Safe learning is essential for deploying learningbased controllers in safety-critical robotic systems, yet existing approaches often enforce multiple safety constraints uniformly or via fixed priority orders, leading to infeasibility and brittle behavior. In practice, safety requirements are heterogeneous and admit only partial priority relations, where some constraints are comparable while others are inherently incomparable. We formalize this setting as poset-structured safety, modeling safety constraints as a partially ordered set and treating safety composition as a structural property of the policy class. Building on this formulation, we propose PoSafeNet, a differentiable neural safety layer that enforces safety via sequential closed-form projection under poset-consistent constraint orderings, enabling adaptive selection or mixing of valid safety executions while preserving priority semantics by construction. Experiments on multi-obstacle navigation, constrained robot manipulation, and vision-based autonomous driving demonstrate improved feasibility, robustness, and scalability over unstructured and differentiable quadratic program-based safety layers.

We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we introduce two novel geometric quantities, the relative Wasserstein angle and the orthogonal projection distance, which provide meaningful measures of non-Gaussianity. We prove that the filling cone generated by any two rays in this space is flat, ensuring that angles, projections, and inner products are rigorously well-defined. This geometric viewpoint recasts Gaussian approximation as a projection problem onto the Gaussian cone and reveals that the commonly used moment-matching Gaussian can \emph{not} be the \(W_2\)-nearest Gaussian for a given empirical distribution. In one dimension, we derive closed-form expressions for the proposed quantities and extend them to several classical distribution families, including uniform, Laplace, and logistic distributions; while in high dimensions, we develop an efficient stochastic manifold optimization algorithm based on a semi-discrete dual formulation. Experiments on synthetic data and real-world feature distributions demonstrate that the relative Wasserstein angle is more robust than the Wasserstein distance and that the proposed nearest Gaussian provides a better approximation than moment matching in the evaluation of Fréchet Inception Distance (FID) scores.

Language model agents often appear capable of self-recovery after failing tool call executions, yet this behavior lacks a formal explanation. We present a predictive theory that resolves this gap by showing that recoverability follows a measurable law. To elaborate, we formalize recoverability through Expected Recovery Regret (ERR), which quantifies the deviation of a recovery policy from the optimal one under stochastic execution noise, and derive a first-order relationship between ERR and an empirical observable quantity, the Efficiency Score (ES). This yields a falsifiable first-order quantitative law of recovery dynamics in tool-using agents. We empirically validate the law across five tool-use benchmarks spanning controlled perturbations, diagnostic reasoning, and real-world APIs. Across model scales, perturbation regimes, and recovery horizons, predicted regret under the ERR-ES law closely matched observed post-failure regret measured from Monte Carlo rollouts, within delta less than or equal to 0.05. Our results reveal that recoverability is not an artifact of model scale or architecture, but a governed property of interaction dynamics, providing a theoretical foundation for execution-level robustness in language agents.

Given a Markov decision process (MDP), we seek to learn representations for a range of policies to facilitate behavior steering at test time. As policies of an MDP are uniquely determined by their occupancy measures, we propose modeling policy representations as expectations of state-action feature maps with respect to occupancy measures. We show that these representations can be approximated uniformly for a range of policies using a set-based architecture. Our model encodes a set of state-action samples into a latent embedding, from which we decode both the policy and its value functions corresponding to multiple rewards. We use variational generative approach to induce a smooth latent space, and further shape it with contrastive learning so that latent distances align with differences in value functions. This geometry permits gradient-based optimization directly in the latent space. Leveraging this capability, we solve a novel behavior synthesis task, where policies are steered to satisfy previously unseen value function constraints without additional training.

We evaluate language models on their ability to explore interactive environments under a limited interaction budget. We introduce three parametric tasks with controllable exploration difficulty, spanning continuous and discrete environments. Across state-of-the-art models, we find systematic under-exploration and suboptimal solutions, with performance often significantly worse than simple explore--exploit heuristic baselines and scaling weakly as the budget increases. Finally, we study two lightweight interventions: splitting a fixed budget into parallel executions, which surprisingly improves performance despite a no-gain theoretical result for our tasks, and periodically summarizing the interaction history, which preserves key discoveries and further improves exploration.

Modern supply chains must balance high-speed logistics with environmental impact and security constraints, prompting a surge of interest in AI-enabled Internet of Things (AIoT) solutions for global commerce. However, conventional supply chain optimization models often overlook crucial sustainability goals and cyber vulnerabilities, leaving systems susceptible to both ecological harm and malicious attacks. To tackle these challenges simultaneously, this work integrates a quantum-inspired reinforcement learning framework that unifies carbon footprint reduction, inventory management, and cryptographic-like security measures. We design a quantum-inspired reinforcement learning framework that couples a controllable spin-chain analogy with real-time AIoT signals and optimizes a multi-objective reward unifying fidelity, security, and carbon costs. The approach learns robust policies with stabilized training via value-based and ensemble updates, supported by window-normalized reward components to ensure commensurate scaling. In simulation, the method exhibits smooth convergence, strong late-episode performance, and graceful degradation under representative noise channels, outperforming standard learned and model-based references, highlighting its robust handling of real-time sustainability and risk demands. These findings reinforce the potential for quantum-inspired AIoT frameworks to drive secure, eco-conscious supply chain operations at scale, laying the groundwork for globally connected infrastructures that responsibly meet both consumer and environmental needs.

The knowledge gradient is a popular acquisition function in Bayesian optimization (BO) for optimizing black-box objectives with noisy function evaluations. Many practical settings, however, allow only pairwise comparison queries, yielding a preferential BO problem where direct function evaluations are unavailable. Extending the knowledge gradient to preferential BO is hindered by its computational challenge. At its core, the look-ahead step in the preferential setting requires computing a non-Gaussian posterior, which was previously considered intractable. In this paper, we address this challenge by deriving an exact and analytical knowledge gradient for preferential BO. We show that the exact knowledge gradient performs strongly on a suite of benchmark problems, often outperforming existing acquisition functions. In addition, we also present a case study illustrating the limitation of the knowledge gradient in certain scenarios.

Cell Painting is a microscopy-based, high-content imaging assay that produces rich morphological profiles of cells and can support drug discovery by quantifying cellular responses to chemical perturbations. At scale, however, Cell Painting data is strongly affected by batch effects arising from differences in laboratories, instruments, and protocols, which can obscure biological signal. We present BALANS (Batch Alignment via Local Affinities and Subsampling), a scalable batch-correction method that aligns samples across batches by constructing a smoothed affinity matrix from pairwise distances. Given $n$ data points, BALANS builds a sparse affinity matrix $A \in \mathbb{R}^{n \times n}$ using two ideas. (i) For points $i$ and $j$, it sets a local scale using the distance from $i$ to its $k$-th nearest neighbor within the batch of $j$, then computes $A_{ij}$ via a Gaussian kernel calibrated by these batch-aware local scales. (ii) Rather than forming all $n^2$ entries, BALANS uses an adaptive sampling procedure that prioritizes rows with low cumulative neighbor coverage and retains only the strongest affinities per row, yielding a sparse but informative approximation of $A$. We prove that this sampling strategy is order-optimal in sample complexity and provides an approximation guarantee, and we show that BALANS runs in nearly linear time in $n$. Experiments on diverse real-world Cell Painting datasets and controlled large-scale synthetic benchmarks demonstrate that BALANS scales to large collections while improving runtime over native implementations of widely used batch-correction methods, without sacrificing correction quality.

Large Language Models (LLMs) are increasingly positioned as decision engines for hiring, healthcare, and economic judgment, yet real-world human judgment reflects a balance between rational deliberation and emotion-driven bias. If LLMs are to participate in high-stakes decisions or serve as models of human behavior, it is critical to assess whether they exhibit analogous patterns of (ir)rationalities and biases. To this end, we evaluate multiple LLM families on (i) benchmarks testing core axioms of rational choice and (ii) classic decision domains from behavioral economics and social norms where emotions are known to shape judgment and choice. Across settings, we show that deliberate "thinking" reliably improves rationality and pushes models toward expected-value maximization. To probe human-like affective distortions and their interaction with reasoning, we use two emotion-steering methods: in-context priming (ICP) and representation-level steering (RLS). ICP induces strong directional shifts that are often extreme and difficult to calibrate, whereas RLS produces more psychologically plausible patterns but with lower reliability. Our results suggest that the same mechanisms that improve rationality also amplify sensitivity to affective interventions, and that different steering methods trade off controllability against human-aligned behavior. Overall, this points to a tension between reasoning and affective steering, with implications for both human simulation and the safe deployment of LLM-based decision systems.

Molecular representations fundamentally shape how machine learning systems reason about molecular structure and physical properties. Most existing approaches adopt a discrete pipeline: molecules are encoded as sequences, graphs, or point clouds, mapped to fixed-dimensional embeddings, and then used for task-specific prediction. This paradigm treats molecules as discrete objects, despite their intrinsically continuous and field-like physical nature. We argue that molecular learning can instead be formulated as learning in function space. Specifically, we model each molecule as a continuous function over three-dimensional (3D) space and treat this molecular field as the primary object of representation. From this perspective, conventional molecular representations arise as particular sampling schemes of an underlying continuous object. We instantiate this formulation with MolField, a hyper-network-based framework that learns distributions over molecular fields. To ensure physical consistency, these functions are defined over canonicalized coordinates, yielding invariance to global SE(3) transformations. To enable learning directly over functions, we introduce a structured weight tokenization and train a sequence-based hyper-network to model a shared prior over molecular fields. We evaluate MolField on molecular dynamics and property prediction. Our results show that treating molecules as continuous functions fundamentally changes how molecular representations generalize across tasks and yields downstream behavior that is stable to how molecules are discretized or queried.

Monitoring the performance of classification models in production is critical yet challenging due to strict labeling budgets, one-shot batch acquisition of labels and extremely low error rates. We propose a general framework based on Stratified Importance Sampling (SIS) that directly addresses these constraints in model monitoring. While SIS has previously been applied in specialized domains, our theoretical analysis establishes its broad applicability to the monitoring of classification models. Under mild conditions, SIS yields unbiased estimators with strict finite-sample mean squared error (MSE) improvements over both importance sampling (IS) and stratified random sampling (SRS). The framework does not rely on optimally defined proposal distributions or strata: even with noisy proxies and sub-optimal stratification, SIS can improve estimator efficiency compared to IS or SRS individually, though extreme proposal mismatch may limit these gains. Experiments across binary and multiclass tasks demonstrate consistent efficiency improvements under fixed label budgets, underscoring SIS as a principled, label-efficient, and operationally lightweight methodology for post-deployment model monitoring.

Indoor localization is a critical enabler for a wide range of location-based services in smart environments, including navigation, asset tracking, and safety-critical applications. Recent graph-based models leverage spatial relationships between Wire-less Fidelity (Wi-Fi) Access Points (APs) and devices, offering finer localization granularity, but fall short in quantifying prediction uncertainty, a key requirement for real-world deployment. In this paper, we propose Spatially-Adaptive Conformal Graph Transformer (SAC-GT), a framework for accurate and reliable indoor localization. SAC-GT integrates a Graph Transformer (GT) model that captures network's spatial topology and signal strength dynamics, with a novel Spatially-Adaptive Conformal Prediction (SACP) method that provides region-specific uncertainty estimates. This allows SAC-GT to produce not only precise two-dimensional (2D) location predictions but also statistically valid confidence regions tailored to varying environmental conditions. Extensive evaluations on a large-scale real-world dataset demonstrate that the proposed SAC-GT solution achieves state-of-the-art localization accuracy while delivering robust and spatially adaptive reliability guarantees.

Large language models (LLMs) are increasingly accessed as remotely hosted services by edge and enterprise clients that cannot run frontier models locally. Since models vary widely in capability and price, routing queries to models that balance quality and inference cost is essential. Existing router approaches assume access to centralized query-model evaluation data. However, these data are often fragmented across clients, such as end users and organizations, and are privacy-sensitive, which makes centralizing data infeasible. Additionally, per-client router training is ineffective since local evaluation data is limited and covers only a restricted query distribution and a biased subset of model evaluations. We introduce the first federated framework for LLM routing, enabling clients to learn a shared routing policy from local offline query-model evaluation data. Our framework supports both parametric multilayer perceptron router and nonparametric K-means router under heterogeneous client query distributions and non-uniform model coverage. Across two benchmarks, federated collaboration improves the accuracy-cost frontier over client-local routers, both via increased effective model coverage and better query generalization. Our theoretical results also validate that federated training reduces routing suboptimality.

Many real-world optimization problems involve an expensive ground-truth oracle (e.g., human evaluation, physical experiments) and a cheap, low-fidelity prediction oracle (e.g., machine learning models, simulations). Meanwhile, abundant offline data (e.g., past experiments and predictions) are often available and can be used to pretrain powerful predictive models, as well as to provide an informative prior. We propose Prediction-Augmented Gaussian Process Upper Confidence Bound (PA-GP-UCB), a novel Bayesian optimization algorithm that leverages both oracles and offline data to achieve provable gains in sample efficiency for the ground-truth oracle queries. PA-GP-UCB employs a control-variates estimator derived from a joint Gaussian process posterior to correct prediction bias and reduce uncertainty. We prove that PA-GP-UCB preserves the standard regret rate of GP-UCB while achieving a strictly smaller leading constant that is explicitly controlled by prediction quality and offline data coverage. Empirically, PA-GP-UCB converges faster than Vanilla GP-UCB and naive prediction-augmented GP-UCB baselines on synthetic benchmarks and on a real-world hypothesis evaluation task grounded in human behavioral data, where predictions are provided by large language models. These results establish PA-GP-UCB as a general and sample-efficient framework for hypothesis generation under expensive feedback.

Large Language Models (LLMs) are rarely static and are frequently updated in practice. A growing body of alignment research has shown that models initially deemed "aligned" can exhibit misaligned behavior after fine-tuning, such as forgetting jailbreak safety features or re-surfacing knowledge that was intended to be forgotten. These works typically assume that the initial model is aligned based on static black-box evaluation, i.e., the absence of undesired responses to a fixed set of queries. In contrast, we formalize model alignment in both the static and post-update settings and uncover a fundamental limitation of black-box evaluation. We theoretically show that, due to overparameterization, static alignment provides no guarantee of post-update alignment for any update dataset. Moreover, we prove that static black-box probing cannot distinguish a model that is genuinely post-update robust from one that conceals an arbitrary amount of adversarial behavior which can be activated by even a single benign gradient update. We further validate these findings empirically in LLMs across three core alignment domains: privacy, jailbreak safety, and behavioral honesty. We demonstrate the existence of LLMs that pass all standard black-box alignment tests, yet become severely misaligned after a single benign update. Finally, we show that the capacity to hide such latent adversarial behavior increases with model scale, confirming our theoretical prediction that post-update misalignment grows with the number of parameters. Together, our results highlight the inadequacy of static evaluation protocols and emphasize the urgent need for post-update-robust alignment evaluation.

Large language models are increasingly applied to materials science reasoning, yet their behavior under physically structured distribution shifts remains poorly understood. We introduce SCALAR (Structural Consistency And Logic Across Regimes), a benchmark for evaluating geometric scale generalization and its connection to structural hallucination, consistency, and reasoning in materials foundation models. Given canonical crystal representations, models must reason about derived nanoparticle structures obtained through supercell expansion and geometric truncation across length scales spanning a few atoms to over 18,000 atoms, totaling $\approx$100,000 structures from DFT-validated unit cells. SCALAR defines three tasks. (i) CIF to property prediction. (ii) A Chain-of-Thought variant with explicit physics-grounded reasoning. (iii) Inverse retrieval identifying crystals from candidates given target properties. Outputs are evaluated via structured metrics capturing numeric error, hallucination, cross-prompt consistency, monotonic reasoning, output validity, and retrieval regret. Experiments across diverse foundation models reveal large, model-dependent shifts under explicit reasoning, often reducing hallucination and error, but frequently destabilizing consistency or validity. These results demonstrate that geometric scale generalization cannot be inferred from accuracy alone. Supplementary materials are available at https://github.com/KurbanIntelligenceLab/SCALAR.

Large language model (LLM)-based agents exhibit strong step-by-step reasoning capabilities over short horizons, yet often fail to sustain coherent behavior over long planning horizons. We argue that this failure reflects a fundamental mismatch: step-wise reasoning induces a form of step-wise greedy policy that is adequate for short horizons but fails in long-horizon planning, where early actions must account for delayed consequences. From this planning-centric perspective, we study LLM-based agents in deterministic, fully structured environments with explicit state transitions and evaluation signals. Our analysis reveals a core failure mode of reasoning-based policies: locally optimal choices induced by step-wise scoring lead to early myopic commitments that are systematically amplified over time and difficult to recover from. We introduce FLARE (Future-aware Lookahead with Reward Estimation) as a minimal instantiation of future-aware planning to enforce explicit lookahead, value propagation, and limited commitment in a single model, allowing downstream outcomes to influence early decisions. Across multiple benchmarks, agent frameworks, and LLM backbones, FLARE consistently improves task performance and planning-level behavior, frequently allowing LLaMA-8B with FLARE to outperform GPT-4o with standard step-by-step reasoning. These results establish a clear distinction between reasoning and planning.

Automatic workflow generation is the process of automatically synthesizing sequences of LLM calls, tool invocations, and post-processing steps for complex end-to-end tasks. Most prior methods cast this task as an optimization problem with limited theoretical grounding. We propose to cast workflow generation as Bayesian inference over a posterior distribution on workflows, and introduce \textbf{Bayesian Workflow Generation (BWG)}, a sampling framework that builds workflows step-by-step using parallel look-ahead rollouts for importance weighting and a sequential in-loop refiner for pool-wide improvements. We prove that, without the refiner, the weighted empirical distribution converges to the target posterior. We instantiate BWG as \textbf{BayesFlow}, a training-free algorithm for workflow construction. Across six benchmark datasets, BayesFlow improves accuracy by up to 9 percentage points over SOTA workflow generation baselines and by up to 65 percentage points over zero-shot prompting, establishing BWG as a principled upgrade to search-based workflow design. Code will be available on https://github.com/BoYuanVisionary/BayesFlow.

Conditional generative models map input variables to complex, high-dimensional distributions, enabling realistic sample generation in a diverse set of domains. A critical challenge with these models is the absence of calibrated uncertainty, which undermines trust in individual outputs for high-stakes applications. To address this issue, we propose a systematic conformal prediction approach tailored to conditional generative models, leveraging density estimation on model-generated samples. We introduce a novel method called CP4Gen, which utilizes clustering-based density estimation to construct prediction sets that are less sensitive to outliers, more interpretable, and of lower structural complexity than existing methods. Extensive experiments on synthetic datasets and real-world applications, including climate emulation tasks, demonstrate that CP4Gen consistently achieves superior performance in terms of prediction set volume and structural simplicity. Our approach offers practitioners a powerful tool for uncertainty estimation associated with conditional generative models, particularly in scenarios demanding rigorous and interpretable prediction sets.

Large Language Models demonstrate remarkable capabilities yet remain fundamentally probabilistic, presenting critical reliability challenges for enterprise deployment. We introduce the Six Sigma Agent, a novel architecture that achieves enterprise-grade reliability through three synergistic components: (1) task decomposition into a dependency tree of atomic actions; (2) micro-agent sampling where each task is executed n times in parallel across diverse LLMs to generate independent outputs; and (3) consensus voting with dynamic scaling, clustering outputs and selecting the answer from the winning cluster with maximum votes. We prove that sampling n independent outputs with error rate p achieves system error O(p^{ceil(n/2)}), enabling exponential reliability gains. Even using cheaper models with 5% per-action error, consensus voting with 5 agents reduces error to 0.11%; dynamic scaling to 13 agents achieves 3.4 DPMO (Defects Per Million Opportunities), the Six Sigma standard. Evaluation across three enterprise use cases demonstrates a 14,700x reliability improvement over single-agent execution while reducing costs by 80%. Our work establishes that reliability in AI systems emerges from principled redundancy and consensus rather than model scaling alone.

We focus on multi-object rearrangement planning in densely cluttered environments using a car-like robot pusher. The combination of kinematic, geometric and physics constraints underlying this domain results in challenging nonmonotone problem instances which demand breaking each manipulation action into multiple parts to achieve a desired object rearrangement. Prior work tackles such instances by planning prerelocations, temporary object displacements that enable constraint satisfaction, but deciding where to prerelocate remains difficult due to local minima leading to infeasible or high-cost paths. Our key insight is that these minima can be avoided by steering a prerelocation optimization toward low-cost regions informed by Dubins path classification. These optimized prerelocations are integrated into an object traversability graph that encodes kinematic, geometric, and pushing constraints. Searching this graph in a depth-first fashion results in efficient, feasible rearrangement sequences. Across a series of densely cluttered scenarios with up to 13 objects, our framework, ReloPush-BOSS, exhibits consistently highest success rates and shortest pushing paths compared to state-of-the-art baselines. Hardware experiments on a 1/10 car-like pusher demonstrate the robustness of our approach. Code and footage from our experiments can be found at: https://fluentrobotics.com/relopushboss.

We introduce Riemannian Lyapunov Optimizers (RLOs), a family of optimization algorithms that unifies classic optimizers within one geometric framework. Unlike heuristic improvements to existing optimizers, RLOs are systematically derived from a novel control-theoretic framework that reinterprets optimization as an extended state discrete-time controlled dynamical system on a Riemannian parameter manifold. Central to this framework is the identification of a Normally Attracting Invariant Manifold (NAIM), which organizes training dynamics into two distinct stages: rapid alignment of the speed state to a target graph, followed by controlled evolution within it. We formalize this by constructing a strict Lyapunov function that certifies convergence to a target manifold. This perspective yields a constructive ``optimizer generator" that not only recovers classic algorithms but enables the principled design of RLOs. We validate our theory via geometric diagnostics and demonstrate that grounding optimizer design in control theory yields state-of-the-art performance in large-scale benchmarks. Overall, RLOs bridge control theory and modern machine learning optimization, providing a unified language and a systematic toolkit for designing stable, effective optimizers.

The quadratic complexity of the attention mechanism severely limits the context scalability of Video Diffusion Transformers (DiTs). We find that the highly sparse spatio-temporal attention patterns exhibited in Video DiTs can be naturally represented by the Monarch matrix. It is a class of structured matrices with flexible sparsity, enabling sub-quadratic attention via an alternating minimization algorithm. Accordingly, we propose VMonarch, a novel attention mechanism for Video DiTs that enables efficient computation over the dynamic sparse patterns with structured Monarch matrices. First, we adapt spatio-temporal Monarch factorization to explicitly capture the intra-frame and inter-frame correlations of the video data. Second, we introduce a recomputation strategy to mitigate artifacts arising from instabilities during alternating minimization of Monarch matrices. Third, we propose a novel online entropy algorithm fused into FlashAttention, enabling fast Monarch matrix updates for long sequences. Extensive experiments demonstrate that VMonarch achieves comparable or superior generation quality to full attention on VBench after minimal tuning. It overcomes the attention bottleneck in Video DiTs, reduces attention FLOPs by a factor of 17.5, and achieves a speedup of over 5x in attention computation for long videos, surpassing state-of-the-art sparse attention methods at 90% sparsity.

Judge agents are fundamental to agentic AI frameworks: they provide automated evaluation, and enable iterative self-refinement of reasoning processes. We introduce JAF: Judge Agent Forest, a framework in which the judge agent conducts joint inference across a cohort of query--response pairs generated by a primary agent, rather than evaluating each in isolation. This paradigm elevates the judge from a local evaluator to a holistic learner: by simultaneously assessing related responses, the judge discerns cross-instance patterns and inconsistencies, whose aggregate feedback enables the primary agent to improve by viewing its own outputs through the judge's collective perspective. Conceptually, JAF bridges belief propagation and ensemble-learning principles: overlapping in-context neighborhoods induce a knowledge-graph structure that facilitates propagation of critique, and repeated, randomized evaluations yield a robust ensemble of context-sensitive judgments. JAF can be instantiated entirely via ICL, with the judge prompted for each query using its associated primary-agent response plus a small, possibly noisy set of peer exemplars. While kNN in embedding space is a natural starting point for exemplars, this approach overlooks categorical structure, domain metadata, or nuanced distinctions accessible to modern LLMs. To overcome these limitations, we develop a flexible locality-sensitive hashing (LSH) algorithm that learns informative binary codes by integrating semantic embeddings, LLM-driven hash predicates, supervision from categorical labels, and relevant side information. These hash codes support efficient, interpretable, and relation-aware selection of diverse exemplars, and further optimize exploration of CoT reasoning paths. We validate JAF with an empirical study on the demanding task of cloud misconfigs triage in large-scale cloud environments.

Limited access to medical infrastructure forces elderly and vulnerable patients to rely on home-based care, often leading to neglect and poor adherence to therapeutic exercises such as yoga or physiotherapy. To address this gap, we propose a low-cost and automated human activity recognition (HAR) framework based on wearable inertial sensors and machine learning. Activity data, including walking, walking upstairs, walking downstairs, sitting, standing, and lying, were collected using accelerometer and gyroscope measurements. Four classical classifiers, Logistic Regression, Random Forest, Support Vector Machine (SVM), and k-Nearest Neighbors (k-NN), were evaluated and compared with the proposed Support Tensor Machine (STM). Experimental results show that SVM achieved an accuracy of 93.33 percent, while Logistic Regression, Random Forest, and k-NN achieved 91.11 percent. In contrast, STM significantly outperformed these models, achieving a test accuracy of 96.67 percent and the highest cross-validation accuracy of 98.50 percent. Unlike conventional methods, STM leverages tensor representations to preserve spatio-temporal motion dynamics, resulting in robust classification across diverse activities. The proposed framework demonstrates strong potential for remote healthcare, elderly assistance, child activity monitoring, yoga feedback, and smart home wellness, offering a scalable solution for low-resource and rural healthcare settings.

While tabular foundation models have achieved remarkable success in classification and regression, adapting them to model time-to-event outcomes for survival analysis is non-trivial due to right-censoring, where data observations may end before the event occurs. We develop a classification-based framework that reformulates both static and dynamic survival analysis as a series of binary classification problems by discretizing event times. Censored observations are naturally handled as examples with missing labels at certain time points. This classification formulation enables existing tabular foundation models to perform survival analysis through in-context learning without explicit training. We prove that under standard censoring assumptions, minimizing our binary classification loss recovers the true survival probabilities as the training set size increases. We demonstrate through evaluation across $53$ real-world datasets that off-the-shelf tabular foundation models with this classification formulation outperform classical and deep learning baselines on average over multiple survival metrics.

Code generation is a core application of large language models (LLMs), yet LLMs still frequently fail on complex programming tasks. Given its success in mathematical reasoning, test-time scaling approaches such as Process Reward Model (PRM)-based Best-of-N selection offer a promising way to improve performance. However, existing PRMs remain ineffective for code generation due to the lack of meaningful step decomposition in code and the noise of Monte Carlo-estimated partial-solution correctness scores (rewards). To address these challenges, we propose FunPRM. FunPRM prompts LLMs to encourage modular code generation organized into functions, with functions treated as PRM reasoning steps. Furthermore, FunPRM introduces a novel meta-learning-based reward correction mechanism that leverages clean final-solution rewards obtained via a unit-test-based evaluation system to purify noisy partial-solution rewards. Experiments on LiveCodeBench and BigCodeBench demonstrate that FunPRM consistently outperforms existing test-time scaling methods across five base LLMs, notably achieving state-of-the-art performance on LiveCodeBench when combined with O4-mini. Furthermore, FunPRM produces code that is more readable and reusable for developers.

This paper revisits the role of positional embeddings (PEs) within vision transformers (ViTs) from a geometric perspective. We show that PEs are not mere token indices but effectively function as geometric priors that shape the spatial structure of the representation. We introduce token-level diagnostics that measure how multi-view geometric consistency in ViT representation depends on consitent PEs. Through extensive experiments on 14 foundation ViT models, we reveal how PEs influence multi-view geometry and spatial reasoning. Our findings clarify the role of PEs as a causal mechanism that governs spatial structure in ViT representations. Our code is provided in https://github.com/shijianjian/vit-geometry-probes

Test-time scaling for code generation commonly relies on Best-of-N selection, in which multiple candidate solutions are sampled from a base model, and the best one is selected by an LLM judge. However, training reliable LLM judges is challenging due to severe distribution shifts, including imbalances between easy and hard problems, mismatches between training tasks and evaluation benchmarks, and trajectory mismatch arising from training data generated by cheaper models whose behavior differs from that of inference-time models. We propose DAJ, a reasoning-based LLM judge trained with verifiable rewards under a bi-level data-reweighted learning framework. The proposed framework learns data-importance weights (either domain-level or instance-level) to optimize generalization performance on a held-out meta set aligned with target benchmarks. To the best of our knowledge, this is the first application of data reweighting to LLM-as-a-Judge training for test-time scaling. Our approach automatically emphasizes hard problems, in-distribution samples, and trajectory-aligned data, without relying on hand-crafted heuristics. Empirically, DAJ achieves state-of-the-art performance on LiveCodeBench and BigCodeBench, outperforming strong test-time scaling baselines as well as leading proprietary models.

Visual Question Answering (VQA) has become an important benchmark for assessing how large multimodal models (LMMs) interpret images. However, most VQA datasets focus on real-world images or simple diagrammatic analysis, with few focused on interpreting complex scientific charts. Indeed, many VQA datasets that analyze charts do not contain the underlying data behind those charts or assume a 1-to-1 correspondence between chart marks and underlying data. In reality, charts are transformations (i.e. analysis, simplification, modification) of data. This distinction introduces a reasoning challenge in VQA that the current datasets do not capture. In this paper, we argue for a dedicated VQA benchmark for scientific charts where there is no 1-to-1 correspondence between chart marks and underlying data. To do so, we survey existing VQA datasets and highlight limitations of the current field. We then generate synthetic histogram charts based on ground truth data, and ask both humans and a large reasoning model questions where precise answers depend on access to the underlying data. We release the open-source dataset, including figures, underlying data, distribution parameters used to generate the data, and bounding boxes for all figure marks and text for future research.