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.
Fairmetrics evaluates fairness in ML models for specific groups.
We explore a relationship between topological properties of orbits of 2-cycles in the symplectomorphism group Symp(M) and the existence of rational curves in M. Under the absence of rational curves hypothesis, we show that evaluation map vanishies on the second homotopy group and obtain a Gottlieb-type vanishing theore…
A new method improves AI fairness assessment by estimating performance across intersectional subgroups.
A new CVaR test reduces group performance disparity detection complexity.
Evaluating the twisted Morita-Mumford classes bar(h)_p on the Artin braid group B_n, we give the stable algebraic independence of the bar(h)_p's on the automorphism group of the free group, Aut(F_n). This is sharper than the results we obtained by restricting them to the mapping class group.
The topology of -representation varieties of the fundamental groups of planar webs so that the meridians are sent to matrices with trace equal to are explored, and compared to data coming from spider evaluation of the webs. Corresponding to an evaluation of a web as a spider is a rooted tree. We associate t…
It is known that every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. In this paper, we give another proof which improves the result of Korkmaz. In addition, Korkmaz defined the genus of a finitely presented group. We also evaluate upper bounds for genera of some finitely…
Study topological twists of massive SQCD with gauge group SU(2) and 3 or fewer fundamental hypermultiplets.
This paper considers extractive summarisation in a comparative setting: given two or more document groups (e.g., separated by publication time), the goal is to select a small number of documents that are representative of each group, and also maximally distinguishable from other groups. We formulate a set of new object…
By evaluating the Burau representation at t=-1, we obtain a symplectic representation of the braid group. We define the congruence subgroups of the braid group to be the preimages of the principal congruence subgroups of the symplectic group. Our main result is that the level four congruence subgroup of the braid group…
Machine learning approaches have been effective in predicting adverse outcomes in different clinical settings. These models are often developed and evaluated on datasets with heterogeneous patient populations. However, good predictive performance on the aggregate population does not imply good performance for specific …
Introduction 1. The two-eigenvalue problem 2. Hecke algebra representations of braid groups 3. Duality of Jones-Wenzl representations 4. Closed images of Jones-Wenzl sectors 5. Distribution of evaluations of Jones polynomials 6. Fibonacci representations
Group Shapley evaluates feature groups in business data, improving explainability in AI.
This study compares and evaluates categorical kernels for Gaussian process regression.
Bayesian design improves accuracy without extra cost.
Method evaluates classification uncertainty with adaptively chosen features.
For M and N closed oriented connected smooth manifolds of the same dimension, we consider the mapping space Map(M,N;f) of continuous maps homotopic to f:M--> N.We show that the evaluation map from the space of maps to the manifold N induces a nontrivial homomorphism on the fundamental group only if the self coincidence…
The paper explores various forms of calibration scores and their implications for fairness.
Unimodal approach for group-level emotion recognition without individual features.
The -means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a -means type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured cl…
New rack and multiple group rack cohomology for surfaces in 3-sphere.
Group averaging boosts model accuracy without training cost.
Infinitesimal calculations link fundamental groups to Lie algebras.
This work is devoted to elaboration on the idea to use block term decomposition for group data analysis and to raise the possibility of modelling group activity with (Lr, 1) and Tucker blocks. A new generalization of block tensor decomposition was considered in application to group data analysis. Suggested approach was…
We develop the Latent Multi-group Membership Graph (LMMG) model, a model of networks with rich node feature structure. In the LMMG model, each node belongs to multiple groups and each latent group models the occurrence of links as well as the node feature structure. The LMMG can be used to summarize the network structu…
Develops a new criterion for subgroup fairness in algorithmic decision support.
Randomized control methods improve asset pricing and performance analysis.
New method improves conditional covariance estimation using targeted groups of assets.
We show that from the asymptotic behavior of an evaluation of the colored Jones polynomial of the figure-eight knot we can extract the Chern--Simons invariant and the twisted Reidemeister torsion associated with a representation of the fundamental group of the knot complement to the two-dimensional complex special line…
Researchers compute determinants and torsions of Rumin complex in specific Lie group representations.
Evaluating data separation in a geometrical space is fundamental for pattern recognition. A plethora of dimensionality reduction (DR) algorithms have been developed in order to reveal the emergence of geometrical patterns in a low dimensional visible representation space, in which high-dimensional samples similarities …
We present a new approach for transferring knowledge from groups to individuals that comprise them. We evaluate our method in text, by inferring the ratings of individual sentences using full-review ratings. This approach, which combines ideas from transfer learning, deep learning and multi-instance learning, reduces t…
In this paper, we consider the joint task of simultaneously optimizing (i) the weights of a deep neural network, (ii) the number of neurons for each hidden layer, and (iii) the subset of active input features (i.e., feature selection). While these problems are generally dealt with separately, we present a simple regula…
We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel of the Burau representation evaluated at t=-1 and also the fundament…
Deep learning approximates geometric measures of planar curves.
Unified framework for studying Torelli group and congruence subgroup maps.
The pioneering work of Jones and Kauffman unveiled a fruitful relationship between statistical mechanics and knot theory. Recently, Jones introduced two subgroups and of the Thompson groups and , respectively, together with a procedure that associates an oriented link diagram to any element o…
Efficient diffusion model for symmetric manifolds reduces training and computation costs.
Paper examines fairness of data augmentation methods, finding vanilla Mixup outperforms Fair Mixup.
Flexible framework assesses multilevel data group heterogeneity.
We discuss the relationship between the m-th homotopy group of the one-point union of r copies of the two-dimensional sphere and the m-th homotopy group of the one-point union of r+1 copies of the Thom space of the oriented two-dimensional universal vector bundle. Using a suitably choosen isomorphism between them a for…
The knot coloring polynomial defined by Eisermann for a finite pointed group is generalized to an infinite pointed group as the longitudinal mapping invariant of a knot. In turn this can be thought of as a generalization of the quandle 2-cocycle invariant for finite quandles. If the group is a topological group then th…
Practitioners in diverse fields such as healthcare, economics and education are eager to apply machine learning to improve decision making. The cost and impracticality of performing experiments and a recent monumental increase in electronic record keeping has brought attention to the problem of evaluating decisions bas…
CLIP models robustness to spurious features is re-evaluated using a new dataset.
SureMap estimates model performance across subpopulations efficiently.
Improves group fairness in tensor completion by augmenting tensors with balanced entities.
A common data mining task on networks is community detection, which seeks an unsupervised decomposition of a network into structural groups based on statistical regularities in the network's connectivity. Although many methods exist, the No Free Lunch theorem for community detection implies that each makes some kind of…
New method for PKM inverse dynamics second derivatives efficiently.