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We prove the Stability Property for the call-by-value $\lambda$-calculus (CbV in the following). This result states necessary conditions under which the contexts of the CbV $\lambda$-calculus commute with intersections of approximants. This…
Reversible distributed programs have the ability to abort unproductive computation paths and backtrack, while unwinding communication that occurred in the aborted paths. While it is natural to assume that reversibility implies full state…
Training Convolutional Neural Networks (CNN) is a resource intensive task that requires specialized hardware for efficient computation. One of the most limiting bottleneck of CNN training is the memory cost associated with storing the…
Reversible computation has been recognised as a potential solution to the technological bottleneck in the future of computing machinery. Rolf Landauer determined the lower limit for power dissipation in computation and noted that…
Landauer-B\"uttiker formula describes the electronic quantum transports in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations.…
Word embeddings are commonly used as a starting point in many NLP models to achieve state-of-the-art performances. However, with a large vocabulary and many dimensions, these floating-point representations are expensive both in terms of…
We introduce a novel cost aggregation network, dubbed Volumetric Aggregation with Transformers (VAT), to tackle the few-shot segmentation task by using both convolutions and transformers to efficiently handle high dimensional correlation…
In this report we define an encoding of Levys call-by-push-value lambda-calculus (CBPV) in the pi-calculus, and prove that our encoding is both sound and complete. We present informal (by-hand) proofs of soundness, completeness, and all…
We show in this article that uncomputability is also a relative property of subrecursive classes built on a recursive relative incompressible function, which acts as a higher-order "yardstick" of irreducible information for the respective…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
In this paper, we study an efficient algorithm for constructing point sets underlying quasi-Monte Carlo integration rules for weighted Korobov classes. The algorithm presented is a reduced fast component-by-component digit-by-digit…
Reversible simulation of irreversible algorithms is analyzed in the stylized form of a `reversible' pebble game. While such simulations incur little overhead in additional computation time, they use a large amount of additional memory space…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
Despite recent advances in architectures for mobile devices, deep learning computational requirements remains prohibitive for most embedded devices. To address that issue, we envision sharing the computational costs of inference between…
The quantum and reversible paradigm merges the principles of quantum mechanics and reversible computation to enable information-preserving processing. It supports next-generation computing architectures that provide improved scalability and…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz…
This paper studies the strength of embedding Call-by-Name ({\tt dCBN}) and Call-by-Value ({\tt dCBV}) into a unifying framework called the Bang Calculus ({\tt dBANG}). These embeddings enable establishing (static and dynamic) properties of…
Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…