On Non-asymptotic Theory of Recurrent Neural Networks in Temporal Point Processes

• URL: http://arxiv.org/abs/2406.00630v1
• Date: Sun, 2 Jun 2024 06:19:25 GMT
• Title: On Non-asymptotic Theory of Recurrent Neural Networks in Temporal Point Processes
• Authors: Zhiheng Chen, Guanhua Fang, Wen Yu,
• Abstract summary: temporal point process (TPP) is an important tool for modeling and predicting irregularly timed events across various domains. Recent neural network (RNN)-based TPPs have shown practical advantages over traditional parametric TPP models. In this paper, we establish the excess risk bounds of RNN-TPPs under many well-known TPP settings.
• Score: 10.4442505961159
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Temporal point process (TPP) is an important tool for modeling and predicting irregularly timed events across various domains. Recently, the recurrent neural network (RNN)-based TPPs have shown practical advantages over traditional parametric TPP models. However, in the current literature, it remains nascent in understanding neural TPPs from theoretical viewpoints. In this paper, we establish the excess risk bounds of RNN-TPPs under many well-known TPP settings. We especially show that an RNN-TPP with no more than four layers can achieve vanishing generalization errors. Our technical contributions include the characterization of the complexity of the multi-layer RNN class, the construction of $\tanh$ neural networks for approximating dynamic event intensity functions, and the truncation technique for alleviating the issue of unbounded event sequences. Our results bridge the gap between TPP's application and neural network theory.

Related papers

• Cumulative Distribution Function based General Temporal Point Processes [49.758080415846884]
  CuFun model represents a novel approach to TPPs that revolves around the Cumulative Distribution Function (CDF) Our approach addresses several critical issues inherent in traditional TPP modeling. Our contributions encompass the introduction of a pioneering CDF-based TPP model, the development of a methodology for incorporating past event information into future event prediction.
  arXiv  Detail & Related papers  (2024-02-01T07:21:30Z)
• PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks [22.39904196850583]
  Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs) We introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs.
  arXiv  Detail & Related papers  (2023-07-21T18:06:27Z)
• Intensity-free Convolutional Temporal Point Process: Incorporating Local and Global Event Contexts [30.534921874640585]
  We propose a novel TPP modelling approach that combines local and global contexts by integrating a continuous-time convolutional event encoder with an RNN. The presented framework is flexible and scalable to handle large datasets with long sequences and complex latent patterns. To our best knowledge, this is the first work that applies convolutional neural networks to TPP modelling.
  arXiv  Detail & Related papers  (2023-06-24T22:57:40Z)
• Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study [55.12108376616355]
  The study on NTK has been devoted to typical neural network architectures, but is incomplete for neural networks with Hadamard products (NNs-Hp) In this work, we derive the finite-width-K formulation for a special class of NNs-Hp, i.e., neural networks. We prove their equivalence to the kernel regression predictor with the associated NTK, which expands the application scope of NTK.
  arXiv  Detail & Related papers  (2022-09-16T06:36:06Z)
• The Spectral Bias of Polynomial Neural Networks [63.27903166253743]
  Polynomial neural networks (PNNs) have been shown to be particularly effective at image generation and face recognition, where high-frequency information is critical. Previous studies have revealed that neural networks demonstrate a $textitspectral bias$ towards low-frequency functions, which yields faster learning of low-frequency components during training. Inspired by such studies, we conduct a spectral analysis of the Tangent Kernel (NTK) of PNNs. We find that the $Pi$-Net family, i.e., a recently proposed parametrization of PNNs, speeds up the
  arXiv  Detail & Related papers  (2022-02-27T23:12:43Z)
• Accurate online training of dynamical spiking neural networks through Forward Propagation Through Time [1.8515971640245998]
  We show how a recently developed alternative to BPTT can be applied in spiking neural networks. FPTT attempts to minimize an ongoing dynamically regularized risk on the loss. We show that SNNs trained with FPTT outperform online BPTT approximations, and approach or exceed offline BPTT accuracy on temporal classification tasks.
  arXiv  Detail & Related papers  (2021-12-20T13:44:20Z)
• Target Propagation via Regularized Inversion [4.289574109162585]
  We present a simple version of target propagation based on regularized inversion of network layers, easily implementable in a differentiable programming framework. We show how our TP can be used to train recurrent neural networks with long sequences on various sequence modeling problems.
  arXiv  Detail & Related papers  (2021-12-02T17:49:25Z)
• Neural Temporal Point Processes: A Review [25.969319777457606]
  Temporal point processes (TPP) are probabilistic generative models for continuous-time event sequences. neural TPPs combine the fundamental ideas from point process literature with deep learning approaches.
  arXiv  Detail & Related papers  (2021-04-08T06:10:50Z)
• Overcoming Catastrophic Forgetting in Graph Neural Networks [50.900153089330175]
  Catastrophic forgetting refers to the tendency that a neural network "forgets" the previous learned knowledge upon learning new tasks. We propose a novel scheme dedicated to overcoming this problem and hence strengthen continual learning in graph neural networks (GNNs) At the heart of our approach is a generic module, termed as topology-aware weight preserving(TWP)
  arXiv  Detail & Related papers  (2020-12-10T22:30:25Z)
• How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks [80.55378250013496]
  We study how neural networks trained by gradient descent extrapolate what they learn outside the support of the training distribution. Graph Neural Networks (GNNs) have shown some success in more complex tasks.
  arXiv  Detail & Related papers  (2020-09-24T17:48:59Z)
• Progressive Tandem Learning for Pattern Recognition with Deep Spiking Neural Networks [80.15411508088522]
  Spiking neural networks (SNNs) have shown advantages over traditional artificial neural networks (ANNs) for low latency and high computational efficiency. We propose a novel ANN-to-SNN conversion and layer-wise learning framework for rapid and efficient pattern recognition.
  arXiv  Detail & Related papers  (2020-07-02T15:38:44Z)

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.