State space representations of the Roesser type for convolutional layers

arXiv:2403.11938v1 Announce Type: cross
Abstract: From the perspective of control theory, convolutional layers (of neural networks) are 2-D (or N-D) linear time-invariant dynamical systems. The usual representation of convolutional layers by the convolution kernel corresponds to the representation of a dynamical system by its impulse response. However, many analysis tools from control theory, e.g., involving linear matrix inequalities, require a state space representation. For this reason, we explicitly provide a state space representation of the Roesser type for 2-D convolutional …

abstract analysis analysis tools arxiv control convolution cs.lg cs.sy eess.iv eess.sp eess.sy however kernel linear networks neural networks perspective representation space state systems theory tools type