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.
Study of splitting maps in Type I Ricci flows for understanding singular set structure.
Characterizes and analyzes the large scale geometry of big mapping class groups of surfaces.
New analysis of stochastic approximation with non-expansive mappings.
Transformers can scale both context and task, but MLPs can only scale task.
Efficiently maps indoor magnetic fields with SKI and D-SKI.
Study of mapping class groups on infinite graphs, focusing on their large-scale geometry.
This paper reviews MDS, Sammon mapping, and Isomap, explaining their theory and applications.
Classifies low-energy harmonic maps from curved surfaces to spheres.
Extends scaling maps theory to manifolds with boundary.
Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our approach relies on radial basis functions (RBFs) to interpolate the inverse map ever…
Large scale online kernel learning aims to build an efficient and scalable kernel-based predictive model incrementally from a sequence of potentially infinite data points. A current key approach focuses on ways to produce an approximate finite-dimensional feature map, assuming that the kernel used has a feature map wit…
The paper explores scaling symmetries in symplectic geometry and their applications to central configurations.
This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and the existence of a constant rank theorem for such maps. It does so by extending t…
Proves uniqueness of Ricci flow with scaling invariant estimates.
Paper proposes PPMM for fast estimation of large-scale OTM.
Large models follow power laws in performance with dataset size or parameters.
Investigates energy minimizers and critical points of scale-invariant tangent-point energies for knots.
We study the large-scale geometry of mapping class groups of surfaces of infinite type, using the framework of Rosendal for coarse geometry of non locally compact groups. We give a complete classification of those surfaces whose mapping class groups have local coarse boundedness (the analog of local compactness). When …
We present new findings in regard to data analysis in very high dimensional spaces. We use dimensionalities up to around one million. A particular benefit of Correspondence Analysis is its suitability for carrying out an orthonormal mapping, or scaling, of power law distributed data. Power law distributed data are foun…
String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly du…
Study identifies and estimates causal LSNM models, proving feature maps are consistent.
Enhances graph classification models on small datasets.
It is well known that quasi-isometric embeddings of Gromov hyperbolic spaces induce topological embeddings of their Gromov boundaries. A more general question is to detect classes of functions between Gromov hyperbolic spaces that induce continuous maps between their Gromov boundaries. In this paper we introduce the cl…
We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform maps. A unified treatment is given to the large scale dimension and the small scale …
Strict type-II blowup in harmonic map flow is proven to have Hölder continuous body map.
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two distributions. To that end, we propose a stochastic dual approach of regularize…
New measure defined on surface strata, invariant under scaling.
We construct a new map from a convex function to a distribution on its domain, with the property that this distribution is a multi-scale exploration of the function. We use this map to solve a decade-old open problem in adversarial bandit convex optimization by showing that the minimax regret for this problem is $\tild…
Framework improves ML flood mapping generalization.
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large …
This paper maps the large-scale variation of the Spanish language by employing a corpus based on geographically tagged Twitter messages. Lexical dialects are extracted from an analysis of variants of tens of concepts. The resulting maps show linguistic variation on an unprecedented scale across the globe. We discuss th…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sides…
We introduce a notion of measuring scales for quantum abelian gauge systems. At each measuring scale a finite dimensional affine space stores information about the evaluation of the curvature on a discrete family of surfaces. Affine maps from the spaces assigned to finer scales to those assigned to coarser scales play …
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
Efficiently applies NTK to large-scale datasets using random features.
Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with sufficient layers and parameters, hierarchical combinations of convolution (matri…
In general, image restoration involves mapping from low quality images to their high-quality counterparts. Such optimal mapping is usually non-linear and learnable by machine learning. Recently, deep convolutional neural networks have proven promising for such learning processing. It is desirable for an image processin…
Improved bounds for non-linear SA with fast convergence.
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational complexity of the diffusion maps algorithm scales with the number of observations. T…
First European crop map created using satellite data.
This study reveals the critical role of scale vectors in large language models, improving optimization and expressivity.
We prove the Farrell-Jones Conjecture for mapping class groups. The proof uses the Masur-Minsky theory of the large scale geometry of mapping class groups and the geometry of the thick part of Teichmueller space. The proof is presented in an axiomatic setup, extending the projection axioms of Bestvina-Bromberg-Fujiwara…
Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampere…
Proposes continuous convolution layers for flexible feature map resizing.
We develop a 2D travel time tomography method which regularizes the inversion by modeling groups of slowness pixels from discrete slowness maps, called patches, as sparse linear combinations of atoms from a dictionary. We propose to use dictionary learning during the inversion to adapt dictionaries to specific slowness…
Running hydrodynamical simulations to produce mock data of large-scale structure and baryonic probes, such as the thermal Sunyaev-Zeldovich (tSZ) effect, at cosmological scales is computationally challenging. We propose to leverage the expressive power of deep generative models to find an effective description of the l…
Liouville's theorem says that in dimension greater than two, all conformal maps are Möbius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally equivalent if they are combinatorially equivalent and the lengths of corresponding …
Maps preserving Carathéodory distance between symmetric domains are rigid.