Mutual information (MI) estimation is used to probe what neural representations encode, including in protein language models, but variational MI estimators have variance that scales at least exponentially in the true MI. We audit a prior neural-MI study of order-resolved epistasis in ESM-2 on the four-site GB1 landscape. Run-to-run differences show no systematic bias and a magnitude comparable to ordinary cross-seed retraining variability, and the evaluation-pairing scheme shifts scores substantially. At the original dimensionality, two of three alternative estimator families stabilize the estimate across seeds and one does not. In a synthetic calibration at the representation dimensionalities of two other protein language models (a Gaussian channel with known MI; no model representations), all three families recover materially less signal than required, despite correct signal ordering and stable seeds. A control critic given the true signal direction, which also reduces its input to one dimension, recovers 93.3% and 98.7% of the analytic MI at gain 1.5 (at 5,120 and 4,096 dimensions), so the signal is recoverable with privileged information, but the control does not identify why blind estimation fails. We package the checks into a reusable diagnostic protocol and conclude that even a stabilized estimator is not currently sufficient for order-resolved dependence claims made under blind search at this dimensionality and sample size.
Maryam Rahimimovassagh, Waldemar Karwowski, Ivan Garibay, Niloofar Yousefi
原文摘要
Protein foundation models support mutation-effect and structural prediction, but predictive performance alone does not reveal which forms of biological interaction information remain accessible through model depth. We ask whether ESM-2 retains higher-order epistatic information as strongly as first- and second-order information across its representation hierarchy, introducing ORBIT-FMIB, a diagnostic framework combining Walsh-based interaction decomposition with subset-conditioned neural dependence estimation. The method is validated on synthetic landscapes with known interaction structure before being applied to the dense four-site GB1 fitness landscape using frozen ESM-2 representations. An initial production run suggested ESM-2 retains higher-order epistatic information less well than lower-order information ($Δ_{\mathrm{HO-LO}}=-0.107$). An independent replication of the complete measurement grid, under matched GPU hardware and identical critic seeds, substantially reduced this contrast ($Δ_{\mathrm{HO-LO}}=-0.017$), and its sign was unstable across otherwise-defensible evaluation-pairing choices applied to the same trained critics ($-0.011$ to $+0.015$). We therefore do not currently have robust evidence that ESM-2 selectively loses higher-order epistatic information, nor that retention is equal across orders; the directional question remains open. The measurement protocol itself, including its documented removal of a positional-subset shortcut in pooled critics, remains validated and is unaffected by this finding. ORBIT-FMIB is offered as a diagnostic framework for probing interaction structure in protein foundation models; this study's own replication result illustrates why such probing requires adequately-powered reproducibility checks before its output is treated as a biological finding.