An AI Approach to Verified Production Cryptographic Libraries

Cryptographic code is critical infrastructure that must be correct, yet formally verifying production libraries remains difficult. Existing language-model proof systems solve isolated obligations with specifications and premises already given, leaving production-library verification unresolved. We present CryptoProver, an AI-based system that synthesizes internal specifications and Verus-checked proofs from high-level API contracts. Without changing executable code, CryptoProver constructs a new independent proof of curve25519-dalek and verifies RustCrypto's previously unverified chacha20 implementation against an RFC 8439 specification. These cryptographic lineages underpin deployed systems including Signal and Shadowsocks; Signal has an estimated 218M global downloads. The independent, human-led curve25519-dalek verification was developed publicly over eight months by five main contributors. Given the API contracts and a fixed trusted library of field specifications, arithmetic facts, axioms, and vstd, CryptoProver synthesizes the internal specifications and proofs in 11.4 hours with USD 466.99 in recorded API cost. CryptoProver follows a trust-first design principle: mechanical gates reject specification weakening, invented axioms, and cross-module breakage, while isolation blocks reference proof retrieval, including from git history.

Lookahead Branching for Neural Network Verification

In this work, we investigate the effect of lookahead branching strategies in neural network verification. We present a general recipe to integrate lookahead into any branch-and-bound verifier and demonstrate how one of the current state-of-the-art branching heuristics, FSB, can be viewed as a special instantiation of the lookahead branching strategy. We also describe how, in addition to improving the quality of branching decisions, lookahead can generate additional lemmas that accelerate verification. We instantiate the method in two representative branch-and-bound-based verifiers (Marabou and $α$-$β$-CROWN), and demonstrate that lookahead leads to consistent speedups in verification time and up to $57\%$ more solved instances. Code is available at https://github.com/ai-ar-research/lookahead-branching.

DIRECT: When and Where Should You Allocate Test-Time Compute in Embodied Planners?

Vision-Language Models (VLMs) are increasingly deployed as high-level planners for embodied agents, with an emerging strategy of scaling test-time compute to improve capability. However, we observe that doing so increases latency, token usage, and FLOPs while yielding uneven, often diminishing gains in downstream success, limiting where embodied agents can be deployed. We argue that choosing when and where to spend test-time compute is central to bringing frontier performance to the real world. We introduce DIRECT, a routing framework that uses multimodal scene context to allocate compute per prompt, improving the success--cost Pareto frontier over fixed model selection. Across three dominant scaling axes, namely chain-of-thought depth, model size, and memory history, our experiments on VLABench and RoboMME show that test-time compute is not a uniform lever: different axes yield qualitatively distinct capability gains. We validate these insights on a physical Franka arm in a DROID setup spanning zero-shot manipulation and long-horizon chaining, where our router matches or exceeds a stronger model's success rate at up to 65% lower average latency. Ultimately, our results show that naively scaling test-time compute is wasteful, and that DIRECT can provide frontier-level embodied planning in robotic systems at a fraction of the cost. Project page can be found at jadee-dao.github.io/direct/.

Faithful Autoformalization via Roundtrip Verification and Repair

When an LLM formalizes natural language, how do we know the output is faithful? We propose a roundtrip verification approach which does not require ground-truth annotations: formalize a statement, translate the result back to natural language, re-formalize, and use a formal tool to check logical equivalence. When the two formalizations agree, this provides evidence of a faithful formalization. When they disagree, a diagnosis step identifies which translation stage failed, and a targeted repair operator attempts to correct that stage. We evaluate our approach on 150 traffic rules using Claude Opus 4.6 and GPT-5.2. Diagnosis-guided repair raises formal equivalence from 45--61% to 83--85% for both models, outperforming a random-repair baseline. An independent NLI analysis confirms that formal equivalence is correlated with less semantic drift.

The FABRIC Strategy for Verifying Neural Feedback Systems

Forward reachability analysis is a dominant approach for verifying reach-avoid specifications in neural feedback systems, i.e., dynamical systems controlled by neural networks, and a number of directions have been proposed and studied. In contrast, far less attention has been given to backward reachability analysis for these systems, in part because of the limited scalability of known techniques. In this work, we begin to address this gap by introducing new algorithms for computing both over- and underapproximations of backward reachable sets for nonlinear neural feedback systems. We also describe and implement an integration of these backward reachability techniques with existing ones for forward analysis. We call the resulting algorithm Forward and Backward Reachability Integration for Certification (FaBRIC). We evaluate our algorithms on a representative set of benchmarks and show that they significantly outperform the prior state of the art.

Self-Supervised Bootstrapping of Action-Predictive Embodied Reasoning

Embodied Chain-of-Thought (CoT) reasoning has significantly enhanced Vision-Language-Action (VLA) models, yet current methods rely on rigid templates to specify reasoning primitives (e.g., objects in the scene, high-level plans, structural affordances). These templates can force policies to process irrelevant information that distracts from critical action-prediction signals. This creates a bottleneck: without successful policies, we cannot verify reasoning quality; without quality reasoning, we cannot build robust policies. We introduce R&B-EnCoRe, which enables models to bootstrap embodied reasoning from internet-scale knowledge through self-supervised refinement. By treating reasoning as a latent variable within importance-weighted variational inference, models can generate and distill a refined reasoning training dataset of embodiment-specific strategies without external rewards, verifiers, or human annotation. We validate R&B-EnCoRe across manipulation (Franka Panda in simulation, WidowX in hardware), legged navigation (bipedal, wheeled, bicycle, quadruped), and autonomous driving embodiments using various VLA architectures with 1B, 4B, 7B, and 30B parameters. Our approach achieves 28% gains in manipulation success, 101% improvement in navigation scores, and 21% reduction in collision-rate metric over models that indiscriminately reason about all available primitives. R&B-EnCoRe enables models to distill reasoning that is predictive of successful control, bypassing manual annotation engineering while grounding internet-scale knowledge in physical execution.

A New Strategy for Verifying Reach-Avoid Specifications in Neural Feedback Systems

Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing backward reachability methods. In this work, we introduce new algorithms that compute both over- and under-approximations of backward reachable sets for such systems. We further integrate these backward algorithms with established forward analysis techniques to yield a unified verification framework for neural feedback systems.

Proof Minimization in Neural Network Verification

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.

Proof-Driven Clause Learning in Neural Network Verification

The widespread adoption of deep neural networks (DNNs) requires efficient techniques for safety verification. Existing methods struggle to scale to real-world DNNs, and tremendous efforts are being put into improving their scalability. In this work, we propose an approach for improving the scalability of DNN verifiers using Conflict-Driven Clause Learning (CDCL) -- an approach that has proven highly successful in SAT and SMT solving. We present a novel algorithm for deriving conflict clauses using UNSAT proofs, and propose several optimizations for expediting it. Our approach allows a modular integration of SAT solvers and DNN verifiers, and we implement it on top of an interface designed for this purpose. The evaluation of our implementation over several benchmarks suggests a 2X--3X improvement over a similar approach, with specific cases outperforming the state of the art.

Pantograph: A Machine-to-Machine Interaction Interface for Advanced Theorem Proving, High Level Reasoning, and Data Extraction in Lean 4

Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in conjunction with proof assistants to perform this task. In this paper, we introduce Pantograph, a tool that provides a versatile interface to the Lean 4 proof assistant and enables efficient proof search via powerful search algorithms such as Monte Carlo Tree Search. In addition, Pantograph enables high-level reasoning by enabling a more robust handling of Lean 4's inference steps. We provide an overview of Pantograph's architecture and features. We also report on an illustrative use case: using machine learning models and proof sketches to prove Lean 4 theorems. Pantograph's innovative features pave the way for more advanced machine learning models to perform complex proof searches and high-level reasoning, equipping future researchers to design more versatile and powerful theorem provers.