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…
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48 results for “enriched categories”
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a f…
Quantizes Kähler manifolds using sheaves and differential operators.
problem Quantizing Kähler manifolds with sheaves and differential operators.
method Constructing a category enriched over sheaves of modules, defining quantizable morphisms, and showing equivalence to differential operator categories.
result Equivalence of quantized categories under certain conditions.
Novel cohomology theories for operadic algebras and spaces.
problem Formulating cohomology theories for operadic algebras.
method Using cotangent complex formalism and spectral Hochschild cohomology.
result Controlled cohomologies of operads and their algebras.
This work interprets supergravity as a super Cartan geometry linking it to Yang-Mills theory.
problem Geometric interpretation of supergravity and its relation to Yang-Mills theory.
method Using enriched categories and super Cartan geometries, the authors link supergravity to Yang-Mills theory.
result Non-extended D=4 supergravity naturally arises in this framework.
Spaces over BO are equivalent to thickened manifolds.
problem Understanding embeddings of manifolds in higher dimensions.
method Formal identification of manifolds with their thickened versions, using geometric constructions.
result The infinity-category of thickened smooth manifolds is equivalent to the infinity-category of finite spaces over BO.
There are two categorifications of the Jones polynomial: "even" discovered by M.Khovanov in 1999 and "odd" dicovered by P.Ozsvath, J.Rasmussen and Z.Szabo in 2007. The first one can be fully constructed in the category of cobordisms (strictly: in the additive closure of that category), where we can build a complex for …
The paper develops a framework for abstracting causal models using category theory.
problem Difficulties in changing the variables used to describe a system, especially from fine-grained to coarse-grained.
method Introduces a category of interventional causal models and uses enriched category theory to prove compositionality properties.
result Compositionality of model transformations is established, with bounded errors for each step.
For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are known as homological representations. Representations of this kind have proved th…
DMRL improves UDA by mixing source and target samples and enriching latent space structures.
problem Lack of class-aware information and insufficient samples for domain-invariant feature extraction.
method Dual Mixup Regularized Learning (DMRL) that conducts category and domain mixup regularizations.
result DMRL achieves state-of-the-art performance on domain adaptation benchmarks.
This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra to define, in particular, the notion of a differential graded algebra in the wo…
In this paper we elaborate a general homotopy-theoretic framework in which to study problems of descent and completion and of their duals, codescent and cocompletion. Our approach to homotopic (co)descent and to derived (co)completion can be viewed as -category-theoretic, as our framework is constructed in the …
In their previous work, Barraud and Cornea enriched the Lagrangian Floer complex by adding cubical chains in the based loop space of the Lagrangian, and recovered the Leray-Serre spectral sequence of the based path space fibration, assuming that the Lagrangian is weakly exact and simply connected. In the present articl…
Enhances machine learning interpretability using category theory.
problem Improving machine learning interpretability and social implementation.
method Develops a categorical framework for structured understanding of supervised learning.
result Introduces the Gauss-Markov Adjunction for clarifying residuals and parameters.
We consider mapping class groups Γ(M) = pi_0 Diff(M fix \partial M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres. We show that if M contains CP^2 (with either orientation) as a connected summand then Γ(M) is independent of the number of boundary components. By repackagi…
Paper proves all Lagrangians unobstructed if one is, using non-archimedean analytic structure.
problem Proving the existence of bounding cochains for unobstructed Lagrangians.
method Introducing non-archimedean analytic structure and using family Floer techniques.
result All Lagrangians in a connected family are unobstructed if one is.
Study reduces memory needs for active learning with enriched queries.
problem Expensive labeling costs in active learning.
method Introduces bounded memory active learning through enriched queries, introduces lossless sample compression.
result Can learn classifiers with bounded memory and query optimality.
Hepworth, Willerton, Leinster and Shulman introduced the magnitude homology groups for enriched categories, in particular, for metric spaces. The purpose of this paper is to describe the magnitude homology group of a metric space in terms of order complexes of posets. In a metric space, an interval (the set of points b…
The definable content of homological invariants II: Čech cohomology and homotopy classificationmath.LO
New cohomology functors refine classical invariants of homotopy types.
problem Classifying maps between specific spaces up to homotopy.
method Descriptive set theory applied to Čech cohomology.
result Definable cohomology functors are complete invariants of homotopy types.
DS2CF-Net learns hierarchical representations with deep coupled factorization and enriched prior.
problem Learning deep hierarchical representations from data.
method Dual-constrained Deep Semi-Supervised Coupled Factorization Network (DS2CF-Net) with enriched prior.
result DS2CF-Net achieves state-of-the-art performance in representation learning and clustering.
This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the intersection cohomology of a real equal-rank Satake compactification of a locally …
Cross-domain collaborative filtering (CF) aims to alleviate data sparsity in single-domain CF by leveraging knowledge transferred from related domains. Many traditional methods focus on enriching compared neighborhood relations in CF directly to address the sparsity problem. In this paper, we propose superhighway const…
Evaluating the Role of Data Enrichment Approaches Towards Rare Event Analysis in Manufacturingstat.ML
This paper evaluates data enrichment techniques for rare event detection in manufacturing.
problem Rare events in manufacturing lead to unplanned downtime and high energy consumption.
method Time series data augmentation, sampling, and imputation techniques combined with supervised machine learning.
result Data enrichment enhances rare failure event detection and prediction by up to 48%.
KANEL: Kolmogorov-Arnold Network Ensemble Learning Enables Early Hit Enrichment in High-Throughput Virtual Screeningphysics.chem-ph
KANEL combines models for early hit enrichment in virtual screening.
problem Assessing model accuracy in chemical bioactivity predictions.
method Ensemble workflow using Kolmogorov-Arnold Networks (KANs) and other models.
result Improves early hit enrichment metrics like PPV@N.
Note on the equivalence of hierarchical variational models and auxiliary deep generative modelsstat.ML
This note compares two recently published machine learning methods for constructing flexible, but tractable families of variational hidden-variable posteriors. The first method, called "hierarchical variational models" enriches the inference model with an extra variable, while the other, called "auxiliary deep generati…
Regression Enrichment Surfaces: a Simple Analysis Technique for Virtual Drug Screening Modelsq-bio.QM
A new method for virtual drug screening detects top treatments.
problem Understanding model performance in virtual drug screening tasks.
method Regression Enrichment Surfaces (RES) method.
result RES detects more top-performing treatments than existing methods.
Study infinitesimal deformations of Lie algebroid pairs.
problem Infinitesimal deformations of Lie algebroid pairs.
method Investigate isomorphism classes of infinitesimal deformations of modulo automorphisms from exponentials of derivations of and those from the exponentials of inner derivations of .
result Find the associated governing -algebras in the sense of extended deformation theory.
Variational autoencoders are powerful algorithms for identifying dominant latent structure in a single dataset. In many applications, however, we are interested in modeling latent structure and variation that are enriched in a target dataset compared to some background---e.g. enriched in patients compared to the genera…
This paper introduces new invariants for time series analysis.
problem Analyzing the diversity and invariants of time series data.
method Introduces new invariants derived from the continuity of magnitude and maximum diversity.
result Demonstrates improved performance in machine learning experiments with real-world data.
The Lax-Hopf formula simplifies the value function of an intertemporal optimization (infinite dimensional) problem associated with a convex transaction-cost function which depends only on the transactions (velocities) of a commodity evolution: it states that the value function is equal to the marginal fonction of a fin…
Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual approach, which consists to enrich a plane field, as this is often practised in cont…
Improves neural network performance by enriching training dataset.
problem Achieving worst-case performance guarantees in neural networks.
method Adapting training dataset during training to reduce worst-case violations.
result Improved worst-case performance guarantees in neural networks.
Paper proposes a method to recover accurate labels from partially valid data in multi-label learning.
problem Tackles noisy supervision in multi-label learning with partially valid labels.
method Develops a two-stage method that estimates label enrichment and ground-truth confidences.
result Demonstrates improved performance over state-of-the-art PML methods.
Data-driven models and computational tools for neurolinguistics: a language technology perspectivecs.LG
Paper reviews neurolinguistics and language technologies, emphasizing mutual enrichment.
problem Understanding brain activity during language processing.
method Brain imaging studies and natural language representations.
result Development of brain-aware natural language representations.
Flowification enriches neural networks with an inverse pass and likelihood monitoring.
problem Neural networks lack an inverse pass and likelihood monitoring, limiting their generative capabilities.
method Introduce flowification, enriching neural networks with a stochastic inverse pass and likelihood monitoring.
result Certain neural network architectures can be enriched to fall under the generalized notion of a normalizing flow.
Homology of tropical fansmath.AG
The paper studies homology of tropical fans and introduces smoothness.
problem Homological properties of tropical fans and smoothness.
method Proposes a notion of smoothness in tropical geometry, proving the Hodge isomorphism theorem.
result Chow rings of smooth unimodular tropical fans are isomorphic to tropical cohomology rings.
Enhances LLMs for predicting stock movements by considering news dissemination and context.
problem Lack of consideration for news dissemination and insufficient contextual data in LLMs for stock price prediction.
method Clusters news for reach assessment, enriches prompts with specific data and instructions, fine-tunes an LLM using the dataset.
result Improves prediction accuracy by 8% compared to existing methods.
Study on women entrepreneurs' access to finance in France.
problem Inequalities in accessing external finance for women entrepreneurs in France.
method Quantitative approach using data from a representative sample of women entrepreneurs.
result Founder status affects access to external finance; increases success in fundraising but reduces bank finance.
Enhanced tree-based classifiers use derivatives and geometry for better function classification.
problem Improving classification of high-dimensional time series data.
method Integrates Functional Data Analysis with tree-based ensemble techniques, leveraging derivative and geometric features.
result Significant improvements over traditional approaches in function classification.
BioBO optimizes gene perturbation design using Bayesian optimization with biological priors.
problem Efficient design of genomic perturbation experiments in drug discovery.
method Integrates Bayesian optimization with multimodal gene embeddings and enrichment analysis.
result Improves labeling efficiency by 25-40% and identifies top-performing perturbations more effectively.
Regression, unlike classification, has lacked a comprehensive and effective approach to deal with cost-sensitive problems by the reuse (and not a re-training) of general regression models. In this paper, a wide variety of cost-sensitive problems in regression (such as bids, asymmetric losses and rejection rules) can be…
In this era of digital information explosion, an abundance of data from numerous modalities is being generated as well as archived everyday. However, most problems associated with training Deep Neural Networks still revolve around lack of data that is rich enough for a given task. Data is required not only for training…
Studies amenable category's monotonicity and its relation to topological complexity.
problem Monotonicity of amenable category for degree-one maps.
method Uses amenable covers and compares with topological complexity.
result Establishes a relation between amenable category and topological complexity.
Formal Contact Categoriesmath.GT
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…
Generative model learns conditional distributions on collective variable levels.
problem Modeling conditional probability distributions on collective variable levels.
method General and efficient learning approach, data enrichment strategy.
result Effective generative models on different level-sets of collective variables.
Formulates a new connection between topological and geometric categories.
problem No specific problem stated; focuses on category formulation.
method Formulates a connection between a topological and geometric category.
result Provides a more precise and improved version of a previous proposal.
Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution. However, freely enriching the family of variational distribution is challenging since…
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…