A New Approach Towards Autoformalization

Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a program. This is a challenging task, and especially for higher-level mathematics found in research papers. Research paper mathematics requires large amounts of background and context. In this paper, we propose an avenue towards tackling autoformalization for research-level mathematics, by breaking the task into easier and more approachable subtasks: unlinked formalization (formalization with unlinked definitions and theorems), entity linking (linking to the proper theorems and definitions), and finally adjusting types so it passes the type checker. In addition, we present arXiv2Formal, a benchmark dataset for unlinked formalization consisting of 50 theorems formalized for the Lean theorem prover sampled from papers on arXiv.org. We welcome any contributions from the community to future versions of this dataset.

Forming Trees with Treeformers

Popular models such as Transformers and LSTMs use tokens as its unit of information. That is, each token is encoded into a vector representation, and those vectors are used directly in a computation. However, humans frequently consider spans of tokens (i.e., phrases) instead of their constituent tokens. In this paper we introduce Treeformer, an architecture inspired by the CKY algorithm and Transformer which learns a composition operator and pooling function in order to construct hierarchical encodings for phrases and sentences. Our extensive experiments demonstrate the benefits of incorporating a hierarchical structure into the Transformer, and show significant improvements compared to a baseline Transformer in machine translation, abstractive summarization, and various natural language understanding tasks.