Papers

Video virtual try-on (VVT) aims to generate realistic videos of a person wearing a target garment. Recent methods leverage a keyframe-driven video generation paradigm to improve in-the-wild performance, yet they still rely on masks to localize try-on regions, making them vulnerable to large motions and severe occlusions. Although mask-free image-based try-on methods have shown promising results by leveraging large-scale pseudo data, extending this paradigm to videos remains difficult, as constructing video-level pseudo data is prohibitively expensive. Furthermore, coarse keyframe sampling and the scarcity of multi-view try-on data limit existing keyframe-driven methods in maintaining garment consistency and handling diverse try-on tasks. To address these challenges, we propose BooM-VVT, a mask-free VVT framework built upon the keyframe-driven paradigm. To achieve mask-free VVT, we introduce a multi-stage training strategy that leverages image-level pseudo data for mask-free localization learning, substantially reducing the need for costly video-level pseudo data. To improve garment consistency, we propose Garment-Sensitive Keyframe Sampling, which selects keyframes based on garment-relevant body regions to better capture garment appearance. We further introduce Frame-Shared 3D-RoPE to establish spatiotemporal correspondences between keyframes and target video frames for accurate garment-detail transfer. Finally, we construct OmniView, a large-scale multi-view try-on dataset to support reliable try-on video generation under complex camera viewpoints and diverse try-on tasks. Extensive experiments demonstrate that BooM-VVT achieves superior temporal consistency and garment fidelity over existing methods. Project page: https://boomvvt.github.io/boomvvt.

We introduce an uncoupled learning algorithm which, when employed by all players of an arbitrary $N$-player normal form game with up to $K$ actions per player, guarantees $O(N^3\log^2 K)$ individual regret, uniformly over the horizon of play. The proposed algorithm - which we call higher-order optimism with discounting (HOOD) is a variant of optimistic follow-the-regularized-leader (OptFTRL) that combines a discounted $(N+1)$-th order predictor with entropic regularization over a suitable "lifting" of the game's strategy space. This combination of ingredients is purposefully designed to dampen large oscillations of the induced sequence of play in a controlled manner, removing in this way a key stumbling block of previous attempts to achieve constant regret in general games. Our approach bears several striking similarities to the concurrent - and completely independent - work of Liu, Farina, and Ozdaglar (arXiv:2608.31166), who very recently derived an $O(N^{21}\log^{4} K)$ regret bound through the use of higher-order optimism and an exponential moving average estimator.

Seeing frames in order does not mean representing time. Modern VideoLMs receive ordered video streams, yet their main supervision acts on generated text rather than video-token representations where event dynamics should first emerge. This mismatch allows models to learn temporal answers from shortcuts such as objects, scenes, and language priors, without requiring internal video representations to capture event progression. To address this, we propose VT-Contrast, a representation-level temporal counterfactual objective for VideoLMs. Its design asks where temporal supervision should act and what temporal differences it should expose. VT-Contrast supervises selected late-layer last-frame video tokens, where temporal information is expected to be integrated before language generation, and contrasts order-preserving views with same-video reordered counterfactuals graded by Kendall tau distance. It requires no architectural changes, is compatible with diverse VideoLM training tasks, and improves overall performance across temporal understanding benchmarks. Our code is available at https://github.com/ANDgate99/VT-Contrast.

Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have emerged as two dominant methods for post-training reasoning LLMs. Prior work uses OPD's dense token-level supervision to complement the sparse RL reward, fusing the two signals within a single step: either as a weighted-additive combination or a teacher-modulated rescaling of the RL advantage. In this paper, we show that a simple two-stage scheme, OPD-then-RL, consistently outperforms pure OPD, pure RLVR, and all such joint baselines across logic and math reasoning benchmarks. Beyond the empirical results, we further provide a systematic understanding of this through pass@$k$ behavior, learning dynamics, and parameter updates, yielding a consistent explanation: OPD expands the student's coverage of teacher-supported solutions and RL sharpens within that support, while jointly optimizing the two signals causes them to interfere. To provide a practical recipe, we find that the OPD validation score is the key signal for when to switch to RL, and that OPD is a better cold start for RL than SFT. Together, our results establish OPD-then-RL as a simple yet strong way to combine the two methods, turning two entangled signals into complementary stages.

Blackwell's 4-bit floating-point (FP4) tensor cores do not automatically make attention faster because softmax conversion and on-chip dependencies dominate once its matrix products shrink. We address this with Direct-P for noncausal inference and a causal path that passes the forward quantization directly into backward. Direct-P maps scores directly to FP4 probabilities and reaches up to 2.13$\times$ the bfloat16 (BF16) forward throughput on an NVIDIA GB200. The causal path reconstructs probabilities from saved quantized queries and keys and uses 8-bit floating-point (FP8) gradient operands, accelerating a complete single-GPU 8-billion-parameter update by up to 1.14$\times$. Matched distributed training retains FP8 probabilities and values; every tested MXFP4 probability/value training trajectory diverges.

This paper presents a new method for headland coverage path planning for arable fields. Several earlier approaches suggest covering the headland with nested polygons and smooth turns, however, covering the field corners entirely requires manoeuvres with reversing. In the new method, the polygon corners are modified to allow a reversing turn. A comparison to two other methods considering gap, overlap, and crossing the field boundary shows an improvement in the coverage result especially in field corners of around 90 degrees, and 240 degrees and above. Applicability of the new method is shown with several examples of real polygonal field maps.

System-wide Dictation on Apple devices runs entirely on-device, and the speech it transcribes reaches the foundation model through a tokenizer: an encoder that maps short windows of waveform onto the representation the language model reads. Because that model is sparsely activated under Instruction-Following Pruning, only a small subset of its experts occupies DRAM at any time, so the always-on tokenizer competes for the same memory, and its parameter count bears directly on power and latency. In this work we study how to compress such a tokenizer by distillation, taking as the supervision target neither the discrete token nor the output distribution but the pre-quantizer latent the model actually consumes - the last representation the two token interfaces share. We train only the student encoder to regress the teacher's per-frame latent under a squared-error objective, with a single affine layer absorbing the teacher-student width mismatch. Because the target precedes both the quantizer and the language-model bridge, one recipe covers both token interfaces we support, and applies both to a tokenizer pretrained alone and to one jointly trained with a language model. At 2.8x compression the distilled student stays within 1.9% relative WER of its teacher on five of six teacher-student pairs without any fine-tuning, and improves on an independently trained tokenizer of identical capacity by 3.9% relative.

Hybrid LLMs pair softmax attention with linear-attention layers such as Gated DeltaNet (GDN), whose recurrent state summarizes the context in fixed size. Early community 4-bit quantizations of Qwen3.8-27B (48 GDN layers, 16 attention layers) left the GDN block in 8- or 16-bit precision – especially its decay and write-strength gates – on the intuition that errors in a recurrence accumulate over long contexts. We test that intuition by building Minima: NVFP4 W4A4 on all 496 linear layers, GDN included. Across perplexity at 4K/32K, MMLU-Pro, GSM8K, AIME'25, GPQA-Diamond, LiveCodeBench, and RULER retrieval to 64K, Minima matches BF16 within seed noise (5-task average -0.52) while being the smallest (17.5 GiB) and fastest-prefill (+14-19%) recipe we compare, and its 32K perplexity gap shrinks with position. A four-part mechanism study explains why: (i) NVFP4's 16-element block scaling localizes the residual stream's extreme outliers, equalizing activation error across layer roles; (ii) the supposedly fragile gate projections are the least sensitive – softplus/exponential and sigmoid parameterizations compress ~11% GEMM error to ~2% output error; (iii) the delta-rule recurrence holds injected noise at a flat plateau over 32K tokens and forgets a state impulse within hundreds of steps, because each write overwrites the state along the current key direction; (iv) the per-token quantization cost washes out with context instead of compounding. We also repair a global-scale mismatch that arises when per-module-calibrated NVFP4 checkpoints are served by kernels that fuse those modules into one GEMM, and show calibrated FP8 KV-cache scales are performance-free. The result: a practical recipe – quantize everything, ship KV scales – and a mechanistic account of why the recurrent half of a hybrid LLM is the easy half to quantize. Checkpoint: https://huggingface.co/minima-ai/mnma_qwen3.8_27b_nvfp4

This paper proposes AdaRoboVLG, a task-adaptive Vision-Language-Grasp (VLG) framework that supports generalizable grasp synthesis across different robotic hands. Unlike existing VLG methods that tightly couple foundation models with end-to-end grasp policies, AdaRoboVLG learns an efficient generalizable base policy that generates and evaluates physically feasible grasp candidates through explicit kinematic mapping and force-closure-based stability estimation, while offloading task-dependent understanding to specialized foundation-model modules. These modules provide composable priors that are integrated into the grasp synthesis process, enabling contextually adaptive grasp synthesis without retraining the underlying grasp policy. Through extensive simulation and real-world experiments, we demonstrate that (i) the base policy exhibits efficient learning and strong cross-hand generalization, (ii) the framework effectively incorporates spatial, cognitive, and temporal priors to address three representative grasping challenges without compromising grasp synthesis performance compared to state-of-the-art methods, and (iii) these priors can operate jointly to enable functional grasping in cluttered and dynamic environments. These results indicate that decoupling physical grasp synthesis from task-dependent understanding provides a scalable paradigm for robotic grasping, allowing future advances in foundation models to be directly translated into improved grasp capabilities without redesigning or retraining the underlying grasp policy. Supplementary videos are available at https://adarobovlg.github.io/

Reinforcement Learning from Verifiable Rewards works well when a task has a programmatic checker, but most long-horizon agent domains have none. We work in the outcome-blind setting, where ground-truth success signals are not available. Multi-criteria rubrics are a popular way to supply such a reward; they are scored once per trajectory, but a single scalar is a poor signal across tens of steps. We propose DRACO: Distributing Rubric-based Advantage for Credit Optimization. It generates rubrics dynamically during training to track the policy's evolving capability, scores those rubrics once per completed trajectory, and redistributes that judgment over the steps responsible for annotated rubrics to produce differentiated per-step advantages in GRPO. The redistribution is closed-form and does not introduce any trained attribution module. On AppWorld, DRACO gains 15.9 points over the base model and 5.3 points over GRPO trained with a sparse ground-truth reward, despite not using any verifiers itself. On out-of-domain Tau-Bench, it gains 5.3 points over the base model even without a frontier judge, beating both ground-truth-reward training and other rubric-based training settings. The code for DRACO is available at https://github.com/IBM/draco.

Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define approximate loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, à la Üstünel.

Dense semantic segmentation allocates computational resources uniformly across the entire image, regardless of scene complexity or task relevance. Inspired by biological vision, we investigate whether semantic understanding can be achieved more efficiently through digital foveated perception. We introduce a lightweight active-vision pipeline that combines saliency-driven fixation selection, high-resolution foveal observations, low-resolution contextual information, semantic accumulation, and adaptive computation. Beyond conventional dense prediction metrics, we use object-level evaluation to measure semantic understanding under sparse observations. On ADE20K-Object, a single foveated observation achieves 95.9% of the baseline Top-1 accuracy and 96.9% of the baseline Top-3 accuracy while requiring only 4.7% of the computational cost. At the scene level, semantic accumulation recovers 90.6% of the baseline object recall while using 58.6% of the computation. These results suggest that substantial semantic understanding can emerge from sparse observations when computation is allocated selectively, highlighting active vision as an efficient alternative to uniform dense processing and motivating evaluation protocols beyond conventional pixel-wise segmentation metrics.

For every coherent and sufficiently expressive finite syntactic system S, we prove the existence of at least one theorem that S cannot produce autonomously. The result is a metatheorem: it proves the existence of a theorem, and applies to every finite syntactic system - security mechanisms, AI systems, formal verifiers, legal systems, economic models, and the formal system in which it is itself proved.

What are the transversality conditions for an optimal control problem when the boundary conditions are defined by differential equations? This seemingly bizarre question is motivated by trajectory optimization problems in the $N$-body system. The question, however, is more fundamental and goes beyond problems in astrodynamics to nonintegrable dynamical systems in general. The main contribution of this paper is the development of generic initial- and final-time transversality conditions for optimal control problems whose boundary conditions are defined in terms of differential equations with side conditions. The mathematical definition of differential boundary conditions are part of the foundations developed in this paper. To support the new fundamentals, the concept of coordinated/uncoordinated clock times and weak adjoint covectors are introduced. In the case of uncoordinated clock times, the new transversality conditions reveal that there exists a special situation where a weak adjoint covector is orthogonal to the vector field of the boundary differential equation. This condition is sharply different from the classical statement of orthogonality with respect to the endpoint manifold. The theorems developed in this paper are generic. An application of the theorems to several cases in the three-body problem are described in separate papers.

MLLM-based embedding models remain limited in compositional retrieval, often failing to distinguish scenes containing the same concepts but different attribute-object bindings. Yet the same backbone can resolve such distinctions when used as a cross-attentive reranker, motivating us to distill its compositional judgments into the embedding model. We propose CORE, which synthesizes candidate lists spanning five compositional matching levels and introduces a Rank-KL objective that trains the embedding model to reproduce the reranker's fine-grained ranking. We further introduce a graded evaluation protocol and compare contrastive learning, pairwise CoSENT, and listwise Rank-KL under the same data and tuning budget. Our comparison shows that both CoSENT and Rank-KL use the multi-level supervision more effectively than contrastive learning, with Rank-KL achieving the strongest overall performance. Across three compositional reasoning benchmarks (COLA, SUGARCREPE++, NEGBENCH), CORE-RERANKER-8B achieves an 82.7% total average, outperforming Jina-Reranker by 10.7 points, while CORE-EMBED-8B achieves the best total average (0.666) among all evaluated embedding models. The improvements transfer to the MCMR benchmark without sacrificing retrieval performance on COCO and Flickr30K.

We give deterministic FPTASes for two dense counting problems on which the known deterministic algorithms, based on zero-free interpolation, run in quasipolynomial time. For fixed $0<\gamma<1/2$ and $0<\theta\leq1$, the first approximates $\mathrm{haf}(A)$ for a symmetric matrix $A$ when its support graph $G$ has minimum degree at least $(1/2+\gamma)n$ and its nonzero entries lie in $[\theta,1]$. It also approximates permanents under the analogous bipartite condition, including full-support matrices in $[\theta,1]$. For fixed $\beta>0$ and $0<\kappa\leq1$, the second approximates the zero-field Ising partition function $Z(J)$ for zero-diagonal real symmetric matrices $J$ satisfying $\max_{i,j}|J_{ij}|\leq\beta/n$ and $\lambda_{\max}(J)\leq1-\kappa$. No separate lower-eigenvalue condition is imposed. We further prove $\log\mathrm{haf}(A)=h_A(G)-n/2+O_{\gamma,\theta}(1)$ and $Z(J)=2^n\det(I-J)^{-1/2}(1+O_{\beta,\kappa}(1/n))$. Here $h_A(G)$ is the maximum weighted fractional-matching entropy. For unweighted graphs, the first formula improves the Cuckler–Kahn error from $o(n)$ to $O_\gamma(1)$ on the fixed-margin class and extends it to weights in $[\theta,1]$. Both algorithms use a common Gaussian truncation principle. Each problem becomes an integral of a product of a fixed entire function over Gaussian coordinates, with possibly indefinite moment matrix entries of order $1/n$. Cancelling the linear term and exactly resumming the quadratic term leaves a coordinate remainder vanishing to order at least three. Complex dilation handles small supports. For large supports, we bound the recombined tail by a large-deviation rate that beats the entropy of the subsets. The truncation error is at most $(CR/n)^{R/2}+e^{-cn}$. This faster-than-geometric decay permits $R\log(en/R)=O(\log n+\log(1/\epsilon))$ and hence polynomial enumeration.

AI agents have recently demonstrated strong performance in automated vulnerability patching. However, existing evaluations often validate a patch only by testing whether the provided Proof-of-Concept (PoC) input still triggers a crash. This leaves two key threats to validity: agents may reproduce memorized historical developer patches, or they may generate surface-level fixes that only suppress the reported crash. We study these concerns for C/C++ vulnerability patching. We introduce a patch similarity metric to detect memorized patches. On average, 25% of the agent patches exhibit substantial similarity to historical developer patches, indicating that patch memorization is a real threat to the validity of vulnerability patching evaluations. Meanwhile, agents also frequently exploit benchmark structures to pass patch validation by patching on the crash stack trace to suppress the crash, rather than localizing and fixing the root cause of the vulnerabilities. To handle these issues, we propose PatchBench, a new benchmark for evaluating AI agents on realistic vulnerability patching tasks. PatchBench selects vulnerabilities whose ground-truth fixes lie outside the crash stack and uses vulnerability transplant and code mutations to migrate historical vulnerabilities into new repository contexts, reducing the risks of surface-level fixes and patch memorization. We develop new patch validation methods that thoroughly evaluate both security and semantic correctness of agent patches. Across 11 state-of-the-art agents, including the top three AIxCC agents, the original PoC-only validation inflates the patching task solve rate of agents by 1.83$\times$ on average. Our results reveal key limitations of current patching agents and point to future research directions for more reliable vulnerability repair.

Pathology foundation models improve transferable representation learning for histopathology, but recent gains often rely on encoders with hundreds of millions of parameters and high inference cost. We propose TAP-Path, a task-adaptive compression framework that directly restructures a pretrained Virchow2 encoder rather than distilling it into a separate student. TAP-Path combines validation-driven transformer-block selection, physical removal of redundant blocks, input-adaptive patch-token pruning, multi-depth feature recovery, and a lightweight gated task head. The final model retains 24 of 32 transformer blocks and 70% of patch tokens after pruning, reducing encoder parameters by 24.96% (631.24M to 473.70M) and analytical encoder compute by 35.20% (340.13G to 220.40G FLOPs). Across three task-head optimization seeds, TAP-Path achieved $87.98 \pm 0.067%$ test accuracy, $81.26 \pm 0.49%$ balanced accuracy, and $82.38 \pm 0.48%$ macro-F1 on a 32-class histopathology benchmark, compared with 86.89% for full Virchow2 and 87.67% for UNI2-h. TAP-Path achieved a Brier score of $0.1800 \pm 0.0005$ and failure-detection AUROC of $0.9047 \pm 0.0060$. A validation-only rare-aware objective improved rare-class balanced accuracy in a secondary operating analysis. Frozen external evaluation on 433 CPTAC samples yielded $91.22 \pm 0.83%$ accuracy and $91.10 \pm 0.81%$ balanced accuracy. These results show that task-adaptive structural and token sparsification can improve the accuracy-efficiency trade-off of large pathology foundation models while preserving reliability under internal and external evaluation.

Bridging the gap between the discrete reasoning of Vision-Language Models and the continuous, physics-constrained nature of autonomous driving remains a significant challenge. In this work, we introduce LaPla, a unified Vision-Language-Action (VLA) framework featuring latent-aligned planning to seamlessly ground semantic understanding in precise motion execution. We first design an action tokenizer based on a residual vector-quantized variational autoencoder (VQ-VAE), capturing vehicle kinematics and encoding trajectory features into a structured latent space. Rather than discrete codebook lookups that inevitably introduce quantization errors, LaPla repurposes this representation as a physical prior to bridge the modality gap between high-dimensional semantics and the raw action space. Specifically, given multimodal inputs integrating multi-view images, historical actions, and textual instructions, LaPla incorporates concurrent action queries to causally attend to the multimodal context in a single forward pass, projecting hidden states directly into the pretrained VQ-VAE latent space. The frozen decoder then translates these continuous latents into actions, effectively eliminating quantization errors and ensuring physically plausible trajectories while bypassing time-consuming autoregressive generation. Extensive experiments on the nuScenes benchmark demonstrate that LaPla achieves competitive open-loop performance, reducing long-horizon L2 error by 15.52% compared to state-of-the-art VLA methods. Closed-loop evaluations on the NVIDIA AlpaSim simulator further confirm its superior capability in ensuring smooth driving progress, improving the success rate by 33.34 percentage points with significantly reduced inference latency.

We develop a convergence theory for geometric multigrid with vertex-patch smoothers applied to cut finite element discretizations of the Poisson problem. The framework addresses non-inherited level forms and the mismatch between the physical and active domains. Using the discrete extension property, we prove two-level convergence bounds uniform in the mesh size and the cut geometry, and W-cycle bounds under an additional smallness assumption on the two-level rate. The numerical experiments intentionally use the stronger V-cycle, for which no convergence bound is claimed here. The convergence constants degrade with the degree $p$. Lowering the ghost penalty improves iteration counts. An aligned two-cell model exhibits a semidefiniteness threshold of order $p^{-2}$, whereas the visibility scale of a degree-$p$ cut mode decreases exponentially. Experiments at the model threshold reduce the iteration counts, but do not establish an assembled-operator threshold.

Reinforcement learning from human feedback (RLHF) has emerged as a powerful yet sample-inefficient approach for learning reward models from human preferences, making active learning a critical component in synthesizing informative preference queries. However, effective uncertainty quantification required for active learning remains a key challenge for large neural network reward models. In this paper, we introduce PreferenceEKF, a sample-efficient approach that tracks reward model uncertainty by framing active preference learning as a sequential Bayesian filtering problem. Instead of relying on computationally prohibitive posterior inference over the full neural network parameter space, our method performs sequential inference via an extended Kalman filter within a low-dimensional parameter subspace, continuously updating the reward model posterior as new preference queries arrive. Our approach enables scalable sampling of neural network parameters to efficiently compute acquisition functions for active reward learning. Experiments on the D4RL and V-D4RL benchmarks demonstrate that our approach achieves better sample efficiency, runtime, scalability, and calibration compared to other Bayesian deep learning approaches, and the learned reward models lead to competitive offline reinforcement learning policy performance. This highlights the potential of scalable Bayesian methods for preference-based reward modeling in RLHF. Our code is available at https://github.com/yutaizhou/bnn_pref.

Group Relative Policy Optimization (GRPO) is widely studied for reinforcement learning with verifiable rewards, where its advantage estimator assigns each rollout a magnitude from within-group reward statistics. In the common case, this magnitude rewards rollouts that reach the correct answer through reasoning. Yet, an overlooked case shares the same surface: a rollout may land on it by guessing, and the formula still assigns a high magnitude, which we identify as the spurious advantage. This arises in three cases: bounded-answer tasks with a small candidate set; open-answer sets hosting bounded sub-cases; and search agents whose budget opens many paths to the same answer. In all three, this misleads the policy toward guess-like behaviors. We propose SIGNBALANCE, whose magnitude is composition-free: it keeps the verifier sign, uses a global scale, and restores zero-mean balance via a stop-gradient per-class rescaling. Across math and search agent benchmarks at different scales, SIGNBALANCE matches GRPO on open-answer math and improves on bounded-answer math and search agents. Code will be released.

Large language models (LLMs) are increasingly used to edit existing code, but correctness alone is not enough: useful repairs should also be minimal, reviewable, and faithful to the original implementation. We study over-editing, the tendency of a model to rewrite code beyond what is required to fix a bug. We construct an evaluation framework from 400 BigCodeBench problems by injecting controlled AST-level corruptions into reference solutions, giving each repair task a known minimal patch. Across frontier LLMs, over-editing is widespread even among strong models like GPT-5.5: high Pass@1 can coexist with unnecessarily large edits and added cognitive complexity. A preservation instruction substantially reduces this behavior, lowering average excess Levenshtein distance from 0.195 to 0.131, reducing added cognitive complexity by 26.6%, and increasing Pass@1 by 2.3 points. However, these gains do not simply follow from a larger reasoning budget or larger models. We next ask whether minimal editing can be learned directly during post-training. We observe that supervised fine-tuning overfits to seen corruption patterns, whereas reinforcement learning gives the best out-of-domain edit-fidelity and performance-retention trade-off. These results position edit fidelity as a distinct axis of code-repair quality and show that it can be measured and learned.

Motivated by numerous parallelizable stochastic search problems, most notable and timely among them being LLM inference-time scaling, we propose and study batched versions of the Pandora's Box problem of Weitzman. In particular, boxes are opened in capacity-constrained batches, each batch has a setup cost, and all rewards in a batch are revealed together. We consider two different variants, motivated by different application environments: one where boxes are reusable (i.e., can provide multiple i.i.d.~samples) and another where they are not. For both variants we rule out most “simple” natural heuristics, and also formally prove NP-hardness of approximation in the traditional sense. We then relax the problem to allow bi-criteria approximations, with respect to both rewards and setup costs, where we exhibit constant approximation algorithms for both the reusable and non-reusable settings. This is obtained through a linear-programming relaxation of Pandora's Box problem, followed by randomized or Pipage rounding.

Post-quantum migration is mandated on published timelines, and silicon that ships with a defect cannot be patched remotely. The standard acceptance gate cannot detect an entire class of ML-DSA defects. Signing resamples until a candidate meets its norm bounds, so the executed path varies with the message, whereas known-answer tests (KATs) sample fixed values and reach only the depths their seeds trigger. Our accelerator passed its full KAT regression while carrying a norm check that outran block-RAM latency, leaving each candidate's final coefficients unverified; the escape surfaced at reject-loop iteration 5. The blind spot lies in the instrument, not the engineer; care cannot remove it. We replace that gate. A byte-exact golden-reference oracle paired with randomized adversarial soak drives the rejection loop past any fixed vector, closing the gap: 301,343 data-dependent signings, zero escapes. Because the gate judges artifacts and never authors, trust becomes separable from authorship, making AI authorship an answerable question. We report 232 logged experiments in which an agentic large language model drove a unified ML-KEM-768 and ML-DSA-65 accelerator with on-chip key custody from RTL to PCIe bring-up on one Kintex-7 XC7K160T, shipped at 98.5% slice occupancy. Success was 71.6%, following a hardware-coupling gradient, 77-85% for documentation and research against 50-53% for synthesis and bring-up, which observability can explain: failure concentrates where corrective signals are physical-side only. That so unreliable an author produced an artifact byte-exact across all six FIPS operations – its deployed baseline surviving the same 779,945-check zero-failure soak – is the claim.

Software users often submit issue reports to a product's issue tracking system to report defects, suggest enhancements, or raise other product-related concerns. Labeling these issue reports supports effective planning and improves community engagement. However, many issue reports remain unlabeled due to the substantial manual effort required to design an appropriate label taxonomy, then assign suitable labels from this taxonomy to new issue reports. Existing automated labeling approaches attempt to mitigate these challenges. However, they suffer from key limitations, such as extensive manual intervention, the assignment of generic labels, and a dependence on existing labeled datasets. To address these limitations, we propose LabelMate, a novel Large Language Model (LLM)-driven framework that (1) derives a comprehensive, project-specific label set from historical issue reports and (2) automatically assigns relevant labels to new issue reports without requiring any pre-labeled training data. We evaluate LabelMate on 16,500 issue reports from 30 popular and diverse GitHub repositories. Based on this dataset, our approach generates a coherent list of 275 labels and achieves an average labeling accuracy of 89.84%, a statistically significant improvement over existing generic label assigning approaches. These results demonstrate that LabelMate offers an efficient, domain-adaptive solution to streamline the issue labeling process.

We partially answer an open problem, posed by Nick Higham, concerning the conditioning of solutions to Sylvester and Lyapunov equations. The question arises in the backward stability analysis of numerical algorithms for these equations. We first show that the solution to the Sylvester equation $AX-XB = C$ can be arbitrarily ill-conditioned even if $A, B, C$ and the Kronecker sum $I \otimes A - B^T \otimes I$ are all perfectly conditioned. We then derive general a priori bounds on the condition number of the solution, as well as bounds for the Sylvester equation when $A$ and $B$ are diagonalizable. We also provide lower bounds involving matrix exponentials and Zolotarev numbers. For the Lyapunov equation $AX+XA^T = -C$, we obtain upper bounds in two settings: (i) when $A$ is symmetric positive definite while $C$ is symmetric negative definite, and (ii) when $A$ is strictly dissipative and $C$ is symmetric positive definite.

Neural machine translation (NMT) systems typically produce a single output per input, obscuring the alternative decision trajectories implicitly available within multilingual decoding. This opacity becomes particularly problematic in low-resource dialect settings, where multiple linguistically valid realizations may differ in lexical authenticity, register, and structural stability. We propose reframing translation as a structured decision space explored by autonomous translation agents. Instead of analyzing a single output, we model distinct translation pathways as agents operating over a shared multilingual backbone. Inter-agent divergence is treated not as error but as an interpretable behavioral signal. We conduct an empirical study on Turkish–Syrian Arabic translation using three agents: (1) zero-shot direct translation, (2) dialect-stabilized translation via lightweight fine-tuning, and (3) pivot translation through English. Evaluation is performed on 5,000 dialogue sentences, while stabilization is trained on 5,000 additional Turkish–Syrian sentence pairs drawn from television dialogue and MADAR-Turk resources. Rather than optimizing for conventional performance metrics, we quantify structured behavioral displacement using dialect marker frequency, lexical proximity to standardized Arabic, and structural variance. Lightweight stabilization nearly doubles dialect marker usage, increasing it from 0.2266 to 0.4988, while significantly reducing structural instability. Pivot mediation introduces normalization pressure and measurable compression effects, whereas zero-shot translation exhibits the highest decision variance. We argue that translation divergence across agents reveals latent decision flexibility within multilingual models and we provide a principled interpretability framework for low-resource dialect generation.

Background: Researchers increasingly use repeated identical prompts to audit stochastic variation in large language model (LLM) brand recommendations, yet no standardized protocol exists for setting iteration counts, selecting stability metrics, or establishing reliability thresholds. Objective: We formalize the Dice Roll Method as a reusable protocol for repeated-query auditing of LLM brand recommendations, grounded in a generative model of temperature-scaled nucleus sampling. Methods: Total response variance is decomposed into sampling, prompt-phrasing, run-to-run, and model-version components. The stack: a negative-binomial mixed model with iterations as repeated measures; Cliff's delta as the distribution-free effect size; dependence-preserving bootstrap; simulation-based power; a generalizability-theory decomposition; drift diagnostics on pinned snapshots. We reanalyse five brand-recommendation auditing studies: approximately 190,000 observations, 270+ brands, 6 languages, iteration counts 5 to 40. Results: The recomputed D-study supports no fixed tiers. Across 250 distinct questions (S5), G is 0.96 at five runs and 1 to 2 runs reach 0.80, also within each model. For five versions of one question (S1 Valentine's subset, Gemini) it is 0.27 (95% CI 0.00 to 0.52), which fixes no run count. Runs follow from a pilot: n = 4 x residual / cell variance. Simulated single-cell power for a large Cliff's delta is 0.15 to 0.19 at five runs and 0.8 at 15 to 25. The four metric families (count, set, embedding, PASOR) are complementary. A pre-registered external validation on three independent corpora reproduces the D-study prediction in 37 of 39 cells with no failures; fixed tiers do not transfer. Conclusion: The protocol gives repeated-query auditing of LLM brand recommendations a statistically principled footing under the conditional, non-Gaussian structure of real autoregressive generation.

What can a single layer of self-attention compute? We study head complexity: the minimum number of attention heads required to compute a function in a one-layer attention-only model. We establish an exact hierarchy under this measure: $k$ heads compute $k$-bit parity but cannot compute $(k+1)$-bit parity. The lower bound is unconditional in the two resources a transformer might otherwise exploit; it holds at unbounded embedding dimension and unbounded numerical precision. The proof rests on an alternating-sum obstruction: after clearing the softmax denominators, every monomial in the resulting decision polynomial omits at least one of the $k+1$ input bits, forcing its correlation with parity to vanish. The same obstruction yields lower bounds for related tasks, including the well-studied multi-hop induction-head task. We also establish compactness bounds for embedding dimension and numerical precision. Specifically, a compactness theorem shows that any function computable at all can be computed with embedding dimension and precision bounded by the discrete data of the task, namely, head count, alphabet size, and length. Thus, potentially unbounded dimension or precision provably cannot substitute for heads. Finally, we derive nearly matching universal bounds for general binary functions: $2^n$ heads suffice to compute every $n$-bit binary function, with one head per monomial in its multilinear expansion, while a counting argument shows almost all such functions require $\Omega(2^n/n^2)$ heads. This lower bound matches the upper bound to within a $\operatorname{poly}(n)$ factor, even when dimension and precision are unbounded. Together, these results characterize head requirements for Boolean computation in this model.