Related papers: CoProver: A Recommender System for Proof Construct…
Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…
Geometry theorem proving forms a major and challenging component in the K-12 mathematics curriculum. A particular difficult task is to add auxiliary constructions (i.e, additional lines or points) to aid proof discovery. Although there…
We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…
Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. A prevalent proof method involves the LLM prover iteratively constructing the proof…
Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
Informed machine learning methods allow the integration of prior knowledge into learning systems. This can increase accuracy and robustness or reduce data needs. However, existing methods often assume hard constraining knowledge, that does…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
We consider the problem of how a trusted, but computationally bounded agent (a 'verifier') can learn to interact with one or more powerful but untrusted agents ('provers') in order to solve a given task. More specifically, we study the case…
Ensuring large language models' (LLMs) responses align with prompt instructions is crucial for application development. Based on our formative study with industry professionals, the alignment requires heavy human involvement and tedious…
Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent…
Traditional proof systems involve a resource-bounded verifier communicating with a powerful (but untrusted) prover. Distributed verifier proof systems are a new family of proof models that involve a network of verifier nodes communicating…
For continual learning, text-prompt-based methods leverage text encoders and learnable prompts to encode semantic features for sequentially arrived classes over time. A common challenge encountered by existing works is how to learn unique…
The development of person search techniques has been greatly promoted in recent years for its superior practicality and challenging goals. Despite their significant progress, existing person search models still lack the ability to…
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…
In recent years the effectiveness of interactive theorem provers has increased to an extent that the bottleneck in the interactive process shifted to efficiency: while in principle large and complex theorems are provable (effectiveness), it…
Language Models (LMs) have proven to be useful in various downstream applications, such as summarisation, translation, question answering and text classification. LMs are becoming increasingly important tools in Artificial Intelligence,…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…