  Over-the-air analog computation allows offloading computation to the wireless
environment through carefully constructed transmitted signals. In this paper,
we design and implement the first-of-its-kind over-the-air convolution and
demonstrate it for inference tasks in a convolutional neural network (CNN). We
engineer the ambient wireless propagation environment through reconfigurable
intelligent surfaces (RIS) to design such an architecture, which we call
'AirNN'. AirNN leverages the physics of wave reflection to represent a digital
convolution, an essential part of a CNN architecture, in the analog domain. In
contrast to classical communication, where the receiver must react to the
channel-induced transformation, generally represented as finite impulse
response (FIR) filter, AirNN proactively creates the signal reflections to
emulate specific FIR filters through RIS. AirNN involves two steps: first, the
weights of the neurons in the CNN are drawn from a finite set of channel
impulse responses (CIR) that correspond to realizable FIR filters. Second, each
CIR is engineered through RIS, and reflected signals combine at the receiver to
determine the output of the convolution. This paper presents a proof-of-concept
of AirNN by experimentally demonstrating over-the-air convolutions. We then
validate the entire resulting CNN model accuracy via simulations for an example
task of modulation classification.
