# Improving the Backpropagation Algorithm with Consequentialism Weight Updates over Mini-Batches

arXiv: https://arxiv.org/abs/2003.05164 · HTML: https://mlsanity.com/paper/2003.05164/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2020.

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

- [Cross-Domain Few-Shot Learning via Adaptive Transformer Networks](https://mlsanity.com/paper/2401.13987/) (2024)

## Abstract (arXiv)

Many attempts took place to improve the adaptive filters that can also be useful to improve backpropagation (BP). Normalized least mean squares (NLMS) is one of the most successful algorithms derived from Least mean squares (LMS). However, its extension to multi-layer neural networks has not happened before. Here, we first show that it is possible to consider a multi-layer neural network as a stack of adaptive filters. Additionally, we introduce more comprehensible interpretations of NLMS than the complicated geometric interpretation in affine projection algorithm (APA) for a single fully-connected (FC) layer that can easily be generalized to, for instance, convolutional neural networks and also works better with mini-batch training. With this new viewpoint, we introduce a better algorithm by predicting then emending the adverse consequences of the actions that take place in BP even before they happen. Finally, the proposed method is compatible with stochastic gradient descent (SGD) and applicable to momentum-based derivatives such as RMSProp, Adam, and NAG. Our experiments show the usefulness of our algorithm in the training of deep neural networks.