SIGNALAI·Jun 10, 2026, 4:00 AMSignal55Medium term

Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss

Source: arXiv cs.LG

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Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss

arXiv:2402.00152v5 Announce Type: replace Abstract: Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent question. This paper explores a comparison between deeper neural networks (DeNNs) with a flexible number of layers and wider neural networks (WeNNs) with limited hidden layers, focusing on their optimal generalization error in Sobolev losses. Analytical investigations reveal that the architecture of a neural network can be significantly influenced by various factor

Why this matters
Why now

The paper provides new analytical insights into neural network architecture at a time when AI model development is rapidly advancing and optimization is critical.

Why it’s important

Understanding the optimal architecture for neural networks, whether deeper or wider, can lead to more efficient and powerful AI models, impacting compute resource utilization and model performance.

What changes

This research provides a theoretical framework to guide architectural choices, potentially shifting the empirical trial-and-error approach towards more principled design in neural networks.

Winners
  • · AI researchers and developers
  • · Hardware manufacturers (optimized compute)
  • · Cloud AI service providers
Losers
  • · Inefficient AI development practices
Second-order effects
Direct

Improved efficiency in training and deploying neural networks.

Second

Faster progress in AI capabilities due to better model designs.

Third

Potentially reduced computational demands for achieving certain AI performance benchmarks.

Editorial confidence: 90 / 100 · Structural impact: 40 / 100
Original report

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Read at arXiv cs.LG
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