Let M be a closed n-dimensional manifold, n > 2, whose first real cohomology group H 1 (M ; R) is non-zero. We present a general method for constructing a Morse 1-form on M , closed but non-exact, and a pseudo-gradient X such that the differential X of the Novikov complex of the pair (, X) has at leas…
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13 results for “pseudo-gradients”
Sparse Representations of Positive Functions via First and Second-Order Pseudo-Mirror Descentstat.ML
Develops first and second-order pseudo-mirror descent methods for nonnegative function estimation.
problem Nonnegative function estimation in settings like MLE and trajectory optimization.
method First and second-order pseudo-mirror descent with pseudo-gradients and projections.
result Establishes tradeoffs and non-asymptotic bounds on model complexity.
Given a compact smooth manifold with non-empty boundary and a Morse function, a pseudo-gradient Morse-Smale vector field adapted to the boundary allows one to build a Morse complex whose homology is isomorphic to the (absolute or relative to the boundary) homology of with integer coefficients. Our approach simp…
New method improves matrix completion accuracy, especially in noisy data.
problem Noisy matrix completion in recommendation systems and signal processing.
method Residual Spectral Matching criterion and pseudo-gradient algorithms.
result Improved numerical performance in noisy data environments.
In this paper, we investigate the geometry and classification of three-dimensional CR Yamabe solitons. In the compact case, we show that any 3-dimensional CR Yamabe soliton must have constant Tanaka-Webster scalar curvature; we also obtain a classification under the assumption that their potential functions are in the …
Heegaard splittings and Heegaard diagrams of a closed 3-manifold M are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on M. We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous pseudo-isotopy problem. In passing, we show how to canc…
The paper proves critical point results for Frechet manifolds.
problem Finding critical points in the context of Frechet manifolds.
method Using a deformation result and sufficient conditions for the Palais-Smale condition.
result Proves a mountain pass theorem and three critical points theorem.
The problem of prescribing conformally the scalar curvature of a closed Riemannian manifold as a given Morse function reduces to solving an elliptic partial differential equation with critical Sobolev exponent. Two ways of attacking this problem consist in subcritical approximations or negative pseudo gradient flows. W…
Researchers prove a method to upgrade Morse-Bott homology to stable homotopy invariants.
problem Proving a method to upgrade Morse-Bott homology to stable homotopy invariants rigorously.
method Rigorous construction of stable normal framings and proof of stable homotopy type recovery.
result The stable homotopy type recovers Σ∞+M and Thom spectra for all reduced KO-theory classes.
GPA improves LLM training speed by 8.71% for Llama-160M models.
problem Training Large Language Models (LLMs) with high memory overhead and slow convergence.
method Generalized Primal Averaging (GPA) extends Nesterov's method to eliminate memory-intensive two-loop structure.
result GPA achieves up to 10.13% speedup over AdamW in training Llama-1B model.
Feature selection (FS) has become an indispensable task in dealing with today's highly complex pattern recognition problems with massive number of features. In this study, we propose a new wrapper approach for FS based on binary simultaneous perturbation stochastic approximation (BSPSA). This pseudo-gradient descent st…
This paper tackles global Nash equilibrium in non-convex multi-player games.
problem Challenges in finding global Nash equilibrium due to non-convexity.
method Conjugate transformation and variational inequality formulation to prove existence and design algorithms.
result Designs an ODE-based algorithm with exponential convergence rate and proves its effectiveness in practical scenarios.
Federated CTMC model estimates bridge deterioration hazards without sharing raw data.
problem Bridge inspection data privacy and cross-organizational data sharing constraints.
method Federated CTMC hazard model with local optimization and FedAvg aggregation.
result Federated model converges on global benchmark parameters without data transfer.