# Real to H-space Encoder for Speech Recognition

## TL;DR

This paper introduces a real-to-quaternion encoder enabling quaternion neural networks to process real-valued speech features, enhancing their ability to model dependencies in speech recognition tasks.

## Contribution

It presents a novel encoder that extends quaternion neural networks to handle real-valued inputs, broadening their applicability in speech recognition.

## Key findings

- Improved modeling of internal and global dependencies in speech signals.
- Enhanced performance of quaternion neural networks on speech recognition tasks.
- Demonstrated effectiveness of the encoder in processing real-valued features.

## Abstract

Deep neural networks (DNNs) and more precisely recurrent neural networks (RNNs) are at the core of modern automatic speech recognition systems, due to their efficiency to process input sequences. Recently, it has been shown that different input representations, based on multidimensional algebras, such as complex and quaternion numbers, are able to bring to neural networks a more natural, compressive and powerful representation of the input signal by outperforming common real-valued NNs. Indeed, quaternion-valued neural networks (QNNs) better learn both internal dependencies, such as the relation between the Mel-filter-bank value of a specific time frame and its time derivatives, and global dependencies, describing the relations that exist between time frames. Nonetheless, QNNs are limited to quaternion-valued input signals, and it is difficult to benefit from this powerful representation with real-valued input data. This paper proposes to tackle this weakness by introducing a real-to-quaternion encoder that allows QNNs to process any one dimensional input features, such as traditional Mel-filter-banks for automatic speech recognition.