Evolutionary Path to Biological Kernel Machines Magnus Jändel Swedish Defence Research Agency

Summary It is comparatively easy for organisms to implement support vector machines. Biological support vector machines provide efficient and cost- effective pattern recognition with one-shot learning [1]. The support vector machine hypothesis is consistent with the architecture of the olfactory system [1]. Bursts in the thalamocortical system may be related to support vector machine pattern recognition [2]. An efficient implementation reuses machinery for learning action sequences [3]. 1) Jändel, M.: A neural support vector machine. Neural Networks 23, (2010). 2) Jändel, M.: Thalamic bursts mediate pattern recognition. Proceedings of the 4th International IEEE EMBS Conference on Neural Engineering 562–565 (2009). 3) Jändel, M.: Pattern recognition as an internalized motor programme. To appear in proc. of ICNN Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Outline Support vector machine definition Evolutionary path to a neural SVM Conclusions and olfactory model Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Support vector machine definition

Maximum margin linear classification Consider binary classification with m training examples: Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Transform to high-dimensional feature space Zero-bias SVM: Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Zero-bias -SVM Maximize: Subject to: and where Solve by iterative gradient ascent in the  -space hyperplane where The margin of the i:th example in feature space! Classification function: Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Evolutionary Path

Stage 1 SSPR Sensor system Simple hard-wired pattern recognizer Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Stage 2 Sensor system Simple hard-wired pattern recognizer SSPR x SM Sensory Memory Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Stage 3 Sensor system Simple hard-wired pattern recognizer SSPR x SM Sensory Memory AM Associative memory Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Stage 4 SSPR x SM AM x y´y´ - Significant patterns and the associated valence are stored in the AM. - Sufficiently similar inputs make the AM recall the valence of a stored pattern. Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010 Zero-bias -SVM

Stage 5 SSPR x SM AM x x´, y´ - Significant patterns and the associated valence are stored in the AM. - Sufficiently similar inputs make the AM recall the valence of a stored pattern - The PR modulates the recalled valence y´ with a similarity measure comparing input x with the stored pattern x´ according to, Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Stage 6 SSPR x SM OM x x i, y i - The OM oscillates between memory states - The PR computes a weighted average over the valences of all stored examples, Stage 6 implements the classification function of a zero-bias SVM. Zero-bias -SVM Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Oscillating Associative Memory Hopfield associative memory N neurons with binary output z i Update rule Imprint m memory patterns x (k) One-shot learning! OM Model m memory patterns The probability of finding the OM in state i is, Each oscillation selects the next state with uniform probability. The average endurance time of state i is T i. Oscillating memory - Firing cell nuclei are exhausted - Active synapses are depleted Modes with perpetual oscillation between attractors. Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Stage 7 SSPR xjxj SM OM xjxj x i, y i - Learning feedback Bij tunes memory weights - Real-world experiments are required B ij x i is the present example presented by the OM x j is the sensory input y j is the valence of x j as learnt from hard-earned experience feedback For each OM oscillation apply the learning rules, and Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Stage 8 SSPR xjxj SM OM xjxj x i, y i - OM patterns are set up in sensory memory while sleeping - OM weights tuned in virtual experiments - No need for external feedback - Implements a zero-bias -SVM B ij xixi Zero-bias -SVM Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Learning SVM weights For each OM oscillation apply the learning rules, and where Averaging over “trapped examples” with probability distribution SSPR xjxj SM OM xjxj x i, y i B ij xixi gives where Zero-bias -SVM Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Conclusions and olfactory model

Summary of support vector machine implementation Classification process SSPR xjxj SM OM xjxj x i, y i B ij xixi x Learning new training examples Learning weights of training examples Zero-bias -SVM Research program Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Trap CL OM OB AOC APC HOBS PPC D1 M2 D3 D5 M1 D2 M3 D4 Olfactory model APC – Anterior piriform cortex PPC – Posterior piriform cortex AOC – Anterior olfactory cortex OB – Olfactory bulb HOBS – Higher-order brain systems Magnus Jändel, Brain Inspired Cognitive Systems, 15 July 2010

Questions?