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Logarithmic distributions prove that intrinsic learning is Hebbian
In this paper, we present data for the lognormal distributions of spike
rates, synaptic weights and intrinsic excitability (gain) for neurons in
various brain areas, such as auditory or visual cortex, hippocampus,
cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of
heavy-tailed, specifically lognormal, distributions for rates, weights and
gains in all brain areas examined. The difference between strongly recurrent
and feed-forward connectivity (cortex vs. striatum and cerebellum),
neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of
activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns
out to be irrelevant for this feature. Logarithmic scale distribution of
weights and gains appears to be a general, functional property in all cases
analyzed. We then created a generic neural model to investigate adaptive
learning rules that create and maintain lognormal distributions. We
conclusively demonstrate that not only weights, but also intrinsic gains, need
to have strong Hebbian learning in order to produce and maintain the
experimentally attested distributions. This provides a solution to the
long-standing question about the type of plasticity exhibited by intrinsic
excitability
Slowness: An Objective for Spike-Timing-Dependent Plasticity?
Slow Feature Analysis (SFA) is an efficient algorithm for
learning input-output functions that extract the most slowly varying features from a quickly varying signal. It
has been successfully applied to the unsupervised learning
of translation-, rotation-, and other invariances in a
model of the visual system, to the learning of complex cell
receptive fields, and, combined with a sparseness
objective, to the self-organized formation of place cells
in a model of the hippocampus.
In order to arrive at a biologically more plausible implementation of this learning rule, we consider analytically how SFA could be realized in simple linear continuous and spiking model neurons. It turns out that for the continuous model neuron SFA can be implemented by means of a modified version of standard Hebbian learning. In this framework we provide a connection to the trace learning rule for invariance learning. We then show that for Poisson neurons spike-timing-dependent plasticity (STDP) with a specific learning window can learn the same weight distribution as SFA. Surprisingly, we find that the appropriate learning rule reproduces the typical STDP learning window. The shape as well as the timescale are in good agreement with what has been measured experimentally. This offers a completely novel interpretation for the functional role of spike-timing-dependent plasticity in physiological neurons
Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of neoHebbian Three-Factor Learning Rules
Most elementary behaviors such as moving the arm to grasp an object or
walking into the next room to explore a museum evolve on the time scale of
seconds; in contrast, neuronal action potentials occur on the time scale of a
few milliseconds. Learning rules of the brain must therefore bridge the gap
between these two different time scales.
Modern theories of synaptic plasticity have postulated that the co-activation
of pre- and postsynaptic neurons sets a flag at the synapse, called an
eligibility trace, that leads to a weight change only if an additional factor
is present while the flag is set. This third factor, signaling reward,
punishment, surprise, or novelty, could be implemented by the phasic activity
of neuromodulators or specific neuronal inputs signaling special events. While
the theoretical framework has been developed over the last decades,
experimental evidence in support of eligibility traces on the time scale of
seconds has been collected only during the last few years.
Here we review, in the context of three-factor rules of synaptic plasticity,
four key experiments that support the role of synaptic eligibility traces in
combination with a third factor as a biological implementation of neoHebbian
three-factor learning rules
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