Sharpness and Complexity Jointly Explain AI Generalization

Ziyu Cheng, Xitong Zhang, Longxiu Huang, Rongrong Wang· June 30, 2026 View original

Summary

Researchers investigate how sharpness and complexity jointly explain deep neural network generalization, finding that function-oriented definitions expand their explanatory scope. While these two factors are informative, the study suggests they do not fully explain generalization, leaving room for further research.

A new study explores the combined explanatory power of sharpness and complexity in understanding the generalization capabilities of deep neural networks. These two factors are widely recognized as central to generalization analysis, but previous quantitative evaluations often focused on them individually. This research employs linear regression and a Pareto-based analysis to assess their joint influence. The authors introduce novel, function-oriented definitions of sharpness and complexity, which are less dependent on raw parameter representations and closer to the function space. They found that these function-oriented definitions significantly broaden the explanatory scope of the two-factor view compared to existing parameter-level metrics. The results affirm that the sharpness-complexity perspective provides a valuable lens for comprehending generalization across diverse settings. However, the study also highlights remaining unexplained aspects, indicating that while informative, this two-factor view may not constitute a complete theory of generalization, suggesting avenues for future research.

Why it matters

For AI researchers and engineers, a deeper understanding of generalization helps in designing more robust and efficient neural networks, improving model performance and reliability in real-world applications.

How to implement this in your domain

  1. 1Incorporate sharpness and complexity metrics into the evaluation of deep learning models.
  2. 2Explore function-oriented definitions of these metrics for a more comprehensive understanding of generalization.
  3. 3Utilize insights from sharpness and complexity to guide model architecture design and training strategies.
  4. 4Consider the trade-offs between model complexity and generalization performance.
  5. 5Contribute to research on other factors influencing generalization beyond sharpness and complexity.

Who benefits

AI ResearchSoftware EngineeringData ScienceMachine Learning

Key takeaways

  • Sharpness and complexity are key factors in deep neural network generalization.
  • Function-oriented definitions expand their explanatory power.
  • The two-factor view is informative but not a complete theory of generalization.
  • Further research is needed to fully explain generalization in deep learning.

Original post by Ziyu Cheng, Xitong Zhang, Longxiu Huang, Rongrong Wang

"arXiv:2606.29043v1 Announce Type: new Abstract: Sharpness and complexity are two central factors in the generalization analysis of deep neural networks. Existing quantitative evaluations of generalization measures have largely focused on individual scalar measures, leaving the jo…"

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Originally posted by Ziyu Cheng, Xitong Zhang, Longxiu Huang, Rongrong Wang on X · view source

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