Department of Electrical Engineering, Columbia University, New York, NY, USA.
Neural Netw. 2013 Aug;44:22-35. doi: 10.1016/j.neunet.2013.02.013. Epub 2013 Mar 14.
We investigate neural architectures for identity preserving transformations (IPTs) on visual stimuli in the spike domain. The stimuli are encoded with a population of spiking neurons; the resulting spikes are processed and finally decoded. A number of IPTs are demonstrated including faithful stimulus recovery, as well as simple transformations on the original visual stimulus such as translations, rotations and zoomings. We show that if the set of receptive fields satisfies certain symmetry properties, then IPTs can easily be realized and additionally, the same basic stimulus decoding algorithm can be employed to recover the transformed input stimulus. Using group theoretic methods we advance two different neural encoding architectures and discuss the realization of exact and approximate IPTs. These are realized in the spike domain processing block by a "switching matrix" that regulates the input/output connectivity between the stimulus encoding and decoding blocks. For example, for a particular connectivity setting of the switching matrix, the original stimulus is faithfully recovered. For other settings, translations, rotations and dilations (or combinations of these operations) of the original video stream are obtained. We evaluate our theoretical derivations through extensive simulations on natural video scenes, and discuss implications of our results on the problem of invariant object recognition in the spike domain.
我们研究了在尖峰域中对视觉刺激进行身份保留变换（IPT）的神经结构。刺激由一群尖峰神经元进行编码；产生的尖峰被处理，最终被解码。演示了许多 IPT，包括忠实的刺激恢复，以及对原始视觉刺激的简单变换，如平移、旋转和缩放。我们表明，如果感受野集满足某些对称性质，那么 IPT 可以很容易地实现，并且可以使用相同的基本刺激解码算法来恢复变换后的输入刺激。使用群论方法，我们提出了两种不同的神经编码架构，并讨论了精确和近似 IPT 的实现。这些在尖峰域处理块中通过“开关矩阵”来实现，该矩阵调节刺激编码和解码块之间的输入/输出连接。例如，对于开关矩阵的特定连接设置，可以忠实恢复原始刺激。对于其他设置，则可以获得原始视频流的平移、旋转和拉伸（或这些操作的组合）。我们通过对自然视频场景的广泛模拟来评估我们的理论推导，并讨论我们的结果对尖峰域中不变目标识别问题的影响。
