where we are able to significantly boost the score of existing models.

Selecting a suitable training dataset is crucial for both general-domain (e.g., GPT-3) and domain-specific (e.g., Codex) language models (LMs). We formalize this data selection problem as selecting a subset of a large raw unlabeled dataset to match a desired target distribution, given some unlabeled target samples. Due to the large scale and dimensionality of the raw text data, existing methods use simple heuristics to select data that are similar to a high-quality reference corpus (e.g., Wikipedia), or leverage experts to manually curate data. Instead, we extend the classic importance resampling approach used in low-dimensions for LM data selection. Crucially, we work in a reduced feature space to make importance weight estimation tractable over the space of text. To determine an appropriate feature space, we first show that KL reduction, a data metric that measures the proximity between selected data and the target in a feature space, has high correlation with average accuracy on 8 downstream tasks (r=0.89) when computed with simple n-gram features. From this observation, we present Data Selection with Importance Resampling (DSIR), an efficient and scalable algorithm that estimates importance weights in a reduced feature space (e.g., n-gram features in our instantiation) and selects data with importance resampling according to these weights. When training general-domain models (target is Wikipedia + books), DSIR improves over random selection and heuristic filtering baselines by 2--2.5% on the GLUE benchmark. When performing continued pretraining towards a specific domain, DSIR performs comparably to expert curated data across 8 target distributions.

Domain generalization (DG) seeks to learn robust models that generalize well under unknown distribution shifts. As a critical aspect of DG, optimizer selection has not been explored in depth. Currently, most DG methods follow the widely used benchmark, DomainBed, and utilize Adam as the default optimizer for all datasets. However, we reveal that Adam is not necessarily the optimal choice for the majority of current DG methods and datasets. Based on the perspective of loss landscape flatness, we propose a novel approach, Flatness-Aware Minimization for Domain Generalization (FAD), which can efficiently optimize both zeroth-order and first-order flatness simultaneously for DG. We provide theoretical analyses of the FAD's out-of-distribution (OOD) generalization error and convergence. Our experimental results demonstrate the superiority of FAD on various DG datasets. Additionally, we confirm that FAD is capable of discovering flatter optima in comparison to other zeroth-order and first-order flatness-aware optimization methods.

Optimizing data mixtures for supervised fine-tuning (SFT) of large language models (LLMs) is critical for developing general-purpose models, yet this area remains underexplored. In this paper, we frame data mixing as an optimization problem and introduce a novel method designed to minimize validation loss. Our approach parametrizes the loss by modeling effective data transferred and leveraging scaling laws for fine-tuning. By experimenting with various small-scale data mixtures, we fit these parameters and derive the optimal weights. We provide both mathematical proofs and empirical results demonstrating that our algorithm achieves excellent overall and individual performance across all domains. Through controlled experiments, we show that models trained with our optimized weights perform on par with those using optimal weights determined via grid search, with per-domain loss only 0.66% higher than the best domain loss from grid search on average. Additionally, we show that reweighting popular SFT datasets using our method improves both validation loss and downstream performance. Finally, we discuss how our method can generalize to guide data selection for domain-specific models and provide insights into SFT.

Medical imaging datasets often vary due to differences in acquisition protocols, patient demographics, and imaging devices. These variations in data distribution, known as domain shift, present a significant challenge in adapting imaging analysis models for practical healthcare applications. Most current domain adaptation (DA) approaches aim either to align the distributions between the source and target domains or to learn an invariant feature space that generalizes well across all domains. However, both strategies require access to a sufficient number of examples, though not necessarily annotated, from the test domain during training. This limitation hinders the widespread deployment of models in clinical settings, where target domain data may only be accessible in real time. In this work, we introduce HyDA, a novel hypernetwork framework that leverages domain characteristics rather than suppressing them, enabling dynamic adaptation at inference time. Specifically, HyDA learns implicit domain representations and uses them to adjust model parameters on-the-fly, effectively interpolating to unseen domains. We validate HyDA on two clinically relevant applications - MRI brain age prediction and chest X-ray pathology classification - demonstrating its ability to generalize across tasks and modalities. Our code is available at TBD.

Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable operator learning approach with reduced memory requirement and better generalization, called multi-grid tensorized neural operator (MG-TFNO). MG-TFNO scales to large resolutions by leveraging local and global structures of full-scale, real-world phenomena, through a decomposition of both the input domain and the operator's parameter space. Our contributions are threefold: i) we enable parallelization over input samples with a novel multi-grid-based domain decomposition, ii) we represent the parameters of the model in a high-order latent subspace of the Fourier domain, through a global tensor factorization, resulting in an extreme reduction in the number of parameters and improved generalization, and iii) we propose architectural improvements to the backbone FNO. Our approach can be used in any operator learning setting. We demonstrate superior performance on the turbulent Navier-Stokes equations where we achieve less than half the error with over 150x compression. The tensorization combined with the domain decomposition, yields over 150x reduction in the number of parameters and 7x reduction in the domain size without losses in accuracy, while slightly enabling parallelism.

Adversarial adaptation models have demonstrated significant progress towards transferring knowledge from a labeled source dataset to an unlabeled target dataset. Partial domain adaptation (PDA) investigates the scenarios in which the source domain is large and diverse, and the target label space is a subset of the source label space. The main purpose of PDA is to identify the shared classes between the domains and promote learning transferable knowledge from these classes. In this paper, we propose a multi-class adversarial architecture for PDA. The proposed approach jointly aligns the marginal and class-conditional distributions in the shared label space by minimaxing a novel multi-class adversarial loss function. Furthermore, we incorporate effective regularization terms to encourage selecting the most relevant subset of source domain classes. In the absence of target labels, the proposed approach is able to effectively learn domain-invariant feature representations, which in turn can enhance the classification performance in the target domain. Comprehensive experiments on three benchmark datasets Office-31, Office-Home, and Caltech-Office corroborate the effectiveness of the proposed approach in addressing different partial transfer learning tasks.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shifts. Although many tasks are naturally characterized by continuous domains, current invariance learning techniques generally assume categorically indexed domains. For example, auto-scaling in cloud computing often needs a CPU utilization prediction model that generalizes across different times (e.g., time of a day and date of a year), where `time' is a continuous domain index. In this paper, we start by theoretically showing that existing invariance learning methods can fail for continuous domain problems. Specifically, the naive solution of splitting continuous domains into discrete ones ignores the underlying relationship among domains, and therefore potentially leads to suboptimal performance. To address this challenge, we then propose Continuous Invariance Learning (CIL), which extracts invariant features across continuously indexed domains. CIL is a novel adversarial procedure that measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates the superiority of CIL over existing invariance learning methods. Empirical results on both synthetic and real-world datasets (including data collected from production systems) show that CIL consistently outperforms strong baselines among all the tasks.

Although learning-based image restoration methods have made significant progress, they still struggle with limited generalization to real-world scenarios due to the substantial domain gap caused by training on synthetic data. Existing methods address this issue by improving data synthesis pipelines, estimating degradation kernels, employing deep internal learning, and performing domain adaptation and regularization. Previous domain adaptation methods have sought to bridge the domain gap by learning domain-invariant knowledge in either feature or pixel space. However, these techniques often struggle to extend to low-level vision tasks within a stable and compact framework. In this paper, we show that it is possible to perform domain adaptation via the noise space using diffusion models. In particular, by leveraging the unique property of how auxiliary conditional inputs influence the multi-step denoising process, we derive a meaningful diffusion loss that guides the restoration model in progressively aligning both restored synthetic and real-world outputs with a target clean distribution. We refer to this method as denoising as adaptation. To prevent shortcuts during joint training, we present crucial strategies such as channel-shuffling layer and residual-swapping contrastive learning in the diffusion model. They implicitly blur the boundaries between conditioned synthetic and real data and prevent the reliance of the model on easily distinguishable features. Experimental results on three classical image restoration tasks, namely denoising, deblurring, and deraining, demonstrate the effectiveness of the proposed method.

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed ell^2 Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP). We provide a ``direct'' parameterization, i.e., a smooth mapping from mathbb R^N onto the set of weights satisfying the SDP-based bound. Moreover, our parameterization is complete, i.e. a neural network satisfies the SDP bound if and only if it can be represented via our parameterization. This enables training using standard gradient methods, without any inner approximation or computationally intensive tasks (e.g. projections or barrier terms) for the SDP constraint. The new parameterization can equivalently be thought of as either a new layer type (the sandwich layer), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. A comprehensive set of experiments on image classification shows that sandwich layers outperform previous approaches on both empirical and certified robust accuracy. Code is available at https://github.com/acfr/LBDN.

Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the necessity of navigating extremely high-dimensional combinatorial and nonlinear hypothesis spaces. Traditional methods of equation discovery largely focus on extracting equations from data alone, often neglecting the rich domain-specific prior knowledge that scientists typically depend on. To bridge this gap, we introduce LLM-SR, a novel approach that leverages the extensive scientific knowledge and robust code generation capabilities of Large Language Models (LLMs) to discover scientific equations from data in an efficient manner. Specifically, LLM-SR treats equations as programs with mathematical operators and combines LLMs' scientific priors with evolutionary search over equation programs. The LLM iteratively proposes new equation skeletons, drawing from its physical understanding, which are then optimized against data to estimate skeleton parameters. We demonstrate LLM-SR's effectiveness across three diverse scientific domains, where it discovers physically accurate equations that provide significantly better fits to in-domain and out-of-domain data compared to the well-established equation discovery baselines

Deep Neural Networks have exhibited considerable success in various visual tasks. However, when applied to unseen test datasets, state-of-the-art models often suffer performance degradation due to domain shifts. In this paper, we introduce a novel approach for domain generalization from a novel perspective of enhancing the robustness of channels in feature maps to domain shifts. We observe that models trained on source domains contain a substantial number of channels that exhibit unstable activations across different domains, which are inclined to capture domain-specific features and behave abnormally when exposed to unseen target domains. To address the issue, we propose a DomainDrop framework to continuously enhance the channel robustness to domain shifts, where a domain discriminator is used to identify and drop unstable channels in feature maps of each network layer during forward propagation. We theoretically prove that our framework could effectively lower the generalization bound. Extensive experiments on several benchmarks indicate that our framework achieves state-of-the-art performance compared to other competing methods. Our code is available at https://github.com/lingeringlight/DomainDrop.

We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and f-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition value-at-risk (CVaR) and average top-k loss. We present Prospect, a stochastic gradient-based algorithm that only requires tuning a single learning rate hyperparameter, and prove that it enjoys linear convergence for smooth regularized losses. This contrasts with previous algorithms that either require tuning multiple hyperparameters or potentially fail to converge due to biased gradient estimates or inadequate regularization. Empirically, we show that Prospect can converge 2-3times faster than baselines such as stochastic gradient and stochastic saddle-point methods on distribution shift and fairness benchmarks spanning tabular, vision, and language domains.

Data augmentation is a popular tool for single source domain generalization, which expands the source domain by generating simulated ones, improving generalization on unseen target domains. In this work, we show that the performance of such augmentation-based methods in the target domains universally fluctuates during training, posing challenges in model selection under realistic scenarios. We argue that the fluctuation stems from the inability of the model to accumulate the knowledge learned from diverse augmentations, exacerbating feature distortion during training. Based on this observation, we propose a novel generalization method, coined Parameter-Space Ensemble with Entropy Regularization (PEER), that uses a proxy model to learn the augmented data on behalf of the main model. The main model is updated by averaging its parameters with the proxy model, progressively accumulating knowledge over the training steps. Maximizing the mutual information between the output representations of the two models guides the learning process of the proxy model, mitigating feature distortion during training. Experimental results demonstrate the effectiveness of PEER in reducing the OOD performance fluctuation and enhancing generalization across various datasets, including PACS, Digits, Office-Home, and VLCS. Notably, our method with simple random augmentation achieves state-of-the-art performance, surpassing prior approaches on sDG that utilize complex data augmentation strategies.

We present anyakrakusuma, an open-source Python library that solves the discrete static Schrödinger bridge problem, the entropically regularized counterpart of optimal transport, through a log-domain Sinkhorn--Knopp iteration and reconstructs the entropic interpolation between two empirical point clouds. The solver is paired with a diagnostic pipeline that characterizes the optimal coupling and the intermediate distributions through information-theoretic and geometric measures. We exercise the library on four idealized planar cases spanning a circle-to-circle dilation, a spiral-to-mixture fragmentation, a rigid reorientation of two moons, and a Lissajous-to-trefoil deformation. The log-domain formulation is necessary rather than merely convenient at the parameters studied, where the cost-to-regularization ratio reaches four hundred and the Gibbs kernel underflows double precision across most of its range; the iteration nonetheless attains a marginal residual of 10^{-9} and unit marginal fidelity in every case. Residual histories decay geometrically over approximately eight decades at per-iteration contraction factors between 0.966 and 0.976, which are local rates near the fixed point that lie many orders of magnitude below the worst-case Hilbert-metric bound. The covariance analysis recovers an imposed ninety-degree reorientation to within 0.07^circ, roughly forty times smaller than its uncertainty, across a masked interval of near-isotropy on which the principal axis is unobservable. The diagnostics are reported with explicit attention to the regimes in which each is well defined, including the differential entropy, which is meaningful only on the open interpolation interval. The presented cases are constructed rather than measured; quantitative application to empirical point clouds requires further study.

Recent advancements in text-to-image generation have inspired researchers to generate datasets tailored for perception models using generative models, which prove particularly valuable in scenarios where real-world data is limited. In this study, our goal is to address the challenges when fine-tuning vision-language models (e.g., CLIP) on generated datasets. Specifically, we aim to fine-tune vision-language models to a specific classification model without access to any real images, also known as name-only transfer. However, despite the high fidelity of generated images, we observed a significant performance degradation when fine-tuning the model using the generated datasets due to the domain gap between real and generated images. To overcome the domain gap, we provide two regularization methods for training and post-training, respectively. First, we leverage the domain-agnostic knowledge from the original pre-trained vision-language model by conducting the weight-space ensemble of the fine-tuned model on the generated dataset with the original pre-trained model at the post-training. Secondly, we reveal that fine-tuned models with high feature diversity score high performance in the real domain, which indicates that increasing feature diversity prevents learning the generated domain-specific knowledge. Thus, we encourage feature diversity by providing additional regularization at training time. Extensive experiments on various classification datasets and various text-to-image generation models demonstrated that our analysis and regularization techniques effectively mitigate the domain gap, which has long been overlooked, and enable us to achieve state-of-the-art performance by training with generated images. Code is available at https://github.com/pmh9960/regft-for-gen

The dominant line of work in domain adaptation has focused on learning invariant representations using domain-adversarial training. In this paper, we interpret this approach from a game theoretical perspective. Defining optimal solutions in domain-adversarial training as a local Nash equilibrium, we show that gradient descent in domain-adversarial training can violate the asymptotic convergence guarantees of the optimizer, oftentimes hindering the transfer performance. Our analysis leads us to replace gradient descent with high-order ODE solvers (i.e., Runge-Kutta), for which we derive asymptotic convergence guarantees. This family of optimizers is significantly more stable and allows more aggressive learning rates, leading to high performance gains when used as a drop-in replacement over standard optimizers. Our experiments show that in conjunction with state-of-the-art domain-adversarial methods, we achieve up to 3.5% improvement with less than of half training iterations. Our optimizers are easy to implement, free of additional parameters, and can be plugged into any domain-adversarial framework.

The problem of domain generalization is to learn from multiple training domains, and extract a domain-agnostic model that can then be applied to an unseen domain. Domain generalization (DG) has a clear motivation in contexts where there are target domains with distinct characteristics, yet sparse data for training. For example recognition in sketch images, which are distinctly more abstract and rarer than photos. Nevertheless, DG methods have primarily been evaluated on photo-only benchmarks focusing on alleviating the dataset bias where both problems of domain distinctiveness and data sparsity can be minimal. We argue that these benchmarks are overly straightforward, and show that simple deep learning baselines perform surprisingly well on them. In this paper, we make two main contributions: Firstly, we build upon the favorable domain shift-robust properties of deep learning methods, and develop a low-rank parameterized CNN model for end-to-end DG learning. Secondly, we develop a DG benchmark dataset covering photo, sketch, cartoon and painting domains. This is both more practically relevant, and harder (bigger domain shift) than existing benchmarks. The results show that our method outperforms existing DG alternatives, and our dataset provides a more significant DG challenge to drive future research.

Sharpness-aware minimization (SAM) reports improving domain generalization by reducing the loss surface curvature in the parameter space. However, generalization during fine-tuning is often more dependent on the transferability of representations in the function space. Trust-region methods (TR) target this goal by regularizing representation curvature to reduce catastrophic forgetting of pre-trained task-agnostic information while adopting task-specific skills. We consider unifying these strategies for low curvature in both parameter space and function space to improve out-of-domain (OOD) generalization. We propose Trust Region Aware Minimization (TRAM), a SAM algorithm fine-tuning for low parameter sharpness and smooth, informative representations preserving pre-trained structure. TRAM uses a trust region bound to inform the SAM adversarial neighborhood, introducing an awareness of function curvature within optimization for flatter minima. We empirically validate TRAM in vision (cross-dataset adaptation) and text (OOD language modeling, zero-shot cross-lingual transfer) tasks where robust domain transfer and representation generality are critical. TRAM outperforms SAM- and TR-based optimization across all tasks, notably surpassing competing methods for hard transfer between anticorrelated domains. TRAM establishes a novel standard in fine-tuning for domain-generalizable models with minimal additional computation over previous sharpness-aware methods.

Recent years have seen a growing interest and adoption of LLMs, with muTransfer becoming a key technique for tuning hyperparameters in large-scale training. Meanwhile, Mixture-of-Experts (MoE) has emerged as a leading architecture in extremely large models. However, the intersection of these two advancements has remained unexplored. In this work, we derive a mu-Parameterization (muP) for MoE, providing theoretical guarantees for feature learning across model widths in both the router and experts. We empirically validate our parameterization and further investigate how scaling the number of experts and granularity affects the optimal learning rate.

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval's identity and introduce a new training strategy through a spectral loss. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems. When compared to numerical solvers of the same accuracy, our method demonstrates a 10times increase in performance speed.

Due to privacy, storage, and other constraints, there is a growing need for unsupervised domain adaptation techniques in machine learning that do not require access to the data used to train a collection of source models. Existing methods for multi-source-free domain adaptation (MSFDA) typically train a target model using pseudo-labeled data produced by the source models, which focus on improving the pseudo-labeling techniques or proposing new training objectives. Instead, we aim to analyze the fundamental limits of MSFDA. In particular, we develop an information-theoretic bound on the generalization error of the resulting target model, which illustrates an inherent bias-variance trade-off. We then provide insights on how to balance this trade-off from three perspectives, including domain aggregation, selective pseudo-labeling, and joint feature alignment, which leads to the design of novel algorithms. Experiments on multiple datasets validate our theoretical analysis and demonstrate the state-of-art performance of the proposed algorithm, especially on some of the most challenging datasets, including Office-Home and DomainNet.

Modern machine learning algorithms are increasingly computationally demanding, requiring specialized hardware and distributed computation to achieve high performance in a reasonable time frame. Many hyperparameter search algorithms have been proposed for improving the efficiency of model selection, however their adaptation to the distributed compute environment is often ad-hoc. We propose Tune, a unified framework for model selection and training that provides a narrow-waist interface between training scripts and search algorithms. We show that this interface meets the requirements for a broad range of hyperparameter search algorithms, allows straightforward scaling of search to large clusters, and simplifies algorithm implementation. We demonstrate the implementation of several state-of-the-art hyperparameter search algorithms in Tune. Tune is available at http://ray.readthedocs.io/en/latest/tune.html.

Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search based approaches to automating this laborious and compute intensive task, the fundamental learning theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data driven setting. We assume that we have a series of deep learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter; our analysis relies on subtle concepts including tools from differential/algebraic geometry and constrained optimization. This can be used to show that the learning theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.

Deep learning models fail on cross-domain challenges if the model is oversensitive to domain-specific attributes, e.g., lightning, background, camera angle, etc. To alleviate this problem, data augmentation coupled with consistency regularization are commonly adopted to make the model less sensitive to domain-specific attributes. Consistency regularization enforces the model to output the same representation or prediction for two views of one image. These constraints, however, are either too strict or not order-preserving for the classification probabilities. In this work, we propose the Order-preserving Consistency Regularization (OCR) for cross-domain tasks. The order-preserving property for the prediction makes the model robust to task-irrelevant transformations. As a result, the model becomes less sensitive to the domain-specific attributes. The comprehensive experiments show that our method achieves clear advantages on five different cross-domain tasks.

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

Despite the remarkable performance that modern deep neural networks have achieved on independent and identically distributed (I.I.D.) data, they can crash under distribution shifts. Most current evaluation methods for domain generalization (DG) adopt the leave-one-out strategy as a compromise on the limited number of domains. We propose a large-scale benchmark with extensive labeled domains named NICO++ along with more rational evaluation methods for comprehensively evaluating DG algorithms. To evaluate DG datasets, we propose two metrics to quantify covariate shift and concept shift, respectively. Two novel generalization bounds from the perspective of data construction are proposed to prove that limited concept shift and significant covariate shift favor the evaluation capability for generalization. Through extensive experiments, NICO++ shows its superior evaluation capability compared with current DG datasets and its contribution in alleviating unfairness caused by the leak of oracle knowledge in model selection.

Domain adaptation of GANs is a problem of fine-tuning the state-of-the-art GAN models (e.g. StyleGAN) pretrained on a large dataset to a specific domain with few samples (e.g. painting faces, sketches, etc.). While there are a great number of methods that tackle this problem in different ways, there are still many important questions that remain unanswered. In this paper, we provide a systematic and in-depth analysis of the domain adaptation problem of GANs, focusing on the StyleGAN model. First, we perform a detailed exploration of the most important parts of StyleGAN that are responsible for adapting the generator to a new domain depending on the similarity between the source and target domains. As a result of this in-depth study, we propose new efficient and lightweight parameterizations of StyleGAN for domain adaptation. Particularly, we show there exist directions in StyleSpace (StyleDomain directions) that are sufficient for adapting to similar domains and they can be reduced further. For dissimilar domains, we propose Affine+ and AffineLight+ parameterizations that allows us to outperform existing baselines in few-shot adaptation with low data regime. Finally, we examine StyleDomain directions and discover their many surprising properties that we apply for domain mixing and cross-domain image morphing.

Large language models (LLMs) with one or more fine-tuning phases have become a necessary step to unlock various capabilities, enabling LLMs to follow natural language instructions or align with human preferences. However, it carries the risk of catastrophic forgetting during sequential training, the parametric knowledge or the ability learned in previous stages may be overwhelmed by incoming training data. In this paper, we find that by regularly resetting partial parameters, LLMs can restore some of the original knowledge. Inspired by this, we introduce Half Fine-Tuning (HFT) for LLMs, as a substitute for full fine-tuning (FFT), to mitigate the forgetting issues, where half of the parameters are selected to learn new tasks while the other half are frozen to remain previous knowledge. We provide a feasibility analysis from the perspective of optimization and interpret the parameter selection operation as a regularization term. Without changing the model architecture, HFT could be seamlessly integrated into existing fine-tuning frameworks. Extensive experiments and analysis on supervised fine-tuning, direct preference optimization, and continual learning consistently demonstrate the effectiveness, robustness, and efficiency of HFT. Compared with FFT, HFT not only significantly alleviates the forgetting problem, but also achieves the best performance in a series of downstream benchmarks, with an approximately 30% reduction in training time.

Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data. Technically, equation discovery is implemented by symbolic regression algorithms. Performance of symbolic regression for equation discovery is measured along two dimensions: Prediction accuracy on test data, and recovery of known groundtruth formulas. For standard regression, accuracy is typically measured on in-domain test data, for instance, by splitting a data set randomly into training and test data. While this makes sense for in-domain interpolation, which is the common goal in ordinary regression, it can be a misleading proxy for true model discovery and generalization. The obvious alternative is to measure out-of-domain accuracy. However, obtaining challenging out-of-domain test data is a non-trivial problem. Therefore, we focus on equation recovery for evaluating symbolic regression algorithms for equation discovery. The rationale is that symbolic regression algorithms that perform well in recovering known groundtruth formulas are good candidates to perform well in unknown equation discovery. Existing benchmarks for symbolic regression include equation recovery tasks, however, with only a small number of groundtruth formulas that are publicly known. Moreover, these benchmarks place less emphasis on evaluating the robustness of algorithms in terms of their behavior under changing dimensionality, sampling size, sampling distribution and sampling domain. This, however, is of central importance to practitioners wanting to discover equations for modeling natural phenomena, since data is almost certainly noisy and comes from diverse domains, distributions, and sample sizes. To fill this gap, we introduce the Equation Recovery Benchmark (ERBench), a new evaluation framework designed to rigorously assess algorithms explicitly targeting the task of equation discovery.

Time series domain adaptation stands as a pivotal and intricate challenge with diverse applications, including but not limited to human activity recognition, sleep stage classification, and machine fault diagnosis. Despite the numerous domain adaptation techniques proposed to tackle this complex problem, they primarily focus on domain adaptation from a single source domain. Yet, it is more crucial to investigate domain adaptation from multiple domains due to the potential for greater improvements. To address this, three important challenges need to be overcome: 1). The lack of exploration to utilize domain-specific information for domain adaptation, 2). The difficulty to learn domain-specific information that changes over time, and 3). The difficulty to evaluate learned domain-specific information. In order to tackle these challenges simultaneously, in this paper, we introduce PrOmpt-based domaiN Discrimination (POND), the first framework to utilize prompts for time series domain adaptation. Specifically, to address Challenge 1, we extend the idea of prompt tuning to time series analysis and learn prompts to capture common and domain-specific information from all source domains. To handle Challenge 2, we introduce a conditional module for each source domain to generate prompts from time series input data. For Challenge 3, we propose two criteria to select good prompts, which are used to choose the most suitable source domain for domain adaptation. The efficacy and robustness of our proposed POND model are extensively validated through experiments across 50 scenarios encompassing four datasets. Experimental results demonstrate that our proposed POND model outperforms all state-of-the-art comparison methods by up to 66% on the F1-score.

Adapting language models (LMs) to novel domains is often achieved through fine-tuning a pre-trained LM (PLM) on domain-specific data. Fine-tuning introduces new knowledge into an LM, enabling it to comprehend and efficiently perform a target domain task. Fine-tuning can however be inadvertently insensitive if it ignores the wide array of disparities (e.g in word meaning) between source and target domains. For instance, words such as chronic and pressure may be treated lightly in social conversations, however, clinically, these words are usually an expression of concern. To address insensitive fine-tuning, we propose Mask Specific Language Modeling (MSLM), an approach that efficiently acquires target domain knowledge by appropriately weighting the importance of domain-specific terms (DS-terms) during fine-tuning. MSLM jointly masks DS-terms and generic words, then learns mask-specific losses by ensuring LMs incur larger penalties for inaccurately predicting DS-terms compared to generic words. Results of our analysis show that MSLM improves LMs sensitivity and detection of DS-terms. We empirically show that an optimal masking rate not only depends on the LM, but also on the dataset and the length of sequences. Our proposed masking strategy outperforms advanced masking strategies such as span- and PMI-based masking.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

Out-of-distribution (OOD) generalization is a favorable yet challenging property for deep neural networks. The core challenges lie in the limited availability of source domains that help models learn an invariant representation from the spurious features. Various domain augmentation have been proposed but largely rely on interpolating existing domains and frequently face difficulties in creating truly "novel" domains. Humans, on the other hand, can easily extrapolate novel domains, thus, an intriguing question arises: How can neural networks extrapolate like humans and achieve OOD generalization? We introduce a novel approach to domain extrapolation that leverages reasoning ability and the extensive knowledge encapsulated within large language models (LLMs) to synthesize entirely new domains. Starting with the class of interest, we query the LLMs to extract relevant knowledge for these novel domains. We then bridge the gap between the text-centric knowledge derived from LLMs and the pixel input space of the model using text-to-image generation techniques. By augmenting the training set of domain generalization datasets with high-fidelity, photo-realistic images of these new domains, we achieve significant improvements over all existing methods, as demonstrated in both single and multi-domain generalization across various benchmarks. With the ability to extrapolate any domains for any class, our method has the potential to learn a generalized model for any task without any data. To illustrate, we put forth a much more difficult setting termed, data-free domain generalization, that aims to learn a generalized model in the absence of any collected data. Our empirical findings support the above argument and our methods exhibit commendable performance in this setting, even surpassing the supervised setting by approximately 1-2\% on datasets such as VLCS.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

Accurately identifying adversarial techniques in security texts is critical for effective cyber defense. However, existing methods face a fundamental trade-off: they either rely on generic models with limited domain precision or require resource-intensive pipelines that depend on large labeled datasets and task-specific optimizations, such as custom hard-negative mining and denoising, resources rarely available in specialized domains. We propose TechniqueRAG, a domain-specific retrieval-augmented generation (RAG) framework that bridges this gap by integrating off-the-shelf retrievers, instruction-tuned LLMs, and minimal text-technique pairs. Our approach addresses data scarcity by fine-tuning only the generation component on limited in-domain examples, circumventing the need for resource-intensive retrieval training. While conventional RAG mitigates hallucination by coupling retrieval and generation, its reliance on generic retrievers often introduces noisy candidates, limiting domain-specific precision. To address this, we enhance retrieval quality and domain specificity through zero-shot LLM re-ranking, which explicitly aligns retrieved candidates with adversarial techniques. Experiments on multiple security benchmarks demonstrate that TechniqueRAG achieves state-of-the-art performance without extensive task-specific optimizations or labeled data, while comprehensive analysis provides further insights.

This work studies the generalization issue of face anti-spoofing (FAS) models on domain gaps, such as image resolution, blurriness and sensor variations. Most prior works regard domain-specific signals as a negative impact, and apply metric learning or adversarial losses to remove them from feature representation. Though learning a domain-invariant feature space is viable for the training data, we show that the feature shift still exists in an unseen test domain, which backfires on the generalizability of the classifier. In this work, instead of constructing a domain-invariant feature space, we encourage domain separability while aligning the live-to-spoof transition (i.e., the trajectory from live to spoof) to be the same for all domains. We formulate this FAS strategy of separability and alignment (SA-FAS) as a problem of invariant risk minimization (IRM), and learn domain-variant feature representation but domain-invariant classifier. We demonstrate the effectiveness of SA-FAS on challenging cross-domain FAS datasets and establish state-of-the-art performance.

Supervised fine-tuning (SFT) is widely used to align large language models (LLMs) with information extraction (IE) tasks, such as named entity recognition (NER). However, annotating such fine-grained labels and training domain-specific models is costly. Existing works typically train a unified model across multiple domains, but such approaches lack adaptation and scalability since not all training data benefits target domains and scaling trained models remains challenging. We propose the SaM framework, which dynamically Selects and Merges expert models at inference time. Specifically, for a target domain, we select domain-specific experts pre-trained on existing domains based on (i) domain similarity to the target domain and (ii) performance on sampled instances, respectively. The experts are then merged to create task-specific models optimized for the target domain. By dynamically merging experts beneficial to target domains, we improve generalization across various domains without extra training. Additionally, experts can be added or removed conveniently, leading to great scalability. Extensive experiments on multiple benchmarks demonstrate our framework's effectiveness, which outperforms the unified model by an average of 10%. We further provide insights into potential improvements, practical experience, and extensions of our framework.

We consider the unsupervised scene adaptation problem of learning from both labeled source data and unlabeled target data. Existing methods focus on minoring the inter-domain gap between the source and target domains. However, the intra-domain knowledge and inherent uncertainty learned by the network are under-explored. In this paper, we propose an orthogonal method, called memory regularization in vivo to exploit the intra-domain knowledge and regularize the model training. Specifically, we refer to the segmentation model itself as the memory module, and minor the discrepancy of the two classifiers, i.e., the primary classifier and the auxiliary classifier, to reduce the prediction inconsistency. Without extra parameters, the proposed method is complementary to the most existing domain adaptation methods and could generally improve the performance of existing methods. Albeit simple, we verify the effectiveness of memory regularization on two synthetic-to-real benchmarks: GTA5 -> Cityscapes and SYNTHIA -> Cityscapes, yielding +11.1% and +11.3% mIoU improvement over the baseline model, respectively. Besides, a similar +12.0% mIoU improvement is observed on the cross-city benchmark: Cityscapes -> Oxford RobotCar.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel at discovering parsimonious models but require researchers to specify candidate basis functions a priori, a limitation that often leads to model failure when critical terms are omitted or when systems exhibit unconventional dynamics. Purely symbolic regression approaches offer unlimited flexibility but struggle with noise sensitivity and frequently produce overly complex, unstable equations. We present AutoSINDy, a hybrid Discovery-then-Solve framework that combines the exploratory power of symbolic regression with the robust sparsity-promoting capabilities of SINDy. Our method operates in three stages: (1) PySR-based symbolic regression discovers candidate functional forms from bootstrapped data chunks; (2) a curation pipeline decomposes, expands, and filters these expressions using collinearity analysis to construct a minimal yet comprehensive library; and (3) SINDy identifies sparse governing equations from this custom-tailored library. Extensive experiments across canonical nonlinear systems demonstrate that AutoSINDy consistently recovers ground-truth equations even under high observational noise, achieving a ground-truth recovery rate of 92.8% across all trials. Compared with standard SINDy using enriched libraries and standalone symbolic regression, AutoSINDy achieves higher predictive accuracy, superior generalization to unseen trajectories, and substantially lower symbolic complexity.

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and inverse problems like geometric design. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

Face anti-spoofing (FAS) based on domain generalization (DG) has been recently studied to improve the generalization on unseen scenarios. Previous methods typically rely on domain labels to align the distribution of each domain for learning domain-invariant representations. However, artificial domain labels are coarse-grained and subjective, which cannot reflect real domain distributions accurately. Besides, such domain-aware methods focus on domain-level alignment, which is not fine-grained enough to ensure that learned representations are insensitive to domain styles. To address these issues, we propose a novel perspective for DG FAS that aligns features on the instance level without the need for domain labels. Specifically, Instance-Aware Domain Generalization framework is proposed to learn the generalizable feature by weakening the features' sensitivity to instance-specific styles. Concretely, we propose Asymmetric Instance Adaptive Whitening to adaptively eliminate the style-sensitive feature correlation, boosting the generalization. Moreover, Dynamic Kernel Generator and Categorical Style Assembly are proposed to first extract the instance-specific features and then generate the style-diversified features with large style shifts, respectively, further facilitating the learning of style-insensitive features. Extensive experiments and analysis demonstrate the superiority of our method over state-of-the-art competitors. Code will be publicly available at https://github.com/qianyuzqy/IADG.

Deep neural networks exploiting millions of parameters are nowadays the norm in deep learning applications. This is a potential issue because of the great amount of computational resources needed for training, and of the possible loss of generalization performance of overparametrized networks. We propose in this paper a method for learning sparse neural topologies via a regularization technique which identifies non relevant weights and selectively shrinks their norm, while performing a classic update for relevant ones. This technique, which is an improvement of classical weight decay, is based on the definition of a regularization term which can be added to any loss functional regardless of its form, resulting in a unified general framework exploitable in many different contexts. The actual elimination of parameters identified as irrelevant is handled by an iterative pruning algorithm. We tested the proposed technique on different image classification and Natural language generation tasks, obtaining results on par or better then competitors in terms of sparsity and metrics, while achieving strong models compression.

We study the problem of transferring a sample in one domain to an analog sample in another domain. Given two related domains, S and T, we would like to learn a generative function G that maps an input sample from S to the domain T, such that the output of a given function f, which accepts inputs in either domains, would remain unchanged. Other than the function f, the training data is unsupervised and consist of a set of samples from each domain. The Domain Transfer Network (DTN) we present employs a compound loss function that includes a multiclass GAN loss, an f-constancy component, and a regularizing component that encourages G to map samples from T to themselves. We apply our method to visual domains including digits and face images and demonstrate its ability to generate convincing novel images of previously unseen entities, while preserving their identity.

Seeking legal advice is often expensive. Recent advancements in machine learning for solving complex problems can be leveraged to help make legal services more accessible to the public. However, real-life applications encounter significant challenges. State-of-the-art language models are growing increasingly large, making parameter-efficient learning increasingly important. Unfortunately, parameter-efficient methods perform poorly with small amounts of data, which are common in the legal domain (where data labelling costs are high). To address these challenges, we propose parameter-efficient legal domain adaptation, which uses vast unsupervised legal data from public legal forums to perform legal pre-training. This method exceeds or matches the fewshot performance of existing models such as LEGAL-BERT on various legal tasks while tuning only approximately 0.1% of model parameters. Additionally, we show that our method can achieve calibration comparable to existing methods across several tasks. To the best of our knowledge, this work is among the first to explore parameter-efficient methods of tuning language models in the legal domain.

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties of orthogonal convolutional layers.We establish necessary and sufficient conditions on the layer architecture guaranteeing the existence of an orthogonal convolutional transform. The conditions prove that orthogonal convolutional transforms exist for almost all architectures used in practice for 'circular' padding.We also exhibit limitations with 'valid' boundary conditions and 'same' boundary conditions with zero-padding.Recently, a regularization term imposing the orthogonality of convolutional layers has been proposed, and impressive empirical results have been obtained in different applications (Wang et al. 2020).The second motivation of the present paper is to specify the theory behind this.We make the link between this regularization term and orthogonality measures. In doing so, we show that this regularization strategy is stable with respect to numerical and optimization errors and that, in the presence of small errors and when the size of the signal/image is large, the convolutional layers remain close to isometric.The theoretical results are confirmed with experiments and the landscape of the regularization term is studied. Experiments on real data sets show that when orthogonality is used to enforce robustness, the parameter multiplying the regularization termcan be used to tune a tradeoff between accuracy and orthogonality, for the benefit of both accuracy and robustness.Altogether, the study guarantees that the regularization proposed in Wang et al. (2020) is an efficient, flexible and stable numerical strategy to learn orthogonal convolutional layers.

In adversarial training, a set of models learn together by pursuing competing goals, usually defined on single data instances. However, in relational learning and other non-i.i.d domains, goals can also be defined over sets of instances. For example, a link predictor for the is-a relation needs to be consistent with the transitivity property: if is-a(x_1, x_2) and is-a(x_2, x_3) hold, is-a(x_1, x_3) needs to hold as well. Here we use such assumptions for deriving an inconsistency loss, measuring the degree to which the model violates the assumptions on an adversarially-generated set of examples. The training objective is defined as a minimax problem, where an adversary finds the most offending adversarial examples by maximising the inconsistency loss, and the model is trained by jointly minimising a supervised loss and the inconsistency loss on the adversarial examples. This yields the first method that can use function-free Horn clauses (as in Datalog) to regularise any neural link predictor, with complexity independent of the domain size. We show that for several link prediction models, the optimisation problem faced by the adversary has efficient closed-form solutions. Experiments on link prediction benchmarks indicate that given suitable prior knowledge, our method can significantly improve neural link predictors on all relevant metrics.

In domain generalization (DG), the target domain is unknown when the model is being trained, and the trained model should successfully work on an arbitrary (and possibly unseen) target domain during inference. This is a difficult problem, and despite active studies in recent years, it remains a great challenge. In this paper, we take a simple yet effective approach to tackle this issue. We propose test-time style shifting, which shifts the style of the test sample (that has a large style gap with the source domains) to the nearest source domain that the model is already familiar with, before making the prediction. This strategy enables the model to handle any target domains with arbitrary style statistics, without additional model update at test-time. Additionally, we propose style balancing, which provides a great platform for maximizing the advantage of test-time style shifting by handling the DG-specific imbalance issues. The proposed ideas are easy to implement and successfully work in conjunction with various other DG schemes. Experimental results on different datasets show the effectiveness of our methods.

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two pivotal properties for effective representations: (i) avoiding dimensional collapse-where the learned features occupy only a low-dimensional subspace, and (ii) enhancing uniformity of the induced distribution. In this work, we introduce T-REGS, a simple regularization framework for SSL based on the length of the Minimum Spanning Tree (MST) over the learned representation. We provide theoretical analysis demonstrating that T-REGS simultaneously mitigates dimensional collapse and promotes distribution uniformity on arbitrary compact Riemannian manifolds. Several experiments on synthetic data and on classical SSL benchmarks validate the effectiveness of our approach at enhancing representation quality.

Deep neural networks include millions of learnable parameters, making their deployment over resource-constrained devices problematic. SeReNe (Sensitivity-based Regularization of Neurons) is a method for learning sparse topologies with a structure, exploiting neural sensitivity as a regularizer. We define the sensitivity of a neuron as the variation of the network output with respect to the variation of the activity of the neuron. The lower the sensitivity of a neuron, the less the network output is perturbed if the neuron output changes. By including the neuron sensitivity in the cost function as a regularization term, we areable to prune neurons with low sensitivity. As entire neurons are pruned rather then single parameters, practical network footprint reduction becomes possible. Our experimental results on multiple network architectures and datasets yield competitive compression ratios with respect to state-of-the-art references.