Going Deeper, Generalizing Better: An Information-Theoretic View for Deep Learning.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Deep Learning

Background:

• Deep learning excels in various AI tasks but lacks clear explanations for its generalization capabilities.
• Key questions persist regarding why deep neural networks (DNNs) outperform shallow ones and the universal benefit of increased network depth.

Purpose of the Study:

• To investigate the theoretical underpinnings of deep neural network generalization.
• To determine the relationship between network depth, information processing, and generalization error.
• To establish conditions under which deeper networks yield improved performance.

Main Methods:

• Deriving an upper bound for the generalization error of neural networks using mutual information.
• Analyzing the impact of information-losing layers (e.g., convolutional, pooling) on generalization.
• Examining the trade-off between generalization error and training error in deep networks.
• Investigating the stability properties of deep learning algorithms and deriving error bounds for noisy stochastic gradient descent (SGD).

Main Results:

• Generalization error is upper bounded by mutual information between last-layer features and output parameters.
• Increasing network depth decreases generalization error under mild conditions, explained by information-losing layers.
• Zero generalization error does not guarantee small test error due to potential increases in training error with depth.
• Deep learning exhibits weak stability properties, with derived generalization bounds for noisy SGD and binary classification.

Conclusions:

• Information-preserving properties, particularly information loss in specific layers, are crucial for deep neural network generalization.
• "Deeper is better" is contingent upon maintaining low training error.
• Theoretical bounds provide insights into the behavior and limitations of deep learning models.