  We analyze the energy and training data requirements for supervised learning
of an $M$-mode linear optical circuit by minimizing an empirical risk defined
solely from the action of the circuit on coherent states. When the linear
optical circuit acts non-trivially only on $k<M$ unknown modes (i.e., a linear
optical $k$-junta), we provide an energy-efficient, adaptive algorithm that
identifies the junta set and learns the circuit. We compare two schemes for
allocating a total energy, $E$, to the learning algorithm. In the first scheme,
each of the $T$ random training coherent states has energy $E/T$. In the second
scheme, a single random $MT$-mode coherent state with energy $E$ is partitioned
into $T$ training coherent states. The latter scheme exhibits a polynomial
advantage in training data size sufficient for convergence of the empirical
risk to the full risk due to concentration of measure on the $(2MT-1)$-sphere.
Specifically, generalization bounds for both schemes are proven, which indicate
the sufficiency of $O(E^{1/2}M)$ training states ($O(E^{1/3}M^{1/3})$ training
states) in the first (second) scheme.

Quantum Physics