arXiv:2501.02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical systems theory. We redefine the notions of linearity and nonlinearity in neural networks by introducing two fundamental transformation units at the neuron level: order-preserving transformations and non-order-preserving transformations. Different transformation modes lead to distinct collective behaviors in wei
The rapid advancement and application of deep learning models necessitate a deeper theoretical understanding to ensure continued progress and address current limitations.
A robust theoretical framework for deep neural networks could unlock new architectural designs, improve training efficiency, and enhance the reliability and interpretability of AI systems.
This research introduces new concepts for analyzing linearity and nonlinearity within neural networks, potentially leading to more deliberate and effective model construction rather than reliance on empirical trial and error.
- · AI researchers
- · Deep learning framework developers
- · Companies using AI for critical applications
- · Empirical-only AI development methodologies
Improved understanding of neural network behavior and learning dynamics.
Development of novel, theoretically grounded neural network architectures and training algorithms.
Accelerated progress in AI capabilities due to more principled design and optimization approaches.
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