The paper finds unique equilibrium states for geodesic flows on certain surfaces.
problem Analyzing geodesic flows on surfaces without focal points.
method Proving the existence of unique equilibrium states for specific potentials.
result There are unique equilibrium states for certain potentials, including geometric multiples of scalar less than 1.
Deep learning detects tennis players' flow state from wearable data.
problem Lack of psychological feedback in wearable devices for sports performance.
method Trained deep neural networks on wearable data and coach labels.
result Deep neural networks achieved 98% accuracy in detecting flow state.
The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability density of the microscopical state is connected with a Perelman's functional of …
CFIL uses coupled flows to model state distributions for imitation learning.
problem Lack of explicit modeling of state distributions in reinforcement and imitation learning.
method Coupled normalizing flows for state and state-action distributions.
result CFIL achieves state-of-the-art performance on benchmark tasks.
Unified framework for continuous-state discrete flow matching models.
problem Discrete generative modeling with continuous probabilities.
method Introducing α-Flow, a family of CS-DFM models based on information geometry. result Optimal flow matching loss for α-flow minimizes generalized kinetic energy. New method for natural policy gradients converges linearly.
problem Improving natural policy gradient methods for better convergence.
method Fisher-Rao gradient flow applied to state-action distributions.
result Linear convergence rate with geometry-dependent factor.
PixelCNN models can achieve state-of-the-art results on CIFAR-10 with exact likelihood computation.
problem Dequantization gap in modeling discrete data like images.
method Introducing subset flows to allow exact computation of likelihoods for discrete data.
result PixelCNN models trained with exact likelihood computation achieve state-of-the-art results on CIFAR-10.
RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
Proves simplicity of Lyapunov exponents for specific Anosov flows.
problem Proving all Lyapunov exponents have multiplicity 1 for certain Anosov flows.
method Perturbative results for flows, modification of eigenvalues, Markov partition, and simplicity criterion.
result In a C1-open and Ck-dense set of Anosov flows, all Lyapunov exponents have multiplicity 1. This study improves state estimation for nonlinear systems using conditional normalizing flows.
problem Performance degradation of traditional filtering algorithms in nonlinear systems with non-Gaussian uncertainty.
method Uses conditional normalizing flows with MLP, transformer, or state-space models for state and parameter estimation.
result Optimal-transport-inspired kinetic loss mitigates overparameterization in flows.
Branching Flows generates sequences of varying lengths using binary trees.
problem Generating sequences of unknown lengths or fixed elements.
method A generative modeling framework that evolves states over binary trees, controlling sequence length.
result Branching Flows can generate sequences of varying lengths and mix different types of state spaces.
Flow++ improves flow-based models by dequantizing with variational methods and using expressive architectures.
problem Flow-based models have poor density estimation compared to autoregressive models.
method Variational dequantization, expressive affine flows, and improved architecture design.
result Flow++ is now the state-of-the-art non-autoregressive model for unconditional density estimation.
FORBES learns flexible belief states for POMDPs using normalizing flows.
problem Accurately modeling belief states in POMDPs for high-dimensional, continuous spaces.
method Integrates normalizing flows into variational inference for continuous belief state learning.
result FORBES learns flexible belief states that enable multi-modal predictions and high-quality reconstructions.
NAF combines neural networks with autoregressive models for better density estimation.
problem Improving density estimation and speech synthesis speed.
method Generalizes autoregressive models using neural networks for invertible transformations.
result NAF is a universal approximator for continuous probability distributions and outperforms IAF.
A new method for Gaussian filtering using gradient flows and Wasserstein metrics.
problem Approximating Gaussian and mixture-of-Gaussians filtering for complex systems.
method Variational approximation via gradient-flow representation on Wasserstein metric space.
result Competitive performance in posterior representation and parameter estimation for systems with multiplicative noise and multi-modal distributions.
Study measures rigidity for random walks and flows via generalized u-Gibbs states.
problem Measure rigidity for stationary measures of random walks and flows.
method Factorization method applied to generalized u-Gibbs states.
result Established extra invariance of generalized u-Gibbs states.
A Hawkes process with state-dependent factor models order flows in limit order books.
problem Modeling order flows in limit order books for better market prediction.
method A Hawkes process with a state-dependent factor for conditional intensity estimation.
result State-dependent formulations improve the fit of LOB models to financial data.
In this paper we present some results on a family of geometric flows introduced by Bourguignon that generalize the Ricci flow. For suitable values of the scalar parameter involved in these flows, we prove short time existence and provide curvature estimates. We also state some results on the associated solitons.
In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…
We show that a steady-state stock-flow consistent macro-economic model can be represented as a Constraint Satisfaction Problem (CSP).The set of solutions is a polytope, which volume depends on the constraintsapplied and reveals the potential fragility of the economic circuit,with no need to study the dynamics. Several …
Improves out-of-distribution detection in neural networks.
problem Detecting out-of-distribution examples in neural networks.
method Normalizing flows and residual flow architecture for expressive density modeling.
result Significantly improved true negative rate (77.5%) compared to state-of-the-art (56.7%).
Deep learning predicts fluid flow in porous media, accelerating simulations by orders of magnitude.
problem Accurate simulation of fluid flow in complex porous media requires excessive computational resources.
method Combining deep learning with direct simulation, using Gated U-Net CNNs trained on datasets of 2D and 3D porous media.
result Deep learning predictions can reach over 90% accuracy for permeability estimation and accelerate simulations by orders of magnitude.
New method reduces discrete flow transitions, improving perplexity estimation.
problem Stochasticity in discrete paths makes rectification strategies ineffective.
method Dynamic-optimal-transport-like minimization objective with minibatch strategies.
result 32 times reduction in transitions for same perplexity.
Improved flow-based models capture dependencies better with multi-scale autoregressive priors.
problem Limited expressiveness of flow-based models for long-range data dependencies.
method Introducing channel-wise dependencies through multi-scale autoregressive priors (mAR) in split coupling flow layers (mAR-SCF).
result Achieves state-of-the-art density estimation results on MNIST, CIFAR-10, and ImageNet.
In this paper we consider the evolution of sets by a fractional mean curvature flow. Our main result states that for any dimension n>2, there exists an embedded surface in Rn evolving by fractional mean curvature flow, which developes a singularity before it can shrink to a point. When n>3 this resul…
The robustness and integrity of IP networks require efficient tools for traffic monitoring and analysis, which scale well with traffic volume and network size. We address the problem of optimal large-scale flow monitoring of computer networks under resource constraints. We propose a stochastic optimization framework wh…
DFMs enable flow-based models for multimodal discrete and continuous data.
problem Combining discrete and continuous data for generative models.
method Discrete Flow Models (DFMs) using Continuous Time Markov Chains.
result DFMs achieve state-of-the-art co-design performance for protein structure and sequence generation.
Generative Flow Networks solve shortest path problems in graphs.
problem Finding shortest paths in graphs.
method Generative Flow Networks with flow regularization.
result Training a GFlowNet can solve pathfinding problems in arbitrary graphs.
Study state-dependent Hawkes processes for limit order book modeling.
problem Modeling feedback loop between order flow and limit order book shape.
method Existence and uniqueness of state-dependent Hawkes processes, simulation, maximum likelihood estimation.
result Excitation effects in order flow are strongly state-dependent.
DLF combines autoregressive and flow-based methods for efficient and high-performance image generation.
problem Limited density estimation performance and parallelizability of flow-based and autoregressive models.
method Dynamic Linear Flow (DLF) with partially autoregressive structure.
result DLF achieves state-of-the-art performance on ImageNet 32x32 and 64x64 images.
ACFM predicts crowd flow adaptively integrating various factors.
problem Adaptive integration of factors affecting crowd flow changes.
method Unified neural network module with attention mechanism.
result Significant improvements over state-of-the-art methods.
Study bi-harmonic flow with forcing term on smooth curves.
problem Analyzing the evolution of smooth, closed planar curves under bi-harmonic flow with a forcing term.
method Reformulated geometric flow using support function, scalar PDE characterization, Monge Ampére structure analysis.
result Convexity is preserved and steady-state solutions converge over long times under specific conditions.
We survey some of the state of the art regarding singularities in Lagrangian mean curvature flow. Some open problems are suggested at the end.
The noncompact Yamabe flow can lead to incomplete metrics over infinite time.
problem Incompleteness of noncompact Yamabe flow solutions over infinite time.
method Analysis of long-time behavior of the noncompact Yamabe flow.
result Existence of a long-time solution that is complete for each time but converges to an incomplete metric.
In this paper, we propose a new volume-preserving flow and show that it performs similarly to the linear general normalizing flow. The idea is to enrich a linear Inverse Autoregressive Flow by introducing multiple lower-triangular matrices with ones on the diagonal and combining them using a convex combination. In the …
COMBO network improves optical flow estimation by combining deep learning with brightness constancy.
problem Optical flow estimation using deep learning requires complex training schemes.
method COMBO network explicitly exploits brightness constancy and combines it with a data-driven approach.
result COMBO network outperforms state-of-the-art methods on various benchmarks.
Model predicts traffic flow dynamics from sparse data.
problem Predict traffic flow from limited data.
method Mesoscopic model using factor graphs and message passing.
result Efficiently estimates traffic conditions with low probe vehicle penetration.
Invites study of contact structures and Reeb flows dynamics.
problem Relating dynamics of two Reeb flows of the same contact structure.
method Gathers results and poses many questions and conjectures.
result Many new questions and conjectures posed.
Study geometric flows with varying parameters and prove continuous dependence.
problem Continuous dependence of flows on parameters in geometric settings.
method Derived suitable topologies for vector fields and flows, proved new continuous dependence.
result Proved continuous dependence of flows on parameters in a general topological space.
RegFlow models future states with flexible probability distributions.
problem Predicting future states under complex, non-deterministic scenarios.
method Hypernetwork architecture and continuous normalizing flow model.
result RegFlow achieves state-of-the-art results on benchmark datasets.
Simplifies residual flows to make flow-based modeling more practical.
problem Extremely high computational cost of residual flows limits their applicability.
method Introduces Quasi-Autoregressive (QuAR) approach to residual flows.
result Significantly reduces compute time and memory requirements for flow-based modeling.
Generative model learns spin-glass dynamics and properties.
problem Complex behavior of many-body systems in statistical physics and computer science.
method Self-supervised learning with normalizing flows.
result Key physical and computational properties of spin-glasses are learned.
Proof that certain Anosov flows are almost equivalent.
problem Proving equivalence of suspension Anosov flows.
method Constructing a genus-one Birkhoff section and analyzing its first-return map.
result Explicit bounds on distances between suspension Anosov flows.
Flow-SSN improves segmentation efficiency and accuracy.
problem Challenges in medical imaging segmentation, especially high-rank pixel-wise covariances.
method Generative segmentation model using discrete-time autoregressive and continuous-time flow variants.
result Flow-SSNs can estimate high-rank pixel-wise covariances efficiently without assuming rank or storing parameters.
Study shows pre-event L2 liquidity state predicts crypto futures liquidity better than event labels.
problem Understanding how crypto futures liquidity changes over time.
method Combining L2 order book data, trade-flow records, and macro-event windows to define discrete liquidity-state transitions and evaluate models.
result Pre-event L2 liquidity state predicts post-event liquidity regimes better than event labels, and order flow adds value only when layered on top of the state model.
We study singularities of Lagrangian mean curvature flow in $\C^n$ when the initial condition is a zero-Maslov class Lagrangian. We start by showing that, in this setting, singularities are unavoidable. More precisely, we construct Lagrangians with arbitrarily small Lagrangian angle and Lagrangians which are Hamiltonia…
ELF simplifies normalizing flows, making them more efficient and universal.
problem Computational inefficiency of normalizing flows.
method ELF introduces a simple, one-layer network with closed-form Lipschitz constants, combining the ease of residual flows with the performance of autoregressive flows.
result ELF is a provably universal density approximator, more efficient computationally and parameter-wise.
Enhances generative models by improving expressivity without high computational cost.
problem Improving expressivity in generative models without increasing computational complexity.
method Proposes a new family of generative flows on an augmented data space, proving they can approximate a Hamiltonian ODE as a universal transport map.
result Demonstrates state-of-the-art performance on flow-based generative modeling benchmarks.