Publications (17)
Higher Order Automatic Differentiation of Higher Order Functions
Mathieu Huot, Sam Staton, Matthijs Vákár
We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher-order language with algebraic data types and we character…
GradInf: Gradient Estimation as Probabilistic Inference
Gaurav Arya, Mathieu Huot, Moritz Schauer +2
Gradient estimation -- the task of computing the gradient of the expected value of a probabilistic program -- has diverse applications in scientific computing, but is notoriously d…
Efficient and Sound Differentiable Programming in a Functional Array-Processing Language
Amir Shaikhha, Mathieu Huot, Shabnam Ghasemirad +3
Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computi…
Towards Denotational Semantics of AD for Higher-Order, Recursive, Probabilistic Languages
Alexander K. Lew, Mathieu Huot, Vikash K. Mansinghka
Automatic differentiation (AD) aims to compute derivatives of user-defined functions, but in Turing-complete languages, this simple specification does not fully capture AD's behavi…
Quantum channels as a categorical completion
Mathieu Huot, Sam Staton
We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoida…
GenMatter: Perceiving Physical Objects with Generative Matter Models
Eric Li, Arijit Dasgupta, Yoni Friedman +5
Human visual perception offers valuable insights for understanding computational principles of motion-based scene interpretation. Humans robustly detect and segment moving entities…
Probabilistic Programming with Programmable Variational Inference
McCoy R. Becker, Alexander K. Lew, Xiaoyan Wang +4
Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less develo…
Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing
Mathieu Huot, Sam Staton, Matthijs Vákár
We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characte…
Differentiating Metropolis-Hastings to Optimize Intractable Densities
Gaurav Arya, Ruben Seyer, Frank Schäfer +7
We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers, allowing us to differentiate through probabilistic inference, even if the model has discrete…
Functional Collection Programming with Semi-Ring Dictionaries
Amir Shaikhha, Mathieu Huot, Jaclyn Smith +1
This paper introduces semi-ring dictionaries, a powerful class of compositional and purely functional collections that subsume other collection types such as sets, multisets, array…
SD: Differentiable Programming for Sparse Tensors
Amir Shaikhha, Mathieu Huot, Shideh Hashemian
Sparse tensors are prevalent in many data-intensive applications, yet existing differentiable programming frameworks are tailored towards dense tensors. This presents a significant…
PAP Spaces: Reasoning Denotationally About Higher-Order, Recursive Probabilistic and Differentiable Programs
Mathieu Huot, Alexander K. Lew, Vikash K. Mansinghka +1
We introduce a new setting, the category of PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is g…
ADEV: Sound Automatic Differentiation of Expected Values of Probabilistic Programs
Alexander K. Lew, Mathieu Huot, Sam Staton +1
Optimizing the expected values of probabilistic processes is a central problem in computer science and its applications, arising in fields ranging from artificial intelligence to o…
Compiling Structured Tensor Algebra
Mahdi Ghorbani, Mathieu Huot, Shideh Hashemian +1
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by d…
Universal Properties in Quantum Theory
Mathieu Huot, Sam Staton
We argue that notions in quantum theory should have universal properties in the sense of category theory. We consider the completely positive trace preserving (CPTP) maps, the basi…
Denotationally Correct, Purely Functional, Efficient Reverse-mode Automatic Differentiation
Mathieu Huot, Amir Shaikhha
Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize.…
GenSQL: A Probabilistic Programming System for Querying Generative Models of Database Tables
Mathieu Huot, Matin Ghavami, Alexander K. Lew +6
This article presents GenSQL, a probabilistic programming system for querying probabilistic generative models of database tables. By augmenting SQL with only a few key primitives f…