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新论文 · v1arXiv:2611.11368

BiVerify: Closing the Loop Between Backward and Forward Verification for Mathematical Self-Correction

Rui Zou, Xin Zhao, Mengqi Wei, Ji-Rong Wen

原文摘要

Large language models (LLMs) have made substantial progress in mathematical reasoning but still produce incorrect solutions to complex problems, indicating the need for more reliable self-correction mechanisms. Mathematical self-correction typically identifies errors through verification, which can proceed backward or forward. The two directions provide complementary verification capabilities. Backward verification checks a candidate answer against the original constraints, bypassing complex intermediate reasoning, but cannot ensure correct reasoning or objective completeness. Forward verification follows the problem conditions and current solution, enabling it to locate reasoning errors and assess objective completeness, but may overlook key constraints in complex solution chains. We propose BiVerify, a dynamically scheduled framework for bidirectional mathematical verification. BiVerify begins with backward verification to screen the answer against the original constraints, followed by forward verification of the reasoning process; subsequent direction switching, state resetting, and re-verification are governed by verification outcomes. Upon failure, the system revises the candidate or verification flow until the same candidate passes both directions. We also introduce shared mathematical tools that separate logical reasoning from precise computation. We systematically evaluate BiVerify on five challenging mathematical reasoning benchmarks using multiple mainstream DeepSeek, GPT, and Gemini models. BiVerify exceeds the strongest representative public baseline evaluated in this work by 13.5 percentage points in average accuracy, with the margin reaching 31.2 percentage points on GPT. Further analysis shows that BiVerify's overall performance exceeds that of either verification direction alone.

cs.AI

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.29549

AMTFV: Agentic Mathematical Tool-Flow Verification for LLM Self-Correction

Rui Zou, Yutao Zhu, Mengqi Wei, Ji-Rong Wen

原文摘要

Large language models have demonstrated strong mathematical problem-solving capabilities, yet reliably verifying their candidate answers remains challenging. Existing representative methods mainly revise outputs through natural-language reflection or assist verification by directly generating verification programs; the former may not reliably support exact computation, whereas the latter prematurely couples mathematical modeling with low-level implementation. We propose AMTFV (Agentic Mathematical Tool-Flow Verification). By introducing Mathematical Tool Flow (MTF) as an interrupt--execute--resume interface, AMTFV decouples verification modeling from concrete execution and supports exact computation through a mathematical toolbox. Specifically, the verification agent first constructs a verification workflow, encodes the mathematical objects and computational intent requiring reliable execution in an MTF request, and sends it to the mathematical toolbox agent. The latter parses the request, generates executable calls, and dispatches them to the backend for exact computation. Tool outputs then support candidate-answer adjudication, answer revision, and verification-workflow revision. We evaluate AMTFV on five challenging mathematical reasoning datasets with seven model configurations from DeepSeek, GPT, and Gemini. Experimental results show that AMTFV outperforms the representative baselines evaluated in this study overall; under an individual model configuration, it improves average accuracy over the strongest baseline by up to 8.3 percentage points, with larger gains on samples of medium and high verification complexity.

cs.AI

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.06670

Polynomial-Time Differentially Private Synthetic Graph Release with Nearly-Linear Additive Error

Marek Eliáš, Gautam Kamath, Janardhan Kulkarni, George Z. Li, Jingcheng Liu, Sepideh Mahabadi, Pan Peng, Jakub Tarnawski 等 10 位作者

原文摘要

We give a polynomial-time $(\varepsilon, δ)$-edge-differentially private algorithm that releases a synthetic graph approximately preserving all cut values of a nonnegative weighted input graph $G$. Our algorithm outputs a nonnegative weighted graph $H$ such that, with probability at least $1-β$, simultaneously for all $S\subseteq V$, \[ \left|w_G(S,V\setminus S)-w_H(S,V\setminus S)\right| \leq γw_G(S,V\setminus S) + O\left(\frac{n}{γ\varepsilon} \log^7 \frac{n}{δβγ\varepsilon}\right). \] For fixed $γ, \varepsilon$ and $δ= β= n^{-10}$, the additive error is $n \operatorname{polylog} n$, improving upon the previous efficient bound of $n^{13/12 + o(1)}$. Furthermore, we establish an $Ω(n/γ\varepsilon)$ lower bound for the relevant parameter regime, showing that our result is tight up to polylogarithmic factors. Our algorithm uses a log-det-regularized SDP to generate fractional queries for multiplicative-weights updates and certify accuracy for all cuts. The privacy analysis charges privacy loss only fractionally per mechanism call, based on the amount of mass on edge coordinates retired from subsequent iterations. Our synthetic graph release yields improved error bounds for several downstream tasks in private graph analysis including correlation clustering, Max-Cut, Max-$k$-Cut, constrained cut problems and hierarchical clustering. Most notably, for unweighted complete-graph correlation clustering, we achieve the optimal $\widetilde O(n)$ additive error while reducing the best previously known approximation ratio for this additive error from several thousand to $1.387$. We also provide a formalization of our results in Lean.

cs.DS · math.ST

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.04721

Pure Differentially Private Query Release via Laplace Input Smoothing

Zongrui Zou

原文摘要

We study the offline release of a public family of $k$ statistical queries on a database of $N$ records from a public universe of size $d$, under pure $\varepsilon$-differential privacy. We give an efficient algorithm that, with probability at least $1-β$, answers all queries simultaneously to error $$O\left(\min\left\{1,\sqrt{\frac{\log(d/β)\log k}{N\varepsilon}}\right\}\right).$$ The output is a synthetic histogram on the data universe, and its running time depends polynomially on $N,d$ and $k$. This resolves a conjecture of Nikolov and Ullman (2021) with an efficient, polynomial-time construction. Fitzsimons (2026) recently established the same square-root error scale via an information-theoretic construction that relies on a computationally intractable Lipschitz envelope over the exponential space of possible outputs. In contrast, we introduce an input-side smoothing approach: we run a selection-only multiplicative-weights process after a single sparse Laplace perturbation of the input histogram. Departing from standard first-order stability analyses, we investigate the stability of stability by establishing a uniform lower bound on the second-order log-derivatives of the output transcript across $T$ rounds of multiplicative weight updates. We then develop an analytic smoothing principle showing that this curvature bound allows a sparse, coordinate-wise perturbation to guarantee pure differential privacy globally, attaining optimal utility through a conceptually simple, polynomial-time pure-DP mechanism.

cs.DS

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.40349

TouchBridge：面向灵巧操作、以触觉为条件的人到机器人迁移

TouchBridge: Tactile-Conditioned Human-to-Robot Transfer for Dexterous Manipulation

Haozhe Zhang, Gu Zhang, Zirui Zou, Yuzheng Chen, Jinlong Wu, Zixuan Hu, Jianke Zhang, Yucheng Hu 等 10 位作者

AI 速读 基于摘要

TouchBridge 通过软硬件协同设计与触觉条件重定向，把人类演示直接转换为机器人训练数据，用于微调 VLA 模型完成接触丰富操作。

cs.RO

arXiv ↗PDF ↗
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Human demonstrations offer an efficient and scalable source of data for dexterous robot manipulation, but differences in sensing and hand morphology complicate the transfer of contact-rich interactions. We present TouchBridge, a hardware--software co-designed framework for human-to-robot data transformation. A wearable human demonstration interface and a corresponding robot interface establish cross-embodiment correspondence in visual and fingertip tactile sensing. We introduce Tac-Retarget, a tactile-conditioned retargeting method that uses measured contact to align fingertip contact patches and preserve their spatial relations within and across hands. Unlike object-aware or simulation-based transfer pipelines, Tac-Retarget requires no object mesh, object-pose estimate, or physics simulation for retargeting, enabling direct and scalable conversion of human demonstrations into robot-domain training data. Combined with visual synthesis and camera-anchored action conversion, TouchBridge produces robot-domain demonstrations for fine-tuning a pretrained vision-language-action (VLA) model. Across four real-world contact-rich tasks, policies fine-tuned solely on TouchBridge-converted human demonstrations achieve a 72.5% average success rate, compared with 77.5% using an equal number of teleoperated robot demonstrations, while human demonstration collection is 7.0x faster. Under the same policy and training setup, Tac-Retarget outperforms DexPilot and UniDex by 25.0 and 42.5 percentage points, respectively.

新论文 · v1arXiv:2610.35262

Conversational Generalized Linear Bandits with Hybrid Feedback

Yurui Zou, Qirun Zeng, Jinhang Zuo

原文摘要

Conversational bandits improve recommendations by actively querying users about key-terms to elicit their item preferences. However, existing methods typically assume homogeneous feedback for items and key-terms, using either absolute rewards or pairwise comparisons. In practice, item feedback often takes the form of clicks or ratings, while comparisons are more natural for key-terms. To address this gap, we study conversational generalized linear bandits with hybrid feedback, combining absolute item rewards and relative key-term comparisons. We propose Conversational UCB with Hybrid Feedback (HyConUCB), which constructs unified confidence bounds from heterogeneous feedback and adaptively selects key-term comparisons by balancing information gain and directional coverage. Through a refined regret analysis that jointly exploits both feedback sources, we establish a regret bound that improves upon reward-only and adapted dueling-only benchmarks. Experiments on synthetic and real-world datasets validate the effectiveness of our algorithm.

cs.LG

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arXiv ↗PDF ↗