OOD Generalization

Current Earth observation benchmarks focus on measuring performance on diverse tasks and applications, typically measuring generalization in-distribution. But when models are deployed, they must generalize to myriad out-of-distribution scenarios, such as new time periods, geographies, scales, and sensors. We introduce EarthShift: the first public testbed for benchmarking robustness across multiple realistic distribution shifts encountered in remote sensing. EarthShift enables users to measure distributional robustness by comparing performance in- and out-of-distribution using datasets from paired datasets from different sources, temporal windows, geographic locations, and sensors. Our experiments on 8 geospatial foundation models (GFMs) and 11 tasks covering 5 shift types show that GFMs consistently perform 15-20% worse out-of-distribution on average regardless of model architecture, size, pre-training or fine-tuning strategy. We show that GFM robustness is similar to that of generic vision foundation models, and even fully-supervised models. This highlights a need for future research to strive for improvements in distributional robustness, not just performance, which can be benchmarked using EarthShift. We release our code and datasets to provide a testbed to guide future work to create foundation models that are robust and reliable in real-world applications. Code and data for EarthShift are available at: https://earthshift.github.io

Recent physics foundation models claim general spatiotemporal forecasting ability, yet their evaluations often collapse performance into a single average score under a fixed training distribution. This makes it difficult to determine whether a model has learned generalizable physical dynamics or only performs well under particular settings. We construct a benchmark with 8 physical dynamics, 3 training-data mixtures, and 25 test regimes induced by dynamic-scale and initial-condition complexity shifts, covering in-distribution, distribution-shift, and out-of-distribution settings. We evaluate five physics foundation model architectures and four model variants per architecture (scratch and three pretrained sizes), resulting in 60,000 measurements. Our results show that current physics foundation models behave as conditional rather than universal generalists: their generality depends on the physical regime, temporal scale, initial-condition setting, pretraining, model size, and architecture. Improving the training data distribution only partially mitigates this limitation. Pretraining and scaling are also unable to reliably remove their ability biases. We argue that improving physics foundation models requires moving beyond scaling models or expanding data, toward learning mechanisms that better capture transferable physical knowledge across regimes, temporal scales, and distribution shifts.

Age estimation from facial images typically relies on training data that includes images of minors, a practice that raises serious ethical, legal, and privacy concerns. In this work, we propose a generalized zero-shot benchmark for facial age estimation that explicitly excludes children's data during training while still assessing model performance on younger populations. We revisit six widely used datasets and introduce standardized splits with strict age-group separation: samples aged 18-59 for training, validation, and testing; samples under 18 reserved exclusively for zero-shot evaluation; and samples 60+ as an unseen validation set for model selection under distribution shift. For datasets with identity annotations, subject-exclusive splits prevent identity leakage and better reflect real-world deployment conditions. Evaluating nine state-of-the-art age estimation methods under this protocol reveals that all evaluated methods consistently fail to generalize to unseen age groups, suffering substantial performance degradation -- on average 46.4%, and up to 52.8% -- relative to the supervised baseline. Moreover, models do not simply degrade: they systematically anchor predictions for unseen ages to nearby seen classes, a manifestation of the well-known seen-class bias in generalized zero-shot learning. By formalizing age estimation without children's data as a generalized zero-shot benchmark on existing datasets, this work highlights a critical gap between current modeling practices and real-world ethical constraints. Our benchmark provides a principled basis for evaluating models under restricted data regimes and encourages the development of methods that are robust to distribution shift and aligned with responsible data use.

Equipping large language models with explicit skills has emerged as a promising paradigm for enabling autonomous agents to solve complex tasks. Agent skills can be inherently divided into general skills for broad cognitive transfer and task-specific skills for dynamic execution. However, existing skill-based reinforcement learning (RL) methods typically force a rigid choice between full externalization, which incurs prohibitive context overhead, and full internalization, which risks overfitting and knowledge conflicts. To address this dilemma, we propose Skill0.5, a novel agentic RL framework that explicitly differentiates skill treatments by combining general skill internalization with task-specific skill utilization. Driven by a dynamic, difficulty-aware router, Skill0.5 streams tasks into distinct mastery tiers to apply tailored optimization strategies: it internalizes general skills via privileged distillation to build a cognitive foundation for hard tasks, while using diagnostic probing on easy tasks to penalize shortcuts and enforce specific skill utilization. Experiments on ALFWorld and WebShop demonstrate that Skill0.5 outperforms both memory-based and skill-based RL baselines, yielding performance improvements across both in-distribution and out-of-distribution scenarios.

Scaling laws guide large language model training by relating compute to cross-entropy loss, and recent work further extends them to predict downstream benchmark performance. However, prior approaches face generalization limitations from two aspects: focusing on benchmark-level performance introduces scenario-specific artifacts, while relying on IID validation loss fails to track capability improvements when training distributions vary. In this work, we argue that downstream scaling should be studied at the capability level, which captures shared skill factors across related tasks while abstracting away benchmark-specific noise. We propose SuperValid, a framework that synthesizes OOD (out-of-distribution), capability-aligned validation data by distilling core concepts from benchmarks within a capability domain and expanding them into diverse, knowledge-rich texts. Extensive experiments spanning 16 benchmarks grouped into 6 capability domains show that SuperValid loss exhibits strong and stable correlation with downstream performance across models of different architectures, scales, and training data distributions. As a training-free metric computable during training without benchmark evaluation, SuperValid enables effective model selection, early stopping, and scaling decisions.

In strategic classification, an institution (e.g., a bank) anticipates adaptation from users who change their features to increase utility in a classification task (e.g., loan repayment). Since a key challenge is the distribution shift induced by users, we turn to causal models, which have been shown to bound the worst-case out-of-distribution (OOD) risk, and establish several new results that link causality and strategic classification. First, we show that causal classification leads to optimal classification error after any sufficiently large adaptation, when the noise is bounded in a certain way. Second, when these assumptions do not hold, we show OOD cross-entropy risk of optimal classifiers decomposes into an OOD bias term and a term arising from not using all observable features, allowing us to understand when causal classifiers have an advantage. Finally, we show that the use of causal features can allow alignment of long-term incentives between institutions and users, contrasting with previous work that highlights social costs of such approaches. We validate our theory empirically on synthetic data, finding that our results predict behavior in practice.

Predictive models trained on observational data often fail to generalise to the distributions they encounter when deployed, especially when the training data is a product of the system being optimised. Recommender systems are a canonical example: they are trained on interaction logs confounded by the deployed policy, past user behaviour, and platform filtering. As a result, the training distribution differs substantially from the candidate distribution scored at serving time, a gap that makes offline metrics unreliable predictors of online performance. We address the distribution shift problem with a method motivated by causal representation learning (CRL). We propose an information-theoretic disentanglement criterion and prove that its optimum depends only on the causal components of the input. We then derive a tractable variational lower bound that makes the criterion optimisable from finite observational data alone. The scope of our method is narrower than that of much of the CRL literature, in that we target better generalisation under distribution shift, not full identification of all latent causal factors. This narrower target is what makes the method practical, requiring only the existing confounded logs, applying to any standard supervised model, and adding no inference-time cost. Our headline evaluation is an A/B test with millions of users on Spotify, applied to a production ranker for personalised playlist generation. A capacity-matched CRL variant performed on par offline but delivered substantial online gains in listener engagement. Complementary evidence on the public KuaiRand recommendation dataset and a synthetic benchmark with known causal structure shows the same pattern: offline parity with baseline, gains under distribution shift. Across all three settings, adding our causal disentanglement objective yields meaningfully better out-of-distribution generalisation.

Causal discovery from time series is critical for many real-world applications, such as tracing the root causes of anomalies. Existing approaches typically rely on dataset-specific optimization, making it difficult to transfer their causal discovery capabilities to new time series governed by diverse causal mechanisms. In this paper, we propose \textbf{PTCD}, a novel \textbf{P}retraining framework for \textbf{T}ime-series \textbf{C}ausal \textbf{D}iscovery, which improves cross-task generalization through context-conditioned modeling and transferable causal augmentation. To model complex temporal causal dependencies, PTCD employs a dual-scale iterative attention mechanism to capture window-level causal relationships, and a Gaussian mixture with a context-level routing mechanism to handle heterogeneous exogenous distributions. To further address distribution shifts across causal graphs, PTCD adopts a pretraining paradigm on synthetic datasets that integrates intervention-based learning and a causal mixup strategy, promoting stable causal discovery and stronger generalization. Extensive experiments on multiple real-world out-of-distribution (OOD) datasets demonstrate that PTCD excels in both causal discovery and root cause identification.

Recent advances in uncertainty quantification increasingly emphasise the distinction between aleatory and epistemic uncertainty in machine learning, motivating the need for more unified frameworks. However, despite much progress in producing reliable predictions, existing methods often lack rigorous guarantees when generalising beyond the training domain. We propose a conformalised imprecise inference framework for robust extrapolation, which is model-agnostic and augments predictive models with imprecision and distance awareness. The proposed approach yields imprecise predictions (probability boxes) that remain valid under distributional shift, maintaining coverage while adaptively expanding uncertainty in extrapolation regimes. Experiments on synthetic and benchmark datasets demonstrate improved robustness and reliable coverage compared to standard probabilistic approaches, particularly under limited data.

Weak-to-strong (W2S) generalization is a promising framework for scalable oversight, yet existing evaluations often test students under matched train-test distributions. Therefore, we study W2S preference learning under zero-shot distribution shift and find that strong students trained on weak preference labels can appear successful in-distribution while failing to transfer across preference datasets. We provide evidence for a representational failure mode in which weak-supervised fine-tuning can pull the strong model toward source-domain features instead of maintaining broadly transferable preference representations. To mitigate this, we propose Representation Anchoring (Anchor), a simple yet effective regularizer that constrains excessive drift from the pretrained strong model's representation space during fine-tuning, while still allowing task-relevant adaptation. Across preference domains, datasets, and model families, Anchor consistently improves out-of-distribution transfer while maintaining competitive in-distribution performance. Together, our evaluation protocol, transfer-aware metrics, and method expose hidden brittleness in current W2S reward modeling and provide a practical path toward more robust preference transfer.

UAV action recognition faces a deployment shift that standard benchmarks often obscure: a model trained on UAV footage captured from low-depression viewpoints may be required to recognize the same action classes from high-depression viewpoints. While the action labels remain unchanged, this shift alters body visibility, motion projection, and scene context, encouraging models to rely on viewpoint-specific shortcuts. We introduce UAV-OVO, an Out-of-Viewpoint generalization benchmark for UAV action recognition. UAV-OVO derives view scores from uncalibrated videos, uses a view-isolation band to assign low-depression videos to the training and in-distribution test splits while reserving high-depression videos for out-of-distribution testing, and constructs ID/OOD test sets matched by class distribution so that performance differences reflect viewpoint shift rather than label imbalance. Across representative video recognizers, UAV-OVO reveals a substantial ID/OOD gap: models that fit the low-depression training distribution well often fail to transfer to held-out high-depression views, exposing viewpoint shortcuts hidden by aggregate accuracy. We further propose LATER, LoRA-Anchored Test-time Re-centering, which first adapts the recognizer with Low-Rank Adaptation (LoRA) and then uses the learned LoRA subspace as a semantic anchor for online feature re-centering. Specifically, LATER projects target-domain displacement onto the orthogonal complement of the LoRA subspace before re-centering features, reducing viewpoint-induced drift while preserving task-relevant semantics. Together, UAV-OVO and LATER provide a controlled testbed and a practical adaptation method for viewpoint-robust UAV video understanding.

Optimizing the trade-off among predictive performance and computational cost is a central focus in the deployment of Large Language Models (LLMs). Current routing methods primarily rely on direct mapping from queries to models based on surface-level features, making them susceptible to the memorization trap and leading to poor generalizability on out-of-distribution (OOD) data. In this paper, we propose DecoR, a novel routing framework that recasts the routing task as a matching process of sifting similar queries from historical logs, effectively mitigating the memorization trap. To enhance matching accuracy, we introduce a query capability deconstruction method that decouples linguistic surface forms from task-intrinsic requirements, directing matching toward capability dimensions to ground decisions in essential task attributes. Furthermore, we develop CodaSet, a comprehensive benchmark for assessing routing generalization, where experimental results demonstrate that DecoR maintains superior accuracy while substantially lowering inference costs across both in-distribution and OOD settings. All the codes and data are available at https://github.com/lvbotenbest/DecoR.

Prediction models trained under the source distribution do not generalize well to a different target distribution. A valid inference about an unseen data distribution must be anchored by the invariance of certain causal mechanisms that generate the source and target data, however, these structural invariances are non-identifiable from the source data alone. Under mild causal assumptions about the data, we show that the optimal prediction in the target is in fact partially identifiable by the source distribution. The result rests on a simple observation: In any domain, the optimal prediction can be factorized into what we call a pair of abduction and deduction maps, where the abduction map makes inference about some unobserved variables (possibly confounders) from the observed variables and the deduction map predicts the label using both the observed and inferred quantities. Access to large source data pins down the optimal prediction, thus constrains the valid abduction-deduction ensembles that produce it -- a non-identifiability that we call the abduction-deduction entanglement. To leverage this, we parameterize the constrained family using what we call a representation transplant, that is a specific linear transformation in the representation space that manipulates the abduction content of the representation while retaining the deduction component. Invariance of the causal mechanism generating the label implies existence of an invariant deduction map between source and target. Thus, we can search the space of plausible target distributions via a parametric transplant. We use this scheme in a learner-adversary game that, under an idealistic optimization, provably terminates with the learner having the minimax-optimal target prediction. Evaluations verify the theory, showing that the method is competitive in DG benchmarks.

Retrieval augmentation provides time series forecasters with historical continuations, yet even candidates that outperform the base forecast may fail to improve the final prediction. We propose ROAR, a Retrieval Opportunity-Aware Refinement framework for zero-shot time series forecasting. To better exploit these improvement opportunities, its training objective allocates additional emphasis across queries based on base-forecast difficulty and the relative improvement offered by retrieved candidates. Using this objective, ROAR first learns to aggregate aligned historical candidates and uses a learned gate to control their correction strength against a fixed base forecaster. It then jointly calibrates the forecasting module and gate to coordinate their contributions, while anchoring the combined prediction to the first-stage refined output. We derive exact decompositions of refinement gains and the opportunity-weighted training loss, and characterize additional gains from joint calibration under a local linearization. Experiments on seven benchmarks show that ROAR achieves the lowest average MSE among the compared methods. Further evaluations demonstrate average forecasting improvements across multiple backbone families and retrieval-augmented forecasters.

Production deep learning systems across enterprise domains operate under constraints that academic benchmarks routinely obscure: labeled data is expensive, inference budgets are tight, and models that cannot explain their behavior are difficult to trust and maintain. We present ChainzRule (CR), a neural architecture replacing typical activations with learnable polynomial layers governed by Differential Regularization (DREG), a layer-wise Jacobian penalty computed analytically during the forward pass at standard inference cost. The core claim is that bounding intermediate derivatives forces the network toward low-frequency, structurally stable representations, simultaneously reducing dependence on labeled data volume, improving robustness to distribution shift, and providing a measurable, gradient-based handle on model behavior. Evaluated across five domains, CR achieves $85.71\% \pm 2.01\%$ on Pima Diabetes (statistically superior to SVM and XGBoost), $46.20\% \pm 0.37\%$ on SST-5 sentiment classification with a frozen encoder (superior to RNTN using approximately 5% of its training data), $55.79\%$ on SST-5 with a fine-tuned BERT backbone (versus BERT-base linear head at $54.9\%$), $70.17\%$ on Yelp Full ordinal regression with 3.2M parameters versus a 10-model average of $66.35\%$, and $+2.32\%$ mean corruption accuracy on CIFAR-10-C. All results with reported $p$-values fall below the $α= 0.05$ threshold after Bonferroni correction. CR maintains a gradient tail ratio $τ$ (p99/mean) of $1.01$--$1.02$ against $1.07$--$1.09$ for all typical activation function baselines across every data fraction, a structural invariant we propose as the mechanistic driver of sample efficiency and a deployment-time proxy for model reliability.

Material segmentation, the pixel-wise classification of physical surface properties, remains a challenging problem in computer vision, requiring physicochemical understanding distinct from object-centric parsing. Despite the introduction of the rigorous Apple Dense Material Segmentation (DMS) dataset, the benchmark has suffered from attrition and stagnation, increasingly overshadowed by geometry-biased foundation models. In this paper, we revive the Apple-DMS benchmark to establish a modern Vision Transformer baseline. We conduct an exhaustive evaluation of SegFormer and Mask2Former architectures, revealing that standard training paradigms fail on amorphous texture fields due to high-variance gradients. To address this, we introduce a stabilized training recipe featuring High-Fidelity Logit Projection, Query Entropy Regularization, and a domain-specific, physics-compliant augmentation pipeline. Our optimized SegFormer-B5 achieves a new State-of-the-Art (SOTA) of 0.4572 mIoU on the original dataset split, significantly surpassing the prior convolutional baseline. Furthermore, we identify a critical "Generalization Paradox": while re-partitioning the dataset into a data-rich 80/10/10 split inflates the metric to 0.5276 mIoU, expert qualitative analysis reveals this induces distributional homogenization, severely degrading real-world, out-of-distribution performance. By releasing our recovered dataset index and robust training framework, we demonstrate that material perception is far from solved and urge the community to leverage the rigorous original split to drive genuine progress in physically grounded artificial intelligence.

Reinforcement learning agents often exhibit unintended goal-directed behaviour outside their training distribution, but we currently lack a principled understanding of how such agents will generalise to novel environments based on their training history. We address this gap for agents trained sequentially on one or more tasks. We study over 100 sequential training pipelines, evaluating behaviour across over 250 out-of-distribution environments. We find that salient features drive generalisation, and that goals learnt early in training can persist and influence those acquired later. To explain these phenomena, we introduce latent policy gradients, a method that predicts what out-of-distribution behaviour a training pipeline will likely induce. Our method simulates the evolution of low-dimensional latent variables during training according to what would achieve high reward on the training objective with respect to a simple model of how the latent variables map to behaviour. It achieves strong predictive accuracy, generalises to unseen types of training pipeline, and is interpretable. Our findings demonstrate that while out-of-distribution RL agent behaviour is dependent on the whole training pipeline, this dependence has an underlying structure we can capture, laying groundwork for understanding goal generalisation from a developmental perspective.

Climate emulation is an out-of-distribution (OOD) projection task. This is precisely the challenge where modern Machine Learning (ML) methods are most prone to failure. Consequently, while current ML emulators trained on present climate achieve high in-distribution performance, their future reliability under the inevitable distribution shifts of a changing climate remains a critical, poorly understood blind spot. Addressing this challenge requires a fundamental shift in how we understand, evaluate, and design climate emulators. In this work, we first confirm that climate change drives a statistically significant and progressively growing shift in atmospheric state distributions, rendering standard evaluation protocols insufficient. We empirically establish that seasonal variation serves as an effective proxy for these long-term climate shifts, providing access to $\textit{real-world}$ distribution shifts without recourse to heuristics like synthetic perturbations. Motivated by this link, we introduce a novel evaluation framework that leverages seasonal shifts as a rigorous, zero-overhead testbed for emulator robustness. Our systematic characterisation confirms that current state-of-the-art hybrid-ML emulators degrade significantly under these realistic shifts. Finally, we chart a path forward by identifying compositional generalisation, the ability to form novel combinations from observed elementary components, as a principled route towards robust climate emulation. We demonstrate that physically motivated decompositions substantially improve OOD performance with only modest trade-offs against in-distribution performance, providing an avenue towards ML-driven climate emulators robust to an unknown future.

Mechanistic interpretability aims to explain a model's behavior by identifying causally responsible internal structures. Dictionary-based explainers such as sparse autoencoders and transcoders are a primary tool, but their faithfulness under out-of-distribution (OOD) shift has received little systematic attention. We show that distribution shift rotates the subspace that the model actively uses, misaligning the explainer's dictionary trained on in-distribution (ID) activations. We formalize this misalignment as the faithfulness gap, a geometric distance between the ID dictionary and the OOD-active subspace, and show that it controls OOD faithfulness degradation. To reduce this gap, we propose the Geometry-Adaptive Explainer (GAE), which realigns the explainer's dictionary with the OOD-active subspace while preserving the original feature structure. This requires only unlabeled OOD activations and no gradient updates. We prove that GAE improves over the unadapted ID explainer, with excess loss bounded quadratically by the second-moment shift. Empirically, GAE even matches or surpasses all training-based baselines in causal faithfulness across multiple models and OOD settings.

Large language models (LLMs) are highly sensitive to the prompts used to specify task objectives and behavioral constraints. Many recent prompt optimization methods iteratively rewrite prompts using LLM-generated feedback, but the resulting prompts often become longer, accumulate narrow sample-specific rules, and generalize poorly beyond the training distribution. We study this failure mode as prompt distributional overfitting and argue that it reflects a lack of representation control in discrete text-space optimization. We formalize this view through representational inefficiency, a dual-factor measure that decomposes prompt inefficiency into capacity cost and scope narrowness, attributing distributional prompt overfitting to their coupled growth during optimization. We propose TextReg, a regularization framework that realizes a soft-penalty objective through regularized textual gradients, combining Dual-Evidence Gradient Purification, Semantic Edit Regularization, and Regularization-Guided Prompt Update. Across multiple reasoning benchmarks, TextReg substantially improves out-of-distribution (OOD) generalization, with accuracy gains of up to +11.8% over TextGrad and +16.5% over REVOLVE.

While empirical scaling laws for LLM reasoning are well-documented, the theoretical mechanisms governing out-of-distribution (OOD) generalization remain elusive. We formalize reasoning via optimal transport, projecting discrete trajectories into a continuous metric space to quantify domain shifts using the Wasserstein-1 distance. Invoking Kantorovich duality, we bound OOD generalization via architectural Lipschitz continuity and functional approximation limits. This exposes two primary constraints. First, position-dependent attention (e.g., Absolute Positional Encoding) fails to preserve shift invariance, yielding an $Ω(1)$ Lipschitz constant and expected risk, whereas shift-invariant mechanisms (e.g., Rotary Embeddings) preserve equivariance and bound the error. Second, by mapping sequential backtracking to a Dyck-$k$ language, we establish a strict circuit depth lower bound for $\text{TC}^0$ Transformers. Scaling physical layer depth is necessary to avert representation collapse -- a constraint that scaling representation width cannot bypass due to irreducible approximation bounds in Barron spaces. Evaluations across 54 Transformer configurations on combinatorial search corroborate these bounds, demonstrating that generalization risk degrades monotonically with the Wasserstein domain shift.

We introduce FLUXtrapolation, a benchmark for extrapolating ecosystem fluxes under progressively harder distribution shifts. Ecosystem fluxes are central to understanding the carbon, water, and energy cycles, yet they can only be measured directly at sparsely located measurement towers. Producing global flux estimates therefore requires training models on observed sites using globally available covariates and predicting in unobserved regions, that is, upscaling. Flux upscaling is a challenging domain generalization problem that is affected by a shift in covariate distribution across climates, ecosystem types, and environmental conditions, as well as by conditional shift: important drivers remain unobserved at global scale. We provide a quantitative analysis of both these shifts in $P_X$ and $P_{Y\mid X}$. FLUXtrapolation is designed based on domain expertise on flux upscaling: it defines temporal, spatial, and temperature-based extrapolation scenarios and evaluates performance across held-out domains, temporal aggregations, and tail errors. In a pilot study, we find that baselines perform similarly under median hourly RMSE, but separate under the proposed tail-focused and multi-scale evaluation. FLUXtrapolation therefore poses a realistic and thus relevant challenge for machine learning methods under distribution shift; at the same time, progress on this benchmark would directly support the scientific goal of improving flux upscaling.

Large language models (LLMs) have enabled web agents that follow natural language goals through multi-step browser interactions. However, agents fine-tuned on specific trajectories and domain often struggle to generalize out of domain, and offline training can be compute-inefficient due to noisy, redundant trajectories and long accessibility-tree (AXTree) states. To address both issues, we propose Weasel, a trajectory selection method for offline training of web agents. Weasel selects a fixed-budget subset of trajectory steps by optimizing an objective that balances unary importance with pairwise diversity over states, websites, and interaction patterns, solving efficiently with a greedy algorithm. We further improve efficiency with target-centered AXTree pruning that keeps only content around the ground-truth action target, and we mitigate style mismatch for reasoning-native models by replacing expert traces with model-generated, style-consistent rationales. Across AgentTrek and NNetNav training datasets, evaluations in WebArena, WorkArena, and MiniWob, and experiments with Qwen2.5-7B, Gemma3-4B, and Qwen3-8B, Weasel improves out-of-domain performance while reducing training cost, producing roughly 9.7-12.5$\times$ training speedups over standard fine-tuning. We make the code available at https://github.com/fatemehpesaran310/weasel.

While humans readily generalize abstract concepts to more complex or larger tasks, building Reinforcement Learning (RL) systems with this ability remains elusive. Here, we present the first theoretical model of how such Out-of-Distribution (OOD) generalization can be achieved in RL agents. Our approach considers Partially Observable Markov Decision Processes (POMDPs) and assumes that an intelligent agent uses an abstraction function to determine which experiences can be treated as equivalent and which must be distinguished. First, we extend the existing state abstraction framework and proof techniques to POMDPs. Then, we define a successor-weighted model reduction, a model reduction variant that enables compression into smaller abstract spaces than prior definitions allow. We derive a bound on the agent's OOD test performance, thereby defining the conditions under which OOD generalization is achievable. This bound decomposes an agent's performance loss into approximation and estimation errors, revealing how reducing an agent's abstract state space size improves test performance and OOD generalization. Our analysis suggests that constraining an agent to operate over a small, finite set of abstract states is necessary for achieving generalization to more complex tasks. Our results motivate further research into learning RL architectures that scale across tasks of varying complexity levels.

Neural operators are often tested on states that differ physically from training data. A distinct failure occurs when the physical dynamics are unchanged but the observed coordinate frame differs from training. PACE-FNO addresses this case by estimating the frame, predicting after pulling the field to a canonical representative, and restoring the requested terminal frame. The default inference path uses one forward prediction; optional test-time adaptation (TTA) updates only the low-dimensional coordinate. On translated and Galilean-shifted Burgers and shallow-water systems, PACE-FNO lowers out-of-distribution (OOD) relative error by up to $12\times$ relative to a data-augmented Fourier Neural Operator (FNO+Aug). A matched-estimator control supports attributing the gain to prediction in the canonical frame rather than added estimator capacity. Our analysis separates the canonical approximation error from the two alignment residuals. We also test regional WeatherBench2 time-series forecasting with the fifth-generation ECMWF reanalysis (ERA5) under natural time OOD, where PACE-FNO and FNO achieve nearly identical performance. Experiments with approximate rotation, other backbones, irregular domains, rollouts, and image data delineate the conditions under which the mechanism is effective.

Time series forecasting under non-stationarity faces a fundamental tension between capturing stable representations and adapting to distribution shifts. Existing methods implicitly rely on static historical assumptions, leading to a critical failure mode we term Phase Amnesia, where models become blind to the evolving global context. To resolve this, we formalize non-stationary dynamics through three physical hypotheses: wold decomposition, dynamical phase evolution, and heteroscedastic manifold generation. These principles inspire PULSE, a physics-informed, plug-and-play framework adopting a Disentangle--Evolve--Simulate design philosophy. Specifically, PULSE utilizes phase-anchored disentanglement to resolve optimization interference caused by dominant trends, employs a Phase Router to actively generate future trajectories, and introduces Statistic-Aware Mixup (SAM) to ensure robustness against out-of-distribution volatility. Empirically, PULSE enables a simple MLP backbone to achieve state-of-the-art or highly competitive performance across 12 real-world benchmarks. This validates that a correct physics-informed inductive bias is far more critical than raw architectural complexity for non-stationary forecasting. The code is available at: https://github.com/Gemost/PULSE.

Neural network surrogate models have emerged as a promising approach to model solution fields for a wide variety of boundary value problems encountered in physical modeling. Stochastic problems represent an area of particularly high interest because of the potential to significantly reduce the repeated evaluation of expensive forward models via traditional numerical solvers when conducting parametric analysis. However, many studies found in the literature primarily focus on the ability of neural network surrogate models to represent deterministic samples or mean field solutions and largely overlook surrogate model performance at the tails of the distribution. The present study examines in detail the ability of neural network surrogate models to capture the full distribution of solution fields over the entire probability space, while emphasis is placed at the tails of the distribution. Serving as a canonical problem is the heat conduction equation with a highly stochastic source term, inducing extremely large variation in the thermal solution field. Comparisons are made between a classic feed-forward fully connected network and a Deep Operator Network architecture, using both data-driven and physics-informed loss functions. Results show that the worst-case prediction errors are an order of magnitude larger than the mean field error, highlighting the importance of the outlier samples. The large errors associated with extreme samples result from the networks having to extrapolate beyond the bounds of the training data. A method for identifying these samples is presented along with a discussion of potential approaches to account of their errors. Among the models considered, the fully connected neural network trained using a weak form residual loss performs best in handling these extrapolated inputs, achieving the highest prediction accuracy for the numerically produced datasets.

Semantic code search has been widely adopted in both academia and industry. These approaches embed natural-language queries and code snippets into a shared embedding space and retrieve results based on vector similarity. Despit strong performance on benchmark datasets, they often suffer from poor explainability and generalization. Retrieved code may appear semantically similar yet miss critical functional requirements of the query, while providing no explanation of why the result was retrieved. Moreover, such failures become more severe under distribution shift, where models struggle to generalize to unseen benchmarks. In this work, we propose XSearch, an intrinsically explainable code search framework. Our key insight is that by relying on global embedding similarity, existing retrievers inherently take an inductive view. They learn statistical patterns rather than truly understanding the query's functional requirements. We address this problem by reformulating code search as a deductive concept alignment problem. XSearch (i) identifies functional concepts in the query and (ii) explicitly aligns them with corresponding code statements. This explain-then-predict design produces inherent concept-level explanations and mitigates shortcut learning that harms out-of-distribution generalization. We train an encoder with explicit concept-alignment objectives and perform retrieval through explicit matching between query concepts and code statements. Experiments show that, trained on CodeSearchNet using GraphCodeBERT (125M parameters), XSearch improves performance on out-of-distribution benchmarks from 0.02 to 0.33 (15x) over eight state-of-the-art retrievers, and consistently outperforms both encoder- and decoder-based baselines with up to 7B parameters. A user study demonstrates that concept-alignment explanations enable users to evaluate retrieved results faster and more accurately.

Continual learning (CL) aims to train models sequentially over multiple domains without forgetting previously learned knowledge. However, existing CL methods optimize for in-domain performance and are therefore prone to learning spurious, domain-specific cues (``shortcut learning''), which limits generalization to unseen domains after deployment. In this paper, we address this limitation through continual learning of domain-invariant representation. We introduce a broad class of CL methods that sequentially learn representations capturing invariant structures across domains. Our methods are motivated by the observation that such invariant structures often preserve the underlying causal mechanisms, which can reduce the risk of overfitting to domain-specific cues and thus offer better out-of-domain generalization. Our proposed CL methods combine replay-based training with a tailored sequential invariance alignment to learn -- and preserve -- invariant structures over time. We evaluate our methods under a deployment-oriented protocol that measures performance on unseen target domains. Across six benchmark and real-world datasets spanning vision, medicine, manufacturing, and ecology, our methods consistently outperform existing CL baselines in terms of generalization to unseen target domains. As an ablation, we further show that naïve extensions of sequential training with existing domain-invariant representation learning (DIRL) methods provide only limited benefits. To the best of our knowledge, this is the first work to develop domain-invariant representation methods for CL.

We present a flow-matching planner for autonomous driving that directly outputs actionable control trajectories defined by acceleration and curvature profiles. The model is conditioned on a bird's-eye-view (BEV) raster of the surrounding scene and generates control sequences in a small number of Ordinary Differential Equations (ODE) integration steps, enabling low-latency inference suitable for real-time closed-loop re-planning. We train exclusively on urban scenarios (real urban city streets, intersections and roundabouts of the city of Parma, Italy) collected from a 2D traffic simulator with reactive agents, and evaluate in closed-loop on both in-distribution and markedly out-of-distribution environments, including multi-lane highways and unseen urban scenarios. Our results show that the model generalizes reliably to these unseen conditions, maintaining stable closed-loop control and successfully completing scenarios that differ substantially from the training distribution. We attribute this to the BEV representation, which provides a geometry-centric view of the scene that is inherently less sensitive to distributional shifts, and to the flow-matching formulation, which learns a smooth vector field that degrades gracefully under distribution shift. We provide video demonstrations of closed-loop behavior at https://marcelloceresini.github.io/DirectControlFlowMatching.