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Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner

Tong Nie, Guoyang Qin, Wei Ma, Jian Sun

TL;DR

A novel paradigm to address the STTD learning problem by parameterizing STTD as an implicit neural representation that can learn implicit low-rank priors and smoothness regularization from the data, making it versatile for learning different dominating data patterns.

Abstract

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific dimensions or source-dependent patterns, restricting them from unifying representations. Here, we present a novel paradigm to address the STTD learning problem by parameterizing STTD as an implicit neural representation. To discern the underlying dynamics in low-dimensional regimes, coordinate-based neural networks that can encode high-frequency structures are employed to directly map coordinates to traffic variables. To unravel the entangled spatial-temporal interactions, the variability is decomposed into separate processes. We further enable modeling in irregular spaces such as sensor graphs using spectral embedding. Through continuous representations, our approach enables the modeling of a variety of STTD with a unified input, thereby serving as a generalized learner of the underlying traffic dynamics. It is also shown that it can learn implicit low-rank priors and smoothness regularization from the data, making it versatile for learning different dominating data patterns. We validate its effectiveness through extensive experiments in real-world scenarios, showcasing applications from corridor to network scales. Empirical results not only indicate that our model has significant superiority over conventional low-rank models, but also highlight that the versatility of the approach extends to different data domains, output resolutions, and network topologies. Comprehensive model analyses provide further insight into the inductive bias of STTD. We anticipate that this pioneering modeling perspective could lay the foundation for universal representation of STTD in various real-world tasks. Code is available at https://github.com/tongnie/traffic_dynamics.

Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner

TL;DR

A novel paradigm to address the STTD learning problem by parameterizing STTD as an implicit neural representation that can learn implicit low-rank priors and smoothness regularization from the data, making it versatile for learning different dominating data patterns.

Abstract

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific dimensions or source-dependent patterns, restricting them from unifying representations. Here, we present a novel paradigm to address the STTD learning problem by parameterizing STTD as an implicit neural representation. To discern the underlying dynamics in low-dimensional regimes, coordinate-based neural networks that can encode high-frequency structures are employed to directly map coordinates to traffic variables. To unravel the entangled spatial-temporal interactions, the variability is decomposed into separate processes. We further enable modeling in irregular spaces such as sensor graphs using spectral embedding. Through continuous representations, our approach enables the modeling of a variety of STTD with a unified input, thereby serving as a generalized learner of the underlying traffic dynamics. It is also shown that it can learn implicit low-rank priors and smoothness regularization from the data, making it versatile for learning different dominating data patterns. We validate its effectiveness through extensive experiments in real-world scenarios, showcasing applications from corridor to network scales. Empirical results not only indicate that our model has significant superiority over conventional low-rank models, but also highlight that the versatility of the approach extends to different data domains, output resolutions, and network topologies. Comprehensive model analyses provide further insight into the inductive bias of STTD. We anticipate that this pioneering modeling perspective could lay the foundation for universal representation of STTD in various real-world tasks. Code is available at https://github.com/tongnie/traffic_dynamics.
Paper Structure (28 sections, 5 theorems, 23 equations, 15 figures, 6 tables, 1 algorithm)

This paper contains 28 sections, 5 theorems, 23 equations, 15 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Spatiotemporal traffic data modeling
  4. Low-rank models for spatiotemporal traffic data
  5. Implicit data and function representation
  6. ST-INR for Generalized Traffic Dynamics Learning
  7. Generalized traffic data leaner through implicit neural representation
  8. Encoding high-frequency components in functional representation
  9. Factorizing spatial-temporal variability through coordinate disentanglement
  10. Learning traffic data in arbitrary domains
  11. High-dimensional extensions and gradient-based optimization
  12. Theoretical Analysis
  13. High frequency encodings
  14. Implicit low-rank regularization
  15. Inherent smoothness from MLPs
  16. ...and 13 more sections

Key Result

Lemma 1

Let $f$ become a deep neural network with parameters $\theta$, the training dynamics of it can be approximated by the NTK defined as: $k_{\text{NTK}}(\mathbf{x}_i,\mathbf{x}_j)=\mathbb{E}_{\theta}\langle\frac{\partial f(\mathbf{x}_i;\theta)}{\partial\theta},\frac{\partial f(\mathbf{x}_j;\theta)}{\pa where $\mathbf{K}$ is the kernel matrix between all data pairs of training data with $k_{i,j}=k_{\t

Figures (15)

  • Figure 1: Representing spatiotemporal traffic data as an implicit neural function.(a) Traffic data at arbitrary spatial-temporal coordinates can be represented as a continuous function in an implicit space. (b) Coordinate-based MLPs map input coordinates to traffic state of interest. (c) With the resolution-independent property, our model can learn a variety of spatiotemporal traffic data from different sources.
  • Figure 2: Overall architecture of the proposed ST-INR model (three-dimensional case).
  • Figure 3: Illustration of the learning objective of ST-INR. The total objective includes a supervised loss over all observed points, and a learnable regularization derived from the property of deep neural networks.
  • Figure 4: TSE performances on discrete grid.
  • Figure 5: TSE performances on continuous space.
  • ...and 10 more figures

Theorems & Definitions (9)

  • Lemma 1: Neural network dynamics through NTK NTK
  • proof
  • Lemma 2: Composing NTK with Fourier features FourierFeature
  • Lemma 3: The equivalence between periodic activation and Fourier features
  • proof
  • Lemma 4: Implicit low-rank regularization of DMF arora2019implicit
  • proof
  • Lemma 5: Spectral smoothness of ST-INR
  • proof