We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo (MCMC) algorithms for Bayesian inverse problems. Here four examples of information metrics are considered, including Fisher-Rao metric, Wasserstein-2 metric, Kalman-Wasserstein m…
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48 results for “accelerated gradient flow”
Hamiltonian Descent Algorithms for Optimization: Accelerated Rates via Randomized Integration Timemath.OC
HF-opt uses Hamiltonian dynamics to optimize functions, achieving accelerated rates with randomized integration time.
problem Optimizing functions efficiently and accelerating convergence rates.
method Randomized Hamiltonian flow (RHF) with accelerated convergence rates.
result RHGD achieves accelerated convergence rates similar to Nesterov's AGD.
ASVGD accelerates SVGD for efficient sampling.
problem Slow SVGD in high-dimensional sampling.
method Accelerated gradient flow in a metric space of probability densities, using Nesterov's method and momentum-based updates.
result ASVGD outperforms SVGD and other methods in sampling efficiency.
SympFormer accelerates attention blocks using inertial dynamics on density spaces.
problem Improving the efficiency of self-attention blocks in Transformers.
method Introduced accelerated attention blocks derived from inertial Nesterov dynamics on density spaces.
result Accelerated attention blocks converge faster than classical blocks while preserving oracle calls.
ASVGD accelerates SVGD for efficient sampling from Gaussian targets.
problem Efficient sampling from Gaussian distributions using SVGD.
method Accelerated gradient flow in a metric space of probability densities, including momentum and Wasserstein regularization.
result ASVGD achieves optimal convergence rate for Gaussian targets, independent of covariance.
This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in (wibisono, et. al. 2016) from vector valued variables to probability distributi…
New method accelerates optimization in fixed time, improving convergence rates.
problem Optimization in large-scale data-driven problems.
method Gradient-based optimization framework with fixed-time stable dynamical systems.
result Achieves convergence to the optimizer in a fixed number of iterations, independent of initialization.
Study accelerates gradient methods in machine learning, revealing risk and stability connections.
problem Understanding the statistical risk of accelerated gradient methods in machine learning.
method Continuous-time analysis of Nesterov's accelerated gradient method and Polyak's heavy ball method for least squares regression.
result Connections between early stopping, stability, and curvature of loss function are revealed.
GFM models neural network training as a dynamical system to forecast final weights.
problem Computational intensity and inefficiency in training deep neural networks.
method Gradient Flow Matching (GFM) treats training as a dynamical system with learned vector fields.
result GFM achieves forecasting accuracy competitive with Transformer-based models and significantly outperforms classical baselines.
Optimization is at the heart of machine learning, statistics and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as spin glasses. Proximal algorithms form a class of methods that are broadly applica…
As one of standard approaches to train deep neural networks, dropout has been applied to regularize large models to avoid overfitting, and the improvement in performance by dropout has been explained as avoiding co-adaptation between nodes. However, when correlations between nodes are compared after training the networ…
A new ParVI framework improves particle-based variational inference methods.
problem Non-trivial kernel design in particle-based variational inference methods.
method Proposes a generalized Wasserstein gradient descent (GWG) framework with broader regularizers.
result Demonstrates strong convergence guarantees and effectiveness on simulated and real data.
Accelerates Riemannian gradient methods with extrapolation.
problem Optimizing functions on manifolds efficiently.
method Extrapolating iterates in Riemannian gradient descent.
result Achieves optimal convergence rate and computational advantage.
Unified geometric flows improve deep learning efficiency and simplify neural network topologies.
problem Improving deep learning performance and simplifying neural network structures.
method Proposes a thermodynamically coupled Ricci flow that dynamically adapts parameter space geometry to loss landscape topology, enabling automated singularity resolution and providing entanglement entropy bounds.
result Demonstrates 2.1× convergence acceleration and 63% topological simplification while maintaining complexity, outperforming Riemannian baselines by 15.2% in few-shot accuracy.
Flow-VQE uses generative flows to optimize VQE efficiently.
problem Complex objective functions and expensive optimization in VQE.
method Generative normalizing flows with parameterized quantum circuits.
result Flow-VQE accelerates convergence and reduces circuit evaluations.
AGNES accelerates gradient descent with noisy gradients.
problem Minimizing smooth convex and strongly convex functions with noisy gradients.
method Generalization of Nesterov's accelerated gradient descent algorithm for noisy conditions.
result AGNES achieves acceleration for noisy gradients with a constant of proportionality up to 1.
Develops accelerated methods for optimization using low-dimensional projected-gradient information.
problem Optimization with low-dimensional projected-gradient information and Nesterov acceleration.
method Randomized-subspace Nesterov accelerated gradient methods for smooth convex and strongly convex optimization.
result Established accelerated oracle-complexity guarantees and unified basis for comparing sketch families.
New method accelerates energetic variational inference using particle dynamics.
problem Efficiently solving variational inference problems with reduced computational cost.
method Particle-based variational inference with implicit scheme, inspired by energy quadratization and operator splitting.
result Significantly reduces computational cost compared to existing methods.
Accelerated gradient method's stability deteriorates exponentially with steps.
problem Algorithmic stability of Nesterov's accelerated gradient method.
method Analysis of two notions of algorithmic stability for Nesterov's accelerated gradient method.
result Stability of Nesterov's accelerated method deteriorates exponentially with the number of gradient steps.
Gradient flow autoencoder improves data efficiency over traditional autoencoders.
problem Sub-optimal latent space representations in autoencoders.
method Gradient flow through ODE with adaptive step size for optimization.
result Gradient flow autoencoder achieves higher data efficiency.
FAKI improves gradient-free inference for inverse problems.
problem Expensive forward models without gradients.
method Temperature annealing with normalizing flows.
result Dramatic improvements in accuracy over EKI.
Accelerates coordinate descent methods for machine learning problems.
problem Slowness of coordinate descent methods in machine learning.
method Extrapolation-based accelerated coordinate descent.
result Significant speed-up in practice compared to existing methods.
Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify variou…
A Continuized View on Nesterov Acceleration for Stochastic Gradient Descent and Randomized Gossipmath.OC
Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.
problem Improving the convergence rate of stochastic gradient descent and gossip algorithms.
method Introducing a continuized variant of Nesterov acceleration, which mixes variables continuously and takes gradient steps at random times.
result The continuized Nesterov acceleration achieves convergence rates similar to Nesterov's original acceleration but with random parameters.
A new method directly encodes data into latent space using gradient flow.
problem Suboptimal representations in physical sciences due to encoder inversion.
method Decoder-only approach using gradient flow and ODEs, avoiding integrals.
result Superior data efficiency and explicit encoding compared to traditional autoencoders.
We analyze Riemannian accelerated methods using a new framework.
problem Understanding Riemannian accelerated gradient methods.
method Riemannian A-HPE framework, focusing on Euclidean A-HPE insights and metric distortion control.
result Characterization of acceleration for various Riemannian methods.
There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error accumulation, a notion made precise in d'Aspremont 2008 and Devolder, Glineur, …
This work accelerates gradient descent with anytime convergence guarantees.
problem Improving the convergence rate of gradient descent methods.
method Proposes a stepsize schedule for gradient descent that achieves anytime convergence rates.
result Gradient descent can achieve convergence rates of for any stopping time .
We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current position in parameter space, but at the estimated position after one step. In this work…
We study learning properties of accelerated gradient descent methods for linear least-squares in Hilbert spaces. We analyze the implicit regularization properties of Nesterov acceleration and a variant of heavy-ball in terms of corresponding learning error bounds. Our results show that acceleration can provides faster …
Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational cost of orthogonal projections would be prohibitive. However, they do not enjoy …
FedAc accelerates Federated Averaging for distributed optimization.
problem Efficiently optimizing distributed machine learning models.
method Federated Accelerated Stochastic Gradient Descent (FedAc) using a potential-based perturbed iterate analysis.
result FedAc achieves faster convergence and lower communication costs than previous methods.
Optimizes convex functions in finite vs infinite dimensions, revealing slow convergence rates.
problem Analyzing gradient flows in finite and infinite-dimensional Hilbert spaces.
method Proves convergence rates and optimality conditions for gradient flows and related methods.
result Gradient flow convergence rates in finite dimensions are slower than in infinite dimensions, with optimal rates achievable in Hilbert spaces.
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte Carlo methods. We propose a new sampling algorithm based on a birth-death mechanis…
Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. While many generalizations and extensions of Nesterov's original acceleration method have been proposed, it is not yet clear what is the natural scope of the acceleration concept. In this paper, we study accelera…
Momentum speeds up evolutionary processes in machine learning.
problem Accelerating convergence in evolutionary dynamics.
method Combining momentum from machine learning with evolutionary dynamics using information divergences as Lyapunov functions.
result Momentum accelerates convergence of evolutionary dynamics, including the replicator equation and Euclidean gradient descent.
PF-LaCG removes the need for knowing smoothness and strong convexity parameters for locally accelerated CG.
problem Locally accelerated CG requires knowledge of smoothness and strong convexity parameters.
method Parameter-Free Locally Accelerated CG (PF-LaCG) algorithm.
result PF-LaCG achieves local acceleration without requiring knowledge of smoothness and strong convexity parameters.
Two new differentially private optimization algorithms derived from accelerated methods.
problem Improving privacy in optimization algorithms while maintaining convergence rates.
method Polyak's heavy ball method and Nesterov's accelerated gradient method with differential privacy.
result The proposed algorithms outperform existing differentially private optimization methods.
Jeffreys Flow improves robustness of Boltzmann generators for rare event sampling.
problem Rare events and metastable trapping in sampling physical systems with rough energy landscapes.
method Introduces Jeffreys Flow, a robust generative framework using Parallel Tempering distillation and symmetric Jeffreys divergence to mitigate mode collapse and improve mode coverage.
result Minimizing Jeffreys divergence suppresses mode collapse and corrects inaccuracies in multi-modal distributions.
No accelerated gradient method for hyperbolic convex functions.
problem Existence of accelerated gradient methods for geodesically convex functions on hyperbolic spaces.
method Analysis of volume growth in negatively curved spaces.
result No-go theorem for accelerated gradient methods on hyperbolic plane.
New methods accelerate gradient descent for convex and strongly convex functions.
problem Improving convergence rates of gradient-based optimization methods.
method Formulated two classes of first-order algorithms with Lyapunov analyses and Hamiltonian assisted gradient method.
result Achieved accelerated convergence rates matching Nesterov's methods in strongly and general convex settings.
This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning where objective functions are estimated from available data. We show that these alg…
Improved symbolic regression finds optimal formulas robust to noise.
problem Finding accurate formulas for noisy data.
method Exploits graph modularity, uses normalizing flows, and statistical hypothesis testing.
result Discoveres many formulas previously unattainable.
Accelerated optimization methods improve robustness and privacy in estimation.
problem Improving robustness and privacy in estimation methods.
method Accelerated gradient methods based on Frank-Wolfe and projected gradient descent, with tailored learning rates and Nesterov's momentum.
result Reduction in iteration complexity, leading to stronger statistical guarantees.
Regularized nonlinear acceleration (RNA) estimates the minimum of a function by post-processing iterates from an algorithm such as the gradient method. It can be seen as a regularized version of Anderson acceleration, a classical acceleration scheme from numerical analysis. The new scheme provably improves the rate of …
Accelerates policy optimization in RL with optimistic and adaptive updates.
problem Improving policy optimization methods in reinforcement learning.
method Integrates foresight into policy improvement step via optimistic and adaptive updates.
result Designs an optimistic policy gradient algorithm, adaptive via meta-gradient learning.
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive gradient) methods are the two main techniques to improve the slow convergence of \text…
Proves equations for high-dimensional gradient-based methods from Gaussian data.
problem High-dimensional asymptotics of gradient-based learning algorithms.
method Closed-form equations derived from dynamical mean-field theory.
result Equations match those from discretized DMFT for gradient flow.