Assessing Neural Network Representations During Training Using Noise-Resilient Diffusion Spectral Entropy

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

Sentence Embeddings using Supervised Contrastive Learning

Sentence embeddings encode sentences in fixed dense vectors and have played an important role in various NLP tasks and systems. Methods for building sentence embeddings include unsupervised learning such as Quick-Thoughts and supervised learning such as InferSent. With the success of pretrained NLP models, recent research shows that fine-tuning pretrained BERT on SNLI and Multi-NLI data creates state-of-the-art sentence embeddings, outperforming previous sentence embeddings methods on various evaluation benchmarks. In this paper, we propose a new method to build sentence embeddings by doing supervised contrastive learning. Specifically our method fine-tunes pretrained BERT on SNLI data, incorporating both supervised crossentropy loss and supervised contrastive loss. Compared with baseline where fine-tuning is only done with supervised cross-entropy loss similar to current state-of-the-art method SBERT, our supervised contrastive method improves 2.8% in average on Semantic Textual Similarity (STS) benchmarks and 1.05% in average on various sentence transfer tasks.