* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download lecture 1 () - Stanford Department of Mathematics
Activity-dependent plasticity wikipedia , lookup
Subventricular zone wikipedia , lookup
Neural engineering wikipedia , lookup
Development of the nervous system wikipedia , lookup
Environmental enrichment wikipedia , lookup
History of neuroimaging wikipedia , lookup
Human brain wikipedia , lookup
Neuropsychology wikipedia , lookup
Aging brain wikipedia , lookup
Limbic system wikipedia , lookup
Embodied language processing wikipedia , lookup
Neuroplasticity wikipedia , lookup
Cognitive neuroscience wikipedia , lookup
Artificial general intelligence wikipedia , lookup
Feature detection (nervous system) wikipedia , lookup
Music-related memory wikipedia , lookup
Cognitive neuroscience of music wikipedia , lookup
State-dependent memory wikipedia , lookup
Eyewitness memory (child testimony) wikipedia , lookup
Metastability in the brain wikipedia , lookup
Brain Rules wikipedia , lookup
Anatomy of the cerebellum wikipedia , lookup
Neuropsychopharmacology wikipedia , lookup
Neurophilosophy wikipedia , lookup
Reconstructive memory wikipedia , lookup
Prenatal memory wikipedia , lookup
Muscle memory wikipedia , lookup
Embodied cognitive science wikipedia , lookup
Channelrhodopsin wikipedia , lookup
Neuroanatomy wikipedia , lookup
Lecture 1 MATHEMATICS OF THE BRAIN with an emphasis on the problem of a universal learning computer (ULC) and a universal learning robot (ULR) Victor Eliashberg Consulting professor, Stanford University, Department of Electrical Engineering Slide 0 WHAT DOES IT MEAN TO UNDERSTAND THE BRAIN? 1. User understanding. 2. Repairman understanding. 3. Programmer (educator) understanding. 4. Systems developer understanding. 5. Salesman understanding. Slide 1 TWO MAIN APPROACHES 1. BIOLOGICALLY-INSPIRED ENGINEERING (bionics) Formulate biologically-inspired engineering / mathematical problems. Try to solve these problems in the most efficient engineering way. This approach had big success in engineering: universal programmable computer vs. human computer , a car vs. a horse, an airplane vs. a bird. It hasn’t met with similar success in simulating human cognitive functions. 2. SCIENTIFIC / ENGINEERING (reverse engineering = hacking) Formulate biologically-inspired engineering or mathematical hypotheses. Study the implications of these hypotheses and try to falsify the hypotheses. That is, try to eliminate biologically impossible ideas! We believe this approach has a better chance to succeed in the area of brain-like computers and intelligent robots than the first one. Why? So far the attempts to define the concepts of learning and intelligence per se as engineering/mathematical concepts have led to less interesting problems than the original biological problems. Slide 2 HUMAN ROBOT Slide 3 CONTROL SYSTEM Slide 4 OUR MOST IMPORTANT PERSONAL COMPUTER Parietal Lobe 12 cranial nerves ; ~1010 neurons in each hemisphere Frontal Lobe Occipital Lobe ~1011 neurons Temporal Lobe Cerebellum 31 pairs of nerves; ~ 107 neurons Cervical Spinal Cord 8 pairs Thoracic Spinal Cord Dura mater Our brain still lives in a sea! 12 pairs Lumbar Spinal Cord 5 pairs Cauda Equina 6 pairs Slide 5 The brain has a very large but topologically simple circuitry The shown cerebellar network has ~1011 granule (Gr) cells and ~2.5 107 Purkinje (Pr) cells. There are around 105 synapses between T-shaped axons of Gr cells and the dendrites of a single Pr cell. Pr Memory is stored in such matrices Slide 6 LTM size: Cerebelum: N=2,5 107 * 105= 2.51012 B= 2.5 TB. Neocortex: N=1010 * 104= 1014 B= 100 TB. Big picture: Cognitive system (Robot,World) External system (W,D) Sensorimotor devices, D W External world, W Computing system, B, simulating the work of human nervous system D B Human-like robot (D,B) B(t) is a formal representation of B at time t, where t=0 is the beginning of learning. B(0) is an untrained brain. B(0)=(H(0),g(0)), where H(0) = H is the representation of the brain hardware, g(0) is the representation of initial knowledge (state of LTM) Slide 7 CONCEPT OF FORCED MOTOR TRAINING External system (W,D) Brain (NS,NM,AM) NS W S D AM M Motor control: M SM associations NM Teacher . During training, motor signals (M) can be controlled byTeacher or by learner (AM) . Sensory signals (S) are received from external system (W,D). Slide 8 Turing’s machine as a system (Robot, World) Slide9 TWO TYPES OF LEARNING Working memory and mental imagery M S NS W AS S S MS associations Motor control D S M NM AM M SM associations M Teacher Slide 10 Mental computations (thinking) as an interaction between motor control and working memory (EROBOT.EXE) Slide 11 Motor and sensory areas of the neocortex Motor control AM Working memory, episodic memory, and mental imagery AS Slide 12 Primary sensory and motor areas, association areas Slide 13 Association fibers (neural busses) Slide 14 SYSTEM-THEORETICAL BACKGROUND Slide 15 Fundamental constraint associated with the general levels of computing power Type 0 Type 0: Turing machines (the highest computing power) Type 1 Type 2 Type 1: Context-sensitive grammars Type 3 Type 2: Context-free grammars (push-down automata) Type 4 Type 3: Finite-state machines Type 4: Combinatorial machines (the lowest computing power) Traditional ANN models are below the red line. Symbolic systems go above the red line but they require a read/write memory buffer. The brain doesn’t have such buffer. Fundamental problem: How can the human brain achieve the highest level of computing power without a memory buffer? Slide 16 General structure of universal programmable systems of different types Type 4: Combinatorial machines X={a,b,c} PROM G x a b c b a c 0 1 0 0 1 1 f Y={0,1} f: X×G→Y y PROM stands for Programmable Read-Only Memory. In psychological terms PROM can be thought of as a Long-Term Memory (LTM). Letter G implies the notion of synaptic Gain. Slide 17 Type 3: Finite-state machines PROM x s G snext y a b c b a c X={a,b,c} 0 a0 0 1 0 1 1 1 1 S=Y={0,1} 1 1 0 0 1 0 0 1 1 f: X×S×G→S×Y y x f s snext register Slide 18 Type 0: Turing machines (state machines coupled with a read/write external memory) PROM f: X×S×G×M→S×M×Y G y x f s snext M Memory buffer, e.g, a tape register Slide 19 Basic arcitecture of a primitive E-machine Association inputs Data inputs to ILTM INPUT LONG-TERM MEMORY (ILTM) DECODING, INPUT LEARNING Similarity function Control inputs E-STATES (dynamic STM and ITM) MODULATION, NEXT E-STATE PROCEDURE Modulated (biased) similarity function CHOICE Data inputs to OLTM Selected subset of active locations of OLTM Control outputs OUTPUT LONG-TERM MEMORY (OLTM) ENCODING, OUTPUT LEARNING Data outputs from OLTM Association outputs Slide 20 The brain as a complex E-machine D SUBCORTICAL SYSTEMS S1 SENSORY CORTEX AS1 ASk W D M1 MOTOR CORTEX SUBCORTICAL SYSTEMS AM1 AMm Slide 21 A GLANCE AT THE SENSORIMOTOR DEVICES Slide 21 VISION Slide 22 EYE Slide 23 EYE MOVEMENT CONTOL Slide 24 AUDITORY AND VESTIBULAR SENSORS Slide 25 AUDITORY PREPROCESSING ~100,000,000 cells ~580,000 cells ~4,000 inner hair cells ~12,000 outer hair cells ~390,000 cells ~90,000 cells ~30,000 fibers Slide 26 OTHER STUFF Slide 27 EMOTIONS (1) Slide 28 EMOTIONS (2) Slide 29 SPINAL MOTOR CONTROL SENSORY FIBERS MOTOR FIBERS Slide 30