Method validates periodic and singular orbits in fast-slow systems with one-dimensional slow variable.
problem Validation of periodic, homoclinic, and heteroclinic orbits in fast-slow systems with one-dimensional slow variable.
method Topological tools (isolating blocks, cone condition, covering relations) and additional techniques (slow shadowing, m-cones) for rigorous numerics.
result Validation of global orbits for fast-slow systems across a wide range of ε.
The paper studies invariant complex manifolds in holomorphic slow-fast systems.
problem Existence of invariant complex manifolds in holomorphic systems.
method Geometric singular perturbation theory, Fenichel and Briot-Bouquet theories.
result Conditions are provided to guarantee the existence of one-dimensional invariant complex manifolds.
Method learns dynamics of slow variables from stochastic data.
problem Modeling unknown multiscale stochastic systems with limited data.
method Data-driven approach to learn effective dynamics from bursts of observation data.
result Generative model accurately captures effective dynamics of slow variables.
Paper introduces slow kill for efficient large-scale variable screening.
problem Challenges in variable selection and parameter estimation for big data.
method Nonconvex constrained optimization, adaptive \(\ell_2\)-shrinkage, and increasing learning rates.
result Slow kill outperforms state-of-the-art algorithms in various situations.
Paper shows how SFA fits into FBM framework for time series separation.
problem Identifying time series decomposition in flow-based models.
method Combining SFA and FBM to make time series decomposition identifiable.
result Time series decomposition becomes identifiable using SFA and FBM.
In this paper we investigate the life-span of classical solutions to the hyperbolic geometric flow in two space variables with slow decay initial data. By establishing some new estimates on the solutions of linear wave equations in two space variables, we give a lower bound of the life-span of classical solutions to th…
Time-lagged autoencoders improve molecular dynamics data analysis.
problem Analyzing slow collective variables in molecular kinetics.
method Modified autoencoder neural network for dimension reduction.
result Time-lagged autoencoders reliably capture slow dynamics.
SRV learns slow molecular modes from simulations.
problem Discovering slow collective motions in molecular dynamics.
method State-free reversible VAMPnets (SRV) for nonlinear CV approximation.
result SRVs capture slow dynamics in complex systems.
MDFS selects important variables considering variable interactions, improving over simple filtering.
problem Discarding variable interactions leads to loss of relevant variables.
method MultiDimensional Feature Selection (MDFS) using information theory and CUDA C.
result Multidimensional analysis provides more reliable rankings of variable importance.
Random forests can be slow or inconsistent in certain models.
problem Performance issues of random forests in specific data-generating models.
method Intuitive arguments and numerical experiments, combined with variable use and importance statistics.
result Simple methods can create a better predictor using a forced random forest.
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables. Our approach is a two-stage quadratic programming method that…
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.
Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schrödinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equati…
Hierarchical pretraining with slow-fast ODEs
problem Causal self-attention vs. slow-fast ODEs
method Instantiating fast-slow ODE formalism as a concrete neural network
result Equilibrium manifold x=φ(y) is exactly the master-equation (ME) stationary distribution Anytime MiniBatch speeds up online distributed optimization by handling slow nodes.
problem Mitigating the impact of slow nodes (stragglers) in distributed optimization.
method Proposes an online distributed optimization method that averages minibatch gradients via consensus rounds.
result Prevents stragglers from slowing progress without wasting work.
New method prevents posterior collapse in generative models.
problem Posterior collapse weakens generative model capacity or requires complex objectives.
method Proposes δ-VAEs that constrain the posterior variational family to a minimum distance from the prior. result Achieves state-of-the-art log-likelihood on CIFAR-10 and ImageNet 32x32.
Seq-U-Net improves sequence modeling efficiency with dilated U-Net.
problem Efficiently modeling long-term dependencies in sequences.
method Causal U-Net architecture with dilated filters and slow feature hypothesis.
result Seq-U-Net achieves comparable performance with speed-ups of over 4x in audio generation.
Sharp comparison for sub-Gaussian random variables in convex order.
problem Comparing sub-Gaussian random variables in convex order.
method Proving dominance using moment generating functions and convex functions.
result Sharp comparison established between specific sub-Gaussian random variables.
A new training method improves autoregressive data completion efficiency.
problem Efficiently completing missing data in autoregressive models.
method Proposed an alternative training procedure (OA++) that reduces overfitting and leverages prior knowledge.
result OA++ achieves better performance with fewer computations and less overfitting.
Koopman models improve molecular kinetics analysis from short off-equilibrium simulations.
problem Estimating molecular kinetics and collective variables from short, non-equilibrium trajectories.
method Koopman operator theory and dynamic mode decomposition (DMD) to extend TICA and VA to non-equilibrium data.
result Variationally optimal equilibrium expectation values and slow collective variables can be computed from short simulations.
The paper defines multivariate confidence intervals that are easy to interpret and retain qualities of one-dimensional counterparts.
problem Applying confidence intervals to multivariate data.
method Defining multivariate confidence intervals that extend one-dimensional definitions and providing efficient approximate algorithms.
result Multivariate confidence intervals retain qualities of one-dimensional counterparts and are easy to interpret.
Crypto crashes show no consistent early warning signal, suggesting they are abrupt shocks rather than critical transitions.
problem Identifying early warning signals for crypto crashes.
method Analysis of seven major BTC liquidation cascades using minute-level price and leverage/order-flow data.
result No variable is event-invariant, and the critical-slowing-down signature is present in only five out of seven events.
DAG models with hidden variables present many difficulties that are not present when all nodes are observed. In particular, fully observed DAG models are identified and correspond to well-defined sets ofdistributions, whereas this is not true if nodes are unobserved. Inthis paper we characterize exactly the set of dist…
Paper tackles conditional learning between different domains.
problem Learning conditional distribution between input and output domains.
method Cooperative training of fast and slow thinking models.
result Jointly trained models improve conditional learning tasks.
Study predicts crypto-currency price collapses using standard deviation.
problem Detecting price collapses in crypto-currencies.
method Phenomenological model and analysis of standard deviation.
result Standard deviation can predict crypto-currency price collapses.
VPNet uses variable projection for efficient neural network training.
problem Efficient and interpretable neural network training for signal processing.
method Variable projection (VP) applied to neural networks.
result VPNet achieves fast learning and good accuracy with low computational cost.
Bayesian variable selection in high dimensions is consistent but MCMC mixing is slow.
problem Bayesian variable selection in high-dimensional settings with sparsity constraints.
method Truncated sparsity prior and Metropolis-Hastings algorithm with spectral gap control.
result Variable selection consistency and rapid mixing achieved with linear mixing time in covariates.
Study one-dimensional topological theories with linear generating functions.
problem Understanding one-dimensional topological theories with defects.
method Construct bases of hom spaces for decorated unoriented one-dimensional cobordisms.
result Gram determinant and linear generating functions constructed.
Generative framework learns effective, lower-dimensional models from high-dimensional data.
problem Predicting long-term behavior of complex, multiscale systems with limited data.
method Physics-aware probabilistic model order reduction with latent variables.
result Guaranteed long-term stability and predictive accuracy in multiscale physical systems.
A framework learns multiscale dynamics from single trajectories using normalizing flows.
problem Learning effective stochastic dynamics from single observed paths of slow variables.
method Data-driven approach based on coupled multiscale SDEs, stochastic averaging, and normalizing flows for density modeling.
result Scalable approach to capturing epistemic uncertainty in multiscale systems.
While records and order statistics of independent and identically distributed (i.i.d.) random variables X_1, ..., X_N are fully understood, much less is known for strongly correlated random variables, which is often the situation encountered in statistical physics. Recently, it was shown, in a series of works, that one…
New algorithm for parallel inference without block partitioning.
problem Slow inference in probabilistic models due to single-variable updates.
method Lower bounds ELBO with forest mixture bound for parallel inference.
result Algorithm converges faster for 'forest-like' models.
Paper develops methods for analyzing forms with synchronized singularities.
problem Analyzing forms with synchronized singularities.
method Exact reduction, analytic transfer, and geometric recomposition.
result Transfer of sparse domination principle to synchronized singular forms.
We formalize and decompose reinforcement learning problems with exogenous state variables and rewards.
problem Exogenous state variables and rewards slow down reinforcement learning.
method Formalized exogenous state variables and rewards, decomposed MDPs, derived variance-covariance condition, developed algorithms.
result Monte Carlo policy evaluation on the endogenous MDP is accelerated compared to using the full MDP.
Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at least one or both associated main effects to be present in the model. Lately, thi…
LSS learns molecular trajectories from MD data.
problem Limited integration time steps in MD simulations.
method Three deep learning networks for slow collective variables, dynamics, and configuration reconstruction.
result Generates ultra-long synthetic folding trajectories.
Model analyzes RFQ markets using stochastic control to optimize dealer performance and inventory.
problem Optimizing market making in aggregator-routed RFQ markets with varying dealer performance scores.
method Two-tier stochastic control model that separates RFQ-level price competition from macro routing.
result Optimal controls can be expressed through derivatives of reduced Hamiltonians, leading to interpretable mappings from optimal win probabilities to optimal offsets.
Researchers provide high-order approximations of slow invariant manifolds for atmospheric models.
problem Constructing slow invariant manifolds for atmospheric models with high accuracy.
method Flow Curvature Method
result Eighteenth-order approximation of the slow manifold for generalized model, thirteenth-order for conservative model.
Detects dependencies between high-dimensional data and outcomes.
problem Analyzing educational data with high-dimensional student skills.
method n-TARP clustering to quantify and validate dependencies.
result Valid dependencies between student skills and course grades observed.
FPO optimizes policies for robust reinforcement learning by adjusting environment variables.
problem Slow learning or suboptimal policies due to unobservable environment variables.
method FPO uses Bayesian optimization to select optimal environment variable distributions.
result FPO efficiently learns robust policies for rare events.
A new travel time tomography method uses adaptive dictionaries to model slowness variations.
problem Modeling and reconstructing slowness maps with varying scales and discontinuities.
method Local model (sparse patches) and global model (smooth constraints) integrated into a maximum a posteriori formulation.
result The LST approach effectively models both smooth and discontinuous slowness features.
This work interprets SFA through variational inference, relaxing linearity constraints.
problem Recover non-linear SFA from variational inference.
method Probabilistic interpretation of SFA through variational inference, relaxing linearity constraints.
result Reinterprets SFA as a variational framework, allowing slowness as a regularizer to reconstruction loss.
Gradient-based method extracts slow features from high-dimensional data.
problem Extracting meaningful low-dimensional features from high-dimensional, temporally varying data.
method Power Slow Feature Analysis (PowerSFA) using gradient-based training of differentiable architectures.
result PowerSFA effectively extracts meaningful low-dimensional features in various data types.
TAEs discover slow modes but mix them with max variance modes.
problem Discovering slow modes in dynamical systems.
method Theoretical and numerical analysis of TAEs.
result TAEs learn a mixture of slow and max variance modes.
We found a new simple family of Cantor sets whose projections are one-dimensional.
problem Finding simple Cantor sets with specific projection properties.
method Developed a new series of self-similar Cantor sets in R3. result All projections of these new Cantor sets are connected and one-dimensional.
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.
Study of one-dimensional non-Hausdorff manifolds and their quotient to CW complexes.
problem Understanding and characterizing one-dimensional non-Hausdorff manifolds.
method Analyzing properties of connected non-Hausdorff manifolds and their quotient spaces to CW complexes.
result Existence of a quotient map from a connected non-Hausdorff manifold to an open one-dimensional CW complex.
Paper proposes PPMM for fast estimation of large-scale OTM.
problem Estimation of large-scale optimal transport maps (OTM) is challenging due to the curse of dimensionality.
method Combines projection pursuit regression and sufficient dimension reduction to adaptively select projection directions.
result PPMM consistently estimates the most informative projection direction and weakly converges to the target OTM.