Vasudevan Srinivas
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View article: The Vizier Gaussian Process Bandit Algorithm
The Vizier Gaussian Process Bandit Algorithm Open
Google Vizier has performed millions of optimizations and accelerated numerous research and production systems at Google, demonstrating the success of Bayesian optimization as a large-scale service. Over multiple years, its algorithm has b…
View article: Fast Approximate Determinants Using Rational Functions
Fast Approximate Determinants Using Rational Functions Open
We show how rational function approximations to the logarithm, such as $\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$, can be turned into fast algorithms for approximating the determinant of a very large matrix. We empirically demonstrate that …
View article: Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces
Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces Open
Let $k$ be a field and let $\text{GW}(k)$ be the Grothendieck-Witt ring of virtual non-degenerate symmetric bilinear forms over $k$. We develop methods for computing the quadratic Euler characteristic $\chi(X/k)\in \text{GW}(k)$ for $X$ a …
View article: Fundamental groups of proper varieties are finitely presented
Fundamental groups of proper varieties are finitely presented Open
It was proven in [1], that the étale fundamental group of a connected smooth projective variety over an algebraically closed field is topologically finitely presented. In this note, we extend this result to all connected proper schemes ov…
View article: An obstruction to lifting to characteristic 0
An obstruction to lifting to characteristic 0 Open
We introduce a new obstruction to lifting smooth proper varieties from characteristic p > 0 to characteristic 0. It is based on Grothendieck's specialization homomorphism and the resulting discrete finiteness properties of etale fundamenta…
View article: Fundamental groups of proper varieties are finitely presented
Fundamental groups of proper varieties are finitely presented Open
It was recently proven by Esnault, Shusterman and the second named author, that the étale fundamental group of a connected smooth projective variety over an algebraically closed field $k$ is finitely presented. In this note, we extend this…
View article: Finite presentation of the tame fundamental group
Finite presentation of the tame fundamental group Open
View article: An obstruction to lifting to characteristic $0$
An obstruction to lifting to characteristic $0$ Open
We introduce a new obstruction to lifting smooth proper varieties in characteristic $p>0$ to characteristic $0$. It is based on Grothendieck's specialization homomorphism and the resulting discrete finiteness properties of étale fundamenta…
View article: Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces
Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces Open
Let $k$ be a field and let $\text{GW}(k)$ be the Grothendieck-Witt ring of virtual non-degenerate symmetric bilinear forms over $k$. We develop methods for computing the quadratic Euler characteristic $χ(X/k)\in \text{GW}(k)$ for $X$ a smo…
View article: Bounding ramification by covers and curves
Bounding ramification by covers and curves Open
We prove that $\bar {\mathbb Q}_\ell$-local systems of bounded rank and ramification on a smooth variety $X$ defined over an algebraically closed field $k$ of characteristic $p\neq \ell$ are tamified outside of codimension $2$ by a finite …
View article: MCMC Should Mix: Learning Energy-Based Model with Neural Transport Latent Space MCMC
MCMC Should Mix: Learning Energy-Based Model with Neural Transport Latent Space MCMC Open
Learning energy-based model (EBM) requires MCMC sampling of the learned model as an inner loop of the learning algorithm. However, MCMC sampling of EBMs in high-dimensional data space is generally not mixing, because the energy function, w…
View article: Learning Energy-based Model with Flow-based Backbone by Neural Transport MCMC
Learning Energy-based Model with Flow-based Backbone by Neural Transport MCMC Open
Learning energy-based model (EBM) requires MCMC sampling of the learned model as the inner loop of the learning algorithm. However, MCMC sampling of EBM in data space is generally not mixing, because the energy function, which is usually p…
View article: FunMC: A functional API for building Markov Chains
FunMC: A functional API for building Markov Chains Open
Constant-memory algorithms, also loosely called Markov chains, power the vast majority of probabilistic inference and machine learning applications today. A lot of progress has been made in constructing user-friendly APIs around these algo…
View article: NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport Open
Hamiltonian Monte Carlo is a powerful algorithm for sampling from difficult-to-normalize posterior distributions. However, when the geometry of the posterior is unfavorable, it may take many expensive evaluations of the target distribution…
View article: A note on fierce ramification
A note on fierce ramification Open
We show that bounding ramification at infinity bounds fierce ramification. This answers positively a question of Deligne posed to the first named author.
View article: Simple, Distributed, and Accelerated Probabilistic Programming
Simple, Distributed, and Accelerated Probabilistic Programming Open
We describe a simple, low-level approach for embedding probabilistic programming in a deep learning ecosystem. In particular, we distill probabilistic programming down to a single abstraction---the random variable. Our lightweight implemen…
View article: Simple, Distributed, and Accelerated Probabilistic Programming
Simple, Distributed, and Accelerated Probabilistic Programming Open
We describe a simple, low-level approach for embedding probabilistic programming in a deep learning ecosystem. In particular, we distill probabilistic programming down to a single abstraction—the random variable. Our lightweight implementa…
View article: TensorFlow Distributions
TensorFlow Distributions Open
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks fo…
View article: A relative version of Gieseker's problem on stratifications in characteristic $p>0$
A relative version of Gieseker's problem on stratifications in characteristic $p>0$ Open
We prove that the vanishing of the functoriality morphism for the étale fundamental group between smooth projective varieties over an algebraically closed field of characteristic $p>0$ forces the same property for the fundamental groups of…
View article: A relative version of Gieseker's problem on stratifications in characteristic $p>0$
A relative version of Gieseker's problem on stratifications in characteristic $p>0$ Open
We prove that the vanishing of the functoriality morphism for the \'etale fundamental group between smooth projective varieties over an algebraically closed field of characteristic $p>0$ forces the same property for the fundamental groups …
View article: Nilpotence of Frobenius action and the Hodge filtration on local cohomology
Nilpotence of Frobenius action and the Hodge filtration on local cohomology Open
An $F$-nilpotent local ring is a local ring $(R, \mathfrak{m})$ of prime characteristic defined by the nilpotence of the Frobenius action on its local cohomology modules $H^i_{\mathfrak{m}}(R)$. A singularity in characteristic zero is said…