# Complex Evolution Recurrent Neural Networks (ceRNNs)

## TL;DR

This paper introduces ceRNNs, a variant of uRNNs that drops the unitary constraint, showing that complex-valued RNNs with linear operators can outperform LSTMs in speech recognition tasks.

## Contribution

The paper proposes ceRNNs, a new RNN variant that relaxes the unitary property of uRNNs, and demonstrates their effectiveness on large-scale speech recognition.

## Key findings

- Dropping the unitary constraint improves learning in linear regression.
- ceRNNs match uRNNs in copy memory tasks, outperforming LSTMs.
- Pre-pending ceRNNs improves speech recognition WER by 0.8%.

## Abstract

Unitary Evolution Recurrent Neural Networks (uRNNs) have three attractive properties: (a) the unitary property, (b) the complex-valued nature, and (c) their efficient linear operators. The literature so far does not address -- how critical is the unitary property of the model? Furthermore, uRNNs have not been evaluated on large tasks. To study these shortcomings, we propose the complex evolution Recurrent Neural Networks (ceRNNs), which is similar to uRNNs but drops the unitary property selectively. On a simple multivariate linear regression task, we illustrate that dropping the constraints improves the learning trajectory. In copy memory task, ceRNNs and uRNNs perform identically, demonstrating that their superior performance over LSTMs is due to complex-valued nature and their linear operators. In a large scale real-world speech recognition, we find that pre-pending a uRNN degrades the performance of our baseline LSTM acoustic models, while pre-pending a ceRNN improves the performance over the baseline by 0.8% absolute WER.