Derivation of effective gradient flow equations and dynamical truncation of training data in Deep Learning
arXiv:2501.07400v2 Announce Type: replace Abstract: We derive explicit equations governing the cumulative biases and weights in Deep Learning with ReLU activation function, based on gradient descent for the Euclidean loss in the input layer, and under the assumption that the weights are, in a precise sense, adapted to the coordinate system distinguished by the activations. We show that gradient descent corresponds to a dynamical process in the input layer, whereby clusters of data are progressively reduced in complexity ("truncated") at an exponential rate that increases with the number of dat
This research provides foundational insights into the mathematical underpinnings of deep learning, emerging from ongoing efforts to de-mystify and optimize AI learning processes.
A deeper theoretical understanding of gradient flow and data truncation mechanisms can lead to more efficient, stable, and explainable AI models, accelerating development across various applications.
The ability to explicitly model and potentially control biases and weights, along with understanding data simplification during training, offers a pathway to more predictable and robust AI system design.
- · AI researchers
- · Deep Learning framework developers
- · AI compute providers
- · Sectors reliant on complex AI models
- · Trial-and-error AI development methodologies
Improved understanding of deep learning dynamics could lead to more stable and efficient AI training algorithms.
This efficiency might reduce the computational resources required for advanced AI, making it more accessible.
Reduced compute demands and increased explainability could broaden AI adoption and democratize advanced AI design capabilities.
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Read at arXiv cs.LG