相关论文: Pairwise Well-Formed Modes and Transformations
Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many…
Many modifications of gravity introduce new scalar degrees of freedom, and in such theories matter fields typically couple to an effective metric that depends on both the true metric of spacetime and on the scalar field and its derivatives.…
Compositional understanding is crucial for human intelligence, yet it remains unclear whether contemporary vision models exhibit it. The dominant machine learning paradigm is built on the premise that scaling data and model sizes will…
We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…
We present new results for the SU(3) "sextet model" with two flavors transforming according to the two-index symmetric representation of the gauge group. The simulations are performed using unimproved Wilson fermions. We measure the meson…
We study the systems of scalar and spinor particles with mixing emitted by external classical sources. The particles wave functions exactly accounting for external sources are obtained directly from the Lorentz invariant wave equations in…
The neural architectures of language models are becoming increasingly complex, especially that of Transformers, based on the attention mechanism. Although their application to numerous natural language processing tasks has proven to be very…
Zipf's law is a paradigm describing the importance of different elements in communication systems, especially in linguistics. Despite the complexity of the hierarchical structure of language, music has in some sense an even more complex…
We consider classical dynamics of two real scalar fields within a model with the potential having a saddle point. The solitons of such model are field configurations that have the form of closed loops in the field space. We study the…
Large Language Models (LLMs) are becoming very popular and are used for many different purposes, including creative tasks in the arts. However, these models sometimes have trouble with specific reasoning tasks, especially those that involve…
Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on lines in PG($n,p$) or codes in the Grassmannian, to form automorphisms groups in the Grassmanian and in its codes. These automorphisms are…
Even with strong sequence models like Transformers, generating expressive piano performances with long-range musical structures remains challenging. Meanwhile, methods to compose well-structured melodies or lead sheets (melody + chords),…
Recently a new Lagrangian framework was introduced to describe interactions between scalar fields and relativistic perfect fluids. This allows two consistent generalizations of coupled quintessence models: non-vanishing pressures and a new…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
The presence of higher index saddles on a multidimensional potential energy surface is usually assumed to be of little significance in chemical reaction dynamics. Such a viewpoint requires careful reconsideration, thanks to elegant…
In (B-Gran, 2004), was given a categorical formulation of the Shifting Lemma which is a characterization of the Congruence Modular Varieties among all the variety of Universal Algebra, introduced in (Gumm, 1983). Starting from a…
Music is a structured and perceptually rich sequence of sounds in time, whose perception is shaped by the interplay of expectation and uncertainty about what comes next. Yet the uncertainty we infer from music depends on how the musical…
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
We analyze a modified $f(R)$ theory of gravity in the Palatini formulation, when an Holst term endowed with a dynamical Immirzi field is included. We study the basic features of the model, especially in view of liminating the torsion field…
A great number of deep learning based models have been recently proposed for automatic music composition. Among these models, the Transformer stands out as a prominent approach for generating expressive classical piano performance with a…