Schr\"odinger bridges (SBs) provide an elegant framework for modeling the
temporal evolution of populations in physical, chemical, or biological systems.
Such natural processes are commonly subject to changes in population size over
time due to the emergence of new species or birth and death events. However,
existing neural parameterizations of SBs such as diffusion Schr\"odinger
bridges (DSBs) are restricted to settings in which the endpoints of the
stochastic process are both probability measures and assume conservation of
mass constraints. To address this limitation, we introduce unbalanced DSBs
which model the temporal evolution of marginals with arbitrary finite mass.
This is achieved by deriving the time reversal of stochastic differential
equations with killing and birth terms. We present two novel algorithmic
schemes that comprise a scalable objective function for training unbalanced
DSBs and provide a theoretical analysis alongside challenging applications on
predicting heterogeneous molecular single-cell responses to various cancer
drugs and simulating the emergence and spread of new viral variants.

该研究提出一种新的神经参数化方法：非平衡扩散 Schrödinger Bridge（DSBs）。该方法可以模拟当端点是概率分布，且质量未被守恒时，人口的时间演化，并可应用于分析癌症药物的单细胞响应和病毒变异的传播过程。

不平衡扩散薛定谔桥

Unbalanced Diffusion Schrödinger Bridge

Many tasks in natural language processing involve predicting structured
outputs, e.g., sequence labeling, semantic role labeling, parsing, and machine
translation. Researchers are increasingly applying deep representation learning
to these problems, but the structured component of these approaches is usually
quite simplistic. In this work, we propose several high-order energy terms to
capture complex dependencies among labels in sequence labeling, including
several that consider the entire label sequence. We use neural
parameterizations for these energy terms, drawing from convolutional,
recurrent, and self-attention networks. We use the framework of learning
energy-based inference networks (Tu and Gimpel, 2018) for dealing with the
difficulties of training and inference with such models. We empirically
demonstrate that this approach achieves substantial improvement using a variety
of high-order energy terms on four sequence labeling tasks, while having the
same decoding speed as simple, local classifiers. We also find high-order
energies to help in noisy data conditions.

本论文提出了几个高阶能量项来捕捉序列标记中标签之间的复杂依赖关系，并使用卷积、循环和自我注意网络的神经参数化来处理该方法。我们在学习基于能量的推理网络框架中使用此方法，在四个序列标记任务上实现了高性能，同时具有与简单的本地分类器相同的解码速度，并发现高阶能量在嘈杂的数据条件下的效果更好。