Dense ReLU Neural Networks for Temporal-spatial Model

• URL: http://arxiv.org/abs/2411.09961v3
• Date: Tue, 26 Nov 2024 04:56:41 GMT
• Title: Dense ReLU Neural Networks for Temporal-spatial Model
• Authors: Zhi Zhang, Carlos Misael Madrid Padilla, Xiaokai Luo, Oscar Hernan Madrid Padilla, Daren Wang,
• Abstract summary: We focus on fully connected deep neural networks utilizing the Rectified Linear Unit (ReLU) activation function for nonparametric estimation. We derive non-asymptotic bounds that lead to convergence rates, addressing both temporal and spatial dependence in the observed measurements. We also tackle the curse of dimensionality by modeling the data on a manifold, exploring the intrinsic dimensionality of high-dimensional data.
• Score: 13.8173644075917
• License:
• Abstract: In this paper, we focus on fully connected deep neural networks utilizing the Rectified Linear Unit (ReLU) activation function for nonparametric estimation. We derive non-asymptotic bounds that lead to convergence rates, addressing both temporal and spatial dependence in the observed measurements. By accounting for dependencies across time and space, our models better reflect the complexities of real-world data, enhancing both predictive performance and theoretical robustness. We also tackle the curse of dimensionality by modeling the data on a manifold, exploring the intrinsic dimensionality of high-dimensional data. We broaden existing theoretical findings of temporal-spatial analysis by applying them to neural networks in more general contexts and demonstrate that our proof techniques are effective for models with short-range dependence. Our empirical simulations across various synthetic response functions underscore the superior performance of our method, outperforming established approaches in the existing literature. These findings provide valuable insights into the strong capabilities of dense neural networks for temporal-spatial modeling across a broad range of function classes.

Related papers

• Autaptic Synaptic Circuit Enhances Spatio-temporal Predictive Learning of Spiking Neural Networks [23.613277062707844]
  Spiking Neural Networks (SNNs) emulate the integrated-fire-leak mechanism found in biological neurons. Existing SNNs predominantly rely on the Integrate-and-Fire Leaky (LIF) model. This paper proposes a novel S-patioTemporal Circuit (STC) model.
  arXiv  Detail & Related papers  (2024-06-01T11:17:27Z)
• Modeling Randomly Observed Spatiotemporal Dynamical Systems [7.381752536547389]
  Currently available neural network-based modeling approaches fall short when faced with data collected randomly over time and space. In response, we developed a new method that effectively handles such randomly sampled data. Our model integrates techniques from amortized variational inference, neural differential equations, neural point processes, and implicit neural representations to predict both the dynamics of the system and the timings and locations of future observations.
  arXiv  Detail & Related papers  (2024-06-01T09:03:32Z)
• Event-based Shape from Polarization with Spiking Neural Networks [5.200503222390179]
  We introduce the Single-Timestep and Multi-Timestep Spiking UNets for effective and efficient surface normal estimation. Our work contributes to the advancement of SNNs in event-based sensing.
  arXiv  Detail & Related papers  (2023-12-26T14:43:26Z)
• Learning Low Dimensional State Spaces with Overparameterized Recurrent Neural Nets [57.06026574261203]
  We provide theoretical evidence for learning low-dimensional state spaces, which can also model long-term memory. Experiments corroborate our theory, demonstrating extrapolation via learning low-dimensional state spaces with both linear and non-linear RNNs.
  arXiv  Detail & Related papers  (2022-10-25T14:45:15Z)
• Theoretical analysis of deep neural networks for temporally dependent observations [1.6752182911522522]
  We study theoretical properties of deep neural networks on modeling non-linear time series data. Results are supported via various numerical simulation settings as well as an application to a macroeconomic data set.
  arXiv  Detail & Related papers  (2022-10-20T18:56:37Z)
• Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
  We consider the impact of the training set and its structure on the quality of the long-term prediction. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
  arXiv  Detail & Related papers  (2021-12-15T20:09:20Z)
• Learning Neural Causal Models with Active Interventions [83.44636110899742]
  We introduce an active intervention-targeting mechanism which enables a quick identification of the underlying causal structure of the data-generating process. Our method significantly reduces the required number of interactions compared with random intervention targeting. We demonstrate superior performance on multiple benchmarks from simulated to real-world data.
  arXiv  Detail & Related papers  (2021-09-06T13:10:37Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Spatio-Temporal Functional Neural Networks [11.73856529960872]
  We propose two novel extensions of the Neural Functional Network (FNN), a temporal regression model whose effectiveness has been proven by many researchers. The proposed models are then deployed to solve a practical and challenging precipitation prediction problem in the meteorology field.
  arXiv  Detail & Related papers  (2020-09-11T21:32:35Z)
• An Ode to an ODE [78.97367880223254]
  We present a new paradigm for Neural ODE algorithms, called ODEtoODE, where time-dependent parameters of the main flow evolve according to a matrix flow on the group O(d) This nested system of two flows provides stability and effectiveness of training and provably solves the gradient vanishing-explosion problem.
  arXiv  Detail & Related papers  (2020-06-19T22:05:19Z)
• Network Diffusions via Neural Mean-Field Dynamics [52.091487866968286]
  We propose a novel learning framework for inference and estimation problems of diffusion on networks. Our framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node infection probabilities. Our approach is versatile and robust to variations of the underlying diffusion network models.
  arXiv  Detail & Related papers  (2020-06-16T18:45:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.