  We unify $\textit{kernel density estimation}$ and $\textit{empirical Bayes}$
and address a set of problems in unsupervised learning with a geometric
interpretation of those methods, rooted in the $\textit{concentration of
measure}$ phenomenon. Kernel density is viewed symbolically as
$X\rightharpoonup Y$ where the random variable $X$ is smoothed to $Y=
X+N(0,\sigma^2 I_d)$, and empirical Bayes is the machinery to denoise in a
least-squares sense, which we express as $X \leftharpoondown Y$. A learning
objective is derived by combining these two, symbolically captured by $X
\rightleftharpoons Y$. Crucially, instead of using the original nonparametric
estimators, we parametrize $\textit{the energy function}$ with a neural network
denoted by $\phi$; at optimality, $\nabla \phi \approx -\nabla \log f$ where
$f$ is the density of $Y$. The optimization problem is abstracted as
interactions of high-dimensional spheres which emerge due to the concentration
of isotropic gaussians. We introduce two algorithmic frameworks based on this
machinery: (i) a "walk-jump" sampling scheme that combines Langevin MCMC
(walks) and empirical Bayes (jumps), and (ii) a probabilistic framework for
$\textit{associative memory}$, called NEBULA, defined \`{a} la Hopfield by the
$\textit{gradient flow}$ of the learned energy to a set of attractors. We
finish the paper by reporting the emergence of very rich "creative memories" as
attractors of NEBULA for highly-overlapping spheres.
