Xuanxi Zhang, Kevin S. Cheng, Weizhou Wang, Aaron R. Dinner, Jonathan Weare
Diffusion models are often inaccurate in critical, data-sparse regions of the target distribution. Sampling from restrained distributions, biased distributions used in classical enhanced sampling to concentrate data near chosen configurations, can control where training data are collected but biases the learned distribution. We establish that this bias cancels exactly when forward noising from restrained data is conditioned on the restrained configuration at an appropriately chosen intermediate time. This allows a pretrained model fine-tuned on restrained data to achieve high accuracy in any chosen region of the target distribution, regardless of its probability, using standard denoising or flow matching objectives without importance weights. When no target data are available, Gibbs sampling enables inference from a model trained exclusively on restrained data.
Xiangyu Liu, Zeting Yan, Zhitong Yin, Boyang Li, Xi Zhang
Background and Objective: Predicting regional blood-oxygen-level-dependent (BOLD) activity from EEG provides a computational approach to studying electrophysiological-hemodynamic associations. However, changes in input representation, readout architecture, and ensembling can obscure the source of a prediction gain. We investigate the contribution of target-relative spectral estimation under matched readout conditions. Methods: MEL converts each preceding 16-second EEG history into calibrated lag-channel-frequency measurements. Four equal-dimensional representations are compared using matched Ridge and multilayer perceptron (MLP) readouts. The retrospective analysis includes 29 resting-state scans from 22 participants, participant-paired uncertainty estimates, aggregation and correspondence controls, leave-one-participant-out regression, and refitted models on an external Oddball cohort. Results: Morlet-Ridge achieved a mean scan-wise correlation of 0.508 across six regional targets and the global signal, compared with 0.432 for canonical Fourier features. The participant-paired mean difference was 0.069 (95% bootstrap confidence interval, 0.037-0.101), with improvements in 19 of 22 participants. The Morlet MLP prediction ensemble reached 0.491. Shared coordinate permutations preserved prediction after refitting, whereas sample-wise permutations degraded it. Canonical Fourier regression reached 0.377 under participant exclusion; external unseen-participant correlation was 0.026. Conclusions: Spectral estimation materially affected regional BOLD prediction without requiring additional nonlinear readout capacity. MEL provides an explicit measurement interface for controlled comparisons, but weak external results constrain its generalizability. Confirmation requires untouched participant-separated data and split-aware preprocessing.