HOW MANY SAMPLES ARE NEEDED TO TRAIN A DEEP NEURAL NETWORK?

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Conflicts of Interest

Identified Weaknesses

Rating Explanation

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Paper Summary

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Deep Learning Needs WAY More Data Than You Think (and We Have Math to Prove It)

This paper establishes a lower bound for the number of samples needed to train a deep ReLU neural network, showing it scales at a rate of 1/√n, slower than classical methods. This theoretical result is supported by experiments on benchmark datasets for image classification and regression tasks. The findings confirm the common belief that deep learning requires a large amount of data for effective training.

Possible Conflicts of Interest

None identified.

Identified Weaknesses

Limited theoretical scope for CNNs

The theoretical results primarily focus on feedforward ReLU networks, while the empirical studies extend to CNNs. This leaves a gap in the theoretical understanding of CNNs.

Assumption of high input dimension

The lower bound assumes high input dimensions and might not hold for low-dimensional data.

Lack of practical sample size guidelines

Although the paper provides a lower bound, it doesn't offer practical guidance on choosing the optimal number of samples for a given task.

Rating Explanation

This paper provides a valuable theoretical and empirical analysis of sample complexity in deep learning. The derived lower bound and supporting experiments offer new insights into why deep learning models often require extensive training data. While the theoretical scope is limited to feedforward networks and assumes high input dimensions, the findings are significant and match existing upper bounds. The paper successfully addresses a fundamental question in deep learning, justifying its 4 rating.

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