Graphs with stronger curvature grow faster.
problem Understanding volume growth on graphs with various curvatures.
method Examined inner-outer and Ricci-Ollivier curvatures to relate them to volume growth.
result Graphs with stronger inner-outer curvature growth have faster volume growth.
We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve state-of-the-art results for various key machine learning optimization problems including …
The paper explores the L1-Liouville property on graphs and its connections to stochastic completeness.
problem Investigating the L1-Liouville property on graphs and its implications. method Characterization of L1-Liouville property in terms of Green function, equivalence with stochastic completeness, and comparison theorems based on inner-outer curvatures. result Equivalence of L1-Liouville property and stochastic completeness on model graphs, and introduction of Dirichlet L1-Liouville property. Study proves energy critical heat equation solutions are Type I blowups for n ≥ 7.
problem Analyzing blowup behavior of energy critical nonlinear heat equations.
method Reverse inner-outer gluing mechanism and bubbling behavior analysis.
result Proves all blowups are of Type I for n ≥ 7.
Proposes a method to balance tasks in multitask learning with a single gradient step update.
problem Balancing tasks in multitask learning to avoid imbalance.
method Gradient-based meta-learning to balance tasks at the gradient level, training shared and task-specific layers separately.
result Achieves state-of-the-art performance on various multitask computer vision problems.
RSGDA improves convergence rates for nonconvex-strongly concave optimization.
problem Optimization of nonconvex-strongly concave problems.
method Randomized Stochastic Gradient Descent Ascent (RSGDA) with optimal loop sizes.
result First almost sure convergence rates for SGDA algorithms on nonconvex-strongly concave settings.
We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to a cluster is generated via the same Hawkes process with specific parameters, an…
The paper classifies noncollapsed translators in 4D space.
problem Classifying entire convex translators in 4D space.
method Developed Fredholm theory and used Lyapunov-Schmidt reduction.
result The one-parameter family of translators is uniquely determined.
The paper constructs many ancient solutions to the Yamabe flow on spheres.
problem Ancient solutions to the Yamabe flow on spheres.
method Non-radial inner--outer gluing scheme, conformal invariance, weighted Hölder estimates.
result Uncountably many non-rotationally symmetric ancient solutions.
New algorithms improve SGD convergence and reduce variance for over-parameterized models.
problem Slower convergence in non-interpolation settings for SGD variants.
method Proposed AdaSPS and AdaSLS with variance reduction for robust convergence.
result Achieves faster convergence rates and robustness in non-interpolation settings.