New deep learning model estimates scattering timescale of FRBs efficiently.
problem Estimating scattering timescale of fast radio bursts (FRBs) is a bottleneck.
method Multimodal Transformer Based Generic Mixture Density Network (MT-GMDN) that ingests dynamic spectrum and timeseries profile.
result Achieves 94% R2 on expected value of τ for measurable scattering. New method disentangles sources of different timescales in planetary seismic data.
problem Unsupervised source separation of multi-scale seismic data from planetary missions.
method Wavelet scattering spectra for multi-scale clustering and variational autoencoder for source separation.
result Disentangles sources with different timescales in InSight mission seismic data.
Synthesizes computational approaches to understand neural timescales.
problem Varying definitions and measurements of neural timescales across studies.
method Reviews data analysis methods, biophysical models, and machine learning models.
result Complements experimental studies with a holistic view of neural timescales.
This study improves convergence of two-timescale SA under Markovian noise in reinforcement learning.
problem Stability and convergence of two-timescale stochastic approximations under Markovian noise.
method Introduced a new control strategy for the fast timescale parameter.
result Established almost sure convergence of TDC with eligibility traces under off-policy learning with linear function approximation.
Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.
problem Non-asymptotic bounds for accuracy of normal approximation in linear two-timescale stochastic approximation algorithms.
method Established bounds for normal approximation in terms of convex distance, focusing on last iterate and Polyak-Ruppert averaging.
result Normal approximation rate for the last iterate improves with increased timescale separation, while it decreases in the averaged setting.
We study the distributions of event-time returns and clock-time returns at different microscopic timescales using ultra-high-frequency data extracted from the limit-order books of 23 stocks traded in the Chinese stock market in 2003. We find that the returns at the one-trade timescale obey the inverse cubic law. For la…
We introduce a framework to infer lead-lag networks between the states of elements of complex systems, determined at different timescales. As such networks encode the causal structure of a system, infering lead-lag networks for many pairs of timescales provides a global picture of the mutual influence between timescale…
The report evaluates heuristics for learning timescale graphical event models.
problem Lack of heuristics for determining hyper-parameters in timescale graphical event models.
method Proposed and evaluated different heuristics for hyper-parameter determination and refined an existing distance measure.
result Conclusions about the applicability of different heuristics on synthetic data.
New analysis shows actor-critic method converges efficiently in practical settings.
problem Understanding finite-time convergence of single-timescale actor-critic methods.
method Investigated online single-timescale actor-critic algorithm with linear function approximation and Markovian sampling.
result Proved convergence to ε-approximate stationary point with sample complexity of O(ε^(-2)).
In this paper we first analyzed the inductive bias underlying the data scattered across complex free energy landscapes (FEL), and exploited it to train deep neural networks which yield reduced and clustered representation for the FEL. Our parametric method, called Information Distilling of Metastability (IDM), is end-t…
In this paper we present a framework to analyze the asymptotic behavior of two timescale stochastic approximation algorithms including those with set-valued mean fields. This paper builds on the works of Borkar and Perkins & Leslie. The framework presented herein is more general as compared to the synchronous two times…
Method detects multi-timescale consumer spending patterns from receipts.
problem Understanding and managing consumer behavior in high-dimensional data.
method Non-negative tensor factorization (NTF) to extract multi-timescale expenditure patterns.
result Consumption patterns are characterized based on spending behavior over different timescales.
Proves convergence of neural networks in a two-timescale regime.
problem Training dynamics of shallow neural networks.
method Two-timescale regime analysis of gradient flow.
result Gradient flow converges to global optimum in non-convex optimization.
Two single-timescale algorithms improve TD learning with nonlinear approximations.
problem Optimizing TD learning with nonlinear smooth function approximation.
method Proposes two single-timescale single-loop algorithms with momentum and variance reduction.
result Achieves O(ε−4) sample complexity for the first algorithm and O(ε−3) for the second. Paper analyzes Greedy-GQ for reinforcement learning with Markovian noise.
problem Analyzing Greedy-GQ for reinforcement learning with Markovian noise.
method Develops finite-sample analysis for Greedy-GQ with linear function approximation under Markovian noise.
result Provides theoretical justification for choosing stepsizes for faster convergence.
A new buffer system improves continual learning in RL agents by adapting to changing environments.
problem Improving RL agents' ability to learn from changing environments over time.
method Multi-timescale replay buffer combined with invariant risk minimization.
result The method shows improvement over baselines in continual learning settings.
Novel approach to learning models based on subjective timescales for better exploration and decision-making.
problem Learning models over multi-step timescales in environments with intermediate states.
method Developed a subjective-timescale model (STM) based on episodic memories, enabling systematic variation of temporal extent of predictions.
result STM produces more informative action-conditioned roll-outs, leading to better decision-making and exploration.
A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered distribution to a reference distribution. The existence of a small timescale regime…
Single-timescale actor-critic finds globally optimal policy.
problem Finding globally optimal policy in reinforcement learning.
method Simultaneous actor and critic updates with linear or deep neural network approximations.
result Actor sequence converges to globally optimal policy at O(K−1/2) rate. Learning and memory are intertwined in our brain and their relationship is at the core of several recent neural network models. In particular, the Attention-Gated MEmory Tagging model (AuGMEnT) is a reinforcement learning network with an emphasis on biological plausibility of memory dynamics and learning. We find that …
Gradient descent-ascent converges to strict local minmax equilibria with a finite timescale separation.
problem Analyzing the convergence of gradient descent-ascent in non-convex, non-concave games with a finite timescale separation.
method Investigates the role of a finite timescale separation parameter τ on gradient descent-ascent in two-player zero-sum games, providing convergence rates and non-convergence results.
result Gradient descent-ascent converges to strict local minmax equilibria for a finite timescale separation parameter τ*.
Study Whittle index learning algorithms for restless bandits with constant stepsizes.
problem Optimizing decisions in restless multi-armed bandits with constant stepsizes.
method Developed Q-learning algorithms with constant stepsizes for index learning in restless bandits, extending to DQN and function approximations.
result The algorithms learn the Whittle index effectively.
Bayesian inference and superstatistics model financial volatility dynamics across different timescales.
problem Modeling correlated volatility in financial time series with heavy tails and long memory.
method Superstatistical dynamics, Bayesian Inference, Metropolis-Hasting sampling.
result The log-Normal model is reliable for short timescales, while inverse-Gamma is preferred for long timescales.
This paper analyzes the sample complexity of two timescale reinforcement learning algorithms.
problem Analyzing the sample complexity of two timescale reinforcement learning algorithms.
method Non-asymptotic analysis of linear and nonlinear TDC and Greedy-GQ algorithms under Markovian sampling with constant stepsize.
result The paper provides non-asymptotic convergence results for two timescale linear and nonlinear TDC and Greedy-GQ algorithms.
The paper analyzes dynamics of momentum in high dimensions with sparse updates.
problem Theoretical analysis of momentum dynamics in high-dimensional sparse settings.
method Theoretical analysis of two models: least squares with sparse inputs and logistic regression with a rare class.
result Characterization of high-dimensional limits of momentum dynamics and phase structure.
Authors improve accuracy analysis for portfolio optimization with multiple timescale factors.
problem Asymptotic accuracy of portfolio optimization approximations for general utility functions and two timescale factors.
method Construct sub- and super-solutions to fully nonlinear problem.
result Rigorous justification of accuracy for portfolio optimization with general utility functions and two timescale factors.
Single-timescale analysis improves convergence in multi-sequence stochastic approximation.
problem Finite-time convergence of nonlinear stochastic approximation with multiple coupled sequences.
method Smoothness property of fixed points and analysis of fine-grained single-timescale SA.
result Improved iteration complexity for achieving ε-accuracy in multi-sequence single-timescale SA.
Develops a new method for efficient stochastic bilevel optimization.
problem Stochastic bilevel optimization problems in machine learning applications.
method Single-Timescale stochAstic BiLevEl optimization (STABLE) method.
result Achieves the same order of sample complexity as stochastic gradient descent for single-level optimization.
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.
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplect…
We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probabil…
Paper explains scattering diagrams' role in mirror symmetry.
problem Reconstruction problem in mirror symmetry.
method Introduction of scattering diagrams and their role in SYZ and HMS conjectures.
result Scattering diagrams help in understanding mirror symmetry.
GRACE-C improves causal learning from time series data.
problem Misleading causal information due to mismatched timescales.
method Combines constraint programming with theoretical insights and prior information.
result Significantly faster and scalable causal learning for large datasets.
New method uses broken scattering to uniquely identify Finsler manifolds.
problem Identifying Finsler manifolds from scattering data.
method Uses broken scattering relation to compare geodesics.
result Two reversible Finsler manifolds with the same broken scattering relation are isometric.
GSAN learns adaptive node representations using geometric scattering and attention.
problem Oversmoothing in node representation learning.
method Attention-based architecture integrating geometric scattering and GCN channels.
result GSAN outperforms previous networks in semi-supervised node classification.
New method learns soliton dynamics from scattering data without assuming known equations.
problem Deriving soliton dynamics from scattering data without prior knowledge.
method Combining IST with weak-form system identification for data-driven discovery.
result Effective soliton dynamics models derived from observed scattering data.
Scattering representations simplify SBI for images without extra compression.
problem Efficiently performing simulation-based inference on images with limited data.
method Use scattering representations for compression and learning, combined with spatial averaging and expressive density estimators.
result Scattering representations provide more information than traditional methods, without requiring additional simulations.
The paper establishes scattering theory for wave equations on Schwarzschild spacetime.
problem Defocusing semilinear wave equations on Schwarzschild spacetime.
method Combining energy and pointwise decay results with Sobolev embedding, constructing scattering operator.
result Construction of a scattering operator mapping past to future scattering data.
Paper develops formulas for shape derivatives in wave scattering.
problem Computing high order shape derivatives for wave scattering is challenging.
method Introduces elegant recurrence formulas using differential forms and Lie derivatives.
result Unified framework for computing high order shape perturbations in scattering problems.
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest in geometric deep learning, which aims to generalize ConvNets to manifold and gra…
Study scattering rigidity on stationary manifolds using geodesics.
problem Scattering rigidity on standard stationary manifolds.
method Use Hamiltonian reduction to relate to MP-systems. result New rigidity results for stationary manifolds.
MODWST improves classification tasks with wavelet scattering.
problem Signal classification challenges.
method Combines MODWT and WST for feature extraction.
result MODWST outperforms CNNs in limited data scenarios.
Study on scattering geodesics on modular surface and their sojourn times.
problem Distribution of scattering geodesics and their sojourn times on modular surface.
method Analysis of scattering geodesics in modular surface, establishing connection to prime divisors in arithmetic progression.
result Established a connection between scattering geodesics and prime divisors in arithmetic progression.
Scattering theory on Riemann surfaces with explicit matrix and generalized period mappings.
problem Scattering theory for harmonic one-forms on Riemann surfaces.
method Construction of scattering theory from boundary value problems involving systems of curves and jump problems. Explicit expression for scattering matrix using Schiffer operators.
result Unitary scattering matrix and general association of polarizing Lagrangian spaces.
Study on recovering Lorentzian metrics from scattering data.
problem Recovering Lorentzian metrics from scattering data on a boundary.
method Analyzing the role of boundary distance functions and linearizing the light ray transform.
result Scattering rigidity can be reduced to boundary rigidity of magnetic systems.
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric…
Bayesian Scattering offers a simple baseline for image data uncertainty.
problem Lack of interpretable, mathematically grounded uncertainty quantification methods for image data.
method Coupling wavelet scattering transform with a simple probabilistic head.
result Bayesian Scattering provides sensible uncertainty estimates under distribution shifts.
Scattering theory for linearised gravity on Schwarzschild black hole exterior.
problem Constructing a scattering theory for linearised gravity equations on Schwarzschild background.
method Building on previous work, constructing Hilbert space-isomorphisms for finite energy initial data and scattering states.
result Past and future linear memories are related by an antipodal map for Bondi-normalised solutions.