OOD Generalization

Multi-channel mixed-SNR training improves out-of-distribution (OOD) generalisation of deep learning channel estimators for IEEE 802.11p vehicular communications, yet the internal mechanism responsible for this remains unexplained. This work presents REACH (Relevance-based Explanation and Architectural Compression for cHannel estimators), a gradient-based interpretability framework that operates at two levels. Input-level attribution identifies a subset of time-frequency features consistently relevant across all evaluated channel conditions, enabling input dimensionality reduction with minimal performance loss. Filter-level attribution reveals a near-universal internal representation, providing a representational account of the observed OOD generalisation. Guided by the resulting filter taxonomy, relevance-guided architecture compression substantially reduces both the number of parameters and the number of floating-point operations (FLOPs) with sub-1 dB normalised mean square error (NMSE) degradation, and OOD generalisation degrades more slowly than within-distribution accuracy under increasing compression.

Existing deep learning models for Positron Emission Tomography (PET) image denoising often suffer from severe performance degradation under distribution shifts, fundamentally restricting their robust clinical deployment. This lack of generalization stems from the conventional paradigm of fixed-parameter models that cannot adapt to variations in test data (e.g., dose levels or scanner types) after training. To overcome this limitation and achieve robust generalization, we introduce U-TTT, a novel U-shaped model that integrates Test-Time Training (TTT) layers to dynamically adjust model parameters during inference through self-supervision, thereby adapting to the specific characteristics of each test instance. Furthermore, to comprehensively capture the complex degradations of 3D PET data, U-TTT features a dual-domain adaptation mechanism comprising a Spatial Test-Time Training (S-TTT) layer and a Frequency Test-Time Training (F-TTT) layer. The S-TTT layer captures and corrects spatial structural degradations, while the F-TTT layer suppresses global noise spectra and restores delicate high-frequency details. Extensive experiments demonstrate that U-TTT achieves state-of-the-art PET denoising performance and exhibits superior generalization under challenging distribution shifts, including both unseen dose levels and unseen scanners. Our code will be available at https://github.com/Yaziwel/U-TTT.

Reliable extrapolation remains a central challenge for generative models in computational physics, because models trained over finite ranges of time, parameters, or geometries may produce physically inconsistent predictions outside the training distribution. We introduce a least-action-principle-guided diffusion, LAPG, a framework that promotes physical consistency during inference rather than relying solely on constraints imposed during training. The method combines a conditional score-based diffusion model with an action-derived physical guidance score. In the first stage, the learned score model generates an in-distribution proposal; in the second, an action-based variational prior refines this proposal toward the target out-of-distribution condition. This formulation turns the principle of least action into a differentiable inference-time correction mechanism and provides an alternative to pointwise residual penalties that often require empirical loss balancing. We evaluate LAPG on representative ordinary- and partial-differential-equation systems, including free fall, conservative and dissipative spring-mass dynamics, interacting point vortices, and potential flow over parameterized airfoils. In temporal, parameter, and geometric extrapolation tests, LAPG reduces phase drift, preserves dissipative decay, captures vortex motion, and improves the lift response of airfoil flows compared with training-time physics-informed baselines.

Remote sensing applications for environmental monitoring and disaster management are frequently constrained by a spatial--temporal trade-off: imagery with fine spatial detail is often acquired less frequently, whereas more temporally available observations are typically coarser. Single-image super-resolution provides a practical means to enhance coarse imagery without changing acquisition schedules, yet many Transformer-based SR models remain computationally expensive and can be sensitive to limited or geographically biased training data, which degrades robustness under out-of-distribution conditions. This paper presents NGram-MoSE, a lightweight Transformer architecture designed to improve both efficiency and texture continuity. NGram-MoSE introduces N-Gram Context Injection to strengthen cross-window local consistency and mitigate window-boundary artifacts, and incorporates a Mixture-of-Experts (MoE) feed-forward design to scale capacity through sparse activation without proportional growth in inference cost. Experiments on a geographically disjoint OOD test set show that NGram-MoSE achieves 31.68,dB PSNR while reducing FLOPs by $14\times$ relative to a heavyweight Transformer reference. Downstream evaluation on a landslide segmentation benchmark further demonstrates that restoring degraded inputs to the detector training scale improves performance, yielding a 4.47% absolute gain in mAP@50 over bicubic upsampling, and exhibits stronger cross-scale consistency under scale extrapolation. These results indicate that NGram-MoSE provides an effective SR module for resource-constrained remote sensing pipelines requiring robust generalization.

Multimodal $ΔΔG$ predictors integrating protein language models with inverse-folding representations achieve strong in-distribution accuracy on the Megascale dataset but exhibit limited robustness on out-of-distribution (OOD) proteins, persistent forward-reverse bias on paired-mutation benchmarks, and under-representation of rare stabilizing mutations. Existing approaches address these limitations primarily through additional architectural components, leaving optimization-level intervention comparatively underexplored. We introduce a constraint-aware optimization framework combining Balanced Mean Squared Error, a Siamese anti-symmetric regularizer, and a novel OOD-margin consistency loss on the per-position feature representation, requiring no architectural changes to the SPURS backbone. Across eleven benchmarks and three random seeds, the framework improves Spearman correlation on S669 from 0.486 to 0.540 ($σ=0.002$ across seeds), matching the published SPURS baseline (0.50) without architectural modification, and on S461 from 0.653 to 0.711, with consistent smaller gains on five additional OOD datasets. A controlled diagnostic on Ssym reveals that anti-symmetric training does not eliminate systematic forward-reverse bias, indicating that gains arise through implicit regularization rather than exact thermodynamic constraint enforcement.

Floods are among the most destructive natural hazards, and their increasing frequency under climate change makes satellite-based inundation mapping essential for disaster response. Geospatial foundation models pretrained on satellite archives offer geographic transferability, but their operational reliability across diverse, unseen events remains uncharacterized. Here we deploy Prithvi-EO-2.0 across 19 out-of-distribution flood events (2017-2025) spanning six continents, eight climate zones, and six flood mechanisms, validating against two independent reference products. Detection accuracy depended jointly on land cover and flood type, with cropland yielding the highest agreement (IoU=52%) and riverine events the strongest detection (F1=0.69), while tree cover and built-up areas showed near-zero detection (IoU=4%) regardless of flood mechanism. Dual-reference validation revealed that apparent model error partly reflects definitional inconsistency between reference products rather than detection failure. Iterative pipeline testing identified 23 failure modes, with pipeline engineering dominating initial error over model capacity. These findings establish environment-dependent detection boundaries for operational satellite flood mapping.

The transformer's emergent ability to perform in-context learning (ICL) has sparked a wide range of studies designed to understand its underlying mechanisms. Existing works often study how training task diversity, defined either as the number of ICL training task vectors or as the number of function classes from which the task vectors are drawn, shapes both the learning dynamics and generalization capabilities of ICL. While both definitions have uncovered many interesting phenomena, many observations under the latter definition remain theoretically unexplained. This paper presents a minimal analytical model under which these phenomena provably emerge from the properties of the training data. By modeling the training task vectors as a mixture of low-rank Gaussians, we show how training task diversity, defined by the number of non-overlapping columns between subspaces that parameterize the covariance matrices, improves both the generalization and optimization trajectory of ICL with linear attention. In particular, we show that our model can explain (i) why training with task diversity shortens the ICL plateau and (ii) why ICL appears to achieve out-of-distribution generalization. We conclude by empirically demonstrating how our results extend to nonlinear transformers and nonlinear function classes. Overall, our work presents a tractable framework to unify existing observations.

Graph Neural Networks (GNNs) have demonstrated remarkable performance across a range of applications involving graph-structured data, particularly in high-stakes domains. However, the opaque nature of their decision-making processes limits their trustworthiness and broader adoption. Existing post-hoc explanation methods aim to improve explainability by identifying subgraphs that influence GNN predictions and adopt mixup strategies to alleviate the out-of-distribution (OOD) issue caused by using subgraphs for prediction. Yet, these approaches typically rely on soft masks, which are inherently unable to fully eliminate label-irrelevant information, allowing redundant structures to leak into the mixup process and hindering the resolution of the OOD problem, thereby degrading explanation fidelity. In this work, we propose HPME, a Hard-Perturbation Mixup Explanation framework grounded in a generalized Graph Information Bottleneck, which leverages graph pooling to extract discrete explanatory subgraphs and to yield an information-capacity bound to thoroughly compress label-irrelevant components. Furthermore, we introduce a novel mixup strategy built upon structure-level replacement, generating in-distribution explanations to effectively mitigate the distribution shift. Extensive experiments on diverse tasks demonstrate that HPME achieves state-of-the-art performance in generating robust and interpretable explanations across both synthetic and real-world datasets.

Near-real-time flood depth prediction demands surrogate models that are accurate, fast, and transferable across watersheds. Supervised surrogates can match physics-based simulators in accuracy but need millions of training rows per watershed and cannot extrapolate beyond their original mesh. We propose a domain-aware coreset construction pipeline that conditions a tabular foundation model at inference time. The pipeline stratifies storms by return period and most-affected watershed, then samples hexagons with a target-aware spatial selector. With 0.7% of the per-watershed training pool, the model attains a mean $R^2$ of 0.663 across nine Houston-area watersheds, within 98.5% of the supervised reference ($R^2$ = 0.673). It transfers to held-out watersheds without task-specific retraining, staying ahead of a coreset-trained supervised baseline. On real storms it exceeds the supervised reference on a far out-of-distribution case and trails it on a mostly in-distribution one. Domain-aware coreset construction lets tabular foundation models deliver data-efficient, watershed-transferable flood predictions without per-watershed training.

Large language models (LLMs) suffer from shortcut learning: they systematically fail on out-of-distribution (OOD) inputs whose semantic surface differs from training data, even when the logical structure is identical. This undermines knowledge distillation pipelines that transfer chain-of-thought reasoning to smaller students. We introduce Invariant Gradient Alignment (IGA), a training framework that aligns gradient updates across semantically diverse but logically isomorphic examples via three innovations: (i) Logical Isomer Sets, groups of problems sharing identical logical structure across distinct semantic domains (mathematics, medicine, law, science); (ii) a differentiable \emph{Continuous Gradient Conflict Mask}, that suppresses parameter dimensions with high cross-domain gradient variance while preserving invariant directions; and (iii) a truncated SVD projection of the masked gradient back onto the LoRA low-rank manifold, maintaining parameter efficiency throughout. Theoretically, IGA yields tighter OOD generalization bounds than ERM, scaling with the number of isomer domains, and converges at the standard SGD rate under mild regularity. Empirically, IGA outperforms eight baselines across four benchmarks with accuracy gains up to 14.3 pp over ERM-SFT and a Logical Consistency Score of 0.031 versus 0.142 -- a fourfold improvement in representational invariance.

Data samples used for training often differ from those encountered during fine-tuning and deployment, and while ML models show promise, their performance remains limited when only small annotated datasets are available. Performance often degrades under distribution shifts caused by diverse sensors, populations, and application settings. Although pre-training helps, models frequently encounter out-of-distribution (OOD) data in real-world settings, leading to reduced robustness. Existing adaptation methods usually assume fixed distribution shifts and struggle when multiple types or severities occur. In particular, they overlook shift severity, for example treating adaptation to a large familiar dataset the same as adaptation to a small dataset with a new task, which limits generalisation. To address this, we propose ADAPTOOD, a novel framework that leverages data uncertainty to quantify distribution shift severity and guide fine-tuning for time series. This uncertainty measures how strongly samples from the target deployment distribution deviate from the pre-training distribution, providing a direct signal of OOD severity. Our framework combines this uncertainty with low-rank model updates and adaptive hyperparameter optimisation to improve adaptation. We show that ADAPTOOD achieves up to 7% higher accuracy and 12.9% higher precision than existing methods in OOD tasks, maintaining strong performance as distribution shift severity increases.

Neural networks suffer from shortcut learning, where learned features generalize well to the training set but not to in-distribution (ID) or out-of-distribution (OOD) test sets. Existing studies are all based on a few standard benchmarks, which are shape-driven. Numerous application domains, however, are texture-driven. In this work, we present shortcut learning analysis for texture-driven domains, and compare it with that of a standard benchmark. We show that texture-driven domains suffer from low-frequency shortcuts. They make the majority of their decisions based on a few low-frequency components (LFCs) with a skewed spectral behavior, despite that their classification information is in higher-frequency, fine-grained details. Pruning LFCs from training and test sets eliminates the shortcut and provides a more balanced spectral behavior, improving the ID accuracy by up to 8%. We show that low-frequency shortcuts make the models highly vulnerable to OOD corruptions, leading up to 70% accuracy drop compared to the ID accuracy. Pruning LFCs significantly improves robustness to low-frequency corruptions, by up to 40%, and introduces a trade-off for high-frequency corruptions; the balanced spectral behavior provides a better generalization performance, whereas the increased dependence on high-frequency features reduces it. OOD accuracy depends on the interaction between these two factors.

Live streaming has emerged as a primary medium for social interaction and digital commerce, yet it is increasingly plagued by sophisticated risks. A fundamental challenge in this domain is \emph{tactical out-of-distribution (OOD) shift}: while malicious actors maintain stable underlying objectives, they continuously redesign narrative packaging to evade detection. Such adversarial shifts expose critical limitations of existing OOD generalization paradigms, whose assumptions are difficult to satisfy in the presence of tightly coupled intent-tactic evolution and ill-defined raw-level counterfactuals. In this paper, we tackle this issue from a \emph{latent causal} perspective and propose \underline{L}atent-\underline{P}redictive \underline{C}ounterfactual \underline{D}ecoupling~(LPCD), a plug-in framework for robust live streaming risk assessment. LPCD enables counterfactual reasoning under adversarial tactical re-packaging by modeling intent and narrative variation at the latent level, and enforces \emph{latent counterfactual consistency} to anchor risk prediction on causally stable malicious intent. At inference time, LPCD applies a lightweight, parameter-free calibration to further mitigate tactic-induced distribution shifts. Extensive experiments on large-scale industrial datasets and online production traffic demonstrate that LPCD consistently outperforms state-of-the-art baselines, validating its effectiveness in moderating evolving adversarial risks in real-world live streaming. The project page is available at https://qiaoyran.github.io/LiveStreamingRiskAssessment/.

Multi-task learning (MTL) aims to construct a joint model for multiple tasks by sharing a common representation across domains. To achieve this goal, existing optimization-centric methods either balance task gradients or modify the shared architecture. However, as these approaches remain agnostic to the content of the shared representation, they fail to disentangle task-relevant structure from spurious context, leading to negative transfer and poor generalization. To overcome this limitation, we propose Causal Orthogonal Representations for Multi-Task Learning (CORE-MTL), a causally motivated representation-centric framework that encourages a structured semantic-residual factorization of the shared representation, concentrating task-relevant structure in the semantic stream while relegating nuisance variation to the residual stream. We instantiate this framework in the visual domain by leveraging physical priors for structured scenes and statistical constraints for attributes. Theoretically, our method enjoys a tighter out-of-distribution generalization bound than optimization-centric methods and reduces task gradient interference without explicit gradient projection or reweighting. Empirically, CORE-MTL consistently outperforms existing methods on visual multi-task benchmarks in both in-distribution and out-of-distribution settings. Code is publicly available at https://github.com/Hope-Rita/CORE-MTL.

Surrogate models for topology optimization (TO) exhibit highly variable out-of-distribution (OOD) generalization under distribution shifts such as changing loads or boundary conditions, yet the source of this variability remains unclear. We hypothesize that OOD performance is governed by how much information the conditioning signal preserves about the adjoint sensitivity (reduced gradient) that drives classical TO. Modeling the TO pipeline as a causal Markov chain, the Data Processing Inequality establishes that, under this abstraction, the sensitivity field is an information-theoretically optimal conditioning signal for topology prediction. However, computing exact adjoint sensitivities can be expensive or unavailable in practice; we observe that certain physical fields can approximate sensitivities through monotone transformations. To formalize this, we introduce \textbf{pseudo-sensitivities} to characterize which fields enable generalization versus those that are information-poor. We then show that a sensitivity-conditioned Bernoulli flow-matching generator empirically confirms these predictions: conditioning on sensitivities yields state-of-the-art OOD performance, while increasingly distant physical fields degrade toward raw parameter conditioning. Results hold across structural TO benchmarks under load shifts and our new CFD-TO dataset under boundary-condition shifts such as multi-outlet configurations. Code and datasets are available at https://tum-pbs.github.io/topotransformer/ .

Out of distribution (OOD) events in multivariate time series forecasting are rare but often dominate real world risk, making average case forecasting insufficient for reliable deployment. Under standard average risk training on mixed ID/OOD distributions, optimization signals from rare OOD events can be overwhelmed by frequent in distribution (ID) patterns, so strong benchmark accuracy may not translate into reliability under high impact shifts. To address this issue, we propose VLBM (Variational Latent Basis Model), a theory guided latent forecasting framework that separates stable dynamics from OOD induced deviations. VLBM learns a shared latent basis that defines a low rank subspace for stable ID dynamics, explicitly decomposes inputs into basis subspace components and orthogonal residual components, and aligns a future aware posterior with a future blind prior so that test time latent inference depends only on historical input. Across 12 benchmark tasks spanning transportation, weather, power systems, and other real world domains, including newly constructed real world OOD traffic datasets, VLBM achieves state of the art OOD robustness and ID accuracy, with average MAE and MSE gains of 15.08% and 7.74% over the strongest baseline. On a synthetic simulation dataset, VLBM also consistently achieves the best performance and better tracks OOD pulse recovery. These results support latent structured forecasting as a principled route to robust prediction under mixed ID and OOD conditions. The code is available at https://github.com/leijieruilq/VLBM_OOD_forecast.

Deepfake detection suffers from poor generalization across forgery methods, as existing models tend to rely on spurious method-specific shortcuts that fail to transfer to unseen manipulations. While recent approaches attempt to improve generalization, they lack an explicit mechanism to identify and suppress such shortcuts in learned representations. In this work, we propose Shortcut Subspace Suppression (S^3) framework that explicitly characterizes and suppresses method-specific shortcuts via subspace modeling. Our key insight is that variations distinguishing different forgery methods capture method-specific artifacts and thus serve as an effective proxy for method-specific shortcuts. To this end, we train a lightweight linear probe for forgery method classification and perform Singular Value Decomposition (SVD) to extract the dominant shortcut subspace. Building on this formulation, we develop two complementary strategies to reduce shortcut reliance. During training, we softly suppress the shortcut subspace in feature representations, encouraging the model to rely on more generalizable cues for real/fake discrimination. At inference time, we introduce a training-free counterpart that attenuates neurons aligned with the identified shortcut directions, enabling plug-and-play generalization enhancement with improved interpretability. Extensive experiments on multiple benchmarks demonstrate that our method significantly improves cross-method generalization while maintaining strong in-domain performance. The code will be released upon acceptance of the submission.

Real-world regression often exhibits shortcuts: attributes that are spuriously correlated with continuous targets in training, yet unreliable under deployment shifts; regressing targets using such shortcuts may fail catastrophically at test time. Existing studies on spurious correlations focus primarily on classification, where labels are categorical and groups are naturally defined. However, many real-world tasks require continuous prediction, where hard label boundaries or discrete group-label pairs do not exist. We define Deep Spurious Regression (DSR) as learning from regression data with attribute-label confounding, addressing continuous spurious correlations, and generalizing to all attribute-label combinations at test time. Motivated by the intrinsic difference between classification and regression shortcuts, we propose to exploit the similarity among spurious attributes in both label and feature spaces, thereby accounting for nearby targets and related groups while calibrating both label and learned feature distributions across attributes. Extensive experiments on common real-world DSR datasets that span computer vision, environmental sensing, and large language model (LLM) regression verify the superior performance of our strategies. Our work fills the gap in benchmarks and techniques for studying spurious correlations in continuous prediction.

Transitive inference is the challenge of inferring that A < C from knowing only adjacent relations (A < B, B < C). It is solved by humans and animals not through logical chaining but via an analogue mental number line, whose signature is the symbolic distance effect: distant comparisons are easier than nearby ones. We ask whether Transformers acquire the same primitive, training small models exclusively on adjacent comparisons from a hidden total order and evaluating generalization to unseen distant pairs. We find that out-of-distribution generalization emerges alongside a striking geometric reorganization: entity embeddings collapse onto a one-dimensional manifold whose principal axis recovers the hidden rank order with near-perfect fidelity, and this structure is sensitive to optimization in ways that produce grokking-like transient dynamics. Critically, even when accuracy is at ceiling, decision confidence and geometric separation both scale monotonically with rank distance, directly mirroring the symbolic distance effect observed across decades of behavioural experiments on humans, primates, and rodents. We further show the same rank-aligned geometry in a pretrained large language model, where it tracks the topology of each ordinal relation: linear for sizes and digits, cyclic for months. These results ground a 50-year-old behavioural regularity in the geometry of learned representations, offering a mechanistic account of transitive inference that bridges cognitive science and modern neural networks.

Large Language Models (LLMs) aligned via outcome-based Reinforcement Learning (RL) frequently exhibit a critical failure mode: they achieve high performance on in-distribution benchmarks while demonstrating brittle reasoning capabilities on out-of-distribution (OOD) tasks. We term this phenomenon Reward-Induced Manifold Collapse. We establish a theoretical framework bridging Structural Causal Models (SCM) and the Information Bottleneck (IB) principle to explain this paradox. We define reasoning as a high-complexity causal process and shortcut learning as the exploitation of low-complexity spurious correlations. Under the implicit inductive bias of Stochastic Gradient Descent (SGD), models optimized for outcome rewards are biased toward shortcut solutions whenever the training distribution allows for a ``Markovian Screening'' of the true causal mechanism. We derive a new generalization bound based on Semantic Coverage Measure ($η$) rather than sample size, showing why data scaling on homogeneous distributions may fail to correct reasoning flaws. We also show that Process Reward Models (PRMs) function as Topological Filters, enforcing step-wise mutual information constraints that render the low-complexity shortcut manifold inadmissible. These results provide a mathematical grounding for the role of process supervision beyond simple credit assignment.

Selection bias is a common and often unavoidable aspect of real-world data that challenges the generalizability of machine learning models. When models trained on biased data are deployed in the broader target population, poor model generalization may lead to real harm, particularly in high-risk settings such as healthcare. This risk highlights the need for practitioners to reliably assess model generalizability prior to deployment. However, existing methods for predicting model performance rely on unrealistic access to the target distribution or knowledge of the selection mechanism causing bias. To address these limitations, we propose a novel upper bound on the worst-case model performance on the target population under the realistic setting where the selection mechanism and the target population data are only partially observed. We demonstrate the validity and practical utility of our method through experiments on fully synthetic data, semi-synthetic data derived from the All of Us Research Program, and real-world selection bias in MIMIC-IV. Our work offers a principled and practical tool to estimate the impact of selection bias in an otherwise intractable setting, thereby enabling practitioners to build safer and more generalizable models in healthcare and beyond.

Modern language-model fine-tuning typically pairs each prompt with a single response, even though many prompts admit multiple valid completions. This effectively reduces a multi-modal conditional distribution to a one-sample view, a phenomenon we call the "mode lottery," where training emphasizes a subset of plausible modes while leaving others underrepresented. We study multi-response training (MRT), which retains multiple responses per prompt, and develop a principled account of when and why it helps. Our key insight is that prompts and responses are distinct statistical resources: additional prompts reduce uncertainty about the input distribution, while additional responses reduce uncertainty about the conditional output distribution. This yields a variance-budget tradeoff that predicts when retaining multiple responses is worthwhile, shows diminishing returns as prompt-level uncertainty dominates, and explains why large redundant corpora can exhibit an implicit multi-response effect. We further analyze response selection, and show that Random-K-of-N is the unbiased default for distributional fine-tuning, reward-based selection can induce mode collapse, and a submodular quality-diversity objective provides an efficient alternative with theoretical guarantees. Controlled simulations validate the predicted variance and selection effects, including a striking failure mode where reward-only selection produces gradients misaligned with the true objective. Across structured and real-world datasets, including a new multi-prompt, multi-response benchmark, MRT consistently improves distributional generalization, with the largest gains in high response-diversity, low prompt-redundancy regimes. MRT reframes response multiplicity as a data-allocation problem with clear guidance: when responses are cheap and diverse, keeping more than one is not a heuristic, but a statistically grounded choice.

We study quantile regression in an extrapolation regime where the covariate takes unusually large values. Under regular variation assumptions, extreme observations can be effectively characterized through their angular components, enabling learning strategies that focus on the angle of the most extreme observations. This approach is formalized through the minimization of an asymptotic conditional risk that localizes learning in the tail of the covariate distribution. We propose a novel Support Vector Machine (SVM) framework for extreme quantile regression, leveraging reproducing kernel Hilbert spaces to handle high-dimensional and nonlinear settings. Our method also accommodates unbounded response variables and avoids restrictive transformations. We establish finite-sample learning guarantees under mild regularity assumptions. The proposed framework unifies ideas from statistical learning and multivariate extremes, providing a tractable and theoretically grounded approach to extrapolation. We complement our theoretical findings with an empirical study on river flow data from the Danube, demonstrating the practical relevance of our methods.

Drug synergy prediction (DSP) aims to identify efficacious drug combinations under various cellular contexts with different targets. However, the continual emergence of novel compounds results in variations in molecular scaffolds and sizes, causing drug synergy data to exhibit out-of-distribution (O.O.D.) shifts with respect to topological structure. Existing works rely on in-distribution (I.D.) assumption, failing to handle the O.O.D. shifts. To solve this problem, we study out-of-distribution generalized drug synergy prediction through a graph large language model for the first time. Nevertheless, O.O.D. generalized DSP is highly non-trivial, posing several challenges: i) how to discover structurally relevant and irrelevant molecular representations with respect to cell targets; ii) how to find the optimal graph neural architectures that accurately calculate molecular representations; and iii) how to jointly leverage molecular structural and semantic information in LLMs. To address these challenges, we propose OOD-GraphLLM, a novel graphLLM framework which is able to accurately predict drug synergy under O.O.D. settings via jointly optimizing molecular graph representation and biomedical semantic language representations in a unified manner. Furthermore, we finetune DrugSyn-LLM, a biomedical LLM, and employ a retrieval-augmented biomedical instruction tuning strategy to align molecular topological information and molecular semantic information with language-based reasoning for O.O.D. generalized DSP. Both the source code (https://github.com/EkkoXiao/Bio-GraphLLM) and released model (https://mn.cs.tsinghua.edu.cn/bio-graphllm/) are publicly available, where users are allowed to download model resources and interactively use the system through a web interface.

Modern learning systems excel at interpolation but struggle to generalize to unseen tasks outside the training distribution's support. This failure occurs even in simple settings, such as handling task parameters beyond the training range, and persists despite advances in foundation models. To this end, we develop the Relational Task Extrapolator (RTE), an algorithm designed to enable systematic extrapolation to novel tasks. The key observation is that extrapolation is inherently relational: extrapolating to unseen tasks requires learning how tasks transform into one another. If a model learns the transformation between tasks A and B during training, it can apply that same transformation to relate known tasks to unseen ones at test time. RTE operationalizes this idea by decomposing each target task into a known anchor task and a transformation linking the anchor and target. It then learns a relational operator, mapping an anchor-transformation pair to predictions for the target task. We instantiate RTE across multiple task extrapolation regimes in function prediction, e.g. where target tasks use out-of-range parameters (parameter extrapolation), have greater compositional depth (length extrapolation), and/or recombine function primitives in unseen ways (compositional extrapolation). We further extend RTE to sequence prediction, integrating it into fine-tuning algorithms for foundation models. Across empirical studies, we find that RTE substantially outperforms existing approaches on extrapolation to novel, unseen tasks.

Supervised Causal Learning (SCL) has shown promise in causal discovery by framing it as a supervised learning problem. However, it suffers from significant out-of-distribution generalization challenges. We reveal three limitations of previous SCL practices: a significant performance gap between synthetic benchmarks and real-world data, fragility to distribution shifts, and failure in compositional generalization, collectively questioning its real-world applicability. To address this, we propose Test-Time Training for Supervised Causal Learning (TTT-SCL), a novel framework that dynamically generates training sets explicitly aligned with any specific test instance. We demonstrate the correlation between TTT-SCL and score-based methods, and design an efficient module for generating training sets based on the classic scoring function. Experiments on synthetic benchmarks, pseudo-real and real-world datasets demonstrate that TTT-SCL significantly outperforms existing SCL and traditional causal discovery methods.

AI-driven respiratory sound classification (RSC) is promising for automated pulmonary disease detection, yet multi-site deployment is hindered by inter-stethoscope variability. We introduce a federated domain generalization (FedDG) formulation for RSC in which clients hold recordings from different stethoscopes and the model is evaluated on an unseen device. Our empirical analysis shows that stethoscope-induced style and disease-relevant content are partially entangled, making deterministic style removal unreliable. In response, we propose BTS-CAFE, a framework combining (i) causality-inspired device-style interventions with constraints designed to limit content distortion, (ii) counterfactual metadata augmentation to relieve device and demographic shortcuts, and (iii) gradient alignment to promote device-invariant decision boundaries across clients. Built on BTS with CLAP, a multimodal language-audio pretraining model, BTS-CAFE improves the out-of-distribution ICBHI Score by 3.69 points on average over five held-out devices relative to its backbone, and outperforms conventional data augmentation and federated learning baselines in simulated device leave-out evaluations on the ICBHI and SPRSound datasets.

Leveraging Large Language Models (LLMs) to automatically formulate and solve optimization problems from natural language has emerged as an efficient paradigm for automated optimization. However, existing methods still exhibit limited generalization: they are sensitive to superficial narrative variations, reuse experience mainly at the case level, and struggle to adapt to shifted or emerging problem types. We propose OptSkills, an archetype-centric skill learning and reasoning agent system for optimization modeling and solving. To improve robust generalization, our system clusters problems by their underlying archetypes rather than surface narratives. To improve in-distribution generalization, it explores diverse modeling paradigms and solver configurations within each cluster, then distills successful trajectories into reusable workflow-level skills. To improve out-of-distribution generalization, it refines existing skills or expands the skill library using newly obtained trajectories. Our system achieves a state-of-the-art micro-averaged accuracy of 68.27% on datasets encompassing diverse problem types and scenarios. In addition, on MIPLIB-NL, a highly challenging large-scale and high-dimensional benchmark, it achieves 26.91% accuracy, outperforming DeepSeek-V3.2-Thinking by 4.53%. After skill learning on Nano-CO, it reaches 72.79% on the OOD NLCO benchmark. Code and skills are available at https://github.com/fujiwaranoM0kou/OptSkills.

Machine learning for molecular property prediction has focused largely on pure compounds, even though many practical applications depend on mixtures with intermolecular interactions. Recent work has expanded the availability of mixture datasets, but evaluation still focuses mainly on absolute accuracy. However, absolute errors in mixtures conflate pure-component contributions with deviations from ideal mixing. We propose an evaluation framework that decomposes mixture-property error into pure-compound and interaction (non-ideal) components. The framework combines leakage-aware split protocols, ideal-mixture baselines, and excess-property metrics. To support reproducible benchmarking, we curate seven matched pure and mixture physicochemical property datasets. Across multiple mixture-property tasks and model families, we find that strong absolute accuracy can mask poor recovery of non-ideal mixture behavior, and that performance drops substantially under strict molecule splits. These results identify transfer to unseen molecules as a central challenge in molecular mixture machine learning and motivate evaluation beyond absolute accuracy alone.

Mainstream strategies for finetuning pretrained multimodal models often degrade out-of-distribution (OOD) robustness, a phenomenon known as catastrophic forgetting. In this paper, we develop a theoretical framework for multimodal contrastive finetuning, yielding closed-form solutions and a geometric decomposition for each strategy. This framework shows that self-distillation is more effective than other regularization approaches to retain the knowledge of the pretrained model. Our analysis reveals a largely overlooked limitation: standard Exponential Moving Average (EMA) teachers, widely used in robust finetuning, suffer from collapse. To solve this, we prove that a Weighted Moving Average (WMA) teacher maintains a persistent regularizing force over finite horizons and yields bias-free convergence in the task subspace while preserving orthogonal knowledge. These insights motivate TRACER (Trajectory-Robust Anchoring for Contrastive Encoder Regularization), which combines contrastive learning with WMA-guided multi-perspective distillation. Extensive experiments on CLIP finetuning demonstrate consistent OOD accuracy and calibration gains across three backbone architectures, and comprehensive ablations confirm that TRACER is both principled and robust to hyperparameter choices. Code is available at https://github.com/HesamAsad/TRACER.