2 citations · 2 across the 11 of their papers we have counts for
11 papers
Probing Structural Mathematical Reasoning in Language Models with Algebraic Trapdoors
Igor Rivin
We introduce a benchmark suite for evaluating structural mathematical reasoning in language models, built on subgroup-construction problems in SL(3, Z) with cryptographic-style ver…
DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale
Alexander Kolpakov, Igor Rivin
Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise…
Linear recurrences and rational Lambert series
Igor Rivin
For a sequence , define \[ L_γ(z):=\sum_{n\ge 1}γ_n\frac{z^n}{1-z^n} =\sum_{n\ge 1}\Bigl(\sum_{d\mid n}γ_d\Bigr)z^n. \] We prove a short rigidity theorem: if …
Permanents of matrix ensembles: computation, distribution, and geometry
Igor Rivin
We report on a computational and experimental study of permanents. On the computational side, we use the GPU to greaatly accelerate the computation of permanents over …
Monte-Carlo Irreducibility and Imprimitivity Detection of Polynomials over
Igor Rivin
We study fast Monte-Carlo methods for testing irreducibility and detecting arithmetic imprimitivity of polynomials over . Building on the subset-sum criterion of Pemant…
Maximal Volume Ideal Polyhedra and the Arithmetic Angle Phenomenon
Igor Rivin
We present a software suite for the analysis and optimization of ideal convex polyhedra in hyperbolic 3-space . Using Rivin's variational characterization of ideal po…
From Euler to Today: Universal Mathematical Fallibility A Large-Scale Computational Analysis of Errors in ArXiv Papers
Igor Rivin
We present the results of a large-scale computational analysis of mathematical papers from the ArXiv repository, demonstrating a comprehensive system that not only detects mathemat…
Computational Resolution of Hadamard Product Factorization for Matrices
Igor Rivin
We computationally resolve an open problem concerning the expressibility of full-rank matrices as Hadamard products of two rank-2 matrices. Through exhaustive search o…
Computing Periodic Billiard Orbits in Balls via Newton's Method and Smale's -Criterion
Igor Rivin
We present a computational method for finding and verifying periodic billiard orbits in balls () using Newton's method applied to a variational formulation. The orbits…
Counting Matrices in SL3(Z) with Fixed Completely Split Character Polynomial: Preliminary Upper Bounds
Igor Rivin
We count matrices in the special linear group SL(n, Z) whose characteristic polynomials split completely over Q.
Eigenvalue spacings for regular graphs
D. Jakobson, S. D. Miller, I. Rivin +1
We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approach…