Representational geometry as a fidelity metric for connectome-constrained networks: evidence from the Drosophila visual system

What does biological wiring actually contribute to neural computation? Behavioral experiments can test whether a model produces the right outputs, but they cannot determine whether its internal representations are biologically faithful. Brunton et al. (2026) made this concrete: a C. elegans worm connectome trained with deep reinforcement learning produces realistic Drosophila fly walking, yet the model is biologically meaningless, because behavioral fidelity is achievable without biological fidelity. We need a population-level metric that discriminates real biological wiring from arbitrary wiring, without requiring a behavioral decoder. We propose representational geometry as that metric, and test it on the Flyvis pretrained Drosophila visual system ensemble (Lappalainen et al. 2024) against three families of random wiring: a weight-shuffled baseline, and two topology-randomizing null schemes, degree-preserving swap and Erdos-Renyi, used throughout the rest of the paper. Using individual-pairwise RDM comparison rather than the weaker ensemble-mean statistic (which can itself exceed its own within-real ceiling, a result that is not possible under an honest comparison), real wiring is clearly distinguishable from random wiring before any training, across all three stimulus conditions tested and both topology-randomizing schemes (p < 10-13 in every case). An apparent exception on the combined ON+OFF stimulus set turns out to be a confound: it measures a coarse, shared ON/OFF-discrimination signal any network reproduces, and disappears once within-polarity structure is isolated. Grounding this in measured biology required first diagnosing and repairing the reference itself. A biological reference constructed from idealized tuning curves fit to Maisak et al. (2013) proved 97.8% explained by circular stimulus structure alone and uninterpretable as a fidelity instrument. We replaced it with a reference built from real per-cell recordings (Henning et al. 2022), substantially less circular (64-82%, depending on reconstruction method) and independently validated as carrying genuine, replicable signal via a synthetic-noise floor and split-half reliability test. With a validated reference in hand, we tested the case Brunton's finding makes urgent directly: does geometry distinguish real, trained wiring from random wiring that has also been trained to task adequacy? Two independent methods largely agree it does not. A biology-mediated comparison finds real and trained-random wiring statistically indistinguishable, once properly size-matched, for both null schemes. A direct RDM comparison requiring no biological reference at all finds the same substantial narrowing, and in one specific case, trained Erdos-Renyi on OFF-polarity structure, closes the gap completely, the only case across either method where that happens outright. Checkpoint-level trajectories show this convergence is abrupt, not gradual, and its magnitude is set entirely by how much distinguishability existed before training began, not by wiring scheme or a separate developmental process. A negative-trending pattern in one comparison, random wiring correlating more strongly with biology than real wiring, motivated two further tests. First, this pattern tracks training generally, not wiring identity: a matched real-versus-untrained-random comparison is itself significant, and the finding generalizes robustly to the trained null schemes once fairly resampled. Second, retraining eight seed networks from identical wiring with different training-noise seeds, following the methodology of Frankle et al. (2020), finds no significant evidence that wiring realization, rather than training-process randomness, determines the direction an individual network's fidelity trend takes, on the more trustworthy of our two biological references. Two networks show internal dynamics beyond simple clustering or scatter, one with a trajectory reversal mid-training that produces three qualitatively different retrained outcomes from identical wiring, suggestive of a genuine dynamical bifurcation rather than noise. Together these results show that representational geometry is a genuine, population-level fidelity signal: it reliably distinguishes real from random wiring before training, corroborated independently by CKA, but that distinction narrows substantially and in specific cases disappears entirely once both are trained to task adequacy, the direct test Brunton's finding raises. We report this as an honest, largely null result on the training question, not the confirmation we set out to find, together with a validated, non-circular biological reference and a diagnosed instance of the ensemble-mean statistical artifact, as resources for evaluating fidelity in connectome-scale emulations more broadly.