# A SOM-based Gradient-Free Deep Learning Method with Convergence Analysis

arXiv: https://arxiv.org/abs/2101.05612 · HTML: https://mlsanity.com/paper/2101.05612/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 12 Jan 2021.

## Builds on (most cited first, 3 of 3)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [CNN-Based Projected Gradient Descent for Consistent Image Reconstruction](https://mlsanity.com/paper/1709.01809/) (2017)
- [All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulation](https://mlsanity.com/paper/1703.01827/) (2017)

## Built on by (most cited first, 1 of 1)

- [On filter design in deep convolutional neural network](https://mlsanity.com/paper/2410.21644/) (2024)

## Abstract (arXiv)

As gradient descent method in deep learning causes a series of questions, this paper proposes a novel gradient-free deep learning structure. By adding a new module into traditional Self-Organizing Map and introducing residual into the map, a Deep Valued Self-Organizing Map network is constructed. And analysis about the convergence performance of such a deep Valued Self-Organizing Map network is proved in this paper, which gives an inequality about the designed parameters with the dimension of inputs and the loss of prediction.