A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
O’Brien, Peter C., Thomas R
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
A brief proof of the statement that the zero-set of a nontrivial real-analytic function in $d$-dimensional space has zero measure is provided.
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The authors propose an S-MILP framework that optimizes group sequential testing boundaries to achieve faster rejection of the null hypothesis compared to traditional methods while controlling type I and type II errors.
Ill-chosen reference states induce spurious long-range strange correlators in trivial SPT phases through magnitude degeneracy of the transfer matrix in MPS representations.
Derives information-theoretic recovery thresholds for two intersecting lines with polynomial mass concentration near the intersection and matches them (up to polylog factors) via a spectral algorithm on a hypergraph built from nearly collinear triples.
Identifiability is proven for recurrent nonlinear switching dynamical systems under flexible assumptions, and ΩSDS is introduced as a flow-based estimator that improves disentanglement and forecasting over VAE-based methods.
Causal effects are identifiable for categorical unobserved confounders via mixture learning and tensor decomposition, yielding consistent estimators with non-asymptotic guarantees.
MMD GANs have unbiased critic gradients but biased generator gradients from sample-based learning, and the Kernel Inception Distance provides a practical new measure for GAN convergence and dynamic learning rate adaptation.
Explicit constructions show that isospectral graphons can arise from distinct geometries and are not combinatorially equivalent, with mixed implications for stability in graphon Kuramoto dynamics.
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Convergence of difference inclusions via a diameter criterion
A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
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A General Framework for Optimal Group Sequential Testing via Mixed-Integer Linear Programming
The authors propose an S-MILP framework that optimizes group sequential testing boundaries to achieve faster rejection of the null hypothesis compared to traditional methods while controlling type I and type II errors.
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Spurious Strange Correlators in Symmetry-Protected Topological Phases
Ill-chosen reference states induce spurious long-range strange correlators in trivial SPT phases through magnitude degeneracy of the transfer matrix in MPS representations.
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Consistent line clustering using geometric hypergraphs
Derives information-theoretic recovery thresholds for two intersecting lines with polynomial mass concentration near the intersection and matches them (up to polylog factors) via a spectral algorithm on a hypergraph built from nearly collinear triples.
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End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems
Identifiability is proven for recurrent nonlinear switching dynamical systems under flexible assumptions, and ΩSDS is introduced as a flow-based estimator that improves disentanglement and forecasting over VAE-based methods.
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Causal Inference with Categorical Unobserved Confounder via Mixture Learning
Causal effects are identifiable for categorical unobserved confounders via mixture learning and tensor decomposition, yielding consistent estimators with non-asymptotic guarantees.
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Demystifying MMD GANs
MMD GANs have unbiased critic gradients but biased generator gradients from sample-based learning, and the Kernel Inception Distance provides a practical new measure for GAN convergence and dynamic learning rate adaptation.
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Graphons, Geometry, and Dynamics: Forward and Inverse Perspectives
Explicit constructions show that isospectral graphons can arise from distinct geometries and are not combinatorially equivalent, with mixed implications for stability in graphon Kuramoto dynamics.