Related papers: Two Decreasing Measures for Simply Typed Lambda-Te…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
Large language models (LLMs) must balance diversity and creativity against logical coherence in open-ended generation. Existing truncation-based samplers are effective but largely heuristic, relying mainly on probability mass and entropy…
We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (``qubits''). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of…
This paper shows that a wide class of effective learning rules -- those that improve a scalar performance measure over a given time window -- can be rewritten as natural gradient descent with respect to a suitably defined loss function and…
The subrank of tensors is a measure of how much a tensor can be ''diagonalized''. This parameter was introduced by Strassen to study fast matrix multiplication algorithms in algebraic complexity theory and is closely related to many central…
Let M be a compact spin manifold with a smooth action of the n-torus. Connes and Landi constructed theta-deformations M_{theta} of M, parameterized by n by n real skew-symmetric matrices theta. The M_{theta}'s together with the canonical…
John Tromp introduced the so-called 'binary lambda calculus' as a way to encode lambda terms in terms of binary words. Later, Grygiel and Lescanne conjectured that the number of binary lambda terms with $m$ free indices and of size $n$…
The act of measurement on a quantum state is supposed to "collapse" the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside…
The notion of collapse is discussed and refined within the Two-State-Vector Formalism (TSVF). We show how a definite result of a measurement can be fully determined when considering specific forward and backward-evolving quantum states.…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most…
Selecting an appropriate evaluation metric for classifiers is crucial for model comparison, parameter optimization, and deployment decisions, yet there is no consensus on a broadly accepted evaluation paradigm explicitly aligned with Total…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
In this work we consider translation-bounded measures over a locally compact Abelian group $\mathbb{G}$, with particular interest for their so-called diffraction. Given such a measure $\Lambda$, its diffraction $\widehat{\gamma}$ is another…
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…
Solutions to a wide variety of transcendental equations can be expressed in terms of the Lambert $\mathrm{W}$ function. The $\mathrm{W}$ function, occurring frequently in applications, is a non-elementary, but now standard mathematical…
Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measures are sensitive to such varying weights. We propose a new…
A semi-measure is a generalization of a probability measure obtained by relaxing the additivity requirement to super-additivity. We introduce and study several randomness notions for left-c.e. semi-measures, a natural class of effectively…
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy…
We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability measure. This provides a refined and unified framework for the…