Editing Perceptron (section)

=== Boolean function ===
When operating on only binary inputs, a perceptron is called a [[Linear separability#Linear separability of Boolean functions in n variables|linearly separable Boolean function]], or threshold Boolean function. The sequence of numbers of threshold Boolean functions on n inputs is [[On-Line Encyclopedia of Integer Sequences|OEIS]] [[oeis:A000609|A000609]]. The value is only known exactly up to <math>n=9</math> case, but the order of magnitude is known quite exactly: it has upper bound <math>2^{n^2 - n \log_2 n + O(n)}</math> and lower bound <math>2^{n^2 - n \log_2 n - O(n)}</math>.<ref name=":4">{{Cite journal |last1=Šíma |first1=Jiří |last2=Orponen |first2=Pekka |date=2003-12-01 |title=General-Purpose Computation with Neural Networks: A Survey of Complexity Theoretic Results |url=https://direct.mit.edu/neco/article/15/12/2727-2778/6791 |journal=Neural Computation |language=en |volume=15 |issue=12 |pages=2727–2778 |doi=10.1162/089976603322518731 |pmid=14629867 |issn=0899-7667}}</ref>

Any Boolean linear threshold function can be implemented with only integer weights. Furthermore, the number of bits necessary and sufficient for representing a single integer weight parameter is <math>\Theta(n \ln n)</math>.<ref name=":4" />