Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks are mainly focus on symbolic inference, but rarely involve the understanding of complex number combination reasoning. In this work, we propose TRIGO, an ATP benchmark that not only requires a model to reduce a trigonometric expression with step-by-step proof but also evaluates a generative LM’s reasoning ability on formulas and capability to manipulate, group, and factor number terms. We gather trigonometric expressions and their reduced forms from web, annotate the simplification process manually, and translate it into the “Lean” formal language system. We then automatically generate additional examples from the annotated samples to expand the dataset. Furthermore, we also create three automatically generated training and testing datasets of varying difficulty and distributions. Our extensive experiments show our proposed TRIGO poses a new challenge for advanced generative LM’s including GPT-4 which is pre-trained on a considerable amount of open-source formal theorem-proving language data, and provide a new tool to study the generative LM’s ability on both formal and mathematical reasoning.

Conversational recommender systems (CRS) aim to timely trace the dynamic interests of users through dialogues and generate relevant responses for item recommendations. Recently, various external knowledge bases (especially knowledge graphs) are incorporated into CRS to enhance the understanding of conversation contexts. However, recent reasoning-based models heavily rely on simplified structures such as linear structures or fixed-hierarchical structures for causality reasoning, hence they cannot fully figure out sophisticated relationships among utterances with external knowledge. To address this, we propose a novel Tree structure Reasoning schEmA named TREA. TREA constructs a multi-hierarchical scalable tree as the reasoning structure to clarify the causal relationships between mentioned entities, and fully utilizes historical conversations to generate more reasonable and suitable responses for recommended results. Extensive experiments on two public CRS datasets have demonstrated the effectiveness of our approach.

Recent advances in neural theorem-proving resort to large language models and tree searches. When proving a theorem, a language model advises single-step actions based on the current proving state and the tree search finds a sequence of correct steps using actions given by the language model. However, prior works often conduct constant computation efforts for each proving state while ignoring that the hard states often need more exploration than easy states. Moreover, they evaluate and guide the proof search solely depending on the current proof state instead of considering the whole proof trajectory as human reasoning does. Here, to accommodate general theorems, we propose a novel Dynamic-Tree Driven Theorem Solver (DT-Solver) by guiding the search procedure with state confidence and proof-level values. Specifically, DT-Solver introduces a dynamic-tree Monte-Carlo search algorithm, which dynamically allocates computing budgets for different state confidences, guided by a new proof-level value function to discover proof states that require substantial exploration. Experiments on two popular theorem-proving datasets, PISA and Mathlib, show significant performance gains by our DT-Solver over the state-of-the-art approaches, with a 6.65% improvement on average in terms of success rate. And especially under low computing resource settings (11.03% improvement on average).

This paper presents a parameter-lite transfer learning approach of pretrained language models (LM) for knowledge graph (KG) completion. Instead of finetuning, which modifies all LM parameters, we only tune a few new parameters while keeping the original LM parameters fixed. We establish this via reformulating KG completion as a “fill-in-the-blank” task, and introducing a parameter-lite encoder on top of the original LMs. We show that, by tuning far fewer parameters than finetuning, LMs transfer non-trivially to most tasks and reach competitiveness with prior state-of-the-art approaches. For instance, we outperform the fully finetuning approaches on a KG completion benchmark by tuning only 1% of the parameters.