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A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…
The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact…
Language-integrated query techniques have been explored in a number of different language designs. We consider two different, type-safe approaches employed by Links and F#. Both approaches provide rich dynamic query generation capabilities,…
Dependent types provide a lightweight and modular means to integrate programming and formal program verification. In particular, the types of programs written in dependently typed programming languages (Agda, Idris, F*, etc.) can be used to…
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type…
Text Simplification improves the readability of sentences through several rewriting transformations, such as lexical paraphrasing, deletion, and splitting. Current simplification systems are predominantly sequence-to-sequence models that…
We present an efficient multi-accuracy algorithm for the computations of a set of special functions of a complex argument, z=x+iy. These functions include the complex probability function w(z), and closely related functions such as the…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…
Fully-Homomorphic Encryption (FHE) offers powerful capabilities by enabling secure offloading of both storage and computation, and recent innovations in schemes and implementations have made it all the more attractive. At the same time, FHE…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
Semantic parsing has made significant progress, but most current semantic parsers are extremely slow (CKY-based) and rather primitive in representation. We introduce three new techniques to tackle these problems. First, we design the first…
Equation-based modelling is a powerful approach to tame the complexity of large-scale simulation problems. Equation-based tools automatically translate models into imperative languages. When confronted with nowadays' problems, however, well…
This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…
Jay and Given-Wilson have recently introduced the Factorisation (or SF-) calculus as a minimal fundamental model of intensional computation. It is a combinatory calculus containing a special combinator, F, which is able to examine the…
Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
Economic complexity algorithms aim to uncover the hidden capabilities that drive economic systems. Here, we present a fundamental reinterpretation of two of these algorithms, the Economic Complexity Index (ECI) and the Economic Fitness and…