A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Universal preconditioning reduces sequential prediction regret.
Stochastic Gradient Langevin Dynamics infuses isotropic gradient noise to SGD to help navigate pathological curvature in the loss landscape for deep networks. Isotropic nature of the noise leads to poor scaling, and adaptive methods based on higher order curvature information such as Fisher Scoring have been proposed t…
The paper explores how dynamic preconditioning affects the CLT in online averaging.
Bayesian sparse learning method improves deep neural network efficiency.
Paper analyzes Langevin dynamics for multimodal Gaussian mixtures, controlling errors across dimensions.
Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for Stochastic Gradient Descent (SGD). These methods improve convergence by adapting to th…
RL accelerates portfolio optimization and option pricing by dynamically adjusting preconditioner sizes.
Paper analyzes Langevin dynamics for solving infinite-dimensional Bayesian inverse problems.
We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics thus providing a practical approach to difficult anisotr…
Layer-wise preconditioning methods improve neural network optimization and feature learning.
We provide an online convex optimization algorithm with regret that interpolates between the regret of an algorithm using an optimal preconditioning matrix and one using a diagonal preconditioning matrix. Our regret bound is never worse than that obtained by diagonal preconditioning, and in certain setting even surpass…
Gradient descent converges geometrically to optimal self-attention parameters.
Paper analyzes Annealed Langevin Dynamics for multimodal sampling stability.
TDprop uses Jacobi preconditioning to improve adaptive optimizers in Deep RL.
Optimal preconditioning improves Langevin sampling efficiency.
Preconditioned neural posterior estimation improves reliability in misspecified models.
Preconditioned gradient methods are among the most general and powerful tools in optimization. However, preconditioning requires storing and manipulating prohibitively large matrices. We describe and analyze a new structure-aware preconditioning algorithm, called Shampoo, for stochastic optimization over tensor spaces.…
In this work, we study data preconditioning, a well-known and long-existing technique, for boosting the convergence of first-order methods for regularized loss minimization. It is well understood that the condition number of the problem, i.e., the ratio of the Lipschitz constant to the strong convexity modulus, has a h…
Bias correction improves language model training performance.
One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one algorithm to approximate such Bayesian posteriors for large models and datasets. SGL…
Preconditioned non-convex gradient descent improves noisy matrix estimation.
Unified framework for understanding and optimizing training acceleration.
This paper optimizes diagonal preconditioning to improve matrix condition numbers.
Two methods solve kernel ridge regression problems efficiently.
Randomized block-diagonal preconditioning improves parallel learning convergence.
PolarGrad optimizes deep learning models by considering matrix structure, outperforming Adam and Muon.
Paper analyzes regret bounds for unconstrained online optimization.
New method speeds up solving orthogonality constrained problems.
In this paper, we analyze different preconditionings designed to enhance robustness of pure-pixel search algorithms, which are used for blind hyperspectral unmixing and which are equivalent to near-separable nonnegative matrix factorization algorithms. Our analysis focuses on the successive projection algorithm (SPA), …
New sampling method using regularized Wasserstein proximal for Gibbs distributions.
A new method improves convergence in low-rank approximation.
Preconditioned NFs speed up sampling from complex posterior distributions in inverse problems.
New research shows how preconditioning can solve sparse linear regression problems efficiently.
A new method reduces complexity of normalizing flows for MCMC preconditioning.
Adaptive learning rate algorithms such as RMSProp are widely used for training deep neural networks. RMSProp offers efficient training since it uses first order gradients to approximate Hessian-based preconditioning. However, since the first order gradients include noise caused by stochastic optimization, the approxima…
Improved convergence for overparameterized low-rank matrix sensing.
The paper explores efficient sampling for Bayesian wide neural networks.
Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing. This problem is referred to as near-separable NMF and requires that there exist…
SignSGD analysis quantifies its effects in high dimensions.
Muon optimizer simplifies matrix optimization with spectral orthogonalization.
When the design matrix has orthonormal columns, "soft thresholding" the ordinary least squares (OLS) solution produces the Lasso solution [Tibshirani, 1996]. If one uses the Puffer preconditioned Lasso [Jia and Rohe, 2012], then this result generalizes from orthonormal designs to full rank designs (Theorem 1). Theorem …
Standard gradient descent methods are susceptible to a range of issues that can impede training, such as high correlations and different scaling in parameter space.These difficulties can be addressed by second-order approaches that apply a pre-conditioning matrix to the gradient to improve convergence. Unfortunately, s…
New analysis of Muon and SignSGD on matrix-valued least squares problems.
Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to make it practical and e…
We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry that exists in Tucker decomposition…
In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some properties of the standard Conjugate Gradient (CG) method, in order to preserve the…
State-of-the-art models are now trained with billions of parameters, reaching hardware limits in terms of memory consumption. This has created a recent demand for memory-efficient optimizers. To this end, we investigate the limits and performance tradeoffs of memory-efficient adaptively preconditioned gradient methods.…
Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data that is widely used in observational sciences. In its classic form, ICA relies on modeling the data as linear mixtures of non-Gaussian independent sources. The maximization of the corresponding likelihood is a challen…