arXiv Machine Learning
Convergence, design and training of continuous-time dropout as a random batch method
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arXiv Machine Learning
Sep 30
Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timesteps
arXiv:2602.12624v2 Announce Type: replace Abstract: Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by h...
arXiv Machine Learning
Oct 15
Strong Gaussian Approximation of Constant Learning Rate SGD: Bias and Trajectory Inference
arXiv:2610. 14567v2 Announce Type: replace-cross Abstract: This paper develops strong Gaussian approximations (KMT type) for constant learning rate stochastic gradient descent (SGD).
arXiv Machine Learning
Oct 21
Diffusion Score Estimation with Shallow Neural Networks: Regularity, Approximation, and Finite-Sample Rates
arXiv:2610.27206v1 Announce Type: cross Abstract: We study the sample complexity of estimating Ornstein--Uhlenbeck diffusion scores in $\mathbb R^d$ using denoising score matching (DSM) with finite-w...
arXiv Machine Learning
Sep 15
Stochastic Gradient Descent over P2
The paper develops a diffusion approximation for stochastic gradient descent (SGD) when the optimization target is a functional on the Wasserstein space ℝ2. By lifting the problem to a Hilbert space via Lions differentiability, the authors construct a Gaussian random-field approximation whose velocity field matches the mean and covariance of the original stochastic gradient. They prove that this Gaussian approximation achieves second‑order weak accuracy, providing a rigorous basis for replacing sample‑driven randomness with analytically tractable Gaussian fluctuations in stochastic optimization over probability measures.
arXiv Machine Learning
Jul 30
Learning Controlled Stochastic Differential Equations
arXiv:2411. 01982v2 Announce Type: replace-cross Abstract: We study the problem of learning controlled stochastic differential equations (SDEs) \[ dX_t = b(t,X_t,u_t)\,dt + \sigma(t,X_t,u_t)\,dW_t, \] whose drift and diffusion depend nonlinearly on time, state, and control values.
arXiv Machine Learning
Oct 16
Stochastic Gradient Descent: A Nonlinear Time Series Perspective
This paper studies the statistical properties of Stochastic Gradient Descent (SGD) with a constant step size using the framework of iterated random functions. It demonstrates convergence in Euclidean distance via Geometric Moment Contraction, establishes quenched central limit theorems, invariance principles, and α-stable convergence for averaged SGD regardless of initialization, and explores the effect of step sizes through derivative processes. The authors further develop a Richardson-Romberg extrapolation with multiple step sizes, propose a bias-reduced variant, and introduce an online inference method that yields empirical confidence intervals with coverage approaching nominal levels as sample size increases.