Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty ofsuch reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing logical reasoning problems intotheorems within Lean, we can solve them by proving or disproving the corresponding theorems. This method reduces the risk of logical inconsistencies with the help of Lean’s symbolic solver. It also enhances our ability to treat complex reasoning tasks using Lean’s extensive library of theorem proofs. Our method achieves state-of-the-art performance on the FOLIO dataset and achieves performance near this level on ProofWriter. Notably, these results were accomplished by fine-tuning on fewer than 100 in-domain samples for each dataset

We argue that disentangling content selection from the budget used to cover salient content improves the performance and applicability of abstractive summarizers. Our method, FactorSum, does this disentanglement by factorizing summarization into two steps through an energy function: (1) generation of abstractive summary views covering salient information in subsets of the input document (document views); (2) combination of these views into a final summary, following a budget and content guidance. This guidance may come from different sources, including from an advisor model such as BART or BigBird, or in oracle mode – from the reference. This factorization achieves significantly higher ROUGE scores on multiple benchmarks for long document summarization, namely PubMed, arXiv, and GovReport. Most notably, our model is effective for domain adaptation. When trained only on PubMed samples, it achieves a 46.29 ROUGE-1 score on arXiv, outperforming PEGASUS trained in domain by a large margin. Our experimental results indicate that the performance gains are due to more flexible budget adaptation and processing of shorter contexts provided by partial document views.