Kun Song

Kun Song, Huimin Ma, Bochao Zou et al.

Due to the limited availability of data, existing few-shot learning methods trained from scratch fail to achieve satisfactory performance. In contrast, large-scale pre-trained models such as CLIP demonstrate remarkable few-shot and zero-shot capabilities. To enhance the performance of pre-trained models for downstream tasks, fine-tuning the model on downstream data is frequently necessary. However, fine-tuning the pre-trained model leads to a decrease in its generalizability in the presence of distribution shift, while the limited number of samples in few-shot learning makes the model highly susceptible to overfitting. Consequently, existing methods for fine-tuning few-shot learning primarily focus on fine-tuning the model's classification head or introducing additional structure. In this paper, we introduce a fine-tuning approach termed Feature Discrimination Alignment (FD-Align). Our method aims to bolster the model's generalizability by preserving the consistency of spurious features across the fine-tuning process. Extensive experimental results validate the efficacy of our approach for both ID and OOD tasks. Once fine-tuned, the model can seamlessly integrate with existing methods, leading to performance improvements. Our code can be found in https://github.com/skingorz/FD-Align.

Kun Song, Zhiquan Tan, Bochao Zou et al.

In this paper, we introduce matrix entropy as an analytical tool for studying supervised learning, investigating the information content of data representations and classification head vectors, as well as the dynamic interactions between them during the supervised learning process. Our experimental results reveal that matrix entropy effectively captures the variations in information content of data representations and classification head vectors as neural networks approach Neural Collapse during supervised training, while also serving as a robust metric for measuring similarity among data samples. Leveraging this property, we propose Cross-Model Alignment (CMA) loss to optimize the fine-tuning of pretrained models. To characterize the dynamics of neural networks nearing the Neural Collapse state, we introduce two novel metrics: the Matrix Mutual Information Ratio (MIR) and the Matrix Entropy Difference Ratio (HDR), which quantitatively assess the interactions between data representations and classification heads in supervised learning, with theoretical optimal values derived under the Neural Collapse state. Our experiments demonstrate that MIR and HDR effectively explain various phenomena in neural networks, including the dynamics of standard supervised training, linear mode connectivity. Moreover, we use MIR and HDR to analyze the dynamics of grokking, which is a fascinating phenomenon in supervised learning where a model unexpectedly exhibits generalization long after achieving training data fit.

Kun Song, Zhiquan Tan, Bochao Zou et al.

In this paper, we use matrix information theory as an analytical tool to analyze the dynamics of the information interplay between data representations and classification head vectors in the supervised learning process. Specifically, inspired by the theory of Neural Collapse, we introduce matrix mutual information ratio (MIR) and matrix entropy difference ratio (HDR) to assess the interactions of data representation and class classification heads in supervised learning, and we determine the theoretical optimal values for MIR and HDR when Neural Collapse happens. Our experiments show that MIR and HDR can effectively explain many phenomena occurring in neural networks, for example, the standard supervised training dynamics, linear mode connectivity, and the performance of label smoothing and pruning. Additionally, we use MIR and HDR to gain insights into the dynamics of grokking, which is an intriguing phenomenon observed in supervised training, where the model demonstrates generalization capabilities long after it has learned to fit the training data. Furthermore, we introduce MIR and HDR as loss terms in supervised and semi-supervised learning to optimize the information interactions among samples and classification heads. The empirical results provide evidence of the method's effectiveness, demonstrating that the utilization of MIR and HDR not only aids in comprehending the dynamics throughout the training process but can also enhances the training procedure itself.