arXiv:2511.02003v2 Announce Type: replace Abstract: We present the bulk--boundary decomposition as a new framework for understanding the training dynamics of deep neural networks. Starting from the stochastic gradient descent formulation, we show that the Lagrangian can be reorganized into a data-independent bulk term and a data-dependent boundary term. The bulk captures the intrinsic dynamics set by network architecture and activation functions, while the boundary reflects stochastic interactions from training samples at the input and output layers. This decomposition exposes the local and ho
The continuous drive to understand and optimize complex deep learning models, coupled with increased computational power, is enabling deeper theoretical insights into neural network mechanics.
A deeper theoretical understanding of neural network training dynamics can lead to more efficient, robust, and explainable AI models, accelerating their development and deployment.
This new framework offers a more granular way to analyze model behavior, potentially allowing for targeted interventions in training and architecture design that were previously speculative.
- · AI researchers
- · Deep learning framework developers
- · Companies deploying AI models
- · Trial-and-error AI development methodologies
Improved understanding of neural network training dynamics through a novel decomposition framework.
More targeted and efficient architecture design and training algorithms, reducing development costs and accelerating AI progress.
Potentially leading to breakthroughs in AI explainability and a more principled approach to creating advanced AI systems.
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