Neural Network Theory: Understanding Statistical Mechanisms, Feature Representation and Holistic Training

Neural networks operate through statistical mechanisms yet encode a wide range of knowledge and capabilities. This paper explores the relationship between their statistical foundations and the complex representations they develop. Using analogies from art and examining the holistic nature of their training process, we demonstrate why understanding neural networks purely in terms of their statistical mechanisms is insufficient. We explore their computational completeness, feature representation capabilities, and the fundamental opacity of their learned structures, suggesting new frameworks for interpreting these systems.

Neural networks have transformed fields from computer vision to natural language processing, yet their underlying nature remains poorly understood. While we can describe their mechanisms with mathematical precision, this description fails to capture the essence of what these models become through training. This understanding has profound implications not only for machine learning, but for our philosophical understanding of computation, meaning, and understanding itself. This paper aims to bridge the gap between understanding neural networks’ statistical foundations and comprehending their emergent capabilities.

Just as Michelangelo’s Pietà is made of marble, neural networks operate through statistical mechanisms — weights and weighted sums processing information in a Bayesian manner (Bishop, 2006). However, saying the Pietà is made of marble tells us almost nothing about its nature as a work of art — its emotional resonance, its representation of human suffering, or its artistic achievement. Similarly, understanding that neural networks operate through statistical mechanisms tells us little about what knowledge, capabilities, or representations they have actually developed.

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