Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cortical Computation via Iterative Constructions   We study Boolean functions of an arbitrary number of input variables that can
be realized by simple iterative constructions based on constant-size
primitives. This restricted type of construction needs little global
coordination or control and thus is a candidate for neurally feasible
computation. Valiant's construction of a majority function can be realized in
this manner and, as we show, can be generalized to any uniform threshold
function. We study the rate of convergence, finding that while linear
convergence to the correct function can be achieved for any threshold using a
fixed set of primitives, for quadratic convergence, the size of the primitives
must grow as the threshold approaches 0 or 1. We also study finite realizations
of this process and the learnability of the functions realized. We show that
the constructions realized are accurate outside a small interval near the
target threshold, where the size of the construction grows as the inverse
square of the interval width. This phenomenon, that errors are higher closer to
thresholds (and thresholds closer to the boundary are harder to represent), is
a well-known cognitive finding.

23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph