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Nearest Neighbor Representations of Neural Circuits
Neural networks successfully capture the computational power of the human brain for many tasks.
Nearest Neighbor Representations of Neurons
It is known that two anchors (the points to which NN is computed) are sufficient for a NN representation of a threshold function, however, the resolution (the maximum number of bits required for the entries of an anchor) is $O(n\log{n})$.
On the Information Capacity of Nearest Neighbor Representations
Specifically, in this paper, we study the representation of Boolean functions in the associative computation model, where the inputs are binary vectors and the corresponding outputs are the labels ($0$ or $1$) of the nearest neighbor anchors.
On Algebraic Constructions of Neural Networks with Small Weights
The expressive power of neural gates (number of distinct functions it can compute) depends on the weight sizes and, in general, large weights (exponential in the number of inputs) are required.
