Do We Really Need Graph Neural Networks for Traffic Forecasting.pdf

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Do We Really Need Graph Neural Networks for Trafﬁc Forecasting?

Xu Liu

Yuxuan Liang

Chao Huang

Hengchang Hu

Yushi Cao

Bryan Hooi

Roger Zimmermann

Abstract

Spatio-temporal graph neural networks (STGNN)

have become the most popular solution to traf-

ﬁc forecasting. While successful, they rely on

the message passing scheme of GNNs to estab-

lish spatial dependencies between nodes, and

thus inevitably inherit GNNs’ notorious inefﬁ-

ciency. Given these facts, in this paper, we pro-

pose an embarrassingly simple yet remarkably

effective spatio-temporal learning approach, en-

titled SimST. Speciﬁcally, SimST approximates

the efﬁcacies of GNNs by two spatial learning

techniques, which respectively model local and

global spatial correlations. Moreover, SimST can

be used alongside various temporal models and

involves a tailored training strategy. We conduct

experiments on ﬁve trafﬁc benchmarks to assess

the capability of SimST in terms of efﬁciency and

effectiveness. Empirical results show that SimST

improves the prediction throughput by up to 39

times compared to more sophisticated STGNNs

while attaining comparable performance, which

indicates that GNNs are not the only option for

spatial modeling in trafﬁc forecasting.

1. Introduction

In recent years, urban trafﬁc forecasting has emerged as

one of the most important components of Intelligent Trans-

portation Systems. Given historical trafﬁc observations

(e.g., trafﬁc speed, ﬂow) collected from sensors on road

networks, the task focuses on predicting future trafﬁc trends

for each sensor, which provides insights for improving ur-

ban planning and trafﬁc management (Zheng et al., 2014).

Spatio-Temporal Graph Neural Networks (STGNNs) have

become the de facto most popular tool for trafﬁc forecasting,

in which sequential models such as Temporal Convolution

Networks (TCNs) or Recurrent Neural Networks (RNNs)

National University of Singapore

University of Hong

Kong

Nanyang Technological University. Correspondence

to: Xu Liu

liuxu@comp.nus.edu.sg

, Yuxuan Liang

<yuxliang@outlook.com>.

Preprint. Under review.

are applied for modeling temporal dependencies (Yu et al.,

2018; Pan et al., 2019; Wu et al., 2020; Lan et al., 2022), and

Graph Neural Networks (GNNs) (Kipf & Welling, 2017;

Defferrard et al., 2016) are utilized to capture spatial corre-

lations among different locations.

After revisiting the STGNNs proposed in recent years, we

ﬁnd that they mostly focus on enhancing the spatial learn-

ing modules (i.e., GNNs) with either complex aggregation

rules or sophisticated layers to improve predictive perfor-

mance. While successful, we note that they rely heavily on

GNNs for performing the message passing step and thus

inevitably inherit GNNs’ notorious inefﬁciencies, especially

when the graphs are large or with dense connections (Chen

et al., 2021a; Zhang et al., 2022). As a concrete example,

the commonly used adaptive adjacency matrix is built by

matrix multiplication of two node embedding tables, pro-

ducing a fully-connected graph (Wu et al., 2019; Bai et al.,

2020; Han et al., 2021). During feature aggregation, such a

fully-connected structure leads to quadratic computational

complexity w.r.t. the number of sensors. Consequently, the

scalability challenges of GNNs hinder the deployment of

STGNNs in large-scale and real-time trafﬁc forecasting sys-

tems that are latency-bound and require fast inference.

Although there are plenty of efforts in the graph domain to

improve the efﬁciency of GNNs, such as via graph simpli-

ﬁcation (Hamilton et al., 2017; Chen et al., 2018; Chiang

et al., 2019; Zeng et al., 2020; Zheng et al., 2020b), the

related studies in STGNNs are still scarce to the best of our

knowledge, as such simpliﬁcation usually leads to informa-

tion loss and performance degradation (Wu et al., 2020).

Given these facts and inspired by recent progress in elim-

inating GNNs for node classiﬁcation (Zhang et al., 2022;

Tian et al., 2022), we may ask:

can we remove GNNs to

trim down the explosive complexity while still remaining

competitive in trafﬁc forecasting accuracy?

Present Work

To answer this question, we ﬁrst demon-

strate the functionalities of GNNs as follows. The superior

performance of GNNs stems from its structure-aware ex-

ploitation of graphs: (1) for each node in the graph, a single

GNN layer is used to ﬁrst aggregate features from nodes’

neighbors and then transform the aggregated representations

via a feed-forward network, and (2) by stacking multiple

layers, the hidden representations of nodes receive messages

from long-distance neighbors.

arXiv:2301.12603v1 [cs.LG] 30 Jan 2023

Do We Really Need Graph Neural Networks for Trafﬁc Forecasting?

In this work, we propose two spatial learning modules to

approximate the above efﬁcacies of GNNs without requiring

message passing, reducing the time complexity to linear.

(1) Local Proximity Modeling. We take a local view and

fragment the trafﬁc network to build an ego-graph for each

node, which is constructed by incorporating historical obser-

vations of the node’s neighbors. Then an MLP is applied to

transform the observations to the hidden states at each time

step. (2) Global Correlation Learning. Inspired by recom-

mender systems that learn user embeddings to reﬂect user

behavioral similarities (He et al., 2017; Zhang et al., 2019),

we propose to use sensor embeddings to represent sensors’

inherent properties and collaboratively capture spatial rela-

tionships between arbitrary sensor pairs in a data-driven

manner. Compared with stacking a number of GNN layers

to enlarge the receptive ﬁeld and build long-range spatial de-

pendencies, our module sets up direct connections between

nodes and thereby learns the global correlations.

In practice, GNNs can be used alongside various temporal

models, such as GRU (Chung et al., 2014), WaveNet (Oord

et al., 2016), and Transformer (Vaswani et al., 2017), for

spatio-temporal learning. Analogously, we empirically ﬁnd

that our proposed spatial modules are agnostic to the tempo-

ral encoders and work in a plug-and-play manner. Moreover,

we devise a new training strategy for SimST to further boost

performance, which increases sample diversity during batch

formation and enhances generalization.

Integrating the above components, we propose a

Sim

ple

yet effective

patio-

emporal learning approach termed

SimST

, which trims the quadratic cost and performs on par

with STGNNs in empirical studies. Our contributions are

summarized as follows.

•

We for the ﬁrst time demonstrate that GNNs are not the

only choice for spatial modeling in trafﬁc forecasting, by

presenting a simple yet admirable method called SimST.

•

Despite its simplicity, SimST achieves remarkable empir-

ical results in terms of throughput and accuracy against

sophisticated state-of-the-art STGNNs: SimST is signiﬁ-

cantly more efﬁcient than baselines, with up to

39×

higher

inference throughput, while performing on par with them.

•

We conduct ablation and case studies to promote a better

understanding of our method and motivate future research

to rethink the importance of GNNs in trafﬁc forecasting.

2. Related Work

Trafﬁc forecasting is a crucial application in smart city ef-

forts. In recent years, STGNNs have become the most

widely used tools for predicting trafﬁc (Cao et al., 2020;

Liu et al., 2022b; Chen et al., 2021b; 2022). Generally,

they integrate GNNs with either RNNs or TCNs to capture

the spatial and temporal dependencies in trafﬁc data. For

example, DCRNN (Li et al., 2018) considered trafﬁc ﬂow

as a diffusion process and combined a novel diffusion con-

volution with GRU. Other efforts (Pan et al., 2019; Fang

et al., 2021; Liu et al., 2022a) were also based on RNNs.

To improve training speed and enjoy parallel computation,

plenty of works (Wu et al., 2019; 2020; Li & Zhu, 2021)

replaced RNNs with dilated causal convolution.

A fundamental problem for using GNNs in trafﬁc model-

ing is how to establish a graph structure. The mainstream

approach to deﬁne such structures is using either a prede-

ﬁned and sparse matrix constructed from the road network

distances between sensors (Yu et al., 2018; Li et al., 2018;

Song et al., 2020), or an adaptive and dense matrix that

records the pairwise relationships between nodes (Wu et al.,

2019; Bai et al., 2020; Han et al., 2021; Choi et al., 2022).

However, researchers have noted that the predeﬁned matrix

is heuristic and does not reﬂect the genuine dependencies

between nodes, which degrades model performance (Wu

et al., 2019; Bai et al., 2020). Models applying the adaptive

matrix generally achieve superior performance. Though

successful, the adaptive matrix discards the sparsity of the

graph and incurs a quadratic computational cost, making it

hard to deploy for latency-constrained or large-scale trafﬁc

applications. Other methods that use attention mechanisms

for spatial learning (Zheng et al., 2020a) also suffer from

quadratic time complexity. In this study, we propose SimST

to alleviate the inefﬁciency issue by eliminating the inefﬁ-

cient GNN component in the model.

3. Preliminary

Trafﬁc Forecasting

Let

G = (V, E)

represent a directed

sensor graph with

|V|

nodes and

|E|

edges, and

∈

|V|×T ×F

denote the features of all nodes from time step 1

, where

is the feature dimension. The features usu-

ally consist of a target attribute (e.g., trafﬁc speed) and other

auxiliary information, such as time of day (Wu et al., 2019).

Following common settings (Li et al., 2018; Wu et al., 2019),

a weighted adjacency matrix

A ∈ R

|V|×|V|

is applied to de-

scribe the graph topology, where

= exp(−

dist(v

)

dist(v

, v

) 6 r

else

= 0

dist(v

, v

)

denotes the

road network distance between sensors

and

is the

standard deviation of distances, and

is a threshold for spar-

sity (Shuman et al., 2013). The non-zero entries in

form

the set of edges in E.

In trafﬁc forecasting, we aim to learn a neural network

to predict the target attribute in future

steps based on

historical observations over the sensor graph:

G, X

−→

(1)

where

∈ R

|V|×T

×F

indicates the observations and

∈ R

|V|×T

×1

is the predictions. A prediction loss, e.g.,

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