Gradient Starvation: A Learning Proclivity in Neural Networks (2011.09468v4)

Abstract: We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

• The paper identifies Gradient Starvation as the dominance of fast-learning features that starves slower yet relevant representations during training.
• It introduces Spectral Decoupling (SD), a novel regularization method that penalizes model outputs to promote balanced learning across features.
• Empirical results on datasets like CIFAR-10, CIFAR-100, and Colored MNIST show improved out-of-distribution performance and robustness using SD.

Overview of Gradient Starvation in Neural Networks

The paper, titled "Gradient Starvation: A Learning Proclivity in Neural Networks," addresses a specific phenomenon observed during the training of over-parameterized neural networks using gradient descent—termed Gradient Starvation (GS). The authors present this as a situation where certain features that contribute predictively to the task are underemphasized or neglected despite their presence due to the neural network's preference for faster-learning features during the optimization process.

Key Insights and Methodology

The authors build a theoretical framework using concepts from Dynamical Systems theory and Neural Tangent Kernel (NTK) analysis to analyze the learning dynamics under cross-entropy loss. They focus particularly on the scenario where feature imbalances arise. The phenomenon is termed Gradient Starvation, where features that learn quickly dominate gradient updates, starving other relevant features.

1. Theoretical Analysis: Through mathematical formalization, the authors show how feature directions are coupled during learning, which can lead to dominance by a subset of those features when gradient descent is employed. The paper shows that this coupling arises naturally due to the statistical structure present in the training data.
2. Spectral Decoupling (SD): The authors propose a regularization technique—Spectral Decoupling (SD)—that aims to decouple these dynamics and tackle GS. SD modifies the regularization scheme by applying a penalty to the model's outputs rather than weights, encouraging learning dynamics to treat different features more evenly.
3. Empirical Evaluation: The paper presents empirical results, including real-world out-of-distribution (OOD) generalization experiments, validating the proposed method's efficacy in mitigating the effects of Gradient Starvation. The experiments indicate that neural networks trained with SD achieve better robustness and accuracy when facing OOD scenarios.

Numerical Results and Experimentation

• Simple 2-D Examples: Through a visual illustration using a two-dimensional classification task, the authors demonstrate how Gradient Starvation can lead to incorrect or less generalizable decision boundaries. SD is shown to produce decision boundaries that better align with the data structure, effectively improving classification margins.
• Classification on Image Datasets: The authors assess the practical impact of GS on popular datasets like CIFAR-10 and CIFAR-100, highlighting the improvement in robustness and classification accuracy when utilizing SD. Perturbation analysis demonstrated enhanced resilience against adversarial attacks.
• Colored MNIST and CelebA Datasets: These experiments underscore how cross-entropy loss can lead networks to latch onto spurious correlations (e.g., color or demographic bias), which affects generalization. SD helps neutralize this dependency, thus aligning learned features more closely with task objectives rather than artefacts.

Implications and Speculations

The theoretical exploration and empirical validations suggest several implications. Practically, controlling GS could improve the reliability and trustworthiness of AI systems by ensuring more balanced feature learning, particularly in safety-critical applications. Theoretically, this work provides insights into how optimization dynamics can be modulated to favor more generalized learning, contributing to ongoing discussions about the interplay of optimization algorithms and model architecture.

Looking forwards, future research could focus on broadening the understanding of GS across different classes of models and a variety of loss functions, possibly yielding novel techniques to enhance model robustness against distributional shifts and adversarial threats.

This paper extends the theoretical landscape around the dynamics of neural networks training, presenting GS as an intrinsic challenge when using gradient-based optimization and proposes a promising method to neutralize its adverse effects, promoting the pursuit of improved generalization in deep learning systems.