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We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Reversible logic represents the basis for many emerging technologies and has recently been intensively studied. However, most of the Boolean functions of practical interest are irreversible and must be embedded into a reversible function…

Metric embedding is a powerful tool used extensively in mathematics and computer science. We devise a new method of using metric embeddings recursively, which turns out to be particularly effective in $\ell_p$ spaces, $p>2$, yielding…

We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…

We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…

Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on…

Traditional neural word embeddings are usually dependent on a richer diversity of vocabulary. However, the language models recline to cover major vocabularies via the word embedding parameters, in particular, for multilingual language…

This paper presents the derivation of an executable Krivine abstract machine from a small step interpreter for the simply typed lambda calculus in the dependently typed programming language Agda.

A restricted Boltzmann machine (RBM) is a two-layer neural network with shared weights and has been extensively studied for dimensionality reduction, data representation and recommendation systems in the literature. The traditional RBM…

Large language models route every input through a learned embedding table of shape |V| x d_model, consuming hundreds of millions to billions of trainable parameters at frontier scale. We introduce Kronecker Embeddings, a deterministic…

By quantizing network weights and activations to low bitwidth, we can obtain hardware-friendly and energy-efficient networks. However, existing quantization techniques utilizing the straight-through estimator and piecewise constant…

Reconstruction based subspace clustering methods compute a self reconstruction matrix over the samples and use it for spectral clustering to obtain the final clustering result. Their success largely relies on the assumption that the…

Search-based dialog models typically re-encode the dialog history at every turn, incurring high cost. Curved Contrastive Learning, a representation learning method that encodes relative distances between utterances into the embedding space…

Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous…

Motivated by the increasing shift to multicore computers, recent work has developed language support for responsive parallel applications that mix compute-intensive tasks with latency-sensitive, usually interactive, tasks. These…

Vector multiplication is a fundamental operation for AI acceleration, responsible for over 85% of computational load in convolution tasks. While essential, these operations are primary drivers of area, power, and delay in modern datapath…

The Krivine machine is an abstract machine implementing the linear head reduction of lambda-calculus. Ehrhard and Regnier gave a resource sensitive version returning the annotated form of a lambda-term accounting for the resources used by…

Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…

This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental…