Few-shot learning is used to adapt quickly to new classes with low annotation cost.

Supervised contrastive learning (SupCL) has emerged as a prominent approach in representation learning, leveraging both supervised and self-supervised losses. However, achieving an optimal balance between these losses is challenging; failing to do so can lead to class collapse, reducing discrimination among individual embeddings in the same class. In this paper, we present theoretically grounded guidelines for SupCL to prevent class collapse in learned representations. Specifically, we introduce the Simplex-to-Simplex Embedding Model (SSEM), a theoretical framework that models various embedding structures, including all embeddings that minimize the supervised contrastive loss. Through SSEM, we analyze how hyperparameters affect learned representations, offering practical guidelines for hyperparameter selection to mitigate the risk of class collapse. Our theoretical findings are supported by empirical results across synthetic and real-world datasets.

In federated learning (FL), model aggregation is a critical step by which multiple clients share their knowledge with one another. However, it is also widely recognized that the aggregated model, when sent back to each client, performs poorly on local data until after several rounds of local training. This temporary performance drop can potentially slow down the convergence of the FL model. Most research in FL regards this performance drop as an inherent cost of knowledge sharing among clients and does not give it special attention. While some studies directly focus on designing techniques to alleviate the issue, an in-depth investigation of the reasons behind this performance drop has yet to be conducted.To address this gap, we conduct a layer-peeled analysis of model aggregation across various datasets and model architectures. Our findings reveal that the performance drop can be attributed to two major consequences of the aggregation process: (1) it disrupts feature variability suppression in deep neural networks (DNNs), and (2) it weakens the coupling between features and subsequent parameters.Based on these findings, we propose several simple yet effective strategies to mitigate the negative impacts of model aggregation while still enjoying the benefit it brings. To the best of our knowledge, our work is the first to conduct a layer-peeled analysis of model aggregation, potentially paving the way for the development of more effective FL algorithms.

Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We present a novel approach that combines the eigenanalysis of a covariance matrix evaluated on a training set with a Hessian matrix evaluated on a deep learning model to achieve optimal class separability in binary classification tasks. Our approach is substantiated by formal proofs that establish its capability to maximize between-class mean distance and minimize within-class variances. By projecting data into the combined space of the most relevant eigendirections from both matrices, we achieve optimal class separability as per the linear discriminant analysis (LDA) criteria. Empirical validation across neural and health datasets consistently supports our theoretical framework and demonstrates that our method outperforms established methods. Our method stands out by addressing both LDA criteria, unlike PCA and the Hessian method, which predominantly emphasize one criterion each. This comprehensive approach captures intricate patterns and relationships, enhancing classification performance. Furthermore, through the utilization of both LDA criteria, our method outperforms LDA itself by leveraging higher-dimensional feature spaces, in accordance with Cover's theorem, which favors linear separability in higher dimensions. Our method also surpasses kernel-based methods and manifold learning techniques in performance. Additionally, our approach sheds light on complex DNN decision-making, rendering them comprehensible within a 2D space.

The prototypical network is a prototype classifier based on meta-learning and is widely used for few-shot learning because it classifies unseen examples by constructing class-specific prototypes without adjusting hyper-parameters during meta-testing. Interestingly, recent research has attracted a lot of attention, showing that training a new linear classifier, which does not use a meta-learning algorithm, performs comparably with the prototypical network. However, the training of a new linear classifier requires the retraining of the classifier every time a new class appears. In this paper, we analyze how a prototype classifier works equally well without training a new linear classifier or meta-learning. We experimentally find that directly using the feature vectors, which is extracted by using standard pre-trained models to construct a prototype classifier in meta-testing, does not perform as well as the prototypical network and training new linear classifiers on the feature vectors of pre-trained models. Thus, we derive a novel generalization bound for a prototypical classifier and show that the transformation of a feature vector can improve the performance of prototype classifiers. We experimentally investigate several normalization methods for minimizing the derived bound and find that the same performance can be obtained by using the L2 normalization and minimizing the ratio of the within-class variance to the between-class variance without training a new classifier or meta-learning.