Emergent Intelligence via Synaptic Tuning Keith L. Downing The - - PowerPoint PPT Presentation

Emergent Intelligence via Synaptic Tuning

Keith L. Downing

The Norwegian University of Science and Technology (NTNU) Trondheim, Norway keithd@idi.ntnu.no

January 19, 2015

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Donald Hebb (1949)

Hebb Rule: Fire Together, Wire Together

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 cells firing B, is increased. △wi,j = λuiv

u1 u2 un v w2 wn w1

pre-synaptic neurons post-synaptic neuron

? ∆w

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Hebbian Learning Rules

General Hebbian: Basic Homosynaptic △wi = λuiv △wi = λ(v −θv)ui Basic Heterosynaptic BCM △wi = λv(ui −θi) △wi = λuiv(v −θv)

Homosynaptic All active synapses are modified the same way, depending only on the strength of the postsynaptic activity. Heterosynaptic Active synapses can be modified differently, depending upon the strength of their presynaptic activity.

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Controlling Hebbian-Learning Weight-Vector Instability

Positive Feedback ⇒ Weight Explosions High post-synaptic firing ⇒ wij ⇑ ⇒ Higher firing ⇒ wij ⇑ ... All activation-function outputs in [0, 1] ⇒ Major trouble! Outputs in [-1, 1] ⇒ Still trouble! Thresholding (e.g. in homosynaptic, heterosynaptic and BCM rules) ⇒ Still trouble! Solutions BCM + dynamic θv: effective, but expensive. Weight normalization: effective, but expensive. Oja rule: △wi = λv(ui −v | wi |) = uiv −v2 | wi |

Forgetting term implicitly controls weight explosion Emergent weight normalization! Achieves Principle Component Analysis (PCA)

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Hebbian Learning with Spiking Neurons

Now learning depends upon the individual spike times of neurons, not their average rate of spike production.

A B C

0.8 0.5 0.4

A B C

Time

Rate Coding Spike Coding Keith L. Downing Emergent Intelligence via Synaptic Tuning

Spike-Timing Dependent Plasticity (STDP)

t s

• 40 ms

40 ms 0.4

• 0.4

Change in synaptic strength (△s) as function of △t = tpre −tpost, the times of the most recent pre- and post-synaptic spikes. The maximum magnitude of change is roughly 0.4% of the maximum possible synaptic strength/conductance.

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Who’s First?

Neuron A Neuron C

50 ms 0 ms

W X Y U V Z

Pairing spikes for STDP calculations is not so easy. A common solution: consider all pairs. Is there a simpler mechanism?

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Song and Abbott, 2000

a b c

Pa

decay

Pb

decay

M

decay

c Fires a Fires b Fires wa wb

wa <= wa - kM wb <= wb - kM wa <= wa + kPa wb <= wb + kPb m+ m+ m- m- > m+

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Emergence in the Song-Abbott Model

m− > m+ insures that random activity produces overall LTD, not LTP . No need to compare spikes across time or space. Memory variables accumulate the key information. Weight normalization - total weight doesn’t get too high or low. Cooperation and Competition: presynaptic neurons that happen to spike simultaneously (cooperate) can

• ut-compete others for control of the post-synaptic neuron.

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Emergent Presynaptic Control

X A C D E F B

T T T T

Small group (C,D) drives neuron X. But A,B,E and F fire close enough to X to get LTP .

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Seizing Control

X A C D E F B

T T T T

LTP LTP

Fires Earlier X A C D E F B

T T T T

LTD

After LTP , the large group can fire X on its own. So X fires earlier, and it fires before C and D, so their efferents have LTD. Now the larger group controls X.

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Prediction: A Key Brain Function

Observer

Time Keith L. Downing Emergent Intelligence via Synaptic Tuning

Predictions via Synaptic Tuning

N Prediction Sensory Input Dendrites Soma LTD LTP P S S+P

Stimulation Intensity Synaptic Strength Change

Predictions (i.e. high activity of predictive neuron) that coincide with sensory input → LTP . Predictions unmatched by N activity → LTD. Many spikes from predictive neuron go unanswered in N → depression in Song-Abbott model also. After LTP , predictions alone can activate N. (Right) Results from Artola et. al. (1990)

Keith L. Downing Emergent Intelligence via Synaptic Tuning

General Declarative Predictive Network (GDPN)

A C B X W Y Z Stimulus A Stimulus C Stimulus B T1 T2 T3 T4

S1 S2 Predictors Detectors

Downing(2009). Based on networks in thalamus, cortex and hippocampus.

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Phase Precession in Hippocampus

Place Cell Firing Rate Space P* Time T*

P*

Prediction: Place cell fires before arriving at the location that it represents. Burgess(2003).

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Emerging Phase Precession via LTP and LTD

X A C D E F B CA1 CA3 Time T* A F X A C D E F B CA1 CA3 STDP

Mehta(2001).

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Learning a Sequence

A B C D E F G

A C D E F B G CA3 Place Cells

• Random recurrence (2-5%)
• No topology

STDP can produce these connections 50 ms STDP Window Keith L. Downing Emergent Intelligence via Synaptic Tuning

Clusters and Concepts

Theta Wave (6-10 Hz) A G E F D B C 50 ms STDP Window C D E F G H I G E F Gamma Waves (40-100 Hz) ride atop the theta waves, with each gamma peak stimulating the next place cell in the sequence. Sensory Input A B C Look- ahead A C D E F B G

Chunking

Gamma waves and LTP compress sequences into clusters ≈ concepts.

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Remapping Context Detectors

C2 C1

B D

Weakened before T3 Enhanced at T3 Enhanced at T1 Enhanced at T2 Weak at T1 C2

C1 B D

Contexts B and D both predict the same concept, but via different neurons: C1 and C2. Assume context D occurs much less than B, then many of the D → C2 links can weaken. When D does fire, it’s shared context with B (pentagons) can lead C1 to fire, but not C2. So D → C1 links strengthen. Eventually, both B and D trigger C1. C2 has been remapped to C1.

Keith L. Downing Emergent Intelligence via Synaptic Tuning

Navigation, Remapping and Emerging Concepts

A B C D E F G

T1 T2 C1 D B C2

T1 T2

C B D C1 = C2 After arena exploration and re-mapping Neuron C may or may not be neuron C1 or C2

C B D

Corridor Arena T1 T2

Keith L. Downing Emergent Intelligence via Synaptic Tuning