IT'S MY PLEASURE TO INTRODUCE VIJAY BALASUBRAMANIAN FOR TODAY'S NEUROSCIENCE SEMINAR SPEAKER. VIJAY IS THE KATHY AND MARK LASARI FIGURES AT THE UNIVERSITY OF PENNSYLVANIA AND ASSOCIATE PROFESSOR OF NEUROSCIENCE. AND VIJAY'S CAREER IS A REALLY INTERESTING EXAMPLE OF HOW YOU CAN, YOU KNOW, YOU'VE GOT CERTAIN FACULTIES YOU CAN REALLY MAKE A MARK IN TWO DIFFERENT FIELDS. VEHEMENT WAS BORN -- VIJAY WAS BORN IN END YAWN, GOT HIS PH.D. IN PHYSIC AT PRINCETON WHICH IS A RATHER GENERAL TITLE FOR HIS THESIS WHICH IS INFORMATION, ENTROPY AND BLACK HOLES. AND AFTER THAT, HE WAS A HARVARD SOCIETY OF FELLOWS WHERE HE STARTED PARTICLE PHYSICS BUT BEGAN CONSORTING AND HANGING OUT WITH SHADY NEUROSCIENCE TYPES LIKE DAVID HUBEL AND MARKUS MICER AND THIS FORMED A BRIDGE WHEN HIS INFORMATION AND THE NERVOUS SYSTEM. AND SO AFTER THAT, HE ACCEPTED A FACULTY POSITION IN THE PHYSICS DEPARTMENT AT PENN AND AS HE WAS MOVING UP THE RANK AND EVENTUALLY BECAME A FULL PROFESSOR. HE WAS INVOLVED IN THE NEUROSCIENCE COMMUNITY AT PENN BECOMING A PROFESSOR, AN ASSOCIATE PROFESSOR IN NEUROSCIENCE AS WELL, AND B VERY INTEGRATED INTO THE VISION COMMUNITY AT PENN. PEOPLE LIKE PETER STERLING AND MICHAEL FREED -- RECORD FOR ENCODING, PROCESSING VISUAL INFORMATION AND ENCODING IT IN THE MOST EFFICIENT WAY POSSIBLE. SO, YOU KNOW, IT'S AMAZING, HE'S REALLY MAINTAINED, THOUGH, IN PARTICLE PHYSICS AND IN NEUROSCIENCE. IN FACT HE HAD GRANTS FROM THE NATIONAL SCIENCE FOUNDATION AT THE SAME TIME AND ONE WAS CALLED WHAT THE RETINA MIGHT KNOW ABOUT NATURAL THEME AND THE OTHER WAS CALLED DREAM THEORY AND PSYCHOLOGICAL SPACE TIMES. >> I DON'T KNOW WHAT THAT MEANS. >> I NORMALLY ADVERTISE THESE POINTS. >> I GOT TO TELL YOU THAT IN ADDITION TO HIS VERY INTERESTING WORK ON INFORMATION PROCESSING IN THE BRAIN, VIJAY IS THE MOST ENTERTAINING SPEAKER I'VE EVER ENCOUNTERED IN SCIENCE. AND SO NOT TO LIKE SET YOU UP HERE. >> THAT IS HARD TO LIVE UP TO. YOU MUST SET EXPECTATIONS LOW. YOU SHOULD HAVE STARTED OUT SAYING HE IS REALLY BORING. >> OKAY. >> THANKS VERY MUCH FOR HAVING ME OUT. IT'S A PLEASURE TO BE HEAR. I'VE ALREADY ENJOYED MY CONVERSATIONS THIS MORNING. SO THE TITLE OF MY TALK IS THE MAPS INSIDE YOUR HEAD. AS I SPEAK I THINK IT WILL BE CLEARLY WHAT EXACTLY I WANT TO MEAN BY THAT. SO AS YOU KNOW, AT EVERY SCALE OF ORGANIZATION OF THE BRAIN, THE BRAIN HAS A DIVERSE POPULATION OF FUNCTIONAL UNITS WHICH COORDINATES WITH ACTIVITY PRODUCES THE DESIRED FUNCTION. MY CURRENT INTEREST IN THE LAB AS A PUREST IS TO BASICALLY UNDERSTAND THE FUNCTIONAL LOGIC IF YOU LIKE HOW LARGE SCALE FUNCTION IS BROKEN UP. THE LOGIC UNDERLYING HOW LARGE SCALE FUNCTION IS BROKEN UP INTO MULTIPLE INTERACTING PIECES. IF YOU WANT TO THINK ABOUT THIS AT THE LEVEL OF ON THE WHOLE BRAIN. IMAGINE THE RECTANGLE -- I MIGHT THINK OF THIS AS THE ALGORITHM OR COMPUTATIONAL UNITS THAT NEED TO BE TAKEN CARE OF. IN WHICH CASE EACH OF THESE BLOBS REPRESENT A BRAIN AREA. IF WE WERE TO THINK IN TERMS OF THE EARLY VISUAL SYSTEM THE -- I MIGHT THINK ABOUT THIS RECTANGLE AT A SPACE OF BEHAVIORAL -- WHATEVER PART OF NATURAL THEMES YOU SHOULD CARE ABOUT. AND THEN EACH OF THESE BLOBS YOU COULD THINK OF LET'S SAY THE SINGLE RETINAL GANG LEGAL TYPE, THE PIECES, THE FEATURES OF THE WORTH THAT EXTRACT REPORTS. YOU CAN THINK OF THE NOSE AND THE CORTEX AND DIFFERENT AREAS OF THE BRAIN AND THE IDEA IS OVERALL THE FUNCTION YOU NEED TO CONFORM IT'S SPLIT UP INTO LIKELY COMPONENTS LIKE A COMPUTER AND LIKE TO UNDERSTAND THE RULES AND MAGIC, IF ANY, THAT GOVERN THE WAY IN WHICH THIS ORGANIZATION COMES. JUST EMPHASIZE THIS ISN'T JUST ABSTRACT WHOHA, LET'S LOOK AT THE BRAIN AT THE LARGEST SCALE OF ORGANIZATION. EVERYBODY KNOWS IN THIS ROOM THAT THE BRAIN IS DIVIDED UP ROUGHLY INTO AREAS. THIS IS OCCIPITAL LOBE, THE FRONTAL LOBE WHERE PERSONALITY FUNCTION ARE, DECISION-MAKING IS LOCALIZED. THERE'S THE BROCA AREA, AND THIS FOR MEMORY. FUNCTIONS OF DIFFERENT KINDS IS KNOWN TO BE LOCALIZED IN DIFFERENT CENTERS OF THE BRAIN AT VERY LARGE SCALE. IF I TAKE ONE OF THESE AREAS, LET'S TAKE THE CORTEX FOR EXAMPLE, THERE ARE TWO. IT ISN'T AS THOUGH AS GOLGI, SOME SORT OF HOLISTIC, SOME ABSTRACT NETWORK OF STUFF THAT SOMEHOW MANAGES TO CONTROL YOUR BODY. THE SURFACE THAT CONTROLS YOUR KNEE ARE UP HERE IN THE MIDDLE OF YOUR HEAD, THE CIRCUITS THAT CONTROL YOUR FACE ARE OVER HERE ON THE SIDE OF YOUR HEAD. AND AS IS SOFTEN THE CASE, THE DOMAIN THAT'S DEVOTED TO A PARTICULAR KIND OF CIRCUIT OR CONTROL, THE MORE IMPORTANT IT IS ROUGHLY THINKING MORE FOR YOUR FACE THAN YOUR KNEE BECAUSE THERE'S MORE STUFF TO DO. AGAIN THIS IS LOCALIZATION OF FUNCTION WHERE THE DIFFERENT ASPECTS OF MOTOR CONTROL ARE LOCALIZED IN DIFFERENT BITS ON THE STRUCTURE. WE CAN GO EVEN DEEPER. HERE I'LL LOOK AT MY FAVORITE BRAIN AREA, THE RETINA. AND THIS IS A FAMOUS DRAWING DRAWN IN 1917, THIS PARTICULAR DRAWING WILL GO ON DISPLAY HERE AT THE NIH VERY SOON. AND AS YOU SEE IN THE PICTURE, THERE ARE MANY DIFFERENT TYPES OF CELLS, RIGHT. RETINA IS ALSO NOT SOME HOLISTIC UNDIFFERENTIATED NETWORK OF NEURONS BUT RATHER YOU SEE HERE HERE ARE THE RECEPTORS, BIPOLAR CELLS. THIS IS SUGGESTING IF YOU COUNT ALL THE INTERNEURONS ALSO, HEARING THE GANG LIEN CELLS WHICH ARE THE CELLS OF THE RETINA, THERE'S SOME 60 TYPES OF CELLS IN THE RETINA ALONE. FOLLOWING THE BIOLOGY THAT'S GOING TO HAPPEN, THAT FORM FOLLOWS FUNCTION, THIS CELL IS SURELY DOING SOMETHING DIFFERENT FROM THIS CELL AND THIS CELL. IT'S AS IF ALL THE FUNCTIONS THAT NEED TO BE PERFORMED IN THE EARLY VISUAL SYSTEM TO TAKE THE PHOTON COMING INTO THE WORLD AND TURN THEM INTO DIFFERENT FEATURES THAT HELP YOU TO SEE THE SUPPORTIVE BEHAVIOR, ALL OF THESE FUNCTIONS HAVE BEEN SPLIT UP INTO PLETHORA OF DIFFERENT TYPES OF CELLS WHICH THEN ACT TOGETHER TO SUPPORT VISION. NOW, COMING OUT OF PHYSICS INTO BIOLOGY, I HAVE TO SAY THAT ONE OF THE MOST INTIMIDATING PICTURES YOU CAN SEE IS SOMETHING LIKE THIS. WHEN YOU REALIZE THAT JUST THE RETINA ALONE HAS 60 TYPES OF COMPONENTS CONNECTED UP IN SOME VERY COMPLI WAY. HOW THE HELL CAN YOU SOLVE THE LOGIC OF SUCH CIRCUIT. REALLY MY MOTIVATION IN TRYING TO UNDERSTAND THIS, I WOULD LIKE TO UNDERSTAND THE DIVERSITY OF COMPONENT TYPES OF HOW THEY HOOK TOGETHER AND WHETHER THERE'S ANY EXPLANATION HOW THIS THING IS PUT TOGETHER. SO AGAIN TO REPEAT WHAT I'VE SAID, OVERALL SO FAR WE'VE SAID THAT AT EVERY SCRAIL OF THE ORGANIZATION OF THE BRAIN, YOU HAVE SOME FUNCTION THAT NEEDS TO BE PERFORMED AND THAT FUNCTION IS SPLIT YOU INTO DIVERSE COLLECTION OF FUNCTIONAL ELEMENTS AND INTERACT AND DO WHATEVER YOU NEED. I TACK THIS KIND OF COMPUTATIONAL REPERTOIRE THAT THE BRAIN IMPLEMENTS, THESE COMPUTATIONAL REPERTOIRE FOR BEHAVIOR AND ARE LEARNED OVER EVOLUTIONARY TYPE ENCODED THE GENOME. THIS IS A LEARNED SET OF COMPUTATIONAL ELEMENTS. AND OF COURSE THESE THINGS ARE PLASTIC, THE BRAIN IS VERY PLASTIC SYSTEM AND ALL OF THESE LITTLE FUNCTIONAL UNITS INTERACT WITH EACH OTHER. AND AS YOU LEARN, AS EXPERIENCE THE WORLD, THE REORGANIZE SOMETIMES TO MOVE AWAY, SOME GET BIGGER, NEW FUNCTIONAL ELEMENTS APPEAR AND THE INTERACTIONS CHANGE THE STRUCTURE ON THE NETWORK. MY INTEREST IS TO ASK WHAT ORGANIZATIONAL PRINCIPLES OR FUNCTIONAL LOGIC DRIVES AND CONTROLS THE COMPUTATION THAT INFORMATION REP -- REPERTOIRES OF THE BRAIN. LIKE THE BRAIN AREA IS DIFFERENT FROM THE RETINA AND UNDERSTAND HOW ALL THESE LAYERS INTERACT WITH ETCH A OTHER. THEATS THE BIG QUESTION I WOULD LIKE TO GO AFTER. NOW HOW DO YOU MAKE PROBLEM IN SUCH A QUESTION. WELL ONE LEVER FOR INVESTIGATION MAYBE NOT NECESSARILY THE RIGHT ONE OR THE ONLY ONE IS TO CONSIDER THE COST OF OPERATING THE BRAIN, RIGHT. SO IT'S AN EXPENSIVE TISSUE. IF YOU THINK ABOUT HOW MUCH YOU LIKE THE BRAIN COST YOU IN SOME METABOLIC LOAD, YOUR BRAIN IS 2% OF YOUR BODY WEIGHT BUT 20% OF THE METABOLIC LOAD. IT COSTS YOU MORE THAN MUSCLE THAN WHEN YOU'RE WORKING OUT. IT'S ALSO VERY PACKED TISSUE. IF YOU CONSIDER A MILLIMETER CUBE THE VOLUME. PUT YOUR FINGERS AND THE LITTLE HOLE IS WIRES. IT'S EXTREMELY PACKED. PEOPLE HAVE ARGUED POWER AND SPACE ARE MAJOR CONSTRAINTS. SO THE COMPUTATION CARRIED OUT BY THE BRAIN CERTAINLY CONFER BENEFITS BEHIFERLLY BUT IT ALSO CARRIES A COST. ON THE OTHER HAND YOU CAN ALSO ARGUE THAT THE TISSUE IS VERY EFFICIENT. SO MY LAPTOP CONSUMES 80 WATTS OF POWER BUT YOUR BRAIN CONSUMES 10-12 WATTS OF POWER. SO APPARENTLY WITH THIS WEAK AMOUNT, THIS WEAK POWER USAGE YOU CAN DO STUFF LIKE ART APPRECIATION WHICH YOUR LAPTOP CERTAINLY CANNOT. IT SUGGESTS WHAT'S GOING ON IS THERE'S SOMETHING ABOUT THE ARCHITECTURE OF THE SYSTEM WHICH ON THE ONE HAND IS VERY EXPENSIVE AND BECAUSE IT'S EXPENSIVE THERE'S A DRIVE TO PRODUCE CIRCUIT ARCHITECTURES THAT ARE, YOU KNOW, LOWER THE COST TO THE SYSTEM. AT LEAST THAT'S ONE IDEA THAT SEEMS REASONABLE AS A MEANS OF GETTING CONTROLS ON THE LOGIC OF ORGANIZATION IN THE BRAIN. INDEED, IF YOU ASK YOURSELF HOW COULD THE BRAIN ACHIEVE E TITION SEE IN ITS EXEUTION, USE UP THE RESOURCES. THERE'S THIS IDEA THAT WOULD COME TO MIND IS BASICALLY ECONOMIC. YOU WOULD SAY THAT SPECIALIZATION OF FUNCTIONS, SPECIALIZATIONS IN THE CIRCUIT REPERTOIRE ADAPTATIFOR THE STRUCTURE OF THE WORLD WOULD BE LIKELY TO SQUEEZE OUT EFFICIENCY FROM THE SYSTEM. WHY IS THIS? ECONOMISTS TALK ALL THE TIME, IN THE DAYS YOU WERE HUNTERS GATHERERS, MADE THE BREAD AND WITH SOCIETY'S PROGRESS ECONOMISTS TELLS US, SOCIOLOGISTS ECONOMISTS TELL US THAT THE FUNCTIONS WE PERFORMED ARE SPECIALIZED. THE BAKER MAKES THE BREAD, THE BANKER DOES WHAT. THE SPECIALIZING FUNCTION, WE COULD SQUEEZE OUT GREATER EFFICIENCY BECAUSE EACH UNIT LEARNS TO DO ITS JOB BETTER. THAT'S THE BASIC PRINCIPLE OF ORGANIZATION THAT PEOPLE TALK ABOUT. SO THE SUGGESTION HERE MAY THE TRUE PROBLEMS THAT WE FACE, ONE IS THE MASSIVE DIVERSITY OF FUNCTIONAL UNITS OF THE BRAIN, AND THE COST OF OPERATING THIS SYSTEM MAY BE ACTUALLY RELATED TO EACH OTHER. AND THAT YOU CAN UNDERSTAND THE STRUCTURE OF COMPUTATION OF A STRUCTURE OF THE DIVERSITY OF FUNCTIONAL UNITS BY THINKING OF THE COSTS OF COMPUTATION AT THE SAME TIME. THAT'S THE BASIC PREMISE OF WHAT I'M GOING TO GET TODAY. SO BROADLY THE IDEA WOULD BE THAT YOU MIGHT BE ABLE TO CONSTRUCT SOMETHING LIKE A THEORY OF MASS IN THE BRAIN SUGGESTING THE BRAIN EXPLOITS STRUCTURE IN THE WORLD TO EFFICIENTLY ALLOCATE THEIR LIMITED COMPUTATION RESOURCES TO MAXIMIZE GAIN IN SOME APPROPRIATE SENSE TO THE ORGANISM. THAT'S THE OVERALL PICTURE I WOULD LIKE TO SUGGEST. THAT'S ALL VERY ABSTRACT AND REALLY THE QUESTION IS CAN WE ACTUALLY DO ANYTHING. IT'S A NICE PHILOSOPHY BUT WHAT CAN YOU DO. I WOULD LIKE TO TRY TO CONVINCE YOU TODAY THAT IT'S VERY VERY USEFUL TO THINK IN THIS WAY AND MANY STRUCTURES AND ORGANIZATIONAL PATTENS IN THE BRAIN ARE MYSTERIOUS BUT BECOME VERY CLEAR IF YOU THINK ABOUT THEM IN THIS LANGUAGE. SO I'M GOING TO TRY TO CONVINCE YOU OF THIS USING THREE EXAMPLES. THE FIRST EXAMPLE IS GOING TO BE TAKEN FROM VISION, THE EARLY VISUAL SYSTEM. THE SECOND EXAMPLE TO CONVINCE YOU THIS ISN'T A SENSORY THING I'LL TAKE A MORE COGNITIVE EXAMPLE. I'LL THINK ABOUT THE SENSE OF PLATE -- IN MEDICINE AND THIRDLY I'LL TELL YOU ABOUT THE WORK IN PROGRESS ABOUT THE SENSE OF SMELL. I'VE CHOSEN THE SENSE OF SMELL BECAUSE IT'S MORE COMPLEX IN MANY WAYS THAN VISION AND INTRODUCE SOME INTERESTING NEW FEATURES. SO OVERALL YOU'LL SEE THAT IN EACH CASE, THE STRUCTURES ANATOMY AND PHYSIOLOGY OF THE CIRCUIT SUGGEST THAT EVOLUTION SEEMS TO HAVE EXPLOITED SOPHISTICATED MATHEMATICAL PRINCIPLES OF INFORMATION PROCESSING THAT HAVE ONLY RECENTLY BEEN DISCOVERED AND THAT WOULD BE CONSISTENT WITH THE OVERALL HYPOTHESES THAT YOU SHOULD DIVERSE FEE YOUR FUNCTIONAL UNITS AND SPREAD AMONGST THEM IN ORDER TO REDUCE THE COMPUTATION. THAT'S THE IDEA. SO FAR ANY QUESTIONS? OKAY. I'M GOING TO START MY FIRST EXAMPLE TO SEE HOW IT WORKS. I'LL THINK ABOUT VISUAL REPERTOIRES. HERE I'LL BASICALLY THINK ABOUT THE RED KNOW AND THINK ABOUT THE REPERTOIRE OF RETINAL GANGLION CELL AND I WOULD LIKE TO ASK HOW THE FUNCTIONS DISTRIBUTE. I'LL START BASICKING THE FOCUSING OF A CIRCUIT FOR SEEING BRIGHT VERSUS DARK. HERE'S THE PICTURE ON THE RETINA THE SAME PICTURE WE SAW EARLIER. THERE ARE THREE KINDS OF CONE PHOTON RECEPTORS WHICH ARE THEN TIMES CELLS DOING VARIOUS KINDS OF ANALOGUE COMPUTATION. BASED ON THE RECEPTORS. THOSE FEED INTO A REPERTOIRE OF I DON'T KNOW 20 RETINAL GANGLION CELLS WHOSE OUTPUT ARE THE SENSE OF THE BRAIN AND ALL OF THE VISION. NOW, SO THESE RETINAL GANGLION CELLS ARE CELLS OF THE RETINA ARE TAUGHT TO EXTRACT VISUAL FEATURES OF THE WORLD. WHAT'S VISUAL FAMILIAR. IT'S THINGS LIKE BRIGHT SPOTS AND DARK SPOTS, COLOR, LOCOMOTION AND THINGS LIKE THAT. AND THEY REPORT THEM TO THE BRAIN. SO FOLLOWING THE BROAD QUESTION THAT I WAS TRYING TO ASK HOW SHOULD YOU ALLOCATE RESOURCES IN THE BRAIN, THE DIFFERENT PARTS OF THE COMPUTATIONAL REPERTOIRE, YOU COULD ASK THE QUESTION HOW SHOULD THIS REPERTOIRE GANGLION CELLS THERE'S ABOUT A MILLION IN HUMAN AND A HUNDRED THOUSAND IN GUINEA PIGS. HOW SHOULD THAT REPERTOIRE BE DIVIDED INTO THE DIFFERENT CELL TYPES THAT RESPOND INTO THE DIFFERENT KINDS OF FEATURES OF THE VISUAL WORLD. CLEARLY YOU CAN MAKE CHOICES HERE, RIGHT. YOU CAN DEVOTE 99% OF THE CELL TO SEEING BRIGHT SPOTS. OR YOU CAN DEVOTE 80% OF THE CELLS WITH DIRECTIONAL LEFT, RIGHT MOTOR. AND DEPENDING HOW YOU PERFORM THE ALLOCATION YOUR ABILITY TO PERFORM DIFFERENT KINDS OF VISUAL PATHS WILL CHANGE AND YOU'LL HAVE FIVE OR YOUR ACCURATE SENSORY. THERE'S A TRADE OFF HERE AND THE QUESTION IS HOW SHOULD THEY BE MADE. TO KEEP IT SIMPLE I'LL CONSIDER THE EXAMPLE OF BRIGHT AND DARK SPOT DETECTORS NAMELY THE ON AND OFF CELLS OF THE RETINA. THAT REMIND YOU. AND THE CELLS ARE ALL RETINAL GANGLION CELL OF THE RETINA RESPONDS TO LIGHT WHICH ARE BRIGHT RELATIVE TO THE NEAR BACKGROUND IN A SENSE OF SOUND AND ORGANIZATION. AND RESPONDS THERE'S A DARK SPACE RELATIVE TO THE NEAR SURROUND. I'M GOING TO APPROACH THIS IN A PARTICULAR WAY. I'M GOING TO ASK MYSELF HOW SHOULD THE SYSTEM BE ORGANIZED AND THEN I'M GOING TO COMPARE THE ACTUAL, THE PREDICTIONS OF THAT KIND OF THINKING HOW SHOULD IT BE ORGANIZED TO THE ACTUAL ORGANIZATION THAT IT CAN SEE IN THE DATA. SO TO ANSWER THE QUESTION OF HOW THE RETINA SHOULD DIVIDE ITS RESOURCES BETWEEN ON CELLS AND OFF CELLS, BRIGHT SPOT DETECTORS AND DARK SPOT DETECTORS THE FIRST THIN TO UNDERSTAND WHAT IS IT TRYING TO PROCESS. FOR THE RETINA IT'S PRYING TO PROCESS THE NATURAL VISUAL WORLD. WHAT IS IT. HERE ARE SOME NATURAL SCENES. THESE ARE PHOTOGRAPHS TAKEN FROM A BELAN HABITAT. YOU CAN TAKE THAT PHOTOGRAPH IN DOWNTOWN PHILADELPHIA OR ANYWHERE ELSE YOU WANT AND THE KIND OF PROPERTIES ARE GOING TO BE SIMILAR ACROSS ALL OF THESE DIFFERENT ENVIRONMENTS. WHAT YOU KIND IS THAT IF YOU LOOK IN ANY COLOR CHANNEL RED BLUE GREEN OR LOOMENCE, YOU'LL HAVE A LOW PEAK AND A LONG TAIL WHERE THE FUNCT SHUPGZ LOOK LONG NORMAL. THIS IS LOW PEAK LONG TAIL DISTRIBUTION OF LIGHT THAT'S GOING TO BE THERE IN ESSENTIALLY ANY VISUAL ENVIRONMENT YOU CAN MAKE. I WOULD LIKE YOU TO REMEMBER THAT. IT HAS THIS KIND OF STRUCTURE. IN PARTICULAR THIS KIND OF STRUCTURE OF LIGHT IN THE WORLD MEANS, IMPLIES THE AVERAGE, THE MEANS LIGHT LEVEL OVER THE PIXEL WILL EXCEED THE MEDIAN. THE MEAN ILL EXCEED THE MEDIAN. THAT'S ONE FACT YOU SHOULD REMEMBER. SECONDLY IT'S ALSO CLEAR LOOKING AT IMAGES THAT LIFE IS -- THIS IS KIND OF RED HERE AND AFTER A WHILE IT'S NOT RED NAME, RIGHT. THAT'S NORMAL BECAUSE THE WORLD IS MADE OF OBJECTS. YOU FIND A BETTER CORRELATION TO DIE OFF IN THE WORLD AT SOME RATE. HERE'S A CRUST CORRELATION OF LIGHT ACROSS POINTS, SEPARATION AND DEGREES AND IT FALLS OFF LIKE THAT. USUALLY THIS IS COURT LIESED WITH SOMETHING CALLED THE POWER SPECTRUM OF LIGHT AND YOU FIND IT LIVES IN A STRAIGHT LINE LIKE THIS. WHAT THAT MEANS CONCEPTUALLY IS THAT THE CORRELATIONS OF LIGHT IN THE WORLD HAVE A PROPERTY OF SCALE IN VARIANCE. WHAT SCALE IN VARIANCE MEANS IS THE FOLLOWING. YOU TAKE THE PHOTOGRAPH AND CUT IT UP INTO QUARTERS. YOU TAKE A QUARTER OF THE PHOTOGRAPH AND YOU BLOW IT UP TO FILL THE WHOLE SCREEN. YOU RECOMPUTE THE CORRELATIONS OF THAT BLOWN UP IMAGE. YOU'LL FIND IT IDENTICAL. SO IN OTHER WORDS NATURAL ENGINES HAVE TWO IMPORTANT PROPERTIES THAT WILL BE IMPORTANT FOR US ANYWAY. THE MEAN LIGHT EXCEEDS THE MEDIAN AND THE CORRELATIONS THEM IN THEM ARE SCALE IN VARIANCE. NAMELY YOU CAN PICK IMAGE AND BLOWING THEM UP AND IT LOOKS THE SAME IN ALL SCALE. I WILL ARGUE FROM THIS, WE CAN ARGUE FROM THIS THAT IF YOU CONSIDER WHAT CONSEQUENCES THIS HAS FOR BRIGHT VERSUS DARK SPOTS OF NECESSITY THERE ARE MORE DARK SPOTS IN THE WORLD. WE ARGUE THAT OF COURSE. SO THAT'S THE EFFECT, THE KIND OF CIRCUITRY THAT YOU BUILD OR PROCESS. OH, THROUGHS NO CHALK HERE. SO THIS IS NOT A BLACKBOARD. LET ME ARGUE WHY THIS IMPLIES THAT THERE ARE MORE DARK SPOTS, OKAY. CONSIDER AN IMAGINARY RETINAL GANGLION CELLS THAT HAS A TINY LITTLE CENTER MAYBE LIKE ONE PIXEL. SO WHAT IT'S GOING TO DO IS IT'S GOING TO REPORT, IT'S GOING TO COMPARE LIGHT ONE POINT IN THE MIDDLE COMPARED TO LIGHT IN THE LARGEST SURROUNDING REGION. NOW THE LIGHT IS GOING TO BE CLOSER TO THE MEDIAN. IF YOU TAKE AVERAGE LIGHT OF THE SOW ROUNDING REGION, RIGHT, IT'S A BIGGER REGION IT'S GOING TO BE CLOSER TO THE MEAN. NOW WE AGREED THAT THE MEAN IN THIS DISTRIBUTION EXCEEDS THE MEDIAN. SO IT'S GOING TO BE THE CASE THAT THE CENTER MINUS THE SURROUND IS GOING TO BE LIKE THE MEDIAN MINE IS THE MEAN AND IT WILL BE NEGATIVE OR LESS THAN ZERO. IN OTHER WORDS STATISTICALLY YOU'RE MORE LIKELY TO GET THE DARK SPOTS THAN THE BRIGHT SPOTS BECAUSE OF THIS DISTRIBUTION OF LIGHT. NOW, YOU MIGHT SAY WELL YOU JUST ARGUED THAT FOR GANGLION CELL BECAUSE A SINGLE PIXEL IN THE MIDDLE. WHAT ABOUT REAL GANGLION CELLS WHERE THE CENTER HAS SOME SIDES. WHAT YOU DO IS YOU USE THESE CORRELATIONS AND TAKE GANGLION CELLS AND MAKE IT BIGGER AND BIGGER AND BIGGER I SHOULD GET THE SAME ANSWER. INDEED, YOU CAN CHECK THAT. SO WHAT YOU CAN DO IS YOU TAKE A BUNCH OF NATURAL IMAGES AND YOU TAKE, YOU MAKE A LITTLE OF A RETINAL GANGLION CELL AND PASS THIS FILTER OVER THE IMAGE AND LOCATE ALL THE BRIGHT AND DARK SPOTS. AND YOU CAN SIMPLY COUNT UP HOW MANY BRIGHT SPOTS AND HOW MANY DARK SPOTS DO YOU HAVE. AND YOU CAN DO THIS WITH LITTLE STEINY GANGLION CELLS, LARGER GANGLION CELLS LIKE THE YELLOW ONE AND EVEN LARGER CELLS WITH THE RED ONE THERE. AND PLOT ON THIS SIDE THE SIZE OF THE RETINAL GANGLION RECEPTOR SEALS AND THIS SIDE ON THE Y AXIS THE PERCENTAGE OF BRIGHT AND DARK SPOTS. AND WHAT YOU SEE IS THAT OF ALL VISUAL SCALES THAT ARE MORE DARK SPOTS THAN BRIGHT SPOTS AS I JUST ARGUED. OKAY. AND THIS IS JUST A PROPERTY OF THE NATURAL VISUAL WORLD. SO WHAT CONSEQUENCE DOES THIS HAVE? SO I COULD ASK AS A PURIST GIVEN THIS PROPERTY OF THE WORLD THAT THERE ARE MORE DARK SPOTS THAN BRIGHT SPOTS. IF I GIVE YOU A POPULATION OF END GANGLION RECEPTOR SEALS AND ASK TO INVEST THEM WISELY -- AND SOME OF THEM TO MAKE BROUGHT SPOT DETECTORS WHAT FRACTION SHOULD YOU SPECIFIC OF EACH IS A QUESTION YOU SHOULD ASK. IF YOU DO THAT, YOU SAY END, THE TOTAL NUMBER OF CELLS IS EQUAL TO THE NUMBER OF OFF CELLS PLUS THE NUMBER OF ON CELLS AND WELL YOU MIGHT SAY WELL LET ME FIND THE OFF TO ON RATIO THAT MAXIMIZES THE TOTAL AMOUNT OF VISUAL INFORMATION. THAT'S THE THING THAT YOU COULD DO. COME BACK TO THE QUESTION SHOULD I HAVE MAXIMIZED INFORMATION OR SOME OTHER QUANTITY. WE'LL COME BACK TO THAT. LET'S JUST DO THIS FOR NOW. AND IF YOU DO THAT, LET'S REASON OUR WAY TO WHAT THE ANSWER IS GOING TO BE. SUPPOSE I GIVE YOU MONEY TO BUY ONE KIND OF CELL. WHICH KIND OF CELL SHOULD YOU BUY? I'M LOOKING FOR AN ANSWER HERE. THANK YOU. IT'S WRITTEN ON THE BLACKBOARD. IT'S AN OFF CELL BECAUSE THE OFF CELL IS MORE LIKELY TO RESPOND. NOW YOU GIVE YOU A LITTLE BIT MORE MONEY YOU AND FILL UP THE RETINA OF AN OFF CELL. BUT THEY ARE OVERLAPPING AND GETTING REDUNDANT TO EACH OTHER. YOU GET MORE MONEY AND BUY SOME ON CELLS BECAUSE NOW THEY TELL YOU THE BRIGHT SPOTS ARE DIFFERENT FROM THE DARK SPOTS INFORMATION. SO THEN YOU START FILLING THE RETINA WITH A CELLS, RIGHT. AND AT SOME POINT THEY'RE OVERLAPPING. THEY ARE REDUNDANT AND SO NOW YOU SHOULD BUY AN OFF CELL. AND YOU HAVE TO BUY AN ON CELL OFF CELL ON CELL OFF CELL. AND THE GAME WE'RE PLAYING WILL GO ON LIKE THIS UNTIL YOU REACH A BALANCE POINT WHERE THE INDIVIDUAL OFF CELL AND THE INDIVIDUAL ON CELL GIVES YOU EXACTLY THE SAME AMOUNT OF INFORMATION. THAT'S THE ONLY WAY IN WHICH THE PROCESS OF CONSTRUCTING THE BEST RETINA COULD END. SO IT MUST BE NO MATTER WHAT THEORY I BUILD OF THE RETINA, BUT THE OPTICAL POINT WOULD BE A BALANCE IN THIS WAY TO THE OFF AND ON CELL. SO THE WAY TO SOLVE THIS PROBLEM IS TO FILLED A PHYSIOLOGICALLY RESPECTIVE MODEL. YOU HAVE TO TAKE ACCOUNT THE NOISE IN GANGLION CELLS THE SIGNALING RANGE WHAT THE FIRING RATE IS, THE MAXIMUM FIRING RATE AND YOU CAN MEASURE ALL OF THESE THINGS OF COURSE FROM THE RETINA AND WE HAVE IN OUR LAB. THEN YOU CAN CONSTRUCT A MODEL AND STICK IT INTO IT BUT YOU KNOW FROM OUR REASONING THAT IT IS GOING TO HAPPEN BUT NO MATTER WHAT MODEL YOU PICK OFF THE RETINA OR HOW YOU DESCRIBE IT AT THE OPTIMAL POINT THAT WOULD BE THE BALANCE WITH AN ON AND OFF CELL. BUT THE ACTUAL FRACTION THAT YOU HAVE OF OFF VERSUS ON WILL DEPEND UPON THE DETAILS OF THE ETIOLOGY. YOU CAN WORK THAT OUT AND GET A PREDICTION OF AN OPTIMAL RATIO OF 1.7 TIMES AS MANY OFF CELLS AS ON CELLS. THE PRECISE NUMBER DEPENDS ON EXACTLY WHAT SHAPE THE GANGLION RETINAL CELL, EXACTLY HOW NOISY IT IS, EXACTLY WHAT ITS RANGE IS AND SO ON. BUT IT'S A BALLPARK NUMBER. I STICK TO THE DATA. FIRST OF ALL IS IT A FACT AT ALL THERE'S ANY ASYMMETRY BETWEEN BRIGHT AND DARK PROCESSING IN THE BRAIN. AND INDEED THERE IS. BEHAVIORAL MEASUREMENTS SHOW IN HUMANS SHOW GREATER SENSITIVITY LIGHTED DETRIMENT DARK SPOTS IN IMAGES. THAT'S THE FIRST FACT. SECOND FAX IS THERE ARE MEASUREMENTS THAT SHOW THE MORE CORTICAL RESPONDS TO DARK SPOTS AS TO BRIGHT SPOTS. AND FINALLY THERE ARE PLENTY OF MEASUREMENTS IN RETINA SHOWING NOW THAT RETINAL OFF CELLS ARE REALLY 1.3 TIME AS NUMEROUS AS ON CELLS. IN FACT, YOU CAN BUILD A STEP BY STEP AND HERE ARE THE CONES AND THEN IF YOU LOOK AT THE CONE BIPOLAR SYNAPSE, THAT'S WHERE THE DIVISION OCCURS AND THERE ARE TWICE AS MANY ON CELL AS OFF CELLS. FINALLY IF YOU GO THROUGH HERE ARE MEASUREMENTS YOU CAN MAKE OF ON AND OFF AND YOU CAN MEASURE ON YOU BIG THEY ARE AND THEN OFF CELLS ARE SMALLER. BECAUSE OF THE RETINA THERE ARE GOING TO BE MORE OFF CELLS. YOU CAN WORK OUT HOW MANY OFF CELLS VERSUS ON CELLS THERE ARE IN THE RETINA. AND YOU FIND THAT THERE'S BETWEEN 1.3 TO TWO TIMES AS MANY OFF CELLS AS ON CELLS A FACT OF CONSERVE ACROSS TYPES OF CELLS AND SPECIES. GUINEA PIGS, RABBITS, MONKEYS, HUMANS HUMANS AND SO ON. GREAT. THIS IS A VERY NICE EXAMPLE OF THE WAY WE'RE THINKING ABOUT HOW THE RETINA SHOULD BE ORGANIZED GIVEN THE STRUCTURE ON THE WORLD, GIVEN A COST. YOU HAVE A CERTAIN NUMBER OF CELLS. VERY NICELY EXPLAINED AND OTHERWISE WE HAVE A WEIRD AND DIFFICULT TO UNDERSTAND FACT. WHY DOES THE BRAIN DEVOTE MORE RESOURCES TO PROCESSING DARK SPOTS. THIS IS VERY PRETTY EXPLANATION OF THAT FACT THAT WE CAN GET IT THIS WAY. BUT MORE GENERALLY YOU MAY RAISE A BUNCH OF QUESTIONS. IS IT SUCCESSFUL EXPLAINING ABOUT THE RETINA. IS IT GOING TO GENERALIZE. ARE MANY DOUBTS WE CAN V THE FIRST QUESTION IS WHAT CAN WE OPTIMIZE. THE ANALYSIS I TOLD YOU B I SAID WHAT YOU CAN DO IS YOU CAN MAXIMIZE THE AMOUNT OF VISUAL INFORMATION YOU CAN GET FROM THE RETINA. WHYED SHOE IT BE INFORMATION IN BITS. WHAT DOES THAT HAVE TO SAY ABOUT ANYTHING. WHAT YOU SHOULD REALLY BE DOING IS TAKING ACCOUNT OF VISUAL BEHAVIOR AND SOMEHOW ASKING THE QUESTION HOW DOES THIS PARTICULAR CIRCUIT SUPPORT THE VARIOUS VISUAL BEHAVIORS AND THE RELATIVE IMPORTANCE THEY HAVE FOR THE ANIMAL. NOW THE PROBLEM OF COURSE IS WE DON'T HAVE A QUANTIFICATION OF VISUAL BEHAVIOR. THAT'S PART OF THE REASON WHY IT'S HARD 3 ON THE OTHER HAND YOU MIGHT ALSO ARGUE THAT IN THE EARLY VISUAL SYSTEM AND OFTEN THE EARLY SENSORY SYSTEM, INDIVIDUAL CELLS DOAJT REALLY HAVE ANY DIRECT SENSE OR ABILITY TO TELL YOU WHAT'S MOST IMPORTANT FOR BEHAVIOR. IN OTHER WORDS IF I'VE GOT A SINGLE RETINAL GANGLION CELL THE DIFFERENCE BETWEEN A TIGER AND MY WIFE. THEY ARE ALL LITTLE DARK SPOTS. THAT ANALYSIS NEEDS TO BE DONE IN TERMS OF LOCAL ELEMENTS OF FOREIGN AND SHAPE THINKS THAT DARK SPOTS, LIGHT SPOTS LOCOMOTION THERE IS MUCH OF A MORE A QUESTION HOW FORRIVE THESE LITTLE FEATURES IN THE WORLD ARE ABOUT VISUAL THING THAN A BROADER MEANING IF YOU'D LIKE OF THE VISUAL INPUT. IT DOESN'T HAVE TO MAKE SENSE IN THE SENSORY PERIPHERY TO OPTIMIZE INFORMATION. THE SECOND QUESTION THAT ONCE YOU ASKED ABOUT THIS WELL THAT WAS NICE OF THIS WORK BUT REALLY SHOULDN'T FORMS AND FUNCTIONS IN THE DIVERSITY TYPES OF CELLS AND CIRCUITS NOT BE DETERMINED BY THIS KIND OF ARGUMENT OF OPTIMIZATION OR SHOULD IT BE DETERMINED BY THE EVOLUTIONARY LINEAGE, THERE'S A PRIMORDIAL CELLS, THERE ARE DIFFERENT CELLS THAT'S HAVE DEVELOPED AND SO ON. IT'S TRUE, THE DEFAULT EXPLANATION FOR ANY PHENOMENA OF STRUCTURE IN BIOLOGY IS JUST A PRODUCT OF THE HISTORY OF THE EVOLUTIONARY HISTORY OF THE ANIMAL. TO ALWAYS CONSIDER THAT IS PERHAPS A DEFAULT OF THE NATURE BUT WITHIN ITS LINEAGE WHICH IS CONSTRAINED IN THE HISTORY SORT OF BETTER ADAPTED FORMS AND FUNCTIONS ARE SELECTED EVERY TIME. HE LOOKS IS NOT SELECTION FOR THE MUCH WORSE IT'S ELECTION FOR THE LIGHTLY BETTER AND VERY LUCKY. SLOWLY OVER TIME IT IS TRUE THE FUNCTIONS ARE SUPPOSED TO BE ADOPTED TO WHATEVER THEY'RE SUPPOSED TO DO. THAT'S BASICALLY THE IDEA THAT'S BEING USED HERE. AND FINALLY, ANOTHER OBVIOUS OBJECTION IS WHAT I DID WAS I TRIED TO DERIVE THESE SORT OF OPTIMAL RETINA GIVEN SOME CONSTRAINTS AND COMPARED THAT TO THE STRUCTURE OF THE RETINA. LIFE IS A WORK IN PROGRESS. WHY SHOULD -- THE ANSWER IS IT SHOULDN'T NECESSARILIMENT I MEAN ONCE YOU TAKE THE OPTIMAL ANSWER. I'LL GIVE ANOTHER EXAMPLE OF THAT IN A LITTLE WHILE BUT IT IS PERHAPS A GUIDE TO THE PRINCIPLES UNDERLYING SACRED ORGANIZATIONS. AND TO THE CONSTRAINTS AT AFFECT THE ORGANIZATION OF CIRCUITS. YOU TAKE IT AS A GUIDE RATHER THAN INSISTING THE CIRCUITS REACH WHATEVER OPTIMAL. OWE FINALLY IN THINKING ABOUT THIS KIND OF APPROACH, I LIKE TO REMEMBER SOMETHING I READ IN CIVIC BOOKS ONE AND THIS IS PROFESSOR -- IN NATURE BUT THOSE WHO LOOK FOR IT HAVE A BETTER CHANCE OF FINDING IT. THAT'S THE ATTITUDE WE SHOULD TAKE. YOU SHOULD LOOK FOR IT AND IF THE ISN'T THERE IT ISN'T THERE BUT IF IT'S THERE YOU'LL FIND IT. SO TAKE A LOOK. THIS IS IN THE PERIPHERY AND IN THE RETINA AND I GAVE YOU ONE EXAMPLE IN RETINA. MY LAB HAS BEEN INVOLVED IN LOOKING AT MANY EXAMPLES OF THIS KIND OF THE EARLY VISUAL SYSTEM. SO WE TALKED ABOUT THE DISTRIBUTION OF PHOTO RECEPTORS, SHAPE OF GANGLION CELLS RECEPTOR FEELS, THE DISTRIBUTION OF INFORMATION OF THE OPTIC NERVE. THE ORGANIZATION OF RETINAL GANGLION AND MANY SUCH PROPERTIES OF THE RETINA, THE STRUCTURAL PROPERTIES OF THE ORGANIZATION OF THE RETINA CAN CLEARLY BE UNDERSTOOD IN THE KIND OF LANGUAGE KNIFE JUST DESCRIBED TO YOU. IN FACT WE'VE PURSUED THIS KIND OF IDEA DEEPER INTO CORTEX AND IT APPEAR THAT SIMILAR IDEAS OF ADAPTATION OF CIRCUITS TO THE DISTRIBUTION OF INFORMATION OF THE WORLD IS ALSO HELPFUL TO UNDERSTAND PERCEPTUAL -- OF VISUAL TEXTURES. SO FROM THIS POINT OF VIEW I WOULD SAY THAT THE CHALLENGE I WOULD POSE MYSELF OURSELVES IS TO ASK WHETHER THE RELATIVE PROPORTION OF THE DIFFERENT ELEMENTS OF THE VISUAL REPERTOIRE CAN BE UNDERSTOOD IN TERMS OF THE VALUE THAT THEY HAVE FOR VISION. SO IN VISION, THIS IS HARD TO DO BECAUSE THE EARLY VISUAL SYSTEM IS NOT PLASTIC BUT AS I'LL DISCUSS LATER IN THE OLFACTION, THIS KIND OF ATTITUDE IS MUCH EASIER TO EXPLORE EXPERIMENTALLY AND WE'LL COME TO THAT IN A MINUTE. NEXT I WANT TO GIVE YOU SECOND EXAMPLE OF THIS KIND OF APPROACH WHERE INSTEAD OF CONSIDERING A SENSORY EXAMPLE I WANT TO CONSIDER A COGNITIVE EXAMPLE. I WANT TO SUPPORT YOUR SENSE OF PLACE. I WANT TO ARGUE THAT USING A SIMILAR APPROACH WHERE WE ASK THAT THE CIRCUIT SUPPORTS A FUNCTION OF BEHAVIOR AND DO SO AT LOWER COSTS, WE WILL BE ABLE TO EXPLAIN OTHERWISE VERY SURPRISING ASPECTS OF THE ORGANIZATION OF THESE GOOD CELL SYSTEMS. SO WHAT IS THE SENSE OF PLACE? SO WHAT IS PLACE FIRST OF ALL. HOW DO WE KNOW WHERE YOU ARE. WE THINK OF PLACE IS SOMETHING VERY CONCRETE, YOU ARE THERE IT'S A PLACE. INSIDE YOUR HEAD OR HERE THERE IS SOME ABSTRACT OF NEURON FIRING AND THESE PATTERNS AS FAR AS PERSONAL NAVIGATION GOES MAINTAIN A MAP OF YOUR LOCATION OF THE WORLD. SO OKAY, WE'D LIKE TO UNDERSTAND SOMETHING ABOUT THAT. BUT AS IN THE CASE OF VISION, ABOUT THE ON AND ASSIST TELL, I WOULD LIKE TO START ASKING BEFORE I LOOK AT THE ACTUAL DATA, HOW WOULD YOU ORGANIZE A NEURAL SYSTEM TO REPRESENT STATES. SO IMAGINE HERE THAT YOU HAVE AN EIGHT METER LINEAR TRACK AND EIGHT METER LINEAR TRACK LET'S SUPPOSE YOU NEED A RESOLUTION OF ONE METER TO SUPPORT BEHAVIOR. SO YOU NEED TO KNOW WHERE YOU ARE WITH ONE METER RESOLUTION. BUT TO ACHIEVE ONE METER RESOLUTION, ONE THING YOU COULD DO IS YOU COULD HAVE EIGHT CELLS PLACE CELLS IF YOU LIKE BUT EACH FIRES WHEN YOU ARE IN THAT LOCATION. SO FOR EXAMPLE IF YOU CELL NOAM THREE AND THIS IS A MOUSE IT WOULD GO BBRRRR AND KEEP QUIET. THAT'S A PLACE CELL REPRESENTATION OF WHERE YOU ARE. A LITTLE BIT LIKE IN THE RETINA, THE RETINA MAP AND IF YOU HAVE A GANGLION CELL HERE IT REPORTS THAT LIFE IS THERE. GANGLION CELLS THERE IT REPORTS THE LIGHT IS THERE. IT'S THAT KIND OF REPRESENTATION, LOCAL REPRESENTATION OF SPACE. SO SOMETHING LIKE THIS OF COURSE MAY HAPPEN TO THE HIPPOCAMPUS BUT IT'S MORE COMPLICATED THE PLACE IS VERY FRAGILE IN FORM SO I'M NOT GOING TO TALK ABOUT THIS FURTHER. THERE ARE A ANOTHER REPRESENTATION OF SPACE WHICH A MATHEMATICIAN OR COMPUTER SCIENCE MIGHT SUPPORT. BUT IN THIS REPRESENTATION WHAT YOU MIGHT DO IS THE FIRST SCALE, THE WHOLE ROOM AND WHAT YOU DO IS YOU COMMIT ONE CELL OF FIRING IF YOU'RE IN THE LEFT HALF OF THE ROOM AND ANOTHER CELL TO FIRE IF YOU'RE IN THE RIGHT HALF OF THE ROOM. THEN YOU GO TO A SECOND SCALE AND HERE YOU COMMIT CELL ONE TO ANOTHER CELL TO FIRE IF YOU'RE THE LEFT HALF OF THE LEFT HALF OF THE ROOM OR IF YOU'RE IN THE LEFT HALF OF THE RIGHT HALF OF THE ROOM. YOU SUBDIVIDE BY TWO. LEFT HALF HERE. THERE'S A THIRD SCALE WHERE YOU SUBDIVIDE AGAIN AND NOW YOU HAVE THESE CELLS THAT ARE PREFIRING CELL HERE AND HERE AND HERE AND HERE. BUT IN THIS REPRESENTATION OF SPACE, THE ANIMAL IS HERE, THEN YOU HAVE ONE FIRING AT SCALE ONE, CELL ONE FIRING AT SCALE TWO AND CELL TWO FIRING AT SCALE TWO, OKAY. THIS IS A REPRESENTATION OF SPACE TWO SO YOU MIGHT SAY THIS ANIMAL'S LOCATION IS ZERO ZERO ONE. BINARY REPRESENTATION OF SPACE AND IT'S EXACTLY THE KIND OF THING THAT'S USED INSIDE A COMPUTER. I WOULD LIKE TO POINT OUT THIS REQUIRED ONLY SIX CELLS TO REPRESENT LOCATION WITH ONE METER RESOLUTION. IT'S A BIT MORE EFFICIENT IN THE USE OF NEURAL UNITS, IF YOU'D LIKE. OKAY. SO WHAT I'M GOING TO TELL YOU IS THAT I'M GOING TO SUGGEST TO YOU OR I'M GOING TO TRY TO ARGUE THAT THE GRID CELL REPRESENTATION OF SPACE AND CORTEX IS BASICALLY THIS THOUGHT OF BASE END NUMBER SYSTEM. AND I'M GOING TO TRY TO ARGUE THAT TO YOU AND I'LL GIVE YOU EVIDENCE. FIRST OF ALL WHAT'S THE PHENOMENOLOGY -- CELLS THAT ARE GOOD CELLS WHICH RESPOND WHEN AN ANIMAL IS PHYSICALLY -- THESE GRIDS FORM 30 MINUTES OF ENCOUNTER -- THE CELLS HAVE RANDOM VARYING OFFSETS. THIS IS ONE GRID AND TAKEN A HORIZONTAL FLIGHT BUT THEM. THERE WILL BE A GREEN CELL THAT FIRES THERE AND THERE AND A BLUE CELL THAT FIRES THERE AND THERE. WHAT'S MORE THE GRIDS INCREASE IN SIZE ALONG THE DORSAL VENTRAL AXIS OF THE CORTEX, RIGHT. IF YOU LOOK YOU HAVE ONE SCALE THAT IS WIDE IN FACT AND THEN NEARBY THERE WILL BE ANOTHER SCALE OF ORGANIZATION OF THE MODULE OF ORGANIZATION FOR THE GROUP THAT'S NARROW AND SKINNY. NOW WE HAVE A PHENOTYPE OUT OF IT LIKE THIS. AND LOOK THIS PICTURE LOOKS SIMILAR TO THE EARLY PICTURE OF A DRAWING OF SOMETHING LIKE A BINARY DIVISION. SO THIS SUGGESTS THAT THE GOOD CELL SYSTEM IS SIGNIFY LIKE A TWO DIMENSIONAL FUZZY NEURAL VERSION OF SOME BASE END NUMBER SYSTEM WHATEVER END MAY BE. BASE TWO WILL BE BINARY. SO WE'RE GOING TO INVESTIGATE THAT POINT. SO THE WAY IN WHICH YOU ANALYZE THIS KIND OF HYPOTHESES IS YOU HAVE TO CONSTRUCT A MODEL OF THE SYSTEM BY ABSTRACTING A WAY WHAT YOU CONSIDER TO BE THE RIGHT FEATUR WHAT YOU TALK ABOUT. HERE IS A DORSAL VENTRAL AXIS OF THE GOOD SYSTEM, RIGHT. AND HERE, IF YOU LOOK AT CELLS IN THE DORSAL AREA YOU FIND THAT THEY FIRE ON GRIDS THAT ARE NARROW AND SKINNY. AND AS YOU GO TO THE DORSAL VENTRAL AREA YOU FIND CELLS THAT FIRE ON GRIDS THAT ARE WIDE. SO WE NEED TO -- AS FOLLOWS TAKES THE DISTANCE BETWEEN NEIGHBORING CENTERS LAND TO EYE TO BE THE SCALE OF THE GRID. I'M GOING TO ASSUME THAT THE LARGEST GRID ARE MATCHED TO THE SCALE OF ENVIRONMENT ON WHICH OF THE LOCAL ENVIRONMENT WHERE I NEED TO MAKE A SINGLE GRID IN ORDER TO BE ABLE TO NAVIGATE. THEN I'LL TAKE YOU TO THE WIDTH OF THE FIRING FIELD. AFTER YOU HAVE THE NOISE THESE THINGS ARE BAD SHAPE AND THE ALLIES ARE THE SIZE OF THAT. WHAT ARE THE PARAMETERS OF THESE GRIDS THE ONES REPORTED IN THE EXPERIMENT. ONE PARAMETER IS THE RATIO OF ADJACENT GRID PERIOD. FOR EXAMPLE, THIS ONE. THERE'S A BUNCH OF RATIOS. YOU ALSO WISH TO -- THE RESOLUTION OF THE GRID. HERE'S A ROOM. HOW MANY SEPARATE PIECES CAN YOU RESOLVE IN THE ROOM. ALL RIGHT. NOW THE WAY TO -- YOU TAKE THE LARGEST SIZE SCALE AND YOU DIVIDE IT BY THE SMALLER SCALE AND THAT WILL GIVE YOU A MEASURE OF HOW MANY PIECES YOU CAN DIVIDE THE ROOM INTO IT. BY THE WAY, THIS NUMBER IS ALSO PRODUCT OF ALL OF THESE RATIOS OF ADJACENT SYSTEMS. NOW, ACCORDING TO ANOTHER PARAMETER THAT'S IMPORTANT HERE IS A NUMBER OF GOOD CELLS YOU NEED TO MAINTAIN THE BEHAVIORALLY REQUIRED RESOLUTION. SO FOR EXAMPLE, WHAT SHOULD THIS NUMBER BE. IF I GIVE YOU ONE OF THESE GRIDS YOU NEED TO HAVE MANY GRIDS AT EACH SCALE IN ORDER TO COVER SPACE BECAUSE YOU NEED MANY SPACIAL PHASES. SO YOU COUNT UP HOW MANY GRIDS YOU NEED IN ORDER TO COVER, SO HOW MANY OF THESE CELLS YOU NEED TO COVER SPACE SO YOU'LL FIND THE NUMBER OF CELLS IS GOING TO BE PROPORTIONAL TO THE PERIOD DIVIDED BY THE WIDTH OF EACH OF THESE FIRING. AND YOU'VE GOT TO SUM UP OVER EACH OF THESE DIFFERENT WIDTH MODULES. OVERALL WHAT'S THE COST OF OPERATING A SYSTEM LIKE THIS WHO REPRESENTS SPACE. WELL, IT'S A NATURAL GUESS WOULD BE THIS COST IS SOME INCREASING FUNCTION OF THE NUMBER OF NEURONS. I'M TAKING THE SAME SORT OF ATTITUDE WE WERE TAKING IN THE RETINAL CASE WHERE YOU ASK TO SORT OF INSTRUCT A SYSTEM THAT PROVIDES THE BEHAVIORALLY NECESSARY RESOLUTION OF SOME KIND OF MINIMUM COST, OR YOU FIX THE COST AND YOU MAXIMIZE THE BENEFIT. YOU CAN DO THAT, YOU CAN FIX THE NUMBER OF GOOD CELLS YOU HAVE AVAILABLE TO YOU AND ASK THAT THE MAXIMIZES RESOLUTION. IT'S THE SAME ATTITUDE BUT A VERY DIFFERENT KIND OF NEURAL CIRCUIT. GOOD. NOW WE CAN ASK WELL FIND THE PARAMETER THE RELEVANT PARAMETER HERE IS THE RATIO BETWEEN ADJACENT SCALES. THESE RATIOS. THOSE RATIOS CONTROL HOW QUICKLY THE GRID GOES PRO THE BIG WIDE GRID TO NARROW GRID. YOU CAN ASK WHAT RATIO OF THE SCALES MINIMIZES THE NUMBER OF CELLS REQUIRED TO ACHIEVE A GIVEN SPACIAL RESOLUTION. THAT'S VENTION LIKE THE QUESTION I WAS POSING IN THE RETINAL CASE. WHAT IS THE STRUCTURE OF THE RETINAL ARRAY NECESSARY TO MAXIMIZE INFORMATION. SO HERE IS WHAT A MODEL WILL LOOK LIKE. HERE IS THE STYLIZED GRIP SYSTEM WHERE YOU HAVE THE RED CELL FIRING HERE OR BLUE CELL FIRING HERE IN THIS SCALE THE RED CELL FIRES HERE AND HERE AND SO ON. AND IT FORMED A REALISTIC DESCRIPTION. THERE'S SOME KIND OF BUMP PEA FIRING FIELD. IN THIS SYSTEM JUST LIKE WHEN WE'RE DISCUSSING THE ORGANIZATION OF THE RETINA, THERE WAS THIS, ONE OF THE BASIC TRADE OFFS INVOLVED RESOLUTION AND REDUNDANCY. REMEMBER IF YOU ARE PUTTING TOO MANY OFF CELLS THAT ARE BEGINNING TO OVERLAP AND THEREFORE BECOME REDUNDANT AND WE HAVE TO PAY FOR SOMETHING ELSE. THERE ARE SIMILAR ISSUES AND TRADE OFFS. SO IMAGINE YOU HAVE THIS GOOD CELL, SUPPOSE THE ANIMAL IS HERE AND SO THIS GOOD CELL FIRES. NOW IMAGINE THE NEXT SCALE OF ORGANIZATION. LET'S SUPPOSE THE PERIOD OF WHAT CONTRACTED A LOT. SO THIS CELL FIRES WHICH HAS THIS PERIODIC FIRING SYSTEM. SEA SO THIS CELL FIRES AND THIS CELL FIRES AND YOU DON'T KNOW WHERE THE ANIMAL IS. SO YOU KNOW THE ANIMAL IS IN THIS REGION. IF THIS CELL FIRES THE ANIMAL MAY BE HERE OR IT MAY BE HERE. WE DON'T KNOW. ON THE OTHER HAND IT'S THE GRID THAT DOES NOT CONTRACT SO MUCH SO THE NEXT SCARE APPEARS BIGGER THAN YOU KNOW FOR SURE THAT THE ANIMAL IS HERE BECAUSE OF COURSE THE SECOND FIRING IS OUTSIDE THE RANGE OF THIS OVER THERE. SO YOU SEE WHAT'S GOING TO HAPPEN THERE'S GOING TO BE A TRADE YEAH WHERE IF YOU CONTRACT THE GRID QUICKLY YOU GET A LOT OF RESOLUTION QUICKLY. YOU GET GOOD RESOLUTION SHRINKING THE GRID FROM SCALE TO SCALE TO SCALE. THE OTHER HAND IF YOU SHEIKH IT TOO QUICKLY YOU START GETTING THIS KIND OF BIGGITY AS TO WHERE YOU ARE MUCH THERE'S GOING TO BE A TRADE OFF WHICH BASICALLY IMPOSES THE PERIOD OF THE GRID OF THE NEXT SCALE DOWN SHOULD BE BIGGER THAN THE WIDTH OF THE FIRING FIELD AT ONE SCALE ABOVE. THAT'S THE CONSTRAINT THAT WAS DEVELOPED IN ANY MODEL OF THIS. WE'RE GOING TO CONSIDER TOO KINDS OF DECODING STRATEGY SO WE CONSIDER HERE WINNER TAKE ALL STRATEGY WHERE YOU LOOK AT THE MOST ACTIVE CELL. ANOTHER STRATEGY YOU COULD USE IS OPTIMAL PROBABILISTIC RECORDING. ANY TIME AS A THEORIST WHEN YOU CONSIDER HOW IS THE NEURAL CIRCUIT ENCODING INFORMATION ONE QUESTION YOU ASK IS WHAT IS THE DECODER DOING, WHAT SORT OF DECODING DOES THE BRAIN DO. VERY OFTEN YOU DON'T KNOW WHAT THE DECODER IS DOING MANY IT'S IMPORTANT TO CONSIDER DIFFERENT ALTERNATIVE DECODERS TO ASK WHAT DIFFERENT MODES OR IN THIS CASE PLACE INFORMATION WHAT CONSEQUENCES THEY WOULD HAVE FOR THE PREDICTIVE ORGANIZATION. SO YOU REACH ALL OF THESE PICTURES I DREW FOR YOU WERE IN ONE DIMENSION. YOU CAN DO THIS IN TWO DIMENSIONS AND YOU GET VERY SIMILAR CONSTRAINTS BETWEEN AMBIGUITY AND THE SCALING OF THE GRID. THE ONE DIFFERENCE IS NOW -- ON WHICH YOU CAN PUT THE GRID. THERE CAN BE MANY DIFFERENT ONES TO. OKAY. I WILL SHOW YOU RESULTS. LET'S OPTIMI THIS. AGAIN IN THIS CASE I'M ACTUALLY SHOWING YOU THE DETAILS OF THE CALCULATION WHEREAS IN THE RETINA CASE I DIDN'T. IN THIS CASE ONCE AGAIN HERE IS A GOOD SYSTEM. INCREASING IN SIZE ALONG THE DORSAL VENTRAL AXIS. IT'S -- RATIOS OF PERIODS OF ADJACENT MODEL. THE RESOLUTION YOU HAVE TO MAINTAIN BECAUSE THAT DICTATES BEHAVIOR, THE SMALLER SCALE BY THE LARGER SCALE. THE NUMBER OF CELL IS PROPORTIONAL TO THE WHICH IS THE PERIOD DIVIDED BY THE SIZE. AND OF COURSE YOU CAN ASSUME THAT THIS PERIOD IS BIGGER THAN THIS PERIOD BECAUSE OF THIS PERIOD AND MY GOAL IS THAT THE MATHEMATICAL GOAL IS TO MINIMIZE THE NUMBER OF CELLS WHILE KEEPING THE RESOLUTION FIXED. NOW WE ALREADY SAID THAT UNAMBIGUOUS DECODING THERE'S A CONSTRAINT THAT DEVELOPED. AND THE CONSTRAINT IS THE PERIOD OF THE NEXT SCALE UP MUST BE BIGGER THAN THE FIELD, THE GOOD FIELD WITH A PARTICULAR SCALE. YES. SO THAT TRANSLATES INTO A CONSTRAINT BUT THE PERIOD DIVIDED BY THE WIDTH OF THE GOOD FIELD MUST EXCEED THESE RATIOS. THE NUMBER OF NEURONS IS PROPORTIONAL TO SOME OF THESE RATIOS. IF YOU WISH TO MAKE THIS AS SMALL AS POSSIBLE WHAT YOU SHOULD DO IS YOU SHOULD SET THIS NUMBER -- THESE RATIOS TO BE EQUAL TO THE SCALE RATIO THAT'S THE WAY TO MINIMIZE QUANTITY. LET'S DO IT. AND IF WE DO THAT, HERE'S THE PROBLEM YOU HAVE TO SOLVE AT THE END OF THE DAY. HERE ARE THESE PARAMETERS WHICH ARE A RATIO. YOU HAVE TO KEEP THIS RESOLUTION. IT'S A PRODUCT OF THESE NUMBER SIX AND WHILE MINIMIZING THE NUMBER OF NEURONS THIS IS THE SUM OF THESE NUMBER. A MATHEMATICAL NUMBER TO BE SOLVED. I'M SHOWING YOU THESE DETAILS BECAUSE I THINK IT'S UNCONVENTIONAL FOR THESE SEMINAR SERIES BASICALLY EMPHASIZE THIS IS NOT, THIS IS COMPLETELY CONCRETE. THIS IS NOT TO ABSTRACT SLIPPING AROUND AND WONDERING HOW TO SOLVE THE PROBLEM. THERE'S AN EXPERIMENTAL DATA FOR ALL OF THESE THINGS. YOU CAN WRITE DOWN THE MODEL AND IT ISN'T EVEN THAT HARD. YOU CAN JUST DO IT ON A PIECE OF PAPER. I'VE DONE EVERYTHING NECESSARY HERE. THE WHOLE TRANSLATION, RIGHT. METHODS AND EVERYTHING. SO NOW YOU CAN DO THIS PROBLEM. I TAKE THE LITTLE WORK AND HERE'S WHAT YOU FIND. THE FIND THAT YOU PREDICT THAT ALL OF THESE RATIOS BETWEEN THE PERIOD OF ADJACENT SCALES ARE CONSTANT IN AN OPTIMAL GOOD SYSTEM. AND EQUAL TO A NUMBER LIKE A BASE R NUMBER SYSTEM. THE SECOND PREDICTION THIS THEORY MAKES IS THIS RATIO R THE GOING TO BE THIS DEEP ROOT OF THE TRANSDENTAL NUMBER E IN D DIMENSION. SO IN TWO DIMENSIONS IS THE SQUARE ROOT OF E. MY STUDENTS CAME AND TOLD ME THIS AND I SAID VERY PRETTY REALLY NICE AND CERTAINLY IRRELEVANT BECAUSE THERE'S NOTHING IN BIOLOGY THAT IS THAT ELEGANT. WAIT AND SEE. I'LL SHOW YOU THE DATA IN A MINUTE. ANYWAY THERE'S A THIRD PREDICTION OF THE RATIO FOR THE PERIOD. NOW THIS WAS ONE DECODING MODEL WHICH WAS A WINNER TAKE ALL KIND OF APPROACH. BUT REALLY MANY PEOPLE THINK THE BRAIN DOES MUCH MORE SOPHISTICATED DECODING. PEOPLE SUGGEST THAT THE BRAIN CAN DO OPTIMAL PROBABILISTIC DECODING BUT REALLY WITH A YOU DO IS GIVEN THE NEURAL FIRING SOMEHOW YOU CONSTRUCT THIS ON YOUR HEAD THE PROBABILITY DISTRIBUTION IF YOU'D LIKE OVER WHATEVER YOU WANT TO DO. IN THIS CASE WHERE YOU ARE AND EVALUATE THE LIKELIHOOD AND PICK THE LOCATION WHERE YOU'RE MOST LIKELY TO BE. FINE IF THAT'S THE WAY THE BRAIN DOES IT WHAT HAPPENS IS THE NEURAL FIRING OF ANY GIVEN NEUJ IN ANY GIVEN PERIOD YOU'LL FIND A PROBABILITY DISTRIBUTION OF LOCATION THAT'S PERIODIC. LIKE HERE'S THE PERIODIC DISTRIBUTION. AND WHY IS THAT? THAT'S BECAUSE THE NEURAL FIRING WAS PERIODIC. YOU FIND SOME PERIODIC PROBABILITY OF WHERE YOU WERE. NOW, IF YOU COMBINE THE FIRING IN DIFFERENT NEURAL MODULES, YOU'D FIND ONE MODULE IS A BLACK DISTRIBUTION, ANOTHER MODEL IS GREEN DISTRIBUTION. IF YOU WERE DOING BECAUSE IT'S A FINER GRID AND YOU WILL BE TOLD THAT SOMEBODY DOING PROBABLYISTIC DECODING PERHAPS THE BRAIN BUT YOU SHOULD MULTIPLY THESE TWO PROBABILITIES TOGETHER TO GET THE OVERALL DISTRIBUTION WHERE YOU ARE. AND LOOK THIS IS WHERE IT'S FURTHER LOCALIZED. I'M NOT COMMITTING TO THE BRAIN DOES OPTIMAL DECODING. I'LL CONSIDER THAT AS AN OPTION WHICH IS AT THE OTHER EXTREME LIMITS OF DECODING COMPLEXITY OF THE WINNER TAKE ALL AND WE'LL COMPARE THE ANSWERS. ALTERNATIVELY YOU MIGHT IMAGINE A GRID SYSTEM WHERE YOU HAVE ONE SCALE WHERE YOU GET THIS BLACK DISTRIBUTION TO WHERE YOU ARE. THAT'S THE LIKELIHOOD WHERE YOU THE NEXT SCALE IS MUCH NARROWER. NOW YOU CAN MULTIPLY THESE DISTRIBUTIONS TO GET AROUND THE AMBIGUITY. THAT'S THE SAME CONSTRAINT THAT I WAS DESCRIBING EARLIER BUT IF THE GRID SYSTEM CONTRACTS TOO QUICKLY, YOUR LOCATION WILL BE AMBIGUOUS. THERE WILL BE SOME CONSTRAINT THAT PREVENTS THIS AMBIGUITY 23R DEVELOPING. EVEN PROBABILISTIC DECODING. YOU CAN PUT ALL THESE FACTS TOGETHER AND OPTIMIZE AND HERE ARE THE ANSWERS IN ONE OF THE DIMENSIONS. SO YOU FIND THE BLUE LINE IS THE WINNER TAKE ALL DECODING WHAT I WAS DESCRIBING EARLY AND THIS IS HERE IS THE PROBABLYISTIC DOUGH CODING AND BOTH MODELS PREDICT A RATIO THAT BELIES THE SAME SHALLOW BASIS. THIS IS THE KIND OF A UNIVERSAL ANSWER. SO THE WAY IN WHICH THAT SHOULD BE DONE IS YOU CONSTRUCT DIFFERENT MODELS, DIFFERENT MODELS OF DECODING OR WHATEVER ELSE YOU'RE DOING. AND THEN TO DO THIS WELL, YOU EITHER FIND THAT THE TWO MODELS MAKE VERY DIFFERENT PREDICTIONS. IF THE TWO MODELS MAKE VERY DIFFERENT PREDICTIONS, THEN YOU CAN USE EXPERIMENTAL DATA TO SEPARATE WHICH OF THESE MODELS IS MORE LIKELY. IF YOU MAKE THE SAME PREDICTION YOU'RE LUCKY BECAUSE IT MEANS THAT THESE PINGS YOU WERE SURVIVING FOLLOWED SOME DEEPER RULE THAT ANY REASONABLE MAWJ MODEL IS GOING TO EMBODY AND WILL BE UNIVERSAL ANDED IN OF ANY DETAIL OF THE MODEL YOU CREATED. AND WE'RE IN AN UNFORTUNATE SITUATION. ANOTHER THING I WANT TO POINT OUT IS PEOPLE DOING THIS KIND OF ANALYSIS WILL TELL YOU WHAT THE OPTIMAL ANSWER THIS LITTLE PING WAS. THAT'S A VERY BAD THING TO DO EVEN FOR A THEORIST. HERE'S WHY. THIS IS A FAIRLY SHALLOW MINIMUM. IT'S RUINED IN BIOLOGY THAT IF SOMETHING IS VERY IMPORTANT TO REGULATE, THEN SYSTEMS WILL INVEST THE MECHANISMS NECESSARY REGULATE IT. BUT IF IT'S NOT NECESSARY TO REGULATE ANYTHING SO CAREFULLY THAN THOSE SYSTEMS WON'T BE THERE. WHAT YOU SHOULD DO IS HERE EXPECT THERE SHOULD BE SOME VARIABILITY OF THE RATIO LIKE THIS. THERE'S SOME OVER WHICH DEVIATION FROM THE OPTIMAL DOESN'T MAKE A WHOLE HELL OF A LOT OF DIFFERENCE. THERE'SRANGE. THAT'S ALL ABOUT THE IMMEDIATE LOGICAL POINT. HERE'S THE ANSWER. THE WINNER TAKES ALL SERIES. -- AND THERE'S THE DATA, THIS IS DATA OF THE -- ONLY 12 CELLS. I'M NOT SURE HOW MUCH YOU SHOULD BELIEVE THAT. BUT HERE'S DATA FROM LAST YEAR. THAT'S HUNDREDS AND HUNDREDS OF CELLS. THIS IS REALLY AMAZING TO ME ANYWAY THAT SUCH AN ABSTRACT IDEA. YOU SHOULD CONSTRUCT A GOOD SYSTEM THAT MINIMIZES THE NUMBER OF NEURONS TO DESCRIBE A GIVEN RESOLUTION WOULD WIPED UP PREDICTING SOMETHING LIKE THE RATIO, THE RATIO OF ADJACENT SCALES IN THE SYSTEM ACROSS MANY MANY SCALES. HE FIND THAT QUITE REMARKABLE AND AS A JUSTIFICATION OF THE APPROACH. INDEED HERE'S THE DATA BEGIN. LIKE WIDE THE THEORY PREDICTS TRYING THE GRID AND THE INTERESTING THING IS THE THEORY ACTUALLY PREDICTED ON THE RATIO OF THE GOOD PEERED OF THE GOOD FIELD WIDTH. THAT'S THIS RED LINE. AND THIS IS -- KNOCK OUT MICE -- IN PARTICULAR TO MAKE THE PREDICTIONS OF THE THREE DIMENSIONAL GRID WHICH MAY APPEAR IN BACK OF THIS MEASURE. I HOPE THIS ALL CONVINCES YOU. THIS IS AN EXAMPLE HIGHLY NOVIAL IN MY VIEW SOMETHING THAT'S DEFINITELY NOT A SYSTEM WHERE THIS KIND OF APPROACH WHERE YOU CONSIDER HOW SHOULD SOMETHING BE DONE BEST ALLOWS YOU TO UNDERSTAND THE ARCHITECTURE OF THE, OF THIS NEUROAL REPERTOIRE. I HAVE LIKE WHAT, FIVE MINUTES LEFT. IN THE LAST FIVE MINUTES I'M GOING TO CONCLUDE BY TALKING ABOUT APPLICATIONS AND OLFACTORY REPERTOIRES. THE REASON WHY I'M PARTICULARLY INTERESTED IN APPLYING THIS KIND OF LIKE THIS OLFACTION IS THE DISCONTENT THAT I PERSONALLY HAVE ABOUT APPLICATIONS OF THESE IDEAS THAT HAVE BEEN OTHERWISE VERY SUCCESSFUL IN VISION IS THE PETS HAVE BEEN SORT OF OBSERVATIONAL. THE THEORY MAKES THE PREDIGOXIN OF SOMETHING THAT'S FIXED, THE ANATOMY OR PHYSICIAN LAWLG OR A THING WHERE SOMEONE HAS MEASURED SOME STRUCTURE AND YOU UNDERSTAND THE FUNCTIONAL RATIONALE FOR THAT HAVE YOU BEEN DHOOR BY LOOKING AT A THEORY LIKE THIS. WHAT WOULD BE REALLY NICE IS TO BE ABLE TO MAKE PREDICTIONS, FORWARD PREDICTIONS FOR PLASTICITY. SO YOU CHANGE THE SENSORY ENVIRONMENT OR YOU CHANGE THE VALUE OF SENSING ONE THING VERSUS ANOTHER THING FOR PURE CONDITIONING. YOU CAN ACCURATELY -- EXPLAIN AND PREDICT THE REMODELING IT WOULD BE MUCH MORE SATISFACTORY. AND THE OLFACTORY SYSTEM IS OF COURSE A PLACE WHERE YOU CAN DO THAT. TO REMIND YOU, IN THE OLFACTORY SYSTEM, THE CHALLENGES FACED ARE MUCH HARDER THAN THE CHALLENGE FACED IN THE VISUAL FIELD. THE FACE OF SMELL, THE FACE OF VOLATILE MOLECULES IS HUGE. MAYBE A MILLION OF THEM, A HUNDRED THOUSAND, I DON'T KNOW. IT'S JUST A VAST NUMBER. AND COMPLEX ODORS CAN CONTAIN A HUNDRED OR MORE MOLECULES. THE MAINS THE ACTUAL SPACE OF MOLECULES IS HUGE TECHNICALLY CALL BEZILLIONS OF MOLECULES. THE ODOR ONLY CONTAINS A FEW OF THE MOLECULES. WHILE THE SPACE OF ODORS CAN EXPLORE ANY ONE OF THESE SORT OF HUNDRED THOUSAND MILLIONS, YOU CAN USE ANY OF THESE MOLECULES, ANY GIVEN ODOR IS SOMEHOW EXCEEDINGLY SPARSE. THAT'S BECAUSE IT ONLY CONTAINS A FEW OF THE MANY MOLECULES THAT COULD BE POSSIBLE. IF YOU ASK A MATHEMATICIAN, I SHOULD SAY ONE MORE THING. SO OF COURSE HOW DO YOU SENSE THESE ODORS. WELL IT BINDS TO OLFACTORY RE RECEPTOR IN THE NOSE. EXPLAIN WHERE THIS IS SUCH A DIFFICULT PROBLEM AND THEREFORE WORTHY OF OUR SOLVING. IMAGINE A MUCH SIMPLER THING. EMERGENCY YOU POINT AT THREE DIMENSION STATES AND CHALLENGE YOU TO REPRESENT THE POINTS OF THREE DIMENSIONAL STATES USING ONE COREDDAL X. CAN YOU DO IT? YES YOU CAN. THE WAY YOU DO IT UCONN KUK SOMETHING CALLED A SPACE FILL -- YOU FILL UP THE SPACE OF IT AND THEN YOU USE THE CURVE SAYING X REPRESENTS THESE POINTS. THAT'S A CRAZY REPRESENTATION BECAUSE WHAT HAPPENS IN THE POINTS IN THREE DIMENSION WILL GET MAPPED AT DISTANT POINTS. YOU CAN'T DO ANYTHING WITH IT. SO HERE'S THE CHALLENGE. YOU HAVE A BEZILLION DIMENSIONAL SPACE OF ORDERS SO YOU HAVE NUMBERS TO THIS. HOW DO YOU DO IT? YOU SEEM TO DO THIS FINE. HOW ARE WE DOING IT. SO YOU CAN ASK AGAIN FOLLOWING THE SAME KIND OF LOGIC OF MY EXAMPLE AND VISION. AND EXAMPLE I'M GOING TO FIRST ASK MYSELF WHAT WOULD A MATHEMATICIAN DO AND I'M GOING TO ASK MYSELF TO GUIDE ME IN MY THINKING ABOUT THE ACTUAL NEURAL CIRCUITRY. HERE'S WHAT A MATT MA TITION WOULD BE. THERE'S A DISCOVERY OF COMPRESSING SENSING THAT GOES LIKE THIS. IMAGINE THAT YOUR DAY TAU VECTOR IS GIANT LONG VECTOR VERY HIGH DIMENSIONAL BUT SPARSE. SO IT'S ARE HUGE BUT I PROMISE EVERY TIME YOU DRAW THE DATA IN THE WORLD ONLY THE ENTRIES ARE NON-VIEW. THIS IS A MOTOR SIGNAL. MATHEMATICS SAYS IF YOU TAKE THIS KIND OF THING AND YOU SENSE IT RANDOMLY NAMELY EVERY SENSOR MEASURES SOME COMPLETELY RANDOM COMBINATION OF ALL OF THESE DIFFERENT SIGNALS HERE AND THEN YOU CONSTRUCT A VERY SMALL MATRIX. THEN YOU'LL FIND THAT IT COMPLETELY RECOVERS THE ORIGINAL ODOR FROM THE SMALL VECTOR AND YOU DO IT IN THE WAY THAT THE SMALL VECTOR IN A PROXIMITY RELATION ARE MAINTAINED WITH VERY HIGH DIMENSIONS AND VERY SMALL DIMENSIONS. EXACTLY, EXACTLY THE KIND OF THING THAT WE WOULD HAVE WANTED. SO YOU COULD ASK THE QUESTION, WHETHER THIS APPLIES TO ODORS, ODORS SENSING. SO THE TYPICAL ODOR MAY BE CONTAINED MAIN A HUNDRED OR 200 MILLIONS OF POSSIBLE MOLECULES. THAT'S THE SAME PLOT I SHOWED YOU EARLIER. AND EACH SENSOR MEASURES A RANDOM COMBINATION OF CONCENTRATIONS, POSSIBLE MOLECULES THEN YOU ONLY NEED A HUNDRED SENSORS TO COMPLETELY REPRESENT ODOR STATE. SO THE QUESTION IS COULD HE LOOKS PRODUCE SUCH A SYSTEM. AND SO THIS IS WORK IN PROGRESS SO I'M JUST GOING TO GIVE YOU SUGGESTIONS. THIS IS A DATA FROM THE LAB OF JOHN CARLSON SHOWING THAT EACH ODOR RECEPTOR BINDS TO ODORS IN A VERY DIFFUSE WAY. IF THIS IS ODOR SPACE ODOR MOLECULE SPACE, THE RECEPTIVE FIELD OF INDIVIDUAL ODOR RECEPTORS IS MORE LIKE THIS THAN LIKE IN VISION WHERE YOU SMALL RECEPTOR FIELDS HOLDING UP -- AND THAT'S ALREADY KIND OF RANDOM OR KIND OF DIFFUSE ANYWAY. IF YOU LOOK AT THE ACTUAL CONNECTIVITY IN THE BRAIN, YOU KIND THAT THE RECEPTOR'S A DIFFERENT TYPE, GATHERED TOGETHER IN THE -- THERE ARE PAPERS SAYING THEY ARE RANDOM. IN ANY CASE HIGHLY DISORDERED. THAT'S HIGHLY SUGGESTED AND AT LEAST ONE REMOVED BEFORE YOU ACTUALLY DO AN ANALYSIS, IT WAS JUST THE BRAIN'S RANDOMIZED ORDER OF INFORMATION AS MATHEMATICIANS WOULD RECOMMEND. SO YOU CAN TEST THIS DIRECTLY AND BECAUSE OF LACK OF TIME I WON'T, YOU CAN ACTUALLY DIRECTLY TEST IT BY TAKING THE ODOR RESPONSES AND TRYING TO RECONSTRUCT MIXTURES FROM THE DATA AND IT SEEMS TO BE VERY, THE IDEA SEEMS TO PAN OUT IN A PRELIMINARY KIND OF WAY. ANOTHER THING YOU CAN DO IS CONSIDER OLFACTORY MODELING. HERE'S A PICTURE OF THIS WIDE RECEPTIVE FIELD, OLFACTORY RECEPTOR NEURON. AND IT'S KNOWN IN MANY EXPERIMENTS THAT THE OLFACTORY RECEPTOR POPULATION REMODELS THIS EXPERIENCE. SO OLFACTORY RECEPTORS ARE DYING CONSTANTLY DURING THE LIFE HAS BEEN REPLACED AND THE SERIES OF EXPERIMENTS HAVE NOW SHOWN DEPENDING ON YOUR EXPERIENCE OF THE WORLD AND YOUR EMOTIONAL EXPERIENCE OF THE WORLD NOT JUST SENSORY EXPERIENCE IT MAY BE AFTER YOU REMODEL THERE ARE MANY MORE OF THIS KIND OF NEURONS AND MANY FEWER OF THIS KIND OF NEURON OLFACTORY. BUT THIS CLEARLY SOME SORT OF INTRICATE DEPENDENCE OF THE POPULATION OF OLFACTORY RECEPTORS THAT YOU HAVE IN THE DISTRIBUTION OF RE RECEPTORS AND YOUR EXPERIENCE OF THE WORLD. WHAT'S MORE OF THIS REMODELING CAN BE TRANSMITTED INTO GERMLINE. YOU CAN PREDICT WHAT THE MODELING WILL DO AND HOW THE NUMBER RECEPTORS HAVE DIFFERENT KINDS OF CHANGES AND WE'RE DISCUSSING THE EXPERIMENTAL GROUP TO DIRECTLY TEST IT. CHANGING THE OLFACTORY ENVIRONMENT AND EXPERIENCE FEEL IN A SPECIFIC WAY AND ASKS HOW THIS REMODELING HAPPENS. SO WE'RE ALL FINISHED. FOR THE FUTURE THE BROAD QUESTION I'M INTERESTED IN WHAT ARE THE PRINCIPLES THAT UNDERLIE THE COMPUTATIONAL REPERTOIRES OF THE BRAIN AND I WANT TO NOW HOW THEY DEVELOP AND REMODEL WITH EXPERIENCE. THAT'S WHAT I WAS DESCRIBING LAST. AND I WANT TO UNDERSTAND HOW THE REPERTOIRES INTERACT ACROSS SCALES TO PRODUCE FLEX FUNCTIONS AND CHARACTERISTIC OF BEHAVIOR. THE ONLY INTERRION IS IN THE GOOD SYSTEM BUT I WANT TO THINK OF THIS IN A MUCH MORE GENERAL WAY GOING FROM THE SMALL NEURAL CIRCUITS. I'LL FINISH BY SAYING THESE IDEAS ARE NOT JUST RELEVANT TO THE ORGANIZATION OF CIRCUITS IN THE BRAIN. SO FOR EXAMPLE, THEY ARE RELEVANT IN UNDERSTANDING FUNCTIONAL REP -- REPERTOIRES ALL OVER THE PLACE. FOR EXAMPLE I CAN DRAW THE SAME CARTOON FOR AN IMMUNE SYSTEM THAT HERE'S THE LANDSCAPE OF PATHOGENS. EACH ANT BOTH HAS SOME RECEPTIVE FIELDS IF YOU'D LIKE IN THE SPACE OF PATHOGEN. THE PURPOSE OF THE ADAPTED IMMUNE SYSTEM IS TO COVER THE SPACE EFFECTIVELY. AND JUST LIKE EVERY OTHER EXAMPLE I GAVE, THERE ARE MANY OF THESE PATHOGENS HERE AND THESE PATHOGENS THERE ARE VERY VIRILOUS. THAT'S EXACTLY ANALOGOU TO THE KIND OF PROBLEM I LAID OUT INDEED -- TO MAKE SOME PREDECKIONS FOR WHAT A WELL ADAPTED IMMUNE SYSTEM WILL LOOK LIKE AND WHICH CAN BE TESTED AND SURVEYED. JUST TO SAY THIS IDEA IS MUCH BROADER IN THE SETTING THAT I'VE BEEN LAKE IT OUT IN. THERE'S SOME FUNCTION. YOU WANT TO DIS DISTRIBUTE IT ACROSS MANY FUNCTION ELEMENTS. THERE'S A WAY TO DO THAT. [APPLAUSE] >> I DIDN'T SAY THAT BUT THERE'S SOMETHING I SAID THAT MADE ME THINK I SAID THAT. WHAT WAS IT. NO. SO THAT WAS A SPECIFIC, THAT WAS A CASE OF BRAIN CIRCUITS REPRESENTING LOCATION IN TWO DIMENSIONAL. SO IF YOU ARE REPRESENTING, THE CIRCUITS REPRESENT LOCATION IN TWO DIMENSIONS THEN THERE'S A SCALING RELATIONSHIP THAT DEVELOPS. IF THE GOOD SYSTEM WAS REPRESENTING THRA DIMENSION IT'S A DIFFERENT RATIO THAT PREDICT. THE REASON I LIKE THAT, THAT'S A NUMBER. IT CAN BE MEASURED -- HE FOUND THERE ARE GOOD CELLS IN FLYING -- THEY ARE THREE DIMENSIONAL. BUT I WOULD LIKE TO CHECK. A GOOD THEORY IS FALSIFIABLE. THIS COULD BE WRONG. IF IT IS, IT IS. YES? IT DID. >> [INDISCERNIBLE]. SO I DON'T, SO OKAY THE NOISE AND GOOD CELLS, HOW WELL IS THAT CHARACTERIZED. THESE SOMETHING THAT'S KNOWN ABOUT IT AND IT'S NOT FULLY INDEPENDENT. THERE'S SOME CORRELATIONS BETWEEN THEM. WE CAN DEFINITELY PUT THOSE CORRELATIONS AND UNDERSTAND. WE CAN'T SO I CAN'T GIVE YOU A SPECIFIC ANSWER. BUT THE DIFFERENT GROUP MODULES ARE NOT HIGHLY CORRELATE IN ANY CASE. THERE IS GOING TO BE SOME CORRELATION BECAUSE GOOD CELLS ARE KNOWN TO FORM DYNAMICALLY OR NON-KNOWN. THEY ARE TO FORM DYNAMICALLY TO ATTRACT A MECHANISM AND THEREFORE THIS INTERNEURON CIRCUITRY WILL AFFECT IT. WITH YOU THESE ARE FAIRLY ROBUST SIGNALING SYSTEMS AND THERE'S LOTS OF CELLS. ANOT WAY OF PUTTING THIS. THERE ARE LOTS OF CELLS IN EACH MODULE. YOU'RE INTEGRATING OVER MANY CELLS AT THE SAME TIME. SO IT DEPENDS ON THE STRUCTURE OF THE NOISE. SO IF THE NOISE IS ADVERSARIAL IN THE CORRECT WAY, YES IT WILL. FINE. AGAIN, WE SHOULD TREAT ALL OF THESE KIND OF THINGS AS HYPOTHESES TO BE TESTED AND IF IT TURNS OUT THAT THE NOISE IS OF THE WRONG KIND FOR THESE KIND OF POPULATIONS THEN THE THEORY'S WRONG. FINE. THAT'S THE WAY IT GOES. BUT I WOULD SUGGEST THAT, I THINK IT'S PROBABLY GOING TO TURN OUT TO BE CORRECT BECAUSE IT'S KIND OF AMAZING IT'S THE RIGHT NUMBER. BUT THEN THAT'S THE GUIDE TO WHAT YOU THINK THE NOISE SHOULD BE. THE NEXT THING TO CHECK IS WHAT DO YOU THINK THE NOISE IS. WELL GO MEASURE IT AND THEN YOU CAN CHECK THAT. A GOOD THEORY IS A GUIDE FOR USEFUL EXPERIMENTS. OKAY. I TRIED TO SAY THE THEORY -- REFLECTING THE WIDTH -- AND THERE'S AN EXPERIMENTAL -- IT'S NOT LIKE THE RATIO OF ANY PAIRS OF CELLS IN ADJACENT MODULES YOU GET EXACTLY THE SAME. YOU DON'T. THEY ARE SPREAD IN INDIVIDUALS. THE SPREAD KIND OF MATCH EACH OTHER. THOUGH I AGREE WITH YOU THAT THE FACT THAT IT MATCHES AS ALL SUGGESTS THAT MAYBE THERE'S A STRONGER PRESSURE AND REFLECTED BY THIS PARTICULAR PERSON. THAT COULD BE THE CASE TOO. AGAIN, THESE ARE GUIDES TO THE NEXT QUESTION AND I AGREE THAT'S A GOOD QUESTION. [APPLAUSE]