Study develops time-continuous models and probabilistic descriptions for agent-based economic market models.
problem Formulating and describing agent-based economic market models in a time-continuous and probabilistic manner.
method Derived time-continuous formulations, discussed impact of time-scaling, proved stability, presented probabilistic descriptions using kinetic theory.
result Time-continuous formulations and probabilistic descriptions for agent-based economic market models.
ODIN uses Gaussian processes to efficiently infer parameters and states from ODEs.
problem Parameter and state inference in time-continuous dynamical systems with limited data.
method Constrained Gaussian processes and ODE-informed regression.
result Outperforms state-of-the-art methods in accuracy and computational cost.
DDAT framework improves machine learning by dynamically adjusting difficulty.
problem Improving time-continuous emotion prediction models.
method Dynamic Difficulty Awareness Training (DDAT) framework.
result DDAT framework outperforms existing methods in emotion prediction.
New model recognizes emotions with missing modalities, improving accuracy.
problem Handling missing modalities in emotion recognition.
method Transformer-based architecture with cross-attention and self-attention mechanisms.
result Improvement of 37% in predicting arousal values and 30% in valence values compared to baseline.
As we enter into the big data age and an avalanche of images have become readily available, recognition systems face the need to move from close, lab settings where the number of classes and training data are fixed, to dynamic scenarios where the number of categories to be recognized grows continuously over time, as we…
TGNN4I model forecasts irregularly observed graph data using ODEs.
problem Forecasting graph-structured data with irregular time steps and partial observations.
method Introduces a time-continuous latent state in each node using ODEs and GRUs, integrating graph neural network layers.
result Validated usefulness of graph structure and time-continuous dynamics in irregular observation settings.
GoTube verifies neural networks over time, scaling to large horizons.
problem Verifying the robustness of time-continuous neural networks.
method Solves Go problems to construct a conservative execution set.
result Substantially outperforms existing tools in size, speed, and scalability.
Latent Replay reduces continual learning computation and storage needs.
problem Catastrophic forgetting in continual learning.
method Store activations volumes at intermediate layers instead of past data, slow down learning below the latent replay layer.
result Latent Replay achieves state-of-the-art performance on complex video benchmarks.
We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R^m into a pseudo-Riemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point i…
New neural networks with variable time constants for better time-series prediction.
problem Improving neural network performance in time-series prediction.
method Constructing networks of linear dynamical systems modulated by nonlinear gates, using numerical differential equation solvers.
result Liquid Time-Constant Networks (LTCs) yield superior performance on time-series prediction tasks.
Paper introduces solving financial problems using time-stepped FBSDE and deep learning.
problem Quantitative finance problems under specific dynamics and instruments.
method Formulate as FBSDE, turn into control problems, time-step, solve with optimization and deep learning.
result Solves financial problems with new methods and deep learning.
Treatment effects can be estimated from observational data as the difference in potential outcomes. In this paper, we address the challenge of estimating the potential outcome when treatment-dose levels can vary continuously over time. Further, the outcome variable may not be measured at a regular frequency. Our propos…
Continuous control imitation learning fails if expert actions are smooth.
problem Continuous control imitation learning fails if expert actions are smooth.
method Study of imitation learning in discrete-time, continuous state-and-action control systems.
result Any smooth, deterministic imitator policy suffers exponentially larger error than the expert.
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.
Let M be a closed manifold and let N be a connected manifold without boundary. For each k∈N the set of k times continuously differentiable maps between M and N has the structure of a smooth Banach manifold where the underlying manifold topology is the compact-open Ck topology. We provide a det…
A neural network solves dictionary learning problems efficiently.
problem Solving dictionary learning problems efficiently.
method Combining top-down feedback and contrastive learning with spiking neurons.
result True gradients for learning are provably computable by individual neurons.
Study evolutes of curves with varying smoothness.
problem Understanding evolutes of curves with low smoothness.
method Analyzing the relationship between curve smoothness and evolute regularity.
result Evolutes have one less order of smoothness than the parent curve in generic cases.
Method infers causal structure from system behaviors using RKHS and kernel ε-machines.
problem Discovering causal structure in systems with varying external and measurement noise.
method Combines causal states and RKHS for efficient representation and inference of causal structure.
result Robustly estimates causal structure in high-dimensional data with varying noise.
Estimates curvature for long-time continuity method solutions.
problem Curvature estimates for long-time continuity method solutions.
method Adapting arguments from Kähler-Ricci flow to semi-ample canonical line bundles.
result Derives curvature bounds for product manifolds.
Automates PDE model reduction with time-scale separation.
problem Computational expense in solving high-dimensional PDEs.
method Combines autoencoder and time-continuous model for latent dynamics.
result Automatically learns independent temporal scales in complex systems.
Let M be a bounded open plane domain. Let f be a continuous function on the closure of M, 3-times continuously differentiable in M, which vanish on the boundary. Polterovich and Sodin proved that the values of f cannot exceed the norm of the hessian of f, averaged over the entire domain M. In this paper we study the eq…
TrajectoryNet models dynamic cellular trajectories using optimal transport.
problem Modeling continuous and non-linear paths in dynamic processes.
method Continuous normalizing flows linked to dynamic optimal transport.
result TrajectoryNet improves interpolation of cellular distributions.
Polynomial-time Gibbs sampling generates DPP samples efficiently.
problem Sampling from continuous Determinantal Point Processes (DPPs).
method Polynomial-time Gibbs sampling algorithm.
result Gibbs sampler generates DPP samples in polynomial time.
We analyze a new type of debt that rewards investors based on company performance.
problem Challenges in accounting and pricing equity-based debt obligations.
method Formulated and solved the associated mathematical problem in discrete and continuous time settings using FBSDE and decoupling fields.
result Solved the continuous time problem using FBSDE and decoupling fields.
Despite increasing attention paid to the need for fast, scalable methods to analyze next-generation neuroscience data, comparatively little attention has been paid to the development of similar methods for behavioral analysis. Just as the volume and complexity of brain data have grown, behavioral paradigms in systems n…
This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images p0 and p1, we calculate an evolution process p(t, \cdot) which transports p0 to p1 by using th…
Paper describes an on-line PCA algorithm for real-time data analysis.
problem Continuity of principal components during real-time analysis.
method Incremental PCA algorithm that updates coefficients on-line without keeping all samples.
result Algorithm maintains the same transformation coefficients as the batch version.
End-to-end network predicts and aligns continuous emotion labels.
problem Inconsistent alignment of continuous emotion labels with speech signals.
method Convolutional neural network with a multi-delay sinc layer.
result State-of-the-art results in predicting and aligning continuous emotion labels.
The abstract discusses graphs with prescribed mean curvature on Riemannian manifolds, including existence and translating graphs.
problem Graphs with prescribed mean curvature on Riemannian manifolds with boundary conditions at infinity.
method Survey and proof of existence theorems for Jenkins-Serrin graphs.
result Existence of translating Jenkins-Serrin graphs.
The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path Stochastic Portfolio Theory of Robert Fernholz. FGPs have been formulated to yield a master equation - a description of their return relative to a passive (buy-and-hold) benchmark portfolio serving as the numérai…
A mesh-free method solves continuum-marginal optimal transport problems.
problem Recovering minimum-energy velocity fields from time-continuous probability marginals.
method Embeds weak continuity equation in a reproducing kernel Hilbert space, optimizing with mini-batch stochastic methods.
result Accurately recovers drift and maintains marginal consistency in synthetic experiments.
Graph neural networks with random features can approximate any function on directed graphs.
problem Approximating functions on directed graphs with graph neural networks.
method Random node features combined with partially random node features in permutation-equivariant neural networks (PENNs).
result Graph neural networks with random features can approximate any measurable permutation-invariant or permutation-equivariant function on directed graphs of fixed size.
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete and continuous stochastic processes (random exchange models) as well as related…
New deep learning method solves stochastic control problems.
problem Solving strongly coupled FBSDEs for stochastic control.
method Modified deep BSDE method with new loss function.
result Empirical convergence of the new method for three problems.
Extends GCN-SIR model for US COVID-19 spread analysis.
problem Modeling COVID-19 spread in the USA using SIR models and graph approaches.
method Coupling GCNs with SIR models to estimate mobility and hyperparameters.
result GCN-SIR approach outperforms existing methods for US data.
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the knowledge of vanilla option prices for a continuum of strikes and maturities that…
Flexible Hawkes model with Gaussian process self-effects for time-dependent data.
problem Modeling time-dependent point processes with history dependence and self-effects.
method Extended Hawkes process with Gaussian process self-effects for both excitatory and inhibitory types, using Bayesian inference and mean-field variational approximation.
result Efficient approximate Bayesian inference achieved via data augmentation and mean-field variational approach.
NDMs enable non-linear transformations in diffusion models for better generative tasks.
problem Limited to linear transformations, diffusion models struggle with generative tasks.
method Presented NDMs that allow time-dependent non-linear transformations.
result NDMs outperform conventional diffusion models in likelihood and sample quality.
This work optimizes reservoir computing models by linking recurrence and non-linear dynamics.
problem Understanding how recurrence and non-linear dynamics in cortical networks contribute to their function.
method Transformed time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels.
result Optimal time-series classifiers can be built from random reservoir networks, demonstrating significant performance gains.
Automated method simplifies stochastic chemical reaction network analysis.
problem Analyzing complex stochastic chemical reaction networks is computationally expensive.
method Uses deep learning to create a discrete-time process from a CTMC, optimizing neural network architecture.
result Automated method improves computational efficiency and accuracy for various CRNs.
Study bounds for European basket call options in a discrete-time market model with price jumps.
problem Bounding the prices of European basket call options in a market model with price jumps.
method Computed bounds using a binomial model and proved that the lower bound coincides with Jensen's bound.
result The upper bound of the price interval of European basket call options can be computed by restricting to a binomial model.
Flow on weighted graphs sharpens Bakry-Émery curvature.
problem Sharp curvature in weighted graphs.
method Bakry-Émery curvature flow on mixed weighted graphs.
result Limits of curvature flow are curvature sharp.
New RNN model handles long-term dependencies in irregularly-sampled time series.
problem Handling long-term dependencies in irregularly-sampled time series data.
method Designing ODE-LSTMs that separate memory from continuous-time state.
result ODE-LSTMs outperform other RNN-based models on non-uniformly sampled data with long-term dependencies.
A method for predicting survival using neural networks for both continuous and discrete time.
problem Survival prediction for both continuous and discrete time data.
method Proposes a scheme for discretizing continuous-time data and two interpolation schemes for continuous-time survival estimates.
result The hazard rate parametrization of neural networks yields better performance than the parametrization of the probability mass function.
This work is a short, self-contained introduction to subriemannian geometry with special emphasis on Chow's Theorem. As an application, a regularity result for the Poincaré Lemma is presented. At the beginning, the definitions of a subriemannian geometry, horizontal vector fields and horizontal curves are given. Then t…
The curse of dimensionality affects neural network optimization, especially with smooth functions.
problem The curse of dimensionality in neural network optimization.
method Examined through the evolution of the parameter distribution under 2-Wasserstein gradient flow.
result The curse of dimensionality persists in neural network optimization, even with smooth functions.
Locally convex classes on manifolds linked to Ricci curvature bounds.
problem Characterizing Kato and Dynkin classes on manifolds with Ricci curvature bounds.
method Using recent results on spectral negative parts and Gaussian heat kernel bounds, the study establishes local convexity of these classes.
result Local Kato and Dynkin classes are independent of the metric and smooth compactly supported functions are dense in the local Kato class.
The recent research report of U.S. Department of Energy prompts us to re-examine the pricing theories applied in electricity market design. The theory of spot pricing is the basis of electricity market design in many countries, but it has two major drawbacks: one is that it is still based on the traditional hourly sche…