How deep is deep enough? -- Quantifying class separability in the hidden layers of deep neural networks

Deep neural networks typically outperform more traditional machine learning models in their ability to classify complex data, and yet is not clear how the individual hidden layers of a deep network contribute to the overall classification performance. We thus introduce a Generalized Discrimination Value (GDV) that measures, in a non-invasive manner, how well different data classes separate in each given network layer. The GDV can be used for the automatic tuning of hyper-parameters, such as the width profile and the total depth of a network. Moreover, the layer-dependent GDV(L) provides new insights into the data transformations that self-organize during training: In the case of multi-layer perceptrons trained with error backpropagation, we find that classification of highly complex data sets requires a temporal {\em reduction} of class separability, marked by a characteristic 'energy barrier' in the initial part of the GDV(L) curve. Even more surprisingly, for a given data set, the GDV(L) is running through a fixed 'master curve', independently from the total number of network layers. Furthermore, applying the GDV to Deep Belief Networks reveals that also unsupervised training with the Contrastive Divergence method can systematically increase class separability over tens of layers, even though the system does not 'know' the desired class labels. These results indicate that the GDV may become a useful tool to open the black box of deep learning

Contrastive Learning with Prompt-derived Virtual Semantic Prototypes for Unsupervised Sentence Embedding

Contrastive learning has become a new paradigm for unsupervised sentence embeddings. Previous studies focus on instance-wise contrastive learning, attempting to construct positive pairs with textual data augmentation. In this paper, we propose a novel Contrastive learning method with Prompt-derived Virtual semantic Prototypes (ConPVP). Specifically, with the help of prompts, we construct virtual semantic prototypes to each instance, and derive negative prototypes by using the negative form of the prompts. Using a prototypical contrastive loss, we enforce the anchor sentence embedding to be close to its corresponding semantic prototypes, and far apart from the negative prototypes as well as the prototypes of other sentences. Extensive experimental results on semantic textual similarity, transfer, and clustering tasks demonstrate the effectiveness of our proposed model compared to strong baselines. Code is available at https://github.com/lemon0830/promptCSE.Comment: Findings of EMNLP 202

Learning Representation for Clustering via Prototype Scattering and Positive Sampling

Existing deep clustering methods rely on either contrastive or non-contrastive representation learning for downstream clustering task. Contrastive-based methods thanks to negative pairs learn uniform representations for clustering, in which negative pairs, however, may inevitably lead to the class collision issue and consequently compromise the clustering performance. Non-contrastive-based methods, on the other hand, avoid class collision issue, but the resulting non-uniform representations may cause the collapse of clustering. To enjoy the strengths of both worlds, this paper presents a novel end-to-end deep clustering method with prototype scattering and positive sampling, termed ProPos. Specifically, we first maximize the distance between prototypical representations, named prototype scattering loss, which improves the uniformity of representations. Second, we align one augmented view of instance with the sampled neighbors of another view -- assumed to be truly positive pair in the embedding space -- to improve the within-cluster compactness, termed positive sampling alignment. The strengths of ProPos are avoidable class collision issue, uniform representations, well-separated clusters, and within-cluster compactness. By optimizing ProPos in an end-to-end expectation-maximization framework, extensive experimental results demonstrate that ProPos achieves competing performance on moderate-scale clustering benchmark datasets and establishes new state-of-the-art performance on large-scale datasets. Source code is available at \url{https://github.com/Hzzone/ProPos}.Comment: Accepted by TPAMI 202

A Theoretical Analysis of Contrastive Unsupervised Representation Learning

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.Comment: 19 pages, 5 figure

Automatically Discovering Novel Visual Categories with Self-supervised Prototype Learning

This paper tackles the problem of novel category discovery (NCD), which aims to discriminate unknown categories in large-scale image collections. The NCD task is challenging due to the closeness to the real-world scenarios, where we have only encountered some partial classes and images. Unlike other works on the NCD, we leverage the prototypes to emphasize the importance of category discrimination and alleviate the issue of missing annotations of novel classes. Concretely, we propose a novel adaptive prototype learning method consisting of two main stages: prototypical representation learning and prototypical self-training. In the first stage, we obtain a robust feature extractor, which could serve for all images with base and novel categories. This ability of instance and category discrimination of the feature extractor is boosted by self-supervised learning and adaptive prototypes. In the second stage, we utilize the prototypes again to rectify offline pseudo labels and train a final parametric classifier for category clustering. We conduct extensive experiments on four benchmark datasets and demonstrate the effectiveness and robustness of the proposed method with state-of-the-art performance.Comment: In Submissio