Origin of high-temperature degradation for bimodal disorder

Determine whether the degradation of effective sample size for bimodal disorder at inverse temperatures below the training range is caused by the uniform shrinking of the dimensionless couplings, which prevents the encoder from resolving differences between disorder realizations.

Background

The model is trained over a discrete set of inverse temperatures and evaluated over a continuous range. For bimodal couplings, the effective sample size decreases sharply in the high-temperature extrapolation regime, where the dimensionless couplings satisfy |K_ij| = beta and become uniformly smaller than the magnitudes encountered during training.

The paper contrasts this behavior with Gaussian disorder, whose continuous coupling distribution exposes the encoder to small dimensionless couplings during training. The stated explanation for the bimodal high-temperature degradation remains a conjecture rather than a demonstrated causal account.