Recent studies show that pretraining a deep neural network with fine-grained labeled data, followed by fine-tuning on coarse-labeled data for downstream tasks, often yields better generalization than pretraining with coarse-labeled data. While there is ample empirical evidence supporting this, the theoretical justification remains an open problem. This paper addresses this gap by introducing a "hierarchical multi-view" structure to confine the input data distribution. Under this framework, we prove that: 1) coarse-grained pretraining only allows a neural network to learn the common features well, while 2) fine-grained pretraining helps the network learn the rare features in addition to the common ones, leading to improved accuracy on hard downstream test samples.

Large language models (LLMs) have shown amazing performance on tasks that require planning and reasoning. Motivated by this, we investigate the internal mechanisms that underpin a network's ability to perform complex logical reasoning. We first construct a synthetic propositional logic problem that serves as a concrete test-bed for network training and evaluation. Crucially, this problem demands nontrivial planning to solve. We perform our study on two fronts. First, we pursue an understanding of precisely how a three-layer transformer, trained from scratch and attains perfect test accuracy, solves this problem. We are able to identify certain "planning" and "reasoning" mechanisms in the network that necessitate cooperation between the attention blocks to implement the desired logic. Second, we study how pretrained LLMs, namely Mistral-7B and Gemma-2-9B, solve this problem. We characterize their reasoning circuits through causal intervention experiments, providing necessity and sufficiency evidence for the circuits. We find evidence suggesting that the two models' latent reasoning strategies are surprisingly similar, and human-like. Overall, our work systemically uncovers novel aspects of small and large transformers, and continues the study of how they plan and reason.

In this paper, we study how the granularity of pretraining labels affects the generalization of deep neural networks in image classification tasks. We focus on the "fine-to-coarse" transfer learning setting, where the pretraining label space is more fine-grained than that of the target problem. Empirically, we show that pretraining on the leaf labels of ImageNet21k produces better transfer results on ImageNet1k than pretraining on other coarser granularity levels, which supports the common practice used in the community. Theoretically, we explain the benefit of fine-grained pretraining by proving that, for a data distribution satisfying certain hierarchy conditions, 1) coarse-grained pretraining only allows a neural network to learn the "common" or "easy-to-learn" features well, while 2) fine-grained pretraining helps the network learn the "rarer" or "fine-grained" features in addition to the common ones, thus improving its accuracy on hard downstream test samples in which common features are missing or weak in strength. Furthermore, we perform comprehensive experiments using the label hierarchies of iNaturalist 2021 and observe that the following conditions, in addition to proper choice of label granularity, enable the transfer to work well in practice: 1) the pretraining dataset needs to have a meaningful label hierarchy, and 2) the pretraining and target label functions need to align well.