Deep neural networks (DNNs) are diverse in size and structure, and their performance heavily depends on their architecture, the dataset and learning algorithm used. However, even the simplest adjustment to the network’s structure necessitates substantial modifications to the analysis. Modern models are so intricate that they tend to surpass practical analytical solutions, making their theoretical study challenging.
The paper reviews various ongoing efforts focused on improving understanding of learning dynamics in DNNs. It discusses exact solutions for simple architectures, where deep linear neural networks are well-understood and solutions exist for specific initial conditions. The neural tangent kernel presents exact solutions for a range of models, a major advancement in the field. Other sections focus on investigating gradient descent as a determinant of DNNs’ generalization performance and exploring a model’s local elasticity, where changes to one feature vector minimally impact dissimilar feature vectors.
The researchers from the University College London proposed a method to examine universal representation learning, centered around explaining commonly observed phenomena within learning systems. They developed an effective theory for how similar data points interact with each other during training when the neural network is large and intricate. The model has demonstrated universal behavior in representation learning dynamics owing to its capacity to explain the dynamics of various deep networks with varying activation functions and architectures.
The theory assesses the representation dynamics at an intermediate layer in DNNs. To obtain accurate results, the theory must apply within the valid layers and the representations must begin closely aligned. If initial weights are minor, then each layer’s average activation gain factor is a constant G, which is less than 1. The initial representational distance decreases depending on the depth of the layer, implying the later network layers will display more accurate results.
The learning rates vary depending on the hidden layers. During standard gradient descent, updates involve increasing parameters, so changes correlate with the number of variables. The number of parameters also varies with the depth of the layer, with encoders often having more variables than decoders in the deeper layers. Therefore, the effective learning rate of the encoder increases with depth, whereas the rate for the decoder decreases.
To encapsulate, the researchers from the University College London have developed a novel theory explaining how neural networks learn. They focus on common learning patterns across different structures, illustrating that networks naturally acquire structured representations when they start with small weights. The paper suggests that gradient descent, a fundamental neural network training method, might back the facets of representation learning. Yet, implementing this approach for larger datasets is challenging, and further research is needed to address these concerns and handle complex data more effectively.
