Regularizes RNNs to handle long-range dependencies and multiple time scales.
problem Identifying nonlinear dynamical systems with varying time scales and long-range dependencies.
method A simple regularization scheme for vanilla RNNs with ReLU activation.
result Regularized RNNs can solve long-range dependency problems and express slow time scales.
Framework learns surrogates for molecular dynamics across multiple time-scales.
problem Stable molecular dynamics simulations require small time-steps, but long-time-scale moments need repeated simulations.
method Implicit Transfer Operator Learning with denoising diffusion probabilistic models and SE(3) equivariant architecture.
result Models can generate self-consistent stochastic dynamics across multiple time-scales.
Study how financial market participants have different objectives at various time scales.
problem Understanding how financial market participants have different objectives at various time scales.
method Use Inverse Reinforcement Learning to compute the effective reward function for the aggregate agent class at each scale.
result Identify differences in reward functions for feature vectors across different scales, indicating different objectives of market participants.
This work proposes a geometric approach to identify slow invariant manifolds in dynamical systems.
problem Identifying slow invariant manifolds in multiple time-scale dynamical systems.
method Differential geometric concepts for submanifolds, sectional curvature, flow invariance.
result Necessary condition for slow invariant manifold invariance stated in terms of differential geometry.
A digital twin for multi-scale systems uses physics-based and machine learning models.
problem Lack of application-specific details in digital twin technology.
method Strategically separates into physics-based and data-driven models; uses mixture of experts with Gaussian Process.
result Robust and accurate predictions at future time-steps for multi-scale systems.
A new geometric method approximates slow invariant manifolds without explicit time-scale separation.
problem Approximating slow invariant manifolds in systems with multiple time-scales.
method Geodesic Stretching and Flow Curvature methods translated into tensorial constructions of Riemannian geometry.
result The method approximates normally attracting invariant manifolds without requiring explicit time-scale separation.
This paper improves traditional Markowitz optimization by considering variance at multiple time scales.
problem Traditional Markowitz optimization limits to a single time scale, ignoring variance across different frequencies.
method Introduces multifrequency optimization allowing specification of target Hurst exponents across multiple time scales.
result Effective risk management strategy that aligns with investor preferences at various time scales.
Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square superstatistics works well on a time scale…
This paper addresses metaconsistency in Bayesian inference for metastable systems.
problem Inference for metastable systems may not be consistent, but can be metaconsistent over large but finite time intervals.
method Introduces metaconsistency in a Bayesian framework, discusses its relation to spectral properties of model dynamics.
result Metaconsistency can be exploited to infer sub-systems efficiently from larger systems.
Improved bounds for non-linear SA with fast convergence.
problem Stochastic approximation with non-linear mappings and multiple time scales.
method Mean squared error bounds with O(1/k) rate for contractive mappings. result First O(1/k) rate for non-linear two-time-scale SA without additional smoothness assumptions. The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question …
Two-step model estimates DLMO using both daily and frequent data.
problem Expensive and time-consuming DLMO measurement.
method Two-step framework combining daily and frequent data.
result Two-step model with two time-scale features has lower errors.
Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological food-webs. We focus on the relation between increasing complexity of the economic n…
The Epps effect varies under different sampling schemes, affecting correlation emergence rates.
problem Uncertainty in choosing time and sampling rates for financial systems.
method Comparison of Epps effect under calendar, volume, and trade time schemes using a Hawkes process model.
result Correlations emerge faster under trade time compared to calendar time, and linearly under volume time.
Study on price fluctuations and persistence in European electricity spot markets.
problem Analyzing variability and persistence of electricity prices in European spot markets.
method Analysis of hourly, intraday, and 15-min intraday market prices; quantification of fluctuations, correlations, and extreme events; classification into circulation weather types.
result Different time scales in market dynamics; multifractal behavior below 12 hours; anti-correlation and mean reversion above 12 hours; long-term behavior influenced by four-day weather patterns; q-Gaussian distributions as best fit. MS-CASTLE learns causal structures across multiple time scales.
problem Inferring causal relationships between time series data at different scales.
method Uses stationary wavelet transform and non-convex optimization to estimate causal structures.
result MS-CASTLE reveals meaningful causal interactions, especially at mid-term time resolutions.
Automates PDE model reduction with time-scale separation.
problem Computational expense in solving high-dimensional PDEs.
method Combines autoencoder and time-continuous model for latent dynamics.
result Automatically learns independent temporal scales in complex systems.
This work shows how approximate reward models can significantly improve inference-time scaling.
problem Improving the efficiency of inference for large language models.
method Identifying the Bellman error of approximate reward models and using Sequential Monte Carlo (SMC) for inference.
result Approximate reward models can reduce computational complexity from exponential to polynomial in T. Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been propos…
AdaCare learns health status from biomarkers across multiple time scales.
problem Lack of explicit extraction of historical biomarker variation and adaptability to diverse patient conditions.
method Scale-adaptive feature extraction and recalibration for interpretability.
result AdaCare achieves state-of-the-art prediction accuracy and provides interpretable results.
Proposes a model to recommend products at the right time to meet user demands.
problem Maximizing product sales by recommending products at the right time to meet user demands.
method Integrates user interests and time-based demands into a Long-Short Demands-Aware Model (LSDM) using recurrent neural networks.
result Demonstrates the effectiveness of the LSDM in next-item recommendation on real-world commerce datasets.
Novel digital twin for complex systems improves performance.
problem Lack of practical implementation details for stochastic nonlinear MDOF systems.
method Decouples time-scales, uses physics-based model, Bayesian filtering, and machine learning.
result Excellent performance of proposed digital twin framework validated by examples.
We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents p± usually vary with the strength of the lar…
We present an empirical analysis of the microstructure of financial markets and, in particular, of the static and dynamic properties of liquidity. We find that on relatively large time scales (15 minutes) large price fluctuations are connected to the failure of the subtle mechanism of compensation between the flows of …
This work explores test-time scaling strategies for LLMs, improving sample efficiency and expressiveness.
problem Understanding the sample efficiency and expressiveness of test-time scaling strategies for LLMs.
method Established separation and expressiveness results for self-consistency, best-of-n, and self-correction strategies. result Self-correction enables Transformers to simulate online learning over multiple tasks without prior knowledge.
Aims to describe neural network training dynamics using two-time-scale models.
problem Lack of a general mathematical description of neural network training.
method Introduces a theoretical framework based on two-time-scale population dynamics.
result Derives selection-mutation equations and effective fitness for hyperparameters.
Time-warping improves RNN transfer learning for diverse time scales.
problem Transfer learning for RNNs with varying time scales.
method Time-warping rescales time in LSTM models for better transfer.
result Time-warping maintains accuracy in transferring RNNs between different time scales.
Study on improving the linear two-time-scale stochastic approximation method with a restarting scheme.
problem Characterizing and optimizing the finite-time complexity of linear two-time-scale stochastic approximation.
method Analysis of mean square errors, introduction of a restarting scheme to improve performance.
result The method achieves an exact convergence to the desired solution with improved complexity under time-varying step sizes.
For a given time horizon DT, this article explores the relationship between the realized volatility (the volatility that will occur between t and t+DT), the implied volatility (corresponding to at-the-money option with expiry at t+DT), and several forecasts for the volatility build from multi-scales linear ARCH process…
Study Morse models for torus algebra related to knot homology.
problem Understanding algebraic structures of tori and knots.
method Construct Morse models and use multiple time scale dynamics.
result Identifies Cord(T_K) with Cord(K) and relates to Legendrian contact homology.
This study examines memory effects in S&P500 market correlations using Langevin models.
problem The neglect of memory effects in market correlations for optimal portfolio selection.
method Fit a generalised Langevin equation (GLE) to S&P500 market correlation data.
result Memory effects in market correlations significantly improve forecasting accuracy and suggest a hidden slow time scale.
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the interaction between traders and hierarchical cascade models to unravel the possi…
Recurrent Neural Processes model time series with conditional independence to capture slow variabilities efficiently.
problem Modeling time series data with slow long-term variabilities efficiently.
method Recurrent Neural Processes (RNP) model state space with conditional independence among subsequences.
result RNP state spaces improve predictive performance on real-world time-series data and nonlinear system identification.
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical interest is computationally infeasible or impractical. In complex systems, with lim…
Deep neural network detects changepoints at multiple scales in multivariate time series.
problem Detecting gradual and abrupt changes in multivariate time series data.
method Proposed a pyramid recurrent neural network (PRN) for multi-scale changepoint detection.
result PRN outperforms state-of-the-art methods in detecting changepoints at multiple scales.
A new SOHP filter improves trend estimation in economic time series.
problem Improving trend estimation in nonlinear economic time series.
method Recursive application of one-sided HP filter on updated cyclical components, combined with an incremental HP filtering algorithm.
result Better performance of SOHP filter compared to other HP-type filters on real economic data.
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary non-Gaussian process which captures many features observed in time series of real stock r…
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
problem Capturing the statistical properties of fluctuating correlations in non-stationary systems.
method Developed a random matrix model to average multivariate amplitude distributions from short time scales to large time scales.
result Explicit multivariate distributions for non-stationary correlation systems are provided, capturing the degree of non-stationarity.
Neural population activity often exhibits rich variability and temporal structure. This variability is thought to arise from single-neuron stochasticity, neural dynamics on short time-scales, as well as from modulations of neural firing properties on long time-scales, often referred to as "non-stationarity". To better …
Investment strategies differ based on short-term and long-term market time scales.
problem Identifying and understanding different time scales in stock market dynamics.
method Empirical Mode Decomposition (EMD) and Hurst Exponent analysis.
result Short-term market dynamics are random, while long-term are correlated with company fundamentals.
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate framework to account simultaneously for correlations across times scales and bet…
The expOU stochastic volatility model is capable of reproducing fairly well most important statistical properties of financial markets daily data. Among them, the presence of multiple time scales in the volatility autocorrelation is perhaps the most relevant which makes appear fat tails in the return distributions. Thi…
We establish decoupled functional CLTs for two-time-scale stochastic approximation.
problem Understanding the asymptotic behavior of two-time-scale stochastic approximation.
method Martingale problem approach and auxiliary sequence.
result The limiting dynamics of two-time-scale SA are independent of each other.
Study reveals how correlation matrix eigenvalues change with time scale in U.S. stocks.
problem Understanding how correlation structure of securities changes with time scale.
method Aggregated one-minute returns of 533 U.S. stocks at different time scales, estimated correlation matrix, lead-lag factor model.
result Emergence of several dominant eigenvalues as time scale increases.
EMD reveals dynamic cross-correlations across financial indices at various time-scales.
problem Characterizing time-varying multidimensional cross-correlations in financial indices.
method Empirical Mode Decomposition applied to intraday time series of financial indices.
result Uncovered rich heterogeneity of interactions dependent on time-scale and led-lag relations.
Extended LSTMs improve volatility prediction by 20%.
problem Predicting asset price volatility with long memory.
method Extended LSTMs with multiple flexible timescales.
result Extended LSTMs outperform rough volatility predictions by 20%.
URGE improves diffusion model quality without gradients or Hessian.
problem Improving sample quality in diffusion models without gradient evaluations.
method Path-wise importance reweighting via Girsanov change of measure.
result URGE achieves better generation quality than existing methods.
Study uses DNM theory to detect early warning signals of market instability.
problem Detecting early warning signals of financial market instability.
method Applying Dynamical Network Marker (DNM) theory to trading data from the Tokyo Stock Exchange.
result Early warning signals of large price movements can be detected on a daily time scale.