Effective Resistance and Graph Neural Network Reliability in Tissue-Specific Interactomes

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.

The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points. No existing work has defined a measurable RG order parameter, tested it under controlled variation of the input distribution, or made quantitative predictions that are empirically verified. We study the simplest architecture for which the analogy is tractable: a pure MLP residual stack trained on masked token prediction over synthetic Markov chain sequences with known spectral properties. We report three findings. (i) The effective rank of the residual stream decreases monotonically with depth after training, consistent with progressive integration of irrelevant degrees of freedom. (ii) This rank collapse is selective: it occurs for chains with short correlation length approximately 1 but is absent for chains with long correlation length approximately 7, measured at the position level to control for mean-pooling artifacts. The network preserves exactly the degrees of freedom relevant to the prediction task, the content of the RG relevance criterion. (iii) Inter-layer kernel drift is concentrated at one or two specific transitions, with the remainder of the network near a fixed point, consistent with a discrete fixed-point plateau. Together these findings constitute the first quantitative, position-level evidence that MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.

Understanding how molecular alterations propagate across biological systems to drive disease remains a central challenge. Although high-throughput profiling enables comprehensive characterization of tumor states, most models neglect structured biological relationships or lack interpretability across scales. Here we present PPI-Net, a hierarchical graph neural network that integrates protein-protein interaction (PPI) networks with pathway-level representations to model disease from molecular interactions to functional processes. Patient-specific molecular profiles are embedded within a shared interaction network from STRING and propagated through a multi-layer Reactome hierarchy using graph attention, enabling aggregation of gene-level signals into higher-order biological programs. Across RNA-seq data from ten cancer types from The Cancer Genome Atlas, PPI-Net achieves robust predictive performance, with balanced accuracy exceeding 90% in multiple cohorts. Comparative analysis on RNA-Seq data from breast cancer demonstrated that PPI-Net's integration of the Reactome hierarchy improved balanced accuracy by 6.7% relative to a PPI-only model, while hierarchical multi-level supervision improved balanced accuracy by 12.3% relative to using only a single top-level prediction head. Applying a multi-omics approach using RNA-seq and methylation data improves model interpretation, recovering canonical oncogenic modules, including TP53-AKT signaling and stress response pathways, while revealing convergence onto coherent programs such as ion signaling and cellular responses to stimuli. These results demonstrate that integrating interaction networks with pathway hierarchies enables accurate prediction while providing mechanistic insight into cancer biology.