Boolean threshold functions, neuron capacity, and memory retrieval

arXiv:2609.29756 · math.PR, cs.DM, cs.NE, math.CO, stat.ML · Submitted 2026-09-24 · Read on arXiv

math.PR, cs.DM, cs.NE, math.CO, stat.ML

Submitted: 2026-09-24

Updated: 2026-09-24

Terminology

• Associative Memory — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode

Sources

• Chamber geometry and specification numbers of Boolean threshold functions
• Polynomial threshold functions, hyperplane arrangements, and random tensors
• Singularity of $\{\pm 1\}$-matrices and asymptotics of the number of threshold functions
• On linear-combinatorial problems associated with subspaces spanned by $\{\pm 1\}$-vectors
• Rank deficiency of random matrices
• Singularity of discrete random matrices
• Cokernels of random matrices satisfy the Cohen-Lenstra heuristics
• Random integral matrices: universality of surjectivity and the cokernel
• Smith Normal Form in Combinatorics
• Are most Boolean functions determined by low frequencies?

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