This repository is a collection of associative memory algorithms operating on sparse distributed representations, which is our brain's data structure.

Our objective is to build a library of highly efficient software components, enabling practical applications of associative content-addressable memories.

The Triadic Memory algorithm, a new kind of tridirectional associative memory, was discovered in 2021. Dyadic Memory, which is based on the same algorithmic idea, is a hetero-associative memory also known as Sparse Distributed Memory.

Machine learning applications can be realized by creating circuits from the algorithmic components in this repository. An example is the Deep Temporal Memory algorithm, a recurring neural network based on multiple Triadic Memory instances and feedback lines.

• Usage and application examples
• Performance benchmarks for different implementations and computer systems
• Discussion of Triadic Memory at Numenta's HTM Forum
• Triadic Memory paper

• C reference implementation
• Chez Scheme
• Javascript
• Julia
• Mathematica, with executable examples
• Odin
• Python
• Rust

Triadic Memory is an associative memory that stores ordered triples of sparse binary hypervectors (also called sparse distributed representations, or SDRs).

As a content-addressable triple store, Triadic Memory is naturally suited for storing semantic information.

Triadic memory allows tridirectional queries: Any part of an SDR triple can be recalled from the other two parts. The algorithm learns new information in one shot. Stored data can be recalled from incomplete or noisy input data.

A Triadic Memory has the capacity to store (n/p)^3 random triples of hypervectors with dimension n and sparse population p. At a typical sparsity of 1 percent, it can therefore store and perfectly retrieve one million triples. The usable capacity is even higher, as associative memories are inherently tolerant to noise and errors.

The original Mathematica code can be found here. The plain C implementation can be compiled as a command line program or as a library. It's also a good starting point for people wanting to port the algorithm to another programming language.

Dyadic Memory realizes a hetero-associative memory for sparse hypervectors which has the functionality of a Sparse Distributed Memory (SDM) as proposed by Pentti Kanerva in 1988.

The present, highly efficient algorithm was discovered in 2021 and is based on a neural network with one hidden layer and combinatorial connectivity. The original implementation was written in Mathematica language and consists of just 10 lines of code.

The memory stores and retrieves heteroassociations x -> y of sparse binary hypervectors x and y. Sparse binary hypervectors are also known as Sparse Distributed Representations (SDR).

The plain C implementation best illustrates the algorithm in procedural language. This version works with vector dimensions up to n = 20,000 and can be used in an asymmetric configuration where x and y have different dimensions.

A temporal memory processes a stream of SDRs, at each step making a prediction for the following step based on previously seen information. It can also be used for learning separate terminated sequences.

Temporal Memory algorithms are based on circuits of two or more Triadic Memory instances with at least one feedback loop, resembling the architecture of recurrent neural networks.

The Elementary Temporal Memory uses two Triadic Memory units arranged in the form of an Elman network.

The Deep Temporal Memory algorithm is a circuit of hierarchically arranged Triadic Memory units with multiple feedback loops. It can recognize longer and more complex temporal patterns than the elementary version based on just two memory units.

Trained with a dataset from the SPMF project, Deep Temporal Memory achieves a prediction accuracy of 99.5 percent.

A plain C implementation can be found here.