# A Trainable Multiplication Layer for Auto-correlation and Co-occurrence Extraction

## TL;DR

This paper introduces a trainable multiplication layer (TML) for neural networks that extracts higher-order auto-correlation and co-occurrence features, enhancing classification and interpretability.

## Contribution

The paper presents a novel trainable multiplication layer that can be integrated into neural networks to learn complex feature interactions end-to-end.

## Key findings

- TML effectively extracts auto-correlation and co-occurrence features.
- Visualizations show learned kernels capture meaningful patterns.
- TML improves classification performance and interpretability.

## Abstract

In this paper, we propose a trainable multiplication layer (TML) for a neural network that can be used to calculate the multiplication between the input features. Taking an image as an input, the TML raises each pixel value to the power of a weight and then multiplies them, thereby extracting the higher-order local auto-correlation from the input image. The TML can also be used to extract co-occurrence from the feature map of a convolutional network. The training of the TML is formulated based on backpropagation with constraints to the weights, enabling us to learn discriminative multiplication patterns in an end-to-end manner. In the experiments, the characteristics of the TML are investigated by visualizing learned kernels and the corresponding output features. The applicability of the TML for classification and neural network interpretation is also evaluated using public datasets.