This survey clarifies dynamic network terminology and reviews GNN models for dynamic networks.
problem Ambiguity in dynamic network terminology and lack of GNN models for dynamic networks.
method Established consistent terminology and notation for dynamic networks, reviewed GNN models.
result Comprehensive survey of dynamic graph neural network models.
Neural ODEs provide a framework for studying the training dynamics of neural networks.
problem Training dynamics of neural networks
method Dynamical mean field theory
result Derive learning curves in the high-dimensional limit
Use simplified layerwise linear models to understand neural dynamics.
problem Complex neural network dynamics are hard to grasp.
method Apply simplified layerwise linear models to explain neural phenomena.
result Simplified models explain neural collapse, emergence, etc.
New neural network designs learn contact dynamics efficiently.
problem Learning contact dynamics in robotics from noisy data.
method Physically structured neural networks.
result Data-efficient learning of discontinuous contact events.
EvoNet predicts the evolution of dynamic graphs using a graph neural network and recurrent architecture.
problem Predicting the evolution of dynamic graphs is challenging and underexplored.
method EvoNet uses a graph neural network and recurrent architecture to predict the evolution of dynamic graphs.
result EvoNet effectively predicts the evolution of dynamic graphs on both artificial and real-world datasets.
Graph Neural Network improves causal inference in dynamic systems.
problem Identifying causal relations among multi-variate time series.
method Graph Neural Network approach with score-based method.
result Graph Neural Network significantly outperformed other methods in dynamic Bayesian network inference.
Study on neural networks with regularisation and its impact on training dynamics.
problem Understanding the dynamics of neural networks with regularization.
method Established explicit dynamics for neural networks with a regularizing term, linearizing around initialisation.
result The regularisation term modifies the standard NTK dynamics, leading to new insights into network training.
Neural GDEs improve graph prediction by blending discrete structures and differential equations.
problem Dynamic graph prediction challenges in irregularly sampled data.
method Continuous-depth graph neural networks (GNNs) with Neural GDEs.
result Neural GDEs enhance performance across various applications.
Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.
problem Understanding and modeling nonlinear dynamical systems.
method Trains neural networks to minimize forecast error based on spectral decomposition in the lifted space.
result Demonstrates effectiveness in eigenvalue estimation and forecast performance.
The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural networks can efficiently model chaotic dynamics by becoming structurally chaotic t…
Survey on statistical theories of neural networks, focusing on approximation, training dynamics, and generative models.
problem Understanding the statistical properties and training dynamics of neural networks.
method Review of existing literature on neural networks from three perspectives: approximation, training dynamics, and generative models.
result Theoretical insights into neural network training dynamics and generative models.
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we present a compact neural circuit for two common numerical integrators: the explicit …
Neural networks improve predictions of complex network dynamics.
problem Improving neural network predictions for complex network dynamics.
method Extended neural network models to complex systems, ensuring they conform to dynamical model assumptions and using a statistical significance test.
result Achieved advanced generalization of neural network predictions for complex systems.
This paper uses neural networks to predict stock prices more accurately.
problem Current stock analysis methods are inaccurate.
method Dynamic neural networks to identify stock price patterns.
result Neural networks outperform traditional stock analysis methods.
Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually known as the graph neural networks, have been applied to advance many graphs relate…
RNNs compute by warping neural representations over time.
problem Understanding how RNNs perform task computations.
method Developed a Riemannian geometric framework to derive the manifold topology and geometry of RNNs.
result Dynamic warping is a fundamental feature of RNN computations.
The paper analyzes neural network dynamics after weights escape the origin.
problem Understanding gradient flow dynamics of neural networks after the origin.
method Analyzes gradient flow of homogeneous neural networks with locally Lipschitz gradients.
result Characterizes the first saddle point encountered after escaping the origin.
GFM models neural network training as a dynamical system to forecast final weights.
problem Computational intensity and inefficiency in training deep neural networks.
method Gradient Flow Matching (GFM) treats training as a dynamical system with learned vector fields.
result GFM achieves forecasting accuracy competitive with Transformer-based models and significantly outperforms classical baselines.
Noether's framework reveals symmetry-breaking in neural networks.
problem Understanding the role of symmetry breaking in neural networks.
method Developed a theoretical framework using Lagrangian mechanics.
result Identified 'kinetic symmetry breaking' and its effect on learning dynamics.
FHRN uses continuous-time dynamics to stabilize reentrant neural computation.
problem Stabilizing reentrant neural computation.
method Formulated as a continuous-time neural-ODE system, revealing norm-regulated reentry.
result Achieves stable oscillatory trajectories through population-level gain modulation.
Neural networks compress and sample WDN contamination dynamics efficiently.
problem Infrastructure monitoring of complex, networked systems like water distribution networks is expensive and challenging.
method Developed Graph Fourier Transform (GFT) operators and neural networks (NN) for efficient data collection and inference.
result High accuracy reconstruction of contamination dynamics using only 5-10% of the sample set.
Unified analysis of DLNs using DMFT reveals dynamics of loss convergence and generalization trade-offs.
problem Understanding the overall dynamics of diagonal linear networks (DLNs) in neural network training.
method Dynamical Mean-Field Theory (DMFT) applied to DLNs.
result Derives low-dimensional effective process capturing high-dimensional gradient flow dynamics.
Parallel neural network training yields better long-term prediction accuracy.
problem Choosing the right training strategy for neural networks in dynamical systems.
method Comparison of parallel and series-parallel training strategies on five neural network architectures and two examples.
result Parallel training consistently outperforms series-parallel training in long-term prediction accuracy.
Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent trajectories. However, simple state transition structures, linear embedding assumpti…
We propose and systematically evaluate three strategies for training dynamically-routed artificial neural networks: graphs of learned transformations through which different input signals may take different paths. Though some approaches have advantages over others, the resulting networks are often qualitatively similar…
Hybrid model combines neural networks and fluid dynamics for efficient, generalized simulations.
problem Inefficient and poor generalization of deep learning approximations of fluid dynamics.
method Combines graph neural networks with a differentiable PDE solver inside a neural network.
result Hybrid model generalizes well to new scenarios and outperforms both neural network and traditional methods.
Proposes a graph neural network for traffic forecasting in WANs.
problem Traffic forecasting challenges in WANs due to dynamic and large data volumes.
method Dynamic diffusion convolutional recurrent neural networks for multistep traffic forecasting.
result Significant improvements in forecasting accuracy compared to classical methods.
Proposes DCNAR for dynamic causal inference from neural time series.
problem Uncertainty and evolution of causal structure in real-world domains.
method Two-stage neural causal modeling integrating discovery and inference.
result Dynamic causal inferences are more stable and meaningful than alternatives.
DGNN predicts financial margin calls under stress tests.
problem Forecasting margin calls in dynamic financial networks.
method Dynamic Graph Neural Network (DGNN) architecture.
result DGNN produces accurate forecasts up to 21 days.
This paper analyzes the training dynamics of binary neural networks using information bottleneck.
problem Training binary neural networks is challenging due to discontinuity in activation functions.
method The approach uses the Information Bottleneck principle to analyze BNN training dynamics.
result Training dynamics of BNNs are different from DNNs, with both phases occurring simultaneously.
DISTANA predicts and denoises spatial wave dynamics.
problem Identifying causality in spatially distributed, non-linear dynamical processes.
method Generative, recurrent graph convolution neural network architecture (DISTANA).
result DISTANA outperforms alternative approaches in denoising and predicting complex spatial wave propagation.
The paper examines how deep linear neural networks behave as they become infinitely wide.
problem Understanding the behavior of deep linear neural networks as they approach infinite width.
method Analyzes the infinite-width limit of deep linear neural networks, proving convergence to deterministic models and providing precise laws for random weights.
result The training dynamics of deep linear neural networks converge to those of a deterministic model, and the weights' behavior is precisely described.
Proposes dynamic channel pruning during neural network training.
problem Pruning neural networks during training to reduce computational cost and improve efficiency.
method Dynamic channel propagation to update channel utility values and selectively prune channels.
result Our scheme trains and prunes neural networks simultaneously, achieving superior performance.
Study on fluctuations in neural network kernels and predictions, focusing on finite width effects.
problem Characterizing fluctuations in finite width neural networks.
method Dynamical mean field theory analysis of wide but finite feature learning neural networks.
result Fluctuations in kernels and predictions are dynamically coupled, leading to reduced variance in feature learning regimes.
Quadratic models explain neural network behavior during training.
problem Understanding neural network dynamics during training with large learning rates.
method Developed and tested Neural Quadratic Models.
result Neural Quadratic Models exhibit the 'catapult phase' similar to neural networks.
Complex high dimensional stochastic dynamic systems arise in many applications in the natural sciences and especially biology. However, while these systems are difficult to describe analytically, "snapshot" measurements that sample the output of the system are often available. In order to model the dynamics of such sys…
Study shows how large neural networks avoid overfitting through decoupling of feature learning and complexity growth.
problem Understanding inductive bias and generalization in large neural networks.
method Dynamical mean field theory applied to large two-layer networks.
result Training dynamics of large networks exhibit a separation of timescales, decoupling feature learning and overfitting.
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.
The paper analyzes the dynamics of a simple neural network using a mean-field approach.
problem Understanding the training dynamics of neural networks, especially in classification tasks.
method Developed an analytic theory using a mean-field limit for a simple neural network.
result Explicitly solved the dynamics of a linearly separable dataset with a linear hinge loss.
Neural network outperforms traditional methods in chaotic dynamics classification.
problem Classifying chaotic and regular dynamics of the Chirikov standard map.
method Trained a convolutional neural network on finite-length trajectories compared to traditional Lyapunov exponent computation.
result Neural network outperforms traditional methods for short periods, converging faster and more robustly.
New neural net learns time-reversible symplectic dynamics.
problem Lack of time-reversibility in neural networks for symplectic systems.
method Proposes a new neural network architecture for time-reversible symplectic systems.
result Demonstrates learning of time-reversible symplectic dynamics from data.
Paper introduces multitask neural networks for efficient stochastic control problems.
problem Infeasibility of simulating state variables in some stochastic control problems.
method Multitask neural networks with dynamic task balancing.
result Multitask neural networks outperform state-of-the-art approaches in derivatives pricing problems.
Study reveals dynamics of neural networks with normalization, weight decay, and SGD.
problem Understanding the equilibrium condition in Spherical Motion Dynamics (SMD).
method Investigates SMD by exploring the cause of equilibrium condition, introducing assumptions, proposing angular update, and verifying theoretical results.
result Proves weight norm and angular update can converge at linear rate under given assumptions.
New fusion blocks improve equivariant neural networks for molecular dynamics.
problem Designing equivariant neural networks for tasks with global symmetries.
method Using fusion diagrams from tensor networks to design novel equivariant components.
result Improved performance with fewer parameters on chemical problems.
The paper studies neural networks' convergence near origin and saddle points.
problem Directional convergence of neural networks near small initializations and saddle points.
method Gradient flow dynamics analysis of two-homogeneous neural networks.
result Neural networks' weights approximately converge in direction to KKT points for small initializations.
Paper develops a neural-fuzzy controller for GPS-intelligent buoys.
problem Optimally track dynamically positioned marine buoys with unknown parameters.
method Dynamic system modeling using neural-fuzzy networks with backstepping technique.
result The controller minimizes position errors and adjusts buoy positions accurately.
Neural EKF improves structural dynamics prediction.
problem Accurately predicting structural response for health monitoring.
method Neural Extended Kalman Filter (Neural EKF) for learning dynamics.
result Significant predictive capabilities demonstrated on simulated and real-world data.
The evolution of a deep neural network trained by the gradient descent can be described by its neural tangent kernel (NTK) as introduced in [20], where it was proven that in the infinite width limit the NTK converges to an explicit limiting kernel and it stays constant during training. The NTK was also implicit in some…