Introduction
In this article, we explore layer-wise semantic dynamics in neural networks. Understanding how features evolve across layers is crucial for:
- Model interpretability
- Detecting biases
- Improving robustness and safety
Background
Neural networks learn hierarchical representations. Each layer captures different levels of abstraction:
- Early layers – capture low-level patterns like edges or textures.
- Intermediate layers – encode motifs or combinations of features.
- Deep layers – abstract high-level semantics, such as object categories or concepts.
"Analyzing intermediate representations helps us understand how the network thinks." – Dr. Marcus Chen
Mathematical Formulation
Consider a neural network with (L) layers. Let the activation of layer (l) be (h^l):
h^l = f(W^l h^{l-1} + b^l)