惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

cs.AI updates on arXiv.org
cs.AI updates on arXiv.org
L
LINUX DO - 最新话题
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
Forbes - Security
Forbes - Security
博客园 - 司徒正美
Hugging Face - Blog
Hugging Face - Blog
W
WeLiveSecurity
Jina AI
Jina AI
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
N
News and Events Feed by Topic
V
V2EX
Stack Overflow Blog
Stack Overflow Blog
Engineering at Meta
Engineering at Meta
PCI Perspectives
PCI Perspectives
Martin Fowler
Martin Fowler
T
The Exploit Database - CXSecurity.com
F
Full Disclosure
WordPress大学
WordPress大学
S
Security Affairs
K
KPMG report finds enterprise disconnect between AI and its ROI | CIO
S
SegmentFault 最新的问题
P
Privacy International News Feed
IT之家
IT之家
M
MIT News - Artificial intelligence
G
GRAHAM CLULEY
Hacker News: Ask HN
Hacker News: Ask HN
D
DataBreaches.Net
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
Google Online Security Blog
Google Online Security Blog
cs.CV updates on arXiv.org
cs.CV updates on arXiv.org
C
Check Point Blog
美团技术团队
Security Latest
Security Latest
Cyberwarzone
Cyberwarzone
N
News and Events Feed by Topic
MyScale Blog
MyScale Blog
H
Help Net Security
宝玉的分享
宝玉的分享
The Hacker News
The Hacker News
The Last Watchdog
The Last Watchdog
The Cloudflare Blog
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
爱范儿
爱范儿
cs.CL updates on arXiv.org
cs.CL updates on arXiv.org
I
Intezer
Threat Intelligence Blog | Flashpoint
Threat Intelligence Blog | Flashpoint
AI
AI
I
InfoQ
N
News | PayPal Newsroom
TaoSecurity Blog
TaoSecurity Blog

math updates on arXiv.org

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization Non-normal spectral signatures of instability in neural network training dynamics Optimization of randomized neural networks for transfer operator approximation Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty LLAMA LIMA: A Living Meta-Analysis on the Effects of Generative AI on Learning Mathematics Learning Decision-Sufficient Representations for Linear Optimization Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses Prabhakar function and unified fractional kinetic equation in bicomplex space Computing Gamma(p/q) with Beta function values Flows on Graded Manifolds Optimal embedding dimension in the Nash--Tognoli theorem An optimal first-order method for smooth and strongly convex composite optimization and its stationary limit Sharp Bohr-Type inequalities for certain classes of close-to-convex functions Invariants of real affine varieties based on their complexifications Topological symmetric and braid homologies A Formal Graph-Theoretic Framework for Pitch Class Set Analysis Finite groups with high commuting probability for Sylow subgroups Performance Bounds for Rollout Policies in Stochastic Shortest Path Problems Real 2-blocks in quasi-simple groups Maximal subalgebras of the Lie algebra $W_n(\mathbb{K})$ Cohomogeneity-One Ruled Hypersurfaces in $\mathbb{CP}^2$ and $\mathbb{C}H^2$ Global analysis of the Kuramoto flow Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy Training-Free Looped Transformers Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries Asymmetric Scaling Laws from Sparse Features Is Dimensionality a Barrier for Retrieval Models? RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs Commutator-Induced Uncertainty in VAEs Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection Instance-Optimal Estimation with Multiple LLM Judges on a Budget Entropy Equivalence Testing Expand More, Shrink Less: Shaping Effective-Rank Dynamics for Dense Scaling in Recommendation Any-Dimensional Invariant Universality Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models Anytime Training with Schedule-Free Spectral Optimization Concise and elegant proofs of three formulas for complete Bell polynomials On Reed-Muller subcodes, Grassmannian partitions and sum-free functions Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology The General Theory of Localization Methods A Comprehensive Study of Clique Graphs and Clique Regular Graphs Every signed planar graph is $5$-choosable: A short proof and refinements General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions PilotWiMAE: Pilot-Native Representation Learning for Wireless Channels Proximal basin hopping: global optimization with guarantees Democratizing Large-Scale Re-Optimization with LLM-Guided Model Patches On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers Stochastic Non-Smooth Convex Optimization with Unbounded Gradients Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space The Geometry of Cooperative Game Solutions: Stratified Egalitarian Shapley Values An Axiomatic Theory of Tie-Breaking: Impossibility, Characterization, and Decomposition PyCSP3-Scheduling: A Scheduling Extension for PyCSP3 Strategic PAC Learnability via Geometric Definability Proximal-Based Generative Modeling for Bayesian Inverse Problems Every Minimal Counterexample to the Erdős-Gyárfás Conjecture is Predominantly Cubic SPHERICAL KV: Angle-Domain Attention and Rate-Distortion Retention for Efficient Long-Context Inference NOVA: Fundamental Limits of Knowledge Discovery Through AI Model-based Bootstrap of Controlled Markov Chains TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects Omni-scale Learning-based Sequential Decision Framework for Order Fulfillment of Tote-handling Robotic Systems Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Towards an Inferentialist Account of Information Through Proof-theoretic Semantics Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks QUIVER: Cost-Aware Adaptive Preference Querying in Surrogate-Assisted Evolutionary Multi-Objective Optimization Robust and Fast Training via Per-Sample Clipping Beyond Continuity: Simulation-free Reconstruction of Discrete Branching Dynamics from Single-cell Snapshots Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems Information-Theoretic Measures in AI: A Practical Decision Guide Inference of Online Newton Methods with Nesterov's Accelerated Sketching A Unified Fractional Regularization Framework for Sparse Recovery Mathematical Foundations for Peer-to-Peer Lattice Computation Geometric Layer-wise Approximation Rates for Deep Networks RateQuant: Optimal Mixed-Precision KV Cache Quantization via Rate-Distortion Theory ML-based approach to classification and generation of structured light propagation in turbulent media Zeroth-Order Optimization at the Edge of Stability Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes Training-Free Rate-Distortion-Perception Traversal With Diffusion Conformal Policy Control Linear Regression with Unknown Truncation Beyond Gaussian Features ArcMark: Distortion-Free Multi-Byte LLM Watermark via Optimal Transport Feature Learning Dynamics in Infinite-Depth Neural Networks ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms Normalizing Flows on Quotient Manifolds via Boundary Quotients What Can Be Recovered Under Sparse Adversarial Corruption? Assumption-Free Theory for Linear Measurements TelecomTS: A Multi-Modal Observability Dataset for Time Series and Language Analysis Program Evaluation with Remotely Sensed Outcomes Efficient Gradient Estimation for Parameterized Quantum Systems with Lie Algebraic Symmetries
Exact Nonnegative Matrix Factorization via Cone-Ray Witnesses: Obtuseness Ranking, Saturation Curves, and an Augmented Alt-LP Breakthrough
[Submitted on 21 Jun 2026] · 2026-06-23 · via math updates on arXiv.org

View PDF HTML (experimental)

Abstract:We study exact nonnegative matrix factorization (NMF) of small exact-rank-r matrices via a cone-ray pipeline combining the truncated SVD, the polyhedral cone of nonnegative preimages, the Double Description Method (DDM, via Fukuda's cddlib), and an alternating linear program (alt-LP) for slack minimisation. Under a uniform-support restriction the factorisation constraint Q P^T = I_r reduces to entrywise nonnegativity of an r x r witness matrix M_T = R_T^{-1} (R_K^T)^{-1} for an r-subset pair (T, K) of cone rays; this closed-form witness recovers an exact NMF in microseconds when feasible.
We characterise feasibility by ranking r-subsets via geometric near-orthogonality ("obtuseness") and walking the top of each list. A 100-trial Monte Carlo at m=n=10 exposes a clean saturation curve: success 44/32/8, 79/85/58, and 79/87/59 of 100 at top-5/200/400 for r=4,5,6 -- beyond top-200 the failures are structural, not budget-limited. Enlarging m,n at fixed r hurts: at m=n=15 success collapses to 37/7/0/0/0 for r=4..8. On Olivetti faces (400x4096) the DDM step itself times out.
Our main contribution is a hybrid that breaks this ceiling: at each pair we first try the closed-form M_T, and when it is infeasible we augment both supports by k=2 maximally angularly-separated rays and solve for mu,nu>=0 by a short slack-LP alternation. On the same m=n=10 Monte Carlo this lifts success from 79/85/58 to 99/95/75 at r=4,5,6, with cone reconstruction error at or near machine precision. We close with the four scaling walls the pipeline faces and concrete next steps.

Submission history

From: Mithil Ramteke Mr [view email]
[v1] Sun, 21 Jun 2026 11:51:35 UTC (24 KB)