helins.htm.sdr.props — io.helins/htm 0.0.0-alpha0

Properties of Sparse Distributed Representations (SDRs).

It is a good practise to learn this namespace as SDRs are omnipresent in HTM. It introduces definitions and basic concepts. The helins.htm.sdr namespace is about creating and acting on concrete SDRs whereas this namespace is about the theory.

Based on :

[1] Ahmad, S., & Hawkins, J. (2015). Properties of sparse distributed representations and their application to hierarchical temporal memory. arXiv preprint arXiv:1503.07469.

cardinality clj

(cardinality capacity sparsity)

The cardinality of an SDR is the number of active bits. It can be computed from the capacity and the required sparsity.

count-inexact-patterns clj

(count-inexact-patterns capacity overlap-score cardinality)

(count-inexact-patterns capacity overlap-score cardinality-1 cardinality-2)

Computes the number of patterns matching an SDR for exactly overlap-score active bits.

They can have different cardinalities which is useful in the context of subsampling and unions.

Generalization of [1] Equation 3, 6, and 14.

count-patterns clj

(count-patterns capacity cardinality)

Computes the number of unique patterns an SDR can produce given a fixed cardinality.

Cf. [1] Equation 1

expected-union-cardinality clj

(expected-union-cardinality pattern-count capacity cardinality-2)

Computes the expected cardinality of a union of patterns.

Cf. [1] Section G and H

P-active-union-bit clj

(P-active-union-bit pattern-count capacity cardinality)

Opposite of P-inactive-union-bit.

P-approx-inexact-match clj

(P-approx-inexact-match capacity overlap-score cardinality)

(P-approx-inexact-match capacity overlap-score cardinality-1 cardinality-2)

Approximates efficiently the result of P-inexact-match.

Specially precise when the smallest cardinality > 7 and overlap-score > (cardinality / 2).

Cf. [1] Equation 5

P-exact-match clj

(P-exact-match capacity cardinality)

Computes the propability of an exact match between two random SDRs with the same properties.

Cf. [1] Equation 2

P-exact-union-match clj

(P-exact-union-match pattern-count capacity cardinality-2)

Computes the probability of a pattern exactly matching a pattern within a union of patterns.

Cf. [1] Equation 13

P-inactive-union-bit clj

(P-inactive-union-bit pattern-count capacity cardinality)

Computes the probability that a given bit is inactive in a union of patterns.

Cf. [1] Equation 12

P-inexact-match clj

(P-inexact-match capacity min-overlap-score cardinality)

(P-inexact-match capacity min-overlap-score cardinality-1 cardinality-2)

Computes the propability of an inexact match between two random SDRs (at least min-overlap-score active bits in common).

They can have different cardinalities which is useful in the context of subsampling and unions.

In order to be robust against noise, an inexact match is a lot more useful than an exact one. The probability of an inexact match represent the probability of a false positive. The higher the capacity and the overlap score, the lower probability.

Linear with respect to (min cardinality-1 cardinality-2).

Generalization of [1] Equation 4, 7, and 15

sparsity clj

(sparsity capacity cardinality)

The sparsity of an SDR is related to its cardinality as it is the percentage of active bits.