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We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
We propose a method that can generate an unambiguous description (known as a referring expression) of a specific object or region in an image, and which can also comprehend or interpret such an expression to infer which object is being…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
The proposed framework provides a general model of concurrent imperative programming. Programs are modeled as formal languages and concurrency as an interleaving (or shuffle) operator. This yields a simple and elegant algebra of programs.…
Stochastic MPECs have found increasing relevance for modeling a broad range of settings in engineering and statistics. Yet, there seem to be no efficient first/zeroth-order schemes equipped with non-asymptotic rate guarantees for resolving…
We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is…
We present modular implicits, an extension to the OCaml language for ad-hoc polymorphism inspired by Scala implicits and modular type classes. Modular implicits are based on type-directed implicit module parameters, and elaborate…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
Motivated by the advantages achieved by implicit analogue net for solving online linear equations, a novel implicit neural model is designed based on conventional explicit gradient neural networks in this letter by introducing a…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
Implicit deep learning prediction rules generalize the recursive rules of feedforward neural networks. Such rules are based on the solution of a fixed-point equation involving a single vector of hidden features, which is thus only…
We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
In this paper, we propose three novel models to enhance word embedding by implicitly using morphological information. Experiments on word similarity and syntactic analogy show that the implicit models are superior to traditional explicit…
The aim of the paper is to provide solid foundations for a programming paradigm natively supporting the creation and manipulation of cyclic data structures. To this end, we describe coFJ, a Java-like calculus where objects can be infinite…
I show that the general implicit-function problem (or parametrized fixed-point problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this…