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Abstract:Synthetic face generators can produce many nominal identities, but nominal count does not determine how many are jointly distinguishable under a specified verification rule. We define finite-dimensional capacity as the supremum of codebook sizes over distinct latent identity codes whose induced identity-conditional embedding distributions satisfy per-identity genuine acceptance and pairwise impostor non-match constraints. For deterministic view-invariant pipelines, fixed-code capacity equals the spherical-code cardinality over the realizable embedding set and reduces to the classical spherical-code cardinality when every sphere direction is realizable. For stochastic identity-conditional embedding distributions concentrated with probability at least $1-\eta$ in spherical caps of angular radius $\rho$, we derive a sufficient center-separation condition, spherical-code capacity lower bounds under full angular expressivity, and positive asymptotic lower-bound exponents for dimension-indexed pipeline families. We also derive prior-constrained random-code lower bounds from pairwise center-separation failure probabilities. When each identity-conditional embedding distribution has support equal to a spherical cap of angular radius $\rho$, we derive necessary zero-error geometric conditions and, for $2\rho<\arccos(\tau)$ under full $\rho$-cap angular expressivity, show that the restricted zero-error capacity equals the classical spherical-code cardinality at minimum angle $\arccos(\tau)+2\rho$. For finite repeated-view samples, a maximum clique in the resulting compatibility graph identifies the largest sampled subset satisfying all empirical genuine and pairwise impostor constraints. We evaluate this sample-restricted quantity on a deterministically selected DigiFace-1M subset under three fixed recognizers with identity-disjoint in-domain threshold calibration.

Submission history

From: Behrooz Razeghi [view email]
[v1] Sun, 12 Apr 2026 13:42:39 UTC (825 KB)
[v2] Tue, 8 Sep 2026 18:05:03 UTC (932 KB)