Analytic inverse problems with finitely many random measurements

What the math gives to ML

The paper establishes a dimension-counting identifiability principle for analytic finite-dimensional model classes: if an infinite-data forward map is injective on a d-dimensional analytic class, then 2d+1 independent random scalar measurements identify every member almost surely. The transferable asset is a constructive randomized measurement bottleneck for high-dimensional structured outputs, including severely ill-posed maps where deterministic designs may require exponentially many measurements. In neural networks, this can reduce input bandwidth and activation memory, but practical noisy recovery requires oversampling beyond the theorem's exact-identifiability threshold and monitoring the projected Jacobian's conditioning.