Enhancing Logical Reasoning of Large Language Models through Logic-Driven Data Augmentation

Combining large language models with logical reasoning enhance their capacity to address problems in a robust and reliable manner. Nevertheless, the intricate nature of logical reasoning poses challenges to gathering reliable data from web for building comprehensive training datasets, subsequently affecting the performance on downstream tasks. To address this, we introduce a novel logic-driven data augmentation approach, AMR-LDA. AMR-LDA converts the original text into an Abstract Meaning Representation (AMR) graph, a structured semantic representation that encapsulates the logic structure of the sentence, upon which operations are performed to generate logically modified AMR graphs. The modified AMR graphs are subsequently converted back into texts to create augmented data. Notably, our methodology is architecture-agnostic and enhances generative large language models, such as GPT-3.5 and GPT-4, through prompt augmentation, and fine-tuning discriminative large language models through contrastive learning with logic-driven data augmentation. Empirical evidence underscores the efficacy of our proposed method with improvement in performance across seven downstream tasks, such as logical reasoning reading comprehension, textual entailment, and natural language inference. Furthermore, our method ranked first on the ReClor leaderboard \url{https://eval.ai/web/challenges/challenge-page/503/leaderboard/1347}. The source code and data are publicly available \url{https://github.com/Strong-AI-Lab/Logical-Equivalence-driven-AMR-Data-Augmentation-for-Representation-Learning}.Comment: Accepted for oral presentation at the LLM@IJCAI 2023 non-archival symposiu

A Systematic Evaluation of Large Language Models on Out-of-Distribution Logical Reasoning Tasks

Large language models (LLMs), such as GPT-3.5 and GPT-4, have greatly advanced the performance of artificial systems on various natural language processing tasks to human-like levels. However, their generalisation and robustness to perform logical reasoning remain under-evaluated. To probe this ability, we propose three new logical reasoning datasets named "ReClor-plus", "LogiQA-plus" and "LogiQAv2-plus", each featuring three subsets: the first with randomly shuffled options, the second with the correct choices replaced by "none of the other options are correct", and a combination of the previous two subsets. We carry out experiments on these datasets with both discriminative and generative LLMs and show that these simple tricks greatly hinder the performance of the language models. Despite their superior performance on the original publicly available datasets, we find that all models struggle to answer our newly constructed datasets. We show that introducing task variations by perturbing a sizable training set can markedly improve the model's generalisation and robustness in logical reasoning tasks. Moreover, applying logic-driven data augmentation for fine-tuning, combined with prompting can enhance the generalisation performance of both discriminative large language models and generative large language models. These results offer insights into assessing and improving the generalisation and robustness of large language models for logical reasoning tasks. We make our source code and data publicly available \url{https://github.com/Strong-AI-Lab/Logical-and-abstract-reasoning}.Comment: Accepted for oral presentation at the LLM@IJCAI 2023 non-archival symposiu

Lesions to Polar/Orbital Prefrontal Cortex Selectively Impair Reasoning about Emotional Material

While it is widely accepted that lesions to orbital prefrontal cortex lead to emotion related disruptions and poor decision-making, there is very little patient data on this issue involving actual logical reasoning tasks. We tested patients with circumscribed, focal lesions largely confined to polar/orbital prefrontal cortex (BA 10 and 11) (N=17) on logical reasoning tasks involving neutral and emotional content, and compared their performance to that of an age and education-matched normal control group (N=22) and a posterior lesion control group (N=24). Our results revealed a significant group by content interaction driven by a selective impairment in the polar/orbital prefrontal cortex group compared to healthy normal controls and to the parietal patient group, in the emotional content reasoning trials. Subsequent analyses of congruent and incongruent reasoning trials indicated that this impairment was driven by the poor performance of patients with polar/orbital lesions in the incongruent trials. We conclude that the polar/orbital prefrontal cortex plays a critical role in filtering emotionally charged content from the material before it is passed on to the reasoning system in lateral/dorsal regions of prefrontal cortex. Where unfiltered content is passed to the reasoning engine, either as a result of pathology (as in the case of our patients) or as a result of individual differences, reasoning performance suffers

Logic tensor networks for semantic image interpretation

Semantic Image Interpretation (SII) is the task of extracting structured semantic descriptions from images. It is widely agreed that the combined use of visual data and background knowledge is of great importance for SII. Recently, Statistical Relational Learning (SRL) approaches have been developed for reasoning under uncertainty and learning in the presence of data and rich knowledge. Logic Tensor Networks (LTNs) are a SRL framework which integrates neural networks with first-order fuzzy logic to allow (i) efficient learning from noisy data in the presence of logical constraints, and (ii) reasoning with logical formulas describing general properties of the data. In this paper, we develop and apply LTNs to two of the main tasks of SII, namely, the classification of an image's bounding boxes and the detection of the relevant part-of relations between objects. To the best of our knowledge, this is the first successful application of SRL to such SII tasks. The proposed approach is evaluated on a standard image processing benchmark. Experiments show that background knowledge in the form of logical constraints can improve the performance of purely data-driven approaches, including the state-of-theart Fast Region-based Convolutional Neural Networks (Fast R-CNN). Moreover, we show that the use of logical background knowledge adds robustness to the learning system when errors are present in the labels of the training data

Invalid Logic, Equivalent Gains: The Bizarreness of Reasoning in Language Model Prompting

Language models can be prompted to reason through problems in a manner that significantly improves performance. However, \textit{why} such prompting improves performance is unclear. Recent work showed that using logically \textit{invalid} Chain-of-Thought (CoT) prompting improves performance almost as much as logically \textit{valid} CoT prompting, and that editing CoT prompts to replace problem-specific information with abstract information or out-of-distribution information typically doesn't harm performance. Critics have responded that these findings are based on too few and too easily solved tasks to draw meaningful conclusions. To resolve this dispute, we test whether logically invalid CoT prompts offer the same level of performance gains as logically valid prompts on the hardest tasks in the BIG-Bench benchmark, termed BIG-Bench Hard (BBH). We find that the logically \textit{invalid} reasoning prompts do indeed achieve similar performance gains on BBH tasks as logically valid reasoning prompts. We also discover that some CoT prompts used by previous works contain logical errors. This suggests that covariates beyond logically valid reasoning are responsible for performance improvements.Comment: ICML 2023 Workshop: Knowledge and Logical Reasoning in the Era of Data-driven Learnin

Improving Certified Robustness via Statistical Learning with Logical Reasoning

Intensive algorithmic efforts have been made to enable the rapid improvements of certificated robustness for complex ML models recently. However, current robustness certification methods are only able to certify under a limited perturbation radius. Given that existing pure data-driven statistical approaches have reached a bottleneck, in this paper, we propose to integrate statistical ML models with knowledge (expressed as logical rules) as a reasoning component using Markov logic networks (MLN, so as to further improve the overall certified robustness. This opens new research questions about certifying the robustness of such a paradigm, especially the reasoning component (e.g., MLN). As the first step towards understanding these questions, we first prove that the computational complexity of certifying the robustness of MLN is #P-hard. Guided by this hardness result, we then derive the first certified robustness bound for MLN by carefully analyzing different model regimes. Finally, we conduct extensive experiments on five datasets including both high-dimensional images and natural language texts, and we show that the certified robustness with knowledge-based logical reasoning indeed significantly outperforms that of the state-of-the-art

LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoning

Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at multiple levels and conducts symbolic reasoning with such structured abstraction. To fill these fundamental gaps, we devise LOGICSEG, a holistic visual semantic parser that integrates neural inductive learning and logic reasoning with both rich data and symbolic knowledge. In particular, the semantic concepts of interest are structured as a hierarchy, from which a set of constraints are derived for describing the symbolic relations and formalized as first-order logic rules. After fuzzy logic-based continuous relaxation, logical formulae are grounded onto data and neural computational graphs, hence enabling logic-induced network training. During inference, logical constraints are packaged into an iterative process and injected into the network in a form of several matrix multiplications, so as to achieve hierarchy-coherent prediction with logic reasoning. These designs together make LOGICSEG a general and compact neural-logic machine that is readily integrated into existing segmentation models. Extensive experiments over four datasets with various segmentation models and backbones verify the effectiveness and generality of LOGICSEG. We believe this study opens a new avenue for visual semantic parsing.Comment: ICCV 2023 (Oral). Code: https://github.com/lingorX/LogicSeg