We consider learning a probabilistic classifier from partially-labelled supervision (inputs denoted with multiple possibilities) using standard neural architectures with a softmax as the final layer. We identify a bias phenomenon that can arise from the softmax layer in even simple architectures that prevents proper exploration of alternative options, making the dynamics of gradient descent overly sensitive to initialization. We introduce a novel loss function that allows for unbiased exploration within the space of alternative outputs. We give a theoretical justification for our loss function, and provide an extensive evaluation of its impact on synthetic data, on standard partially labelled benchmarks and on a contributed novel benchmark related to an existing rule learning challenge.

Abstract Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates useful lemmas for automated theorem provers, demonstrating improvement for several representative systems and solving a hard problem not solved by any system for twenty years. By focusing on condensed detachment problems we simplify the setting considerably, allowing us to get at the essence of lemmas and their role in proof search.

Our paper explores the game theoretic value of the 7-in-a-row game. We reduce the problem to solving a finite board game, which we target using Proof Number Search. We present a number of heuristic improvements to Proof Number Search and examine their effect within the context of this particular game. Although our paper does not solve the 7-in-a-row game, our experiments indicate that we have made significant progress towards it.