It should be possible to extract the information in the Neural Network and collapse it into a flat content addressable memory. The Neural Network is basically a matrix of stored values. The input to the network is a vector. The output is a vector of weights.

Each input / output pair recognized could be stored in a CAM, giving O(1) lookup.

You could "invert" it by using the output vector as the key, giving the input on lookup.

Of course, you are unlikely to find an exact match on the input vectors. Instead you'd like to be able to provide an "interval" for each input vector entry. Values that fall within the interval provide a fuzzy match, essentially a Fuzzy Content Addressable Memory (FCAM).

Such fuzzy matches are easier to implement in an analog fashion, such as a charge on a capacitor. An interesting question would be how to modify the circuit mentioned in the Wikipedia article above to provide analog matching.

FCAMs would make an interesting model of neurons if their "match" was dependent on their history of access as measured by the charge remaining on the capacitor, which would leak over time if not accessed.