Spike timing-dependent plasticity:Rules and use of synaptic adaptation

Rudy GuyonneauRufin van Rullen

and Simon J. Thorpe

R étroaction lors de l‘I ntégration V isuelle: vers une A rchitecture GE nérique

• What is STDP anyway? - Biological evidence - Theoretical studies- Synthesis

• Learning with STDP and asynchronously spiking neurons- The « controlled » learning paradigm (theory and biologically plausible

implications)- The « autonomous » learning paradigm (growing filters and connectivity design)

Overview

I. Biological evidence of synaptic adaptation

« When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency as one of the cell firing B, is increased » [Hebb, 1949]

Which fires together wires together

(taken from Markram 1997)(taken from Bi & Poo 1998)

I. Experimental to functional

(taken from Abbott & Nelson, NatureN, 2000)

STDP… … regulatory mechanism for rate and variability of post-synaptic firing … coincidence detector … introduces competition between synapses to control the firing rate (correlation factor) … suppresses strong recurrent excitatory loops

« In general, STDP greatly expands the capability of Hebbian learning to address temporally sensitive computational tasks. »

I. Modelling stuff

STDP can act as a learning mechanism for generating neuronal responses selective to input timing, order and sequence.

sequence learning and prediction [Abbott & Blum, 96]spatial path learning in navigation [Blum & Abbott, 96; Mehta, Neuron, 00]direction selectivity in visual responses [Mehta, Neuron, 00]

STDP also as « temporal difference learning » [Rao & Sejnowski, NeuralComp, 01]

(Taken from Song et al., NatureN, 2000)

(Taken from Gerstner & Kistler, BioCyb, 2002)

I. Spike timing-dependent plasticity

So what have we got?

The neuron’s activity, its spikes history, gives rise to modifications of the efficacy of its excitatory

synapsesthat in turn affects its own spiking behaviour.

That means we have synaptic adaptation in the autopoeitic sense.

The retina provides evidence for highly reproducible firing events...[Berry et al., 97]

... And individual spikes with high temporal precision have been reported throughout the ventral stream.

[from the retina (Sestokas, 91) to IT (Nakamura, 98); MT (Bair and Koch, 96)]

Importantly, the latency of the first spike in the spike train is the most reliable.[Mainen & Sejnowski, 95]

stimulus-locked spike timings are temporally (quite) precise!

Spikes reproducibility

What does that mean when we consider STDP in the context of reproducible spike trains?

II. What happens when a neuron repeatedly receives the same stimulus?

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Spike time

OUTPUT

1/3 + 1/3 + 1/3 = 1 t3

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Step 1 Spike time

STDP

Synapses get modified at t3

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Step 1 Spike time

OUTPUT

1/3 + 2/3 = 1 t2

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Spike timeStep 2

STDP

Synapses get modified at t2

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Step 2 Spike time

OUTPUT

2/3 + 3/3 = 5/3 t2

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Spike timeStep 3

STDP

Synapses get modified at t2

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Step 3 Spike time

OUTPUT

3/3 = 1 t1

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Spike timeStep 4

STDP

Synapses get modified at t1

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Step 4 Spike time

OUTPUT

3/3 = 1 t1

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Spike timeStep 5

STDP

Synapses get modified at t1

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Step 5 Spike time

OUTPUT

3/3 = 1 t1

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Spike timeStep 6

STDP

Synapses get modified at t1

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Step 6 Spike time

OUTPUT

3/3 = 1 t1

1/3

3/3

2/3

0/3t0 t1 t2 t3

Wei

gh

t

INPUT

Spike timeStep 7

Step na wave of spikes elicits a post-synaptic response and triggers STDP-like learning rule synapses carrying spikes just preceding the post-synaptic one are potentiated.

Step n+1Re-propagating the input spike-wave, the latency of the post-synaptic spike is slightly decreased. synapses carrying even earlier spikes are potentiated and later ones depressed.

ReiterateBy iterating the processus on and on from an(y) initial state allowing a post-synaptic response, it follows that the earliest synapses get maximally potentiated and later ones are depressed.

Main assumption Reproducibility of the spike wave (saccades, oscillations).

II. Results

Stimulus is composed of … 20Hz reproducible spike trains (Poisson process) by 1000 input neurons… to which a 5ms jitter is added5Hz spontaneous activity

Typical input spike trains Dynamics of the simulation

II. Latency versus…

… firing rate(Gerstner, 97)

no spontaneous activity – 5ms jitter

… synchronicity(Abeles)

5 Hz spontaneous activity - no jitter

II. Selectivity

50000 distractor spike-trains

II. Neuron population case

Retina to V1 (preliminary results)

V1 to V2? (preliminary results)

« Autonomous learning »

Given the reliability and form of retinal input,what happens when a reductive, simili, but still biologically plausible, visual system « experiments » a simili natural world?

Extension

It may be possible that through STDP, areas build their selectivities from correlated afferents.

The end.

General conclusions• STDP is accountable for adaptation at the cellular level.• Definition of a learning paradigm for asynchronously spiking neuron networks.• Connectivity…

(taken from Felleman & vanEssen, 91) (taken from vanRullen & Thorpe, 02)