Computing With Residue Numbers in High-Dimensional Representation

Area of Science:

• Computational neuroscience
• Computer science
• Machine learning

Background:

• Traditional computing methods face challenges with large dynamic ranges and noise.
• Representing numerical data efficiently is crucial for complex computations.

Purpose of the Study:

• To introduce residue hyperdimensional computing (RHDC), a unified framework.
• To demonstrate RHDC's efficiency, scalability, and noise robustness.
• To explore RHDC's applications in visual perception, optimization, and neuroscience.

Main Methods:

• Unifying residue number systems with an algebra over random, high-dimensional vectors.
• Representing residue numbers as high-dimensional vectors for parallelizable operations.
• Employing efficient factorization methods for high-dimensional vectors.

Main Results:

• RHDC represents and operates on large dynamic ranges with logarithmic resource scaling.
• The framework demonstrates significant robustness to noise.
• Improved performance in visual perception and combinatorial optimization tasks compared to baseline methods.

Conclusions:

• RHDC offers a computationally efficient and scalable alternative for numerical data manipulation.
• The framework provides insights into grid cell computation in the brain.
• RHDC suggests novel machine learning architectures for numerical data processing.