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.
New findings show market dynamics differ from statistical models, necessitating a new approach.
problem Market dynamics differ from statistical models, leading to inaccurate assumptions.
method Analyzed NASDAQ ITCH data to identify market dynamics and propose a new approach.
result Most market dynamics information is contained in spikes, indicating fast excitation and slow relaxation.
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.
We study the dynamics of the limit order book of liquid stocks after experiencing large intra-day price changes. In the data we find large variations in several microscopical measures, e.g., the volatility the bid-ask spread, the bid-ask imbalance, the number of queuing limit orders, the activity (number and volume) of…
Bounds on chemical reaction network relaxation rates using convex analysis.
problem Understanding relaxation dynamics in chemical reaction networks.
method Convex analysis, generalized gradient flows, singular values of stoichiometric matrix.
result Bounds on Kullback-Leibler divergence to equilibrium for CRNs.
A new framework for sparse regression models with slow variations.
problem Parameter estimation for sparse regression models with slow variations.
method Formulated as a mixed-integer optimization problem, then reformulated as a binary convex optimization problem with a novel relaxation technique.
result Efficiently solves the problem to provable optimality using a cutting plane-type algorithm.
Analyzes how transient conditions affect first-passage times in random walks.
problem Understanding first-passage times in random walks under transient conditions.
method Solves the generalized master equation analytically for a linear chain of states.
result The average first-passage time decreases with a power law dependence on the relaxation rate.
New method CROWN-IBP combines IBP and CROWN for efficient verifiable robust neural networks.
problem Training verifiably robust neural networks is challenging and computationally expensive.
method CROWN-IBP combines interval bound propagation and linear relaxation for efficient training.
result CROWN-IBP achieves significant improvements in verifiable robustness on MNIST and CIFAR datasets.
The paper proposes a method to improve Koopman operator estimation using indicator functions.
problem Difficulty in identifying good observables for Koopman operator expansion.
method Clustering procedure based on Hidden Markov Model (HMM) to infer surrogate observables.
result Inferred indicator functions significantly improve estimation of Koopman operator eigenvalues and transition timescales.
Study shows slow decay of impact in equity markets after metaorders.
problem Understanding the decay of impact in equity markets after metaorders.
method Empirical study using a large dataset of metaorders executed by institutional investors.
result Impact decay follows a power-law function at short time scales and converges to a non-zero asymptotic value at long time scales.
Study on black hole interiors with matter fields, showing oscillation condition impacts blow-up.
problem Examining Strong Cosmic Censorship in the presence of matter fields.
method Einstein equations coupled with charged/massive scalar fields, spherically symmetric data, relaxation rate analysis.
result Oscillation condition on event horizon determines whether matter fields blow up or not.
Generative models accelerate molecular dynamics by four orders of magnitude.
problem Femtosecond time steps limit access to slow molecular processes.
method Deep generative modeling framework that accelerates sampling.
result Quantitative characterization of equilibrium ensembles and dynamical relaxation processes.
A new deep learning model speeds up MRI by reconstructing from undersampled data.
problem Slow MRI due to undersampling in k-space.
method Unrolling primal-dual hybrid gradient algorithm into a deep network, gradually relaxing constraints.
result Superior MR reconstructions from highly undersampled data.
Reducing volatility proxy improves apparent market correlation dynamics.
problem Attributing apparent slow collective market dynamics to intrinsic or driver inheritance.
method Coupled Ornstein-Uhlenbeck model with VIX proxy, decomposing and controlling for autocorrelation.
result VIX-coupled model reduces effective relaxation time from 298 to 61 trading days, improving fit over bare mean reversion.
Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and low-rank sparse bilinear regression as potential ap…
Paper analyzes convergence of FedAvg on non-iid data and provides theoretical guarantees.
problem Analyzing convergence of Federated Averaging on non-iid data.
method Theoretical analysis of convergence rate and trade-offs between communication-efficiency and convergence rate.
result Established a convergence rate of O(T1) for strongly convex and smooth problems. 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.
A scalable gradient-based framework for sparse portfolio selection.
problem Sparse minimum-variance portfolio selection with cardinality constraint.
method Gradient-based optimization with Boolean relaxation and tunable parameter.
result Matches commercial solvers in most instances, differing by a few assets with negligible error in portfolio variance.
Deeptime simplifies learning dynamical models from time series data.
problem Understanding complex systems through dynamical models from time series data.
method Various tools for estimating dynamical models including conventional and kernel/deep learning methods.
result Estimates dynamical models from time series data efficiently and with rich analysis methods.
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.
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.
New method solves nonsmooth low-rank matrix optimization problems efficiently.
problem Nonsmooth and low-rank matrix optimization problems in statistics and machine learning.
method Low-rank Extragradient Method with warm-start initialization.
result The extragradient method converges to an optimal solution with rate O(1/t) and requires only two low-rank SVDs per iteration. 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.
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.
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 proposes new gradient codes for robust distributed machine learning.
problem Robustness against slow machines (stragglers) in distributed machine learning.
method Constructs gradient codes based on probabilistic and Kronecker product methods.
result Gradient codes exist for a wide range of system parameters with comparable error performance.
New geometric approach to slow invariant manifolds in dynamical systems.
problem Characterizing slow invariant manifolds in a coordinate-independent manner.
method Exploiting curvature concepts and variational approach in Hamiltonian mechanics.
result Differential geometric definition of slow invariant manifolds proposed.
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…
ZORB speeds up neural network training without sacrificing accuracy.
problem Slow and strenuous training of neural networks using gradient descent.
method Uses pseudoinverse of targets instead of gradients for backpropagation.
result ZORB converges 300 times faster than Adam on MNIST without hyperparameter tuning.
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.
Paper develops zeroth and first order stochastic Frank-Wolfe algorithms for constrained optimization.
problem Optimization problems with difficult-to-project deterministic constraints and efficient projection constraints.
method Stochastic Frank-Wolfe algorithms with momentum and trimmed variants.
result Guaranteed fast convergence rates comparable to unconstrained problems.
We propose a faster and more accurate method for learning classification trees.
problem Learning optimal binary classification trees is challenging and slow.
method We introduce a stronger MIP formulation and Benders' decomposition method.
result Our method is 50 times faster and improves out-of-sample performance.
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. New technique halves scan time for multi-echo MR images.
problem Slow acquisition of multi-echo magnetic resonance images.
method Structured deep dictionary learning for adaptive reconstruction.
result Scan time reduced by half compared to state-of-the-art.
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.
New conic relaxations improve sparse signal recovery with fewer observations.
problem Recovering sparse signals from noisy data.
method Comparing two semidefinite relaxations for sparse linear regression.
result Dong's relaxation requires fewer observations for exact recovery.
Convex relaxations improve CNNs with fixed weights.
problem Improving CNNs with fixed weights.
method Convex relaxations for CNNs with fixed weights using second order cone programs.
result The relaxation recovers the global minimum under a planted model assumption.
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.
New method improves neural network verification by considering multivariate input space of ReLU neurons.
problem Improving the effectiveness of neural network verification algorithms.
method A new tightened convex relaxation for ReLU neurons considering multivariate input space.
result Our convex relaxation is significantly stronger than the commonly used univariate-input relaxation.
New semidefinite relaxation improves robustness certification of neural networks.
problem Certifying robustness of neural networks against adversarial examples.
method Proposed a new semidefinite relaxation for certifying robustness of arbitrary ReLU networks.
result Our proposed relaxation is tighter than previous relaxations and produces meaningful robustness guarantees.
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.
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