abstract—face recognition is a widely used technology with numerous large-scale applications, such as surveillance, social media
and law enforcement. there has been tremendous progress in face recognition accuracy over the past few decades, much of which
can be attributed to deep learning based approaches during the last five years. indeed, automated face recognition systems are now
believed to surpass human performance in some scenarios. despite this progress, a crucial question still remains unanswered: given a
face representation, how many identities can it resolve? in other words, what is the capacity of the face representation? a scientific
basis for estimating the capacity of a given face representation will not only benefit the evaluation and comparison of different face
representation methods, but will also establish an upper bound on the scalability of an automatic face recognition system. we cast the
face capacity estimation problem under the information theoretic framework of capacity of a gaussian noise channel. by explicitly
accounting for two sources of representational noise: epistemic (model) uncertainty and aleatoric (data) variability, our approach is
able to estimate the capacity of any given face representation. to demonstrate the efficacy of our approach, we estimate the capacity
of a 128-dimensional deep neural network based face representation, facenet [1], and that of the classical eigenfaces [2]
representation of the same dimensionality. our numerical experiments on unconstrained faces indicate that, (a) our capacity estimation
model yields a capacity upper bound of 5.8×108 for facenet and 1×100 for eigenface representation at a false acceptance rate (far)
of 1%, (b) the capacity of the face representation reduces drastically as you lower the desired far (for facenet representation; the
capacity at far of 0.1% and 0.001% is 2.4×106 and 7.0×102 , respectively), and (c) the empirical performance of the facenet
representation is significantly below the theoretical limit.
index terms—face recognition, face representation, channel capacity, gaussian noise channel, bayesian inference