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Performance Guarantees of Recurrent Neural Networks for the Subset Sum Problem.

Zengkai Wang1, Weizhi Liao1, Youzhen Jin1

  • 1College of Artificial Intelligence, Jiaxing University, Jiaxing 314001, China.

Biomimetics (Basel, Switzerland)
|April 25, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces novel recurrent neural networks (RNNs) for the subset sum problem, offering performance guarantees. The proposed ASS-NN model achieves approximate solutions with mathematically proven, small errors compared to optimal solutions.

Keywords:
deep learningdynamic programmingperformance guaranteerecurrent neural networkssubset sum problem

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Operations Research

Background:

  • The subset sum problem is a well-known NP-hard problem with various existing solution methods.
  • Neural network approaches show promise for combinatorial optimization, but performance guarantees for RNNs on subset sum are underexplored.

Purpose of the Study:

  • To investigate the performance guarantees of recurrent neural networks (RNNs) for solving the subset sum problem.
  • To develop a novel RNN construction method for computing exact and approximate subset sum solutions.

Main Methods:

  • Developed a construction method for RNNs to solve subset sum problems.
  • Rigorously defined the mathematical model for each hidden layer in the proposed RNNs.
  • Provided mathematical proofs for the correctness and performance analysis of the RNNs.

Main Results:

  • Proved that the proposed RNNs achieve approximate solutions (wNN) with a guaranteed performance bound relative to the optimal solution (wOPT), specifically wNN ≥ wOPT(1-ε).
  • Demonstrated that the errors between approximate and optimal solutions are small and consistent with theoretical expectations.
  • Validated the RNNs' effectiveness through examples, showing close alignment between actual and theoretical error values.

Conclusions:

  • The proposed RNN-based approach provides a mathematically sound method for solving the subset sum problem with performance guarantees.
  • Recurrence relations from dynamic programming can effectively simulate solution construction within RNNs.
  • This research establishes a foundation for using RNNs in solving NP-hard combinatorial optimization problems.