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Robust Deep Network Learning of Nonlinear Regression Tasks by Parametric Leaky Exponential Linear Units (LELUs) and a Diffusion Metric

arXiv 2507.06765 ↗First posted 9 Jul 2025cs.LGcited by 0

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Abstract (arXiv)

This document proposes a parametric activation function (ac.f.) aimed at improving multidimensional nonlinear data regression. It is a established knowledge that nonlinear ac.f's are required for learning nonlinear datasets. This work shows that smoothness and gradient properties of the ac.f. further impact the performance of large neural networks in terms of overfitting and sensitivity to model parameters. Smooth but vanishing-gradient ac.f's such as ELU or SiLU (Swish) have limited performance and non-smooth ac.f's such as RELU and Leaky-RELU further impart discontinuity in the trained model. Improved performance is demonstrated with a smooth "Leaky Exponential Linear Unit", with non-zero gradient that can be trained. A novel diffusion-loss metric is also proposed to gauge the performance of the trained models in terms of overfitting.

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References · 15

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
  3. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  4. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
  5. 2020A survey on modern trainable activation functionscited by 89
  6. 2020Rational neural networkscited by 75
  7. 2021Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functionscited by 49
  8. 2022How important are activation functions in regression and classification? A survey, performance comparison, and future directionscited by 29
  9. 2023Deep neural networks have an inbuilt Occam's razorcited by 28
  10. 2023Mind the spikes: Benign overfitting of kernels and neural networks in fixed dimensioncited by 26
  11. 2019A simple and efficient architecture for trainable activation functionscited by 10
  12. 2020Measuring Model Complexity of Neural Networks with Curve Activation Functionscited by 5
3 more
  1. 2023Approximation and interpolation of deep neural networkscited by 4
  2. 2016Neural Networks with Smooth Adaptive Activation Functions for Regressioncited by 3
  3. 2017Gaussian Process Neurons Learn Stochastic Activation Functionscited by 3

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