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.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “slowness surfaces”
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.
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…
Quasiclassical generalized Weierstrass representation (GWR) for highly corrugated surfaces with slow modulation in the four-dimensional Euclidean space is proposed. Integrable deformations of such surfaces are described by the dispersionless Davey-Stewartson hierarchy. Quasiclassical GWRs for other four-dimensional spa…
Optimal Liouville theorem for minimal disks in any codimension.
problem Characterizing harmonic functions on minimal disks in high-dimensional spaces.
method Analyzing harmonic functions and using Liouville's theorem.
result Optimal Liouville theorem for minimal disks in any codimension.
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.
Neural networks estimate spatial process likelihoods efficiently.
problem Challenges in estimating spatial processes with slow or intractable likelihoods.
method Convolutional neural networks trained on a classification task to learn likelihood function.
result Neural likelihood surfaces provide fast and accurate parameter estimation.
Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension …
During this last decades, several attempts to construct slow invariant manifold of the Lorenz-Krishnamurthy five-mode model of slow-fast interactions in the atmosphere have been made by various authors. Unfortunately, as in the case of many two-time scales singularly perturbed dynamical systems the various asymptotic p…
Travel time tomography with adaptive dictionariesphysics.geo-ph
We develop a 2D travel time tomography method which regularizes the inversion by modeling groups of slowness pixels from discrete slowness maps, called patches, as sparse linear combinations of atoms from a dictionary. We propose to use dictionary learning during the inversion to adapt dictionaries to specific slowness…
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.
We propose Power Slow Feature Analysis, a gradient-based method to extract temporally slow features from a high-dimensional input stream that varies on a faster time-scale, as a variant of Slow Feature Analysis (SFA) that allows end-to-end training of arbitrary differentiable architectures and thereby significantly ext…
Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical an…
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 …
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 with one-dimensional slow variable . Our validation procedure is based on topological tools called isolatin…
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.
We present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences; however, systematically testing it has until now been infeasibly slow, and current techniques only apply to specific families of knots. As a …
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.
The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a high-dimensional space (standard coordinates). Tollefson's Q-theory speeds up this operation by using a much smaller space (quadrilateral coord…
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.
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.
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.
Slow-Growing Treesstat.ML
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.
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 is exactly the master-equation (ME) stationary distribution
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.
Covariant geometric characterization of slow invariant manifolds: New concepts and viewpointsmath.DS
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…
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…
Affine Connection Approach to the Realization of Nonholonomic Constraints by Strong Friction Forcesmath-ph
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.
Neuromorphic Computing is a nascent research field in which models and devices are designed to process information by emulating biological neural systems. Thanks to their superior energy efficiency, analog neuromorphic systems are highly promising for embedded, wearable, and implantable systems. However, optimizing neu…
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.
Cooperative Training of Fast Thinking Initializer and Slow Thinking Solver for Conditional Learningstat.ML
This paper studies the problem of learning the conditional distribution of a high-dimensional output given an input, where the output and input may belong to two different domains, e.g., the output is a photo image and the input is a sketch image. We solve this problem by cooperative training of a fast thinking initial…
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 residual reduction with primitive samples.
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion is given by an averaged ordinary differential equation. We then demonstrate that…
We study the quasi-local energy (QLE) and the surface geometry for Kerr spacetime in the Boyer-Lindquist coordinates without taking the slow rotation approximation. We also consider in the region , which is inside the ergosphere. For a certain region, , the Gaussian curvature of the surface with co…
The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simpl…
Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dim…
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.
The identification of slow invariant manifolds (SIMs) is an essential part in model-order reduction for reactive systems. The mathematical definition of the SIM by Fenichel can be considered unsatisfactory, because it is only applicable to so-called slow-fast system and does not provide the uniqueness of the SIM. Obser…
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.
Study reveals conditions for neural networks to forget learned features.
problem Understanding feature unlearning in neural networks.
method Infinite-width limit analysis with stochastic gradient descent, fast-slow dynamics.
result Conditions for feature unlearning are determined by the strength of nonlinear terms and initial weights.
Study of manifolds with nonnegative Ricci curvature and slow relative volume growth.
problem Understanding fundamental groups of manifolds with specific volume growth.
method Defined a function RV(s) to describe volume growth and studied fundamental groups with slow relative volume growth.
result If RV(s) grows sublinearly, fundamental groups are almost abelian or finite.
Quadratic approximation of slow factor of volatility in a Multi-factor Stochastic volatility Modelq-fin.PR
In the present work, we propose a new multifactor stochastic volatility model in which slow factor of volatility is approximated by a parabolic arc. We retain ourselves to the perturbation technique to obtain approximate expression for European option prices. We introduce the notion of modified Black-Scholes price. We …
Experimenting, Fast and Slow: Bayesian Optimization of Long-term Outcomes with Online Experimentscs.LG
Bayesian optimization for long-term outcomes using fast and slow experiments.
problem Optimizing long-term system effects with short-term misleading results.
method Combining fast and slow experiments for Bayesian optimization.
result Sequential optimization over large action spaces in a short time.
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow entropies", they describe the polynomial growth rate of the number of balls (fo…
Different technological domains have significantly different rates of performance improvement. Prior theory indicates that such differing rates should influence the relative speed of diffusion of the products embodying the different technologies since improvement in performance during the diffusion process increases th…
We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globaliz…