Self-similarity Analysis in Deep Neural Networks

Current research has found that some deep neural networks exhibit strong hierarchical self-similarity in feature representation or parameter distribution. However, aside from preliminary studies on how the power-law distribution of weights across different training stages affects model performance,there has been no quantitative analysis on how the self-similarity of hidden space geometry influences model weight optimization, nor is there a clear understanding of the dynamic behavior of internal neurons. Therefore, this paper proposes a complex network modeling method based on the output features of hidden-layer neurons to investigate the self-similarity of feature networks constructed at different hidden layers, and analyzes how adjusting the degree of self-similarity in feature networks can enhance the classification performance of deep neural networks. Validated on three types of networks MLP architectures, convolutional networks, and attention architectures this study reveals that the degree of self-similarity exhibited by feature networks varies across different model architectures. Furthermore, embedding constraints on the self-similarity of feature networks during the training process can improve the performance of self-similar deep neural networks (MLP architectures and attention architectures) by up to 6 percentage points.

Large Language Models Meet Symbolic Provers for Logical Reasoning Evaluation

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing benchmarks often rely on extensive human annotation or handcrafted templates, making it difficult to achieve the necessary complexity, scalability, and diversity for robust evaluation. To address these limitations, we propose a novel framework called ProverGen that synergizes the generative strengths of Large Language Models (LLMs) with the rigor and precision of symbolic provers, enabling the creation of a scalable, diverse, and high-quality FOL reasoning dataset, ProverQA. ProverQA is also distinguished by its inclusion of accessible and logically coherent intermediate reasoning steps for each problem. Our evaluation shows that state-of-the-art LLMs struggle to solve ProverQA problems, even with CoT prompting, highlighting the dataset's challenging nature. We also finetune Llama3.1-8B-Instruct on a separate training set generated by our framework. The finetuned model demonstrates consistent improvements on both in-distribution and out-of-distribution test sets, suggesting the value of our proposed data generation framework. Code available at: https://github.com/opendatalab/ProverGen

An Investigation of LLMs' Inefficacy in Understanding Converse Relations

Large Language Models (LLMs) have achieved remarkable success in many formal language oriented tasks, such as structural data-to-text and semantic parsing. However current benchmarks mostly follow the data distribution of the pre-training data of LLMs. Therefore, a natural question rises that do LLMs really understand the structured semantics of formal languages. In this paper, we investigate this problem on a special case, converse binary relation. We introduce a new benchmark ConvRe focusing on converse relations, which contains 17 relations and 1240 triples extracted from popular knowledge graph completion datasets. Our ConvRE features two tasks, Re2Text and Text2Re, which are formulated as multi-choice question answering to evaluate LLMs' ability to determine the matching between relations and associated text. For the evaluation protocol, apart from different prompting methods, we further introduce variants to the test text and few-shot example text. We conduct experiments on three popular LLM families and have observed various scaling trends. The results suggest that LLMs often resort to shortcut learning and still face challenges on our proposed benchmark.