A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Generative model for morphisms in free categories learns from wiring diagrams.
It is proved that the category of simplicial complete bornological spaces over carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is also a monoidal model category with all cofibrant objects being flat. In particu…
TXtract extracts structured knowledge from thousands of product categories.
Paper proposes CNE-net to tackle incremental learning in (T)ACSA tasks.
In real world machine learning applications, testing data may contain some meaningful new categories that have not been seen in labeled training data. To simultaneously recognize new data categories and assign most appropriate category labels to the data actually from known categories, existing models assume the number…
Model for assembly map of bordism-invariant functors.
The paper discusses strictification and non-strictification of monoidal categories.
Cube category simplifies set modeling.
Model dynamic customer sensitivities across categories.
Language models allocate information storage, not collapsing into uniform representations.
Adversarial MoE learns category-specific models for product search.
The extension functors between categories of Cartan geometries can be used to define different categories of Cartan geometries with additional morphisms. The Cartan geometries modeled on skeletons can be used for the description of such categories of Cartan geometries and therefore we develop the theory of Cartan geome…
New bandit model for e-commerce with ordered categories.
Studies amenable category's monotonicity and its relation to topological complexity.
This paper shows vector bundles and differential bundles are equivalent in smooth manifolds.
To each oriented surface S, we associate a differential graded category Ko(S). The homotopy category Ho(Ko(S)) is a triangulated category which satisfies properties akin to those of the contact categories studied by K. Honda. These categories are also related to the algebraic contact categories of Y. Tian and to the bo…
It is known that every ribbon category with unimodality allows symmetrized -symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category . We define the mirror conjugate symmetry of -symbols instead and sho…
New smooth models for string groups defined in ∞-categories.
We consider the problem of learning soft assignments of items to categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity mat…
Study integrates attentional and spacing factors to improve category learning models.
This paper proposes a method for estimating consumer preferences among discrete choices, where the consumer chooses at most one product in a category, but selects from multiple categories in parallel. The consumer's utility is additive in the different categories. Her preferences about product attributes as well as her…
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract setting for differential geometry by axiomatizing key aspects of the subject which all…
Study homotopy sheaves on categories and their presheaves, proving descent properties.
The paper develops a framework for abstracting causal models using category theory.
Formulates a new connection between topological and geometric categories.
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study …
Localizes smooth spaces to study their homotopy properties.
Model structures on multicomplexes help study complex geometry.
Recent work on single-view 3D reconstruction shows impressive results, but has been restricted to a few fixed categories where extensive training data is available. The problem of generalizing these models to new classes with limited training data is largely open. To address this problem, we present a new model archite…
We continue the program of structural differential geometry that begins with the notion of a tangent category, an axiomatization of structural aspects of the tangent functor on the category of smooth manifolds. In classical geometry, having an affine structure on a manifold is equivalent to having a flat torsion-free c…
We realise Stroppel's extended arc algebra in the Fukaya-Seidel category of a natural Lefschetz fibration on the generic fiber of the adjoint quotient map on a type nilpotent slice with two Jordan blocks, and hence obtain a symplectic interpretation of certain parabolic two-block versions of Bernstein-Gelfan'd-Gelf…
We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs…
Novel -categories derived from gauge theories for manifold homologies.
We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.
The paper defines new TQFTs from non-semisimple categories and proves spherical categories are chromatic.
Spider category comparison proves equivalence to Sikora's quotient category.
We symmetrise neural networks for groups using Markov categories.
In principle, zero-shot learning makes it possible to train a recognition model simply by specifying the category's attributes. For example, with classifiers for generic attributes like \emph{striped} and \emph{four-legged}, one can construct a classifier for the zebra category by enumerating which properties it posses…
We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category structure drops down to the localization. In our construction the spaces of 1- …
We generalize the notion of monetary value measures developed with category theory in [Adachi, 2014] by extending their base category from the category \c{hi} to the category of probability spaces Prob introduced in [Adachi and Ryu, 2016].
ETQFTs created from non-semisimple modular categories.
Studies modules over a category of Jacobi diagrams in handlebodies.
We compare various different definitions of "the category of smooth objects". The definitions compared are due to Chen, Frölicher, Sikorski, Smith, and Souriau. The method of comparison is to construct functors between the categories that enable us to see how the categories relate to each other. This produces a diagram…
GRU-PFG model extracts inter-stock correlations from stock factors using graph neural networks.
We define a symmetric monoidal (4,3)-category with duals whose objects are certain enriched multi-fusion categories. For every modular tensor category , there is a self enriched multi-fusion category giving rise to an object of this symmetric monoidal (4,3)-category. We conjecture that the e…
DisCoPyro combines category theory with machine learning for program learning.
We show that once-extended anomalous 3-dimensional topological quantum field theories valued in the 2-category of k-linear categories are in canonical bijection with modular tensor categories equipped with a square root of the global dimension in each factor.
We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative modular categories, a class of ribbon categories which are modeled on representations…