# Second-order methods

45 papers with code • 0 benchmarks • 0 datasets

Use second-order statistics to process data.

## Benchmarks

These leaderboards are used to track progress in Second-order methods
## Most implemented papers

# Second-Order Stochastic Optimization for Machine Learning in Linear Time

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity.

# ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning

We introduce ADAHESSIAN, a second order stochastic optimization algorithm which dynamically incorporates the curvature of the loss function via ADAptive estimates of the HESSIAN.

# Newtonian Monte Carlo: single-site MCMC meets second-order gradient methods

NMC is similar to the Newton-Raphson update in optimization where the second order gradient is used to automatically scale the step size in each dimension.

# Low Rank Saddle Free Newton: A Scalable Method for Stochastic Nonconvex Optimization

In this work we motivate the extension of Newton methods to the SA regime, and argue for the use of the scalable low rank saddle free Newton (LRSFN) method, which avoids forming the Hessian in favor of making a low rank approximation.

# M-FAC: Efficient Matrix-Free Approximations of Second-Order Information

We propose two new algorithms as part of a framework called M-FAC: the first algorithm is tailored towards network compression and can compute the IHVP for dimension $d$, if the Hessian is given as a sum of $m$ rank-one matrices, using $O(dm^2)$ precomputation, $O(dm)$ cost for computing the IHVP, and query cost $O(m)$ for any single element of the inverse Hessian.

# Near out-of-distribution detection for low-resolution radar micro-Doppler signatures

We emphasize the relevance of OODD and its specific supervision requirements for the detection of a multimodal, diverse targets class among other similar radar targets and clutter in real-life critical systems.

# A Gauss-Newton Approach for Min-Max Optimization in Generative Adversarial Networks

It modifies the Gauss-Newton method to approximate the min-max Hessian and uses the Sherman-Morrison inversion formula to calculate the inverse.

# Optimization Methods for Supervised Machine Learning: From Linear Models to Deep Learning

We then discuss some of the distinctive features of these optimization problems, focusing on the examples of logistic regression and the training of deep neural networks.

# Online Second Order Methods for Non-Convex Stochastic Optimizations

This paper proposes a family of online second order methods for possibly non-convex stochastic optimizations based on the theory of preconditioned stochastic gradient descent (PSGD), which can be regarded as an enhance stochastic Newton method with the ability to handle gradient noise and non-convexity simultaneously.

# Large batch size training of neural networks with adversarial training and second-order information

Our method exceeds the performance of existing solutions in terms of both accuracy and the number of SGD iterations (up to 1\% and $5\times$, respectively).