Discourse-Aware Graph Networks for Textual Logical Reasoning

Textual logical reasoning, especially question-answering (QA) tasks with logical reasoning, requires awareness of particular logical structures. The passage-level logical relations represent entailment or contradiction between propositional units (e.g., a concluding sentence). However, such structures are unexplored as current QA systems focus on entity-based relations. In this work, we propose logic structural-constraint modeling to solve the logical reasoning QA and introduce discourse-aware graph networks (DAGNs). The networks first construct logic graphs leveraging in-line discourse connectives and generic logic theories, then learn logic representations by end-to-end evolving the logic relations with an edge-reasoning mechanism and updating the graph features. This pipeline is applied to a general encoder, whose fundamental features are joined with the high-level logic features for answer prediction. Experiments on three textual logical reasoning datasets demonstrate the reasonability of the logical structures built in DAGNs and the effectiveness of the learned logic features. Moreover, zero-shot transfer results show the features' generality to unseen logical texts

REM-Net: Recursive Erasure Memory Network for Commonsense Evidence Refinement

When answering a question, people often draw upon their rich world knowledge in addition to the particular context. While recent works retrieve supporting facts/evidence from commonsense knowledge bases to supply additional information to each question, there is still ample opportunity to advance it on the quality of the evidence. It is crucial since the quality of the evidence is the key to answering commonsense questions, and even determines the upper bound on the QA systems performance. In this paper, we propose a recursive erasure memory network (REM-Net) to cope with the quality improvement of evidence. To address this, REM-Net is equipped with a module to refine the evidence by recursively erasing the low-quality evidence that does not explain the question answering. Besides, instead of retrieving evidence from existing knowledge bases, REM-Net leverages a pre-trained generative model to generate candidate evidence customized for the question. We conduct experiments on two commonsense question answering datasets, WIQA and CosmosQA. The results demonstrate the performance of REM-Net and show that the refined evidence is explainable.Comment: Accepted by AAAI 202

Discourse-Aware Graph Networks for Textual Logical Reasoning.

Textual logical reasoning, especially question-answering (QA) tasks with logical reasoning, requires awareness of particular logical structures. The passage-level logical relations represent entailment or contradiction between propositional units (e.g., a concluding sentence). However, such structures are unexplored as current QA systems focus on entity-based relations. In this work, we propose logic structural-constraint modeling to solve the logical reasoning QA and introduce discourse-aware graph networks (DAGNs). The networks first construct logic graphs leveraging in-line discourse connectives and generic logic theories, then learn logic representations by end-to-end evolving the logic relations with an edge-reasoning mechanism and updating the graph features. This pipeline is applied to a general encoder, whose fundamental features are joined with the high-level logic features for answer prediction. Experiments on three textual logical reasoning datasets demonstrate the reasonability of the logical structures built in DAGNs and the effectiveness of the learned logic features. Moreover, zero-shot transfer results show the features' generality to unseen logical texts

TRIGO: Benchmarking Formal Mathematical Proof Reduction for Generative Language Models

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 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 proofs but also evaluates a generative LM's reasoning ability on formulas and its capability to manipulate, group, and factor number terms. We gather trigonometric expressions and their reduced forms from the 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 develop an automatic generator based on Lean-Gym to create dataset splits of varying difficulties and distributions in order to thoroughly analyze the model's generalization ability. 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.Comment: Accepted by EMNLP 2023. Code is available at https://github.com/menik1126/TRIG

LEGO-Prover: Neural Theorem Proving with Growing Libraries

Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results, but they still struggle to prove even middle school level theorems. One common limitation of these methods is that they assume a fixed theorem library during the whole theorem proving process. However, as we all know, creating new useful theorems or even new theories is not only helpful but crucial and necessary for advancing mathematics and proving harder and deeper results. In this work, we present LEGO-Prover, which employs a growing skill library containing verified lemmas as skills to augment the capability of LLMs used in theorem proving. By constructing the proof modularly, LEGO-Prover enables LLMs to utilize existing skills retrieved from the library and to create new skills during the proving process. These skills are further evolved (by prompting an LLM) to enrich the library on another scale. Modular and reusable skills are constantly added to the library to enable tackling increasingly intricate mathematical problems. Moreover, the learned library further bridges the gap between human proofs and formal proofs by making it easier to impute missing steps. LEGO-Prover advances the state-of-the-art pass rate on miniF2F-valid (48.0% to 57.0%) and miniF2F-test (45.5% to 47.1%). During the proving process, LEGO-Prover also manages to generate over 20,000 skills (theorems/lemmas) and adds them to the growing library. Our ablation study indicates that these newly added skills are indeed helpful for proving theorems, resulting in an improvement from a success rate of 47.1% to 50.4%. We also release our code and all the generated skills