Early Stage Convergence and Global Convergence of Training Mildly
Parameterized Neural Networks
- URL: http://arxiv.org/abs/2206.02139v3
- Date: Mon, 29 May 2023 05:39:13 GMT
- Title: Early Stage Convergence and Global Convergence of Training Mildly
Parameterized Neural Networks
- Authors: Mingze Wang, Chao Ma
- Abstract summary: We show that the loss is decreased by a significant amount in the early stage of the training, and this decrease is fast.
We use a microscopic analysis of the activation patterns for the neurons, which helps us derive more powerful lower bounds for the gradient.
- Score: 3.148524502470734
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The convergence of GD and SGD when training mildly parameterized neural
networks starting from random initialization is studied. For a broad range of
models and loss functions, including the most commonly used square loss and
cross entropy loss, we prove an ``early stage convergence'' result. We show
that the loss is decreased by a significant amount in the early stage of the
training, and this decrease is fast. Furthurmore, for exponential type loss
functions, and under some assumptions on the training data, we show global
convergence of GD. Instead of relying on extreme over-parameterization, our
study is based on a microscopic analysis of the activation patterns for the
neurons, which helps us derive more powerful lower bounds for the gradient. The
results on activation patterns, which we call ``neuron partition'', help build
intuitions for understanding the behavior of neural networks' training
dynamics, and may be of independent interest.
Related papers
- Fractional-order spike-timing-dependent gradient descent for multi-layer spiking neural networks [18.142378139047977]
This paper proposes a fractional-order spike-timing-dependent gradient descent (FOSTDGD) learning model.
It is tested on theNIST and DVS128 Gesture datasets and its accuracy under different network structure and fractional orders is analyzed.
arXiv Detail & Related papers (2024-10-20T05:31:34Z) - Topological obstruction to the training of shallow ReLU neural networks [0.0]
We study the interplay between the geometry of the loss landscape and the optimization trajectories of simple neural networks.
This paper reveals the presence of topological obstruction in the loss landscape of shallow ReLU neural networks trained using gradient flow.
arXiv Detail & Related papers (2024-10-18T19:17:48Z) - Learning a Neuron by a Shallow ReLU Network: Dynamics and Implicit Bias
for Correlated Inputs [5.7166378791349315]
We prove that, for the fundamental regression task of learning a single neuron, training a one-hidden layer ReLU network converges to zero loss.
We also show and characterise a surprising distinction in this setting between interpolator networks of minimal rank and those of minimal Euclidean norm.
arXiv Detail & Related papers (2023-06-10T16:36:22Z) - Globally Optimal Training of Neural Networks with Threshold Activation
Functions [63.03759813952481]
We study weight decay regularized training problems of deep neural networks with threshold activations.
We derive a simplified convex optimization formulation when the dataset can be shattered at a certain layer of the network.
arXiv Detail & Related papers (2023-03-06T18:59:13Z) - And/or trade-off in artificial neurons: impact on adversarial robustness [91.3755431537592]
Presence of sufficient number of OR-like neurons in a network can lead to classification brittleness and increased vulnerability to adversarial attacks.
We define AND-like neurons and propose measures to increase their proportion in the network.
Experimental results on the MNIST dataset suggest that our approach holds promise as a direction for further exploration.
arXiv Detail & Related papers (2021-02-15T08:19:05Z) - Topological obstructions in neural networks learning [67.8848058842671]
We study global properties of the loss gradient function flow.
We use topological data analysis of the loss function and its Morse complex to relate local behavior along gradient trajectories with global properties of the loss surface.
arXiv Detail & Related papers (2020-12-31T18:53:25Z) - Gradient Starvation: A Learning Proclivity in Neural Networks [97.02382916372594]
Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task.
This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks.
arXiv Detail & Related papers (2020-11-18T18:52:08Z) - Over-parametrized neural networks as under-determined linear systems [31.69089186688224]
We show that it is unsurprising simple neural networks can achieve zero training loss.
We show that kernels typically associated with the ReLU activation function have fundamental flaws.
We propose new activation functions that avoid the pitfalls of ReLU in that they admit zero training loss solutions for any set of distinct data points.
arXiv Detail & Related papers (2020-10-29T21:43:00Z) - Plateau Phenomenon in Gradient Descent Training of ReLU networks:
Explanation, Quantification and Avoidance [0.0]
In general, neural networks are trained by gradient type optimization methods.
The loss function decreases rapidly at the beginning of training but then, after a relatively small number of steps, significantly slow down.
The present work aims to identify and quantify the root causes of plateau phenomenon.
arXiv Detail & Related papers (2020-07-14T17:33:26Z) - Modeling from Features: a Mean-field Framework for Over-parameterized
Deep Neural Networks [54.27962244835622]
This paper proposes a new mean-field framework for over- parameterized deep neural networks (DNNs)
In this framework, a DNN is represented by probability measures and functions over its features in the continuous limit.
We illustrate the framework via the standard DNN and the Residual Network (Res-Net) architectures.
arXiv Detail & Related papers (2020-07-03T01:37:16Z) - The Break-Even Point on Optimization Trajectories of Deep Neural
Networks [64.7563588124004]
We argue for the existence of the "break-even" point on this trajectory.
We show that using a large learning rate in the initial phase of training reduces the variance of the gradient.
We also show that using a low learning rate results in bad conditioning of the loss surface even for a neural network with batch normalization layers.
arXiv Detail & Related papers (2020-02-21T22:55:51Z)
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.