Gradient methods converge better for alternating updates in bilinear zero-sum games.
problem Understanding the dynamics of gradient algorithms for bilinear zero-sum games.
method Systematic analysis of popular gradient updates for simultaneous and alternating versions of bilinear zero-sum games.
result Alternating updates converge better than simultaneous ones, with optimal parameter setup and rates.
In this article, we mathematically study several GAN related topics, including Inception score, label smoothing, gradient vanishing and the -log(D(x)) alternative. --- An advanced version is included in arXiv:1703.02000 "Activation Maximization Generative Adversarial Nets". Please refer Section 6 in 1703.02000 for deta…
TSSM splits neural networks for parallel training with minimal accuracy loss.
problem Accuracy degradation in parallel training of deep neural networks.
method TSSM reformulates alternating minimization to achieve parallelism with minimal accuracy loss.
result TSSM achieves significant speedup without accuracy loss on multiple datasets.
In this paper, we investigate the attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates for the algorithm…
This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a non-linear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating bac…
Alt-GDA outperforms Sim-GDA in minimax games with near-optimal local convergence.
problem Minimax optimization convergence rate comparison
method Alternating Gradient Descent-Ascent (Alt-GDA) vs. Simultaneous Gradient Descent-Ascent (Sim-GDA)
result Alt-GDA achieves near-optimal local convergence rate for strongly convex-strongly concave problems, while Sim-GDA converges slower.
Combines Integrated Gradients and PatternAttribution into PGIG, outperforming alternatives.
problem Improving neural network explainability methods.
method Combines Integrated Gradients and PatternAttribution into Pattern-Guided Integrated Gradients (PGIG).
result PGIG outperforms other explainability methods in a large-scale image degradation experiment.
Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiable games often proceed by simultaneous or alternating gradient updates. In machine learning, games are gaining new importance through formulations like generative adversarial netwo…
AGF explains feature learning in neural networks through alternating steps.
problem Understanding what features neural networks learn and how they learn them.
method AGF is an algorithmic framework that approximates the dynamics of feature learning in two-layer networks.
result AGF provides a unified framework to understand feature learning in neural networks, matching experimental results across various architectures.
New method improves matrix factorization speed and accuracy.
problem Matrix factorization optimization problems suffer from biased solutions and lack of convergence guarantees.
method Proposes a novel Bregman distance for matrix factorization, enabling non-alternating schemes with convergence proof.
result Convergence to a stationary point proved for matrix factorization problems.
Alternative proof for 4D shrinking Ricci solitons with constant scalar curvature.
problem Proving the structure of four-dimensional shrinking gradient Ricci solitons with constant scalar curvature.
method Analyzing the asymptotic geometry at infinity.
result Alternative proof that such solitons are finite quotients of R^2 x S^2.
New method solves sparse PCA and CCA with guaranteed convergence.
problem Sparse PCA and CCA for large-scale data analysis.
method Alternating manifold proximal gradient method.
result Unified convergence analysis for the proposed method.
AGD converges in polynomial iterations to optimal matrix factorization.
problem Matrix factorization optimization with alternating gradient descent.
method Alternating gradient descent with fixed step size, proving convergence in polynomial iterations.
result AGD reaches ε-optimal factorization in T iterations with high probability.
New guarantees for SGD in non-convex optimization without strict noise bounds.
problem Efficiently escaping saddle points in non-convex optimization.
method Mean-square arguments and relaxed gradient noise variance bounds.
result Gradient descent can efficiently escape saddle points with a more relaxed gradient noise variance bound.
We consider sequential decision making problems for binary classification scenario in which the learner takes an active role in repeatedly selecting samples from the action pool and receives the binary label of the selected alternatives. Our problem is motivated by applications where observations are time consuming and…
This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Fr…
The alternating gradient descent (AGD) is a simple but popular algorithm which has been applied to problems in optimization, machine learning, data ming, and signal processing, etc. The algorithm updates two blocks of variables in an alternating manner, in which a gradient step is taken on one block, while keeping the …
Chirality affects the curvature of molecular networks, influencing their shape and stability.
problem Understanding how chirality influences the curvature of molecular networks.
method Langevin dynamics simulations and constrained gradient optimization of square lattice networks.
result Linking chirality dictates the sign of Gaussian curvature in molecular chainmail networks.
APGD algorithm efficiently recovers over-parameterized matrices from noisy measurements.
problem Matrix sensing problem with over-parameterization and noisy measurements.
method Alternating preconditioned gradient descent (APGD) algorithm incorporating preconditioning terms.
result APGD converges to a near-optimal error at a linear rate.
Paper proposes algorithms for solving nonconvex-nonconcave problems with complexity guarantees.
problem Nonconvex-nonconcave minimax problems with PL condition.
method Zeroth-order AGDA and VRAGDA algorithms.
result Iteration complexities for obtaining ε-stationary points.
ES optimization improved by structured control variates.
problem Improving accuracy of Evolution Strategies in RL.
method RL-specific variance reduction through structured control variates.
result Structured control variates outperform general variance reduction methods.
Study shows a linear quadratic regulator's imitation learning converges globally.
problem Global convergence of imitation learning for linear quadratic regulators.
method Analyzed alternating gradient algorithm and established Q-linear rate of convergence.
result Established a unique saddle point for globally optimal policy and reward function.
In the paper, we study the stochastic alternating direction method of multipliers (ADMM) for the nonconvex optimizations, and propose three classes of the nonconvex stochastic ADMM with variance reduction, based on different reduced variance stochastic gradients. Specifically, the first class called the nonconvex stoch…
A new method improves stochastic gradient descent for faster and more efficient estimation.
problem Efficient and fast parametric estimation methods.
method Projected stochastic gradient descent corrected by Fisher scoring.
result The method is faster and more efficient than traditional methods.
This work improves dictionary learning speed without sacrificing accuracy.
problem Prohibitive computational cost of standard dictionary learning methods.
method Approximate dictionary learning using unrolling and gradient descent.
result Unrolling outperforms standard methods in support estimation and early iterations.
RUMBoost combines RUMs and deep learning for better choice modelling.
problem Creating interpretable and robust discrete choice models.
method Gradient Boosted Regression Trees for utility functions, with constraints for interpretability and monotonicity.
result RUMBoost outperforms ML and RUM benchmarks in predictive performance and interpretability.
New estimators reduce variance in training variational autoencoders with discrete latent variables.
problem Training variational autoencoders with discrete latent variables requires efficient gradient estimation.
method Introduce ReinMax-Rao and ReinMax-CV estimators using Rao-Blackwellisation and control variates.
result Demonstrate superior performance on training variational autoencoders with discrete latent spaces.
Compact shrinking Kähler-Ricci solitons with positive curvature are proven to be finite.
problem Characterizing shrinking Kähler-Ricci solitons with positive bisectional curvature.
method Alternative proof using Munteanu and Wang's argument.
result Compactness of shrinking gradient Kähler-Ricci solitons with positive bisectional curvature.
The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. In dimension three we also generalize the result by removing the κ-non-collapsing assumption. In high dimension this new method allows us to prove a classification result on gradient shrinking sol…
ScaledGD improves gradient descent for ill-conditioned low-rank matrix estimation.
problem Efficiently solving ill-conditioned low-rank matrix estimation problems.
method Scaled Gradient Descent (ScaledGD) with adaptive pre-conditioners.
result Linear convergence rate independent of condition number, low per-iteration cost.
To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the straight-through gradient method, which enables back-propagation through the quantization ma…
ARM policy gradient reduces variance for binary actions.
problem High variance in policy gradients for binary actions.
method Augment-Reinforce-Merge (ARM) policy gradient estimator.
result ARM estimator achieves significant variance reduction and faster convergence.
Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework. However, it is unclear whether such algorithms can recover the ground-truth feature matrix when the wei…
Blind Descent avoids gradient issues, using a different learning approach.
problem Gradient issues like exploding and vanishing gradients.
method Does not use gradients to guide learning; instead, it is a more fundamental learning process.
result Gradient descent is a specific case of Blind Descent.
A faster method for estimating effects in large data using fixed-point trees.
problem Estimating heterogeneous effects in large dimensions with computational efficiency.
method Fixed-point approximation to eliminate Jacobian estimation and speed up GRFs.
result Significant computational efficiency improvement without sacrificing statistical accuracy.
Paper uses Super-App data to improve income estimation models.
problem Improving accuracy of income estimation models.
method TreeSHAP method for Stochastic Gradient Boosting Interpretation.
result Alternative data from Super-Apps capture more information than traditional financial data.
STORM-PG uses momentum for faster policy gradient updates.
problem Improving policy gradient methods for reinforcement learning.
method Introduces STORM-PG, a SARAH-based algorithm with exponential moving average.
result Achieves O(1/ε3) sample complexity, matching best-known rate. In this paper, we design and analyze a new zeroth-order online algorithm, namely, the zeroth-order online alternating direction method of multipliers (ZOO-ADMM), which enjoys dual advantages of being gradient-free operation and employing the ADMM to accommodate complex structured regularizers. Compared to the first-ord…
We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class C1,1. These results are then used to prove new alternating Steiner formulæ for hypersurfaces of positive reach. Furthermore, it will turn out that every hypersurface that sat…
A new method for SVGD reduces variance in high dimensions.
problem High-dimensional variance in SVGD.
method Grassmann Stein Variational Gradient Descent (GSVGD) projects onto arbitrary subspaces and uses coupled Grassmann-valued diffusion.
result GSVGD explores high-dimensional problems with intrinsic low-dimensional structure efficiently.
DANTE trains neural networks using an alternating minimization approach.
problem Training neural networks with mixed activation functions efficiently.
method DANTE uses alternating minimization and quasi-convexity to handle neural networks with both differentiable and non-differentiable activation functions.
result DANTE-trained neural networks are promising and competitive in terms of quality and training speed.
SPIGOT bypasses gradients of argmax functions in neural nets with discrete latent variables.
problem Training neural networks with discrete latent variables.
method Structured projected intermediate gradient optimization technique (SPIGOT).
result SPIGOT bypasses gradients of argmax functions effectively.
This paper presents a new class of gradient methods for distributed machine learning that adaptively skip the gradient calculations to learn with reduced communication and computation. Simple rules are designed to detect slowly-varying gradients and, therefore, trigger the reuse of outdated gradients. The resultant gra…
Constructs retractions of CAT(1) spaces to convex subsets.
problem Geometric description of an analytic tool.
method Gradient flow of time-dependent locally Lipschitz semiconcave functions.
result Existence of gradient flows proved for independent interest.
This paper explores gradient flows for sampling distributions without normalization constants.
problem Sampling from distributions with unknown normalization constants.
method Gradient flows in the space of probability measures, focusing on Kullback-Leibler divergence, Fisher-Rao metric, and affine invariance.
result Gradient flows derived from Kullback-Leibler divergence do not depend on the normalization constant.
AM converges super-linearly for solving mixed linear regression problems.
problem Learning linear regressors from unlabeled observations in multiple linear regression models.
method Alternating Minimization (AM) algorithm, which alternates between label estimation and regression solving.
result AM converges super-linearly in certain parameter regimes, requiring only O(log log(1/ε)) iterations to achieve an error of ε.
By providing a simple and efficient way of computing low-variance gradients of continuous random variables, the reparameterization trick has become the technique of choice for training a variety of latent variable models. However, it is not applicable to a number of important continuous distributions. We introduce an a…
FPGA-based multi-layer equalizer adapts to changing channels.
problem Real-time adaptation to time-varying channel impairments.
method Multi-layer machine learning on FPGA with on-chip gradient backpropagation training.
result Real-time adaptation to changing channel conditions achieved.