Daily Papers

The widespread adoption of deep neural networks (DNNs) requires efficient techniques for verifying their safety. DNN verifiers are complex tools, which might contain bugs that could compromise their soundness and undermine the reliability of the verification process. This concern can be mitigated using proofs: artifacts that are checkable by an external and reliable proof checker, and which attest to the correctness of the verification process. However, such proofs tend to be extremely large, limiting their use in many scenarios. In this work, we address this problem by minimizing proofs of unsatisfiability produced by DNN verifiers. We present algorithms that remove facts which were learned during the verification process, but which are unnecessary for the proof itself. Conceptually, our method analyzes the dependencies among facts used to deduce UNSAT, and removes facts that did not contribute. We then further minimize the proof by eliminating remaining unnecessary dependencies, using two alternative procedures. We implemented our algorithms on top of a proof producing DNN verifier, and evaluated them across several benchmarks. Our results show that our best-performing algorithm reduces proof size by 37%-82% and proof checking time by 30%-88%, while introducing a runtime overhead of 7%-20% to the verification process itself.

Recent progress in large language models (LLMs) has shown promise in formal theorem proving, yet existing benchmarks remain limited to isolated, static proof tasks, failing to capture the iterative, engineering-intensive workflows of real-world formal mathematics libraries. Motivated by analogous advances in software engineering, we introduce the paradigm of Automated Proof Engineering (APE), which aims to automate proof engineering tasks such as feature addition, proof refactoring, and bug fixing using LLMs. To facilitate research in this direction, we present APE-Bench I, the first realistic benchmark built from real-world commit histories of Mathlib4, featuring diverse file-level tasks described in natural language and verified via a hybrid approach combining the Lean compiler and LLM-as-a-Judge. We further develop Eleanstic, a scalable parallel verification infrastructure optimized for proof checking across multiple versions of Mathlib. Empirical results on state-of-the-art LLMs demonstrate strong performance on localized edits but substantial degradation on handling complex proof engineering. This work lays the foundation for developing agentic workflows in proof engineering, with future benchmarks targeting multi-file coordination, project-scale verification, and autonomous agents capable of planning, editing, and repairing formal libraries.

Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods address this separately, first translating theorems and then generating proofs, creating a fundamental disconnect vis-a-vis true proof auto-formalization. This two-step process and its limitations were evident even in AlphaProof's silver-medal performance at the 2024 IMO, where problem statements needed manual translation before automated proof synthesis. We present ProofBridge, a unified framework for automatically translating entire NL theorems and proofs into Lean 4. At its core is a joint embedding model that aligns NL and FL (NL-FL) theorem-proof pairs in a shared semantic space, enabling cross-modal retrieval of semantically relevant FL examples to guide translation. Our training ensures that NL-FL theorems (and their proofs) are mapped close together in this space if and only if the NL-FL pairs are semantically equivalent. ProofBridge integrates retrieval-augmented fine-tuning with iterative proof repair, leveraging Lean's type checker and semantic equivalence feedback to ensure both syntactic correctness and semantic fidelity. Experiments show substantial improvements in proof auto-formalization over strong baselines (including GPT-5, Gemini-2.5, Kimina-Prover, DeepSeek-Prover), with our retrieval-augmented approach yielding significant gains in semantic correctness (SC, via proving bi-directional equivalence) and type correctness (TC, via type-checking theorem+proof) across pass@k metrics on miniF2F-Test-PF, a dataset we curated. In particular, ProofBridge improves cross-modal retrieval quality by up to 3.28x Recall@1 over all-MiniLM-L6-v2, and achieves +31.14% SC and +1.64% TC (pass@32) compared to the baseline Kimina-Prover-RL-1.7B.

Large language model (LLM) powered code agents are rapidly transforming software engineering by automating tasks such as testing, debugging, and repairing, yet the security risks of their generated code have become a critical concern. Existing benchmarks have offered valuable insights but remain insufficient: they often overlook the genuine context in which vulnerabilities were introduced or adopt narrow evaluation protocols that fail to capture either functional correctness or newly introduced vulnerabilities. We therefore introduce SecureAgentBench, a benchmark of 105 coding tasks designed to rigorously evaluate code agents' capabilities in secure code generation. Each task includes (i) realistic task settings that require multi-file edits in large repositories, (ii) aligned contexts based on real-world open-source vulnerabilities with precisely identified introduction points, and (iii) comprehensive evaluation that combines functionality testing, vulnerability checking through proof-of-concept exploits, and detection of newly introduced vulnerabilities using static analysis. We evaluate three representative agents (SWE-agent, OpenHands, and Aider) with three state-of-the-art LLMs (Claude 3.7 Sonnet, GPT-4.1, and DeepSeek-V3.1). Results show that (i) current agents struggle to produce secure code, as even the best-performing one, SWE-agent supported by DeepSeek-V3.1, achieves merely 15.2% correct-and-secure solutions, (ii) some agents produce functionally correct code but still introduce vulnerabilities, including new ones not previously recorded, and (iii) adding explicit security instructions for agents does not significantly improve secure coding, underscoring the need for further research. These findings establish SecureAgentBench as a rigorous benchmark for secure code generation and a step toward more reliable software development with LLMs.

Large language models show promise for autoformalization, the task of automatically translating natural language into formal languages. However, current autoformalization methods remain limited. The last reported state-of-the-art performance on the ProofNet formalization benchmark for the Lean proof assistant, achieved using Codex for Lean 3, only showed successful formalization of 16.1% of informal statements. Similarly, our evaluation of GPT-4o for Lean 4 only produces successful translations 34.9% of the time. Our analysis shows that the performance of these models is largely limited by their inability to generate formal statements that successfully type-check (i.e., are syntactically correct and consistent with types) - with a whopping 86.6% of GPT-4o errors starting from a type-check failure. In this work, we propose a method to fix this issue through decoding with type-check filtering, where we initially sample a diverse set of candidate formalizations for an informal statement, then use the Lean proof assistant to filter out candidates that do not type-check. Using GPT-4o as a base model, and combining our method with self-consistency, we obtain a +18.3% absolute increase in formalization accuracy, and achieve a new state-of-the-art of 53.2% on ProofNet with Lean 4.

The Know Your Customer (KYC) and Anti Money Laundering (AML) are worldwide practices to online customer identification based on personal identification documents, similarity and liveness checking, and proof of address. To answer the basic regulation question: are you whom you say you are? The customer needs to upload valid identification documents (ID). This task imposes some computational challenges since these documents are diverse, may present different and complex backgrounds, some occlusion, partial rotation, poor quality, or damage. Advanced text and document segmentation algorithms were used to process the ID images. In this context, we investigated a method based on U-Net to detect the document edges and text regions in ID images. Besides the promising results on image segmentation, the U-Net based approach is computationally expensive for a real application, since the image segmentation is a customer device task. We propose a model optimization based on Octave Convolutions to qualify the method to situations where storage, processing, and time resources are limited, such as in mobile and robotic applications. We conducted the evaluation experiments in two new datasets CDPhotoDataset and DTDDataset, which are composed of real ID images of Brazilian documents. Our results showed that the proposed models are efficient to document segmentation tasks and portable.