Distribution Shift Robustness

Large multi-modal language models are increasingly deployed in high-stakes domains, making well-calibrated uncertainty essential. Traditional Bayesian methods approximate posteriors over all model weights, which becomes intractable for modern large models. For this reason, recent work instead considers Bayesian low-rank adaptation to enable tractable posterior approximation. Due to a lack of a standardized benchmark to evaluate these approaches, it remains unclear where these methods provide meaningful benefits. To fill this gap, we introduce Bayesian Adaptation Gym (BAG), a benchmark for the Bayesian adaptation of multi-modal language models. BAG provides reference implementations of classic Bayesian baselines and state-of-the-art adaptation methods, along with a multi-modal dataset and task suite designed to probe calibration, robustness under distribution shift, and decision-making under uncertainty via active learning. Using BAG, we conduct and report extensive experiments across model sizes, datasets, and tasks to highlight the successes and failures of current Bayesian adaptation approaches. To enable further research, BAG is fully open source: https://github.com/SRI-CSL/BayesAdapt.

Detectors for GNSS radio-frequency impairments (jamming, spoofing, multipath) are usually reported with a single AUC measured on the distribution they were tuned on. That number falls once conditions move, and the size of the drop is rarely known in advance because labelled field data is scarce. We ask whether this optimism can be predicted before any out-of-distribution data is seen. On an open, parameter-grounded synthetic testbed with a tunable severity shift, we evaluate thirteen detectors (five physics baselines, full-feature logistic regression and multilayer perceptrons, and single-feature learned controls) across four impairment classes. The optimism gap, the difference between in-distribution and shifted AUC, grows monotonically as the shift deepens (mean Spearman correlation 0.50). It is driven by how many observables a detector uses rather than by whether it is learned, and it varies systematically by class. Centrally, a ridge model built only from in-distribution score statistics predicts the gap for a detector it has never seen (R^2 = 0.47) and for an impairment class it has never seen (R^2 = 0.46); both are significant against a 2000-fold permutation null (p < 0.001) and survive removing the feature that is, by construction, part of the target. The headline findings are synthetic. We then run the pre-registered protocol on three open field corpora: on Jammertest 2024 the cross-detector prediction holds (R^2 = 0.11, p = 0.009), and on SatGrid, whose spoofer power sweep gives a calibrated severity axis, in-distribution AUC overstates higher-severity AUC by up to 0.22 and to the point of sign inversion, with in-distribution AUC and realised gap perfectly rank-correlated (Spearman rho = 1.0). The mechanism survives contact with real data, at smaller magnitude than in simulation. We release the testbed, a software-receiver front end, the ingest adapters and the protocol.

Machine learning systems deployed in dynamic environments frequently operate under nonstationary data distributions, where controlled distribution shift can progressively degrade predictive performance. However, many widely used tabular benchmark datasets lack explicit temporal structure, limiting reproducible evaluation of drift adaptation methods. This work proposes a cluster-induced distribution shift simulation framework that transforms static tabular datasets into controlled evolving data streams through structured perturbations across featurespace partitions. Using this framework, six adaptation strategies are systematically evaluated: static learning, sliding-window retraining, global ADWIN retraining, cluster-local ADWIN retraining, random subspace drift detection, and feature-partitioned drift detection. Experiments are conducted on five benchmark datasets covering both classification and regression tasks using diverse predictive model families, including linear models, k-Nearest Neighbours, tree ensembles, boosting methods, and adaptive online learners.

Calibration aligns a model's predictive uncertainty with the frequencies of its empirical outcomes and is important for understanding and trusting reported probabilities. Recent work shows that enforcing calibration at the level of individual predictors can improve ensemble accuracy and calibration, with mixture-of-experts (MoE) models showing strong empirical improvements in particular; however, the conditions under which calibration helps MoE are not well understood. In this work, we study how MoE models behave under distribution shift, focusing on how routing mechanisms interact with expert-level calibration. We show that expert calibration is sufficient to ensure calibration of the overall model under a broad class of distribution shifts in hard-routed models, but is insufficient for calibrating soft-routed models. To address this, we propose an adversarial reweighting that penalizes calibration errors of the routed aggregate under distribution shift, and we demonstrate that it improves the accuracy-calibration tradeoff both on average and on difficult subsets of the data, across model classes, prediction tasks, and distribution shifts.

This work investigates the application of a domain-shift aware neural network for regression tasks aimed at estimating unbalance masses in rotating shafts under varying operating conditions. Experimental data were collected from a test rig in which a primary shaft, equipped with a flange carrying unbalanced masses, was driven at different rotational speeds, while a secondary shaft could be optionally activated to introduce domain discrepancy. The unbalance masses were positioned at a fixed radial distance, and the dynamic response of the system was recorded using triaxial accelerometers. The inverse problem of mass estimation is formulated within a domain adaptation framework, where the network is trained with a maximum mean discrepancy strategy to align feature representations across source and target distributions. The results demonstrate the effectiveness of explicitly addressing domain shift in improving prediction accuracy, especially when the system's physical behavior and sources of domain discrepancy are not fully known and fall outside the training conditions. These findings highlight the potential of domain-shift aware models for regression tasks in Structural Health Monitoring.

Online learning in non-stationary streams is often formulated as tracking a point estimate, but many applications require predicting the full data-generating distribution. We study online distributional prediction under drift and adversarial corruption. Our approach represents each candidate law through a latent cluster geometry: a variable-size configuration of centers that organizes probability mass and induces a predictive distribution. A Gibbs quasi-posterior over these configurations yields an online predictor by posterior averaging, and the resulting variable-dimensional posterior can be sampled with reversible-jump MCMC. The method therefore avoids specifying a parametric streaming law while retaining a structured latent space for uncertainty, regularization, and comparison. We evaluate performance by cumulative Wasserstein-1 regret against the time-varying true law. The analysis separates two effects: corruption perturbs the loss-based posterior update, whereas drift makes long-horizon posterior memory stale. We address the latter with a restarted variant that temporally localizes the same quasi-Bayesian update. The resulting high-probability bounds decompose into a PAC-Bayesian complexity term, a corruption-sensitive posterior perturbation term, and a dynamic optimal-transport term driven by $A_T^{\mathrm{OT}}=\sum_{t=2}^T W_2^2(p_{t-1}^*,p_t^*)$. Under bounded support, stable latent geometry, predictive-map regularity, oracle realizability, localized restart windows, sublinear transport action, and sublinear corruption budget, the restarted predictor achieves sublinear cumulative Wasserstein regret. These guarantees require no parametric model for the stream, drift mechanism, or corruption process.

Positional encoding is a fundamental component of Transformer architectures, as it injects information about the spatial or sequential arrangement of inputs. Among recent alternatives to standard absolute and sinusoidal encodings, similarity-based positional encoding (simPE) has emerged as a flexible framework for representing positional structure through pairwise relations. simPE was originally designed for medical imaging applications, where geometric robustness is especially relevant: small rotations naturally arise during image acquisition, induced by imaging instruments, patient positioning, or slight acquisition misalignments. Despite its empirical promise, the theoretical behavior of simPE under geometric perturbations has not been fully characterized. In this paper, we study the robustness of simPE with respect to rotations, combining formal theoretical analysis with experimental validation. We first show that simPE is generally not rotation-invariant. We then prove that, under mild Lipschitz assumptions on the elementary components, simPE is stable under rotational perturbations and derive explicit perturbation bounds in Frobenius norm. We validate these findings experimentally on four controlled datasets--a synthetic Arrow dataset, a synthetic Shapes dataset (four geometric shape categories), a synthetic Digits dataset, and a benchmark image classification dataset (FashionMNIST)--in which training and validation images are kept in a fixed canonical orientation while test images are subjected to increasing rotation angles. Across all datasets, simPE consistently outperforms standard learned positional encoding in terms of accuracy, F1 score, precision, and recall under rotation, particularly in the small-to-moderate angle regime, corroborating the theoretical stability guarantees.

Reinforcement learning (RL) systems often degrade when operating conditions differ from those previously encountered, reflecting distributional shifts in the underlying data-generating process. Such shifts may occur between training and evaluation, as in In-Distribution (ID) and Out-of-Distribution (OOD) generalization, or within non-stationary settings where environment dynamics evolve over time. However, the formal relationship between these views remains unclear, and existing work mainly focuses on mitigation rather than the causal origin of shift within the agent-environment interaction. This work develops a unified causal-origin taxonomy that characterizes sources of distributional shift in RL and relates ID/OOD generalization to non-stationary settings. We transfer the classical dataset-shift principle from supervised learning to RL by reformulating distributional shift in terms of the generative interaction process. Using a Partially Observable Markov Decision Process (POMDP), we decompose the interaction into structural components, including the state distribution, observation process, policy, reward, and transition dynamics, together with the shifted-time boundary. The proposed taxonomy distinguishes internal (agent-driven) and external (environment-driven) distributional shifts. The shifted-time boundary perspective further characterizes explicit, implicit, and hybrid shifts. This formulation unifies ID/OOD generalization and non-stationarity as structured changes in the underlying process. We also introduce an evaluation framework for measuring shift impact and adaptation through performance degradation and recovery metrics. By grounding distributional shift in the causal-origin structure of RL, this work supports systematic analysis of robustness under distributional shift.

Conformal prediction (CP) has been used to obtain probabilistic bounds on the error between a learned dynamics model and the true but unknown system. Such CP bounds can then be embedded into robust control Lyapunov function (CLF) and control barrier function (CBF) frameworks. However, such an approach does not retain stability/safety guarantees because of the distribution shift between the closed-loop trajectory distribution under the deployed CLF/CBF policy and the trajectory distribution from which the CP bound and its guarantees were derived. To address this issue, we propose an episodic framework that iteratively updates the robust conformal CLF/CBF policy while maintaining stability/safety guarantees across episodes. We achieve this by (1) using adversarially robust conformal prediction, and (2) quantifying a distribution shift budget that allows us to control how much the model error can increase across policy updates. This distribution shift budget is derived via a closed-loop trajectory sensitivity analysis, yielding an implicit and an explicit update rule for the CP bound. We analyze convergence of our algorithm, which we demonstrate on three case studies. To the best of our knowledge, these are the first results that provide stability/safety guarantees for robust conformal CBF/CLF policies.

We consider the problem of uncertainty quantification for a pretrained classification model deployed under unknown distribution shift. We propose Audited Conformal Prediction (ACP), a method that leverages a small labeled dataset from the target population to train an auxiliary audit model identifying inputs where the legacy model is likely to fail. By integrating the audit model's outputs into the conformal prediction framework, ACP produces prediction sets that guarantee marginal coverage while achieving substantially higher conditional coverage in practice than existing approaches. We develop and analyze two complementary integration strategies -- one targeting marginal coverage with improved conditional performance, the other providing explicit group-conditional coverage guarantees -- and establish theoretical guarantees for both. Experiments on synthetic and real-world datasets validate the method and illustrate trade-offs between prediction set size and conditional coverage.

Understanding how a prediction model will perform in a new environment before deployment is essential to preventing harm when algorithms inform decision-making. Two common sources of model performance degradation are (i) covariate shift, where the target covariate distribution differs from the source, and (ii) selective labels, where the observability of outcomes depends on historical decisions. We study pre-deployment model evaluation under the joint presence of covariate shift and labeling of outcomes selectively based on observed features. In particular, we present a double machine learning procedure for estimating the target risk of an arbitrary black-box prediction model under a general loss function. We show identification of this estimand under standard assumptions and derive a bias-corrected estimator based on the influence function of the target risk. Finally, we evaluate our estimator through experiments using the eICU electronic health records database, showing that it tracks the true target risk more accurately than methods that address either selective labels or covariate shift alone, as well as baselines that combine standard plug-in approaches.

Neural responses in cortex exhibit substantial trial-to-trial variability in response to repeated stimuli, while peripheral sensory neurons respond far more consistently, leading many to wonder whether stochasticity may carry meaning. Existing work has argued that noise and signal correlations may be optimized for discrimination in animals, whereas artificial neural network (ANN) studies have shown similar benefits of noise in machine learning tasks, although most ANN work has neglected the effects of correlations. Here we investigate whether correlated noise improves the robustness of artificial neural networks to adversarial attacks and naturalistic image modifications. Using the covariance of activations under modified versus clean inputs, we find that structured noise may significantly improve network robustness. Robustness to naturalistic image modifications benefits most from structure, but this structure transfers poorly across modification types. In contrast, noise structure from adversarial attacks can generalize to other kinds of attacks. These results suggest that structured noise in ANN activations generally improves robustness, establishing a biologically plausible strategy for creating robust artificial neural networks that only relies on local information.

When working with real-world temporal data, it is common to encounter features whose distribution is changing over time. The naive employment of Machine Learning models on this unstable data might lead to rapidly degrading performance, especially if the new distribution is much different from what was previously seen during training. In order to cope with this problem, it is critical to automatically identify features that are changing over time. With these features detected, data scientists and other practitioners will be able to mitigate the issue (for instance, by applying data transformations), deploying more robust models that retain high performance for longer periods of time. In this paper, we describe which temporal changes a feature should not suffer from, and propose TEDD, a technique to a) identify when a dataset might lead to an unstable Machine Learning model and b) automatically detect which features cause such lack of robustness. In order to achieve it, we leverage a regression model to highlight which features contribute to a good prediction of an instance's timestamp. We compare our approach to other methods in real and synthetic data, testing their detection capability on all simple change patterns. We show that our method: detects all types of basic changes, both for numerical and categorical features; can detect multivariate drifts; returns a comparable value measuring the amount of change of each feature; requires no parameter tuning; and is scalable both on number of features and instances of the dataset.

Physiological awareness is important for service, social, and assistive robots that interact with humans in everyday environments. Remote photoplethysmography (rPPG) enables non-contact heart-rate (HR) estimation from an RGB camera, making it a promising sensing modality for robot-mounted vision systems. However, illumination variation remains a major barrier to robust deployment. This paper presents an end-to-end spatial-temporal transformer framework for remote HR estimation on a new dataset with varied illumination. Our estimator integrates PRNet-based 3D face alignment, clip-level illumination augmentation, the Residual Temporal Standardization Module, and controlled hybrid temporal-frequency supervision. The training objective combines a Soft-Shifted Pearson waveform loss with a spectral Kullback-Leibler divergence loss, where a tuned weight ($\mathbfβ$) controls the contribution of frequency-domain heart-rate guidance. Experiments on a static all-level mix protocol covering three illumination levels show that $\mathbfβ=5$ provides the strongest result among the tested beta settings, achieving a best-run HR mean absolute error (MAE) of 0.79 bpm and an HR correlation of 0.982. Compared with the PhysFormer baseline evaluated on our dataset, our estimator reduces HR MAE by 93.6 %, while increasing HR correlation from 0.088 to 0.982, making it usable when illumination varies.

We propose Conformal QoT, a policy-driven framework that combines statistically guaranteed QoT estimation with operational decision policies, enabling reliable lightpath-feasibility predictions under domain shift and improving accuracy from 92% to 99.6% on open datasets.

Conformal predictive systems (CPS) output calibrated bands of CDFs under exchangeability. We extend generalized CPS to non-exchangeable settings by encoding distributional shifts through observation-specific permutation weights. This yields shift-aware predictive systems that remain valid whenever the test point is, conditionally on the unordered sample, a weighted draw from the observed atoms. Since such weights are typically estimated, we introduce weight-uncertainty boxes and construct robust CPS envelopes with finite-sample or asymptotic confidence guarantees. We derive efficient computation for conformity-measure CPS, conformal binning, and conformal isotonic distributional regression. Experiments under covariate shift and feedback-driven biomolecular design show calibrated predictive bands that widen under stronger shifts and tighten as sample size increases.

Performance estimation under distribution shift aims to predict how a model behaves on an unlabeled test set whose distribution differs from the training data, a scenario that requires reliable indicators that can faithfully reflect model behavior without ground-truth labels. Existing approaches rely solely on the outputs of the given model whose biases are amplified once the distribution shifts, weakening the correlation with the true performance. Motivated by this limitation, we propose Fused Reference Alignment Prediction (FRAP), which leverages the complementary strengths of an external foundation model and the base model to construct a more reliable surrogate of the ground-truth labels. FRAP aligns the prediction distribution of the foundation model with that of the base model by applying temperature-scaled calibration that minimizes their divergence. The aligned predictions are fused through confidence-based weighting into a refined reference distribution that integrates robustness from the foundation model and domain-specific expertise from the base model, and performance estimation is obtained by measuring how closely the base model predictions agree with this reference. Extensive experiments across diverse datasets and architectures show that FRAP provides consistent and substantial improvements over representative performance-estimation methods under distribution shift.

We present CHALIS (Challenging Language Identification Samples), a new benchmark dataset explicitly designed to address difficult cases in language identification: cousin languages and orthographic noise. Our dataset has two parts: First, we collected sentences shared across mutually intelligible language pairs (Czech/Slovak, Spanish/Catalan, Portuguese/Galician, Danish/Norwegian). The second part tests for orthography noise: we transliterate text across multiple scripts, remove diacritics, simulate homoglyph attacks, and use Internet slang. We evaluate four widely used language identification systems on CHALIS and demonstrate that all struggle substantially in these scenarios, especially on lower-resource languages within cousin pairs and on transliterated input. The resource is publicly available at https://huggingface.co/datasets/michal-tichy/CHALIS.

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/.

Entropy minimization (EM) is the dominant objective for test-time adaptation, yet its failure mode, model collapse, remains poorly understood. In this work, we show that distribution shifts can cause feature clusters corresponding to distinct classes in the model's representation space to merge, while the decision boundary remains fixed. This induces a systematic skew in the predicted class distribution, referred to as prediction bias. Prediction bias refers to a shift in the predicted class distribution, with some classes overrepresented and others suppressed. We show that entropy minimization amplifies this prediction bias by tightening the existing clusters, reinforcing the incorrect groupings until all predictions collapse to a trivial solution. Next, to demonstrate the significance of prediction bias and mitigate it, we further propose Distribution Shift Bias Reduction (DSBR), a bias-correcting objective that specifically targets this failure mode by equalizing the contribution of each predicted class to the unsupervised entropy minimization loss. To study this failure mode, we design suitable adaptation settings using four medical-imaging datasets and additionally evaluate on ImageNet-C. We find that DSBR consistently stabilizes test-time adaptation, prevents model collapse, and matches or outperforms state-of-the-art methods. Moreover, DSBR operates solely at test-time.

The standard generalization bounds assume that the training and deployment distributions are the same, or are static, and don't consider regime switching environments where the ratio of calm vs crisis states is different. This paper proposes a framework that generalizes regime-aware models by quantifying the extra risk due to regime composition mismatch, when distribution shifts are Markov-switching. We obtain an exact decomposition, separating regime mismatch from regime sensitivity; we extend the bound to beta-mixing data using the effective sample size corrected for the spectral gap; and we show a minimax lower bound for synthetic data and on 25 years of global equity indices. The proposed penalty is an ex post realized generalization gap, whereas the training-only estimator does not show significant correlation: the feature geometry of crises can be detected, but not the temporal arrival. Thus, the framework is not a forecast machine. Forecasting the composition of the future regime is an open question in the rare cases of regime change.

Sequential conformal prediction (CP) provides valid uncertainty quantification under the assumption of residual exchangeability. However, this assumption is often violated in real-world time series due to temporal dependencies and distributional shifts. While recent methods attempt to approximate exchangeability through reweighting, identifying optimal weights remains an open challenge. To address this limitation, we propose DistMatch, a binning-based method that recursively partitions residuals within a binary tree using the Kolmogorov-Smirnov (KS) statistic. We theoretically show that this partitioning induces approximately exchangeable leaves, thereby avoiding the need for reweighting. By applying quantile regression with online updates within each leaf, DistMatch enables locally adaptive inference and improves robustness to distributional shifts. Extensive experiments demonstrate that DistMatch outperforms existing sequential CP methods.

We propose a unified framework for addressing three key challenges of distribution shift: (1) estimating a model's performance on an unlabeled target domain, (2) explaining the shift by identifying the features responsible, and (3) improving the target domain performance. Our method, Entropic Projection Alignment (EPA), aligns the source distribution to the target by matching carefully selected moments while simultaneously minimising the KL divergence from the source. This formulation yields a unique closed-form solution for importance weights, achieving robustness through implicit variance control. Drawing on domain adaptation theory, we establish that moment matching is sufficient for reliable estimation and adaptation, avoiding the need for full density ratio recovery. Extensive experiments, together with strong theoretical guarantees, demonstrate that EPA consistently outperforms state-of-the-art baselines while offering substantial computational efficiency.

Detecting covariate shift is critical for building reliable vision systems. While most prior work focuses on improving robustness to shift, explicitly detecting covariate shift remains underexplored. Existing approaches typically rely on fully supervised training, requiring labeled examples from both original and shifted distributions, which is often impractical. In this paper, we show that covariate shift detection can be effectively addressed with weaker supervision using Positive Unlabeled (PU) learning. However, under covariate shift, in distribution and shifted data overlap significantly, making classical PU methods unstable and sensitive to noise. To overcome this challenge, we introduce Spectral PU Neighborhood Annotation (SPUNA), a geometry aware framework that progressively discovers shifted data by leveraging the local manifold structure of visual features. Extensive experiments show that SPUNA achieves state of the art performance in PU settings and remarkably matches the performances of fully supervised methods. Moreover, our approach transfers robustly across different types of shifts, demonstrating strong generalization capabilities.

Modern deep networks remain fragile under distribution shift and adversarial perturbations, often due to excessive or poorly structured input sensitivity. We introduce TASER (Task-Aware Stein Regularisation), a training-time regularisation framework derived from Langevin Stein operators. By penalising pointwise Stein residuals under the training distribution, TASER encourages geometric compatibility between predictors and data density, inducing anisotropic, data-aware smoothness. We provide theoretical links between Stein regularisation and reduced first-order shift sensitivity, develop scalable implementation variants compatible with modern architectures, and demonstrate improved robustness and stability across regression and vision benchmarks. Across CIFAR-10 experiments, TASER consistently improves the adversarial robustness of established training methods without incurring statistically significant clean-accuracy degradation.

Standard Set Representation Learning methods typically excel on curated data but often overlook the challenge of inference-time element corruption. This refers to scenarios where deployed models encounter element-level degradations, such as outliers or missing components, that may distort set representation and degrade performance. We propose SW-DRSO, a distributionally robust optimization framework tailored for sets. Rather than minimizing loss solely on observed training data, SW-DRSO optimizes a tractable surrogate of the worst-case expected loss over a family of plausible inference-time variations. We introduce a barycentric adversary that approximates the intractable search over corrupted sets by a differentiable training-time optimization over simplex weights. Extensive experiments across four tasks demonstrate that SW-DRSO effectively enhances robustness against corruption while maintaining high overall performance.

Positional embeddings (PEs) in Vision Transformers (ViTs) are known to impact performance and robustness, but their role in shaping internal spatial representations is not well understood. In this work, we study how different forms of PEs influence the representational geometry of ViTs and how these changes relate to robustness under content-disrupting distribution shifts. We introduce a metric, the Spatial Similarity Distance Correlation (SSDC), to quantify spatial structure in token representations. Using this metric, we show that ViTs trained without PEs still develop non-trivial spatial structure, but this structure is driven by visual content and collapses under token permutation. In contrast, we find that all PEs considered (learned absolute, sinusoidal, and rotary) are associated with a consistent shift toward an index-anchored spatial organization. Representations in these models remain stable under perturbations that disrupt content, and exhibit substantially improved robustness to such distributional shifts. We further show that while different PEs produce distinct depth-wise trajectories of spatial structure, their robustness properties are largely similar (with secondary variation across encoding schemes), suggesting that robustness appears to depend on the presence of a stable positional reference frame more than it depends on the specific encoding mechanism. These results offer a geometric account of how positional encodings shape internal representations, with implications for the principled design of future encoding schemes.

Semantic segmentation is crucial for autonomous navigation in off-road environments, enabling precise classification of surroundings to identify traversable regions. However, distinctive factors inherent to off-road conditions, such as source-target domain discrepancies and sensor corruption from rough terrain, can result in distribution shifts that alter the data differently from the trained conditions. This often leads to inaccurate semantic label predictions and subsequent failures in navigation tasks. To address this, we propose ST-Seg, a novel framework that expands the source distribution through style expansion (SE) and texture regularization (TR). Unlike prior methods that implicitly apply generalization within a fixed source distribution, ST-Seg offers an intuitive approach for distribution shift. Specifically, SE broadens domain coverage by generating diverse realistic styles, augmenting the limited style information of the source domain. TR stabilizes local texture representation affected by style-augmented learning through a deep texture manifold. Experiments across various distribution-shifted target domains demonstrate the effectiveness of ST-Seg, with substantial improvements over existing methods. These results highlight the robustness of ST-Seg, enhancing the real-world applicability of semantic segmentation for off-road navigation.