# Isotropic sequence order learning

## Bernd Porr and Florentin Wörgötter

## Neural Comp., 15, 831-864.

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In this article we present an isotropic, unsupervised algorithm for
temporal sequence learning. No special reward signal is used such that
all inputs are completely isotropic. All input signals are bandpass
filtered before converging onto a linear output neuron. All synaptic
weights change according to the correlation of bandpass-filtered
inputs with the derivative of the output. We investigate the algorithm
in an open- and a closed-loop condition, the latter being defined by
embedding the learning system into a behavioural feedback loop. In the
open-loop condition we find that the linear structure of the algorithm
allows analytically calculating the shape of the weight change which
is strictly hetero-synaptic and follows the shape of the weight change
curves found in spike-time dependent plasticity. Furthermore, we show
that synaptic weights stabilise automatically when no more temporal di
erences exist between the inputs without additional normalising
measures. In the second part of this study, the algorithm is is placed
into an environment which leads to closed sensor-motor loop. To this
end a robot is programmed with a pre-wired retraction reflex reaction
in response to collisions. Through ISO-learning the robot achieves
collisions avoidance by learning the correlation between his early
range-finder signals and the later occuring collision signal. Synaptic
weights stabilise at the end of learning as theoretically
predicted. Finally we discuss the relation of ISO-learning with other
drive reinforcement models and with the commonly used temporal di
erence (TD-) learning algorithm. This study is followed up by a
mathematical analysis of the closed-loop situation in the accompanying
article.