Studies of neural networks that are more general than $\mathbb{R}^n\mapsto\mathbb{R}^k$ include

• Deep Complex Networks (2017)
• Deep Quaternion Networks (2017)
• P-Adic Neural Networks (2004)
• Deep Learning on Lie Groups (2017)

A general overview is provided in Neural Networks on Groups (2019).

One general thing to keep in mind in this context is that the training of the network by steepest descent will rely on continuous differentiability.

Studies of neural networks that are more general than $\mathbb{R}^n\mapsto\mathbb{R}^k$ include

• Deep Complex Networks (2017)
• Deep Quaternion Networks (2017)
• P-Adic Neural Networks (2004)
• Deep Learning on Lie Groups (2017)

A general overview is provided in Neural Networks on Groups (2019).

One general thing to keep in mind in this context is that the training of the network by steepest descent will rely on continuous differentiability, which not all implementations provide.

Deep Learning on Lie Groups for Skeleton-Based Action Recognition (2017) studies a neural network structure where the data space as well as the weight space of each layer correspond to a Lie group.

One general thing to keep in mind in this context is that the training of the network by steepest descent will rely on continuous differentiability. This training requirement is not a complication of the Lie group based networks, but may become an obstacle for other implementations.

Studies of neural networks that are more general than $\mathbb{R}^n\mapsto\mathbb{R}^k$ include

• Deep Complex Networks (2017)
• Deep Quaternion Networks (2017)
• P-Adic Neural Networks (2004)
• Deep Learning on Lie Groups (2017)

A general overview is provided in Neural Networks on Groups (2019).

One general thing to keep in mind in this context is that the training of the network by steepest descent will rely on continuous differentiability.