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.
Derives a biologically plausible neural network for Slow Feature Analysis.
problem Learning latent features from time series data.
method Starting from an SFA objective, derives Bio-SFA with a biologically plausible neural network implementation.
result Validates Bio-SFA on naturalistic stimuli, reproducing interesting properties of brain cells.
Improved stochastic approximation method reduces residual error.
problem Reducing residual error in stochastic approximation algorithms.
method Fixed-schedule one-quarter barrier and bias-corrected acceleration.
result Achieves T−1/2+o(1) residual reduction with O(1) primitive samples. 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 We consider the action of a pseudo-Anosov mapping class on PML(S). This action has north-south dynamics and so, under iteration, laminations converge exponentially to the stable lamination. We study the rate of this convergence and give examples of families of pseudo-Anosov mapping classes where the rate go…
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.
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.
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.
Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction to the slow flow. The focus of this work is on a proposition and discussion of a …
Regularization leads to balancedness in deep linear networks.
problem Balancedness in deep linear networks.
method Geometric invariant theory and Riemannian geometry of fibers.
result Balancing flows converge to the balanced manifold at a uniform exponential rate.
We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system x′=f(x,y,ε),y′=εg(x,y,ε) with one-dimensional slow variable y. Our validation procedure is based on topological tools called isolatin…
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such time-varying smoothness is not accounted for, one can obtain misleading inf…
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.
Efficiently estimates optimal transport maps with rigorous guarantees.
problem Estimating optimal transport maps between distributions efficiently.
method Entropic version of Brenier's theorem, Sinkhorn's algorithm.
result Estimator is parallelizable and efficient for massive data sets.
A fast and practical method for learning transport maps.
problem Slow and computationally expensive methods for learning transport maps.
method Approximated transport mapping using Gaussian (Bures-Wasserstein) transport and local transport plans.
result Significantly faster and more efficient than existing methods.
Study the averaging principle for non-autonomous slow-fast systems and apply it to financial local stochastic volatility models.
problem Understanding the behavior of non-autonomous slow-fast systems of stochastic differential equations.
method Prove the averaging principle under specific conditions and apply it to a financial model.
result Prices of derivatives converge to those calculated using the limit model under a risk-neutral measure.
A new geometric approach to identify slow invariant manifolds in complex systems.
problem The mathematical definition of slow invariant manifolds is unsatisfactory and limited to slow-fast systems.
method Formulate slow invariant manifolds geometrically within the context of differential geometry, focusing on covariant formulations.
result A more general definition of slow invariant manifolds is provided, independent of coordinate choice.
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.
Quasiclassical generalized Weierstrass representation for highly corrugated surfaces with slow modulation in the three-dimensional space is proposed. Integrable deformations of such surfaces are described by the dispersionless Veselov-Novikov hierarchy.
The study examines 3-manifolds with slow scalar curvature decay and finds Whitehead manifold properties.
problem Investigating open simply-connected 3-manifolds with slow decay of positive scalar curvature.
method Analyzing topological properties and using Whitehead manifold results.
result Open simply-connected 3-manifolds with the specified properties are homeomorphic to S2imesR. 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.
A single slow-growing tree matches Random Forest's performance.
problem Matching Random Forest's performance with a single tree.
method SGT uses a learning rate to tame CART's greedy algorithm, improving on greedy ML algorithms.
result SGT and tree ensembles like Booging, BT, and RF improve performance.
Researchers reconstruct stiffness tensors from limited data in anisotropic elasticity.
problem Reconstructing stiffness tensors from partial data around one polarization.
method Using algebraic geometry and slowness surfaces, the approach leverages the algebraic geometry of families of slowness surfaces.
result For tensors in a dense open subset, a small amount of data around one polarization uniquely determines the entire slowness surface and stiffness tensor.
This work learns effective dynamics from short-term data of stochastic systems.
problem Learning effective dynamics from short-term data of stochastic systems.
method Proposes a novel algorithm using a neural network (Auto-SDE) to learn invariant slow manifold from data.
result Validated through numerical experiments to be accurate, stable, and effective.
The paper studies the Teichmüller harmonic map flow and its limits.
problem Understanding the behavior of the Teichmüller harmonic map flow as the coupling constant approaches zero.
method Analyzes the flow equations, convergence of flows, and rescaling of time.
result The Teichmüller harmonic map flows converge to harmonic map flows as the coupling constant approaches zero.
This thesis optimizes neuromorphic systems by slowing down their dynamics, improving performance.
problem Timescale mismatch between analog neuromorphic circuits and real-time sensory inputs.
method Proposes and tests solutions to slow down the dynamics of spiking neural networks.
result Spiking neural networks on analog neuromorphic systems can achieve significant performance boosts.
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.
Slow feature analysis (SFA) is a method for extracting slowly varying driving forces from quickly varying nonstationary time series. We show here that it is possible for SFA to detect a component which is even slower than the driving force itself (e.g. the envelope of a modulated sine wave). It is shown that it depends…
Paper separates financial time series into fast and slow components.
problem Multiscale behavior in financial time series data.
method Uses variance and tail stationarity criteria as generalized eigenvalue problems.
result Identifies slow and fast components in asset returns and prices.
Study MMD for critical transitions in fast-slow systems, showing it's a good binary classifier.
problem Detecting change points in multiscale systems with critical transitions.
method Link between dynamical theory of critical transitions and statistical MMD, leading-order approximation.
result MMD is a good binary classifier for detecting change points in critical transitions.
We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties t…
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.
Slow feature analysis (SFA) is an unsupervised-learning algorithm that extracts slowly varying features from a multi-dimensional time series. A supervised extension to SFA for classification and regression is graph-based SFA (GSFA). GSFA is based on the preservation of similarities, which are specified by a graph struc…
The paper derives oracle inequalities for estimators with fast and slow rates.
problem Developing fast and slow oracle inequalities for estimators.
method Direct study of analysis estimator and adaptation of Dalalyan, Hebiri and Lederer's arguments.
result Constant-friendly rates for (square root) total variation regularized estimators over graphs.
Study on friction forces for nonholonomic systems using affine connections.
problem Realizing nonholonomic constraints with strong friction forces.
method Affine connection approach, covariant derivatives, recursive procedure.
result Approximations of slip velocities and dynamics up to second order.
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.
DRNets combine deep learning and reasoning for complex tasks.
problem Solving complex tasks, especially in scientific discovery, with limited supervision.
method DRNets integrate logic and neural network optimization to encode structured latent spaces constrained by prior knowledge.
result DRNets outperform state-of-the-art models in scientific discovery tasks, recovering more precise crystal structures.
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.
Regularized contextual bandits use bins to solve multi-armed bandit problems.
problem Contextual bandit problems with a known baseline policy.
method Nonparametric model, splitting context space into bins, solving bandit instances independently.
result Intermediate convergence rates interpolating between slow and fast rates.
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 homogenizes equations on parallelizable manifolds using tensor localization and periodicity.
problem Homogenizing oscillating linear elliptic equations on parallelizable manifolds.
method Two-scale convergence through localization and periodicity induced by geometry.
result Explicit cell formulae for the homogenization limit and a theory of two-scale convergence of tensors.
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…
SFPO optimizes LLM reasoning by repositioning before updating, improving stability and efficiency.
problem Noisy gradients from low-quality rollouts cause instability and inefficient exploration in on-policy RL algorithms.
method Decomposes each step into three stages: a short fast trajectory, repositioning, and slow correction, preserving the objective and rollout process unchanged.
result SFPO consistently improves stability, reduces rollouts, and accelerates convergence, outperforming GRPO on math reasoning benchmarks.
EM algorithm converges slowly for weakly identifiable Gaussian mixtures.
problem Slow convergence of EM algorithm for weakly identifiable Gaussian mixtures.
method Localized argument with two stages, each involving epoch-based arguments for surrogate EM operators at the population level.
result EM algorithm converges in $n^{ rac{3}{4}}$ steps with estimates at Euclidean distance of $n^{- rac{1}{8}}$ and $n^{- rac{1}{4}}$ from true parameters.
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.
Efficiently simulates slow dynamics of high-dimensional stochastic systems.
problem Simulating high-dimensional stochastic systems with slow dynamics and fast modes.
method Designs an algorithm to estimate an invariant manifold and its dynamics, averaging out fast modes.
result Efficient simulator of effective dynamics on low-dimensional invariant manifold.