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Adaptive multi-fidelity optimization with fast learning rates Enhancing AI and Dynamical Subseasonal Forecasts with Probabilistic Bias Correction Sample Complexity Bounds for Stochastic Shortest Path with a Generative Model The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback Stylistic-STORM (ST-STORM) : Perceiving the Semantic Nature of Appearance Collective Kernel EFT for Pre-activation ResNets PRIM-cipal components analysis One-Shot Generative Flows: Existence and Obstructions Structural interpretability in SVMs with truncated orthogonal polynomial kernels Amortized Optimal Transport from Sliced Potentials MinShap: A Modified Shapley Value Approach for Feature Selection Unsupervised feature selection using Bayesian Tucker decomposition Multi-User mmWave Beam and Rate Adaptation via Combinatorial Satisficing Bandits Best of both worlds: Stochastic & adversarial best-arm identification Scalable Model-Based Clustering with Sequential Monte Carlo Expert-Guided Class-Conditional Goodness-of-Fit Scores for Interpretable Classification with Informative Missingness: An Application to Seismic Monitoring Lightweight Geometric Adaptation for Training Physics-Informed Neural Networks Gating Enables Curvature: A Geometric Expressivity Gap in Attention Zeroth-Order Optimization at the Edge of Stability Differentially Private Conformal Prediction CLion: Efficient Cautious Lion Optimizer with Enhanced Generalization Generative Augmented Inference Improving Machine Learning Performance with Synthetic Augmentation PAC-MCTS: Bias-Aware Pruning for Robust LLM-Guided Search and Planning Path-Sampled Integrated Gradients Heat and Matérn Kernels on Matchings Doubly Outlier-Robust Online Infinite Hidden Markov Model Momentum Further Constrains Sharpness at the Edge of Stochastic Stability Multistage Conditional Compositional Optimization BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization
Neural Collapse for Cross-entropy Class-Imbalanced Learni...
Hien Dang, Tho Tran, Tan Nguyen, Nhat Ho · 2024-01-04 · via stat.ML updates on arXiv.org

The current paradigm of training deep neural networks for classification tasks includes minimizing the empirical risk that pushes the training loss value towards zero, even after the training error has been vanished. In this terminal phase of training, it has been observed that the last-layer features collapse to their class-means and these class-means converge to the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is termed as Neural Collapse (NC). To theoretically understand this phenomenon, recent works employ a simplified unconstrained feature model to prove that NC emerges at the global solutions of the training problem. However, when the training dataset is class-imbalanced, some NC properties will no longer be true. For example, the class-means geometry will skew away from the simplex ETF when the loss converges. In this paper, we generalize NC to imbalanced regime for cross-entropy loss under the unconstrained ReLU feature model. We prove that, while the within-class features collapse property still holds in this setting, the class-means will converge to a structure consisting of orthogonal vectors with different lengths. Furthermore, we find that the classifier weights are aligned to the scaled and centered class-means with scaling factors depend on the number of training samples of each class, which generalizes NC in the class-balanced setting. We empirically prove our results through experiments on practical architectures and dataset.