Understanding Optimization of Deep Learning via Jacobian Matrix and
Lipschitz Constant
- URL: http://arxiv.org/abs/2306.09338v3
- Date: Sun, 12 Nov 2023 07:13:58 GMT
- Title: Understanding Optimization of Deep Learning via Jacobian Matrix and
Lipschitz Constant
- Authors: Xianbiao Qi, Jianan Wang and Lei Zhang
- Abstract summary: This article provides a comprehensive understanding of optimization in deep learning.
We focus on the challenges of gradient vanishing and gradient exploding, which normally lead to diminished model representational ability and training instability, respectively.
To help understand the current optimization methodologies, we categorize them into two classes: explicit optimization and implicit optimization.
- Score: 18.592094066642364
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This article provides a comprehensive understanding of optimization in deep
learning, with a primary focus on the challenges of gradient vanishing and
gradient exploding, which normally lead to diminished model representational
ability and training instability, respectively. We analyze these two challenges
through several strategic measures, including the improvement of gradient flow
and the imposition of constraints on a network's Lipschitz constant. To help
understand the current optimization methodologies, we categorize them into two
classes: explicit optimization and implicit optimization. Explicit optimization
methods involve direct manipulation of optimizer parameters, including weight,
gradient, learning rate, and weight decay. Implicit optimization methods, by
contrast, focus on improving the overall landscape of a network by enhancing
its modules, such as residual shortcuts, normalization methods, attention
mechanisms, and activations. In this article, we provide an in-depth analysis
of these two optimization classes and undertake a thorough examination of the
Jacobian matrices and the Lipschitz constants of many widely used deep learning
modules, highlighting existing issues as well as potential improvements.
Moreover, we also conduct a series of analytical experiments to substantiate
our theoretical discussions. This article does not aim to propose a new
optimizer or network. Rather, our intention is to present a comprehensive
understanding of optimization in deep learning. We hope that this article will
assist readers in gaining a deeper insight in this field and encourages the
development of more robust, efficient, and high-performing models.
Related papers
- Understanding Optimization in Deep Learning with Central Flows [53.66160508990508]
We show that an RMS's implicit behavior can be explicitly captured by a "central flow:" a differential equation.
We show that these flows can empirically predict long-term optimization trajectories of generic neural networks.
arXiv Detail & Related papers (2024-10-31T17:58:13Z) - Efficiency optimization of large-scale language models based on deep learning in natural language processing tasks [6.596361762662328]
Internal structure and operation mechanism of large-scale language models are analyzed theoretically.
We evaluate the contribution of adaptive optimization algorithms (such as AdamW), massively parallel computing techniques, and mixed precision training strategies.
arXiv Detail & Related papers (2024-05-20T00:10:00Z) - Analyzing and Enhancing the Backward-Pass Convergence of Unrolled
Optimization [50.38518771642365]
The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks.
A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form.
This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method.
A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
arXiv Detail & Related papers (2023-12-28T23:15:18Z) - Investigation into the Training Dynamics of Learned Optimizers [0.0]
We look at the concept of learneds as a way to accelerate the optimization process by replacing traditional, hand-crafted algorithms with meta-learned functions.
Our work examines their optimization from the perspective of network architecture symmetries and update parameters.
We identify several key insights that demonstrate how each approach can benefit from the strengths of the other.
arXiv Detail & Related papers (2023-12-12T11:18:43Z) - Optimization Methods in Deep Learning: A Comprehensive Overview [0.0]
Deep learning has achieved remarkable success in various fields such as image recognition, natural language processing, and speech recognition.
The effectiveness of deep learning largely depends on the optimization methods used to train deep neural networks.
We provide an overview of first-order optimization methods such as Gradient Descent, Adagrad, Adadelta, and RMSprop, as well as recent momentum-based and adaptive gradient methods such as Nesterov accelerated gradient, Adam, Nadam, AdaMax, and AMSGrad.
arXiv Detail & Related papers (2023-02-19T13:01:53Z) - Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks.
One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver.
This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
arXiv Detail & Related papers (2023-01-28T01:50:42Z) - An Empirical Evaluation of Zeroth-Order Optimization Methods on
AI-driven Molecule Optimization [78.36413169647408]
We study the effectiveness of various ZO optimization methods for optimizing molecular objectives.
We show the advantages of ZO sign-based gradient descent (ZO-signGD)
We demonstrate the potential effectiveness of ZO optimization methods on widely used benchmark tasks from the Guacamol suite.
arXiv Detail & Related papers (2022-10-27T01:58:10Z) - Teaching Networks to Solve Optimization Problems [13.803078209630444]
We propose to replace the iterative solvers altogether with a trainable parametric set function.
We show the feasibility of learning such parametric (set) functions to solve various classic optimization problems.
arXiv Detail & Related papers (2022-02-08T19:13:13Z) - Tutorial on amortized optimization [13.60842910539914]
This tutorial presents an introduction to the amortized optimization foundations behind these advancements.
It overviews their applications in variational inference, sparse coding, gradient-based meta-learning, control, reinforcement learning, convex optimization, optimal transport, and deep equilibrium networks.
arXiv Detail & Related papers (2022-02-01T18:58:33Z) - Unified Convergence Analysis for Adaptive Optimization with Moving Average Estimator [75.05106948314956]
We show that an increasing large momentum parameter for the first-order moment is sufficient for adaptive scaling.
We also give insights for increasing the momentum in a stagewise manner in accordance with stagewise decreasing step size.
arXiv Detail & Related papers (2021-04-30T08:50:24Z) - Reverse engineering learned optimizers reveals known and novel
mechanisms [50.50540910474342]
Learneds are algorithms that can themselves be trained to solve optimization problems.
Our results help elucidate the previously murky understanding of how learneds work, and establish tools for interpreting future learneds.
arXiv Detail & Related papers (2020-11-04T07:12:43Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.