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.
Unified framework for analyzing neural networks trained by gradient descent.
This paper proves AdaGrad and Adam converge linearly under PL inequality.
New PL-invariants defined for 4-manifolds with boundary.
Lower bounds for PL 4-manifolds with boundary are improved.
New analysis shows GMD can converge linearly under PL-like conditions.
A simplified proof for embedding higher-dimensional complexes into manifolds.
Study on Wasserstein gradient flow for MMD between Coulomb measures.
SGD and stochastic gradient descent converge at optimal rates for certain non-convex functions.
Quantized Stochastic Primal-Dual Methods for Distributed Optimization
Gradient descent converges linearly in finite-width networks with positive NTK and compatible conditions.
Using polar convex bodies and the -bounds from Guan and Ni \cite{PL}, we obtain a uniform lower bound on the Gauss curvature of the normalized solution of the Gauss curvature flow without using Chow's Harnack inequality \cite{Ch2}.
The study examines how gamma positivity and PL homeomorphism types affect simplicial spheres.
In 1963, Polyak proposed a simple condition that is sufficient to show a global linear convergence rate for gradient descent. This condition is a special case of the Łojasiewicz inequality proposed in the same year, and it does not require strong convexity (or even convexity). In this work, we show that this much-older…
The paper classifies certain PL manifolds using PL cobordism.
Predictive analytics is increasingly used to guide decision-making in many applications. However, in practice, we often have limited data on the true predictive task of interest, and must instead rely on more abundant data on a closely-related proxy predictive task. For example, e-commerce platforms use abundant custom…
PLS-Lasso integrates dimension reduction into regression for financial index tracking.
Proves PL cobordism category's homotopy type, analogous to smooth case.
We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n=4, succeeds to solve completely the PL-homeomorphism problem among the catalogu…
Paper confirms conjecture for PL foliations of codimension 2.
Suppose M is a noncompact connected PL 2-manifold. In this paper we study the topological property of the triple (H(M)_0, H^PL(M)_0, H^PL, c(M)_0), where H(M)_0 is the identity component of the homeomorphism group {\cal H}(M) of M with the compact-open topology, and H^PL(M)_0 and H^PL, c(M)_0 are the identity component…
High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framewo…
Finite type invariants separate PL links in 3D space.
The purpose of this note is to scrutinize the proof of Burago and Zalgaller regarding the existence of isometric embeddings of compact surfaces into . We conclude that their proof does not admit a direct extension to higher dimensions. Moreover, we show that, in general, manifolds of dimens…
There are 2^n possible resolutions of a smooth pseudodiagram with n precrossings. If we consider piecewise-linear (PL) pseudodiagrams and resolutions that themselves are PL, certain resolutions of the pseudodiagram may not exist in three-space. We investigate this situation and its impact on the weighted resolution set…
Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In the method, multiple PLS models are trained on sub-training sets, derived from the…
This study examines the relationship between PLS and OLS regression using eigenvalue distributions.
A new method for fair representation learning using PLS.
Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving stochastic gradient methods named predictive local smoothness (PLS). First, we …
Algorithm identifies spheres with maximal Buchstaber number.
Study PL bordism theories with quantitative bounds on filling simplices.
Study compact PL 4-manifolds with special handle decompositions.
We argue that a stochastic model of economic exchange, whose steady-state distribution is a Generalized Beta Prime (also known as GB2), and some unique properties of the latter, are the reason for GB2's success in describing wealth/income distributions. We use housing sale prices as a proxy to wealth/income distributio…
Smooth symplectic manifolds can be approximated by PL symplectic manifolds.
New method speeds up NIR spectroscopy calibration by 400x.
We extend results of Pachner and Casali to give finite sets of moves relating triangulations of PL manifolds respecting filtrations by locally flat manifolds and stratifications in which a finite family of simple local models exists for neighborhoods of strata.
Study PL topology theorems for cubical complexes, solving Habegger and Funar's conjecture.
We prove that the norm version of the adaptive stochastic gradient method (AdaGrad-Norm) achieves a linear convergence rate for a subset of either strongly convex functions or non-convex functions that satisfy the Polyak Lojasiewicz (PL) inequality. The paper introduces the notion of Restricted Uniform Inequality of Gr…
Review of gem theory's interactions with Kirby diagrams and trisections.
After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete Morse theory are equivalent, in the sense that every discrete Morse vector on some PL triangulation is also a PL handle vector, an…
Simple crystallizations are edge-coloured graphs representing PL 4-manifolds with the property that the 1-skeleton of the associated triangulation equals the 1-skeleton of a 4-simplex. In the present paper, we prove that any (simply-connected) PL -manifold admitting a simple crystallization admits a special hand…
R-PLS improves analysis of brain functional connectivity matrices.
Bing's house-like spines approximate all PL manifolds.
Arguments on PL,(=piecewise linear) topology work over any ordered field in the same way as over the real field, and those on differential topology do over a real closed field R in an o-minimal structure that expands (R,<,0,1,+,cdot). One of the most fundamental properties of definable sets is that a compact definable …
This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the conditional mean of the labels and accounting for the linearisation error. PL has s…
PL-MCMC samples from normalizing flows' conditional distributions.
New examples show non-locally-flat PL-disk bounds in rational homology balls but not in integer homology balls.
Let M be a PL 2-manifold and X be a compact subpolyhedron of M and let E(X, M) denote the space of embeddings of X into M with the compact-open topology. In this paper we study an extension property of embeddings of X into M and show that the restriction map from the homeomorphism group of M to E(X, M) is a principal b…
Proves common stellar subdivisions for all PL homeomorphic polyhedra.