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Dynamic Universal Approximation Theory: Foundations for Parallelism in Neural Networks

Wei Wang, Qing Li

TL;DR

This work addresses the bottleneck of serial inference in deep networks by introducing Dynamic Universal Approximation Theory (DUAT) and a parallel Transformer architecture, Para-Former, to decouple layer depth from inference time. By reformulating neural operations via the Matrix-Vector Method and enabling input-dependent parameter dynamics, the approach aims to retain or improve function-fitting capacity while achieving favorable speedups on deep models. Empirical results on multiple image datasets show that deeper parallel configurations generally improve performance and that data scale and diversity critically influence outcomes, with fine-tuning of pre-trained ViTs helping when data is limited. The proposed DUAT-based design offers a principled path toward fast, scalable inference in very deep networks, with implications for both CV and NLP tasks and large-model deployment.

Abstract

Neural networks are increasingly evolving towards training large models with big data, a method that has demonstrated superior performance across many tasks. However, this approach introduces an urgent problem: current deep learning models are predominantly serial, meaning that as the number of network layers increases, so do the training and inference times. This is unacceptable if deep learning is to continue advancing. Therefore, this paper proposes a deep learning parallelization strategy based on the Universal Approximation Theorem (UAT). From this foundation, we designed a parallel network called Para-Former to test our theory. Unlike traditional serial models, the inference time of Para-Former does not increase with the number of layers, significantly accelerating the inference speed of multi-layer networks. Experimental results validate the effectiveness of this network.

Dynamic Universal Approximation Theory: Foundations for Parallelism in Neural Networks

TL;DR

This work addresses the bottleneck of serial inference in deep networks by introducing Dynamic Universal Approximation Theory (DUAT) and a parallel Transformer architecture, Para-Former, to decouple layer depth from inference time. By reformulating neural operations via the Matrix-Vector Method and enabling input-dependent parameter dynamics, the approach aims to retain or improve function-fitting capacity while achieving favorable speedups on deep models. Empirical results on multiple image datasets show that deeper parallel configurations generally improve performance and that data scale and diversity critically influence outcomes, with fine-tuning of pre-trained ViTs helping when data is limited. The proposed DUAT-based design offers a principled path toward fast, scalable inference in very deep networks, with implications for both CV and NLP tasks and large-model deployment.

Abstract

Neural networks are increasingly evolving towards training large models with big data, a method that has demonstrated superior performance across many tasks. However, this approach introduces an urgent problem: current deep learning models are predominantly serial, meaning that as the number of network layers increases, so do the training and inference times. This is unacceptable if deep learning is to continue advancing. Therefore, this paper proposes a deep learning parallelization strategy based on the Universal Approximation Theorem (UAT). From this foundation, we designed a parallel network called Para-Former to test our theory. Unlike traditional serial models, the inference time of Para-Former does not increase with the number of layers, significantly accelerating the inference speed of multi-layer networks. Experimental results validate the effectiveness of this network.
Paper Structure (16 sections, 12 equations, 8 figures, 6 tables)

This paper contains 16 sections, 12 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. UAT to Parallel Network
  3. Introduction of UAT
  4. The Problems in Designing parallel Network Based on UAT
  5. DUAT to Parallel Network
  6. Introduction of DUAT
  7. Para-former
  8. Speed-up Ratio
  9. Experiments
  10. Dataset
  11. The Feasibility of Para-Former
  12. Model Depth Effect
  13. Dataset Effect
  14. Conclusion
  15. The DUAT Format of single layer ViT
  16. ...and 1 more sections

Figures (8)

  • Figure 1: The general description of the serial network and parallel network based on UAT.
  • Figure 2: The process of Transformer module.
  • Figure 3: The process of Transformer module.
  • Figure 4: The structure of the Para-Former-1-n represents Para-Former with 1 depth of n layers.
  • Figure 5: The structure of the Para-Former-m-n represents Para-Former with m depth of n layers.
  • ...and 3 more figures