Collaborator: Henning Sprekeler, Christian Michaelis

Slow Feature Analysis (SFA) is an abstract algorithm based on slowness as a learning principle. The objective is to minimize the variance of the time derivative of the normalized output signals. It has proven a powerful tool for modeling the unsupervised learning of complex cell receptive fields, visual invariances, and place cells in the hippocampus. However, the algorithm is far from being physiologically plausible, because it is based on a generalized eigenvalue problem on a covariance and a time-derivative covariance matrix. In this project we have investigated whether SFA can be implemented with spiking model neurons.

The first conceptual step in this direction is to realize that for continuous signals instead of minimizing the time derivative one can also maximize the variance of the low-pass-filtered normalized output-signal, which can be done with a modified Hebbian learning rule. If one uses a low-pass filter with a power spectrum of an upside-down parabola, the results are identical, see  Figure 1.derivative vs. low-pass filter (11  kB)Figure 1: Minimizing the variance of the time-derivative is equivalent to maximizing the variance of the low-pass filtered signal. 

The next step is to translate the modified Hebbian learning rule into an STDP learning rule for spiking Poisson units. Interestingly, the resulting learning window reproduces the kind of learning windows measured experimentally, see Figure 2.comparison between theoretical  and experimental STDP learning window (8 kB)Figure 2: Comparison between theoretical (solid line) and experimental (points) STDP learning window. Data taken from [Bi & Poo, 1998].

Furthermore, it turns out that it is not the learning window per se that is of functional relevance but the learning window convolved with the EPSP. According to our theory the asymmetric shape of the standard STDP learning window might have nothing to do with causality issues but with the fact that the asymmetric low-pass filtering effect of the EPSP has to be compensated. The functionally relevant learning window might actually symmetric. Thus, our analysis offers a completely novel interpretation for the asymmetric
shape of the standard STDP learning window.

The Institut für Neuroinformatik (INI) is a central research unit of the Ruhr-Universität Bochum. We aim to understand the fundamental principles through which organisms generate behavior and cognition while linked to their environments through sensory systems and while acting in those environments through effector systems. Inspired by our insights into such natural cognitive systems, we seek new solutions to problems of information processing in artificial cognitive systems. We draw from a variety of disciplines that include experimental approaches from psychology and neurophysiology as well as theoretical approaches from physics, mathematics, electrical engineering and applied computer science, in particular machine learning, artificial intelligence, and computer vision.

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