Biological nervous systems constitute important sources of inspiration
towards computers that are faster, cheaper, and more energy efficient.
Neuromorphic disciplines view the brain as a coevolved system, simultaneously
optimizing the hardware and the algorithms running on it. There are clear
efficiency gains when bringing the computations into a physical substrate, but
we presently lack theories to guide efficient implementations. Here, we present
a principled computational model for neuromorphic systems in terms of
spatio-temporal receptive fields, based on affine Gaussian kernels over space
and leaky-integrator and leaky integrate-and-fire models over time. Our theory
is provably covariant to spatial affine and temporal scaling transformations,
and with close similarities to the visual processing in mammalian brains. We
use these spatio-temporal receptive fields as a prior in an event-based vision
task, and show that this improves the training of spiking networks, which
otherwise is known as problematic for event-based vision. This work combines
efforts within scale-space theory and computational neuroscience to identify
theoretically well-founded ways to process spatio-temporal signals in
neuromorphic systems. Our contributions are immediately relevant for signal
processing and event-based vision, and can be extended to other processing
tasks over space and time, such as memory and control.

生物神经系统是计算机更快、更便宜和更能效的重要灵感源泉。神经形态学学科将大脑视为一个共同进化的系统，同时优化硬件和运行在其上的算法。本文提出了一个基于时空感受野的神经形态系统的有原则的计算模型，通过空间上的仿射高斯核和时间上的漏积分器和漏积分发放模型。我们的理论在空间和时间尺度变换上可证明是协变的，并与哺乳动物大脑的视觉处理有很多相似之处。我们将这些时空感受野作为事件驱动视觉任务中的先验知识，并展示这能够提高脉冲网络的训练效果，在事件驱动视觉中通常被认为是有问题的。本研究结合了尺度空间理论和计算神经科学的努力，寻找在神经形态系统中处理时空信号的理论基础，这对信号处理和事件驱动视觉具有直接的相关性，并且可以扩展到其他空间和时间处理任务，如记忆和控制。

神经形态计算的协变时空感受野

Covariant spatio-temporal receptive fields for neuromorphic computing

The influence of natural image transformations on receptive field responses
is crucial for modelling visual operations in computer vision and biological
vision. In this regard, covariance properties with respect to geometric image
transformations in the earliest layers of the visual hierarchy are essential
for expressing robust image operations and for formulating invariant visual
operations at higher levels. This paper defines and proves a joint covariance
property under compositions of spatial scaling transformations, spatial affine
transformations, Galilean transformations and temporal scaling transformations,
which makes it possible to characterize how different types of image
transformations interact with each other. Specifically, the derived relations
show the receptive field parameters need to be transformed, in order to match
the output from spatio-temporal receptive fields with the underlying
spatio-temporal image transformations.

该论文研究自然图像变换对感受野响应的影响，通过定义和证明一种联合协方差属性，可以表征不同类型的图像变换相互作用的方式，从而使得可以匹配时空接受野与底层时空图像变换的输出。

广义高斯模型下的时空感受野对于几何图像变换的联合协方差特性

Joint covariance property under geometric image transformations for  spatio-temporal receptive fields according to generalized Gaussian model for  receptive fields