In theorem proving, the task of selecting useful premises from alarge library to unlock the proof of a given conjecture is crucially important. This presents a challenge foralltheorem provers,especially theonesbasedonlanguage models, due to their relative inability to reason over huge volumes of premises in text form.

Premise selection is a key bottleneck for scaling theorem proving in large formal libraries. Yet existing language-based methods often treat premises in isolation, ignoring the web of dependencies that connects them. We present a graph-augmented approach that combines dense text embeddings of Lean formalizations with graph neural networks over a heterogeneous dependency graph capturing both state-premise and premise-premise relations. On the LeanDojo Benchmark, our method outperforms the ReProver language-based baseline by over 25\% across standard retrieval metrics. These results suggest that relational information is beneficial for premise selection.

We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics.

We propose a deep learning-based approach to the problem of premise selection: selecting mathematical statements relevant for proving a given conjecture. We represent a higher-order logic formula as a graph that is invariant to variable renaming but still fully preserves syntactic and semantic information. We then embed the graph into a vector via a novel embedding method that preserves the information of edge ordering. Our approach achieves state-of-the-art results on the HolStep dataset, improving the classification accuracy from 83% to 90.3%.

We represent a higher-order logic formula as a graph that is invariant to variable renaming but still fully preserves syntactic and semantic information.

We study the effectiveness of neural sequence models for premise selection in automated theorem proving, a key bottleneck for progress in formalized mathematics. We propose a two stage approach for this task that yields good results for the premise selection task on the Mizar corpus while avoiding the hand-engineered features of existing state-of-the-art models. To our knowledge, this is the first time deep learning has been applied theorem proving on a large scale.

Despite the remarkable progress in neural models, their ability to generalize, a cornerstone for applications like logical reasoning, remains a critical challenge. We delineate two fundamental aspects of this ability: compositionality, the capacity to abstract atomic logical rules underlying complex inferences, and recursiveness, the aptitude to build intricate representations through iterative application of inference rules. In the literature, these two aspects are often confounded together under the umbrella term of generalization. To sharpen this distinction, we investigated the logical generalization capabilities of pre-trained large language models (LLMs) using the syllogistic fragment as a benchmark for natural language reasoning. Though simple, this fragment provides a foundational yet expressive subset of formal logic that supports controlled evaluation of essential reasoning abilities. Our findings reveal a significant disparity: while LLMs demonstrate reasonable proficiency in recursiveness, they struggle with compositionality. To overcome these limitations and establish a reliable logical prover, we propose a hybrid architecture integrating symbolic reasoning with neural computation. This synergistic interaction enables robust and efficient inference, neural components accelerate processing, while symbolic reasoning ensures completeness. Our experiments show that high efficiency is preserved even with relatively small neural components. As part of our proposed methodology, this analysis gives a rationale and highlights the potential of hybrid models to effectively address key generalization barriers in neural reasoning systems.