# Oracle Inequality

When target samples are limited, conditional flow matching can borrow a covariate representation learned from a related source population. TFM-Freeze keeps the source encoder fixed and trains only a target velocity head; TFM-Adapt jointly learns the head and a representation correction under a functional anchoring penalty. In simulations with related five-dimensional representations and 10000 source samples, unpenalized TFM-Adapt lowered energy discrepancy from 0.3158 for TFM-Freeze to 0.2325, a 26.4% reduction; target validation falls back to a target-only generator when transfer does not help.

When target samples are limited, conditional flow matching can borrow a covariate representation learned from a related source population. TFM-Freeze keeps the source encoder fixed and trains only a target velocity head; TFM-Adapt jointly learns the head and a representation correction under a functional anchoring penalty. In simulations with related five-dimensional representations and 10000 source samples, unpenalized TFM-Adapt lowered energy discrepancy from 0.3158 for TFM-Freeze to 0.2325, a 26.4% reduction; target validation falls back to a target-only generator when transfer does not help.

A simulation-based inference framework jointly learns a low-dimensional summary statistic and an amortized posterior estimator with non-asymptotic guarantees: in exponential-family and smooth-model settings, the training size needed for a target accuracy grows only polynomially with observation dimension, not exponentially as in classical nonparametric conditional distribution estimation.

A simulation-based inference framework jointly learns a low-dimensional summary statistic and an amortized posterior estimator with non-asymptotic guarantees: in exponential-family and smooth-model settings, the training size needed for a target accuracy grows only polynomially with observation dimension, not exponentially as in classical nonparametric conditional distribution estimation.