Exploring Weight Importance and Hessian Bias in Model Pruning

Abstract

Model pruning is an essential procedure for building compact and computationally-efficient machine learning models. A key feature of a good pruning algorithm is that it accurately quantifies the relative importance of the model weights. While model pruning has a rich history, we still don't have a full grasp of the pruning mechanics even for relatively simple problems involving linear models or shallow neural nets. In this work, we provide a principled exploration of pruning by building on a natural notion of importance. For linear models, we show that this notion of importance is captured by covariance scaling which connects to the well-known Hessian-based pruning. We then derive asymptotic formulas that allow us to precisely compare the performance of different pruning methods. For neural networks, we demonstrate that the importance can be at odds with larger magnitudes and proper initialization is critical for magnitude-based pruning. Specifically, we identify settings in which weights become more important despite becoming smaller, which in turn leads to a catastrophic failure of magnitude-based pruning. Our results also elucidate that implicit regularization in the form of Hessian structure has a catalytic role in identifying the important weights, which dictate the pruning performance.

28 pages

References in corpus (9)

• Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks
• Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks
• In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning
• The LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements
• Proving the Lottery Ticket Hypothesis: Pruning is All You Need
• Training Skinny Deep Neural Networks with Iterative Hard Thresholding Methods
• Overparameterized Nonlinear Learning: Gradient Descent Takes the Shortest Path?
• Luck Matters: Understanding Training Dynamics of Deep ReLU Networks
• One-Shot Pruning of Recurrent Neural Networks by Jacobian Spectrum Evaluation