# Quantization robustness from dense representations of sparse functions in high-capacity kernel associative memory

arXiv: https://arxiv.org/abs/2604.20333 · HTML: https://mlsanity.com/paper/2604.20333/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 19 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [Kernel Logistic Regression Learning for High-Capacity Hopfield Networks](https://mlsanity.com/paper/2504.07633/) (2025)
- [Self-Organization and Spectral Mechanism of Attractor Landscapes in High-Capacity Kernel Hopfield Networks](https://mlsanity.com/paper/2511.13053/) (2025)
- [Quantitative Attractor Analysis of High-Capacity Kernel Hopfield Networks](https://mlsanity.com/paper/2505.01218/) (2025)

## Built on by (most cited first, 1 of 1)

- [Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks](https://mlsanity.com/paper/2605.00366/) (2026)

## Abstract (arXiv)

High-capacity associative memories based on Kernel Logistic Regression (KLR) achieve strong retrieval performance but typically require substantial computational resources. This paper investigates the compressibility of KLR Hopfield networks to clarify the geometric principles underlying their robust representations. We present a geometric interpretation based on spontaneous symmetry breaking and Walsh analysis, and examine it through compression experiments involving quantization and pruning. The experiments reveal a clear asymmetry: the network remains robust under low-precision quantization while exhibiting strong sensitivity to pruning. We interpret this behavior through a "sparse function, dense representation" principle, in which a sparse input mapping is implemented through a dense bimodal parameterization. These findings suggest a practical route toward hardware-efficient kernel associative memories and provide insight into the geometric principles underlying robust representation in neural systems.