New Complexity-Theoretic Frontiers of Tractability for Neural Network Training

2026-07-23 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A new study by Cornelius Brand, Robert Ganian, and Mathis Rocton addresses the computational complexity of optimally training neural networks, specifically those with linear and ReLU activation functions. While recent research has established tighter lower bounds for these problems, progress in identifying novel polynomial-time tractable network architectures has been limited. This work introduces new algorithmic upper bounds, extending the known boundaries of tractability. For ReLU networks, the authors demonstrate polynomial-time tractability for all architectures where hidden neurons have an out-degree of 1, improving upon the previous algorithm by Arora, Basu, Mianjy, and Mukherjee. For networks with linear activation functions, the study identifies the first non-trivial polynomial-time solvable class, achieved via an algorithm that optimally trains architectures satisfying a novel data throughput condition.

Key takeaway

For machine learning engineers designing neural networks, this research indicates that certain architectures are now provably tractable for optimal training. If you are working with ReLU networks, consider architectures where hidden neurons have an out-degree of 1, as these can now be optimally trained in polynomial time. For linear networks, new algorithms enable optimal training for architectures meeting specific data throughput conditions, potentially guiding your design choices towards more efficient and provably optimal models.

Key insights

New algorithms expand polynomial-time tractability for optimal training of specific linear and ReLU neural network architectures.

Topics

• Neural Network Training
• Computational Complexity
• ReLU Networks
• Linear Networks
• Polynomial-Time Algorithms
• Network Architectures

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.