A fast method for training linear classifiers maximizes margins.
problem Training linear classifiers with maximum margins.
method Momentum-based gradient method derived from convex dual with Nesterov acceleration.
result Exponentially faster convergence rate compared to standard methods.
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these metho…
New method improves image and signal processing with nonconvex rank surrogates and dual momentum.
problem Optimizing nonconvex rank minimization problems in image processing.
method Proposes a novel nonconvex rank surrogate, uses ADMM with dual momentum trick.
result Effective in image and signal processing applications, outperforming state-of-the-art methods.
DanSmp predicts stock movement using a hybrid-relational MKG and dual attention networks.
problem Predicting stock price trends in volatile financial markets.
method Constructs a bi-typed MKG with hybrid-relations and uses DanSmp, a dual attention network, to learn momentum spillover signals.
result DanSmp improves stock prediction accuracy using the MKG.
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…
This paper is a rigorous study of the dual pair structure of the ideal fluid and the dual pair structure for the n-dimensional Camassa-Holm (EPDiff) equation, including the proofs of the necessary transitivity results. In the case of the ideal fluid, we show that a careful definition of the momentum maps leads natura…
New algorithm accelerates single-pass SGD for generalized linear prediction.
problem Improving single-pass non-quadratic stochastic optimization.
method Data-dependent proximal method incorporating dual-momentum acceleration.
result Momentum acceleration resolves open problem in streaming setting.
Introduces comomentum sections and proves they are Poisson maps.
problem Generalizing Poisson maps to Hamiltonian Lie algebroids.
method Introduces comomentum sections and proves they are Lie algebroid morphisms and Poisson maps.
result Comomentum sections are Poisson maps between proper Poisson manifolds.
Two single-timescale algorithms improve TD learning with nonlinear approximations.
problem Optimizing TD learning with nonlinear smooth function approximation.
method Proposes two single-timescale single-loop algorithms with momentum and variance reduction.
result Achieves O(ε−4) sample complexity for the first algorithm and O(ε−3) for the second. We generalize various symplectic reduction techniques to the context of the optimal momentum map. Our approach allows the construction of symplectic point and orbit reduced spaces purely within the Poisson category under hypotheses that do not necessarily imply the existence of a momentum map. We construct an orbit red…
We generalize the notions of dual pair and polarity introduced by S. Lie and A. Weinstein in order to accommodate very relevant situations where the application of these ideas is desirable. The new notion of polarity is designed to deal with the loss of smoothness caused by the presence of singularities that are encoun…
For a spacelike 2-surface in spacetime, we propose a new definition of quasi-local angular momentum and quasi-local center of mass, as an element in the dual space of the Lie algebra of the Lorentz group. Together with previous defined quasi-local energy-momentum, this completes the definition of conserved quantities i…
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.
We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in [26] to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group…
In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and C∗-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a quantisation of the Lie-Poisson structure of the dual of a Lie algebroid which deals wit…
The paper extends Vlasov kinetic theory to time-dependent dynamics using cosymplectic and cocontact manifolds.
problem Extending Vlasov kinetic theory to time-dependent dynamics.
method Introducing geometric kinetic theories within cosymplectic and cocontact manifolds.
result Alternative realizations of cosymplectic and cocontact kinetic theories linked via Poisson/momentum maps.
MDA optimizer performs similarly to SGD+M in CV and Adam in NLP.
problem Performance degradation due to choosing the wrong optimizer.
method Modernized Dual Averaging (MDA) optimizer, inspired by dual averaging.
result MDA performs as well as SGD+M in CV and as Adam in NLP.
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.
New method improves optimization algorithms without Lipschitz smoothness.
problem Improving optimization algorithms in the absence of Lipschitz smoothness.
method Dual kernel conditioning (DKC) to provide dual Lipschitz continuity.
result First complexity bounds and iterate convergence for random reshuffling mirror descent.
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.
Cryptocurrency forecasting model considers macro, sentiment, and technical indicators.
problem High price volatility in cryptocurrency markets.
method Dual-prediction mechanism incorporating macroeconomic fluctuations, technical indicators, and individual cryptocurrency price changes.
result The proposed model outperforms ten comparison methods in short-term cryptocurrency forecasting.
New algorithm solves minimax games with linear constraints.
problem Nonconvex minimax games with coupled linear constraints.
method Primal-dual alternating proximal gradient (PDAPG) algorithm.
result Achieves ε-stationary solution within O(ε^(-2)) iterations for strongly concave settings.
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.
In this paper we study Poisson actions of complete Poisson groups, without any connectivity assumption or requiring the existence of a momentum map. For any complete Poisson group G with dual G⋆ we obtain a suitably connected integrating symplectic double groupoid $\calS$. As a consequence, the cotangent lift …
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…
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…
DEAM optimizes momentum weights dynamically to improve deep learning model training.
problem Errors in momentum weights propagate errors in optimization algorithms like ADAM.
method DEAM computes adaptive momentum weights based on discriminative angles, reducing hyperparameters and introducing a backtrack term.
result DEAM achieves faster convergence rates in both convex and non-convex deep learning model training.
Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.
problem Nonconvex minimax problems with coupled linear constraints.
method Zeroth-order primal-dual alternating projected gradient (ZO-PDAPG) and zeroth-order regularized momentum primal-dual projected gradient (ZO-RMPDPG) algorithms.
result Iteration complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints.
Adapting momentum from optimization to reinforcement learning.
problem Improving the convergence and stability of reinforcement learning algorithms.
method Introducing Momentum Value Iteration (MoVI) by incorporating an average of consecutive state-action value functions, inspired by the concept of momentum in optimization.
result MoVI improves the convergence and stability of reinforcement learning algorithms, as demonstrated by experiments on Atari games.
Sparse learning speeds up neural network training without sacrificing accuracy.
problem Training deep neural networks efficiently while maintaining performance.
method Sparse momentum algorithm that redistributes and grows weights based on momentum magnitude.
result State-of-the-art sparse performance on various datasets with up to 5.61x faster training.
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.
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.
Study uses deep learning to predict stock trends with superior performance.
problem Predicting short-term equity trends with high accuracy.
method Dual-task multilayer perceptron (MLP) integrating technical signals and deep learning.
result Deep learning model outperforms linear baselines in multi-factor stock selection.
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.
GMC uses global momentum for sparse communication in distributed learning.
problem Latency and bandwidth limitations in network communication for large-scale deep learning models.
method GMC utilizes global momentum for sparse communication in DMSGD, improving convergence and accuracy.
result GMC and GMC+ achieve higher test accuracy and faster convergence compared to local momentum methods.
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.
The paper investigates momentum and liquidity in crypto markets.
problem Exploring the relationship between momentum effects and liquidity in cryptocurrency markets.
method Formed and rebalanced portfolios based on momentum-liquidity bivariate sorts across various cryptocurrencies over time.
result Strong momentum effect in the most liquid cryptocurrencies supports herding behavior theories.
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 …
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.