Linearithmic Clean-up for Vector-Symbolic Key-Value Memory with Kroneker Rotation Products

​Already subscribed to our Luma?
Join livestream directly on our YouTube Channel (https://www.youtube.com/@CentaurAIInstitute/streams) or our LinkedIn Page: (https://www.linkedin.com/company/centaur-ai-institute)

​Abstract: A computational bottleneck in current Vector-Symbolic Architectures (VSAs) is the "clean-up" step, which decodes the noisy vectors retrieved from the architecture. Clean-up typically compares noisy vectors against a "codebook" of prototype vectors, incurring computational complexity that is quadratic or similar. We present a new codebook representation that supports efficient clean-up, based on Kroneker products of rotation-like matrices. The resulting clean-up time complexity is linearithmic, i.e. O(N log N), where N is the vector dimension and also the number of vectors in the codebook. Clean-up space complexity is O(N). Furthermore, the codebook is not stored explicitly in computer memory: It can be represented in O(log N) space, and individual vectors in the codebook can be materialized in O(N) time and space. At the same time, asymptotic memory capacity remains comparable to standard approaches. Computer experiments confirm these results, demonstrating several orders of magnitude more scalability than baseline VSA techniques.

​Link to paper: https://proceedings.mlr.press/v284/liu25b.html

​Bio: Ruipeng Liu is a Ph.D. student at Syracuse University advised by Dr. Garrett Katz. His research interests are in neuro-symbolic AI and reinforcement learning. His recent work includes publications at ICML 2024 on the feasibility of single-pass, full-capacity learning in neural systems and at NeSy 2025 on efficient clean-up methods for vector-symbolic key-value memory.