We introduce the concept of spontaneous symmetry breaking to arbitrage modeling. In the model, the arbitrage strategy is considered as being in the symmetry breaking phase and the phase transition between arbitrage mode and no-arbitrage mode is triggered by a control parameter. We estimate the control parameter for mom…
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
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48 results for “Momentum Control”
The study analyzes momentum-based optimization algorithms from dynamical systems perspective.
problem Understanding convergence rates of momentum-based optimization algorithms.
method Exploits dynamical systems, control theory, and symplectic perspectives to analyze convergence rates.
result Provides closed-form expressions relating algorithm parameters to convergence rates.
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.
Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.
problem Reduction of controlled Lagrangian systems with symmetry and momentum map.
method Using Legendre transformation and Euler-Lagrange vector field, the paper extends symmetric reduction theory.
result Established regular reduction theory for RCL systems with symmetry and momentum map.
To overcome the oscillation problem in the classical momentum-based optimizer, recent work associates it with the proportional-integral (PI) controller, and artificially adds D term producing a PID controller. It suppresses oscillation with the sacrifice of introducing extra hyper-parameter. In this paper, we start by …
A new family of momentum coefficients improves the convergence rate of accelerated algorithms.
problem Improving the convergence rate of accelerated gradient methods for strongly convex functions.
method Introducing a family of controllable momentum coefficients for forward-backward accelerated methods.
result Established a controllable $O\left(1/k^{2α}
ight)$ convergence rate for the NAG- method.
Mime algorithm improves federated learning by adapting centralized methods.
problem Mitigating client drift in federated learning.
method Combines control variates and server-level statistics to adapt centralized algorithms to federated learning.
result Mime outperforms any centralized method in federated learning.
Control data constructed for smooth weak deformation retraction of stratified spaces.
problem Construct control data for smooth weak deformation retraction of stratified spaces.
method Show smooth local triviality with conical fibers, construct control data, use fiber-wise scalar multiplications.
result Obtain neighbourhood smooth weak deformation retraction of stratified spaces.
L2GMOM learns financial networks and optimizes momentum strategies.
problem Expensive databases and financial expertise limit network construction accessibility.
method End-to-end machine learning framework (L2GMOM) that learns networks and optimizes trading signals.
result Significant improvement in portfolio profitability and risk control with Sharpe ratio of 1.74.
In 1996, Huisken-Yau proved that every three-dimensional Riemannian manifold can be uniquely foliated near infinity by stable closed surfaces of constant mean curvature (CMC) if it is asymptotically equal to the (spatial) Schwarzschild solution. Later, their decay assumptions were weakened by Metzger, Huang, Eichmair-M…
Model optimizes trading strategy with unobservable toxicity.
problem Maximizing daily trading profit with unobservable toxicity.
method Formulated as a partially observable stochastic control problem, solved in two steps.
result P&L performance gap is negligible (0.01%) in all scenarios.
FedNNNN improves FL by adjusting model update vector norms.
problem Slow convergence and low prediction accuracy in FL.
method Norm-Normalized Neural Network Aggregation (FedNNNN) with momentum control.
result Up to 5.4% accuracy improvement on multiple datasets.
Randomized control methods improve asset pricing and performance analysis.
problem Challenges in drawing inferences from traditional random portfolios in performance evaluation.
method Geometric random walks and Markov chain Monte Carlo methods to construct flexible control groups.
result Captured premia associated with size, value, quality, and momentum in a constrained setting.
SUSTAIN algorithm tackles stochastic bilevel optimization with near-optimal complexity.
problem Stochastic bilevel optimization problems with specific convexity and smoothness properties.
method SUSTAIN algorithm using single-timescale double-momentum stochastic approximation.
result SUSTAIN achieves near-optimal complexity for finding ε-stationary solutions.
Symmetric Reduction and Hamilton-Jacobi Equations of the Controlled Underwater Vehicle-Rotor Systemmath.SG
In this paper, we first give the regular point reduction and the two types of Hamilton-Jacobi equation for a regular controlled Hamiltonian (RCH) system with symmetry and momentum map on the generalization of a semidirect product Lie group. Next, as an application of the theoretical results, we consider the underwater …
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.
Study the commutativity of reduction and symplectification in contact Hamiltonian systems.
problem Understanding the commutativity of reduction and symplectification in contact Hamiltonian systems.
method Introduce symplectic and contact geometry, perform reduction via momentum map, analyze symplectification process.
result Commutativity relations between reduction and symplectification in contact Hamiltonian systems.
In this paper, we carry a detailed study of mechanical systems with configuration space for which the base variables are being controlled. The overall system's motion is considered to be induced from the base one due to the presence of general non-holonomic constraints. It is shown that the…
Customer Momentumq-fin.PR
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 studies deep learning methodologies for portfolio optimization in the US equities market. We present a novel residual switching network that can automatically sense changes in market regimes and switch between momentum and reversal predictors accordingly. The residual switching network architecture combines …
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.
Reduces multisymplectic Lie systems through symmetry analysis.
problem Solving multisymplectic Lie systems using symmetry reduction.
method Using momentum maps for reduction and reconstruction of multisymplectic Lie systems.
result Solves the original problem by analyzing simpler multisymplectic Lie systems.
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to , the bundle of vertically adapted linear frames over the bundle of field configurations . 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.
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…
Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithmquant-ph
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.
3MSBM learns smooth trajectories from multiple snapshots.
problem Capturing long-range temporal dependencies in complex systems.
method Lifts dynamics to phase space, generalizes stochastic bridges to multi-marginal conditional problems, learns transport maps preserving intermediate marginals.
result Significantly improves convergence and scalability in capturing complex dynamics.
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.
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 …
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…
Constructibility of momentum maps and linear variation for singular symplectic reduced spacesmath.SG
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.
The use of momentum in stochastic gradient methods has become a widespread practice in machine learning. Different variants of momentum, including heavy-ball momentum, Nesterov's accelerated gradient (NAG), and quasi-hyperbolic momentum (QHM), have demonstrated success on various tasks. Despite these empirical successe…
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.
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 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.
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.
In this paper, we introduce Symplectic ODE-Net (SymODEN), a deep learning framework which can infer the dynamics of a physical system, given by an ordinary differential equation (ODE), from observed state trajectories. To achieve better generalization with fewer training samples, SymODEN incorporates appropriate induct…