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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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Convolution computations can be simplified by utilizing their inherent properties.
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The important convolution properties include width, area, differentiation, and integration properties.
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Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
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Augmenting interaction effects in convolutional networks with taylor polynomial gated units.

Ligeng Zou1, Qi Liu1, Jianhua Dai1

  • 1Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha 410081, China; College of Information Science and Engineering, Hunan Normal University, Changsha 410081, China.

Neural Networks : the Official Journal of the International Neural Network Society
|February 12, 2025
PubMed
Summary

Researchers developed a new activation function, Taylor Polynomial Gated Unit (TPGU), for convolutional neural networks (CNNs). TPGU enhances model performance by efficiently capturing input interactions without attention mechanisms.

Keywords:
Convolutional neural networksPolynomial activation functionsTaylor polynomials

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Area of Science:

  • Computer Vision
  • Artificial Intelligence
  • Machine Learning

Background:

  • Transformer-based vision models are often favored for their ability to capture long-range dependencies.
  • However, recent convolutional neural network (CNN) models like ConvNeXt challenge the notion of Transformer superiority.
  • This suggests alternative methods for modeling input interactions in CNNs are valuable.

Purpose of the Study:

  • To explore efficient methods for modeling input interactions in CNNs without relying on attention mechanisms.
  • To introduce a novel activation function that captures interaction effects within convolutional architectures.
  • To investigate the potential of polynomial-based functions in modern neural networks.

Main Methods:

  • Proposed the Taylor Polynomial Gated Unit (TPGU) as a novel activation function.
  • TPGU replaces the cumulative distribution function in GELU with a learnable Taylor polynomial.
  • Evaluated TPGU's performance by replacing GELU in ConvNeXt models under identical training conditions.

Main Results:

  • Swapping GELU with TPGU activation functions significantly improved model performance.
  • TPGU demonstrated a particularly favorable impact on pure convolutional networks.
  • ConvNeXt-T performance was enhanced by 0.7% on the ImageNet-1K dataset using TPGU.

Conclusions:

  • The Taylor Polynomial Gated Unit (TPGU) offers an effective alternative to existing activation functions for CNNs.
  • Polynomial-based functions show promise for improving contemporary neural network architectures.
  • TPGU provides a method to efficiently model input interactions without attention, boosting performance in convolutional models.