Title: Closed-Loop Activation Density Control for Sparse Distributed Memory
Primary area: learning theory
Keywords: associative memory, sparse distributed memory, control theory, high-dimensional memory, feedback control, binomial distribution

Abstract: Associative memory models often suffer from sensitive parameters that hinder stable operation in high-dimensional settings. In particular, Pentti Kanerva's Sparse Distributed Memory (SDM) requires setting a Hamming distance threshold $T$ to determine which memory locations are activated on a query, a choice that critically affects performance. 

We address a fundamental parameter sensitivity problem in SDM: directly tuning the threshold $T$ is ill-conditioned around the nominal operating point (half the dimension), where a minute change in $T$ causes an enormous swing in the count of activated locations $k$. To solve this, we propose controlling the activation density $p = k/L$ (the fraction of memory locations activated) as a well-posed alternative to tuning $T$. 

We combine inverse-CDF actuation with slope-normalized integral feedback to neutralize the large plant gain near $n/2$. The result is a closed-loop SDM that adapts $T$ on the fly to achieve a desired sparsity level $p^*$ across queries. 

Our control law achieves near-perfect target tracking ($R^2 \approx 1.00$) and dramatically improves query efficiency, reducing activation error by $\sim 4.9\times$ compared to naive threshold control at equal query budgets. Standard bisection achieves similar raw error but requires $\sim 1.9\times$ more queries, yielding worse cost-efficiency. 

Finally, our method generalizes robustly across dimensions $n \in \{512, 1024, 2048\}$ and target densities $k^* \in \{3, 6, 12\}$.

TL;DR: We solve the parameter sensitivity problem in Sparse Distributed Memory by controlling activation density rather than threshold, achieving 4.9× better error reduction through slope-normalized integral feedback control.