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.
Language models allocate information storage, not collapsing into uniform representations.
UMAP connects to Information Geometry principles.
This paper extends link invariants using functors on nanophrases.
PC-GAIN improves GAIN's imputation by incorporating category information.
GRU-PFG model extracts inter-stock correlations from stock factors using graph neural networks.
We prove that a positive allowable Lefschetz fibration, PALF in short, admits a structure of exact Lefschetz fibration in the sense of Seidel \cite{Se08}. If the two-fold first Chern class of the total space is zero, we obtain the Fukaya-Seidel category. We prove that the derived Fukaya-Seidel category of PALF is indep…
This paper upgrades instanton TQFT to infinity-categories for better simplification.
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…
MILCCI integrates labels across categories for better understanding of multi-trial data.
In this paper, we model dependence between operational risks by allowing risk profiles to evolve stochastically in time and to be dependent. This allows for a flexible correlation structure where the dependence between frequencies of different risk categories and between severities of different risk categories as well …
Attribute-aware CF models aims at rating prediction given not only the historical rating from users to items, but also the information associated with users (e.g. age), items (e.g. price), or even ratings (e.g. rating time). This paper surveys works in the past decade developing attribute-aware CF systems, and discover…
Statistical models usually require vector representations of categorical variables, using for instance one-hot encoding. This strategy breaks down when the number of categories grows, as it creates high-dimensional feature vectors. Additionally, for string entries, one-hot encoding does not capture information in their…
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…
We propose a method based on finite mixture models for classifying a set of observations into number of different categories. In order to demonstrate the method, we show how the component densities for the mixture model can be derived by using the maximum entropy method in conjunction with conservation of Pythagorean m…
Verification determines whether two samples belong to the same class or not, and has important applications such as face and fingerprint verification, where thousands or millions of categories are present but each category has scarce labeled examples, presenting two major challenges for existing deep learning models. W…
Given a dataset of careers and incomes, how large a difference of income between any pair of careers would be? Given a dataset of travel time records, how long do we need to spend more when choosing a public transportation mode instead of to travel? In this paper, we propose a framework that is able to infer or…
Online social platforms have been the battlefield of users with different emotions and attitudes toward each other in recent years. While sexism has been considered as a category of hateful speech in the literature, there is no comprehensive definition and category of sexism attracting natural language processing techn…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (…
Representation stability is a theory describing a way in which a sequence of representations of different groups is related, and essentially contains a finite amount of information. Starting with Church-Ellenberg-Farb's theory of -modules describing sequences of representations of the symmetric groups, we now have …
In this paper we suggest a new general formalism for studying the invariants of polyhedra and manifolds comming from the theory of von Neumann algebras. First, we examine generality in which one may apply the construction of the extended abelian category, which was suggested in the previous publications of the author, …
This paper proposes a zero-shot learning approach for audio classification based on the textual information about class labels without any audio samples from target classes. We propose an audio classification system built on the bilinear model, which takes audio feature embeddings and semantic class label embeddings as…
Deep learning methods improve subsurface flow modeling efficiency.
GAME improves matrix completion by considering subgroup-specific latent structures.
Informally, -manifolds are 'manifolds' with -graded coordinates and a sign rule determined by the standard scalar product of their -degrees. Such manifolds can be understood in a sheaf-theoretic framework, as supermanifolds can, but with significant differences, in par…
Abstract: New geometric incarnation of isomonodromy functors.
We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provi…
We give a simple proof of Lee's result from [Adv. Math. 179 (2005) 554-586; arXiv:math.GT/0210213], that the dimension of the Lee variant of the Khovanov homology of a c-component link is 2^c, regardless of the number of crossings. Our method of proof is entirely local and hence we can state a Lee-type theorem for tang…
Studies amenable category's monotonicity and its relation to topological complexity.
Even in the absence of any explicit semantic annotation, vast collections of audio recordings provide valuable information for learning the categorical structure of sounds. We consider several class-agnostic semantic constraints that apply to unlabeled nonspeech audio: (i) noise and translations in time do not change t…
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…
Skein theory classifies UFCs with specific fusion rules.
Formulates a new connection between topological and geometric categories.
In recent years, air traffic communication data has become easy to access, enabling novel research in many fields. Exploiting this new data source, a wide range of applications have emerged, from weather forecasting to stock market prediction, or the collection of information about military and government movements. Ty…
Paper proposes redundancy-free features for zero-shot object recognition.
Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently large dimension are isomorphic in the given category. This paper studies such questi…
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 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.
Cone structures in quantum field theory linked to information geometry.
Spider category comparison proves equivalence to Sikora's quotient category.
The consultative papers for the Basel II Accord require rating systems to provide a ranking of obligors in the sense that the rating categories indicate the creditworthiness in terms of default probabilities. As a consequence, the default probabilities ought to present a monotonous function of the ordered rating catego…
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…
Develops a new volatility model for prediction markets.
Develops a new volatility model for prediction markets.
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…