Papers

Just as Socrates recognized the limits of his own knowledge, Retrieval-Augmented Language Models (RALMs) should learn to abstain when the retrieved evidence cannot support a reliable response. Existing approaches largely rely on monolithic LLMs to handle heterogeneous retrieval failures in a single step, resulting in limited abstention performance and high computational costs. We instead decompose retrieval failures into two distinct states: (i) the unanswerable state, where the required evidence is absent, and (ii) the distracted state, where relevant evidence is mixed with conflicting, negated, or adversarial information. Based on this decomposition, we introduce a lightweight module (Sieve) that screens retrieved document sets for distracting evidence before invoking a costly LLM (Sage) for grounded generation and abstention. Evaluated across both general and high-stakes expert domains, our Sieve and Sage framework preemptively detects distracting noise, improving system accuracy by up to 69.4 percentage points and Macro-F1 by 55.2 percentage points compared to one-stage baselines. Furthermore, it achieves up to a 1.99x speedup, establishing a highly efficient and reliable abstention pipeline for RALM with abstention.

Sampling many responses and keeping one that passes a verifier lets large language models solve problems beyond their single-response ability, but this search must be paid again for every query, while many deployments answer with a single response. Post-training on verified responses can transfer the benefit of search into the model. With a fixed budget, selecting by correctness alone spends slots on problems the model already answers correctly, leaving fewer to correct its failures. To address this imbalance, we propose GapFT, which trains on the gap between Pass@K and Pass@1: problems that the source model fails with one response but solves within K samples. GapFT keeps the objective and training budget fixed and changes only which verified responses enter training; an exact decomposition splits the resulting Pass@1 change into corrected failures and regressions on problems the source model already solved. On LogiQA 2.0 and ReClor with three model families, GapFT is above budget-matched uniform rejection-sampling fine-tuning (RFT) in every setting, with a positive pooled effect, and on Llama-3.1-8B and Mistral-7B it recovers about two thirds to four fifths of the gain of fine-tuning on the entire verified pool with 11-34% of its problems. Further analyses reveal that the gain comes from failures that the first few search samples recover, while failures found only by deeper search displace replay and add no net gain, that filling the same budget with gold-labeled failures search cannot reach lowers accuracy, and that the gain is bounded by how many transferable failures search exposes.

Industrial predictive maintenance increasingly depends on learning from equipment spread across sites whose sensor data cannot easily be pooled. Federated averaging (FedAvg) solves this with a central aggregation server; gossip learning removes the server, but its behaviour for recurrent failure-detection models has not been measured under controlled conditions. We compare synchronous ring gossip with FedAvg, isolated local training and a centralized reference for a stacked LSTM that detects imminent failure on the NASA C-MAPSS turbofan benchmark. All methods share one open implementation, architecture, initialization, optimizer, data split and training budget, and the primary endpoint uses one terminal window per test engine to avoid the statistical dependence of overlapping windows. On FD001 (five seeds), gossip reached a terminal-window F1 of 89.6 +/- 1.3%, compared with 89.9 +/- 1.1% for FedAvg, 83.6 +/- 6.7% for local training and 93.5 +/- 2.1% for centralized training, while transmitting the same payload as FedAvg without a coordinator. Node models agreed closely but not exactly (1.8% pairwise decision disagreement versus 5.6% without communication). Across FD002-FD004, peer communication improved terminal-window F1 over local training by 13-28 points; gossip matched FedAvg on FD003 and FD004 but was 4.3 points lower on the multi-condition FD002 subset. Simulated message loss, node failure and server outage changed neither method appreciably, whereas larger rings degraded gossip faster. Ring gossip is therefore a practical serverless alternative when data heterogeneity is moderate, and faster-mixing topologies become important as heterogeneity grows.

Intrathecal contrast-enhanced MRI shows how a tracer injected into the cerebrospinal fluid spreads through the brain, but requires repeated scans over 24–48\,h. We therefore ask how much of the later tracer distribution can be predicted from the pre-contrast scan and elapsed time alone. Using 104 training patients (878 MRI volumes), we compared a direct image-to-image regression model with a more complex generative model based on conditional flow matching, and tested both on 23 held-out patients and on 51 patients from a separate cohort with idiopathic normal pressure hydrocephalus (INPH). The direct model reduced the error of simply copying the pre-contrast scan by about 60% in held-out patients and 25% in the INPH cohort, and its predicted change maps agreed with the observed tracer enhancement rather than only reproducing anatomy. The generative model was less accurate in both cohorts. A substantial part of the later tracer distribution is therefore predictable from the patient's brain anatomy as seen on pre-contrast MRI, and the added model complexity gave no benefit at this data scale. With prospective validation, such forecasts could be studied for patient stratification and treatment planning in intrathecal therapies.

Quantitative analysis of experimental powder X-ray diffraction data remains challenging when evaluating complex multiphase materials and noisy measurements. We introduce a hybrid quantum neural network framework designed to extract quantitative parameters, such as phase weight fractions and scale factors, directly from one-dimensional powder diffraction patterns without iterative refinement. The model combines noise-aware classical simulator pre-training with fast downstream fine-tuning on quantum processing unit features, ensuring stability against hardware decoherence. We demonstrate the practical utility of this approach by deploying the trained network onto an IBM quantum computer to analyse experimental X-ray diffraction computed tomography datasets from a three-phase solid oxide fuel cell containing ca. 10,000 patterns and a four-phase lithium-ion battery containing ca. 20,000 patterns). The network successfully reconstructs quantitative spatial phase maps in strong agreement with classical Rietveld refinement, paving the way for using quantum computing hardware to analyse real-world materials characterisation data.

Transient pressure diffusion in heterogeneous porous media becomes difficult to resolve efficiently when permeability is discontinuous and spans several orders of magnitude. We develop a domain-decomposed random-feature evolutional deep neural network (DD RF-EDNN) that separates spatial approximation from temporal evolution. Permeability-informed random features are compressed into an orthonormal pressure space, and a conservative finite-volume operator is projected onto this space so that only the reduced coordinates are advanced in time. This formulation retains the dissipative structure of the discrete flow problem without repeated neural-network optimization. The analysis quantifies dictionary and singular-value truncation errors, proves contractivity under an energy-consistent dissipativity correction, and derives a conditional grid-level estimate for homogeneous dynamics and time-independent data admitting a steady lifting. Experiments on low-permeability inclusions, high-conductivity channels and blocks, and three-dimensional grids demonstrate consistent accuracy across distinct coefficient structures. The method reaches a final-time relative $L^2$ error of $9.54\times10^{-4}$ in the principal benchmark and maintains errors on the order of $10^{-2}$ at a permeability contrast of $10^3$. Numerical diagnostics further show that the observed error balance and temporal convergence are consistent with the analysis. These results support DD RF-EDNN as a structure-preserving and interpretable reduced formulation for transient simulations on prescribed heterogeneous media.

We explore the use of hybrid quantum-classical generative adversarial networks for synthesising CAD-ready vector geometries. Unlike prior work that operates in rasterised or single-Bézier domains, we introduce HMB-GAN (Hybrid Multi-Bézier GAN), an end-to-end differentiable generative framework that constructs closed shapes through stitched multi-segment Bézier representations with geometric continuity enforced by construction. We compare a quantum-enhanced generator with a classical generator within this architecture and evaluate them across point cloud distribution metrics and geometric shape statistics. Results show that despite faster convergence, a reduction in model parameter count, and slightly improved performance on point cloud metrics, the quantum generator suffers from excessive simulator overhead and thus classically-simulated evaluation suffers from hardware constraints. These results demonstrate the feasibility of modelling structured geometries through hybrid quantum architectures whilst highlighting contemporary hardware limitations.

Molecular solubility directly affects key aspects of molecular development such as reaction feasibility, formulation performance, separation efficiency, and solvent selection. However, experimental measurement across solutes, solvents, and temperatures remains costly and sparsely sampled. Existing computational models often rely on fixed-solvent assumptions, deterministic formulations, or simplified representations of solute-solvent interactions, limiting their ability to capture complex molecular interactions, continuous temperature effects, and experimental uncertainty. Here, we introduce EnSol, an environment-aware probabilistic framework for molecular solubility prediction. EnSol represents the solute and solvent as molecular graphs and learns separate representations for each before bringing them together through cross-attention to capture solute-solvent interactions. Temperature is incorporated directly into the solvent environment through feature-wise modulation, and a mixture density network predicts full solubility distributions to capture both temperature-dependent behavior and experimental uncertainty. On the independent SolProp and Leeds benchmark datasets, EnSol achieved Spearman correlations of 0.876 and 0.601, respectively, outperforming state-of-the-art solubility prediction models across both benchmarks. Beyond computational benchmarking, experimental validation across chemically diverse solute-solvent pairs showed that EnSol maintained strong predictive performance and supported reliable solvent ranking, achieving a Spearman correlation of 0.715. These results show that EnSol can support reliable solubility prediction and solvent selection across diverse chemical systems while accounting for predictive uncertainty.

Octopus crawling motivates soft robots that exploit redundancy, yet discovering and organizing diverse coordination modes for adaptation remains challenging. To address this, we introduce a Diffusion-based Uncertainty-aware Optimization (DUO) algorithm that learns demonstration-free crawling controllers for a simulated, muscle-actuated CyberOctopus. This work represents the first application of diffusion-based control to soft multi-arm robots in contact-rich simulations. By embedding a variety of locomotion behaviors within a shared control distribution, this approach enables the simulated octopus to navigate dynamic physical constraints, demonstrating that learned coordination diversity inherently facilitates robust adaptation. The main contributions include: (i) a symmetry-structured policy representation that folds radially equivalent controllers into a canonical directional sector, (ii) an online black-box optimization strategy, the DUO algorithm, that discovers and retains diverse coordination modes, and (iii) a control editing technique that adapts existing controllers to novel actuator constraints without retraining. These results show how learned coordination diversity makes motor abundance a practical resource for adaptation in soft multi-arm robots.

We propose a decoupled, layerwise method for structurally sparsifying the fully connected layers of pretrained neural networks. Rather than penalizing all layers jointly, our approach extracts shallow two-layer subnetworks, normalizes the inner weights, and applies a structured group penalty to the outer weight matrix of each block, processing layers sequentially to prune neurons and reduce the width of each layer. We prove that the constrained decoupled objective is equivalent at optimality to a specific joint penalty on the inner and outer weights, for any positively homogeneous activation, and thus admits a clean projected and proximal formulation. Our central finding is that this decoupled reformulation is more robust than coupled methods. In numerical experiments it provides a wider usable range of the regularization strength and a lower rate of catastrophic over-pruning than the tested joint baseline while maintaining comparable accuracy. We establish these properties in controlled classification and sparse-recovery studies, and examine their scope in a high-dimensional PINN stress test and in the feed-forward layers of OPT-1.3B.

The dominant method of processing sonar data is using image-based representations, requiring the preprocessing of image data on autonomous systems. We propose an alternative data processing method for remote sensing applications via the use of data in Comma-Seperated Value format. Experimentation on our alternative approach shows a reduction of processing time by 91.18%, an improvement in accurate object detection by Machine Learning, and an increase in SNR (Signal-to-noise ratio), PSNR (Peak signal-to-noise ratio), and other evaluation metrics.

Recent advances in large language models have improved their effectiveness as back-end components for voice assistants, particularly in intent understanding and context-aware input classification. However, online-hosted models introduce network dependency and variable inference latency, limiting their suitability for time-critical autonomous driving applications. In this work, we address these issues by developing Jarvis, an offline voice assistant for high-level behavioral commands of autonomous vehicles. Its architecture integrates speech recognition and synthesis with natural language command classification into a lightweight, local framework. Jarvis core component is a text-to-command classifier, built using a domain-specific fine-tuning of the Mistral 7B model, demonstrating low-latency inference. Our experimental evaluation demonstrates that our solution outperforms larger online-hosted models, achieving 97.63 % intent recognition accuracy with an average processing latency of 1.39 s, making it well-suited for operations requiring quick response times. To support further research and fine-tuning, we provide an open-source implementation.

Deep reinforcement learning (DRL) has achieved strong performance across a wide range of continuous-control problems. These continuous-control policies, however, are often defined as direct mappings from an observed state to an action or action distribution, requiring a single feed-forward network to construct an optimal control decision in one pass. While effective, this formulation leaves little opportunity for the policy to reconsider or progressively improve an action once an initial prediction has been formed. In this work, we explore an alternative approach: rather than learning only to directly predict an action, can a policy learn to iteratively improve one, and can this iterative process provide advantages during policy learning? We introduce Iterative Action Refinement (IAR), an iterative action-construction method that constructs control actions through a sequence of learned residual corrections. Starting from an initial proposal, a shared refinement network repeatedly conditions on the observed state and the current action proposal, allowing each refinement step to revise the action constructed by preceding steps. The final refined proposal is then used to determine the action executed by the agent. We integrate this iterative action-construction mechanism with Proximal Policy Optimization (PPO), yielding REFINEPPO. We evaluate REFINEPPO across 14 benchmark control tasks, complemented by controlled ablations of refinement depth and update schedules and analyses aimed at understanding why iterative refinement is effective. Across these environments, REFINEPPO matches or exceeds the performance of standard PPO while demonstrating faster convergence on several tasks.

In this work, we examine the topology of information flow patterns within attention graphs to effectively distinguish hallucinated from non-hallucinated responses. We analyze the Forman-Ricci curvature to identify structural patterns indicating information bottlenecks in attention graphs. We then introduce a method that captures both semi-local and global information-flow characteristics of attention heads associated with hallucinated responses. We evaluate our approach extensively across several LLMs and established benchmarks. Empirical results demonstrate that our proposed single-pass approach provides consistent improvements over existing attention-based and multi-response baselines across two hallucination-detection benchmarks, while achieving competitive performance across diverse LLM architectures. Further analysis reveals that impaired context sharing among tokens during causal generation is strongly associated with hallucination occurrences in LLMs. In particular, hallucinated responses are consistently characterized by an over-reliance on self-attention, diffused context retrieval from earlier tokens, or information over-squashing, especially in the final transformer layer.

Gaussian processes (GPs) provide principled probabilistic predictions while encoding prior knowledge, including equivariances. Yet, their use in large-scale scientific problems is limited by computational cost. Equivariant neural networks are common but typically lack the uncertainty quantification offered by GPs, which is valuable in applications such as molecular research. High-dimensional inputs and large symmetry groups further demand scalability. We establish results pertaining to the interplay of GP equivariance and conditioning and leverage them to obtain equivariant sparse GPs through suitable mean functions and covariance kernels. We instantiate this framework with a flexible class of integration-free equivariant kernels, yielding scalable and data-efficient GP inference. In particular, we introduce triply scalable equivariant Gaussian processes. We employ equivariant sparse variational Gaussian processes for $\mathrm{SO}(2)$-equivariant vector fields and molecular property prediction. Alongside the SVGP, we develop a matrix-free equivariant full-GP implementation that combines an exact Kronecker reduction with preconditioned conjugate-gradient solves, enabling fast and scalable evaluation of the full joint predictive density. We further compare different approaches for selecting inducing points in the equivariant sparse GP models. Our test cases include synthetic $\mathrm{SO}(2)$-equivariant fields as well as the prediction of electric dipole moments of N-methylformamide based on quantum chemistry simulations, achieving accurate, uncertainty-aware predictions at a fraction of the computational cost of classical GP inference.

Behavioral tasks measuring facial affect perception assume that identical stimuli impose equivalent perceptual difficulty across participants. However, this assumption is systematically violated by individual differences in perceptual sensitivity. Using an affective perception task as our testbed, we propose a framework to normalize for perceptual difficulty that directly estimates each participant's Just Noticeable Difference (JND) along the facial affect spectrum via cognitively lightweight perceptual adjustment queries (PAQs). We use these PAQ-inferred JNDs to re-express stimulus distances, constructing difficulty-equated tasks in perceptual space. We validate the framework in a Two-Alternative Forced-Choice (2AFC) task using two complementary behavioral measures: binary metacognitive difficulty judgments and response time variance decomposition. We find that PAQ calibration significantly equalizes perceived task difficulty at an individual level when compared to both the non-calibrated baseline and population-level Weibull calibration, while also reducing mean response time and between-subject variance in response time. These results establish PAQ as a principled and practical instrument for individualized perceptual calibration in facial affect recognition.

Federated learning (FL) enables collaborative model training without sharing raw data, but its performance degrades under non-IID data and stochastic client participation. Remedies built on classical Federated Averaging (FedAvg) typically presuppose that client participation probabilities are known to the server, which is rarely the case in deployed systems. We first discuss and then characterize the optimization problem that distributionally agnostic FedAvg actually solves when participation is entirely unknown, possibly highly skewed, and of variable size across rounds: uniform aggregation is shown to minimize a well-defined stochastic objective, weighted by the participation-induced marginal, at a standard $\mathcal{O}(1/\sqrt{T})$ rate for convex and possibly nonsmooth losses. Building on this characterization, we propose Federated Risk-Averse Averaging (FedeRage), a risk-averse extension of FedAvg that embeds the Conditional Value-at-Risk (CVaR) into the local objective within a natural distributionally robust optimization (DRO) framework. FedeRage implicitly upweights high-loss and infrequently participating clients while adding only a single scalar per-client, and admits an $\mathcal{O}(\kappa/\sqrt{T})$ rate in which the factor $\kappa$ is the upper bound on the “price" of risk aversion. In contrast with aggregation-alignment schemes based on optimal transport, which require the availability distribution as an input, FedeRage remains agnostic to it. Several experiments on three heterogeneous benchmarks indicate consistent improvements over state-of-the-art methods in accuracy, fairness, and convergence speed.

Image diffusion models have shown impressive image generation capabilities but are often hard to control, in contrast to classical computer graphics pipelines such as physically based rendering. However, we observe that there is a bridge between light transport phenomena and the distribution of latent space values produced by such models. Thus, we introduce physically based rendering in the feature space learned by the variational autoencoders in generative models, enabling light transport simulation in the latent space. This allows us to leverage physically based rendering techniques to output latent maps for physically guided content generation. We propose modifications to the rendering equation, which, when paired with a differentiable renderer, can yield an optimal set of scene parameters that require only minimal refinement to accurately render into the pretrained latent space. We train our method on a single rendered image, and then demonstrate the generalization of the method to scene geometry changes, lighting changes, and camera view changes.

Covariate-rich time-series forecasting requires deciding how external variables enter the target forecasting path. Existing Transformer-based forecasters usually build a covariate representation and pass it to the encoder without an explicit admission stage. This paper studies pre-encoder covariate admission as an input-side interface that regulates that representation immediately before encoder processing. We implement the interface with a lightweight representation-level pre-encoder gate that assigns sigmoid scores to representation units, and we also study a usage-regularized variant that penalizes average admission. The interface is evaluated as a plug-in module for TimeXer, Inverted Transformer (iTransformer), and Patch Time Series Transformer (PatchTST) under a zero-extra-tuning protocol, where each gated model inherits the corresponding baseline configuration. Experiments on the Electricity Transformer Temperature minute-level (ETTm1 and ETTm2) datasets, Traffic, Energy, and influenza-like illness (ILI) include paired forecasting comparisons, gate-placement ablation, initialization ablation, controlled covariate-admission analysis, and a variance inflation factor (VIF)-informed permutation feature importance (PFI) diagnostic case study. In the tested settings, the gate is competitive with the corresponding baselines, and the usage penalty reduces average admission scores while keeping forecasting errors close to the unpenalized TimeXer setting.

A pervasive structural pattern in modern deep learning is the linear factorization block: a submodule of the form $W = BA$ in which two parameter matrices are multiplied directly, with no intervening nonlinearity. Such blocks appear in LoRA adapters, low-rank compressed layers, query-key products of self-attention, and share a common pathology: the factorization is non-unique, which can destabilize training and limit usable learning rates. Despite this, factorization blocks are typically optimized with standard Euclidean methods that ignore the underlying geometry. We introduce Stiefel-AdamW, a near drop-in replacement for AdamW for use wherever such blocks appear. By constraining one factor on the Stiefel manifold while leaving the other Euclidean, Stiefel-AdamW relaxes the full $\mathrm{GL}(\mathbb{R}^r)$ gauge symmetry to a compact orthogonal symmetry, ruling out factor blow-up while retaining the coordinate-wise diagonal preconditioning that gives AdamW its practical strength. Moment estimation is performed in the ambient Euclidean space, with geometry entering only through a tangent-space projection and a manifold retraction. The implementation overhead over AdamW is minimal, and we show that the resulting optimizer inherits both the stability benefits of Riemannian methods and standard convergence guarantees. We validate Stiefel-AdamW on LoRA-style fine-tuning of GPT2, ViT, and Mistral 7B and on full pretraining of GPT2 on OpenWebText, showing consistent improvements over strong baselines at essentially no additional cost over AdamW.

Science advances not in isolation but through collaboration, yet existing agentic systems capture little of this. Whether communicating agents help remains an open question with mixed prior results. We show that test-time communication can substantially outperform independent parallel attempts on challenging tasks, where sharing a breakthrough can push the whole group forward. We first study the effect of scaling multi-agent test-time communication, where agents have no predefined roles and communicate via a shared directory, on ARC-AGI-3, a benchmark requiring novel problem solving. We find that a team of $k$ communicating agents, team@$k$, matches the success rate of $4k$ independent agents, and this advantage grows with $k$, suggesting gains compound with scale. The effect is not merely efficiency: a task that no single agent can solve, a team of agents can solve reliably. Furthermore, these gains transfer to research-oriented tasks, given sufficient compute. On polyomino packing, communicating agents outperform best@$k$ and exceed the prior best-known score. On MNIST classifier compression, communication surpasses the best-known human solution. A team of four agents produced a 1,957-byte classifier submission achieving 99.4% test accuracy, smaller than both the best-known human solution and the best single-agent result. These gains are not unconditional. Independent agents may outperform communication when compute is limited or when a clear measure of progress is absent. However, under sufficient compute and clear feedback, multi-agent communication consistently yields stronger results.

We study data-driven early stopping for spectral regularisation methods in the classical non-parametric regression setting. Building on the discrepancy principle, we propose a multi-scale stopping rule that applies to general kernel estimators and show that, unlike previous approaches, it achieves full adaptivity over all smoothness levels in the well-specified case. A key contribution of our work is an extension based on random feature approximations, which reduces computational cost on large datasets while preserving minimax-optimal statistical guarantees. Our procedure not only selects an optimal stopping time but also provides a fully data-driven choice of the number of random features needed to achieve optimal rates. Through the established connection between random features and neural networks in the neural tangent kernel regime, our method further yields a principled, data-driven recommendation for the network width. We prove that the resulting simultaneously chosen width and stopping time allow neural networks to attain minimax-optimal learning rates without prior knowledge of smoothness or capacity parameters.

Artistic style classification is usually studied on complete artworks, where models can exploit global composition, spatial organisation, and iconographic structure. In archaeological settings, however, artworks often survive only as fragmented remains, forcing recognition from incomplete, irregular, and context-limited visual evidence. We study fresco-fragment style classification using a progressive transformer-based framework. Starting from a ViT-B/16 baseline, we introduce foreground-guided masking to suppress background-only tokens, inpainting-based geometric regularisation to align irregular fragment supports with the ViT patch grid, and a supervised contrastive objective that operates on predictive distributions through a Kullback-Leibler similarity and consistently improves every branch. We combine the branches with a deliberately simple learnable logit ensemble. Experiments on CLEOPATRA and POMPAAF show that fragment-aware modelling improves over the standard ViT baseline, with the ensemble increasing accuracy from 0.604 to 0.656 and macro-F1 from 0.596 to 0.648 on CLEOPATRA, and outperforming the best single branch in four of six fragmentation settings on POMPAAF. We additionally evaluate a more complex graph-fusion variant and find that it matches the simple ensemble on POMPAAF while offering only a small, dataset-specific gain on CLEOPATRA, which does not justify its added complexity. Beyond these empirical gains, our contribution is twofold: a distribution-level contrastive objective that consistently sharpens single-branch recognition, and an interpretability analysis that verifies the models exploit genuine painted evidence, while quantifying that the inpainting-based branch draws part of its attribution from the synthesised surround.

Substantial efforts have been devoted to making deep learning objectives, representations, and architectures interpretable, with the goal of improving the safety, robustness, and generalisation of learning systems in diverse real-world applications. The recently proposed maximal coding rate reduction ($\mathrm{MCR}^{2}$) offers a promising information-theoretic framework for learning structured, discriminative representations of class-wise submanifolds and has inspired interpretable white-box architectures. However, we observe that $\mathrm{MCR}^{2}$ can completely fail under distribution shift, motivating our study of its out-of-distribution (OOD) generalisation limits. We establish two limitations of $\mathrm{MCR}^{2}$ for OOD generalisation. First, the $\mathrm{MCR}^{2}$ objective alone can admit complete prediction failure: a representation based entirely on unstable environmental features can achieve the global coding optimum yet fail completely after correlation reversal, despite an available perfectly stable feature. This exact-optimum example includes test inputs that cannot occur during training. Even when every possible test input can also occur during training, coding quality can be arbitrarily close to optimal while prediction error is arbitrarily close to 100%. Second, directly incorporating the invariance principle underlying widely successful invariant risk minimisation (IRM) and risk extrapolation (REx) does not eliminate this failure. The failing representation admits the same optimal coding operator across training environments, showing that shared coding optimality does not ensure stable prediction. Reliable OOD guarantees for $\mathrm{MCR}^{2}$ therefore require additional new assumptions or learning principles that establish stable predictive relationships across environments.

Latent variable generative models are commonly fit using simple priors over latent variables, but draws from these priors often fail to produce realistic data. This failure is due to a mismatch between the prior and the aggregated posterior, the distribution of latent variables induced by the fitted model and the data. This mismatch is often viewed as evidence that the prior is misspecified and should be replaced. Alternatively, in modern generative models, a two-stage strategy is increasingly used where first, the model is fit, and second, the aggregated posterior is estimated (van den Oord et al.,2017; Rombach et al., 2022.). Synthetic data are then obtained by sampling from this aggregated posterior instead of the prior. To check such procedures, we introduce the aggregated posterior predictive check (APPC). Theoretically, we establish sufficient conditions under which the APPC is asymptotically calibrated. For probabilistic principal component analysis, we show that the APPC can remain calibrated under a misspecified latent prior when pervasive factors permit recovery of the signal space. Experiments with variational autoencoders show that aggregated posterior sampling improves generation for heavy-tailed and clustered data relative to Gaussian prior sampling while performing comparably to models with more flexible latent priors.

Symbolic regression aims to recover closed-form equations from observations, providing interpretable models for scientific discovery. Existing approaches struggle to combine flexible structural search with efficient inference. Search-based methods can refine expression structure but often rely on costly combinatorial optimization with random initialization. Pretrained neural models generate formulas almost instantly, but their predictions often contain symbolic errors. We introduce MOSAIC-SR, which uses a pretrained Transformer to propose multiple initial sketches. These sketches initialize searches in several promising regions, avoiding random starts in the vast expression space. Each search jointly recovers structure and constants through scale-aware constant optimization and local symbolic repair. We evaluate MOSAIC-SR on the SRSD-Feynman dataset with and without dummy variables and on six additional benchmarks. MOSAIC-SR obtains the highest symbolic solution rate on every dataset while ranking among the top two methods in predictive accuracy. This advantage persists in the presence of irrelevant dummy inputs. The results show that learned priors can focus search on promising equation structures, and that numerical optimization and symbolic repair are important for recovery.

Physiological emotion recognition using wearable sensors has important applications in mental health monitoring, affective computing, and human-computer interaction. However, existing studies typically evaluate a single model, sensing configuration, or dataset, limiting our understanding of how these factors influence recognition performance. We present a comparative study of temporal deep learning architectures for physiological emotion recognition using two multimodal wearable datasets: WESAD and EmoWear. Bidirectional long short-term memory (LSTM), temporal convolutional network (TCN), and Transformer models are evaluated under wrist-only, chest-only, and multimodal sensing configurations using participant-independent leave-one-subject-out cross-validation (LOSO-CV). We also investigate soft-voting ensembles, sensor ablation, sampling frequency, and gradient-based saliency. The Transformer achieved the highest multimodal accuracy on WESAD (99.02% +/- 0.51%), whereas the LSTM achieved the best multimodal accuracy on EmoWear for both arousal (91.80% +/- 1.06%) and valence (89.96% +/- 0.36%). These results show that relative architecture performance depends on dataset characteristics rather than one architecture being uniformly superior. Multimodal sensing consistently outperformed wrist-only and chest-only configurations across both datasets. Sampling-frequency analysis showed that 4 Hz provides a practical operating point, with performance comparable to higher frequencies at substantially lower training cost. These findings provide guidance for selecting architectures, sensing modalities, and sampling frequencies for wearable physiological emotion recognition.

Reinforcement learning (RL) controllers have been recently adopted for Unmanned Aerial Vehicles (UAV) navigation and control. However, they are susceptible to action-space attacks that overwrite the action commands after the policy generates them and before the actuators execute them. While most existing defenses target attacks on the policy's inputs, those addressing action-space attacks retrain the policy at training time and are not resilient to corrupted actions at runtime. We propose ASGARD, a two-phase teacher-student pipeline for making RL-based UAV control resilient to action-space attacks. In the teacher phase, an encoder combines the UAV's physical state with action-attack-related privileged information to produce an action-attack-aware latent that trains the RL control policy and a monitor that outputs corrected action commands to the actuators. In the student phase, both the encoder and the monitor are trained via supervised learning from their teacher counterparts to run on-board using only the UAV's physical state history. We evaluate ASGARD across attack scenarios targeting different action commands on UAV. We find that ASGARD is resilient to action-space attacks and completes the missions despite the attack. We further find that ASGARD generalizes to unseen attacks and remains resilient against stealthy attacks.

High-consequence subsurface decisions often rely on sparse data that permit competing geological interpretations. Determining consistency of these interpretations with the available observations remains challenging. We present a workflow that addresses this challenge by translating competing geologic interpretations into alternative priors and ranking them according to their consistency with hydraulic-head observations. A key step in this workflow is exploiting the broad knowledge of image-generation foundation models to transform nuanced geologic interpretations into data ready for computer modeling. For each interpretation, a text-to-image foundation model generates an ensemble of geologic images, and a separately trained variational autoencoder learns an interpretation-specific latent representation. A supervised inverse network maps head observations into this latent space, and the frozen decoder reconstructs an image that is mapped to a log-conductivity field. Steady-state flow simulations predict heads, and the aggregate normalized head error determines the ranking. We evaluate the framework using a synthetic benchmark based on the Johansen Formation with three interpretations of decreasing consistency with the reference geology. Across 595 test cases, the Precise & Accurate interpretation produces lower normalized errors than Accurate in 58.5% of cases and Mismatched in 82.5% of cases. Accurate outperforms Mismatched in 65.5% of cases. We then compare spatial representations of two published conceptual models of the Culebra Dolomite Member at the Waste Isolation Pilot Plant. The revised representation yields an aggregate normalized error of 7.598, compared with 8.595 for the original, consistent with the documented conceptual-model revision. The framework enables quantitative comparison of competing geological interpretations using available hydraulic observations.

Complex problem solving (CPS) with large language models (LLMs) is often framed as a matter of stronger reasoning or longer generation. Yet early-step error amplification, prompt brittleness, and failures to revise incorrect commitments are difficult to explain by missing knowledge or expressive capacity alone. This survey interprets CPS as a sequential estimation-and-decision problem over a latent solution state. A controller maintains a belief about an unobserved solution trajectory, updates it as noisy intermediate evidence arrives, and decides whether to commit, verify, branch, roll back, or abstain to minimize expected loss. Reasoning supplies candidate transitions and interpretations, whereas process control shapes and evaluates those proposals and regulates subsequent transitions and observations. Within this framework, we organize existing methods around five components: explicit state representation, transition structuring, validation and constraint enforcement, search and rollback, and uncertainty management. We also interpret evaluation metrics according to the statistical quantities they estimate. The framework further yields a diagnostic hypothesis: interventions should be most effective when they target the error or uncertainty component implicated by an observed failure. We distinguish systematic, stochastic, and irreducible error together with epistemic and aleatoric uncertainty, and call this alignment problem-control fit and its failure control mismatch. For example, additional sampling may reduce sampling variability while leaving a shared systematic error unchanged. This perspective clarifies what current methods estimate and control, what remains uncontrolled, and why reliable validation, targeted recovery, calibrated uncertainty, and matched-budget evaluation are central open problems.