The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the expression of the stochastic process is found. An application of the model propo…
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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 “memory stochastic”
Unified treatment of RC in stochastic and deterministic settings.
problem Understanding and generalizing reservoir computing in both deterministic and stochastic contexts.
method Investigation of state-space systems, analysis of fading memory and solution stability, introduction of stochastic echo states.
result Generality of fading memory and solution stability in state-space systems, even without the echo state property.
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential eq…
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
Gravitational wave memory increases faster than Brownian motion in early universe and astrophysical sources.
problem Detecting gravitational wave memory from early universe and astrophysical sources.
method Investigated gravitational wave sources in early universe and astrophysical settings, showing memory increases faster than Brownian motion.
result Gravitational wave memory increases following a power law, faster than the scaling law of Brownian motion.
The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example of Markov processes with spurious memory is stochastic process driven by a non-…
SMGD trains low-bit neural networks with memory constraints.
problem Training large neural networks with limited memory.
method Stochastic Markov Gradient Descent (SMGD).
result Encouraging numerical results and theoretical guarantees.
The choice of how to retain information about past gradients dramatically affects the convergence properties of state-of-the-art stochastic optimization methods, such as Heavy-ball, Nesterov's momentum, RMSprop and Adam. Building on this observation, we use stochastic differential equations (SDEs) to explicitly study t…
New neural operators model turbulence with memory and randomness.
problem Modeling turbulence in complex fluid dynamics with memory and randomness.
method Symmetrized activation functions, fractional derivatives, and stochastic noise.
result Theoretical guarantees for approximation quality in turbulent phenomena.
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financia…
Heavy-tail driven by memoryq-fin.ST
We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation and the closed form momen…
Deep neural networks estimate long memory parameters efficiently.
problem Estimating long memory parameters in stochastic processes.
method Scale-invariant 1D Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) models trained with synthetic data.
result Neural models outperform conventional methods in precision, speed, consistency, and robustness.
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differen…
Bayesian neural networks can be partially stochastic without losing predictive power.
problem The necessity of fully stochastic parameters in Bayesian neural networks.
method Theoretical and empirical investigation of partially stochastic networks compared to fully stochastic ones.
result Expressive predictive distributions require only small amounts of stochasticity, and partially stochastic networks can match or outperform fully stochastic networks.
A general market model with memory is considered in terms of stochastic functional differential equations. We aim at representation formulae for the sensitivity analysis of the dependence of option prices on the memory. This implies a generalization of the concept of delta.
We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation. The moment …
The study analyzes prediction errors in systems with memory kernels, providing bounds and stability results.
problem Prediction errors in stochastic dynamical systems with memory kernels.
method Analysis of generalized Langevin equations (GLEs) with Volterra equations, integrating synchronized noise coupling and weighted norms.
result Prediction discrepancies decay at a rate determined by the memory kernel's decay, quantitatively bounded by kernel estimation errors.
The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as no…
New algorithms for streaming bandits with limited memory.
problem Optimizing decisions in a stream of uncertain outcomes with limited memory.
method Developed algorithms for minimizing regret and identifying the best arm under bounded memory constraints.
result Upper and lower bounds on sample complexity for best-arm identification algorithms.
Delay-SDE-net models time series with memory and uncertainty, outperforming other models.
problem Accurately modeling time series with memory and uncertainty.
method Stochastic delay differential equations (SDDEs) neural network model with aleatoric and epistemic uncertainty.
result The Delay-SDE-net consistently outperforms other models in predicting time series values and uncertainties.
RAD estimates gradients with less memory, faster than small batch sizes.
problem Training deep models with stochastic gradient descent requires exact gradients, but they are not needed.
method Developed a framework for randomized automatic differentiation (RAD) to compute unbiased gradient estimates with reduced memory.
result RAD converges in fewer iterations than using a small batch size for feedforward networks and similar number for recurrent networks.
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity observed in the stock markets. …
Deep neural networks solve stochastic control problems with delay.
problem Challenges in stochastic control problems with delay due to path-dependence and high dimensions.
method Employing recurrent neural networks (RNNs) to parameterize policies and optimize objectives.
result RNNs, especially LSTMs, efficiently capture path-dependence and outperform feedforward networks in training and performance.
Nonlinear RNNs' memory capacity varies widely, making it impractical.
problem The usefulness of memory capacity as a metric for linear RNNs is questioned.
method Analysis of random nonlinear RNNs with varying input scales.
result Memory capacity of nonlinear RNNs is arbitrary and impractical.
New constraints on space and adaptivity in bandits force more batches and memory use.
problem Simultaneous space and adaptivity constraints in stochastic bandits.
method Proved lower bounds and constructed an algorithm with near-minimax regret.
result Near-minimax regret requires more batches and memory than previously thought.
Memory-efficient algorithm reduces variance in off-policy RL.
problem High variance in off-policy policy optimization.
method Memory-efficient, stochastically variance-reduced algorithm using off-policy samples.
result Empirically validated effectiveness of the proposed algorithm.
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised. Connections with the class of ARCH() processes are sketched.
New algorithm reduces memory-regret trade-off for bandits.
problem Optimizing memory usage in stochastic multi-armed bandits.
method Designing an algorithm with specific regret bound and proving lower bound.
result Optimal regret characterization in terms of memory and rounds.
SRG improves optimization efficiency with reduced memory and computation overhead.
problem Limited applicability of variance-reduced optimization algorithms.
method SRG (stochastic reweighted gradient) using importance sampling.
result SRG outperforms SGD and provably improves convergence in strongly-convex cases.
We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic vari…
Modeling a Financial System with Memory via Fractional Calculus and Fractional Brownian Motionq-fin.ST
Modeling financial markets with memory using fractional calculus and Brownian motion.
problem Capturing memory effects in financial markets using stochastic models.
method Fractional Langevin equation with colored noise generated by fractional Brownian motion.
result Anomalous marginal glass phase observed in some regions of the system.
Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memoryq-fin.MF
In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy,…
New algorithms improve GP inference without approximations, achieving better results.
problem Inexact stochastic optimization methods in Gaussian Processes leading to biased results.
method Exact stochastic inference for GPs with finite dimensional RKHS, extending to infinite dimensions.
result Achieves better experimental results than existing methods in constrained resource settings.
Long memory stochastic volatility in option pricingcond-mat.other
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence. We consider the option price as a sum of classical Black-Scholes pric…
Stochastic attention learns to retrieve and generate from memory without training.
problem Learning to retrieve and generate from memory efficiently.
method Langevin dynamics on modern Hopfield energy for stochastic attention.
result Stochastic attention can retrieve and generate from memory without training, matching gold standards.
State-of-the-art models are now trained with billions of parameters, reaching hardware limits in terms of memory consumption. This has created a recent demand for memory-efficient optimizers. To this end, we investigate the limits and performance tradeoffs of memory-efficient adaptively preconditioned gradient methods.…
New algorithm reduces decision switching in dynamic environments.
problem Online learning with memory and non-stationary environments.
method Dynamic policy regret, novel ensemble approach, meta-base decomposition.
result Proves optimal dynamic policy regret for memory length, non-stationarity, and time horizon.
New algorithm reduces memory usage for multi-pass bandit problems.
problem Memory-efficient multi-pass bandit algorithms for large action spaces.
method Develops a -pass algorithm with memory that achieves optimal regret.
result Sharp memory-regret trade-off: memory suffices for regret in passes.
In this work we propose a new class of long-memory models with time-varying fractional parameter. In particular, the dynamics of the long-memory coefficient, , is specified through a stochastic recurrence equation driven by the score of the predictive likelihood, as suggested by Creal et al. (2013) and Harvey (2013)…
New perspective on SGD reveals short-range memory effects in deep learning.
problem Understanding the efficacy of stochastic gradient descent (SGD) in deep learning.
method Proposed that SGD is a discretization of an SDE driven by fractional Brownian motion (FBM).
result SGD stays longer in flat minima, favoring generalization.
Neural SDEs improve time series generation efficiency.
problem High memory and computational costs in GANs for time series.
method Conditional Neural Stochastic Differential Equations (SDEs).
result More memory efficient and faster than traditional methods.
fSDE-Net generates time series with long-term memory using neural networks.
problem Generating time series with long-term memory from irregularly sampled data.
method fSDE-Net: neural fractional Stochastic Differential Equation Network using fractional Brownian motion.
result fSDE-Net can replicate distributional properties of real time-series data.
Kanerva++: extending The Kanerva Machine with differentiable, locally block allocated latent memorycs.NE
New memory allocation scheme improves image generation performance.
problem Improving episodic and semantic memory representation in neural networks.
method Developed a hierarchical latent variable model with differentiable, locally block allocated latent memory.
result Improved conditional likelihood values on various datasets.
The paper introduces a new stochastic volatility model with long-term memory and jumps.
problem Developing a model for variance and volatility swaps with long-term memory and jumps.
method Fractional Barndorff-Nielsen and Shephard model incorporating long-term memory and jumps.
result Arbitrage-free prices for variance and volatility swaps derived for the new model.
Communication-Efficient, 2D Parallel Stochastic Gradient Descent for Distributed-Memory Optimizationcs.DC
HybridSGD improves SGD performance by balancing computation and communication.
problem Limited scalability and performance of SGD due to communication costs.
method 2D parallel SGD method (HybridSGD) that trades off between 1D -step SGD and 1D Federated SGD (FedAvg).
result HybridSGD achieves better convergence than FedAvg at similar processor scales and up to 121x speedup over FedAvg.
Global convergence of an online (stochastic) limited memory version of the Broyden-Fletcher- Goldfarb-Shanno (BFGS) quasi-Newton method for solving optimization problems with stochastic objectives that arise in large scale machine learning is established. Lower and upper bounds on the Hessian eigenvalues of the sample …
DAM with MRL improves relational reasoning in MANNs.
problem Limited performance of associative memory networks on complex relational reasoning tasks.
method Distributed Associative Memory architecture with Memory Refreshing Loss.
result Enhanced relation reasoning performance of MANNs on long temporal sequence data.
Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set be- comes essentially infinite. Recently, the stochastic MISO (S-MISO) algorithm i…