On SBMs, GCN + BRIDGE reaches about 99% on synthetic SBM graph benchmarks. On heterophilic real graphs we see consistent gains, e.g. Actor +4.8 pts, Chameleon +2.7 pts, while Cora, Citeseer, Pubmed stay near baseline. Code and docs: github.com/jr419/BRIDGE 8/8

We prove the optimal structures for message passing are disjoint unions of single‑class clusters and two‑class bipartite clusters. This insight gives BRIDGE, a block‑resampling rewiring that uses predicted labels to sample an “optimal” graph. 7/8

In SBMs we provide explicit asymptotic formulae of higher-order order homophily in terms of mean degree and expected edge homophily. Predicted SNR tracks accuracy on real graphs, and the node‑wise test flags where the graph helps before any training. 6/8

This yields a local test that predicts when a GNN will beat a plain FNN. If same‑class nodes are poorly connected over multiple hops, message passing cannot lift SNR, no matter how you tune the model. 5/8

The key limiter of SNR is class‑bottlenecks. We define a local class‑bottlenecking score and show that higher‑order homophily bounds signal sensitivity. 4/8

We introduce a simple way to evaluate GNN performance using an SNR that splits into two parts: feature stats and feature‑agnostic sensitivities to class signal, local noise, and global shifts. 3/8

The paper reveals precisely when, where and why graph neural networks struggle in node classification: We show it's not just about structural bottlenecks -- rather the interaction between structural bottlenecks and class labels, unifying heterophily & bottleneck literatures for the first time. 2/8

🚨 Opening in mid-July:

🔹 Up to 8x 2-year Independent Fellowships in AI in Science, supported by @schmidtsciences.bsky.social
🔹 Up to 2x 2-year Joint Fellowships with ICR & CNRS
🔹 Up to 3x 1-year Linked Fellowships at Imperial (followed by a 1 year linked fellowship at AIMS and NCBS).

2/2

Calorie restriction (CR) is known to improve healthy ageing and we find indications that CR rats have lowered levels of cryptic mtDNA mutations. CR can increase mtDNA numbers and our theory predicts that higher mtDNA copy-numbers slow accumulation of mtDNA mutations. 6/6

Over 7 datasets, in multiple tissues in humans, mice and rats, cells with cryptic mtDNA mutations have gene expression changes consonant with ageing including immune effects and protein misfolding. We give experimental corroboration in human cell lines. 5/6

The accumulation of mutations is nonlinear with a phase coinciding with mid-late life where mutations hit high levels. By late life ~a third of all cells have a mutation that has taken over the whole population. Our inferred mutation rate is consonant with literature values. 4/6

We developed theory to account for the accumulation of these mutations and a hierarchical Bayesian inference framework to fit our models. We find that the accumulation of mutations conforms to our theory. We can predict an individual’s age from their levels of mutation. 3/6

We find evidence that a mutation type, invisible in bulk, cryptic mtDNA mutation, makes up the majority of mtDNA mutations in aged post-mitotic tissues. Notably these mutations show weak evidence of negative selection despite many mtDNA mutations having physiological effects. 2/6