Exact second-order optimization for deep learning reduces computational cost and improves performance.
problem Inadequate use of second-order optimization methods in deep learning due to high computational cost and non-convexity.
method Developed an exact stochastic second-order Newton method that addresses the non-convexity issue and provides an expression for the stochastic Hessian.
result Exact second-order Newton direction formula and its application in deep learning datasets.
Second-order guarantees for federated learning algorithms.
problem Non-convex optimization in federated learning with saddle-points as bottlenecks.
method Drawing on recent results on second-order optimality in centralized and decentralized settings, establish second-order guarantees for federated learning algorithms.
result Established second-order guarantees for federated learning algorithms.
Proposes a new stock prediction method that accounts for market dynamics.
problem The dynamic nature of the stock market invalidates traditional machine learning assumptions.
method Develops a second-order learning paradigm with multi-scale patterns.
result Demonstrates effectiveness in stock prediction on real-world data.
AdamQLR optimizes Adam with K-FAC heuristics, achieving comparable performance to tuned benchmarks.
problem Improving the performance of Adam optimizers with stabilizing heuristics.
method Combining Adam's update directions with K-FAC's heuristics (damping and learning rate selection).
result Untuned AdamQLR can achieve comparable performance to tuned benchmarks.
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we …
Negative step sizes improve second-order methods for neural networks.
problem Second-order methods discard negative curvature, limiting their effectiveness.
method Introduce negative step sizes in second-order methods combined with Wolfe line search.
result Negative step sizes lead to global convergence and improved performance.
A new framework for measuring uncertainty in machine learning models.
problem Uncertainty measures for second-order distributions in machine learning models have theoretical flaws.
method Formal criteria and a general framework based on the Wasserstein distance.
result The Wasserstein distance-based measure satisfies all proposed criteria for meaningful uncertainty measures.
Two new algorithms improve federated optimization under second-order similarity.
problem Federated learning under communication constraints and second-order similarity.
method SVRP and Catalyzed SVRP algorithms combining proximal point evaluations, client sampling, and variance reduction.
result Achieves superior performance and uniformly improves upon existing algorithms for federated optimization under second-order similarity and strong convexity.
Paper introduces FoMoH for optimization without backpropagation.
problem Optimizing machine learning models without backpropagation.
method Second-order hyperplane search, forward-mode stochastic gradient method, hyper-dual numbers, FoMoH.
result Developed a novel optimization algorithm that avoids backpropagation.
New method speeds up deep learning optimization.
problem Scalable second-order optimization for deep learning.
method Second-order optimization with algorithmic and numerical improvements.
result Significant convergence and wall-clock time improvements.
Paper proposes a new method for efficient second-order neural network training.
problem Infeasibility of Hessian calculation and noisy second-order information in deep learning.
method Adopting complex-step directional derivative (CSFD) for accurate Hessian computation and designing an effective Newton Krylov procedure.
result Our method outperforms existing methods and often converges one-order faster.
The second order method as Newton Step is a suitable technique in Online Learning to guarantee regret bound. The large data is a challenge in Newton method to store second order matrices as hessian. In this paper, we have proposed an modified online Newton step that store first and second order matrices of dimension m …
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.
New algorithm TURTLE outperforms MAML and meta-learner LSTM.
problem Learning new tasks quickly with limited data and compute power.
method Combining insights from MAML and meta-learner LSTM, TURTLE uses second-order gradients.
result TURTLE outperforms MAML and meta-learner LSTM in few-shot learning tasks.
The paper debiases mini-batch approximations in deep learning for more accurate optimization and uncertainty quantification.
problem Bias in mini-batch approximations distorts the shape of quadratic approximations used in deep learning.
method Developed and evaluated debiasing strategies for mini-batch approximations.
result Debiasing strategies improve the accuracy of second-order optimization and uncertainty quantification in deep learning.
New findings show second-order scoring rules can't accurately represent epistemic uncertainty.
problem Lack of epistemic uncertainty representation in second-order learners.
method Generalised second-order scoring rules introduced to prove theoretical limitations.
result No loss function incentivizes second-order learners to accurately represent epistemic uncertainty.
New method explains predictive uncertainty by focusing on second-order effects.
problem Explaining predictive uncertainty in machine learning models.
method CovLRP, CovGI, etc., based on second-order effects.
result Predictive uncertainty is dominated by second-order effects.
SONODEs and ANODEs improve learning of second order dynamics.
problem Learning dynamics governed by second order laws.
method Extended adjoint sensitivity method and theoretical analysis of ANODEs.
result SONODEs and ANODEs can learn higher order dynamics efficiently.
Data whitening and second order optimization harm generalization by reducing access to dataset information.
problem Harmful effects of data whitening and second order optimization on generalization in machine learning.
method Analysis of fully connected models and experimental verification.
result Data whitening and second order optimization reduce or prevent generalization by limiting access to dataset information.
Second-order methods improve differential privacy in convex optimization.
problem Improving differential privacy in convex optimization.
method Developed a private variant of the regularized cubic Newton method for strongly convex loss functions.
result Achieves quadratic convergence and optimal excess loss for strongly convex loss functions.
Paper introduces variance-based measures for second-order uncertainty quantification in classification problems.
problem Uncertainty in machine learning predictions and decision-making.
method Second-order uncertainty quantification using variance-based measures.
result Variance-based measures effectively quantify uncertainty on a class-based level and are competitive with entropy-based measures.
Proves and tests methods for learning time-series with breaks.
problem Learning time-series with structural breaks.
method Complete proofs and experimental validation of a regularized loss function.
result Experimental results support the validity of the techniques.
Loss minimisation fails to capture epistemic uncertainty in second-order predictors.
problem Capturing epistemic uncertainty in machine learning models.
method Analysis of a second-order learner approach using loss minimisation.
result Loss minimisation does not faithfully represent epistemic uncertainty in second-order predictors.
SOAR improves deep networks' robustness against adversarial examples.
problem Improving deep neural networks' robustness against adversarial examples.
method Formulated adversarial robustness problem under robust optimization framework, approximated loss function using second-order Taylor series expansion.
result SOAR significantly improves robustness of networks against adversarial perturbations.
Improved Local SGD convergence for general convex objectives with bounded second-order heterogeneity.
problem Understanding when and why Local SGD outperforms alternatives in distributed optimization.
method Established improved convergence guarantees for Local SGD on general convex objectives under bounded second-order heterogeneity.
result Upper bounds for Local SGD are nearly tight, providing a sharper convergence theory.
Most of the existing approaches focus on specific visual tasks while ignoring the relations between them. Estimating task relation sheds light on the learning of high-order semantic concepts, e.g., transfer learning. How to reveal the underlying relations between different visual tasks remains largely unexplored. In th…
Efficient method classifies locally stationary time series based on second-order characteristics.
problem Classifying locally stationary time series for various applications.
method Autoregressive approximation, ensemble aggregation, distance-based threshold.
result Zero misclassification error rate asymptotically for mildly differing second-order characteristics.
Second-order economic theory considers new variables to improve price volatility predictions.
problem Current economic models focus on first-order variables, missing second-order variables that affect price volatility.
method Introduces second-order economic theory with new variables composed of sums of squares of agents' transactions.
result Second-order economic theory complements first-order variables and introduces new macroeconomic variables.
SONIA optimizes machine learning problems with a novel algorithm.
problem Empirical risk minimization in machine learning.
method Symmetric Blockwise Truncated Optimization (SONIA) algorithm combining second-order and steepest descent steps.
result SONIA converges to stationary points in both convex and nonconvex cases.
A new optimization method improves deep learning accuracy without hyper-parameter tuning.
problem Computational demands and convergence behavior in deep learning training.
method Stochastic quasi-Gauss-Newton (SQGN) optimization method combining stochastic quasi-Newton, Gauss-Newton, and variance reduction.
result SQGN provides excellent accuracy without hyper-parameter experimentation, improving convergence and computational performance.
ADAHESSIAN optimizes machine learning models with adaptive second-order methods.
problem Efficiently optimizing machine learning models with second-order methods.
method Dynamic Hessian estimation via adaptive estimates, incorporating fast approximations and moving averages.
result ADAHESSIAN achieves state-of-the-art performance across various tasks.
EvoGrad improves efficiency in meta-learning and hyperparameter optimization.
problem Efficiently compute hypergradients for larger network architectures.
method Uses evolutionary techniques to estimate hypergradients without second-order derivatives or longer computational graphs.
result Significant improvements in efficiency, enabling scaling to bigger architectures.
Second-order optimizers retain residual information after data deletion, affecting machine unlearning.
problem Residual information in second-order optimizers after data deletion.
method Comparison of first-order and second-order learners, eigendecomposition analysis.
result Second-order optimizers retain residual information, not detectable by first-order analysis.
Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in \emph{second-order} methods, which rely on both gradients and Hessians. In principle, second-order methods can require …
Recently, we proposed to transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average, and use separate shortcut connections to model the linear dependencies instead. We continue the work by firstly introducing a third transformation to normalize the scal…
Gradient-based meta-learning has proven to be highly effective at learning model initializations, representations, and update rules that allow fast adaptation from a few samples. The core idea behind these approaches is to use fast adaptation and generalization -- two second-order metrics -- as training signals on a me…
SOLBP extends efficient inference to uncertain Bayesian networks.
problem Inference in uncertain Bayesian networks with second-order probabilities.
method Extends Loopy Belief Propagation to second-order Bayesian networks.
result Generates inferences consistent with sum-product networks, more efficient and scalable.
Developed a theory of local convexity for second order differential equations on Lie algebroids.
problem Analyzing convexity in differential equations on Lie algebroids.
method Theory development for local convexity of SODEs on Lie algebroids.
result Extensive discussion of homogeneous quadratic SODEs on Lie algebroids.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
problem Capturing higher-order tail behavior and dependence effects in risk measures.
method Second-order asymptotic expansions using extreme value theory and regular variation theory.
result Second-order approximations reduce approximation errors, especially at extreme confidence levels.
Simplified argument for second order estimate in quaternionic Calabi-Yau problem.
problem Second order estimates for quaternionic Calabi-Yau problem on hyperkähler manifolds.
method Simplified argument to derive the estimate.
result Simplified derivation of second order estimate.
LIBS2ML is a library based on scalable second order learning algorithms for solving large-scale problems, i.e., big data problems in machine learning. LIBS2ML has been developed using MEX files, i.e., C++ with MATLAB/Octave interface to take the advantage of both the worlds, i.e., faster learning using C++ and easy I/O…
Paper studies second order tail probabilities in risk models.
problem Analyzing tail probabilities in risk models with constant interest force.
method Asymptotic expansion and weighted Kesten-type inequality for second order subexponential random variables.
result Second order asymptotic formulae for continuous-time renewal risk models are derived.
A dynamical system on the total space of the fibre bundle of second order accelerations, T2M, is defined as a third order vector field S on T2M, called semispray, which is mapped by the second order tangent structure into one of the Liouville vector field. For a regular Lagrangian of second order we prove that …
Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.
problem Exploring properties of second order symmetric parallel tensors in generalized f.pk-space forms.
method Analyzes the properties of second order symmetric parallel tensors and deduces the existence or non-existence of certain tensors and hypersurfaces.
result There does not exist second order skew-symmetric parallel tensor in f.pk-space form. There is no parallel hypersurface in a generalized f.pk-space form but there is semi-parallel hypersurface.
With the rapid adoption of machine learning systems in sensitive applications, there is an increasing need to make black-box models explainable. Often we want to identify an influential group of training samples in a particular test prediction for a given machine learning model. Existing influence functions tackle this…
Paper generalizes connections between Lie groups and affine connections.
problem Exploring properties of infinitesimal groups and affine connections.
method Introducing second-order infinitesimal groups and using them to define Lie brackets and connections.
result Generalized correspondence between symmetric and non-symmetric affine connections.
New method learns population dynamics from snapshots, outperforming existing models.
problem Capturing periodic and other dynamical properties of population dynamics.
method Wasserstein Lagrangian Mechanics (WLM) for learning second-order dynamics from observed marginals.
result WLM outperforms existing methods across various dynamics, including vortex dynamics, embryonic development, and flocking.
Study proposes BFEL framework for privacy-preserving FL in personalized healthcare.
problem Privacy and security concerns in traditional cloud-centric ML, especially in wearable devices.
method Develops a blockchain-enhanced federated edge learning (BFEL) framework based on FedCurv, incorporating fisher information matrix and public key encryption.
result Significant reduction in communication cost and high efficiency for federated training on non-iid and heterogeneous data.