Theoretical Foundations of Deep Learning: Why Neural Networks Actually Work

This article explains the theoretical principles behind how deep learning models work, including entropy, KL divergence, probability distributions, and optimization.

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The article delves into the core theoretical concepts that underpin deep learning. It explains that the fundamental objective is to align the model's output probability distribution with the true data distribution. Entropy is a key measure of how unpredictable or difficult the data is to learn, with higher entropy indicating a harder problem. The loss function used in training, such as cross-entropy, is directly derived from the KL divergence between the model's predicted distribution and the true data distribution. Deep learning models should be viewed as learning a probability distribution, not just a deterministic function. This shift in perspective explains concepts like softmax and log-likelihood. The article also highlights the importance of the manifold assumption - that real-world data has an inherent structure that deep networks can leverage to generalize. By understanding these theoretical foundations, developers can better debug and optimize their deep learning models.