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Found 21 papers, 2 papers with code
Assemblies of neurons learn to classify well-separated distributions
Here we present such a mechanism, and prove rigorously that, for simple classification problems defined on distributions of labeled assemblies, a new assembly representing each class can be reliably formed in response to a few stimuli from the class; this assembly is henceforth reliably recalled in response to new stimuli from the same class.
Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space
We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in very high dimension, upwards of 100, 000, can be sampled efficiently $\textit{in practice}$.
Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation
A key ingredient of our analysis is a proof of an analog of the KLS conjecture for Gibbs distributions over manifolds.
Max vs Min: Tensor Decomposition and ICA with nearly Linear Sample Complexity
We present a simple, general technique for reducing the sample complexity of matrix and tensor decomposition algorithms applied to distributions.
Unsupervised Learning through Prediction in a Model of Cortex
We show that PJOIN can be implemented in Valiant's model.
Algorithmic Theory of ODEs and Sampling from Well-conditioned Logconcave Densities
We apply this to the sampling problem to obtain a nearly linear implementation of HMC for a broad class of smooth, strongly logconcave densities, with the number of iterations (parallel depth) and gradient evaluations being $\mathit{polylogarithmic}$ in the dimension (rather than polynomial as in previous work).
Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices
We also prove convergence guarantees in R\'enyi divergence of order $q > 1$ assuming the limit of ULA satisfies either the log-Sobolev or Poincar\'e inequality.
Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions
We study Hamiltonian Monte Carlo (HMC) for sampling from a strongly logconcave density proportional to $e^{-f}$ where $f:\mathbb{R}^d \to \mathbb{R}$ is $\mu$-strongly convex and $L$-smooth (the condition number is $\kappa = L/\mu$).
The Communication Complexity of Optimization
We first resolve the randomized and deterministic communication complexity in the point-to-point model of communication, showing it is $\tilde{\Theta}(d^2L + sd)$ and $\tilde{\Theta}(sd^2L)$, respectively.
Robustly Learning Mixtures of $k$ Arbitrary Gaussians
We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions.
The Mirror Langevin Algorithm Converges with Vanishing Bias
The Mirror Langevin Diffusion (MLD) is a sampling analogue of mirror flow in continuous time, and it has nice convergence properties under log-Sobolev or Poincare inequalities relative to the Hessian metric, as shown by Chewi et al. (2020).
Provable Lifelong Learning of Representations
We prove that for any desired accuracy on all tasks, the dimension of the representation remains close to that of the underlying representation.
How and When Random Feedback Works: A Case Study of Low-Rank Matrix Factorization
We also show that FA can be far from optimal when $r < \mbox{rank}(Y)$.
Convergence of the Riemannian Langevin Algorithm
We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution with density $\nu$ with respect to the natural measure on a manifold with metric $g$.
Constant-Factor Approximation Algorithms for Socially Fair $k$-Clustering
We study approximation algorithms for the socially fair $(\ell_p, k)$-clustering problem with $m$ groups, whose special cases include the socially fair $k$-median ($p=1$) and socially fair $k$-means ($p=2$) problems.
Condition-number-independent convergence rate of Riemannian Hamiltonian Monte Carlo with numerical integrators
We show that for distributions in the form of $e^{-\alpha^{\top}x}$ on a polytope with $m$ constraints, the convergence rate of a family of commonly-used integrators is independent of $\left\Vert \alpha\right\Vert _{2}$ and the geometry of the polytope.
Beyond Moments: Robustly Learning Affine Transformations with Asymptotically Optimal Error
We present a polynomial-time algorithm for robustly learning an unknown affine transformation of the standard hypercube from samples, an important and well-studied setting for independent component analysis (ICA).
Sampling with Barriers: Faster Mixing via Lewis Weights
We introduce a hybrid of the Lewis weights barrier and the standard logarithmic barrier and prove that the mixing rate for the corresponding RHMC is bounded by $\tilde O(m^{1/3}n^{4/3})$, improving on the previous best bound of $\tilde O(mn^{2/3})$ (based on the log barrier).
Computation with Sequences in a Model of the Brain
Here we show that, in the same model, time can be captured naturally as precedence through synaptic weights and plasticity, and, as a result, a range of computations on sequences of assemblies can be carried out.
Gaussian Cooling and Dikin Walks: The Interior-Point Method for Logconcave Sampling
The Dikin walk uses a local metric defined by a self-concordant barrier for linear constraints.
Calibrated Language Models Must Hallucinate
For "arbitrary" facts whose veracity cannot be determined from the training data, we show that hallucinations must occur at a certain rate for language models that satisfy a statistical calibration condition appropriate for generative language models.
