Origin-Destination (OD) matrices record directional flow data between pairs
of OD regions. The intricate spatiotemporal dependency in the matrices makes
the OD matrix forecasting (ODMF) problem not only intractable but also
non-trivial. However, most of the related methods are designed for very short
sequence time series forecasting in specific application scenarios, which
cannot meet the requirements of the variation in scenarios and forecasting
length of practical applications. To address these issues, we propose a
Transformer-like model named ODformer, with two salient characteristics: (i)
the novel OD Attention mechanism, which captures special spatial dependencies
between OD pairs of the same origin (destination), greatly improves the ability
of the model to predict cross-application scenarios after combining with 2D-GCN
that captures spatial dependencies between OD regions. (ii) a PeriodSparse
Self-attention that effectively forecasts long sequence OD matrix series while
adapting to the periodic differences in different scenarios. Generous
experiments in three application backgrounds (i.e., transportation traffic, IP
backbone network traffic, crowd flow) show our method outperforms the
state-of-the-art methods.

提出了 ODformer 模型，使用 OD Attention 机制捕捉 OD 对的特殊空间依赖关系，在与 2D-GCN 相结合后大大提高了模型在不同应用方案下的预测能力，并使用 PeriodSparse 自注意力有效预测不同场景下长序列 OD 矩阵系列。经过大量实验证明，该方法优于现有的最先进方法。

ODformer：基于时空 Transformer 的长序列出行 OD 矩阵预测跨应用场景研究

ODformer: Spatial-Temporal Transformers for Long Sequence Origin-Destination Matrix Forecasting Against Cross Application Scenario

In this thesis, we try to build a connection between the two schools by
introducing syntactic inductive biases for deep learning models. We propose two
families of inductive biases, one for constituency structure and another one
for dependency structure. The constituency inductive bias encourages deep
learning models to use different units (or neurons) to separately process
long-term and short-term information. This separation provides a way for deep
learning models to build the latent hierarchical representations from
sequential inputs, that a higher-level representation is composed of and can be
decomposed into a series of lower-level representations. For example, without
knowing the ground-truth structure, our proposed model learns to process
logical expression through composing representations of variables and operators
into representations of expressions according to its syntactic structure. On
the other hand, the dependency inductive bias encourages models to find the
latent relations between entities in the input sequence. For natural language,
the latent relations are usually modeled as a directed dependency graph, where
a word has exactly one parent node and zero or several children nodes. After
applying this constraint to a Transformer-like model, we find the model is
capable of inducing directed graphs that are close to human expert annotations,
and it also outperforms the standard transformer model on different tasks. We
believe that these experimental results demonstrate an interesting alternative
for the future development of deep learning models.

我们在本文中介绍了两种归纳偏差方法，分别针对语法结构和依赖关系，实现了深度学习模型的归纳偏差，并通过这些方法建立了深度学习模型的潜在分层表示，使模型能够处理复杂的序列结构并在语言处理任务中取得了优秀的效果。