Pure Math · Mathematics & Statistics
Metric Geometry
The newest papers in Metric Geometry that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
14 papers, from 16 September 2026 to 1 November 2026: 14 arXiv preprints.
Get the few papers worth your time in Metric Geometry every morning.
Follow Metric Geometry and ReadSearch reads its new papers each day, then brings you the few worth reading, each with its key finding in a sentence.
Newest papers
Improved lower bounds for the kissing number in dimensions 49 to 61
We give explicit kissing configurations in R^d for every d = 49, ..., 61.Optimal Average Distortion for Non-Expansive Embeddings of Euclidean Metrics into the Line: With applications to cut-matching games and vertex expansion
We show that any $n$-point Euclidean metric admits a non-expansive embedding into the line with average distortion at most $O\left(\sqrt{\frac{\log n}{\log\log n}}\right)$, matching a known lower…Formalizing the Intrinsic Dimension of Objective Landscapes by a Generalized Notion of Co-dimension
In this work, we formalize the concept of intrinsic dimension of objective landscapes introduced in Li et al. (2018), which measures the structural complexity of learning problems by training along…Boundary Geometry Determines Optimal Shallow ReLU Approximation under Weighted Coefficient Constraints
We study how boundary geometry affects $L^q$ approximation by shallow ReLU neural networks on convex bodies $K\subset\mathbb R^d$.The Geometry of Limits in ReLU Function Spaces
We study the geometry and closure of spaces of functions realized by ReLU neural networks of fixed architecture.A Linear Lower Bound for Convex Body Chasing in Every $\ell_p$ Norm
We establish an $Ω(d)$ lower bound on the competitive ratio of convex body chasing in $\mathbb{R}^d$ with $\ell_p$ movement costs for any $p \in [1, \infty)$.The Geometry of Anisotropic Dilation for Optimal Regularization
A central question in data-driven inverse problems is how to construct a regularizer that adapts to the geometry of the data distribution.Spacetime Quasicrystals and Computational Complexity Theory in the Road Towards Quantum Gravity
Part I: Semiclassical Gravity Efficiently Solves $\mathsf{NP}$-Complete Problems Assuming the gravitational field is classical and that it couples to quantum fields via the semiclassical Einstein…Quantum codes in the Lee metric
We introduce a quantum coding framework for discrete small-shift noise, in which errors on qudits are modeled as low-weight $X$- and $Z$-type Pauli shifts, analogous to small phase-space…The twisted convolution identity and ghost $r$-SICs from finite quantum dilogarithms
Radchenko and Wheeler (RW) recently proved a finite pentagon relation for real quadratic special values of the modular quantum dilogarithm and used it to establish the rank-$1$ twisted convolution…Dual lattice attacks for bounded distance decoding, revisited
Analyses of dual lattice attacks have often assumed that the individual scores associated with short dual vectors are mutually independent.Smooth Sailing through Spherical Shells: Provable Random-Lattice Sieving in Time $2^{0.292n}$
In an attempt to close the gap between the best provable and heuristic algorithms for hard lattice problems, such as the shortest (SVP) and closest vector problem (CVP), we analyze lattice sieving…Continuous Optimization for p-adic Models
We present the first method for native, continuous gradient descent for machine learning models with $p$-adic parameters.A quantitative tree-likeness bound from average hyperbolicity
Chatterjee and Sloman proved that a bounded measurable similarity function with sufficiently small average Gromov hyperbolicity admits a tree representation with small mean approximation error.