Slowness: An Objective for Spike-Timing–Dependent Plasticity?

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Abstract
Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this “temporal stability” or “slowness” approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing–dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the “trace rule.” The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons. Neurons interact by exchanging information via small connection sites, so-called synapses. Interestingly, the efficiency of synapses in transmitting neuronal signals is not static, but changes dynamically depending on the signals that the associated neurons emit. As neurons receive thousands of synaptic input signals, they can thus “choose” the input signals they are interested in by adjusting their synapses accordingly. This adaptation mechanism, known as synaptic plasticity, has long been hypothesized to form the neuronal correlate of learning. It raises a difficult question: what aspects of the input signals are the neurons interested in, given that the adaptation of the synapses follows a certain mechanistic rule? We address this question for spike-timing–dependent plasticity, a type of synaptic plasticity that has raised a lot of interest in the last decade. We show that under certain assumptions regarding neuronal information transmission, spike-timing–dependent plasticity focuses on aspects of the input signals that vary slowly in time. This relates spike-timing–dependent plasticity to a class of abstract learning rules that were previously proposed as a means of learning to recognize objects in spite of contextual changes such as size or position. Based on this link, we propose a novel functional interpretation of spike-timing–dependent plasticity.