SIGNALAI·Jun 26, 2026, 4:00 AMSignal55Medium term

Theory of the Frequency Principle for General Deep Neural Networks

Source: arXiv cs.LG

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Theory of the Frequency Principle for General Deep Neural Networks

arXiv:1906.09235v3 Announce Type: replace Abstract: Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training. The F-Principle has been very useful in providing both qualitative and quantitative understandings of DNNs. In this paper, we rigorously investigate the F-Principle for the training dynamics of a general DNN at three stages: initial stage, intermediate stage, a

Why this matters
Why now

The continuous evolution of deep learning research demands deeper theoretical understanding to optimize model performance and address existing limitations.

Why it’s important

This research provides a rigorous theoretical foundation for an observed phenomenon in deep learning, potentially leading to more efficient training methodologies and predictable AI behavior.

What changes

The explicit theory behind the Frequency Principle offers a new lens for designing and training deep neural networks, potentially improving their learning trajectory and speed.

Winners
  • · AI researchers
  • · Deep learning practitioners
  • · AI software developers
Losers
  • · Inefficient AI training methods
  • · Trial-and-error deep learning approaches
Second-order effects
Direct

Improved understanding of deep neural network training dynamics will accelerate research in model optimization.

Second

More robust and efficient AI models could be developed, leading to faster deployment and better performance in real-world applications.

Third

The theoretical advancements might contribute to foundational breakthroughs in artificial general intelligence by elucidating learning mechanisms.

Editorial confidence: 85 / 100 · Structural impact: 40 / 100
Original report

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