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. △ w i , j = λ u i v ? ∆ w u1 w1 w2 u2 v post-synaptic neuron wn un pre-synaptic neurons Keith L. Downing Emergent Intelligence via Synaptic Tuning
Hebbian Learning Rules General Hebbian: Basic Homosynaptic △ w i = λ u i v △ w i = λ ( v − θ v ) u i Basic Heterosynaptic BCM △ w i = λ v ( u i − θ i ) △ w i = λ u i v ( v − θ v ) 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 ⇒ w ij ⇑ ⇒ Higher firing ⇒ w ij ⇑ ... 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 θ v : effective, but expensive. Weight normalization: effective, but expensive. Oja rule: △ w i = λ v ( u i − v | w i | ) = u i v − v 2 | w i | 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. 0.8 A 0.4 C 0.5 Rate Coding B A C Spike B Coding Time Keith L. Downing Emergent Intelligence via Synaptic Tuning
Spike-Timing Dependent Plasticity (STDP) s 0.4 t 0 0 40 ms -40 ms -0.4 Change in synaptic strength ( △ s ) as function of △ t = t pre − t post , 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? U W V Neuron A X Y Z Neuron C 0 ms 50 ms 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 wa <= wa - kM wb <= wb - kM a b b a Fires Fires m+ m+ wa wb decay decay Pb Pa c m- > m+ m- wa <= wa + kPa c decay wb <= wb + kPb Fires 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 out-compete others for control of the post-synaptic neuron. Keith L. Downing Emergent Intelligence via Synaptic Tuning
Emergent Presynaptic Control T T T T A B C D E F X 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 T T T T T T T T A B C D E F A B C D E F LTP LTP LTD Fires Earlier X X 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 Prediction LTP S+P Synaptic Strength S Change Dendrites 0 LTD P Soma N Sensory Input Stimulation Intensity 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) Predictors Z Y W S1 X T3 S2 T2 Detectors A C B T4 T1 Stimulus Stimulus Stimulus A C B Downing(2009). Based on networks in thalamus, cortex and hippocampus. Keith L. Downing Emergent Intelligence via Synaptic Tuning
Phase Precession in Hippocampus P* T* Time Place Cell Firing Rate P* Space 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 Time A B C D E F CA3 F A X CA1 T* STDP A B C D E F CA3 CA1 X Mehta(2001). Keith L. Downing Emergent Intelligence via Synaptic Tuning
Learning a Sequence A B C D E F G 50 ms STDP Window CA3 E Place Cells B F - Random recurrence (2-5%) - No topology D STDP can G produce these connections A C Keith L. Downing Emergent Intelligence via Synaptic Tuning
Clusters and Concepts Sensory Theta Wave (6-10 Hz) Input C A I E G D H B Look- F F ahead E G C E B E G F F D D 50 ms A G STDP Window Gamma Waves (40-100 Hz) ride A B atop the theta waves, with each gamma peak stimulating the C C Chunking next place cell in the sequence. Gamma waves and LTP compress sequences into clusters ≈ concepts. Keith L. Downing Emergent Intelligence via Synaptic Tuning
Remapping Context Detectors C1 C1 Enhanced at T1 Weak at T1 Enhanced at T2 C2 C2 Weakened before T3 Enhanced at T3 B B D D Contexts B and D both predict the same concept , but via different neurons: C 1 and C 2 . Assume context D occurs much less than B, then many of the D → C 2 links can weaken. When D does fire, it’s shared context with B (pentagons) can lead C 1 to fire, but not C 2 . So D → C 1 links strengthen. Eventually, both B and D trigger C 1 . C 2 has been remapped to C 1 . Keith L. Downing Emergent Intelligence via Synaptic Tuning
Navigation, Remapping and Emerging Concepts A B C D E F G T1 Corridor T2 T2 T1 Arena B C1 C2 T1 C1 = C2 C T2 D B D C After arena exploration and re-mapping B D Neuron C may or may not be neuron C1 or C2 Keith L. Downing Emergent Intelligence via Synaptic Tuning
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