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版本更新 · v3arXiv:2605.10379

Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness

Ivo Petrov, Jasper Dekoninck, Dimitar I. Dimitrov, Martin Vechev

原文摘要

Large language models (LLMs) have become capable mathematical problem-solvers, often producing correct proofs for challenging problems. However, correctness alone is not sufficient: mathematical proofs should also be clear, insightful, contain transferable knowledge, and be generally useful to the reader. While proof quality is subjective and depends on the reader and context, many of its components can be made concrete. In this work, we identify such components and introduce ProofRank, a benchmark curated from challenging competitions that measures several scalable proxies of proof quality: (i) conciseness - quantifying whether proofs avoid unnecessary steps; (ii) computational ease - the extent to which a proof relies on tedious calculations; (iii) cognitive simplicity - how accessible the used proof techniques are; (iv) diversity - how varied a model's proofs for a single problem are; and (v) adaptivity - how well a model can follow a specified technique. We find proof quality varies substantially across models along dimensions that correctness largely fails to capture. Every proof-level proxy can be steered through prompting, but often at a moderate correctness cost. ProofRank thus captures important aspects of mathematical proofs beyond correctness, and indicates the need for models that produce proofs which are not only correct but also valuable.

cs.CL

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2306.10426

Understanding Certified Training with Interval Bound Propagation

Yuhao Mao, Mark Niklas Müller, Marc Fischer, Martin Vechev

原文摘要

As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case loss over a robustness specification. Curiously, training methods based on the imprecise interval bound propagation (IBP) consistently outperform those leveraging more precise bounding methods. Still, we lack an understanding of the mechanisms making IBP so successful. In this work, we thoroughly investigate these mechanisms by leveraging a novel metric measuring the tightness of IBP bounds. We first show theoretically that, for deep linear models, tightness decreases with width and depth at initialization, but improves with IBP training, given sufficient network width. We, then, derive sufficient and necessary conditions on weight matrices for IBP bounds to become exact and demonstrate that these impose strong regularization, explaining the empirically observed trade-off between robustness and accuracy in certified training. Our extensive experimental evaluation validates our theoretical predictions for ReLU networks, including that wider networks improve performance, yielding state-of-the-art results. Interestingly, we observe that while all IBP-based training methods lead to high tightness, this is neither sufficient nor necessary to achieve high certifiable robustness. This hints at the existence of new training methods that do not induce the strong regularization required for tight IBP bounds, leading to improved robustness and standard accuracy.

cs.LG · cs.AI

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arXiv ↗PDF ↗
版本更新 · v5arXiv:2512.01782

Dual Randomized Smoothing: Beyond Global Noise Variance

Chenhao Sun, Yuhao Mao, Martin Vechev

原文摘要

Randomized Smoothing (RS) is a prominent technique for certifying the robustness of neural networks against adversarial perturbations. With RS, achieving high accuracy at small radii requires a small noise variance, while achieving high accuracy at large radii requires a large noise variance. However, the global noise variance used in the standard RS formulation leads to a fundamental limitation: there exists no global noise variance that simultaneously achieves strong performance at both small and large radii. To break through the global variance limitation, we propose a dual RS framework which enables input-dependent noise variances. To achieve that, we first prove that RS remains valid with input-dependent noise variances, provided the variance is locally constant around each input. Building on this result, we introduce two components: (i) a variance estimator predicts an optimal noise variance for each input, (ii) this estimated variance is then used by a standard RS classifier. The variance estimator is independently smoothed via RS to ensure local constancy, enabling flexible design. We also introduce training strategies to iteratively optimize the two components. Experiments on CIFAR-10 demonstrate that our dual RS method provides strong performance for both small and large radii-unattainable with global noise variance-while incurring only a 60% computational overhead at inference. Moreover, it outperforms prior input-dependent noise approaches across most radii, with gains at radii 0.5, 0.75, and 1.0 of 15.6%, 20.0%, and 15.7%. On ImageNet, dual RS remains effective across all radii, with advantages of 8.6%, 17.1%, and 9.1% at radii 0.5, 1.0, and 1.5. Additionally, the dual RS framework provides a routing perspective for certified robustness, improving the accuracy-robustness trade-off with off-the-shelf expert RS models.

cs.LG · cs.AI

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arXiv ↗PDF ↗
版本更新 · v5arXiv:2410.06816

Expressiveness of Multi-Neuron Convex Relaxations in Neural Network Certification

Yuhao Mao, Yani Zhang, Martin Vechev

原文摘要

Neural network certification methods heavily rely on convex relaxations to provide robustness guarantees. However, these relaxations are often imprecise: even the most accurate single-neuron relaxation is incomplete for general ReLU networks, a limitation known as the *single-neuron convex barrier*. While multi-neuron relaxations have been heuristically applied to address this issue, two central questions arise: (i) whether they overcome the convex barrier, and if not, (ii) whether they offer theoretical capabilities beyond those of single-neuron relaxations. In this work, we present the first rigorous analysis of the expressiveness of multi-neuron relaxations. Perhaps surprisingly, we show that they are inherently incomplete, even when allocated sufficient resources to capture finitely many neurons and layers optimally. This result extends the single-neuron barrier to a *universal convex barrier* for neural network certification. On the positive side, we show that completeness can be achieved by either (i) augmenting the network with a polynomial number of carefully designed ReLU neurons or (ii) partitioning the input domain into convex sub-polytopes, thereby distinguishing multi-neuron relaxations from single-neuron ones which are unable to realize the former and have worse partition complexity for the latter. Our findings establish a foundation for multi-neuron relaxations and point to new directions for certified robustness, including training methods tailored to multi-neuron relaxations and verification methods with multi-neuron relaxations as the main subroutine.

cs.LG · cs.AI

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arXiv ↗PDF ↗
版本更新 · v5arXiv:2410.10347

A Unified Approach to Routing and Cascading for LLMs

Jasper Dekoninck, Maximilian Baader, Martin Vechev

原文摘要

The availability of a wide range of large language models (LLMs) embedded in various agentic systems has significantly increased the potential of model selection strategies to improve the cost-performance tradeoff. Existing strategies involve either routing, where a single model is chosen per query, or cascading, which sequentially runs increasingly larger models until a satisfactory answer is found. However, current approaches face three key limitations: they (1) lack formal proofs of optimality, (2) fail to identify the conditions under which these strategies are most effective to improve the cost-performance tradeoff, and (3) are unable to combine both paradigms for further improvements. To address these issues, we first derive a novel optimal strategy for cascading and prove the optimality of an existing routing strategy. Further, we propose cascade routing, a unified framework that integrates routing and cascading into a theoretically optimal strategy. Through our analysis, we identify good quality estimators as the critical factor for the success of model selection paradigms. Finally, in our experiments, we show that cascade routing consistently outperforms the individual approaches by a large margin and we analyze quality estimators to determine when routing and/or cascading are useful paradigms for model selection.

cs.CL

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.35987

PROBE: Frontier Coding Agents Find Different Bugs Than Maintainers Fix

Marco Paina, Mark Niklas Müller, Niels Mündler-Sasahara, Martin Vechev

原文摘要

Proactive bug discovery is an important software-engineering problem. Even though coding agents are already widely deployed in this domain, their capabilities remain understudied. In particular, the challenging task of finding all bugs that human maintainers would repair across an entire repository has not been studied yet. To close this gap, we introduce PROBE, a benchmark consisting of all 2,457 bugs fixed over the course of 18 months across 20 diverse GitHub repositories, together with a method for matching candidate findings to this partial reference set. We evaluate coding agents across frontier models and find they all achieve a recall of below $21\%$ and a precision of less than $9\%$ with respect to the reference set. While stronger models increase recall substantially from $8\%$ to $17\%$, they do not improve precision. Surprisingly, despite the low precision, LLM and human evaluators still judge $85\%$ of findings valid. Crucially, we find that found bug distributions are similar across agents but differ substantially from those of bugs fixed by maintainers. The practical relevance of bug discovery and the low recall of frontier models make this benchmark a valuable resource for both model users and developers.

cs.SE · cs.AI · cs.LG

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.35199

Can Open Be Too Open? On the Security and Trustworthiness of Fully Transparent LLMs

Sheila Zingg, Florian Tramèr, Martin Vechev, Srdjan Čapkun

原文摘要

There are different levels of transparency for LLMs: open weights, open data, and/or open pipeline. Recently, more interest has emerged in fully transparent LLMs, i.e., LLMs with fully open weights, data, and training pipeline. Drawing analogies to other fields such as software security, it is often believed that increasing transparency inherently increases the security and trustworthiness of the LLM. However, we argue that such claims need to be critically re-evaluated in the context of LLMs. In this paper, we analyze the impact of transparency on LLM security and trustworthiness by reviewing the relevant literature. Our core findings are that, due to the limited reproducibility of LLM pipelines, in practice, users cannot verify the correspondence between open weights and the associated open data and pipeline. Thus, in order to trust a model, users still need to trust that developers acted honestly, reducing the benefits over models that provide less "transparency". Moreover, we find that even when LLMs are fully transparent and trusted, this openness can favor adversaries. Open weights in particular, but also open data and pipelines, can increase the success rate of attacks. Although the same mechanisms can be used to improve the model and protect it against attacks, the current lack of robust lightweight mechanisms to patch LLM vulnerabilities limits the benefits of openness at this time. We note that our analysis is based on current LLM capabilities and analysis tools, and that future developments may require a re-evaluation of these points.

cs.CR

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.34462

End-to-End Neural Modeling of EM Response and Design Performance for Free-Form RFIC Passives

Yuhao Mao, Chenhao Chu, Martin Vechev, Hua Wang

原文摘要

Passive matching networks are critical components in radio-frequency integrated circuits (RFICs), but their design is bottlenecked by expensive finite-difference-based electromagnetic (EM) simulation. We propose an end-to-end neural framework for free-form RFIC passives that predicts both EM response and downstream design performance under varying frequency and circuit contexts, combining a frequency-conditioned neural simulator with a circuit-conditioned neural solver. To improve design performance prediction, the simulator outputs a neural EM response consisting of both the explicit EM response and a complementary response, together with a dependence regularizer that encourages the two responses to capture orthogonal information. To evaluate the proposed framework, we construct a large-scale dataset of free-form passive layouts, synthesized from both expert-designed contours and random paths. Our 21M-parameter model achieves high accuracy across a broad frequency range, circuit contexts and passive matching settings, with $R^2>0.98$ for almost all targets, while providing orders-of-magnitude faster evaluation than traditional EM simulation. Code available at https://github.com/ETH-IDEAS/RFIC-NeuralSim.

eess.SP · cs.LG

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arXiv ↗PDF ↗