133 citations · 198 across the 12 of their papers we have counts for
4 papers · 1 filter
Stability of Measure-to-Measure Transformers on Sub-Gaussian Data
Frank Cole, Nicholas H. Nelsen, Takashi Furuya
Transformers have exhibited impressive empirical success across various domains, but their theoretical foundations remain less developed. This work constitutes a mathematical study…
Universal Approximation of Measure-to-Measure Operators by Pushforwards
Takashi Furuya, Nicholas H. Nelsen, Frank Cole
Many learning tasks map an input distribution to an output distribution. A natural way to model such an operator is to transform each input sample using a continuous function that…
One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators
Panos Tsimpos, Edoardo Calvello, Ayoub Belhadji +1
Probabilistic conditioning is concerned with the identification of a distribution of a random variable given a random variable . It is a cornerstone of scientific and engine…
A short tour of operator learning theory: Convergence rates, statistical limits, and open questions
Simone Brugiapaglia, Nicola Rares Franco, Nicholas H. Nelsen
This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical…