The electromagnetic spectrum appears to be arbitrarily divisible. This means that for any subset of the spectrum, we can subdivide that subset into an arbitrarily large number of intervals. So, for example, we can, as a theoretical matter matter, subdivide the visible spectrum into as many intervals as we’d like. This means that if we have a light source that can emit a particular range of frequencies, and a dataset that we’d like to encode using frequencies of light from that range, we can assign each element of the dataset a unique frequency.
So let’s assume we have a dataset of items, and a light source that is capable of emitting at least unique frequencies of light. It follows that we can encode the dataset using the frequencies of light emitted by the light source, using a simple mapping, where vector is represented by some unique frequency . So in short, if we want to represent the observation of vector , we could cause the light source to generate frequency . Because laser and interferometer technology is very sensitive, this shouldn’t be a problem for most practical purposes, and we can probably represent fairly large datasets this way.
If we shine two beams of light, each with their own frequency, through a refractive medium, like a prism, then the exiting angle of those beams will be different. As a result, given an input vector, and a dataset of vectors, all of which are then encoded as beams of light, it should be very easy to find which vector from the dataset is most similar to the input vector, using some version of refraction, or perhaps interferometry. This would allow for nearest-neighbor deep learning to be implemented using a computer driven by light, rather than electricity.
I’ve already shown that vectorized nearest-neigbor is an extremely fast, and accurate method of implementing machine learning. Perhaps by using a beam-splitter, we can simultaneously test an input vector against an entire dataset, which would allow for something analogous to vectorization using beams of light.