A Learning Rule for Extracting Spatio-temporal Invariances

The inputs to photoreceptors tend to change rapidly over time, whereas physical parameters (e.g. surface depth) underlying these changes vary more slowly. Accordingly, if a neuron codes for a physical parameter then its output should also change slowly, despite its rapidly uctuating inputs. We demonstrate that a model neuron which adapts to make its output vary smoothly over time can learn to extract invariances implicit in its input. This learning consists of a linear combination of Hebbian and anti-Hebbian synaptic changes, operating simultaneously upon the same connection weights but at diierent time scales. This is shown to be suucient for the unsupervised learning of simple spatio-temporal invariances. We present a learning rule, based upon temporal correlations, that allows a single model neuron to extract important information from its input concerning temporal parameters (i.e. invariances). Primary sensory areas such as striate cortex tend to use a place-coding of input features (such as edge-orientation) in which the identity of the neuron responding may be more important than its response magnitude. Such a coding demands many neurons. We show that a smaller number of neurons, adapting in accord with the learning rule we deene, could alter their synaptic connections to transmit the same amount of information. This is achieved by use of a frequency-coding in which response magnitude has high information content. Many Hebbian-learning models exploit spatial correlations in their inputs, whereas only a few exploit temporal correlations 1, 2, 3]. These temporal models update synaptic strengths between neurons according to exponentially weighted time-averages of post-synaptic (or pre-synaptic) activity over the recent past. Using these exponential traces with Hebbian synaptic modiication allows each neuron to make strong connections to others with which it is temporally correlated. Essentially, these invariance-seeking model neurons simply compute a logical OR on a subset of their inputs. For example, a neuron that learns to be selective for edge-orientation, whilst invariant to edge-position, forms uniformly strong connections to the subset of all input neurons having the appropriate orientation selectivity, regardless of spatial position, because activity within this subset is temporally correlated. These models are limited because they require an output neuron to represent each subset of input neurons. If there are input neurons responsive to n ranges of orientation, there must be n output neurons to maintain orientation discrimination; the result is a place-code for orientation in which the output-value of the responding neuron carries only a small amount …