Related papers: Pairwise Well-Formed Modes and Transformations

Natural language exhibits statistical dependencies at a wide range of scales. For instance, the mutual information between words in natural language decays like a power law with the temporal lag between them. However, many statistical…

Words can be represented by composing the representations of subword units such as word segments, characters, and/or character n-grams. While such representations are effective and may capture the morphological regularities of words, they…

The goal of this article is to clarify the relationship between the topos of triads and the neo-Riemannian PLR-group. To do this, we first develop some theory of generalized interval systems: 1) we prove the well known fact that every pair…

There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…

Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…

Symmetric strongly shifted ideals are a class of monomial ideals which come equipped with an action of the symmetric group and are analogous to the well-studied class of strongly stable monomial ideals. In this paper we focus on algebraic…

Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed…

In this note, we consider discriminant forms that are given by the norm form of real quadratic fields and their induced Weil representations. We prove that there exists an isomorphism between the space of vector-valued modular forms for the…

The equable, Pythagorean and natural scales are built on the basis of a mathematical logic.

Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…

We investigate the Universe at the late stage of its evolution and inside the cell of uniformity 150-370 Mpc. We consider the Universe to be filled at these scales with dust like matter, a minimally coupled Galileon field and radiation. We…

We show that a class of previously defined maps, called self-dual and causal morphisms, form classical symmetries of Yang-Mills fields in four complex dimensions. These maps generalize conformal transformations, and admit a nonlocal…

Large language models (LLMs) take sequences of subwords as input, requiring them to effective compose subword representations into meaningful word-level representations. In this paper, we present a comprehensive set of experiments to probe…

The Spiral Model (SM) corresponds to a new class of kinetically constrained models introduced in joint works with D.S. Fisher [8,9]. They provide the first example of finite dimensional models with an ideal glass-jamming transition. This is…

We introduce a geometric and operator-theoretic formalism viewing optimization algorithms as discrete connections on a space of update operators. Each iterative method is encoded by two coupled channels-drift and diffusion-whose algebraic…

We use a hybrid Monte Carlo algorithm to simulate the shaking of spheres at different vibrational amplitudes, and find that spontaneous crystallisation occurs in specific dynamical regimes. Several crystallising transitions are typically…

Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…

The presence of skew quadrupole fields will linearly couple the x and y motions. The x and y motions can then be written as the sum of two normal modes >. This paper presents analytical perturbation theory results for the tunes of the…

The simplest toroidally compactified string theories exhibit a duality between large and small radii: compactification on a circle, for example, is invariant under R goes to 1/R. Compactification on more general Lorentzian lattices (i.e.…

We present three Lagrangian algebras in the modular 2-category associated to the 3+1D $\mathbb{Z}_2$ topological order and discuss their physical interpretations, connecting algebras with gapped boundary conditions, and interestingly, maps…