Emergent Dynamical Properties of the BCM Learning Rule
By Lawrence C. Udeigwe, Paul W. Munro, G. Bard Ermentrout. 2017
21 citations recorded by the source corpus.
The Bienenstock–Cooper–Munro (BCM) learning rule provides a simple setup for synaptic modification that combines a Hebbian product rule with a homeostatic mechanism that keeps the weights bounded. The homeostatic part of the learning rule depends on the time average of the post-synaptic activity and provides a sliding threshold that distinguishes between increasing or decreasing weights. There are, thus, two essential time scales in the BCM rule: a homeostatic time scale, and a synaptic modification time scale. When the dynamics of the stimulus is rapid enough, it is possible to reduce the BCM rule to a simple averaged set of differential equations. In previous analyses of this model, the time scale of the sliding threshold is usually faster than that of the synaptic modification. In this paper, we study the dynamical properties of these averaged equations when the homeostatic time scale is close to the synaptic modification time scale. We show that instabilities arise leading to oscillations and in some cases chaos and other complex dynamics. We consider three cases: one neuron with two weights and two stimuli, one neuron with two weights and three stimuli, and finally a weakly interacting network of neurons.
Subfields: Artificial Intelligence, Cognitive Neuroscience
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In Artificial Intelligence
- Friedemann Zenke
- Surya Ganguli
- Wulfram Gerstner
- Rahaf Aljundi
- Yoshua Bengio
- Greg Yang
- Sam Schoenholz
- Tinne Tuytelaars
In Cognitive Neuroscience
- Friedemann Zenke
- Surya Ganguli
- Wulfram Gerstner
- Pierre Yger
- Andrea Soltoggio
- Claudia Clopath
- Matthieu Gilson
- Nicolas Frémaux
Citations in the corpus
- The temporal paradox of Hebbian learning and homeostatic plasticity (2017, background): “Such oscillations and run-away are demonstrated in Figure 3 for several compensatory mechanisms with feedback timescales that are chosen to be too slow, including the Bienenstock–Cooper–Munro (BCM) rule [6 ,52], and triplet spike-timing-dependent plasticity (STDP) [36] with either synaptic scaling [”