Search Results for author: Santosh S. Vempala

Found 21 papers, 2 papers with code

Calibrated Language Models Must Hallucinate

no code implementations24 Nov 2023 Adam Tauman Kalai, Santosh S. Vempala

Recent language models generate false but plausible-sounding text with surprising frequency.

Hallucination

Gaussian Cooling and Dikin Walks: The Interior-Point Method for Logconcave Sampling

no code implementations24 Jul 2023 Yunbum Kook, Santosh S. Vempala

The Dikin walk uses a local metric defined by a self-concordant barrier for linear constraints.

Computation with Sequences in a Model of the Brain

no code implementations6 Jun 2023 Max Dabagia, Christos H. Papadimitriou, Santosh S. Vempala

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.

Mathematical Proofs Memorization +2

Sampling with Barriers: Faster Mixing via Lewis Weights

no code implementations1 Mar 2023 Khashayar Gatmiry, Jonathan Kelner, Santosh S. Vempala

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).

Beyond Moments: Robustly Learning Affine Transformations with Asymptotically Optimal Error

no code implementations23 Feb 2023 He Jia, Pravesh K . Kothari, Santosh S. Vempala

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).

Condition-number-independent convergence rate of Riemannian Hamiltonian Monte Carlo with numerical integrators

no code implementations13 Oct 2022 Yunbum Kook, Yin Tat Lee, Ruoqi Shen, Santosh S. Vempala

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.

Constant-Factor Approximation Algorithms for Socially Fair $k$-Clustering

no code implementations22 Jun 2022 Mehrdad Ghadiri, Mohit Singh, Santosh S. Vempala

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.

Clustering

Convergence of the Riemannian Langevin Algorithm

no code implementations22 Apr 2022 Khashayar Gatmiry, Santosh S. Vempala

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 $g$.

Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space

1 code implementation3 Feb 2022 Yunbum Kook, Yin Tat Lee, Ruoqi Shen, Santosh S. Vempala

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 $\textit{in practice}$.

Provable Lifelong Learning of Representations

no code implementations27 Oct 2021 Xinyuan Cao, Weiyang Liu, Santosh S. Vempala

We prove that for any desired accuracy on all tasks, the dimension of the representation remains close to that of the underlying representation.

Continual Learning

Assemblies of neurons learn to classify well-separated distributions

1 code implementation7 Oct 2021 Max Dabagia, Christos H. Papadimitriou, Santosh S. Vempala

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.

The Mirror Langevin Algorithm Converges with Vanishing Bias

no code implementations24 Sep 2021 Ruilin Li, Molei Tao, Santosh S. Vempala, Andre Wibisono

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).

Robustly Learning Mixtures of $k$ Arbitrary Gaussians

no code implementations3 Dec 2020 Ainesh Bakshi, Ilias Diakonikolas, He Jia, Daniel M. Kane, Pravesh K. Kothari, Santosh S. Vempala

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.

Clustering Tensor Decomposition

The Communication Complexity of Optimization

no code implementations13 Jun 2019 Santosh S. Vempala, Ruosong Wang, David P. Woodruff

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.

Distributed Optimization

Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions

no code implementations7 May 2019 Zongchen Chen, Santosh S. Vempala

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 $\kappa = L/\mu$).

Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices

no code implementations NeurIPS 2019 Santosh S. Vempala, Andre Wibisono

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.

Algorithmic Theory of ODEs and Sampling from Well-conditioned Logconcave Densities

no code implementations15 Dec 2018 Yin Tat Lee, Zhao Song, Santosh S. Vempala

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).

Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation

no code implementations17 Oct 2017 Yin Tat Lee, Santosh S. Vempala

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

no code implementations9 Dec 2014 Santosh S. Vempala, Ying Xiao

We present a simple, general technique for reducing the sample complexity of matrix and tensor decomposition algorithms applied to distributions.

Tensor Decomposition

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