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Algorithms and data structures for automatic precision estimation of neural networks

arXiv 2509.24607 ↗First posted 29 Sep 2025cs.DS cs.AI cs.LGcited by 0

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Abstract (arXiv)

We describe algorithms and data structures to extend a neural network library with automatic precision estimation for floating point computations. We also discuss conditions to make estimations exact and preserve high computation performance of neural networks training and inference. Numerical experiments show the consequences of significant precision loss for particular values such as inference, gradients and deviations from mathematically predicted behavior. It turns out that almost any neural network accumulates computational inaccuracies. As a result, its behavior does not coincide with predicted by the mathematical model of neural network. This shows that tracking of computational inaccuracies is important for reliability of inference, training and interpretability of results.

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References · 22

  1. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  2. 2019Universal Approximation with Deep Narrow Networkscited by 200
  3. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 98
  4. 2024Convolutional Kolmogorov-Arnold Networkscited by 77
  5. 2024A Survey on Kolmogorov-Arnold Networkcited by 68
  6. 2024KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physicscited by 59
  7. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 53
  8. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 49
  9. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  10. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 40
  11. 2024rKAN: Rational Kolmogorov-Arnold Networkscited by 35
  12. 2020The universal approximation theorem for complex-valued neural networkscited by 28
10 more
  1. 2016A Universal Approximation Theorem for Mixture of Experts Modelscited by 18
  2. 2017On the Complexity of Learning Neural Networkscited by 18
  3. 2024Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noisecited by 17
  4. 2023Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirscited by 16
  5. 2021Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networkscited by 12
  6. 2025Universal Approximation Theorem of Deep Q-Networkscited by 6
  7. 2018Neural Networks in Adversarial Setting and Ill-Conditioned Weight Spacecited by 5
  8. 2023Universal approximation with complex-valued deep narrow neural networkscited by 3
  9. 2024Algorithms and data structures for numerical computations with automatic precision estimationcited by 2
  10. 2024Geometrical structures of digital fluctuations in parameter space of neural networks trained with adaptive momentum optimizationcited by 1

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