Year: 2021
Type: preprint
Abstract: Jacobian-vector products (JVPs) form the backbone of many recent developments in Deep Networks (DNs), with applications including faster constrained optimization, regularization with generalization guarantees, and adversarial example sensitivity assessments. Unfortunately, JVPs are computationally expensive for real world DN architectures and require the use of automatic differentiation to avoid manually adapting the JVP program when changing the DN architecture. We propose a novel method to quickly compute JVPs for any DN that employ Continuous Piecewise Affine (e.g., leaky-ReLU, max-pooling, maxout, etc.) nonlinearities. We show that our technique is on average $2\times$ faster than the fastest alternative over $13$ DN architectures and across various hardware. In addition, our solution does not require automatic differentiation and is thus easy to deploy in software, requiring only the modification of a few lines of codes that do not depend on the DN architecture.
Source: arXiv (Cornell University)
Authors: Balestriero, Randall, Baraniuk, Richard
Institution: Rice University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1483339860, G1523888516, G1717380892, G2167961191, G2308282352, BIGDATA: F: Collaborative Research: Theory and Practice of Randomized Algorithms for Ultra-Large-Scale Signal Processing, Collaborative Research: Computational Photo-Scatterography: Unraveling Scattered Photons for Bio-Imaging, G5121974832, G6098521345, G6706517093, G7840735550, G8006577219, G8252795151, CIF: Small: A Probabilistic Theory of Deep Learning via Spline Operators, G8876996369
OpenAlex ID: W3140106748