Related papers: Automatic Differentiation via Effects and Handlers…
Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate data can be highly expensive. Here, machine learning (ML) models can help to be data economic as they can be successfully constrained using the…
Automatic diagnosis (AD), a critical application of AI in healthcare, employs machine learning techniques to assist doctors in gathering patient symptom information for precise disease diagnosis. The Transformer-based method utilizes an…
We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…
We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation (AD). The concept emerges from deep learning but is not only limited to training…
Many problems in Physics and Chemistry are formulated as the minimization of a functional. Therefore, methods for solving these problems typically require differentiating maps whose input and/or output are functions -- commonly referred to…
Automatic differentiation (AD) is an essential primitive for machine learning programming systems. Tangent is a new library that performs AD using source code transformation (SCT) in Python. It takes numeric functions written in a syntactic…
Parameter identification for mechanistic Ordinary Differential Equation (ODE) models underpins prediction and control in several applications, yet remains a manual and labor-intensive process: datasets are noisy and partial, models can be…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…
We study the algebraic effects and handlers as a way to support decision-making abstractions in functional programs, whereas a user can ask a learning algorithm to resolve choices without implementing the underlying selection mechanism, and…
Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…
Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is well understood for many smooth problems but the…
In this note we derive the backward (automatic) differentiation (adjoint [automatic] differentiation) for an algorithm containing a conditional expectation operator. As an example we consider the backward algorithm as it is used in Bermudan…
The foundational theory of differentiation was developed as part of the original release of ACL2(r). In work reported at the last ACL2 Workshop, we presented theorems justifying the usual differentiation rules, including the chain rule and…
Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently,…
Argument component detection (ACD) is an important sub-task in argumentation mining. ACD aims at detecting and classifying different argument components in natural language texts. Historical annotations (HAs) are important features the…
For a real function, automatic differentiation is such a standard algorithm used to efficiently compute its gradient, that it is integrated in various neural network frameworks. However, despite the recent advances in using complex…
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow…
Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called…
Based on a class of associative algebras with zero-divisors which are called real-like algebras by us, we introduce a way of defining automatic differentiation and present different ways of doing automatic differentiation to compute the…