AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
problem High memory and computational costs of orthogonal momentum updates.
method AuON uses normalized nonlinear scaling and a 'emergency brake' to handle exploding attention logits.
result AuON achieves strong performance without approximate orthogonal matrices, preserving structural alignment and reconditioning.
A new optimizer preserves orthogonality constraints on matrices efficiently.
problem Optimization on Stiefel manifold with orthogonality constraints.
method Interplay between continuous and discrete dynamics leading to a gradient-based optimizer with momentum.
result The method optimizes matrices on Stiefel manifold efficiently and accurately.
Muon with Newton-Schulz converges to the same stationary point as SVD-polar, up to a constant factor.
problem Improving the convergence rate of Muon optimizer.
method Using Newton-Schulz steps for momentum orthogonalization, proving convergence rate and constant factor.
result Muon with Newton-Schulz converges to the same stationary point as SVD-polar, up to a constant factor.
MuonEq improves training of matrix-valued parameters by rebalancing momentum before orthogonalization.
problem Training matrix-valued parameters with orthogonalized-update optimizers like Muon.
method MuonEq introduces three lightweight pre-orthogonalization equilibration schemes: two-sided row/column normalization (RC), row normalization (R), and column normalization (C).
result Row/column normalization acts as a zeroth-order surrogate for whitening and improves the geometry seen by orthogonalization.
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to LVY, the bundle of vertically adapted linear frames over the bundle of field configurations Y. Specifically, the generalized field momentum obs…
The paper analyzes and improves a deep learning optimization technique using matrix gradient orthogonality.
problem Improving deep learning training through more effective optimization methods.
method Develops a stochastic non-Euclidean trust-region gradient method for deep learning optimization.
result Proves state-of-the-art convergence results for the proposed algorithm in various scenarios.
Integrates momentum into RNNs to improve training.
problem Vanishing gradient in RNNs during training.
method Established connection between RNN dynamics and GD, integrated momentum.
result MomentumRNNs alleviate vanishing gradient issue and improve convergence.
This paper is a rigorous study of two dual pairs of momentum maps arising in the context of fluid equations whose configuration Lie group is the group of automorphism of a trivial principal bundle, generically called here non-abelian fluids. It is shown that the actions involved are mutually completely orthogonal, whic…
A new method uses trivialized momentum to generate data on Lie groups.
problem Generating data on Lie groups with high fidelity and efficiency.
method Introducing an auxiliary momentum variable that stays in a fixed vector space, and using a manifold preserving integrator.
result Achieves state-of-the-art performance on protein and RNA torsion angle generation and high-dimensional Lie groups.
This study classifies quadric surfaces in 3-sphere as Weingarten surfaces.
problem Extension of quadric surfaces of revolution to 3-sphere.
method Rigorous classification and characterization using spherical angular momentum.
result Spherical ellipsoids, hyperboloids, and paraboloids are Weingarten surfaces with a specific cubic relation between principal curvatures.
This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian systems. It should be accessible to readers with a general knowledge of basic notions …
Develops a gradient flow for Muon optimizer, a method for optimization.
problem Optimization of complex systems with matrix-valued parameters.
method Gradient flow on probability measures induced by regularized Muon optimizer.
result Derives continuous-time limits and proves Hamiltonian dissipation.
The study finds that factor momentum is significant only at short lags compared to stock momentum.
problem Investigating the relationship between factor momentum and stock momentum.
method Replicated earlier findings and conducted a spanning test controlling for stock momentum and factor exposure.
result Factor momentum is significant only at short lags after controlling for stock momentum and factor exposure.
We test the price momentum effect in the Korean stock markets under the momentum universe shrinkage to subuniverses of the KOSPI 200. Performance of the momentum strategy is not homogeneous with respect to change of the momentum universe. It is found that some submarkets generate the higher momentum returns than other …
Introduces homotopy momentum sections on multisymplectic manifolds.
problem No specific problem stated; focuses on introducing a new concept.
method Introduces a new concept of homotopy momentum sections on multisymplectic manifolds.
result Shows that a gauged nonlinear sigma model with Wess-Zumino term has homotopy momentum section structure.
Customer momentum is a positive relationship between a firm's returns and past returns of its customers.
problem Understanding the relationship between a firm's returns and its customers' past returns.
method Examined customer momentum using a long-short equally-weighted decile portfolio and Fama-French factor models.
result Customer momentum generates significant monthly returns and is statistically significant.
This paper examines momentum spillover across multiple asset classes using only pricing data.
problem Challenges in studying momentum spillover across diverse asset classes due to lack of common characteristics.
method Utilised a linear and interpretable graph learning model to reveal momentum spillover network.
result Network momentum strategy yields a Sharpe ratio of 1.5 and an annual return of 22%.
The paper analyzes how hyperparameters affect SGD with momentum's convergence rate.
problem The role of hyperparameters in SGD with momentum's convergence rate.
method Theoretical analysis using a hyperparameters-dependent stochastic differential equation (hp-dependent SDE).
result The optimal linear rate of convergence depends on both the learning rate and the momentum coefficient.
The paper diagnoses factor models using characteristic axes and zero-curve restrictions.
problem Tackles systematic sign reversals and overcorrections in factor model pricing errors.
method Extends cap-axis integral diagnostic to general characteristic axes, measuring pricing errors as bridge-alpha curves.
result Axis-level pricing errors are nearly orthogonal to maximum-Sharpe gains, showing systematic sign reversals and overcorrections.
The paper diagnoses factor-model pricing errors using characteristic axes and bridge-alpha curves.
problem Tackles systematic sign reversals and overcorrections in factor-model pricing errors.
method Extends cap-axis integral diagnostic to characteristic axes, measures pricing errors as bridge-alpha curves, and uses a predetermined characteristic order to generate zero-curve restrictions.
result Axis-level pricing errors are nearly orthogonal to maximum-Sharpe gains, showing significant sign reversals and overcorrections.
We give a detailed discussion about existence and uniqueness of Lu's momentum map. More precisely, we introduce the infinitesimal momentum map, and we study its properties. This allows us to describe the theory of reconstruction of the momentum map from the infinitesimal one. We provide the conditions for the uniquenes…
Momentum ResNets improve ResNets' memory efficiency.
problem Memory inefficiency in deep residual neural networks (ResNets).
method Adding a momentum term to the forward rule of ResNets to make them invertible.
result Momentum ResNets can learn any linear mapping up to a multiplicative factor, improving memory efficiency.
The paper analyzes how momentum affects convergence in stochastic gradient methods.
problem Lack of clear understanding of momentum's impact on convergence and performance.
method Unified analysis of several popular algorithms using the QHM formulation.
result Provides practical guidelines for setting learning rate and momentum parameters.
We introduce various quantitative and mathematical definitions for price momentum of financial instruments. The price momentum is quantified with velocity and mass concepts originated from the momentum in physics. By using the physical momentum of price as a selection criterion, the weekly contrarian strategies are imp…
New algorithm Momentum-QNG improves optimization of quantum circuits.
problem Optimizing variational quantum circuits to avoid local minima.
method Applied Langevin dynamics to QNG, introducing momentum term.
result Momentum-QNG outperforms basic QNG and other optimizers.
We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to…
Momentum speeds up evolutionary processes in machine learning.
problem Accelerating convergence in evolutionary dynamics.
method Combining momentum from machine learning with evolutionary dynamics using information divergences as Lyapunov functions.
result Momentum accelerates convergence of evolutionary dynamics, including the replicator equation and Euclidean gradient descent.
Contact manifolds' momentum polytopes are convex.
problem Understanding the structure of contact manifolds.
method Using isomorphism to toric varieties.
result Momentum polytopes of contact manifolds are convex.
Unified model learns from both time-series and cross-sectional momentum features.
problem Separate time-series and cross-sectional momentum strategies do not consider concurrent relationships.
method Spatio-Temporal Momentum strategies using neural networks to combine both types of momentum.
result Simple neural network with single fully connected layer generates trading signals for all assets.
SMG combines shuffling and momentum for non-convex optimization.
problem Non-convex finite-sum optimization problems.
method Shuffling Gradient-based method with momentum.
result Established state-of-the-art convergence rates for SMG.
New method shows stochastic momentum can converge quickly on optimization problems.
problem Improving convergence of stochastic optimization methods.
method Stochastic heavy ball momentum with minibatching.
result Stochastic heavy ball momentum retains fast linear rate on quadratic problems.
The paper analyzes dynamics of momentum in high dimensions with sparse updates.
problem Theoretical analysis of momentum dynamics in high-dimensional sparse settings.
method Theoretical analysis of two models: least squares with sparse inputs and logistic regression with a rare class.
result Characterization of high-dimensional limits of momentum dynamics and phase structure.
Optimization algorithms with momentum, e.g., (ADAM), have been widely used for building deep learning models due to the faster convergence rates compared with stochastic gradient descent (SGD). Momentum helps accelerate SGD in the relevant directions in parameter updating, which can minify the oscillations of parameter…
One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true energy-momentum tensor. This problem is solved in the framework of the multimomentum …
Improved tensor GLM estimation for complex data.
problem Complex tensor data in GLMs leads to high-dimensional, ill-posed estimation.
method Proposed LSRTR-M algorithm using Muon updates for faster convergence and lower errors.
result LSRTR-M converges faster and achieves lower errors than LSRTR.
The paper extends a theorem about momentum maps to singular symplectic spaces.
problem Extending a theorem about momentum maps to singular symplectic spaces.
method Using integral affine stratification and equivariant locally trivial fibrations, the paper extends the linear variation theorem to singular values of the momentum map.
result Cohomology classes of symplectic forms on reduced spaces vary linearly within strata.
This paper analyzes momentum Q-learning with finite-sample guarantees.
problem Improving Q-learning performance with momentum schemes.
method Proposes MomentumQ algorithm integrating Nesterov and Polyak's momentum schemes, analyzes convergence for function approximations.
result Establishes finite-sample convergence rates for MomentumQ, demonstrating better performance than vanilla Q-learning.
Momentum improves deep learning generalization by stabilizing noise and learning features.
problem Improving generalization in deep learning models.
method Empirical and theoretical analysis of gradient descent with momentum (GD+M) vs. gradient descent (GD) in binary classification tasks.
result GD+M outperforms GD in generalization, especially in datasets with shared features and varying margins.
Generalizes momentum map to Courant algebroid for constrained mechanics.
problem Generalizing momentum map to new geometric structures.
method Generalized momentum section on Lie algebroid to Courant algebroid, constructed cohomological formulations.
result Identified momentum section in constrained Hamiltonian mechanics with Courant algebroid symmetry.
Momentum SGD fails to track nonstationary optima due to drift amplification.
problem Tracking nonstationary optima in stochastic optimization.
method Theoretical analysis of SGD and momentum variants under strong convexity and smoothness.
result Momentum incurs a drift-amplification penalty that diverges as the momentum parameter approaches 1, leading to systematic lag.
This paper concentrates on the time series momentum or contrarian effects in the Chinese stock market. We evaluate the performance of the time series momentum strategy applied to major stock indices in mainland China and explore the relation between the performance of time series momentum strategies and some firm-speci…
A new accelerated method with simpler momentum update rules.
problem Optimizing parameters in machine learning models.
method Proposes a novel accelerated stochastic gradient method with simpler momentum update rules.
result The method outperforms Sgdm and Adam in practical problems.
The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate schemes, such as AdaGrad and Adam, and (2) accelerated schemes, such as heavy-ball an…
New method uses momentum to converge in DC optimization with small batches.
problem Lack of convergence properties for stochastic difference-of-convex optimization with small batch sizes.
method Introduces momentum to enable convergence under standard assumptions for any batch size.
result Proves convergence of the algorithm under smoothness and bounded variance assumptions.
Dynamic econometric models improve trading signals in momentum strategies.
problem Static momentum strategies are inefficient; dynamic models enhance accuracy.
method Dynamic binary classifier model to learn time-varying momentum importance.
result Dynamic classifier outperforms traditional naive time series momentum strategy.
Stochastic proximal point algorithm with momentum converges faster and is more stable than standard methods.
problem Improving convergence and stability of stochastic optimization methods.
method Developed and analyzed the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM).
result SPPAM converges faster and is more stable than standard stochastic proximal point algorithm (SPPA) and stochastic gradient descent with momentum (SGDM).
Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.
problem Deriving transformation formulae for mass and angular momentum under BMS transformations.
method Two approaches: from curvature tensor and metric coefficients.
result Exact expressions for Drey-Streubel angular momentum of a general section.
Negative momentum accelerates convergence in minimax games but at a suboptimal rate.
problem The convergence rate of negative momentum in minimax games is suboptimal.
method Extending variational inequality formulation, connecting momentum method with Chebyshev polynomials.
result Negative momentum accelerates convergence locally but at a suboptimal rate.