Related papers: Equilibrium Propagation Without Limits
We analyze the expressivity of a universal deep neural network that can be organized as a series of nested qubit rotations, accomplished by adjustable data re-uploads. While the maximal expressive power increases with the depth of the…
We propose a novel algorithm to solve the expectation propagation relaxation of Bayesian inference for continuous-variable graphical models. In contrast to most previous algorithms, our method is provably convergent. By marrying convergent…
We recast the finite-region analysis of Einstein's equations that underpins the ER=EPR program into the loop quantum gravity (LQG) framework. By translating curvature-energy uncertainty relations into holonomy-flux kinematics, and by…
Bayesian meta-learning enables robust and fast adaptation to new tasks with uncertainty assessment. The key idea behind Bayesian meta-learning is empirical Bayes inference of hierarchical model. In this work, we extend this framework to…
The Free Energy Principle (FEP) states that self-organizing systems must minimize variational free energy to persist, but the path from principle to implementable algorithm has remained unclear. We present a constructive proof that the FEP…
Approximate inference techniques are the cornerstone of probabilistic methods based on Gaussian process priors. Despite this, most work approximately optimizes standard divergence measures such as the Kullback-Leibler (KL) divergence, which…
Physics-informed neural solvers offer a promising route to model-based reinforcement learning in continuous time, where optimal feedback synthesis is governed by Hamilton--Jacobi--Bellman (HJB) equations. Practical implementations often…
Recent approximations to backpropagation (BP) have mitigated many of BP's computational inefficiencies and incompatibilities with biology, but important limitations still remain. Moreover, the approximations significantly decrease accuracy…
Mixture of linear regression is well studied in statistics and machine learning, where the data points are generated probabilistically using $k$ linear models. Algorithms like Expectation Maximization (EM) may be used to recover the ground…
The nearest-neighbor level-spacing distributions are a fundamental quantity of disordered systems and universal. It is well-known that extended and localized states of random Hermitian systems follow the Wigner-Dyson and the Poison…
Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…
We show that deep networks can be trained using Hebbian updates yielding similar performance to ordinary back-propagation on challenging image datasets. To overcome the unrealistic symmetry in connections between layers, implicit in…
Exceptional points (EPs) have been suggested for ultra-sensitive sensing because the eigenfrequency splitting grows as the nth-root of a perturbation, suggesting divergent responsivity. In ideal linear devices, however, this responsivity…
It is unclear how changing the learning rule of a deep neural network alters its learning dynamics and representations. To gain insight into the relationship between learned features, function approximation, and the learning rule, we…
A recent breakthrough in biologically-plausible normative frameworks for dimensionality reduction is based upon the similarity matching cost function and the low-rank matrix approximation problem. Despite clear biological interpretation,…
We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of…
We study the exponential convergence to the stationary state for nonequilibrium Langevin dynamics, by a perturbative approach based on hypocoercive techniques developed for equilibrium Langevin dynamics. The Hamiltonian and overdamped…
A family of discrete Schr\"{o}dinger equations with imaginary potentials $V(x)$ is studied. Inside the domain ${\cal D}$ of unitarity-compatible values of $V(x)$, the reality of all of the bound-state energies survives up to the…
Signal recovery from unitarily invariant measurements is investigated in this paper. A message-passing algorithm is formulated on the basis of expectation propagation (EP). A rigorous analysis is presented for the dynamics of the algorithm…
Generalized linear models (GLMs) arguably represent the standard approach for statistical regression beyond the Gaussian likelihood scenario. When Bayesian formulations are employed, the general absence of a tractable posterior distribution…