Just How Flexible are Neural Networks in Practice?
Ravid Shwartz-Ziv, Micah Goldblum, Arpit Bansal, C. Bayan Bruss, Yann LeCun, Andrew Gordon Wilson
2024-06-18
Summary
This paper explores how flexible neural networks are when it comes to fitting data. It challenges the common belief that a neural network can easily learn from a dataset that has at least as many samples as its parameters, and it investigates what actually limits their flexibility in practice.
What's the problem?
Many people think that neural networks can learn from any dataset as long as it has enough examples. However, in reality, the way these networks are trained and the specific techniques used can restrict their ability to learn effectively. This means that even if a neural network has a lot of parameters (the settings it can adjust), it might not be able to fit all the data well, especially if the training process isn't optimal.
What's the solution?
The authors conducted experiments to see how well neural networks can fit data under different conditions. They found that standard training methods often lead to situations where the model can only handle fewer training samples than it actually has parameters for. They also discovered that convolutional networks (which are good for images) are more efficient than other types like multi-layer perceptrons (MLPs) or vision transformers (ViTs). Additionally, they noted that using stochastic gradient descent (SGD), a common training method, helps models fit more data compared to using all data at once. The study highlights how different factors, like the type of training and the model's structure, influence how well a neural network can learn from data.
Why it matters?
This research is important because it provides insights into the real capabilities and limitations of neural networks. Understanding how these models work in practice helps researchers and developers improve their designs and training methods, leading to better performance in tasks like image recognition, natural language processing, and more. By revealing the complexities behind neural network training, this work can guide future advancements in artificial intelligence.
Abstract
It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.