Ensuring safety and driving consistency is a significant challenge for autonomous vehicles operating in partially observed environments. This work introduces a consistent parallel trajectory optimization (CPTO) approach to enable safe and consistent driving in dense obstacle environments with perception uncertainties. Utilizing discrete-time barrier function theory, we develop a consensus safety barrier module that ensures reliable safety coverage within the spatiotemporal trajectory space across potential obstacle configurations. Following this, a bi-convex parallel trajectory optimization problem is derived that facilitates decomposition into a series of low-dimensional quadratic programming problems to accelerate computation. By leveraging the consensus alternating direction method of multipliers (ADMM) for parallel optimization, each generated candidate trajectory corresponds to a possible environment configuration while sharing a common consensus trajectory segment. This ensures driving safety and consistency when executing the consensus trajectory segment for the ego vehicle in real time. We validate our CPTO framework through extensive comparisons with state-of-the-art baselines across multiple driving tasks in partially observable environments. Our results demonstrate improved safety and consistency using both synthetic and real-world traffic datasets.

Generative diffusion models have emerged as a powerful tool for high-quality image synthesis, yet their iterative nature demands significant computational resources. This paper proposes an efficient time step sampling method based on an image spectral analysis of the diffusion process, aimed at optimizing the denoising process. Instead of the traditional uniform distribution-based time step sampling, we introduce a Beta distribution-like sampling technique that prioritizes critical steps in the early and late stages of the process. Our hypothesis is that certain steps exhibit significant changes in image content, while others contribute minimally. We validated our approach using Fourier transforms to measure frequency response changes at each step, revealing substantial low-frequency changes early on and high-frequency adjustments later. Experiments with ADM and Stable Diffusion demonstrated that our Beta Sampling method consistently outperforms uniform sampling, achieving better FID and IS scores, and offers competitive efficiency relative to state-of-the-art methods like AutoDiffusion. This work provides a practical framework for enhancing diffusion model efficiency by focusing computational resources on the most impactful steps, with potential for further optimization and broader application.

Bias and fairness risks in Large Language Models (LLMs) vary substantially across deployment contexts, yet existing approaches lack systematic guidance for selecting appropriate evaluation metrics. We present a decision framework that maps LLM use cases, characterized by a model and population of prompts, to relevant bias and fairness metrics based on task type, whether prompts contain protected attribute mentions, and stakeholder priorities. Our framework addresses toxicity, stereotyping, counterfactual unfairness, and allocational harms, and introduces novel metrics based on stereotype classifiers and counterfactual adaptations of text similarity measures. We release an open-source Python library, \texttt{langfair}, for practical adoption. Extensive experiments on use cases across five LLMs and five prompt populations demonstrate that fairness risks cannot be reliably assessed from benchmark performance alone: results on one prompt dataset likely overstate or understate risks for another, underscoring that fairness evaluation must be grounded in the specific deployment context.

Federated Learning (FL) is a distributed and privacy-preserving machine learning paradigm that coordinates multiple clients to train a model while keeping the raw data localized. However, this traditional FL poses some challenges, including privacy risks, data heterogeneity, communication bottlenecks, and system heterogeneity issues. To tackle these challenges, knowledge distillation (KD) has been widely applied in FL since 2020. KD is a validated and efficacious model compression and enhancement algorithm. The core concept of KD involves facilitating knowledge transfer between models by exchanging logits at intermediate or output layers. These properties make KD an excellent solution for the long-lasting challenges in FL. Up to now, there have been few reviews that summarize and analyze the current trend and methods for how KD can be applied in FL efficiently. This article aims to provide a comprehensive survey of KD-based FL, focusing on addressing the above challenges. First, we provide an overview of KD-based FL, including its motivation, basics, taxonomy, and a comparison with traditional FL and where KD should execute. We also analyze the critical factors in KD-based FL in the appendix, including teachers, knowledge, data, and methods. We discuss how KD can address the challenges in FL, including privacy protection, data heterogeneity, communication efficiency, and personalization. Finally, we discuss the challenges facing KD-based FL algorithms and future research directions. We hope this survey can provide insights and guidance for researchers and practitioners in the FL area.

Fine-tuning large language models (LLMs) is crucial for improving their performance on downstream tasks, but full-parameter fine-tuning (Full-FT) is computationally expensive and memory-intensive. Parameter-efficient fine-tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), address this by optimizing only a small subset of parameters. However, LoRA may underperform Full-FT in certain scenarios due to the intrinsic limitations of its low-rank gradients. In this work, we reveal an asymmetric, collapsible structure in LoRA's update: the low-rank modification to W can be reformulated as a single-layer linear regression, implying that one of the LoRA factors can be frozen without sacrificing expressivity. Leveraging this insight, we introduce LoRA-FA, which freezes the projection-down matrix A and trains only the projection-up matrix B. We further close the gap to Full-FT by deriving closed-form gradient corrections that minimize the discrepancy between the induced low-rank gradient and the full gradient. Through extensive experiments on diverse benchmarks, including GLUE, GSM8K, MT-Bench, and HumanEval, we demonstrate that LoRA-FA consistently achieves comparable performance to existing PEFT methods and Full-FT. Experiments on system efficiency show that LoRA-FA significantly reduces activation memory consumption and computational workload in fine-tuning. Our code is available at https://github.com/huggingface/peft.

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient numerical methods that can resolve the dependence of the PDE on the unbounded variable over at least several orders of magnitude. We propose a solution to such problems by combining two classes of numerical methods: (i) adaptive spectral methods and (ii) physics-informed neural networks (PINNs). The numerical approach that we develop takes advantage of the ability of physics-informed neural networks to easily implement high-order numerical schemes to efficiently solve PDEs and extrapolate numerical solutions at any point in space and time. We then show how recently introduced adaptive techniques for spectral methods can be integrated into PINN-based PDE solvers to obtain numerical solutions of unbounded domain problems that cannot be efficiently approximated by standard PINNs. Through a number of examples, we demonstrate the advantages of the proposed spectrally adapted PINNs in solving PDEs and estimating model parameters from noisy observations in unbounded domains.

Low-rank factorization is a standard way to make structured optimization problems in machine learning more tractable by replacing matrix variables with compact factors. For positive semidefinite (PSD) variables, the symmetric Burer--Monteiro factorization (sBMF) writes $Z=XX^\top$ with a single low-rank factor $X$. A recent asymmetric alternative (aBMF) writes $Z=XY^\top$ and adds a quadratic penalty $(γ/2)\|X-Y\|_F^2$ to encourage symmetry. This split is attractive because it yields a biconvex objective with alternating convex subproblems, but its practical value depends strongly on how the penalty parameter $γ$ is chosen. We study a unified regularized aBMF framework and derive an explicit lower bound on $γ$ that guarantees exactness: under mild assumptions, any $γ$ above this threshold makes aBMF and sBMF share the same critical points. This gives a principled way to use the asymmetric formulation without altering the critical-point structure of the symmetric problem. In particular, it answers the open question of whether an exact penalty exists for asymmetric relaxation.

We extend Probability Bracket Notation (PBN), inspired by the Dirac notation in quantum mechanics, to multivariable probability systems and static Bayesian networks (BNs). By defining probability distributions and conditional expectations in a unified, basis-independent algebraic form, PBN provides a systematic way to represent and manipulate dependencies among random variables. Using the well-known Student BN as an illustrative probabilistic graphical model, we demonstrate prediction, bottom-up and top-down inference, and expectation calculations within the PBN framework. We show that, for a large N-node binary BN, after a one-time preprocessing, inference along a d-separable chain with k intermediate nodes requires O(k2^k) operations, compared to O(N2^N) for direct computation from the full joint distribution. We further extend PBN to networks with continuous variables, including linear Gaussian models, and introduce a hybrid Healthcare BN that combines discrete and continuous variables. In this model, discrete-display nodes serve as proxies for continuous parents, enabling user-specific predictions. Overall, PBN provides an operator-based framework that unifies representation and computation, with potential applications in education, data analytics, and machine learning.

Reinforcement learning with verifiable rewards (RLVR) generates hundreds of thousands of tokens per training step, with rollout generation dominating the computational cost. The overall token budget can be controlled along two main dimensions: (i) deciding which prompts to allocate rollouts to, and (ii) deciding how long each rollout should be. Prior work has generally controlled only one of these dimensions at a time. We show that jointly tuning both decisions under a shared compute budget improves both reasoning quality and wall-clock training time. We instantiate this view as \textbf{DU}al-controlled tok\textbf{E}n alloca\textbf{T}ion (DUET), a computationally efficient layer over GRPO that uses a lightweight pre-rollout surrogate of prompt informativeness to set how many rollouts each prompt receives, and a marker-gated abort rule with importance reweighting to set when to stop them. On Qwen3-1.7B trained on MATH, DUET outperforms full-budget GRPO and the other three budget-aware baseline methods. DUET's advantage further generalizes to other benchmarks across math and coding, and is on par with the best baseline on the scientific Q\&A domain, while also achieving a $1.62\times$ wall-clock speedup. More notably, using only 50\% of the token budget, DUET still outperforms all baseline methods at their full budget, achieving an even higher $2.51\times$ speedup over full-budget GRPO. We verify the high performance of DUET on other backbone LLMs, including Qwen3-4B and Llama-3.2-3B-Instruct. Notably, the gap between DUET and the strongest baseline \emph{widens} as the budget tightens, contrary to the usual pattern in which efficient methods trade off quality as compute decreases. More broadly, these results suggest that DUET budget-aware control strategies are valuable not only for accelerating training, but also for improving the quality of the learning signal.

Adversarial purification with diffusion models seeks to project adversarial examples back toward the data manifold, but balancing semantic preservation and robustness against adaptive attacks remains challenging. Recent work shows that standard diffusion purification can fail under adaptive evaluation, while test-time score-based optimization is more resilient. Existing optimization defenses, however, typically rely on a single diffusion noise regime or treat timesteps uniformly, overlooking the distinct roles of coarse and fine denoising scales. We propose Temporal Adversarial Rectification Optimization (TARO), an inference-time purification method that builds a temporally guided score prior from multiple denoising views along the diffusion trajectory. TARO forms a coarse-to-fine residual target: high-noise experts provide globally smoothed structure with reduced adversarial sensitivity, while low-noise experts restore image-specific, class-relevant details. A guidance strength controls this temporal correction, allowing TARO to balance robust global rectification with semantic preservation. Empirically, TARO improves robust accuracy across datasets and adaptive threat models in a zero-shot setting, while remaining compatible with complementary adversarial-likelihood objectives for further robustness gains.

Existing benchmarks for legal AI focus primarily on tasks where LLMs must produce legal arguments or documents, yet the capacity to \emph{judge} such arguments -- weighing competing claims, applying doctrine to facts, and rendering reasoned decisions -- is arguably as fundamental to a well-functioning legal system as advocacy itself. We introduce Magis-Bench, a benchmark for evaluating LLMs on magistrate-level writing tasks derived from recent Brazilian competitive examinations for judicial positions. Magis-Bench comprises 74 questions from eight examinations conducted between 2023 and 2025, including discursive legal analysis questions with multi-turn structure and practical exercises requiring the composition of complete civil and criminal judicial sentences. We evaluate 23 state-of-the-art LLMs using an LLM-as-a-judge methodology with four independent frontier models as evaluators. Our results show strong inter-judge agreement (Kendall's $W = 0.984$; pairwise Kendall's $τ\ge 0.897$), with Google's Gemini-3-Pro-Preview achieving the highest average score (6.97/10), followed by Gemini-3-Flash-Preview (6.67) and Claude-4.5-Opus (6.46). Even the best-performing models score below 70\% of the maximum, indicating that judicial-level legal reasoning and writing remain challenging for current LLMs. We release the complete benchmark, model outputs, and evaluation code to support further research on legal AI capabilities.

We introduce a meshfree exterior calculus (MEEC) for learning structure-preserving descriptions of physics on point clouds, and use it to build MEEC-Net, a data-efficient surrogate that transfers across resolutions, geometries, and physical parameters. MEEC equips an $\varepsilon$-ball graph with virtual node and edge measures via a single sparse Schur complement solve; the resulting complex satisfies discrete conservation exactly, is end-to-end differentiable in the point positions, and exposes a direct geometry-to-physics link without the mesh-generation step required by conventional structure-preserving discretizations. MEEC-Net learns unknown physics as a shared edge-wise flux law in an SO($d$)-invariant local frame, so the same kernel produces compatible fluxes on any point cloud whose features lie in the training range. We prove a solution-error bound that splits into discretization and kernel-approximation terms which is independent of problem geometry, explaining the observed transfer from very few examples. We show that single-solution training transfers to unseen geometries, boundary conditions, and physical parameters. On five canonical PDE benchmarks MEEC-Net achieves 1-2 orders of magnitude lower out-of-distribution error than baseline neural-operator approaches. On the SimJEB structural-bracket benchmark it achieves competitive error while using substantially fewer training geometries.

Calibration measures whether a model's predicted confidence aligns with its empirical accuracy, and is central to the reliable deployment of large language models (LLMs) in high-stakes domains such as medicine and law. While much recent work focuses on improving LLM calibration, the equally important question of how to evaluate it in realistic settings remains underdeveloped. Open-ended question answering (QA), the most common deployment setting for modern LLMs, is where existing evaluation methods fall short: logit-based metrics need restricted output formats and internal probabilities; verbalized confidence is self-reported and often overconfident; and sampling-based methods rely on task-specific extraction rules without a clear finite-sample target. We introduce Sem-ECE (Semantic-Sampling Expected Calibration Error), a calibration evaluation framework for open-ended QA that samples answers from the model, groups them into semantic classes, and uses the resulting frequencies as confidence. We study two estimators within this framework: Sem$_1$-ECE, the same-sample self-consistency score, and Sem$_2$-ECE, a held-out variant that separates answer selection from confidence evaluation. We prove both are asymptotically unbiased, and further show that they agree on easy questions but diverge on hard ones with Sem$_2$ achieving strictly smaller calibration error, so their gap also serves as a diagnostic for question difficulty. Experiments on three open-ended QA benchmarks across five leading commercial LLMs match our theoretical predictions and show that Sem-ECE outperforms verbalized confidence and existing sampling-based methods, while complementing logit-based evaluation when internal probabilities are unavailable.

Self-play red team is an established approach to improving AI safety in which different instances of the same model play attacker and defender roles in a zero-sum game, i.e., where the attacker tries to jailbreak the defender; if self-play converges to a Nash equilibrium, the model is guaranteed to respond safely within the settings of the game. Although the parameter sharing enforced by the use of the same model for the two roles improves stability and performance, it introduces fundamental theoretical and architectural limitations. We show that the set of Nash equilibria that can be reached corresponds to a broad class of behaviours that includes trivial always refuse strategies and oracle-like defenders, thus limiting practical applicability. We then show that when attacker and defender share and update the same base model, the dynamics collapse to self-consistency, so that attacks do not enforce adversarial pressure on the defender. In response, we propose Anchored Bipolicy Self-Play, which trains distinct role-specific LoRA adapters on top of a frozen base model, thereby maintaining stable optimisation while preserving adversarial pressure through explicit role separation. In relation to standard self-play, we show up to 100x greater parameter efficiency than finetuning and consistent improvements in safety compared to self-play fine-tuned models. We evaluate on Qwen2.5-{3B, 7B,14B}-IT models across widely used safety benchmarks, showing improved robustness without loss of reasoning ability. Cross-play experiments further show that our attacker and defender models are superior to self-play in terms of adversarial defence and safety.

Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability measures over probability measures, introducing a Wasserstein-on-Wasserstein (WoW) formulation. Leveraging the nested Wasserstein geometry, we show that measures over transport plans naturally induce velocity fields that realize metameasure flows. This yields a principled generalization of Wasserstein flow matching via coupled outer and inner transport plans. To address the substantial computational cost of WoW transport, we propose scalable approximations based on sliced and linear Wasserstein distances, enabling efficient training while promoting numerically stable, near-straight trajectories. Our framework unifies and extends existing approaches to point cloud and set generation, providing a practical and theoretically grounded method for generative modelling in WoW spaces.

We present a data-adaptive method for parameter-efficient fine-tuning of large neural networks. Standard low-rank adaptation methods improve efficiency by restricting each layer update to a fixed low-rank form, but this static parameterization can be too rigid when the appropriate correction depends on the input and on the evolving depth-wise computation of the network. Our approach replaces a purely layer-local adapter with a shared queryable memory of low-rank update atoms. For each block of layers, the model forms a query from the current low-rank state and a running summary of previous blocks, uses this query to retrieve a content-dependent combination of shared update components via attention, and applies the resulting routed operator within the low-rank bottleneck. In this way, the method retains the efficiency and scalability of low-rank adaptation while allowing the effective update to vary across inputs and to share reusable structure across layers. The resulting architecture provides a principled middle ground between static LoRA-style updates and fully generated parameter updates: it remains compact and parameter-efficient while supporting dynamic, context-sensitive adaptation. Further, we incorporate instruction-regularization by augmenting routing logits with a language-induced prior over update atoms, thereby biasing the selection of low-rank transformations toward semantically relevant directions without generating unconstrained parameter updates. Experiments on noisy non-linear regression tasks and LLM fine-tuning suggest that this queryable update-memory formulation can improve final test performance and training stability compared to standard low-rank adaptation, while using a comparable number of trainable parameters.

Visual Document Retrieval (VDR) models mostly rely on late interaction architectures, in which documents are represented by a set of local patch embeddings and then matched against query tokens. While efficient, this architecture prioritizes local similarity over global layout structure of documents to estimate relevancy between documents and query. In practice, this leads to errors as relevance originates from layout structure of documents with heterogeneous layouts combining figures, tables, and text. We make document layout learnable without changing inference. We propose a multimodal encoder that augments local patch representations with a global layout embedding, trained via textual descriptions encoding document layout information. Across four ViDoRe-v2 datasets, our model improves over the strongest architecturally comparable ColPali/ColQwen baseline by +2.4 nDCG@5 and +2.3 MAP@5, with statistically significant per-dataset gains over ColQwen.

Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while the adversarial optimization underlying robustness makes robust evaluation computationally demanding. To address these difficulties, we consider the natural small-ambiguity regime under Kullback--Leibler ambiguity sets and propose an approximate DRRL framework based on a first-order expansion of the relevant robust functional. This yields an approximate robust Bellman equation that removes the adversarial optimization while remaining first-order accurate in the ambiguity radius. To learn the fixed point of this approximate equation, we propose Mean-Variance Stochastic Approximation (MVSA), a model-free algorithm that uses only one-sample updates. This is achieved via a lifted stochastic approximation dynamics and a two-time-scale design. We then prove convergence and a central limit theorem for MVSA: its main iterate satisfies a central limit theorem at the canonical $n^{-1/2}$ scale, with explicitly characterized asymptotic covariances. Finally, we validate our theoretical findings with a numerical experiment.

Jurisprudence, the study of how judges should properly decide cases, and alignment, the science of getting AI models to conform to human values, share a fundamental structure. These seemingly distant fields both seek to predict and shape how decisions by powerful actors, in one case judges and in the other increasingly powerful artificial intelligences, will be made in the unknown future. And they use similar tools of the specification and interpretation of language to try to accomplish those goals. The great debates of jurisprudence, about what the law is and what it should be, can provide insight into alignment, and lessons from what does and does not work in alignment can help make progress in jurisprudence. This essay puts the two fields directly into conversation. Drawing on leading accounts of jurisprudence, particularly Dworkin's principle-oriented interpretivism and Sunstein's positivist account of law as analogical reasoning, and on cutting-edge alignment approaches, namely Constitutional AI and case-based reasoning, it illustrates the value of a more sophisticated legally-inspired approach to the interplay of rules and cases in finetuning alignment and points to ways that AI can provide a better understanding of how the law works and how it can be improved by the introduction of AI. AI systems and the law should operate to empower people to act in the world, helping to expand their capabilities and the extent to which they are able to achieve their goals. As AI continues to improve in capacity, and as the constraints that legal theory places on human judges seem be coming undone, the conversation between these two fields will become increasingly essential and may help point to a better version of both.

Since the advent of Large Language Models (LLMs), a significant area of research has focused on their intrinsic biases, particularly in political discourse. This study investigates a different but related concept, "political plasticity", which is defined as the capacity of models to adapt their responses based on the user supplied context. To analyze this, a testing framework was developed using an expanded corpus of 200 politically-oriented questions across economic and personal freedom axes, based on a prior framework by Lester (1996). The study explored several methods to induce political bias, including simplified and topic-based system prompts, as well as user prompts with few-shot examples. The results show that while system prompts were largely ineffective, user prompts successfully elicited significant ideological shifts, particularly along the Economic Freedom axis in larger and newer models. Through a validation experiment, we examined whether models answer questionnaires by recognizing the underlying question format. Inverting the sense of the questions revealed unexpected, counter-intuitive shifts in most models, suggesting potential data leakage. Finally, we also analyzed how model plasticity varies when the experiment is conducted in different languages. The results reveal subtle yet notable shifts across each of the analyzed languages. Overall, our results indicate that small and older LLMs exhibit limited or unstable political plasticity, whereas newer frontier models display reliable, expected adaptability.

Multimodal Large Language Models (MLLMs) have made rapid progress in single-video understanding, yet their ability to reason across multiple independent video streams remains poorly understood. Existing multi-video benchmarks rely largely on human-annotated real-world footage, limiting the precision of spatial, temporal, and physical ground truth and making it difficult to diagnose model failures. We introduce SYNCR, a controlled synthetic benchmark for cross-video reasoning with programmatically verified grounding. Built using Habitat, Kubric, and CLEVRER simulator engines, SYNCR contains 8,163 multi-video question-answer pairs grounded in 9,650 unique videos. It evaluates MLLMs across eight tasks spanning four diagnostic pillars: Temporal Alignment, Spatial Tracking, Comparative Reasoning, and Holistic Synthesis. Our zero-shot evaluation of leading open- and closed-weight MLLMs reveals a substantial gap between current models and humans: the best model achieves only 52.5% average accuracy, compared to an 89.5% human baseline. Models perform relatively well on temporal ordering but struggle with precise physical and spatial reasoning, with the best model reaching only 26.0% accuracy on Kinematic Comparison. We further find that parameter scaling and reasoning-specialized post-training improve temporal alignment capabilities, but do not reliably address fine-grained physical tracking or global spatial synthesis. Finally, an exploratory sim-to-real correlation analysis suggests that several SYNCR tasks track model-level trends on real-world multi-video benchmarks, while also exposing reasoning capabilities underrepresented by existing evaluations. Code available at https://github.com/SaraGhazanfari/SYNCR.

Conversational AI has a fundamental flaw as a knowledge interface: sycophantic chatbots induce epistemic entrenchment and delusional belief spirals even in rational agents. We propose the problem does not stem from the AI model, rooted instead in a systemic consequence of the paradigm shift from user-driven knowledge search to users and agents engaged in strategic, repeated-play communication. We formalize the problem as a Crawford-Sobel cheap talk game, where costless user signals induce a pooling equilibrium. Agents optimized for user satisfaction produce sycophantic strategies that provide identical reinforcement across user types with opposite epistemic incentives: exploratory ``Growth-seekers'' ($θ_G$) and confirmatory ``Validation-seekers'' ($θ_V$). Under repeated play, this identification failure creates a coordination trap -- analogous to a Prisoner's Dilemma -- where locally rational feedback loops drive users toward pathologically certain false beliefs. We propose an inference-time mechanism design intervention called an Epistemic Mediator that breaks this pooling equilibrium by introducing a costly signal (epistemic friction), forcing type revelation based on users' asymmetric cognitive costs for processing resistance. A key contribution is Belief Versioning, a git-inspired epistemic meta-memory system that stores healthy beliefs and rollbacks when validation-seeking resistance is detected. In simulation, this intervention achieves a separating equilibrium achieving a $48\times$ differential in spiral rates while passing a learning preservation criterion), evidence that epistemic safety in AI is fundamentally a problem of strategic information environment design rather than simple model alignment.

Physics-informed neural networks (PINNs) provide a flexible framework for solving forward and inverse problems governed by partial differential equations (PDEs), but standard PINN training typically relies on soft penalty formulations that combine PDE residuals, data mismatch, and initial/boundary conditions using manually chosen weights. This often leads to ill-conditioning, sensitivity to loss weights, and poor constraint satisfaction. In this work, we reformulate PINN training as an equality-constrained optimization problem and propose a novel Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN (AdamFLIP). The key idea is to view the constraint residuals as the output of a controlled dynamical system and to compute the Lagrange multiplier as a feedback input that locally drives these residuals toward stable linear contraction dynamics. AdamFLIP then applies Adam-style first- and second-moment adaptation to the resulting feedback-linearized Lagrangian gradient, combining principled constraint handling with the scalability and robustness of adaptive neural-network optimization. We test AdamFLIP on a range of benchmark forward and inverse PDE problem, and it consistently outperforms both the standard soft-constrained PINN and state-of-the-art constrained optimizers. Specifically, on the Navier--Stokes equations benchmark, AdamFLIP \textbf{reduces relative $L_2$ error by more than two thirds} for the predicted solution compared to the next best method. Our AdamFLIP framework provides an effective and computationally scalable hard constraint optimization method for PINN training.

Explaining how to get from A to B can be challenging. It requires mentally simulating what the listener will do based on what they are told. To capture this process, we propose a computational model that converts utterances into action plans: a large language model translates an explanation into program-like guidance (a policy prior and value map), and a planning agent executes it under partial observability. We score explanations by the efficiency and reliability of the resulting paths, penalizing replanning. Across four preregistered experiments, we collect a corpus of 1,200 explanations over 24 maps, elicit helpfulness judgments, measure baseline navigation, and test behavior with explanations of differing quality. Higher-scored explanations are judged more helpful and improve navigation: participants with explanations outperform those without, and high-scoring explanations help more than low-scoring ones. Together, these results show procedural explanation as utility-guided communication shaped by how language can be grounded into action under uncertainty.

How do LLMs learn in-context? Is it by pattern-matching recent tokens, or by inferring latent structure? We probe this question using a toy graph random-walk across two competing graph structures. This task's answer is, in principle, decidable: either the model tracks global topology, or it copies local transitions. We present two lines of evidence that neither account alone is sufficient. First, reconstructing the internal representation structure via PCA reveals that at intermediate mixture ratios, both graph topologies are encoded in orthogonal principal subspaces simultaneously. This pattern is difficult to reconcile with purely local transition copying. Second, residual-stream activation patching and graph-difference steering causally intervene on this graph-family signal: late-layer patching almost fully transfers the clean graph preference, while linear steering moves predictions in the intended direction and fails under norm-matched and label-shuffled controls. Taken together, our findings are most consistent with a dual-mechanism account in which genuine structure inference and induction circuits operate in parallel.

This work investigates the use of large language models (LLMs) for tasks in smart cities. The core idea is to leverage remote sensing imagery to characterize the built environment, including design suggestions, constructability assessment, landuse patterns, and risk identification. We examine remote sensing imagery at multiple spatial scales as inputs for multimodal language modeling and evaluate their effects on built-environment-related reasoning. In addition, we compare state-of-the-art LLMs, including InternVL and Qwen, in terms of accuracy and reliability when generating built environment recommendations. The results demonstrate the potential of integrating remote sensing imagery with large language models to assist smart cities and decision-making.

Tool-augmented language models can extend small language models with external executable skills, but scaling the tool library creates a coupled challenge: the library must evolve with the planner as new reusable subroutines emerge, while retrieval from the growing library must remain within a fixed context budget. Existing tool-use and skill-library methods typically treat tools as flat or text-indexed memories, causing prompt cost to grow with library size and obscuring the typed, compositional structure of executable code. We propose CoCoDA, a framework that co-evolves the planner and tool library through a single code-native structure: a compositional code DAG. Nodes are primitive or composite tools, edges encode invocation dependencies, and each node stores a typed signature, description, pre/post-condition specification, and worked examples. At inference time, Typed DAG Retrieval prunes candidates by symbolic signature unification, ranks survivors by descriptions, filters them by behavioral specifications, and disambiguates with examples, keeping expensive context materialization on progressively smaller candidate sets. At training time, successful trajectories are folded into validated composite tools, while the planner is updated with a DAG-induced reward that credits composites by their primitive expansion size. We provide theoretical results showing retrieval cost reduction, sublinear retrieval time, compositional advantage under the shaped reward, monotone co-evolution under conservative updates, and DAG well-formedness. Across mathematical reasoning, tabular analysis, and code task benchmarks, CoCoDA enables an 8B student to match or exceed a 32B teacher on GSM8K and MATH and consistently improves over strong tool-use and library-learning baselines.

The increasing complexity of modern computational environments often burdens researchers with infrastructure management, authentication protocols, and container deployments. We present Sci-Orchestra, a layered orchestration framework designed to fully automate experimental workflows, allowing scientists to prioritize scientific discovery over backend operations. By abstracting execution through an API-driven interface, the system assumes responsibility for secure authentication, resource management, and scalable deployment across diverse high-performance computing environments using Kubernetes architectures. A key innovation of Sci-Orchestra is its autonomous marketplace, which serves as a catalyst for cross-institutional collaboration. Through an intuitive user interface, researchers can rapidly deploy and share specialized services via simple selections, eliminating the need for complex installations and technical setups. This modular infrastructure is specifically designed to facilitate industry partnerships as it provides a secure execution environment and allows external collaborators to test and validate proprietary tools without the need for source-code exchange. This ``black-box'' interoperability protects intellectual property while enabling seamless integration into broader scientific pipelines, ultimately accelerating the transition from laboratory prototypes to industrial-scale applications.

Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant source of error. Existing non-asymptotic analyses provide convergence guarantees, but are typically too loose and too insensitive to diffusion parameters to guide practical design: broad families of schedules receive the same rates, which depend on coarse worst-case quantities such as the dimension or the drift Lipschitz constant. We take a less ambitious but more informative route. In the exact-score setting, we derive first-order asymptotic expansions of the Euler-Maruyama weak and Fréchet discretization errors. These formulas hold for general smooth reverse diffusions and become fully explicit under Gaussian data. They show how discretization error adapts to the geometry of the data through the covariance spectrum, and how this geometry interacts with key diffusion parameters, including the diffusion schedules and the diffusion-term coefficient. This yields tractable objectives for geometry-aware parameter optimization. Finally, we show that the qualitative predictions of the Gaussian formulas remain robust across diffusion sampling problems with different geometries, including image generation on different datasets and image posterior sampling.

Sequence prediction methods for dynamical systems with long memory, i.e. marginally stable systems, typically achieve regret that grows polynomially with the hidden dimension of the underlying generative model. Universal Sequence Preconditioning (USP) is a method that compresses any sequence which comes from a linear dynamical system into a "preconditioned" sequence which requires exponentially shorter memory for accurate prediction. However, the preconditioned sequence yields exponentially larger diameters and gradients, hindering USP from unlocking optimal regret bounds. Inspired by the minimum description length principle, we show that the Vovk-Azoury-Warmuth (VAW) algorithm is naturally matched to the USP regime. Indeed, it takes advantage of the memory compression while remaining robust to the exponential explosion of the diameter. We prove that combining USP with VAW achieves astoundingly strong results: for any marginally-stable linear dynamical system, this algorithm achieves polylogarithmic regret $O \left( \log^3 T \right)$ even in the presence of asymmetric hidden transition matrices. Finally, we extend the applicability of USP beyond bounded-spectrum systems by providing new complex-analytic bounds on Chebyshev polynomials, allowing for systems with constant complex arguments.