Pattarawut Charatpangoon

arXiv2026

A Geometry-Based Capacity Theory for Finite-Feature Associative Memory

We develop a geometry-based capacity theory for exact-key retrieval in compressed finite-feature Hebbian associative memory. For random or approximately isotropic values, retrieval interference separates into finite-feature noise, which decreases with feature dimension, and structural interference, which is determined by squared kernel overlap among stored keys and persists in the infinite-feature limit. This yields a fit-free prediction of retrieval quality, reveals a geometry-dependent capacity ceiling, and predicts the feature budget required for a target retrieval quality. When stored values are correlated, we show that retrieval depends jointly on the key kernel and value Gram matrix, and derive finite-feature approximations that account for this interaction. We validate the theory on synthetic, visual, and medical-image representations. Overall, the framework links representation geometry directly to memory capacity and distinguishes when performance can be improved by increasing the feature budget and when the representation itself must be changed. Across these settings, the predicted retrieval curves closely match empirical behavior and correctly identify changes in the preferred memory design.

cs.LG↗

arXiv2026

PredRA: Fast Medical Image Translation by Deterministic Component Extraction and Controlled Stochastic Refinement

Strongly paired medical image translation contains a substantial component that can be predicted directly from the source. The current reality is that pure deterministic prediction can smooth away fine detail, while generative models can recover detail but may also introduce unnecessary or potentially harmful variation. We propose PredRA, a fast framework that uses the deterministic prediction as a stable reference and further extracts additional deterministic components from the residual during generative refinement, thereby improving fidelity while maintaining perceptual quality. The goal is simple: we view the entire residual-based generative process as an optimization problem and derive a practical solution that recovers useful residual detail through controlled refinement while keeping the prediction close to the paired target. Mechanism studies further show that useful residual information follows structured patterns, but its usefulness is difficult to estimate reliably at the voxel level. We therefore globally control how much of the residual refinement is added to the deterministic prediction, thereby reducing the accumulation of unnecessary uncertainty. PredRA therefore combines deterministic component extraction with controlled stochastic refinement for fast, fidelity-preserving, and perceptually strong medical image translation. We validate the approach across multiple real-world datasets, showing that controlled refinement improves fidelity to the paired target compared with full residual refinement while retaining much of the perceptual benefit of generative modeling. PredRA achieves competitive or superior performance to substantially larger state-of-the-art models with 1.4-11.9x fewer total parameters and 3.1-26.2x fewer trainable parameters, while its 32-step flow sampler requires 31.25x fewer sampling steps than the matched 1000-step DDPM.

cs.CV↗