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. Representational geometry — the structure of pairwise distances between population responses to different stimuli — captures how a neural circuit organizes its representational space, independently of what behavior it drives. We apply representational similarity analysis (RSA) and centered kernel alignment (CKA) to the Flyvis pretrained Drosophila melanogaster visual system ensemble (Lappalainen et al. (2024)): 50 networks whose architecture is fixed to the Flyvis connectome (reconstructed from partial electron-microscopy sources), compared against stability-constrained random baselines (sign-preserving weight shuffles, rejection-sampled for dynamic stability, n = 50).

Connectome-constrained networks produce a smooth circular direction geometry that random networks capture only coarsely: RSA Spearman r = 0.686 ( p < 0.0001) for ON edge stimuli and r = 0.846 ( p < 0.0001) for ON+OFF edge stimuli, corroborated by CKA ( p < 0.05 in both experiments). A high r here indicates that the CC geometry is a more resolved version of a structure the random baseline approximates, not that the two are interchangeable. We also compared the geometry against a T4/T5 direction-tuning reference reconstructed from published summary parameters (Maisak et al. 2013), but that comparison proves uninterpretable by construction. Maisak et al. (2013) report that T5 cells respond selectively to OFF edges and “mostly failed to respond to moving ON edges”; on the ON-only stimulus set the reference therefore reduces to the four T4 subtypes, which are tuned to the four cardinal directions with a common von Mises width. A cosine RDM over four same-width curves at 90° spacing is necessarily near-identical to a pure angular-distance matrix, and indeed the reference correlates with one at r = 0.978. Raw correlations against it consequently measure circular organization rather than direction-tuning fidelity: for every network condition the raw biological correlation falls within 0.01 of that network’s circular correlation, and the raw CC-versus-random gap (Δ r = 0.330) equals the gap in circularity (Δ r = 0.338). Partialling out circular structure leaves a residual that is larger for connectome-constrained networks than for random ones ( r = 0.145 vs. r = 0.061) but is significant for neither at n = 50 ( p _perm = 0.120 and 0.323). The biological-fidelity evidence therefore rests on the within-polarity direction structure, where the connectome-constrained network shows strong circular direction tuning in each polarity channel (ON–ON r = 0.937, OFF–OFF r = 0.799) against an explicit circular reference, and the random baseline does not (ON–ON r = 0.38, OFF–OFF r = 0.49). Within each stimulus polarity, the ON pathway encodes direction with stronger geometric separation than the OFF pathway (Δ r = 0.138, 95% CI [0.091, 0.236]); we report this as a property of the model ensemble’s representations rather than an established biological difference: Maisak et al. (2013) find T4 and T5 functionally equivalent except in contrast polarity. To address the training confound, we compared untrained networks against shuffled baselines. That comparison cannot be made: the untrained networks’ representational dissimilarity matrices have a dynamic range of 1.66 × 10 ⁻⁸ , eleven times below the float32 round-off floor of the responses they derive from (1.93 × 10 ⁻⁷ ). A cancellation-free metric cross-check (per-model Kendall τ = 1.0000 between cosine and Euclidean-normalized rank orders, across all 150 models) confirms this is a resolution failure rather than an artifact of the distance function. An earlier version of this work reported r = 0.260 ( p _perm = 0.041) and r = 0.215 ( p _perm = 0.048) from these matrices; those are permutation tests on rounding and are withdrawn. Two perturbation sweeps show the failure is not a matter of insufficient noise: increasing bias perturbation drives the population vectors toward a common bias-dominated direction and reduces the RDM’s dynamic range fortyfold, while increasing synapse-strength perturbation raises it but inflates responses, silences up to half the cell-type connections, and destabilizes the network before the matrix becomes resolvable. We therefore report that untrained connectome-constrained networks have no measurable representa-tional geometry within the regime where they remain connectome-constrained, and make no claim about a pre-training wiring prior.

These results show that representational geometry distinguishes connectome-constrained from weight-shuffled wiring under matched training, using only population responses to a structured stimulus set. Whether it discriminates real wiring from trained random wiring — the case Brunton’s result makes urgent — requires training random-wired networks on the identical task; we ran this test directly (Experiment 5), training two null connectome schemes (degree-preserving and degree-breaking, n = 10 each) to the identical optic-flow task and comparing their representational geometry against the same biological reference used in Experiment 3. This comparison inherits the identical circularity confound: both null schemes’ raw correlations with biology ( r = 0.832, r = 0.738) collapse to statistical noise ( r = −0.033, r = −0.011) once corrected for circular stimulus structure, and the degree-preserving-versus-degree-breaking contrast this test was designed to resolve is not answerable with this reference. We therefore offer representational geometry as a candidate fidelity metric whose decisive test — discriminating real wiring from trained random wiring — has been attempted but remains unresolved, not for want of trying but because the available biological reference cannot support it, and sketch a path toward fidelity metrics for connectome-scale emulations approaching mammalian cortex.