arXiv subjects

Zhouxing Shi

Publications and source records attributed to Zhouxing Shi.

At least 19 recordsLinked to original sources

arXiv2026

Formalize Once, Edit the Rest: Efficient Lean-Based Answer Selection for Math Reasoning

With large language models (LLMs) increasingly applied to mathematical reasoning, formal proof assistants such as Lean can be leveraged to verify reasoning outputs with machine-checkable rigor, enabling use cases such as answer selection in test-time scaling with K sampled candidate answers. However, employing Lean requires that LLM outputs, originally in natural language, first be formalized. Existing Lean-based answer-selection work uses an autoformalization model to generate a formal statement in Lean for each candidate answer independently, incurring a significant computational cost. We propose BASE, a base-and-edit pipeline that formalizes a single base candidate per problem and derives the remaining K-1 statements by editing the answer expression in place. To facilitate this, we train a rewriter model LEANSCRIBE to localize the answer in the base formalization and generate a reusable edit function for the other K-1 candidates. BASE simultaneously improves selection accuracy and reduces formalization cost - a Pareto improvement that holds on all 12 (dataset, solver) configurations across four benchmarks and three solvers, cutting autoformalizer calls by about 5x at K=8, with the reduction expected to become larger as K grows. Code is available at https://github.com/ucr-rai/base-and-edit.

cs.CL↗

arXiv2026

Evaluating the Robustness of Proof Autoformalization in Lean 4

Proof autoformalization aims to translate a mathematical informal proof written in natural language into a formal proof in a formal language such as Lean~4. Several works have developed LLM-based models for proof autoformalization. However, existing evaluations have typically focused on translating well-formed informal proofs from curated datasets. We argue that a robust proof autoformalizer must remain faithful even for informal proofs that diverge from these idealized ones, and we present the first study on the robustness of proof autoformalization models. We formulate two categories of perturbations and evaluate robustness under each: a global perturbation paraphrases the informal proof in a different style, under which the formalization should remain consistent; a local perturbation alters a value, symbol, or proof step, possibly in a counterfactual way, and a robust formalization should faithfully reflect the perturbation rather than reverting to the original one or inferring a different one on its own. We build a benchmark with both perturbations on miniF2F and MATH-500, and automatically measure how stable a proof autoformalization's correctness is under global perturbations and how faithfully its output reflects local perturbations. We evaluate seven recent models, all of which are sensitive to global perturbations and mostly fail to remain faithful under local perturbations. Code and data are available via https://github.com/ucr-rai/robust-proof-autoformalization.

cs.CL↗

arXiv2026

GRLO: Towards Generalizable Reinforcement Learning in Open-Ended Environments from Zero

Post-training has become a crucial step for unlocking the capabilities of large language models, with reinforcement learning (RL) emerging as a critical paradigm. Recent RL-based post-training has increasingly split into two paradigms: reinforcement learning from human feedback (RLHF), which optimizes models using human preference signals in target domains, and reinforcement learning from verifiable rewards (RLVR), which operates in verifier-backed environments. The latter has dominated recent reasoning-oriented post-training because it delivers stronger gains and higher efficiency on domain-specific tasks (e.g., reasoning). However, although in-domain RL training achieves promising performance, it still requires a substantial amount of GPU compute, which remains a major barrier to broad adoption. In this work, we study the generalization ability of RLHF learned from scratch from a small set of interactions in open-ended environments, and investigate whether the conversational abilities it explicitly acquires can implicitly transfer to downstream tasks such as mathematical reasoning and code generation, namely GRLO. Specifically, on Qwen3-4B-Base backbone, GRLO improves the average performance across all domains from 24.1 to 63.1 with only 5K prompts and 22.7 GPU hours, requiring about $46\times$ less data and $68\times$ less compute than a strong in-domain RLVR baseline. The resulting model is even competitive with Qwen's released post-trained models which required a much larger training cost. Notably, a subsequent in-domain RLVR stage brings only selective gains, mainly on harder competition-math benchmarks. We hope GRLO offers a simple and efficient recipe for building broadly capable post-trained models. Our code and data will be available at: \href{https://github.com/SJY8460/GRLO}{https://github.com/SJY8460/GRLO}.

cs.LG↗

arXiv2026

PIKA: Expert-Level Synthetic Datasets for Post-Training Alignment from Scratch

High-quality instruction data is critical for LLM alignment, yet existing open-source datasets often lack efficiency, requiring hundreds of thousands of examples to approach proprietary performance. In this work, we find that beyond the widely recognized importance of prompt-response quality, prompt difficulty itself plays a critical role in driving alignment gains. Motivated by this observation, we introduce PiKa, a data-efficient family of expert-level alignment datasets that concentrates supervision on high-difficulty instructions. The PiKa-SFT dataset contains only 30k examples, an order of magnitude fewer than state-of-the-art open datasets like Magpie-Pro. Despite its small size, fine-tuning Llama-3-8B-Base on PiKa-SFT even outperforms the official Llama-3-8B-Instruct model trained on over 10M proprietary examples on widely used benchmarks such as AlpacaEval 2.0 and Arena-Hard. We also validate the generalizability of PiKa across the Qwen2.5 series (0.5B-7B), consistently surpassing their official instruction-tuned counterparts. Additionally, we provide 30k high-quality preference optimization examples to further enhance alignment. Our results demonstrate that promising alignment is achievable with significantly reduced data, democratizing access for resource-constrained research. Our code and data will be available at https://github.com/SJY8460/PiKa.

cs.CL↗

arXiv2026

Certified Training with Branch-and-Bound for Lyapunov-stable Neural Control

We study the problem of learning verifiably Lyapunov-stable neural controllers that provably satisfy the Lyapunov asymptotic stability condition within a region-of-attraction (ROA). Unlike previous works that adopted counterexample-guided training without considering the computation of verification in training, we introduce Certified Training with Branch-and-Bound (CT-BaB), a new certified training framework that optimizes certified bounds, thereby reducing the discrepancy between training and test-time verification that also computes certified bounds. To achieve a relatively global guarantee on an entire input region-of-interest, we propose a training-time BaB technique that maintains a dynamic training dataset and adaptively splits hard input subregions into smaller ones, to tighten certified bounds and ease the training. Meanwhile, subregions created by the training-time BaB also inform test-time verification, for a more efficient training-aware verification. We demonstrate that CT-BaB yields verification-friendly models that can be more efficiently verified at test time while achieving stronger verifiable guarantees with larger ROA. On the largest output-feedback 2D Quadrotor system experimented, CT-BaB reduces verification time by over 11X relative to the previous state-of-the-art baseline using Counterexample Guided Inductive Synthesis (CEGIS), while achieving 164X larger ROA. Code is available at https://github.com/shizhouxing/CT-BaB.

cs.LG↗

arXiv2026

Talking with Verifiers: Automatic Specification Generation for Neural Network Verification

Neural network verification tools currently support only a narrow class of specifications, typically expressed as low-level constraints over raw inputs and outputs. This limitation significantly hinders their adoption and practical applicability across diverse application domains where correctness requirements are naturally expressed at a higher semantic level. This challenge is rooted in the inherent nature of deep neural networks, which learn internal representations that lack an explicit mapping to human-understandable features. To address this, we bridge this gap by introducing a novel component to the verification pipeline, making existing verification tools applicable to a broader range of domains and specification styles. Our framework enables users to formulate specifications in natural language, which are then automatically analyzed and translated into formal verification queries compatible with state-of-the-art neural network verifiers. We evaluate our approach on both structured and unstructured datasets, demonstrating that it successfully verifies complex semantic specifications that were previously inaccessible. Our results show that this translation process maintains high fidelity to user intent while incurring low computational overhead, thereby substantially extending the applicability of formal DNN verification to real-world, high-level requirements.

cs.LG↗

arXiv2026

PII-VisBench: Evaluating Personally Identifiable Information Safety in Vision Language Models Along a Continuum of Visibility

Vision Language Models (VLMs) are increasingly integrated into privacy-critical domains, yet existing evaluations of personally identifiable information (PII) leakage largely treat privacy as a static extraction task and ignore how a subject's online presence--the volume of their data available online--influences privacy alignment. We introduce PII-VisBench, a novel benchmark containing 4000 unique probes designed to evaluate VLM safety through the continuum of online presence. The benchmark stratifies 200 subjects into four visibility categories: high, medium, low, and zero--based on the extent and nature of their information available online. We evaluate 18 open-source VLMs (0.3B-32B) based on two key metrics: percentage of PII probing queries refused (Refusal Rate) and the fraction of non-refusal responses flagged for containing PII (Conditional PII Disclosure Rate). Across models, we observe a consistent pattern: refusals increase and PII disclosures decrease (9.10% high to 5.34% low) as subject visibility drops. We identify that models are more likely to disclose PII for high-visibility subjects, alongside substantial model-family heterogeneity and PII-type disparities. Finally, paraphrasing and jailbreak-style prompts expose attack and model-dependent failures, motivating visibility-aware safety evaluation and training interventions.

cs.AI↗

arXiv2025

SoundnessBench: A Soundness Benchmark for Neural Network Verifiers

Neural network (NN) verification aims to formally verify properties of NNs, which is crucial for ensuring the behavior of NN-based models in safety-critical applications. In recent years, the community has developed many NN verifiers and benchmarks to evaluate them. However, existing benchmarks typically lack ground-truth for hard instances where no current verifier can verify the property and no counterexample can be found. This makes it difficult to validate the soundness of a verifier, when it claims verification on such challenging instances that no other verifier can handle. In this work, we develop a new benchmark for NN verification, named SoundnessBench, specifically for testing the soundness of NN verifiers. SoundnessBench consists of instances with deliberately inserted counterexamples that are hidden from adversarial attacks commonly used to find counterexamples. Thereby, it can identify false verification claims when hidden counterexamples are known to exist. We design a training method to produce NNs with hidden counterexamples and systematically construct our SoundnessBench with instances across various model architectures, activation functions, and input data. We demonstrate that our training effectively produces hidden counterexamples and our SoundnessBench successfully identifies bugs in state-of-the-art NN verifiers. Our code is available at https://github.com/mvp-harry/SoundnessBench and our dataset is available at https://huggingface.co/datasets/SoundnessBench/SoundnessBench.

cs.LG↗

arXiv2025

Bridging Efficiency and Safety: Formal Verification of Neural Networks with Early Exits

Ensuring the safety and efficiency of AI systems is a central goal of modern research. Formal verification provides guarantees of neural network robustness, while early exits improve inference efficiency by enabling intermediate predictions. Yet verifying networks with early exits introduces new challenges due to their conditional execution paths. In this work, we define a robustness property tailored to early exit architectures and show how off-the-shelf solvers can be used to assess it. We present a baseline algorithm, enhanced with an early stopping strategy and heuristic optimizations that maintain soundness and completeness. Experiments on multiple benchmarks validate our framework's effectiveness and demonstrate the performance gains of the improved algorithm. Alongside the natural inference acceleration provided by early exits, we show that they also enhance verifiability, enabling more queries to be solved in less time compared to standard networks. Together with a robustness analysis, we show how these metrics can help users navigate the inherent trade-off between accuracy and efficiency.

cs.LG↗

arXiv2025

Neural Network Verification with Branch-and-Bound for General Nonlinearities

Branch-and-bound (BaB) is among the most effective techniques for neural network (NN) verification. However, existing works on BaB for NN verification have mostly focused on NNs with piecewise linear activations, especially ReLU networks. In this paper, we develop a general framework, named GenBaB, to conduct BaB on general nonlinearities to verify NNs with general architectures, based on linear bound propagation for NN verification. To decide which neuron to branch, we design a new branching heuristic which leverages linear bounds as shortcuts to efficiently estimate the potential improvement after branching. To decide nontrivial branching points for general nonlinear functions, we propose to pre-optimize branching points, which can be efficiently leveraged during verification with a lookup table. We demonstrate the effectiveness of our GenBaB on verifying a wide range of NNs, including NNs with activation functions such as Sigmoid, Tanh, Sine and GeLU, as well as NNs involving multi-dimensional nonlinear operations such as multiplications in LSTMs and Vision Transformers. Our framework also allows the verification of general nonlinear computation graphs and enables verification applications beyond simple NNs, particularly for AC Optimal Power Flow (ACOPF). GenBaB is part of the latest $α$,$β$-CROWN, the winner of the 4th and the 5th International Verification of Neural Networks Competition (VNN-COMP 2023 and 2024). Code for reproducing the experiments is available at https://github.com/shizhouxing/GenBaB.

cs.LG↗

arXiv2024

Defending LLMs against Jailbreaking Attacks via Backtranslation

Although many large language models (LLMs) have been trained to refuse harmful requests, they are still vulnerable to jailbreaking attacks which rewrite the original prompt to conceal its harmful intent. In this paper, we propose a new method for defending LLMs against jailbreaking attacks by ``backtranslation''. Specifically, given an initial response generated by the target LLM from an input prompt, our backtranslation prompts a language model to infer an input prompt that can lead to the response. The inferred prompt is called the backtranslated prompt which tends to reveal the actual intent of the original prompt, since it is generated based on the LLM's response and not directly manipulated by the attacker. We then run the target LLM again on the backtranslated prompt, and we refuse the original prompt if the model refuses the backtranslated prompt. We explain that the proposed defense provides several benefits on its effectiveness and efficiency. We empirically demonstrate that our defense significantly outperforms the baselines, in the cases that are hard for the baselines, and our defense also has little impact on the generation quality for benign input prompts. Our implementation is based on our library for LLM jailbreaking defense algorithms at \url{https://github.com/YihanWang617/llm-jailbreaking-defense}, and the code for reproducing our experiments is available at \url{https://github.com/YihanWang617/LLM-Jailbreaking-Defense-Backtranslation}.

cs.CL↗

arXiv2024

Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation

Learning-based neural network (NN) control policies have shown impressive empirical performance in a wide range of tasks in robotics and control. However, formal (Lyapunov) stability guarantees over the region-of-attraction (ROA) for NN controllers with nonlinear dynamical systems are challenging to obtain, and most existing approaches rely on expensive solvers such as sums-of-squares (SOS), mixed-integer programming (MIP), or satisfiability modulo theories (SMT). In this paper, we demonstrate a new framework for learning NN controllers together with Lyapunov certificates using fast empirical falsification and strategic regularizations. We propose a novel formulation that defines a larger verifiable region-of-attraction (ROA) than shown in the literature, and refines the conventional restrictive constraints on Lyapunov derivatives to focus only on certifiable ROAs. The Lyapunov condition is rigorously verified post-hoc using branch-and-bound with scalable linear bound propagation-based NN verification techniques. The approach is efficient and flexible, and the full training and verification procedure is accelerated on GPUs without relying on expensive solvers for SOS, MIP, nor SMT. The flexibility and efficiency of our framework allow us to demonstrate Lyapunov-stable output feedback control with synthesized NN-based controllers and NN-based observers with formal stability guarantees, for the first time in literature. Source code at https://github.com/Verified-Intelligence/Lyapunov_Stable_NN_Controllers

cs.LG↗

arXiv2023

Improving the Generation Quality of Watermarked Large Language Models via Word Importance Scoring

The strong general capabilities of Large Language Models (LLMs) bring potential ethical risks if they are unrestrictedly accessible to malicious users. Token-level watermarking inserts watermarks in the generated texts by altering the token probability distributions with a private random number generator seeded by its prefix tokens. However, this watermarking algorithm alters the logits during generation, which can lead to a downgraded text quality if it chooses to promote tokens that are less relevant given the input. In this work, we propose to improve the quality of texts generated by a watermarked language model by Watermarking with Importance Scoring (WIS). At each generation step, we estimate the importance of the token to generate, and prevent it from being impacted by watermarking if it is important for the semantic correctness of the output. We further propose three methods to predict importance scoring, including a perturbation-based method and two model-based methods. Empirical experiments show that our method can generate texts with better quality with comparable level of detection rate.

cs.CL↗

arXiv2023

Effective Robustness against Natural Distribution Shifts for Models with Different Training Data

"Effective robustness" measures the extra out-of-distribution (OOD) robustness beyond what can be predicted from the in-distribution (ID) performance. Existing effective robustness evaluations typically use a single test set such as ImageNet to evaluate the ID accuracy. This becomes problematic when evaluating models trained on different data distributions, e.g., comparing models trained on ImageNet vs. zero-shot language-image pre-trained models trained on LAION. In this paper, we propose a new evaluation metric to evaluate and compare the effective robustness of models trained on different data. To do this, we control for the accuracy on multiple ID test sets that cover the training distributions for all the evaluated models. Our new evaluation metric provides a better estimate of effective robustness when there are models with different training data. It may also explain the surprising effective robustness gains of zero-shot CLIP-like models exhibited in prior works that used ImageNet as the only ID test set, while the gains diminish under our new evaluation. Additional artifacts including interactive visualizations are provided at https://shizhouxing.github.io/effective-robustness.

cs.LG↗

arXiv2023

Red Teaming Language Model Detectors with Language Models

The prevalence and strong capability of large language models (LLMs) present significant safety and ethical risks if exploited by malicious users. To prevent the potentially deceptive usage of LLMs, recent works have proposed algorithms to detect LLM-generated text and protect LLMs. In this paper, we investigate the robustness and reliability of these LLM detectors under adversarial attacks. We study two types of attack strategies: 1) replacing certain words in an LLM's output with their synonyms given the context; 2) automatically searching for an instructional prompt to alter the writing style of the generation. In both strategies, we leverage an auxiliary LLM to generate the word replacements or the instructional prompt. Different from previous works, we consider a challenging setting where the auxiliary LLM can also be protected by a detector. Experiments reveal that our attacks effectively compromise the performance of all detectors in the study with plausible generations, underscoring the urgent need to improve the robustness of LLM-generated text detection systems.

cs.CL↗

arXiv2022

On the Adversarial Robustness of Vision Transformers

Following the success in advancing natural language processing and understanding, transformers are expected to bring revolutionary changes to computer vision. This work provides a comprehensive study on the robustness of vision transformers (ViTs) against adversarial perturbations. Tested on various white-box and transfer attack settings, we find that ViTs possess better adversarial robustness when compared with MLP-Mixer and convolutional neural networks (CNNs) including ConvNeXt, and this observation also holds for certified robustness. Through frequency analysis and feature visualization, we summarize the following main observations contributing to the improved robustness of ViTs: 1) Features learned by ViTs contain less high-frequency patterns that have spurious correlation, which helps explain why ViTs are less sensitive to high-frequency perturbations than CNNs and MLP-Mixer, and there is a high correlation between how much the model learns high-frequency features and its robustness against different frequency-based perturbations. 2) Introducing convolutional or tokens-to-token blocks for learning high-frequency features in ViTs can improve classification accuracy but at the cost of adversarial robustness. 3) Modern CNN designs that borrow techniques from ViTs including activation function, layer norm, larger kernel size to imitate the global attention, and patchify the images as inputs, etc., could help bridge the performance gap between ViTs and CNNs not only in terms of performance, but also certified and empirical adversarial robustness. Moreover, we show adversarial training is also applicable to ViT for training robust models, and sharpness-aware minimization can also help improve robustness, while pre-training with clean images on larger datasets does not significantly improve adversarial robustness.

cs.CV↗

arXiv2022

Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagation

Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to small networks. In this paper, we develop an efficient framework for computing the $\ell_\infty$ local Lipschitz constant of a neural network by tightly upper bounding the norm of Clarke Jacobian via linear bound propagation. We formulate the computation of local Lipschitz constants with a linear bound propagation process on a high-order backward graph induced by the chain rule of Clarke Jacobian. To enable linear bound propagation, we derive tight linear relaxations for specific nonlinearities in Clarke Jacobian. This formulate unifies existing ad-hoc approaches such as RecurJac, which can be seen as a special case of ours with weaker relaxations. The bound propagation framework also allows us to easily borrow the popular Branch-and-Bound (BaB) approach from neural network verification to further tighten Lipschitz constants. Experiments show that on tiny models, our method produces comparable bounds compared to exact methods that cannot scale to slightly larger models; on larger models, our method efficiently produces tighter results than existing relaxed or naive methods, and our method scales to much larger practical models that previous works could not handle. We also demonstrate an application on provable monotonicity analysis. Code is available at https://github.com/shizhouxing/Local-Lipschitz-Constants.

cs.LG↗

arXiv2022

On the Sensitivity and Stability of Model Interpretations in NLP

Recent years have witnessed the emergence of a variety of post-hoc interpretations that aim to uncover how natural language processing (NLP) models make predictions. Despite the surge of new interpretation methods, it remains an open problem how to define and quantitatively measure the faithfulness of interpretations, i.e., to what extent interpretations reflect the reasoning process by a model. We propose two new criteria, sensitivity and stability, that provide complementary notions of faithfulness to the existed removal-based criteria. Our results show that the conclusion for how faithful interpretations are could vary substantially based on different notions. Motivated by the desiderata of sensitivity and stability, we introduce a new class of interpretation methods that adopt techniques from adversarial robustness. Empirical results show that our proposed methods are effective under the new criteria and overcome limitations of gradient-based methods on removal-based criteria. Besides text classification, we also apply interpretation methods and metrics to dependency parsing. Our results shed light on understanding the diverse set of interpretations.

cs.CL↗