Recent work has observed an intriguing ''Neural Collapse'' phenomenon in well-trained neural networks, where the last-layer representations of training samples with the same label collapse into each other. This appears to suggest that the last-layer representations are completely determined by the labels, and do not depend on the intrinsic structure of input distribution. We provide evidence that this is not a complete description, and that the apparent collapse hides important fine-grained structure in the representations. Specifically, even when representations apparently collapse, the small amount of remaining variation can still faithfully and accurately captures the intrinsic structure of input distribution. As an example, if we train on CIFAR-10 using only 5 coarse-grained labels (by combining two classes into one super-class) until convergence, we can reconstruct the original 10-class labels from the learned representations via unsupervised clustering. The reconstructed labels achieve $93\%$ accuracy on the CIFAR-10 test set, nearly matching the normal CIFAR-10 accuracy for the same architecture. We also provide an initial theoretical result showing the fine-grained representation structure in a simplified synthetic setting. Our results show concretely how the structure of input data can play a significant role in determining the fine-grained structure of neural representations, going beyond what Neural Collapse predicts.

In this paper, we propose a comprehensive benchmark to investigate models' logical reasoning capabilities in complex real-life scenarios. Current explanation datasets often employ synthetic data with simple reasoning structures. Therefore, it cannot express more complex reasoning processes, such as the rebuttal to a reasoning step and the degree of certainty of the evidence. To this end, we propose a comprehensive logical reasoning explanation form. Based on the multi-hop chain of reasoning, the explanation form includes three main components: (1) The condition of rebuttal that the reasoning node can be challenged; (2) Logical formulae that uncover the internal texture of reasoning nodes; (3) Reasoning strength indicated by degrees of certainty. The fine-grained structure conforms to the real logical reasoning scenario, better fitting the human cognitive process but, simultaneously, is more challenging for the current models. We evaluate the current best models' performance on this new explanation form. The experimental results show that generating reasoning graphs remains a challenging task for current models, even with the help of giant pre-trained language models.