Benchmarking deep learning against matched filtering for single-event graviton-dispersion tests on LIGO data

General relativity predicts a massless graviton; a broad class of theories beyond it gives the graviton a small rest mass mg, which would make gravitational waves dispersive and imprint a calculable, frequency-dependent phase on a binary-black-hole inspiral. Mea- suring that phase tests whether the graviton has mass. We benchmark a deep-learning discriminator against the optimal matched filter on a single gravitational-wave event-a demanding regime, since the strongest current bound, λg = h/(mg c) >9.8×1013 km, is set only by combining the event catalogue, and whether a learned model can beat matched filtering on one event has not been tested on observational strain. We inject general-relativistic and massive-graviton inspirals—source parameters from the GWTC-4.0 catalogue, dispersion phase to leading order in 1/λ2g -into LIGO H1 strain near GW150914 at controlled signal-to-noise ratios ρopt ∈{20,50}, scan the graviton Compton wavelength λg , and on identical data compare two discriminators: the oracle matched filter, given the true source parameters, and a compact (1.7 ×105-parameter) convolutional–transformer classifier, given only whitened strain. On observed strain both reach only AUC = 0.45–0.50-indistinguishable from each other and from chance at every grid cell-whereas on noise-free signals both separate the classes perfectly. A noise ladder localises the cause: in stationary Gaussian noise of the measured power spectrum the classes stay separable at strong dispersion yet collapse to chance on real strain—so the strain’s non-Gaussian content sets the single-event limit—while near the bound the inter-class difference is itself below the single-event noise. For the model, training and noise studied, deep learning gives no per-event advantage over the Gaussian-optimal matched filter; since that filter is optimal only under the Gaussian likelihood, a method that models the non-Gaussian noise remains a route to improvement we do not exclude. We provide this as a validated, openly reproducible benchmark