The effectiveness of neural processes (NPs) in modelling posterior prediction
maps -- the mapping from data to posterior predictive distributions -- has
significantly improved since their inception. This improvement can be
attributed to two principal factors: (1) advancements in the architecture of
permutation invariant set functions, which are intrinsic to all NPs; and (2)
leveraging symmetries present in the true posterior predictive map, which are
problem dependent. Transformers are a notable development in permutation
invariant set functions, and their utility within NPs has been demonstrated
through the family of models we refer to as TNPs. Despite significant interest
in TNPs, little attention has been given to incorporating symmetries. Notably,
the posterior prediction maps for data that are stationary -- a common
assumption in spatio-temporal modelling -- exhibit translation equivariance. In
this paper, we introduce of a new family of translation equivariant TNPs that
incorporate translation equivariance. Through an extensive range of experiments
on synthetic and real-world spatio-temporal data, we demonstrate the
effectiveness of TE-TNPs relative to their non-translation-equivariant
counterparts and other NP baselines.

本文介绍了一种新的具有平移等变性的神经过程（TNPs）家族，通过对合成和真实世界的时空数据进行广泛的实验，相对于非平移等变性对照组和其他 NP 基线，我们证明了 TE-TNPs 的有效性。

等变变换神经网络过程的翻译

Translation Equivariant Transformer Neural Processes

Siamese trackers turn tracking into similarity estimation between a template
and the candidate regions in the frame. Mathematically, one of the key
ingredients of success of the similarity function is translation equivariance.
Non-translation-equivariant architectures induce a positional bias during
training, so the location of the target will be hard to recover from the
feature space. In real life scenarios, objects undergoe various transformations
other than translation, such as rotation or scaling. Unless the model has an
internal mechanism to handle them, the similarity may degrade. In this paper,
we focus on scaling and we aim to equip the Siamese network with additional
built-in scale equivariance to capture the natural variations of the target a
priori. We develop the theory for scale-equivariant Siamese trackers, and
provide a simple recipe for how to make a wide range of existing trackers
scale-equivariant. We present SE-SiamFC, a scale-equivariant variant of SiamFC
built according to the recipe. We conduct experiments on OTB and VOT benchmarks
and on the synthetically generated T-MNIST and S-MNIST datasets. We demonstrate
that a built-in additional scale equivariance is useful for visual object
tracking.

本文旨在向 Siamese 网络中加入内置比例等变性，以捕捉目标的自然变化，提出可缩放等变性 Siamese 跟踪器（SE-SiamFC），并通过实验证明其在视觉对象跟踪中的有效性。

尺度等变性改进孪生跟踪

Scale Equivariance Improves Siamese Tracking

We introduce the Convolutional Conditional Neural Process (ConvCNP), a new
member of the Neural Process family that models translation equivariance in the
data. Translation equivariance is an important inductive bias for many learning
problems including time series modelling, spatial data, and images. The model
embeds data sets into an infinite-dimensional function space as opposed to a
finite-dimensional vector space. To formalize this notion, we extend the theory
of neural representations of sets to include functional representations, and
demonstrate that any translation-equivariant embedding can be represented using
a convolutional deep set. We evaluate ConvCNPs in several settings,
demonstrating that they achieve state-of-the-art performance compared to
existing NPs. We demonstrate that building in translation equivariance enables
zero-shot generalization to challenging, out-of-domain tasks.

本研究介绍了卷积条件神经过程 (ConvCNP)，它是神经过程家族中的新成员，能够建模数据中的平移等变性。研究表明，加入平移等变性的建模有助于更好地处理时间序列、空间数据和图像，而且卷积深度集能够实现任何平移等变嵌入。研究还证明，ConvCNP 在多个设置中取得了良好的性能，并且能够在挑战性的任务中实现零样本泛化。