We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts. We produce several versions of the prover, parameterized by different learning and guiding algorithms. The strongest version of the system is trained on a large corpus of mathematical problems and evaluated on previously unseen problems. The trained system solves within the same number of inferences over 40% more problems than a baseline prover, which is an unusually high improvement in this hard AI domain. To our knowledge this is the first time reinforcement learning has been convincingly applied to solving general mathematical problems on a large scale.

In practice, today's best ATP system are however still far weaker than trained mathematicians in most research domains. Machine learning from many proofs could be used to improveonthis.

The nineteenth century saw the emergence of proofs so involved that they could only be verified by a handful of specialists.

Fine-tuning large language models (LLMs) is crucial for adapting them to specific tasks, yet it remains computationally demanding and raises concerns about correctness and privacy, particularly in untrusted environments. Although parameter-efficient methods like Low-Rank Adaptation (LoRA) significantly reduce resource requirements, ensuring the security and verifiability of fine-tuning under zero-knowledge constraints remains an unresolved challenge. To address this, we introduce VeriLoRA, the first framework to integrate LoRA fine-tuning with zero-knowledge proofs (ZKPs), achieving provable security and correctness. VeriLoRA employs advanced cryptographic techniques -- such as lookup arguments, sumcheck protocols, and polynomial commitments -- to verify both arithmetic and non-arithmetic operations in Transformer-based architectures. The framework provides end-to-end verifiability for forward propagation, backward propagation, and parameter updates during LoRA fine-tuning, while safeguarding the privacy of model parameters and training data. Leveraging GPU-based implementations, VeriLoRA demonstrates practicality and efficiency through experimental validation on open-source LLMs like LLaMA, scaling up to 13 billion parameters. By combining parameter-efficient fine-tuning with ZKPs, VeriLoRA bridges a critical gap, enabling secure and trustworthy deployment of LLMs in sensitive or untrusted environments.

Inference using deep neural networks is often outsourced to the cloud since it is a computationally demanding task.

We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts. We produce several versions of the prover, parameterized by different learning and guiding algorithms. The strongest version of the system is trained on a large corpus of mathematical problems and evaluated on previously unseen problems. The trained system solves within the same number of inferences over 40% more problems than a baseline prover, which is an unusually high improvement in this hard AI domain. To our knowledge this is the first time reinforcement learning has been convincingly applied to solving general mathematical problems on a large scale.

Neural Information Processing Systems http://nips.cc/