arXiv subjects

Chris Li

Publications and source records attributed to Chris Li.

3 recordsLinked to original sources

arXiv2026

Topological Field Theories and the Algebraic Structures of the Two-Sphere

We give two presentations for bordisms of $S^2$ in the 3-dimensional oriented bordism category $\operatorname{Cob}(3) $, encoding the algebraic structures on $S^2$. After passing through topological field theories, we define two kinds of monoids which we call P-monoids and L-monoids. In addition to both being commutative Frobenius monoids, P-monoids are equipped with a class of endomorphisms while L-monoids are equipped with a class of unit morphisms, all of which are labelled by closed oriented irreducible prime 3-manifolds. They turn out to be equivalent. The new prime structures satisfy some countable relations with the commutative Frobenius structure, the most notable of which we call "legs relations." We then restrict to the setting of algebras and show that the legs relations place strong constraints on the new prime endomorphisms which forces them to act by multiplications by prime units, rendering the additional prime structures remarkably simple. We also propose an $\infty$-operad which encodes these prime structures and contains the $\infty$-little 3-cube operad as a sub-operad.% We briefly discuss the relations between P/L-algebras and J-algebras which classify 3-dimensional TFTs.

math.AT↗

arXiv2025

A model of composite gravity with Pauli-Villars regulators

We revisit a model of composite gravity, in the form of a reparametrization invariant, non-polynomial, metric-independent action for scalar fields. Previously, the emergence of a composite massless spin 2 particle, the graviton, was demonstrated by analyzing a two-into-two scalar scattering amplitude. Working in the limit of a large number of physical scalars and using dimensional regularization, it was shown that the scattering amplitude had a pole corresponding to a graviton exchange, provided that a certain fine-tuning was implemented; the Planck mass was determined as a function of the dimensional regularization parameter and a mass scale. Here we demonstrate that the presence of the composite graviton is a robust feature of this model and not an artefact of the choice of regulator, by replacing dimensional regularization with Pauli-Villars fields. The presence of the massless graviton is conditioned by a similar fine-tuning as before. This is arguably a more physical regularization, since the Planck mass now depends on the specifics of the Pauli-Villars regulator fields, e.g. their mass as well as their multiplicity.

hep-th↗

arXiv2017

Modeling of the Latent Embedding of Music using Deep Neural Network

While both the data volume and heterogeneity of the digital music content is huge, it has become increasingly important and convenient to build a recommendation or search system to facilitate surfacing these content to the user or consumer community. Most of the recommendation models fall into two primary species, collaborative filtering based and content based approaches. Variants of instantiations of collaborative filtering approach suffer from the common issues of so called "cold start" and "long tail" problems where there is not much user interaction data to reveal user opinions or affinities on the content and also the distortion towards the popular content. Content-based approaches are sometimes limited by the richness of the available content data resulting in a heavily biased and coarse recommendation result. In recent years, the deep neural network has enjoyed a great success in large-scale image and video recognitions. In this paper, we propose and experiment using deep convolutional neural network to imitate how human brain processes hierarchical structures in the auditory signals, such as music, speech, etc., at various timescales. This approach can be used to discover the latent factor models of the music based upon acoustic hyper-images that are extracted from the raw audio waves of music. These latent embeddings can be used either as features to feed to subsequent models, such as collaborative filtering, or to build similarity metrics between songs, or to classify music based on the labels for training such as genre, mood, sentiment, etc.

cs.SD↗