Science & Mathematics

Masked diffusion language models have emerged as an alternative to autoregressive models, enabling parallel token generation. However, standard masked diffusion language models use a shared noise schedule across positions without explicitly encoding which positions should be resolved first. Many tasks exhibit a natural priority among positions: document titles and section headings can guide the generation of body text, while Sudoku cells determined directly from the initial clues can help resolve more difficult cells. To incorporate this notion of priority (or hierarchy) among token positions, we introduce the Hierarchical Masked Diffusion Language Model (HMDLM), which augments each token position with a hierarchy level available as part of the training data, and requires zero or minimal additional annotations. It factors generation into two passes: the first predicts a hierarchy distribution over masked positions, the second predicts token distributions conditioned on it. Giving each hierarchy level its own noise schedule induces a soft, controllable preference for revealing higher-priority positions earlier while keeping decoding fully parallel. Our formulation is mathematically grounded, and we re-derive the forward and reverse processes and the NELBO for this factorization. Our evaluation shows that for the task of language generation on LM1B, HMDLM reduces perplexity by more than 1.5 points over Anchored Diffusion Language Model (ADLM), a recently proposed strong diffusion baseline; on WikiHow, we see a drop in perplexity of up to 4.4 pts on ADLM and up to 7 pts against MDLM. An LLM judge on WikiHow prefers HMDLM generations (the two variants combined) more than $2\times$ as often as the baseline. On the task of solving Sudoku puzzles requiring multi-step reasoning, it improves solution accuracy by up to $8.6\%$ absolute points over existing diffusion baselines.

Large audio-language models (LALMs) understand music, yet struggle to locate a described moment in time. We ask whether this reflects missing temporal information or a bottleneck in how the time span is extracted. Using a paired-query probe built from Slakh2100 stem activations, we attach a state query (e.g., ``only piano and bass are playing'') and a change query (e.g., ``the guitar drops out, leaving piano and bass'') to the same span and vary how much preceding audio the model is shown. Across frozen LALMs, three ways of extracting the span ask different questions: full-track prompting asking whether the model can say when; windowed yes/no scoring asking whether it verifies the moment when handed the segment, and whether it needs what came before; attention asking whether it can find the moment on its own. State queries score above baseline without context, while change queries improve with preceding context in most short-segment models; 30s padded encoders show no comparable recovery. Prompting and attention expose almost none of this. Prompting failures thus understate what LALMs can verify, though not what they can locate, by an amount set by query type and encoder.

As-built BIM reconstruction from point clouds demands semantic, volumetric, parametric, and editable building components, beyond 2D layouts or planar abstractions. Yet existing scan-to-BIM pipelines often rely on handcrafted rules, heuristic optimization, or manual correction, while learning-based methods fall short of recovering wall thickness, opening geometry, and component-level BIM structure. We introduce CRAB, a BIM-ready cuboid reconstruction framework that encodes walls, doors, windows, beams, and columns as compact architectural cuboids with IFC-compatible semantics and parameters. CRAB bridges point clouds and editable BIM by combining ProposalNet, which predicts coarse component cuboids, with AssemblyNet, a relation-aware Flow Matching model that refines geometry, predicts structural relationships, and enables automatic structural correction and human-guided editing. To address limited cuboid-level supervision, we extend Structured3D with component-wise cuboid annotations and construct cuboid-based procedural scenes. Experiments show CRAB surpasses floor plan and plane-based alternatives in component completeness, geometric accuracy, and generalization. For interior wall thickness estimation, CRAB achieves a mean error of 2.80 cm, with 79.50% of matched walls within 3 cm. The project page is available at https://vcc.tech/research/2026/CRAB.

We study group distributionally robust optimization (GDRO) over decentralized networks, where workers collaborate to learn robust models by minimizing the maximum local risk. Existing methods optimize only dual-regularized surrogates and establish guarantees for a globally averaged model that is not available to workers. In this paper, we directly optimize the original GDRO objective and establish guarantees for local models in semi-decentralized (SemiDec) and fully decentralized (Dec) settings. A key difficulty is that applying the primal-dual decomposition from centralized GDRO yields worker-dependent losses whose evaluation requires unavailable cross-worker information. To address this challenge, we develop a novel error decomposition that recasts decentralized GDRO as (i) a decentralized online convex optimization (D-OCO) problem and a prediction-with-expert-advice problem in SemiDec, and as (ii) two coupled D-OCO problems in Dec, with discrepancy terms capturing inconsistencies among local decisions. By isolating consensus errors in analysis, we develop modular frameworks that support different consensus routines. We then establish the \emph{first} per-worker convergence guarantees for optimizing the original GDRO objective over decentralized networks. Instantiations with accelerated gossip and Choco-gossip achieve an $O(\sqrt{(\log m)/T})$ convergence rate over $T$ update rounds, while experiments demonstrate improved worst-worker performance over baselines.

The main challenge in applying deep neural networks to real-world scenarios lies in distributional discrepancies between training and test datasets, often caused by variations in data acquisition conditions. Assessing the performance of pre-trained models without labels is crucial for safety, but this is complicated by deep models' overly optimistic probabilistic outputs, often exacerbated by class imbalances, leading to unreliable predictions. To address these issues, we introduce MOVAL, a novel MOdel eVALuation tool that estimates performance using unlabeled test data. MOVAL incorporates class-wise confidence calibration to adjust model outputs, allowing for the estimation of metrics beyond accuracy and mitigating the detrimental effects of class imbalance on confidence calibration. Additionally, we propose an ensemble approach that combines multiple calibrated confidence scores for a more robust solution. We validate MOVAL on natural and medical image datasets with various acquisition shifts, covering tasks from classification to segmentation. It achieves state-of-the-art results across evaluation metrics such as accuracy, F1-Score, AUC, and more. Furthermore, we demonstrate that MOVAL provides accurate performance estimations at the class, instance, and pixel levels, ensuring the transparent and safe deployment of machine learning models. We provide MOVAL as a deployment tool for monitoring and estimating performance under a range of domain shifts.

Large pretrained robot foundation models provide strong priors for manipulation, yet adapting them to target tasks with offline teleoperated demonstrations often fails to cover the contact-rich, recovery, and precision-critical states encountered during deployment. Existing methods mitigate this issue by augmenting offline demonstrations with human-in-the-loop data or online reinforcement learning. Despite this, offline post-training adapts slowly because it cannot immediately absorb deployment experience, while online RL typically relies on value functions or auxiliary actor-critic models, increasing both training complexity and instability. We present TIDE (Training In DEployment), a human-in-the-loop online post-training system. TIDE introduces a provenance-conditioned supervised learning framework that updates the policy online from human interventions and policy-generated rollouts collected during deployment, without a learned critic, reward model, or action scorer. Across four real-world bimanual manipulation tasks, TIDE improves milestone-normalized task progress and binary full-task completion over the warm-start policy and matched additional offline demonstrations, and performs comparably to the fixed-policy collection baseline while making updated checkpoints available during deployment. Each task-specific online post-training session, from the start of deployment rollouts until the final checkpoint is available, completes in less than one hour while learning and checkpoint handling run asynchronously.

Radar heart sounds capture cardiac mechanical activity without contact, while echocardiography characterizes ventricular and valvular function. Paired measurements connect these signals to structural heart disease, yet such data remain sparsely represented in public resources. Here we present 537 radar heart-sound recordings paired with one echocardiographic report for each of 162 patients. The cohort covers three overlapping phenotypes: left ventricular ejection fraction (LVEF) below 50%, regional wall-motion abnormality and at least moderate valvular regurgitation, present in 38, 43 and 39 patients, respectively. Original complex signals, processed radar heart sounds and temporal quality segmentation support signal-to-phenotype analysis. Technical validation retains 95.93% of signal duration and confirms reproducible waveform reconstruction. Patient-level five-fold evaluation achieves a mean outer-test AUROC of $0.770\pm0.138$ for reduced LVEF, identifying mechanical information associated with ventricular systolic dysfunction. This resource supports research linking non-contact cardiac mechanical signals to echocardiographic structural and functional phenotypes.

Retrieval-augmented generation (RAG) systems face security, privacy, and copyright risks including content leakage, source reconstruction, unauthorized access, data poisoning, and prompt injection. Yet RAG protection studies use incompatible evaluation metrics, datasets, and threat models. We present a systematic survey and human-coded evidence map of 118 full-text-confirmed RAG defense papers, organized by measured endpoint rather than claimed goal or defense mechanism. Our seven-family taxonomy covers content disclosure, formal privacy proxies, access control and suppression, corpus-use detection, and pipeline integrity and attribution. Thirty-two annotators double-coded the papers kappa=0.867. The survey identifies three gaps. First, retrieval reranking and context rewriting each span five or six endpoint families, so mechanisms do not identify protection outcomes. Second, only 17.8% of studies use content disclosure or reconstruction as their primary endpoint; under the frozen copyright/ownership relation label, 73.3% of records have corpus-use detection as their primary endpoint, and none have an emitted-expression primary endpoint. Third, most evaluations use general-purpose question-answering datasets and non-adaptive attacks rather than sensitive data and adaptive, multi-turn extraction. Our controlled RAG testbed shows that preventing verbatim copying does not prevent private-fact recovery: a normalized 8-gram guard reduces 20-token copying to 0.0%, but a three-query adaptive attacker recovers 48.3% of hidden facts on Qwen3-8B. We release the taxonomy, dataset, coding protocols, and testbed to enable comparable, claim-aligned RAG security evaluation.

Analogical reasoning is widely considered a fundamental component of human intelligence. Few benchmarks are designed to explicitly test far analogical reasoning - reasoning between domains that are superficially dissimilar yet share deep relational or structural similarities. In this work, we introduce an analogical reasoning benchmark called Abstraction and Reasoning Corpus of ANAlogy (ARCANA). The tasks of ARCANA require performing far analogical mappings from real-world objects or physical phenomena to abstract grid-based transformations, different from the well-known ARC-AGI benchmark which primarily emphasized innate human priors. We validate ARCANA through a human study, demonstrating that humans solve these tasks reliably. In contrast, evaluations across a range of large language models show a distinct performance gap compared to humans, revealing systematic failure modes that remain challenging for current models. To address this gap, we propose ConceptSIR, a reasoning framework based on concept slippage, introspection, and reflection. Experiments demonstrate that ConceptSIR enables standard LLMs to solve several challenging ARCANA tasks that were unsolved by direct prompting in our evaluation. Overall, our results suggest that far analogical reasoning remains an open problem for contemporary LLMs. All the materials are available at sites.google.com/view/arcanacogtest. The complete codebase, including benchmark, and ConceptSIR, is publicly available at https://github.com/density-11/arcana-test. All ARCANA data and task instances can be accessed and explored at https://arcanacogtest.org/.

Image registration underpins measurement across scanning, camera, and microscopy imaging, yet a fundamental question is rarely posed: when is the sample-to-position map recoverable at all, and when does any estimator that reports a position necessarily fabricate one? We show that in reference-perturbed sampled imaging, where samples are localized through a perturbed reference, position fidelity (where samples land) and phase fidelity (which reference index becomes each block's origin) are logically independent: no policy acting on position information alone can guarantee phase fidelity. We derive a tight resolution threshold separating recoverable from provably-unidentifiable registration, and a recovery framework that certifies identifiable regions--recovering them exactly--while abstaining on provably-unidentifiable regions rather than hallucinating structure. On a deployed scanning system we measure a direction-bimodal registration offset consistent with the theory. Against classical and learned restoration baselines, certificate-free offset estimators fabricate structure on the unidentifiable regime, whereas the certified method abstains rather than fabricating. Finally, the certified-abstention mechanism carries across scanning, rolling-shutter, and cryo-electron-microscopy imaging--declining rather than fabricating on the regime it flags--though how completely it abstains and how tightly it bounds kept-region risk stay modality-specific (at extreme SNR the cryo-EM certificate abstains only partially): a structural-versus-statistical boundary in registration reliability.

Vision-language-action (VLA) models enable robots to perform tasks specified through natural-language instructions, but their large weight footprint challenges deployment on memory-constrained onboard platforms. Ultra-low-bit quantization reduces this footprint, yet preserving task performance and controlling weight recovery costs remain challenging. We propose Action-Guided Quantization, which combines action sensitivity with a measured proxy for weight recovery cost to allocate matrix bitwidths under storage budgets. Per-channel calibration compensates for quantization error, while a uniform bitwidth within each matrix preserves regular layouts. Bit-dependent grouped lossless coding reduces resident weight storage, and block-wise recovery limits temporary buffers. On LIBERO, AGQ achieves 92.7% task success at W3, exceeding AWQ and GPTQ by 1.2 and 3.7 percentage points, respectively, and retains 70.5% success at W2.5. An asymmetric configuration, denoted W1.5$^{*}$, uses W4 vision weights and a parameter-weighted average of 1.5 bits for language weights. With lossless coding, it achieves $6.10\times$ complete-model compression relative to BF16 while retaining 25.5% task success. Code and experimental results are available at https://github.com/Qiuxu00/AGQ

Let $C$ be an $[n,k,d]_q$ Griesmer code, where $q=p^f$ with $p$ prime, and write $e=ν_p(d)$. Ward conjectured that $C$ is $p^{\max\{0,e-f+1\}}$-divisible. In this paper, we prove this conjecture.

Designing effective multi-agent systems (MAS) remains a challenging and resource-intensive task. We propose a Bayesian Evolutionary Optimization framework for automatically discovering task-specific MAS topologies. The approach combines evolutionary operators to generate diverse workflow graphs with Bayesian optimization to focus cost intensive evaluations on promising candidates. In contrast to LLM-based candidate selection, our approach uses a graph-aware Gaussian Process and Expected Improvement to provide an explicit selection criterion during evolutionary search. We evaluate the method on BigCodeBench for code generation and on a tabular preprocessing benchmark using TabPFN. On BigCodeBench, evolved architectures achieve the highest overall performance among the evaluated agent systems. On temporal tabular datasets, optimized MAS preprocessing improves over the default TabPFN model on several tasks, while remaining competitive on IID datasets. Overall, the results demonstrate the potential of Bayesian selection for guiding evolutionary MAS search under expensive evaluation budgets.

We study Largest Cardinality Subset Sum (LCSS): given $n$ nonnegative integers and a target $t$, compute a subset summing to $t$ with maximum cardinality. We also consider its all-targets version (ATLCSS), which asks for this maximum for every sum $s\in\{1,\ldots,t\}$. The LCSS problem sits squarely between the subset sum and the knapsack problem. A straightforward dynamic-programming algorithm runs in time $O(nt)$ and solves ATLCSS, and using Jin and Bringmann (both in STOC 2024, independent work) $0$-$1$ knapsack results we achieve a $\widetilde{O}(n + a_{\max}^2)$-time deterministic algorithm for LCSS. Our main result is a randomized $\widetilde{O}(n+\sqrt{n}\,t)$-time algorithm for LCSS. Then, we complement this result with a randomized $\widetilde{O}(n+t^{3/2})$-time algorithm for ATLCSS. Together, our two algorithms give a $\widetilde{O}(n+t\min\{\sqrt{n},\sqrt{t}\})$-time algorithm for LCSS. As an application of ATLCSS, we solve the search version of Projection Subset Sum, introduced by Dutta and Rajasree (SYNSAC 2023), in $\widetilde{O}(n+t^{3/2})$ time for every fixed $\ell_p$ norm with $p\geq 1$. For $\ell_1$, we obtain $\widetilde{O}(n+t)$ time, removing the unique-representation assumption required by their algorithm. Both algorithms output an optimal modified vector and a witnessing subset.

Reinforcement learning with verifiable rewards (RLVR), particularly through group-relative policy optimization (GRPO), has emerged as a central paradigm for the post-training of large language models (LLMs). While RLVR is highly effective at enhancing the reasoning capabilities of LLMs, it commonly induces \textit{distribution sharpening}, whereby the policy distribution becomes excessively peaked and rare-yet-correct trajectories are progressively suppressed, thus diminishing sample diversity. To this end, we promote flat-reward optima in RLVR to smooth the policy distribution. We theoretically link flat reward RLVR to reduced distribution sharpening, and empirically show improved sample diversity while maintaining single-attempt accuracy. Our method, called \texttt{Flat}-RLVR, searches for flat reward regions via sharpness-aware minimization during LLM post-training, combining this with GRPO variants to achieve better trade-offs between sampling efficiency and reasoning capacity.