  Given a time-series of noisy measured outputs of a dynamical system z[k],
k=1...N, the Identifying Regulation with Adversarial Surrogates (IRAS)
algorithm aims to find a non-trivial first integral of the system, namely, a
scalar function g() such that g(z[i]) = g(z[j]), for all i,j. IRAS has been
suggested recently and was used successfully in several learning tasks in
models from biology and physics. Here, we give the first rigorous analysis of
this algorithm in a specific setting. We assume that the observations admit a
linear first integral and that they are contaminated by Gaussian noise. We show
that in this case the IRAS iterations are closely related to the
self-consistent-field (SCF) iterations for solving a generalized Rayleigh
quotient minimization problem. Using this approach, we derive several
sufficient conditions guaranteeing local convergence of IRAS to the correct
first integral.
