Unitary RNN
Unitary RNN
A **Unitary RNN** is a recurrent neural network architecture that uses a unitary hidden to hidden matrix. Specifically they concern dynamics of the form:

$$ h\_{t} = f\left(Wh\_{t−1} + Vx\_{t}\right) $$

where $W$ is a unitary matrix $\left(W^{†}W = I\right)$. The product of unitary matrices is a unitary matrix, so $W$ can be parameterised as a product of simpler unitary matrices:

$$ h\_{t} = f\left(D\_{3}R\_{2}F^{−1}D\_{2}PR\_{1}FD\_{1}h\_{t−1} + Vxt\right) $$

where $D\_{3}$, $D\_{2}$, $D\_{1}$ are learned diagonal complex matrices, and $R\_{2}$, $R\_{1}$ are learned reflection matrices. Matrices $F$ and $F^{−1}$ are the discrete Fourier transformation and its inverse. P is any constant random permutation. The activation function $f\left(h\right)$ applies a rectified linear unit with a learned bias to the modulus of each complex number. Only
the diagonal and reflection matrices, $D$ and $R$, are learned, so Unitary RNNs have fewer parameters than [LSTMs](https://paperswithcode.com/method/lstm) with comparable numbers of hidden units.

Source: [Associative LSTMs](https://arxiv.org/pdf/1602.03032.pdf)
Unitary Evolution Recurrent Neural Networks
https://paperswithcode.com/paper/unitary-evolution-recurrent-neural-networks
Unitary Evolution Recurrent Neural Networks