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Generative Language Modeling for Automated Theorem Proving

This work presents an automated prover and proof assistant, GPT-f, for the Metamath formalization language, and analyzes its performance, finding new short proofs that were accepted into the mainMetamath library, which is to this knowledge, the first time a deep-learning based system has contributed proofs that are adopted by a formal mathematics community.
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Formal Mathematics Statement Curriculum Learning

It is shown that at same compute budget, expert iteration, by which the authors mean proof search interleaved with learning, dramatically outperforms proof search only and is capable of finding and solving a curriculum of increasingly difficult problems, without the need for associated ground-truth proofs.
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MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics

The miniF2F benchmark currently targets Metamath, Lean, and Isabelle and consists of 488 problem statements drawn from the AIME, AMC, and the International Mathematical Olympiad, as well as material from high-school and undergraduate mathematics courses.
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Unsupervised Neural Machine Translation with Generative Language Models Only

By using GPT-3’s zero-shot translation capability, this method achieves a new state-of-the-art in unsupervised translation on the WMT14 English-French benchmark, attaining a BLEU score of 42.1.
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Proof Artifact Co-training for Theorem Proving with Language Models

PACT is proposed, a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective and applied to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date.
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The Stellar Consensus Protocol (SCP)

SCP is an open Byzantine agreement protocol resistant to Sybil attacks. It allows Internet infrastructure stakeholders to reach agreement on a series of values without unanimous agreement on what…

ING WITH LANGUAGE MODELS

This work proposes PACT (Proof Artifact Co-Training), a general methodology for extracting abundant self-supervised data from kernel-level proof terms for joint training alongside the usual tactic prediction objective and applies this methodology to Lean, a proof assistant host to some of the most sophisticated formalized mathematics to date.

Discrepancy-Sensitive Dynamic Fractional Cascading, Dominated Maxima Searching, and 2-d Nearest Neighbors in Any Minkowski Metric

An efficient data structure for dominated maxima searching in a dynamic set of points in the plane is provided, which in turn leads to an efficient dynamic data structure that can answer queries for nearest neighbors using any Minkowski metric.
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Personal Storage Clouds from Portable Components

A number of applications would seem to benefit from storing data “in the cloud”—that is at application storage providers such as Amazon S3. The cloud model is appealing because it relieves end users…
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