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.
New feature mapping approach improves recommendation accuracy and explainability.
Explains exceptional surgeries connecting maps and knot orbifolds.
1-Lipschitz neural networks produce clearer, more focused Saliency Maps for explainable AI.
This paper reviews MDS, Sammon mapping, and Isomap, explaining their theory and applications.
This paper presents an unsupervised method to learn a neural network, namely an explainer, to interpret a pre-trained convolutional neural network (CNN), i.e., the explainer uses interpretable visual concepts to explain features in middle conv-layers of a CNN. Given feature maps of a conv-layer of the CNN, the explaine…
timeXplain bridges AI and time series, making predictions understandable.
Improve exposition and explain metric bundle equivalence.
FCDD explains deep anomaly detection by mapping anomalies away and providing heatmap explanations.
The study reveals simplicity bias in neural networks leading to better compositional mappings.
CDAM improves attention maps for ViTs, making them more class-sensitive.
Explains Uhlenbeck's work on maps and fields.
This survey studies equivariant harmonic maps arising from Higgs bundles. We explain the non-abelian Hodge correspondence and focus on the role of equivariant harmonic maps in the correspondence. With the preparation, we review current progress towards some open problems in the study of equivariant harmonic maps.
These lecture notes explain the geometry and discuss some of the analytical questions underlying image registration within the framework of large deformation diffeomorphic metric mapping (LDDMM) used in computational anatomy.
A conformal map from a Riemann surface to the Euclidean four-space is explained in terms of its twistor lift. A local factorization of a differential of a conformal map is obtained. As an application, the factorization of a differential provides an upper bound of the area of a super-conformal map around a branch point.
WassersteinGrad improves weather forecasting explanations by addressing geometric misalignment issues.
Study evaluates saliency maps on artificial data with different backgrounds.
Paper explains dynamics of homeomorphisms to mapping tori geometry.
We establish a connection between recent developments in the study of vortices in the abelian Higgs models, and in the theory of structure-preserving discrete conformal maps. We explain how both are related via conformal mapping problems involving prescribed linear combinations of the curvature and volume form, and sho…
We introduce a new tool for interpreting neural net responses, namely full-gradients, which decomposes the neural net response into input sensitivity and per-neuron sensitivity components. This is the first proposed representation which satisfies two key properties: completeness and weak dependence, which provably cann…
We study Dirac structures associated with Manin pairs (\d,\g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach in terms of quasi-Poisson structures. We explain how these two distinct frameworks are related to each other, pro…
Improves machine learning models by incorporating physical laws into feature maps.
We consider the problem of explaining the decisions of deep neural networks for image recognition in terms of human-recognizable visual concepts. In particular, given a test set of images, we aim to explain each classification in terms of a small number of image regions, or activation maps, which have been associated w…
This paper classifies typhoon damage features using aerial photography.
Sharp bounds found for energy in projective space mappings.
The article explains Rao distances and conformal mappings for 3D objects.
This review explores XAI in finance, highlighting common techniques and areas needing improvement.
In this paper we study the modular classes of Dirac manifolds and of Dirac maps, and we discuss their basic properties. We apply these results to explain the relationship between the modular classes of the various structures involved in the reduction of a Poisson manifold under the action by of a Poisson Lie group.
New invariants explain topological properties of pseudo-Anosov maps.
The Teichmüller harmonic map flow, introduced in [9], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy as quickly as possible. In this paper, we develop the geometric analysis of holomo…
A conformal map from a Riemann surface to a Euclidean space of dimension greater than or equal to three is explained by using the Clifford algebra, in a similar fashion to quaternionic holomorphic geometry of surfaces in the Euclidean three- or four-space. The Weierstrass representation, the spin transform, the Darboux…
For a hyperbolic link complement with a triangulation, there are hyperbolicity equations of the triangulation, which guarantee the hyperbolic structure of the link complement. In this paper, we explain that the number of the essential solutions of the equations is equal to or bigger than the extension degree of the inv…
Explains mapping properties of elliptic operators in conical spaces.
We explain how the formal aspects of the theory of Kahler-Einstein metrics can be developed in the framework of moment maps. The central result we use is the Berndtsson convexity theorem, which is interpreted as defining a metric on the space of complex structures. We discuss some applications of these ideas to the Kah…
We analyze the signature type of a cascade of periodic orbits associated to period doubling renormalizable maps of the two dimensional disk. The signature is a sequence of rational numbers which describes how periodic orbits turn each other and is invariant by topological conjugacies that preserve orientation. We prove…
Develops TCD maps to relate discrete differential geometry and cluster algebras.
We explain a new phenomenon on non compact complete Riemannian four manifolds, where d^+ image of one forms can not exhaust densely on L^2 self dual forms on each compact subset, if a certain L^2 self dual harmonic form exists. This leads to construct a new functional analytic framework on the Seiberg-Witten map.
In this paper, we are interested in the construction of quasiconformal mappings between domains of the Heisenberg group H that minimise a mean distortion functional. We propose to construct such mappings by considering a corresponding problem between domains of Poincaré half-plane . The first map we construc…
Survey of Laplacian-based methods for data dimensionality reduction and embedding.
Much effort has been devoted to understanding the decisions of deep neural networks in recent years. A number of model-aware saliency methods were proposed to explain individual classification decisions by creating saliency maps. However, they are not applicable when the parameters and the gradients of the underlying m…
Local decision boundary approximation improves model explanations for complex models.
This article has two purposes. The first is to give an expository account of the integrable systems approach to harmonic maps from surfaces to Lie groups and symmetric spaces, focusing on spectral curves for harmonic 2-tori. The most unwieldy aspect of the spectral curve description is the periodicity conditions and th…
New method for explaining neural network activation functions.
New findings show mapping class groups of certain high-dimensional manifolds are not residually finite.
Survey on random walks on mapping class groups and their properties.
Notes on quasiregular maps between Riemannian manifolds, preserving Sobolev forms.
Kontsevich's formula for a deformation quantization of Poisson structures involves a Feynman series of graphs, with the weights given by some complicated integrals (using certain pullbacks of the standard angle form on a circe). We explain the geometric meaning of this series as degrees of maps of some grand configurat…
Two modified tests improve the reliability of evaluating explanation methods.
This is a commentary on Teichm{ü}ller's paper Ein Verschiebungssatz der quasikonformen Abbildung (A displacement theorem of quasiconformal mapping), published in 1944. We explain in detail how Teichm{ü}ller solves the problem of finding the quasiconformal mapping from the unit disc to itself, sending 0 to a strictly ne…