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01.
arXiv (CS.AI) 2026-06-18

Where Did the Variability Go? From Vibe Coding to Product Lines by Regeneration

arXiv:2606.19042v1 Announce Type: cross Abstract: In vibe coding, an emerging AI-driven paradigm, an LLM generates an entire program from a natural language prompt, but what happens to the variability that traditional software engineering carefully builds into code? To answer this question, we conducted an exploratory analysis on 10 vibe coded C/C++ projects, which suggests that there is near-zero in-artifact variability, i.e., at compile and runtime. All variability decisions are resolved at a single new binding time, generation time, the moment the LLM produces the source code. Rather than treating this as a defect to fix, we propose Variability by Regeneration (VbR), to our knowledge the first product-line approach in which the LLM acts as the derivation engine, generating a purpose-built, free of dead code binary for each variant from a declarative specification, while a variant dispatcher transparently routes user requests to the matching binary. We formalise VbR, contrast it with classical SPL derivation, and demonstrate its full pipeline on a wc product family. For SPL engineering, variability in AI-generated software belongs in the specification, not in the code.

02.
arXiv (CS.AI) 2026-06-15

Safety-Contract Graph Multi-Agent Reinforcement Learning for Autonomous Network Security Response

arXiv:2606.13832v1 Announce Type: cross Abstract: Autonomous network-security response systems promise to reduce Security Operations Centre (SOC) reaction latency, but reward-only multi-agent reinforcement learning (MARL) can improve security reward while remaining non-deployable. We present a safety-contract graph MARL framework and instantiate it as ACD$^3$-GAT (Adaptive Constrained Counterfactual Decisioning with a Graph Attention Network encoder), an architecture that separates simulator observations from reusable operational budgets, constrained optimization, graph state encoding, and counterfactual action screening. We evaluate the method in CAGE Challenge 4, where agents operate under budgets for Mean Time to Recover (MTTR), false-positive response, and firewall change-management disruption. Across the benchmark, every unconstrained method violates the SOC downtime budget in 100% of evaluated episodes, with mean downtime proxy costs of 311-430 against a budget of 50. This complements prior CAGE Challenge 4 findings by showing that reward-only learning lacks operational discipline. Constrained MAPPO-GAT (C-MAPPO-GAT) isolates Lagrangian operational-cost control and budget-aware screening, while ACD$^3$-GAT adds budget context, CVaR tail-risk estimation, opponent-belief state, and Graph Counterfactual Risk Propagation (G-CRP). The replicated comparison includes three 200-episode seeds for IPPO, MAPPO-GAT, C-MAPPO-GAT, and ACD$^3$-GAT. C-MAPPO-GAT reduces downtime violation from 100% to 0.3% and mean downtime cost from 355.4 to 15.5 relative to MAPPO-GAT. ACD$^3$-GAT reduces mean downtime cost to 48.2 with a 13.8% violation rate, placing it on the safety-contract frontier rather than at the most conservative compliance point. Topology-seed and coupled adaptive Red-process stress tests preserve this contrast and show lower worst adaptive degradation for safety-constrained policies than reward-only MAPPO-GAT.

03.
arXiv (CS.CL) 2026-06-16

Beyond NL2Code: A Structured Survey of Multimodal Code Intelligence

While LLMs have substantially advanced text-to-code synthesis, many real programming tasks specify intent through visual artifacts such as screenshots, charts, documents, vector drawings, videos, and interactive states. These tasks require models to connect visual perception to executable programs, because correctness depends not only on syntax but also on layout, geometry, data semantics, editability, interaction behavior, and domain-specific constraints that apply after execution. This survey examines Multimodal Code Intelligence, covering systems that generate, edit, refine, execute, or reason with code under visually grounded inputs and outputs. We first formulate the field by the role that code plays in each task, distinguishing code as a rendered artifact, an editable symbolic structure, a scientific representation, an intermediate reasoning trace, or an executable policy or tool interface. We then organize benchmarks and methods into four domains: Graphical User Interface, Scientific Visualization, Structured Graphics, and Frontier Tasks and Frameworks. This taxonomy connects mature artifact-generation problems to emerging agentic and unified settings and allows us to compare how different tasks treat evidence of correctness. Looking ahead, we argue that future research may benefit from four verification-centered directions. Multi-signal validation can combine complementary evidence of correctness, multi-state verification can test behavior across execution trajectories, cross-task transfer testing can probe reusable visual-code skills, and verifiable agent traces can reveal whether agent actions are grounded in visual evidence. Together, these directions may move multimodal code generation from single-output imitation toward evidence-grounded executable systems.

04.
arXiv (CS.CL) 2026-06-11

Dual-Stance Evaluation of Sycophancy: The Structure of Agreement and the Limits of Intervention

Activation steering can shift LLM behaviour, but standard evaluations do not typically test whether a sycophancy-reduction direction also suppresses agreement with factually correct statements. We introduce dual-stance evaluation, which tests both stances of each topic, and apply it to centroid-difference steering on Llama-3-8B-Instruct. We find a dissociation: the model represents sycophantic and factual agreement in geometrically distinct subspaces, yet the steering direction projects equally onto both and cannot differentially target either. The direction accordingly reduces agreement with factually correct statements (e.g. that the Earth is round) as well as sycophantic ones. All other static properties of the two activation groups are matched, suggesting the behavioural dissociation arises from generation dynamics or from finer-grained structure that residual-stream analysis cannot resolve. The pattern illustrates a general gap: representations that are readable from activations may not be writable through them.

05.
arXiv (CS.AI) 2026-06-19

PSCT-Net: Geometry-Aware Pediatric Skull CT Reconstruction via Differentiable Back-Projection and Attention-Guided Refinement

arXiv:2606.19867v1 Announce Type: cross Abstract: Computed Tomography (CT) is essential for diagnosing pediatric craniofacial abnormalities, yet poses radiation risks to developing anatomies. Reconstructing 3D CT from sparse bi-planar X-rays offers a low-dose alternative but is severely ill-posed. Existing methods employ geometry-agnostic feature lifting, naively projecting 2D features into 3D without explicit spatial modeling, causing depth ambiguity and degraded osseous boundaries. We present PSCT-Net, a geometry-aware framework with differentiable back-projection. Differentiable back-projection establishes a spatially faithful volumetric prior, alleviating depth ambiguity. An Attention-Guided Projection (AGP-3D) module then learns non-linear voxel-wise correspondences between 2D regions and 3D locations. A Bidirectional Mamba (BiM-3D) module captures long-range volumetric dependencies with linear complexity. We further curate a private institutional pediatric skull CT cohort, PedSkull-CT, comprising normal and pathological cases for internal evaluation, addressing the gap in adult-centric, trunk-focused datasets.

06.
arXiv (CS.CL) 2026-06-19

Omnilingual SONAR: Cross-Lingual and Cross-Modal Sentence Embeddings Bridging Massively Multilingual Text and Speech

Cross-lingual sentence encoders typically cover only a few hundred languages and often trade downstream quality for stronger alignment, limiting their adoption. We introduce OmniSONAR, a new family of omnilingual, cross-lingual and cross-modal sentence embedding models that natively embed text, speech, code, and mathematical expressions in a single semantic space, while delivering state-of-the-art downstream performance at the scale of thousands of languages, from high-resource to extremely low-resource varieties. To reach this scale without representation collapse, we use progressive training. We first learn a strong foundational space for 200 languages with an LLM-initialized encoder-decoder, combining token-level decoding with a novel split-softmax contrastive loss and synthetic hard negatives. Building on this foundation, we expand to several thousands language varieties via a two-stage teacher-student encoder distillation framework. Finally, we demonstrate the cross-modal extensibility of this space by seamlessly mapping 177 spoken languages into it. OmniSONAR halves cross-lingual similarity search error on the 200-language FLORES dataset and reduces error by a factor of 15 on the 1,560-language BIBLE benchmark. It also enables strong translation, outperforming NLLB-3B on multilingual benchmarks and exceeding prior models (including much larger LLMs) by 15 chrF++ points on 1,560 languages into English BIBLE translation. OmniSONAR also performs strongly on MTEB and XLCoST. For speech, OmniSONAR achieves a 43% lower similarity-search error and reaches 97% of SeamlessM4T speech-to-text quality, despite being zero-shot for translation (trained only on ASR data). Finally, by training an encoder-decoder LM, Spectrum, exclusively on English text processing OmniSONAR embedding sequences, we unlock high-performance transfer to thousands of languages and speech for complex downstream tasks.

07.
arXiv (math.PR) 2026-06-12

Sticky CIR process with potential: invariant measure and exact sampling

arXiv:2605.13648v4 Announce Type: replace Abstract: We study the sticky Cox–Ingersoll–Ross (CIR) process in one dimension, a diffusion on $[0,\infty)$ with a sticky boundary condition at the origin, arising as the marginal process in a sparse Bayesian inference framework based on Hadamard–Langevin dynamics. For the parameter range $\delta\in(1,2)$, in which the origin is accessible but not absorbing, we prove well-posedness of the process and uniqueness of its invariant measure, which is a mixture of a point mass at zero and a weighted gamma-type density on the interior. We derive an explicit Green's function for the resolvent in terms of confluent hypergeometric functions, and use this to construct an exact sampler for the invariant measure in the zero-potential case. For a non-trivial potential $G$, we establish existence and uniqueness of the tilted invariant measure via a Girsanov change of measure, and develop two sampling algorithms: a Metropolis–Hastings corrected sampler that targets the invariant measure exactly, and a cheaper, biased unadjusted Langevin algorithm (ULA) for a boundary-clamped variant of which we prove a first-order expansion of the stationary bias with an explicit constant: the leading error is a rank-one transfer of mass $K_\star h|\log h| $ onto the atom, so the total-variation bias is of exact order $h|\log h | $ – independent of $\delta$ – whenever the potential has nonzero boundary drift. Numerical experiments confirm the predicted behaviour: the Metropolis–Hastings sampler achieves the target invariant measure at all step sizes, while the ULA bias follows the proven first-order law, including its constant.

10.
arXiv (CS.AI) 2026-06-17

MemTrace: Probing What Final Accuracy Misses in Long-Term Memory

arXiv:2606.17328v1 Announce Type: new Abstract: LLM agents increasingly maintain long-term memory of user facts across sessions. Yet such memory is usually evaluated by aggregating accuracy over question rows or episodes. Because this approach scores question rows independently, even when several questions probe the same fact, it cannot show how that fact behaves as conditions change. We introduce MemTrace, a benchmark whose unit of measurement is the knowledge point: a single typed fact about the user, rather than an individual question. MemTrace probes each fact along three controlled dimensions: memory age, defined by how many sessions ago the fact appeared in the history; question type, covering current state, earlier state, and trajectory of change; and evidence condition, covering present, missing, and contradicted-by-false-premise settings. Evaluating 13 memory-system configurations across four paradigms, we find that similar pooled accuracy hides different failures: recovering a fact's current and earlier states does not imply tracking how it changed, and safe abstention does not imply correcting a false premise. The dominant bottleneck is evidence use, not retrieval: when systems fail, the evidence was retrievable 10 times more often than it was missing. These results suggest that improving long-term memory requires better use of reachable evidence, not simply more storage or retrieval.

11.
arXiv (CS.LG) 2026-06-15

Uncertainty Estimation and Generalization Bounds for Modern Deep Learning

arXiv:2606.13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems. While neural networks achieve remarkable predictive performance, their ability to generalize and to quantify uncertainty remains only partly understood. This thesis approaches this challenge from both methodological and theoretical angles: unifying Bayesian inference, function-space modeling, and large-deviation theory under a common probabilistic perspective. On the methodological side, the thesis introduces the Deep Variational Implicit Process (DVIP), a scalable Bayesian framework that extends implicit processes to deep architectures. Complementing this, two post-hoc methods – the Variational Linearized Laplace Approximation (VaLLA) and the Fixed-Mean Gaussian Process (FMGP) – are proposed to equip pretrained deterministic networks with calibrated uncertainty estimates. The theoretical contributions focus on one of the central open questions in modern machine learning: why do large, over-parameterized neural networks generalize so well? To address this, the thesis develops a unified probabilistic framework that connects three key mechanisms – diversity, smoothness, and stochasticity – within the language of PAC-Bayesian and large-deviation theory.

12.
arXiv (CS.AI) 2026-06-11

What Limits Does Quantization Place on Dense Top-$k$ Retrieval? A Theoretical Study

arXiv:2606.11780v1 Announce Type: cross Abstract: We establish conditions for embedding a corpus of $N$ documents as $d$-dimensional vectors such that every $k$-subset $S \subseteq [N]$ is realizable as a result of top-$k$ retrieval by some query vector. Recent work shows that $d = O(k)$ suffices for such embeddings to exist in $\mathbb{R}^d$, independently of $N$. We theoretically prove that this corpus-independent bound is specific to infinite precision. With $B$ bits per coordinate, perfect top-$k$ retrieval requires $Bd = \Omega(k \ln N)$; thus, at any fixed precision, the dimension must grow at least logarithmically with $N$. Specializing to a $\ell_2$-normalized $B$-bit uniform scalar quantization model, we also identify a threshold on the precision $B^{*} = O(\ln \ln N)$ below which no dimension suffices, together with two further regimes that bound the feasible $(B, d)$ pairs. Our result implies that in practical vector databases and dense retrieval systems where quantization is standard, the embedding dimension and possibly the precision must grow with the corpus size.

13.
arXiv (CS.LG) 2026-06-16

Evaluating Local Explainability Metrics for Machine Learning Models on Tabular Data

arXiv:2605.27618v2 Announce Type: replace Abstract: Despite the wide use of explainability techniques to attempt to understand the behavior of Artificial Intelligence (AI), the generated explanations may not always be reliable. An explanation can appear plausible to humans but fail to capture the internal reasoning of a model, particularly when dealing with complex tabular data. This paper studies the trustworthiness of local explainability techniques when applied to complex tabular classification tasks, considering evaluated metrics for three main properties: faithfulness to the model's predictions, robustness to input data variations, and complexity of the explanation itself. A benchmark was performed for Local Interpretable Model-Agnostic Explanations (LIME), Kernel SHapley Additive exPlanations (SHAP), and Feature Ablation techniques, across 32 datasets and different types of machine learning models. Model performance ranges were analyzed to identify two groups: consensus-correct, which are samples that all models predicted correctly, and consensus-wrong, samples that all models predicted incorrectly. The obtained results demonstrate that that the explanations are not always correlated with a model's predictive performance. Instead, dataset complexity and feature distributions seem to be the main factors affecting explanation quality and reliability.

14.
arXiv (CS.AI) 2026-06-11

\texttt{Range-Arithmetic}: Verifiable Deep Learning Inference on an Untrusted Party

arXiv:2505.17623v2 Announce Type: replace-cross Abstract: Verifiable computing (VC) has gained prominence in decentralized machine learning systems, where resource-intensive tasks like deep neural network (DNN) inference are offloaded to external participants due to blockchain limitations. This creates a need to verify the correctness of outsourced computations without re-execution. We propose \texttt{Range-Arithmetic}, a novel framework for efficient and verifiable DNN inference that transforms non-arithmetic operations, such as rounding after fixed-point matrix multiplication and ReLU, into arithmetic steps verifiable using sum-check protocols and concatenated range proofs. Our approach avoids the complexity of Boolean encoding, high-degree polynomials, and large lookup tables while remaining compatible with finite-field-based proof systems. Experimental results show that our method not only matches the performance of existing approaches, but also reduces the computational cost of verifying the results, the computational effort required from the untrusted party performing the DNN inference, and the communication overhead between the two sides.

15.
arXiv (CS.CV) 2026-06-18

Domain Generalizable Adaptation of 3D Vision-Language Models via Regularized Fine-Tuning

Domain adaptation remains a central challenge in 3D vision, especially for multimodal foundation models that align 3D point clouds with visual and textual data. While these models demonstrate strong general capabilities, adapting them to downstream domains with limited data often leads to overfitting and catastrophic forgetting. To address this, we introduce ReFine3D, a regularized fine-tuning framework designed for domain-generalizable tuning of 3D large multimodal models (LMMs). ReFine3D combines selective layer tuning with two targeted regularization strategies: multi-view consistency across augmented point clouds and text diversity through synonym-based prompts generated by large language models. Additionally, we incorporate point-rendered vision supervision and a test-time augmentation mechanism with confidence-based aggregation to further enhance robustness. Extensive experiments across different 3D domain generalization benchmarks show that ReFine3D improves base-to-novel class generalization by 1.36%, cross-dataset transfer by 2.43%, robustness to corruption by 1.80%, and few-shot accuracy by up to 3.11%, outperforming prior state-of-the-art methods with minimal added computational overhead.

16.
arXiv (quant-ph) 2026-06-16

Bi-qutrit entangled edge states of positive partial transposes with largest ranks

arXiv:2606.16265v1 Announce Type: new Abstract: Whenever $E$ is an eight dimensional subspace of the bi-qutrit quantum system whose orthogonal complement is spanned by a vector of Schmidt rank three, we show that there exist PPT entangled edge states with the range space $E$ whose partial transposes are of rank six, which is the largest possible rank. In this way, we exhibit a huge family of bi-qutrit PPT entangled edge states of type $(8,6)$. They make faces of the convex set of all PPT states, and we find bi-qutrit PPT entangled edge states of other types on the boundaries of such faces.

17.
arXiv (CS.CL) 2026-06-18

UMA-Split: unimodal aggregation for both English and Mandarin non-autoregressive speech recognition

This paper proposes a unimodal aggregation (UMA) based nonautoregressive model for both English and Mandarin speech recognition. The original UMA explicitly segments and aggregates acoustic frames (with unimodal weights that first monotonically increase and then decrease) of the same text token to learn better representations than regular connectionist temporal classification (CTC). However, it only works well in Mandarin. It struggles with other languages, such as English, for which a single syllable may be tokenized into multiple fine-grained tokens, or a token spans fewer than 3 acoustic frames and fails to form unimodal weights. To address this problem, we propose allowing each UMA-aggregated frame map to multiple tokens, via a simple split module that generates two tokens from each aggregated frame before computing the CTC loss.

18.
arXiv (CS.CV) 2026-06-11

Adv-TGD: Adversarial Text-Guided Diffusion for Face Recognition Impersonation Attacks

The widespread adoption of face recognition (FR) technologies raises serious privacy concerns, as facial data can be exploited without consent. To address this challenge, we propose Adv-TGD, a generative adversarial attack framework that synthesizes photorealistic faces capable of impersonating target identities and deceiving face recognition systems. Built upon Stable Diffusion, Adv-TGD performs per-sample LoRA fine-tuning conditioned on concise textual prompts to generate natural yet adversarially manipulated identities. Unlike conventional identity-attack approaches, our method optimizes lightweight cross-attention adapters for each source-target pair within a single-step denoising process. Latent blending is constrained by a face-local heatmap mask to ensure spatially precise identity manipulation while preserving non-sensitive regions. We introduce a composite objective that integrates masked epsilon-MSE reconstruction, thresholded identity divergence in FR embedding space, directional feature alignment, and source-similarity suppression to balance adversarial attack and visual realism. Optionally, LLaVA-generated attribute prompts enhance fine-grained semantic details without reintroducing identity cues. Under the black-box evaluation protocol, Adv-TGD attains an average attack success rate (ASR) of 85.90% across IR152, IRSE50, MobileFace, and FaceNet, surpassing the semantic SOTA baseline Adv-CPG by +6.25 points, diffusion-based makeup method DiffAIM by +3 points, and noise-based P3-Mask by +16 points. Despite its strong attack efficacy, Adv-TGD preserves high visual fidelity (PSNR = 27.15 dB, SSIM = 0.981). Furthermore, we demonstrate the flexibility of our framework by successfully extending it to in-the-wild datasets (LADN), general object classification (ImageNet), and transformer-based diffusion models (FLUX.1).

19.
arXiv (math.PR) 2026-06-17

Convergence rate of Euler–Maruyama scheme to the invariant probability measure under total variation distance for the SDEs

arXiv:2505.04218v3 Announce Type: replace Abstract: This article shows the geometric decay rate of Euler-Maruyama scheme for one-dimensional stochastic differential equation towards its invariant probability measure under total variation distance. Firstly, the existence and uniqueness of invariant probability measure and the uniform geometric ergodicity of the chain are studied through introduction of non-atomic Markov chains. Secondly, the equivalent conditions for uniform geometric ergodicity of the chain are discovered, by constructing a split Markov chain based on the original Euler-Maruyama scheme.

20.
arXiv (CS.CV) 2026-06-12

Possibilistic Predictive Uncertainty for Deep Learning

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency. Code is available at https://github.com/MaxwellYaoNi/DAPPr.

21.
arXiv (CS.CL) 2026-06-18

REVES: REvision and VErification–Augmented Training for Test-Time Scaling

Test-time scaling via sequential revision has emerged as a powerful paradigm for enhancing Large Language Model (LLM) reasoning. However, standard post-training methods primarily optimize single-shot objectives, creating a fundamental misalignment with multi-step inference dynamics. While recent work treats this as multi-turn reinforcement learning (RL), conventional approaches optimize over the multi-step trajectories directly, failing to further exploit the high-quality mistakes in intermediate steps that model can learn from correcting them. We propose a two-stage iterative framework that alternates between online data/prompt augmentation and policy optimization. By converting the intermediate steps (``near-miss'' answers) in the successful recovery trajectories into decoupled revision and verification prompts, our approach concentrates training on both effective answer transformation and error identification. This approach enables efficient off-policy data generation and reduces the computational overhead of long-horizon sampling compared to standard multi-turn RL. On LiveCodeBench, using publicly available test cases as feedback, we observe gains of +6.5 points over the RL baseline and +4.0 points over standard multi-turn training. Beyond coding, our approach matches the previously reported SOTA result on circle packing while using the smallest base model (4B) and far fewer rollouts than the much larger evolutionary search systems. Math results under ground-truth verification further confirm improved correction ability. It also generalizes to out-of-distribution constraint-satisfaction puzzles such as n\_queens and mini\_sudoku, where correctness is defined entirely by problem constraints. Code is available at https://github.com/yxliu02/REVES.git.

22.
arXiv (CS.AI) 2026-06-16

Adaptive Memory Crystallization for Autonomous AI Agent Learning in Dynamic Environments

arXiv:2604.13085v2 Announce Type: replace-cross Abstract: Autonomous AI agents operating in dynamic environments face a persistent challenge: acquiring new capabilities without erasing prior knowledge. We present Adaptive Memory Crystallization (AMC), a memory architecture for progressive experience consolidation in continual reinforcement learning. AMC is conceptually inspired by the qualitative structure of synaptic tagging and capture (STC) theory, the idea that memories transition through discrete stability phases, but makes no claim to model the underlying molecular or synaptic mechanisms. AMC models memory as a continuous crystallization process in which experiences migrate from plastic to stable states according to a multi-objective utility signal. The framework introduces a three-phase memory hierarchy (Liquid–Glass–Crystal) governed by an Itô stochastic differential equation (SDE) whose population-level behavior is captured by an explicit Fokker–Planck equation admitting a closed-form Beta stationary distribution. We provide proofs of: (i) well-posedness and global convergence of the crystallization SDE to a unique Beta stationary distribution; (ii) exponential convergence of individual crystallization states to their fixed points, with explicit rates and variance bounds; and (iii) end-to-end Q-learning error bounds and matching memory-capacity lower bounds that link SDE parameters directly to agent performance. Empirical evaluation on Meta-World MT50, Atari 20-game sequential learning, and MuJoCo continual locomotion consistently shows improvements in forward transfer (+34–43\% over the strongest baseline), reductions in catastrophic forgetting (67–80\%), and a 62\% decrease in memory footprint.

23.
arXiv (CS.LG) 2026-06-16

Taming Curvature: Architecture Warm-Up for Stable Transformer Training

arXiv:2606.16768v1 Announce Type: new Abstract: Training billion-parameter Transformers is often brittle, with transient loss spikes and divergence that waste compute. Even though the recently developed Edge of Stability (EoS) theory provides a powerful tool to understand and control the stability of optimization methods via the (preconditioned) curvature, these curvature-controlling methods are not popular in large-scale Transformer training due to the complexity of curvature estimation. To this end, we first introduce a fast online estimator of the largest (preconditioned) Hessian eigenvalue (i.e., curvature) based on a warm-started variant for power iteration with Hessian-vector products. We show theoretically, and verify empirically, that the proposed method makes per-iteration curvature tracking feasible at billion parameter scale while being more accurate. Using this tool, we find that training instabilities coincide with surges in preconditioned curvature and that curvature grows with depth. Motivated by these observations, we propose architecture warm-up: progressively growing network depth to carefully control the preconditioned Hessian and stabilize training. Experiments on large Transformers validate that our approach enables efficient curvature tracking and reduces instabilities compared to existing state-of-the-art stabilization techniques without slowing down convergence.

24.
arXiv (CS.AI) 2026-06-15

MA-ProofBench: A Two-Tiered Evaluation of LLMs for Theorem Proving in Mathematical Analysis

arXiv:2606.13782v1 Announce Type: new Abstract: Large Language Models (LLMs) have made notable progress in automated theorem proving, yet existing formal benchmarks remain limited in both mathematical coverage and difficulty. Most are concentrated in areas that are easier to formalize, such as algebra and elementary number theory, and provide limited coverage of subfields that require deeper reasoning, including mathematical analysis. To address this gap, we introduce MA-ProofBench, to the best of our knowledge, the first formal theorem-proving benchmark dedicated to Mathematical Analysis. The benchmark contains 200 formalized theorems covering 6 core topics and 27 subcategories, including measure and integration theory, complex analysis, and functional analysis. The problems are divided into two difficulty levels, an undergraduate level (Level I, 100 problems) and a Ph.D. qualifying level (Level II, 100 problems), to evaluate how well LLMs perform formal reasoning at different mathematical depths. Each problem is constructed through a human-led, LLM-assisted formalization pipeline followed by independent expert review, ensuring that the formal statements remain faithful to the original mathematics. We evaluate a range of recent general-purpose reasoning models and formal theorem provers on MA-ProofBench. However, most models perform poorly: even the best-performing model, GPT-5.5, achieves only 16% Pass@8 on Level I and 5% on Level II, while most models stay close to 0% on Level II. Further analysis identifies Mathlib hallucinations and incomplete proofs as the two dominant failure modes, while an evaluation on the natural-language version of the benchmark exposes a clear gap between informal and formal reasoning. MA-ProofBench is intended to serve as a reliable reference for tracking progress in formal mathematical reasoning in advanced domains.

25.
arXiv (math.PR) 2026-06-18

On a class of unbalanced step-reinforced random walks

arXiv:2504.14767v4 Announce Type: replace Abstract: A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability $\alpha$, the so-called positively step-reinforced random walk repeats one of its previous steps, chosen randomly and uniformly from its entire history. Alternatively, with probability $1-\alpha$, it makes an independent move. For the so-called negatively step-reinforced random walk, the process is similar, but any repeated step is taken with its direction reversed. These random walks have been introduced respectively by Simon (1955) and Bertoin (2024) and are sometimes refered to the self-confident step-reinforced random walk and the counterbalanced step-reinforced random walk respectively. In this work, we introduce a new class of unbalanced step-reinforced random walks for which we prove the strong law of large numbers and the central limit theorem. In particular, our work provides a unified treatment of the elephant random walk introduced by Schutz and Trimper (2004) and the positively and negatively step-reinforced random walks.