  Contemporary Artificial Intelligence (AI) stands on two legs: large training
data corpora and many-parameter artificial neural networks (ANNs). The data
corpora are needed to represent the complexity and heterogeneity of the world.
The role of the networks is less transparent due to the obscure dependence of
the network parameters and outputs on the training data and inputs. This raises
problems, ranging from technical-scientific to legal-ethical. We hypothesize
that a transparent approach to machine learning is possible without using
networks at all. By generalizing a parameter-free, statistically consistent
data interpolation method, which we analyze theoretically in detail, we develop
a network-free framework for AI incorporating generative modeling. We
demonstrate this framework with examples from three different disciplines -
ethology, control theory, and mathematics. Our generative Hilbert framework
applied to the trajectories of small groups of swimming fish outperformed
state-of-the-art traditional mathematical behavioral models and current
ANN-based models. We demonstrate pure data interpolation based control by
stabilizing an inverted pendulum and a driven logistic map around unstable
fixed points. Finally, we present a mathematical application by predicting
zeros of the Riemann Zeta function, achieving comparable performance as a
transformer network. We do not suggest that the proposed framework will always
outperform networks as over-parameterized networks can interpolate. However,
our framework is theoretically sound, transparent, deterministic, and parameter
free: remarkably, it does not require any compute-expensive training, does not
involve optimization, has no model selection, and is easily reproduced and
ported. We also propose an easily computed method of credit assignment based on
this framework, to help address ethical-legal challenges raised by generative
AI.
