A new optimization method improves deep learning model training speed.
problem Optimizing large models with natural gradient descent.
method Kronecker-factored eigenbasis for diagonal variance approximation.
result Improves optimization speed for deep network architectures.
SINGD improves KFAC for memory-efficiency and stability in low-precision training.
problem Memory inefficiency and numerical instability of KFAC in low-precision training.
method Formulated inverse-free KFAC update and imposed structures in Kronecker factors.
result SINGD is memory-efficient and numerically robust, often outperforming AdamW in half precision.
Improved neural network inference with eigenvalue correction.
problem Inference of flexible variational posteriors is computationally expensive.
method Eigenvalue correction to matrix-variate Gaussian posterior.
result Empirically, the method outperforms existing algorithms.
Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to compute for large models, and most approximations either require an expensive it…
PPOKFAC combines PPO and K-FAC for better sample efficiency and scalability.
problem Improving sample efficiency and scalability of Proximal Policy Optimization.
method Combines PPO objective with K-FAC natural gradient optimization.
result PPOKFAC outperforms PPO in sample complexity and training speed.
A new iterative K-FAC algorithm reduces training time and memory usage.
problem Training deep learning models efficiently.
method Uses conjugate gradient to approximate Fisher information matrix without generating the matrix or factors.
result Time and memory complexity of iterative CG-FAC is less than standard K-FAC.
A new method for optimizing deep neural networks using TKFAC.
problem Optimizing deep neural networks with second-order methods.
method Proposes Trace-restricted Kronecker-factored Approximate Curvature (TKFAC) for Fisher information matrix approximation.
result TKFAC improves performance on deep network architectures compared to state-of-the-art algorithms.
KF-LAX uses KFAC to improve sample efficiency in reinforcement learning.
problem Sample efficiency and low variance in gradient-based optimization methods.
method Kronecker-factored curvature estimation (KFAC) applied to RELAX gradient estimator.
result Improved performance on synthetic and Atari games.
This paper speeds up K-FAC for deep learning by focusing on only a few eigen-modes.
problem Time-consuming computation of Kronecker factors in K-FAC for large layers.
method Theoretical analysis and randomized numerical linear algebra to approximate eigen-spectrum decay.
result Reduces time complexity from cubic to quadratic in layer width, improving efficiency.
Develops efficient quasi-Newton methods for training deep neural networks.
problem Training deep neural networks with large-scale Hessian matrices.
method Approximates Hessian as block-diagonal Kronecker product of smaller matrices, applies damping.
result Outperforms or matches state-of-the-art methods in autoencoder models.
We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-Factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases…
We develop a coordinate-free approach to natural gradient descent for scalable neural networks.
problem First-order optimization methods are sensitive to model parameterization.
method We construct a coordinate-free natural gradient and analyze its invariance properties for K-FAC.
result K-FAC's natural gradient matches the coordinate-free update, maintaining invariance to affine transformations.
A new method for learning Bayesian neural networks using layerwise inference.
problem Learning Bayesian neural networks efficiently and accurately.
method Bayesian layerwise inference, treating neural networks as stacked Bayesian linear models, with pseudo-targets defined by backpropagated gradients.
result The method converges quickly and performs well on various benchmarks.
KF-RTRL approximates RTRL for online learning of long-term dependencies.
problem Lack of efficient algorithms for learning long-term dependencies in RNNs.
method KF-RTRL uses Kronecker factorization to approximate RTRL gradients.
result KF-RTRL is an unbiased, memory-efficient online learning algorithm with lower noise than UORO.
Improved CNN training speed with K-FAC on large datasets.
problem Challenges in training large-scale neural networks with distributed processors.
method Scalable K-FAC design, layer-wise distribution, inverse-free second-order gradient evaluation, dynamic K-FAC update decoupling.
result Distributed K-FAC implementation converges to 75.9% MLPerf baseline in 18-25% less time than SGD.
EigenDamage reduces neural network size and FLOPs with structured pruning in the Kronecker-Factored Eigenbasis.
problem Reducing neural network size and FLOPs while maintaining accuracy for resource-constrained devices.
method Kronecker-Factored Eigenbasis reparameterization and Hessian-based structured pruning.
result Empirically validated improvements in model size and FLOPs with negligible accuracy loss.
Bayesian online learning method improves neural network performance.
problem Overcoming catastrophic forgetting in neural networks.
method Kronecker factored online Laplace approximation for Bayesian online learning.
result Achieves over 90% test accuracy across 50 MNIST tasks.
Method learns invariances in deep nets without human validation.
problem Manual selection of data augmentation parameters is cumbersome.
method Differentiable Laplace approximation for Bayesian model selection.
result Method successfully recovers invariances and improves generalization.
New methods improve Fisher Matrix approximations for neural networks at low cost.
problem High cost of solving Fisher Information Matrix (FIM) in neural networks.
method Direct minimization via Kronecker product singular value decomposition.
result Improved approximations to FIM provide more accurate and faster optimization.
New methods use Kronecker-factored approximations for faster deep learning optimization.
problem Optimizing deep learning models with rich curvature information.
method Approximate Hessian using Kronecker products for efficient quasi-Newton methods.
result New methods outperform first-order methods and perform comparably to second-order methods.
This paper investigates Shampoo's heuristics and decouples preconditioner updates.
problem Improving Shampoo's heuristics for training neural networks.
method Decomposing preconditioner updates, correcting eigenvalues, and adapting eigenbasis computation frequency.
result Principled techniques to remove Shampoo's heuristics and improve training algorithms.
Improved continual learning for neural networks with BN layers using K-FAC extension.
problem Continual learning challenges in neural networks with BN layers.
method Extended K-FAC method to account for inter-example relations, weight merging, and reparameterization for BN layers; proposed weight merging and reparameterization for BN layers; proposed method to select hyperparameters without source task data.
result Better performance in continual learning tasks with BN layers compared to baselines.
K-FAC speeds up training of modern neural networks with linear weight-sharing.
problem Efficiently training modern neural networks with linear weight-sharing layers.
method Kronecker-Factored Approximate Curvature (K-FAC) applied to linear weight-sharing layers.
result K-FAC-reduce is generally faster than K-FAC-expand for deep linear networks.
Enhances Deep Hedging with K-FAC for financial data.
problem High computational burden in training neural networks for financial applications.
method Integrates Kronecker-Factored Approximate Curvature (K-FAC) optimization with LSTM networks.
result Significant improvements in convergence and hedging efficacy, reducing transaction costs and P&L variance.
Faster convergence and handling larger mini-batches for deep neural networks.
problem Generalization gap in large-scale distributed training of deep neural networks.
method Second-order optimization using Kronecker-factored approximate curvature.
result Achieved 75% Top-1 validation accuracy with mini-batch size of 131,072 in 978 iterations.
Second-order optimization speeds up deep hedging for complex options.
problem Hedging exotic options with market frictions in realistic markets.
method Second-order optimization scheme leveraging pathwise differentiability and Kronecker-factoring.
result Our method optimizes the policy in 1/4 the steps of standard optimization.
Sketchy reduces memory and compute requirements for adaptive regularization in deep learning.
problem Prohibitive memory and running time for adaptive regularization methods in deep learning.
method Low-rank sketching approach using Frequent Directions (FD) to reduce memory and compute requirements.
result Efficient interpolation between resource requirements and degradation in regret guarantees with rank k. ViViT efficiently computes curvature for deep networks without approximations.
problem Efficiently computing curvature for deep networks without approximations.
method Leverages the GGN's low-rank structure without further approximations.
result ViViT allows for efficient computation of eigenvalues, eigenvectors, and directional derivatives.
A new optimization method reduces memory and compute requirements for deep learning.
problem Memory and compute constraints in second-order stochastic optimizers for deep learning.
method Proposes KrAD, a novel factorization to approximate inverse Fisher matrix without inversion, leading to KrADagrad.
result Improves performance over Shampoo for 32-bit precision and comparable/generalization on real datasets.
LQF linearizes deep models for better interpretability.
problem Lack of interpretability in deep neural networks.
method Simple modifications to architecture, loss function, and optimization.
result Comparable performance to non-linear fine-tuning, with interpretability.
This paper studies iteration convergence of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model and MSE convergence rates. The KGlasso model, originally called the transposable regularized covariance model by …
Natural gradients boost performance in non-conjugate Gaussian process models.
problem Improving inference in non-conjugate Gaussian process models.
method Use of natural gradients in non-conjugate stochastic settings with hyperparameter learning.
result Natural gradients significantly improve performance, especially for ill-conditioned posteriors.
TANGO optimizes models with small learning rates, converging to natural gradient.
problem Optimizing models with small learning rates to converge to natural gradient.
method TANGO, a simple algorithm that converges to natural gradient descent.
result TANGO achieves natural gradient descent with small learning rates.
New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
Natural-gradient methods improve Bayesian inference in complex models.
problem Computational challenges in Bayesian inference for complex models.
method Derive fast natural-gradient updates for variational inference.
result Natural-gradient methods provide more accurate local approximations.
Natural gradient simplification for deep learning networks.
problem Efficiency in training deep Bayesian networks.
method Analysis of two geometries of Fisher information matrix and development of a method to simplify natural gradient for the second geometry.
result A method to simplify natural gradient for deep networks using an auxiliary recognition model.
A new natural gradient accounts for correlated variational parameters in variational inference.
problem Traditional natural gradients fail to correct for correlations in variational inference.
method Construct a new natural gradient called the Variational Predictive Natural Gradient (VPNG).
result VPNG accounts for the relationship between model parameters and variational parameters.
New method for natural policy gradients converges linearly.
problem Improving natural policy gradient methods for better convergence.
method Fisher-Rao gradient flow applied to state-action distributions.
result Linear convergence rate with geometry-dependent factor.
We extend natural-gradient methods to mixtures of exponential-family distributions, improving inference speed.
problem Complex, multimodal posterior distributions are difficult to approximate with simple exponential-family distributions.
method We use minimal conditional-EF representations and derive simple natural-gradient updates.
result Our natural-gradient method converges faster than black-box methods with reparameterization gradients.
A framework for natural gradient with arbitrary similarity measures.
problem Unclear metric for natural gradient in non-Euclidean spaces.
method Derive a metric for natural gradient given an arbitrary similarity measure.
result General framework for natural gradient in non-Euclidean spaces.
Square-root natural-gradient improves variational inference convergence.
problem Challenges in establishing theoretical convergence guarantees for natural-gradient descent.
method Square-root parameterization for Gaussian covariance.
result Establishes novel convergence guarantees for natural-gradient Gaussian inference.
The natural gradient allows for more efficient gradient descent by removing dependencies and biases inherent in a function's parameterization. Several papers present the topic thoroughly and precisely. It remains a very difficult idea to get your head around however. The intent of this note is to provide simple intuiti…
Natural gradient descent avoids the magic of model parametrization, leading to different optimization outcomes.
problem Understanding the impact of model parametrization on optimization and generalization in deep learning.
method Characterization of natural gradient flow in deep linear networks and nonlinear neural networks.
result Natural gradient descent fails to generalize in some cases, while gradient descent with the right architecture performs well.
Natural gradient improves deep Q-learning performance.
problem Improving deep Q-learning stability and performance.
method Integrates natural-gradient techniques into deep Q-learning.
result Natural-gradient deep Q-learning (NGDQN) outperforms standard DQN without target networks and performs similarly to DQN with target networks.
Paper presents a rank-1 approximation method for natural policy gradients in deep RL.
problem Computing natural gradients requires inverting the Fisher Information Matrix, which is computationally expensive.
method Develops a rank-1 approximation to the inverse Fisher Information Matrix for efficient natural policy optimization.
result The rank-1 approximation converges faster and has similar sample complexity to stochastic policy gradient methods.
Natural gradient is equivalent to Kalman filtering for parameter estimation.
problem Parameter estimation in probabilistic models from observations.
method Casting natural gradient as an extended Kalman filter for parameter estimation.
result Exact algebraic correspondence between natural gradient and Kalman filtering.
A new method uses natural gradients for efficient distribution optimization.
problem Challenges in computing natural gradients for many distributions.
method Reframe optimization as a surrogate distribution with easy natural gradient computation.
result Expands set of distributions efficiently targetable with natural gradients.
Trust-region methods and natural gradients are equivalent in certain policy search scenarios.
problem Improving policy search methods in continuous control tasks.
method Introducing compatible policy search (COPOS) that uses natural parameterization and compatible value function approximation to control entropy loss.
result COPOS yields state-of-the-art results in challenging tasks and reduces entropy loss.