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Related Experiment Videos

NP-Hardness of Minimizing Neurons in Two-Hidden-Layer ReLU Neural Networks.

Sangrock Lee

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |July 8, 2026
    PubMed
    Summary

    Determining the minimum neurons for accurate neural networks is NP-hard. This complexity applies to designing feedforward neural networks with ReLU activation functions, making minimal configurations computationally unachievable.

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    Area of Science:

    • Computational complexity theory
    • Artificial intelligence
    • Machine learning

    Background:

    • Identifying the minimum number of neurons for a specified accuracy in neural networks is a significant challenge.
    • Feedforward neural networks with Rectified Linear Unit (ReLU) activation functions are widely used in deep learning.

    Purpose of the Study:

    • To explore the complexity of designing feedforward neural networks with ReLU activation functions.
    • To determine if minimizing the number of neurons in a two-hidden-layer ReLU network to approximate an $L^{p}$ function is computationally tractable.

    Main Methods:

    • The study employs a polynomial-time reduction from the Geometric Set Cover Problem.
    • This reduction is used to prove the NP-hardness of minimizing the structure of ReLU networks.

    Main Results:

    • It is NP-hard to determine the minimum number of neurons required for a two-hidden-layer ReLU network to approximate an $L^{p}$ function.
    • Attaining a minimal neural network configuration within polynomial time is computationally unachievable.

    Conclusions:

    • The findings provide theoretical justification for using heuristic approximation methods in designing ReLU neural networks.
    • The inherent complexity suggests that exact minimization is often infeasible, guiding practical approaches in neural network design.