Rafael Moschopoulos

Jerry Han, Rafael Moschopoulos, Ella Colby et al. · princeton

How can we measure intelligence beyond human capability? Human-authored benchmarks saturate, and above human capability, examiners may not know which tasks are both hard and verifiable. We argue that this difficulty is inherent to absolute-scale evaluation and propose a new paradigm based on relative measurement in which models generate public challenges that separate other systems. Aggregating these outcomes yields an adversarial psychometric rating system that can scale with the systems being measured. We describe practical protocols that reduce incentives for private-information attacks, support judge-free adjudication, and naturally scale with agent capabilities. We instantiate the framework across verifiable and open-ended, non-verifiable domains, illustrating how model-generated evaluation can continue to measure systems beyond the human frontier.

Noam Koren, Rafael Moschopoulos, Kira Radinsky et al. · princeton

Partial differential equations (PDEs) govern complex systems, yet neural operators often struggle to efficiently capture the long-range, nonlocal interactions inherent in their solution maps. We introduce Spectral Filtering Operator (SFO), a neural operator that parameterizes integral kernels using the Universal Spectral Basis (USB), a fixed, global orthonormal basis derived from the eigenmodes of the Hilbert matrix in spectral filtering theory. Motivated by our theoretical finding that the discrete Green's functions of shift-invariant PDE discretizations exhibit spatial Linear Dynamical System (LDS) structure, we prove that these kernels admit compact approximations in the USB. By learning only the spectral coefficients of rapidly decaying eigenvalues, SFO achieves a highly efficient representation. Across six benchmarks, including reaction-diffusion, fluid dynamics, and 3D electromagnetics, SFO achieves state-of-the-art accuracy, reducing error by up to 40% relative to strong baselines while using substantially fewer parameters.