New Theory Explains Knowledge Distillation Convergence in P2P Networks.

Lucas Qingyang Fang, Tiyao Liu, Jinhao Jing, Zeji Li, Kaijie Chen, Harikrishna Kuttivelil, Katia Obraczka· September 3, 2026 View original

Key takeaways

  • Knowledge Distillation enables decentralized learning across heterogeneous model architectures.
  • A new theory explains KD convergence in asynchronous P2P networks.
  • KD contracts functional disagreement significantly more than isolated training.
  • The theory provides insights into the stability and efficiency of decentralized KD.

Who benefits

Edge ComputingIoTDistributed AIHealthcare (federated learning)Telecommunications

Summary

This paper provides the first convergence theory for fully decentralized, asynchronous peer-to-peer knowledge distillation (KD), where devices with different model architectures can learn collaboratively by exchanging soft predictions. It demonstrates how KD contracts functional disagreement and achieves stationarity.

Decentralized learning, particularly in serverless peer-to-peer (P2P) networks, faces a challenge when devices run models with varying architectures, as traditional decentralized SGD (Stochastic Gradient Descent) cannot average models with different parameter counts. Knowledge Distillation (KD) offers a solution by exchanging soft predictions instead of weights, bypassing this architectural incompatibility. This research presents the first comprehensive convergence theory for fully decentralized, asynchronous P2P KD. It shifts the focus of consensus from parameter space to function (output) space, analyzing KD events as geometric contraction operators in logit space. The theory demonstrates that, under specific assumptions, the time-averaged functional stationarity and function-space disagreement converge to a stable neighborhood. Empirical results across diverse network configurations (homogeneous, width-heterogeneous, mixed-family) show that KD significantly reduces function disagreement by 40-61 times, a stark contrast to isolated training. The findings confirm the predicted transient behavior and the trade-off between neighborhood size and step-size.

Why it matters

For professionals building or deploying decentralized AI systems, this theory provides a foundational understanding and validation for using knowledge distillation in heterogeneous P2P networks, enabling robust and scalable federated learning solutions.

How to implement this in your domain

  1. 1Explore implementing knowledge distillation in decentralized learning scenarios with heterogeneous device architectures.
  2. 2Design P2P gossip networks for collaborative model training, leveraging KD for functional consensus.
  3. 3Evaluate the trade-offs between learning rate and convergence stability in asynchronous KD systems.
  4. 4Consider using KD for privacy-preserving federated learning where direct model averaging is not feasible.

Original post by Lucas Qingyang Fang, Tiyao Liu, Jinhao Jing, Zeji Li, Kaijie Chen, Harikrishna Kuttivelil, Katia Obraczka

"arXiv:2609.01952v1 Announce Type: new Abstract: Decentralized, serverless learning increasingly connects devices running different architectures, where the standard tool, decentralized SGD, is undefined as models with different parameter counts cannot be averaged. Knowledge disti…"

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Originally posted by Lucas Qingyang Fang, Tiyao Liu, Jinhao Jing, Zeji Li, Kaijie Chen, Harikrishna Kuttivelil, Katia Obraczka on X · view source

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