by spectra-temporal receptive fields that can be well modelled by Gaussian derivates over logarithmic frequencies and windowed Fourier transforms over time with the window functions being temporal scale-space kernels. Deep learning and scale space In the area of classical computer vision, scale-space theory has established itself as a theoretical framework for early vision, with Gaussian derivatives constituting a canonical model for the first layer of receptive fields. With the introduction of deep learning, there has also been work on also using Gaussian derivatives or Gaussian kernels as a general basis for receptive fields in deep networks. Using the transformation properties of the Gaussian derivatives and Gaussian kernels under scaling transformations, it is in this way possible to obtain scale covariance/equivariance and scale invariance of the deep network to handle image structures at different scales in a theoretically well-founded manner. There have also been approaches developed to obtain scale covariance/equivariance and scale invariance by learned filters combined with multiple scale channels. Specifically, using the notions of scale covariance/equivariance and scale invariance, it is possible to make deep networks operate robustly at scales not spanned by the training data, thus enabling scale generalization. Time-causal temporal scale space For processing pre-recorded temporal signals or video, the Gaussian kernel can also be used for smoothing and suppressing fine-scale structures over the temporal domain, since the data are pre-recorded and available in all directions. When processing temporal signals or video in real-time situations, the Gaussian kernel cannot, however, be used for temporal smoothing, since it would access data from the future, which obviously cannot be available. For temporal smoothing in real-time situations, one can instead use the temporal kernel referred to as the time-causal limit kernel, which possesses similar properties in a time-causal situation (non-creation of new structures towards increasing scale and temporal scale covariance) as the Gaussian kernel obeys in the non-causal case. The time-causal limit kernel corresponds to convolution with an infinite number of truncated exponential kernels coupled in cascade, with specifically chosen time constants to obtain temporal scale covariance. For discrete data, this kernel can often be numerically well approximated by a small set of first-order recursive filters coupled in cascade, see for further details. For an earlier approach to handling temporal scales in a time-causal way, by performing Gaussian smoothing over a logarithmically transformed temporal axis, however, not having any known memory-efficient time-recursive implementation as the time-causal limit kernel has, see,