Integer Factorization with Compositional Distributed Representations

• In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural networks and potentially implemented on parallel neuromorphic hardware. We introduce a method for encoding numbers in distributed vector spaces and explain how the resonator network can solve the integer factorization problem. We evaluate the approach on factorization of semiprimes by measuring the factorization accuracy versus the scale of the problem. We also demonstrate how the proposed approach generalizes beyond the factorization of semiprimes; in principle, it can be used for factorization of any composite number. This work demonstrates how a well-known combinatorial search problem may be formulated and solved within the framework of Vector Symbolic Architectures, and it opens the door to solving similarly difficult problems in other domains.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Farkostteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Vehicle Engineering (hsv//eng)

Keyword

Collective-State Computing

Fractional Power Encoding

Hyperdimensional Computing

Integer Factorization

Resonator network

Vector Symbolic Architectures

Encoding (symbols)

Factorization

Network architecture

Network coding

Resonators

Vector spaces

Distributed representation

Encodings

Fractional power

Neural-networks

Vector symbolic architecture

Vectors

Publication and Content Type

ref (subject category)

kon (subject category)