The Computational Brain Computational Neuroscience Terrence J. Sejnowski and Tomaso A. Poggio, editors Methods in Neuronal Modeling: From Synapses to Networks, edited by Christof Koch and Idan Segev, 1989 Neural Nets in Electric Fish, Walter Heiligenberg, 1991 The Computational Brain, Patricia S. Churchland and Terrence J. Sejnowski, 1992 The Computational Brain Patricia S. Churchland and Terrence J. Sejnowski A Bradford Book The MIT Press Cambridge, Massachusetts London, England Fourth printing, 1996 © 1992 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Palatino by Asco Trade Typesetting Ltd., Hong Kong and was printed and bound in the United States of America. ii 1. Contents 1. CONTENTS.......................................................................................................................................... III PREFACE............................................................................................................................................... VI 1. INTRODUCTION .............................................................................................................................. 1 2. NEUROSCIENCE OVERVIEW ...................................................................................................... 14 1. INTRODUCTION.................................................................................................................................... 14 2. LEVELS IN NERVOUS SYSTEMS ............................................................................................................ 14 Levels of Analysis ....................................................................................................................... 14 Levels of Organization ................................................................................................................. 15 Levels of Processing ................................................................................................................... 19 3. STRUCTURE AT VARIOUS LEVELS OF ORGANIZATION ................................................................................. 22 Systems ...................................................................................................................................... 23 Topographic Maps ...................................................................................................................... 25 Layers and Columns ................................................................................................................... 28 Local Networks ............................................................................................................................ 30 Neurons ....................................................................................................................................... 32 Synapses .................................................................................................................................... 36 Molecules .................................................................................................................................... 39 4. A SHORT LIST OF BRAIN FACTS .......................................................................................................... 40 Selected Readings ...................................................................................................................... 50 Selected Journals and Reviews .................................................................................................. 51 3. COMPUTATIONAL OVERVIEW .................................................................................................... 52 1. INTRODUCTION.................................................................................................................................... 52 Functions: Computable or Noncomputable, Linear or Nonlinear .................................................52 Computers, Pseudocomputers, and Cryptocomputers ...............................................................54 2. LOOKING UP THE ANSWER .................................................................................................................. 58 3. LINEAR ASSOCIATORS.......................................................................................................................... 64 4. CONSTRAINT SATISFACTION: HOPFIELD NETWORKS AND BOLTZMANN MACHINES................................................68 5. LEARNING IN NEURAL NETS.................................................................................................................. 80 6. COMPETITIVE LEARNING....................................................................................................................... 85 7. CURVE FITTING.................................................................................................................................. 86 8. FEEDFORWARD NETS: TWO EXAMPLES.................................................................................................... 88 Exclusive "or"................................................................................................................................ 89 Discriminating Sonar Echoes........................................................................................................ 93 NETtalk......................................................................................................................................... 95 9. RECURRENT NETS.............................................................................................................................. 95 10. FROM TOY WORLD TO REAL WORLD.................................................................................................. 102 11. WHAT GOOD ARE OPTIMAZATION PROCEDURES TO NEUROSCIENCE?..........................................................107 12. MODELS: REALISTIC AND ABSTRACT.................................................................................................... 110 13. CONCLUDING REMARKS.................................................................................................................... 111 4. REPRESENTING THE WORLD..................................................................................................... 114 1. INTRODUCTION.................................................................................................................................. 114 2. CONSTRUCTING A VISUAL WORLD........................................................................................................ 115 3. THUMBNAIL SKETCH OF THE MAMMALIAN VISUAL SYSTEM.......................................................................... 119 4. REPRESENTING IN THE BRAIN: WHAT CAN WE LEARN FROM THE VISUAL SYSTEM?.........................................126 5. WHAT IS SO SPECIAL ABOUT DISTRIBUTION?......................................................................................... 131 What Is Vector Coding?.............................................................................................................. 132 The Conceptual Fecundity of "State Space"............................................................................... 133 6. WORLD ENOUGH AND TIME................................................................................................................. 138 What Is Coarse Coding? ............................................................................................................ 141 Does Tuning Selectivity of Neurons Imply Local Coding.?..........................................................141 7. SHAPE FROM SHADING: A NEUROCOMPUTATIONAL STUDY......................................................................... 145 8. STEREO VISION................................................................................................................................ 149 Psychological Parameters........................................................................................................... 150 Neurophysiology and Anatomy................................................................................................... 156 iii 9. COMPUTATIONAL MODELS OF STEREO VISION......................................................................................... 158 Finding Compatibilities: Matching and Coarse Stereopsis.......................................................... 161 Using a Cooperative Algorithm ................................................................................................... 166 Unsupervised Learning of Stereo Invariants............................................................................... 169 Depth Cues and the Real World.................................................................................................. 171 10. HYPERACUITY: FROM MYSTERY TO MECHANISM.....................................................................................174 From Three Cones to 10,000 Hues by Coarse Coding .............................................................. 175 Vernier-style Hyperacuity............................................................................................................ 176 Hyperacuity in Depth Perception................................................................................................. 177 Vergence and Absolute Depth Judgments.................................................................................. 182 11. VECTOR AVERAGING........................................................................................................................ 184 12. CONCLUDING REMARKS.................................................................................................................... 187 Selected Readings...................................................................................................................... 187 5. PLASTICITY: CELLS, CIRCUITS, BRAINS, AND BEHAVIOR.....................................................189 1. INTRODUCTION.................................................................................................................................. 189 2. LEARNING AND THE HIPPOCAMPUS ....................................................................................................... 192 3. DONALD HEBB AND SYNAPTIC PLASTICITY.............................................................................................. 194 4. MEMORIES ARE MADE OF THIS: MECHANISMS OF NEURONAL PLASTICITY.......................................................200 Long-Term Potentiation (LTP)..................................................................................................... 201 LTP and Cell Populations............................................................................................................ 208 Beyond Vanilla LTP..................................................................................................................... 214 LTP at the Molecular Level ......................................................................................................... 217 Extrasynaptic and Non-NMDA LTP............................................................................................. 219 5. CELLS AND CIRCUTS......................................................................................................................... 223 6. DECREASING SYNAPTIC STRENGTH ...................................................................................................... 229 7. BACK TO SYSTEMS AND BEHAVIOR....................................................................................................... 233 8. BEING AND TIMING............................................................................................................................ 241 9. DEVELOPMENT OF NERVOUS SYSTEMS.................................................................................................. 242 9. MODULES AND NETWORKS.................................................................................................................. 249 Selected Readings...................................................................................................................... 257 6. SENSORIMOTOR INTEGRATION................................................................................................. 258 1. INTRODUCTION ................................................................................................................................. 258 2. LEECHNET....................................................................................................................................... 263 Computer Models of Network for Dorsal Bending....................................................................... 266 3. COMPUTATION AND THE VESTIBULO-OCULAR REFLEX ............................................................................... 274 Plasticity in the VOR................................................................................................................... 282 4. TIME AND TIME AGAIN....................................................................................................................... 293 Generating Repeatable Patterns: All God's Critters Got Rhythm................................................ 295 Oscillating Circuits in the Spinal Cord......................................................................................... 295 5. THE SEGMENTAL SWIMMING OSCILLATOR............................................................................................... 300 6. MODELING THE NEURON..................................................................................................................... 308 7. CONCLUDING REMARKS...................................................................................................................... 318 Selected Readings...................................................................................................................... 318 7. CONCLUDING AND BEYOND...................................................................................................... 320 Mead and Analog VLSI .............................................................................................................. 322 Ballard and Active Perception..................................................................................................... 323 Brooks and Mobots..................................................................................................................... 326 Afterword..................................................................................................................................... 329 APPENDIX: ANATOMICAL AND PHYSIOLOGICAL TECHNIQUES.............................................. 330 1. PERMANENT LESIONS........................................................................................................................ 330 Human Studies............................................................................................................................ 330 Animal Models............................................................................................................................. 331 2. REVERSIBLE LESIONS AND MICROLESIONS.............................................................................................. 332 3. IMAGING TECHNIQUES........................................................................................................................ 333 4. GROSS ELECTRICAL AND MAGNETIC RECORDING..................................................................................... 337 5. SINGLE-UNIT RECORDING................................................................................................................... 338 iv 6. ANATOMICAL TRACT TRACING.............................................................................................................. 341 NOTES.............................................................................................................................................. 342 GLOSSARY ..................................................................................................................................... 354 REFERENCES.................................................................................................................................. 378 v Preface T o understand how neurons give rise to a mental life, we must know what they do, both individually as single cells and collectively as coherent systems of cells. The idea that brains are computational in nature has spawned a range of explanatory hypotheses in theoretical neurobiology. This book represents one slant on current computational research relevant to neurobiology, a slant both on the conceptual foundations and the benchmark studies. We mustered our plans for this book against the backdrop of several earlier projects: Parallel Distributed Processing, edited by Dave Rumelhart and Jay McClelland (1986), and Neurophilosophy (P.S. Churchland, 1986). Since those books went to press, much has changed. Powerful new tools for modeling neurons and circuits of neurons have become available, and a conceptual framework for neuro-computational projects has been steadily greening out. Puzzling questions abound on every side, however, concerning such matters as algorithms for weight-setting in neural nets and the extent to which they can be valuable in neuromodeling; concerning biological realism in neural net models and what degree of realism is necessary to make a model useful; and highly focused questions such as what exactly is "Hebbian learning" and what are "grandmother" cells. The questions that became pivotal in The Computational Brain were questions that have been biting our heels more or less incessantly. The book is thus shaped by what has bothered or beguiled us, individually and jointly. We learned a great deal from the conversations in the laboratory, some of which extended over many months. Francis Crick launched the institution of afternoon tea in the Computational Neurobiology Laboratory at the Salk, and teatime quickly became the daily occasion for close discussion of ideas and data, flying untried balloons, and giving the broad questions a heating. It was a time for emerging from the comfortable burrows of safe detail into the wide-open prairie of no- holds-barred. Crick characteristically pushed the questions about how the brain works further and more relentlessly. Moreover, it was typically his hunches, breadth, and steel-edged skepticism that supplied a sense of balance both when we thought we knew what we were doing and when we were pretty sure we didn't. Virtually everyone who visited the Computational Neurobiology Lab was coaxed or bullied into dilating on the philosophical (grand-scale, background, or fuzzy) questions facing computational neuroscience. From these "confessions," we drew ideas and inspiration, and garnered the pluck to stick our necks out a bit. Several explanations-cum-apologies are in order. The first is for our decision to facilitate easy reading by including only the unavoidable minimum of references in the text itself. We found that long lists of authors in the text make the reader stumble, and hence we elected to use notes for many references rather than follow standard practice in technical writing. Despite our best efforts to refer as fully as possible in the notes, we undoubtedly have missed some essential references, and we apologize in advance for unwitting omissions. The next apology is owed because in choosing instances of research to exemplify a point, we inevitably found ourselves drawing on the research that was most familiar to us, and that often meant research based in California, especially in San Diego. Important and interesting work in computational neuroscience is going on all over the globe, and to have done an exhaustive survey before beginning to write would have meant a deadline receding faster than the progress line. We therefore apologize if we seem rather provincial in our selection preferences. The third apology is for the length. We began the project with the strict understanding that primers are best if brief. In the execution, alas, it became impossible to live within the bounds. As it is, a number of additional topics might well have been included but for permitting the book an embarrassing girth. We therefore apologize—both because the book is too long and because it is too short. Fourth, we decided in the interests of smooth reading to abide by the practice of using "he" as the third-person pronoun referring indifferently to males and females. This reflects nothing ideological. If anything, it is a concession to Mrs. Lundy, whose unflinching dictum in grammar school was that ideological shoe- horning frustrates readability. Many people helped enormously in writing the book; it simply could not have been done by just the two of us. Most particularly, Paul Churchland gave unstintingly of his imagination and ideas; the daily ritual was to think through everything, page by page, model by model, over capuccino at 11 Fomaio. Antonio and Hanna Damasio talked through every major issue with us; they br. oadened and deepened our perspective in all dimensions, but especially in thinking about what neuropsychological results could tell us about micro-orga-nization. Beatrice Golomb, V. S. Ramachandran, Diane Rogers- Ramachandran, Alexandre Pouget, Karen Dobkins, and Tom Albright helped with representation in general and visual representations in particular; Rodolfo Llinás helped with many issues, but vi especially in thinking about time; Gyori Buzsáki, Larry Squire, David Amaral, Wendy Suzuki, and Chuck Stevens with plasticity; Carver Mead with thinking about the nature of computation, time, and representation. Shawn Lockery, Steve Lisberger, Tom Anastasio, A1 Selverston, Thelma Williams, Larry Jordan, Susan Shefchyk, and James Buchanan gave us much useful advice on sensorimotor coordination. Mark Konishi and Roderick Corriveau gave us invaluable criticism and advice on many chapters and saved us from several embarrassments. Many thanks are also owed to Paul Bush for preparing the glossary, Shona Chatterji for drawing and cheerfully redrawing many figures, Mark Churchland for the cover and for useful criticism, GeorgSchwarz for manuscript preparation, and David Lawrence for rescues from macfrazzles. A special debt is owed to Rosemary Miller, whose wit and wisdom kept the boat afloat. Others who helped in indispensable ways include: Richard Adams, Dana Ballard, Tony Bell, Anne Churchland, Hillary Chase Benedetti, Richard Gregory, Geoff Hinton, Harvey Karten, Christof Koch, Bill Lytton, Steve Nowlan, Leslie Orgel, Hal Pashler, Steve Quartz, Paul Rhodes, Paul Viola, Ning Qian, and Jack Wathey. P.S.C. was supported by a University of California President's Humanities Fellowship, a grant from the National Science Foundation (87-06757), and the James S. McDonnell Foundation. T.J.S. was supported by the Howard Hughes Medical Institute and grants from the Drown Foundation, the Mathers Foundation, the National Science Foundation, and the Office of Naval Research. vii viii 1. Introduction M ajor advances in science often consist in discovering how macroscale phenomena reduce to their microscale constituents. These latter are often counterintuitive conceptually, invisible observationally, and troublesome experimentally. Thus, for example, temperature in a gas turned out to be mean kinetic energy of the constituent molecules; the varied properties displayed by matter turned out to be a function of the component atoms and their arcane properties such as electron shells; bacteria—not Divine vengeance—were found to be the proximal cause of smallpox and bubonic plague; and the reproduction of organisms, we now know, depends on the arrangement of four bases in the molecule DNA. Our psychological life, too, is a natural phenomenon to be understood. Here as well, the explanations will draw on properties of the infrastructure that are certainly veiled and probably arcane, an infrastructure whose modus operandi may seem alien to our customary self-conception. Perhaps this is inevitable, since the very brain we wish to understand is also the brain whose unaided observation is focused at the macrolevel and whose design seems to favor large-scale concepts for the explanation of its own behavior; for example, superstructure concepts such as "is hungry," "wants food," "believes honey is in the hole up the oak tree," and "sees the grizzly bear approaching." Neurons are the basic structural components of the brain. A neuron is an individual cell, specialized by architectural features that enable fast changes of voltage across its membrane as well as voltage changes in neighboring neurons. Brains are assemblies of just such cells, and while an individual neuron does not see or reason or remember, brains regularly do. How do you get from ion movement across cell membranes to memory or perception in brains? What is the nature of neuron-neuron connectivity and interactivity? What makes a clump of neurons a nervous system? At this stage in the evolution of science, it appears highly probable that psychological processes are in fact processes of the physical brain, not, as Descartes concluded, processes of a nonphysical soul or mind. Since this issue has been discussed at length elsewhere (for example, P.M. Churchland 1984, P.S. Churchland 1986), and since Cartesian dualism is not taken very seriously either in mainstream philosophy or mainstream neuroscience, it is not necessary to repeat the details of the arguments here. Suffice it to say that the Cartesian hypothesis fails to cohere with current physics, chemistry, evolutionary biology, molecular biology, embryology, immunology, and neuroscience. To be sure, materialism is not an established fact, in the way that the four-base helical structure of DNA, for example, is an established fact. It is possible, therefore, that current evidence notwithstanding, dualism might actually be true. Despite the rather remote possibility that new discoveries will vindicate Descartes, materialism, like Darwinian evolution, is the more probable working hypothesis. That being so, it does not seem worthwhile to modify the basic neuroscience research program and its scaffolding of physicalistic presuppositions to accommodate the Cartesian hypothesis, though scientific tolerance counsels that the door not be closed until the facts themselves well and truly close it. Whether modifications to micro/nano/pico level sciences such as quantum physics will be called for as a result of advances in neuropsychology is likewise conceivable (Penrose 1989), but so far there is no moderately convincing reason to expect that they will. Arguments from ignorance are to be especially guarded against in this context. Their canonical form is this: neuroscience is ignorant of how to explain X (consciousness, for instance) in terms of the nervous system; therefore it cannot be so explained. Rather, it can eventually be explained in terms of Y (pick your favorite thing, for example, quantum wave packets, psychons, ecto-plasmic retrovibrations, etc.). The canonical form lends itself to endless seductive variations, particularly ones in which failures of imagination massage intuition: "We cannot imagine how to explain consciousness in terms of neu- ronal activity...; how could physical processes like ions crossing membranes explain the awfulness of pain?" In its denuded rendition, the argument from ignorance is not mildly tempting, but in full regalia, it may seem beguiling and exactly what reharmonizes such "intuition dissonance" as is provoked by reflecting on the physical basis of the mental. A version of the argument convinced the German mathematician and philosopher, Leibniz (1714), and in the past two decades, variations on Leibniz' basic theme have surfaced as the single most popular and appealing justification for concluding that neuro-biological explanations of psychological phenomena are impossible. (For instances of the argument in many different and alluring guises, see Thomas Nagel 1974, J. C. Eccles 1977, John Searle 1980, 1990, and Roger Penrose 1989.) From the revolutions wrought by Copemicus, Galileo, 1 Darwin, and Einstein, it is all too apparent that "intuition dissonance" is a poor indicator of truth; it is a good indicator only of how one idea sits with well-favored others. Establishing truth or probability requires rather more. The working hypothesis underlying this book is that emergent properties are high-level effects that depend on lower-level phenomena in some systematic way. Turning the hypothesis around to its negative version, it is highly improbable that emergent properties are properties that cannot be explained by low-level properties (Popper 1959), or that they are in some sense irreducible, causally sui generis, or as philosophers are wont to say, "nomologically autonomous," meaning, roughly, "not part of the rest of science" (Fodor 1974, Pylyshyn 1984). The trouble with characterizing certain properties as irreducibly emergent is that it assumes we can tell in advance whether something can be explained—ever explained. Obviously such a claim embodies a prediction, and as the history of science shows all too clearly, predictions grounded in ignorance rather than knowledge often go awry. In advance of a much more highly developed neurobiology than currently exists, it is much too soon to be sure that psychological phenomena cannot be explained in terms of neurobio-logical phenomena. Although a given phenomenon such as protein folding or awareness of visual motion cannot now be explained, it might yield to explanation as time and science go on. Whether it does or not is a matter of empirical fact, not a matter of a priori divination. Searching for reductive explanations of emergent properties does not entail that we should expect the explanations to be simpleminded or breezily cobbled up or straightforwardly readable off the data points; it means only that the betting man keeps going. Two groundbreaking discoveries in the nineteenth century established the foundations for a science of nervous systems: (1) macro effects displayed by nervous systems depend on individual cells, whose paradigm anatomical structures include both long tails (axons) for sending signals and treelike prolifera-tions (dendrites) for receiving signals (figure I. I); (2) these cells are essentially electrical devices; their basic business is to receive and transmit signals by causing and responding to electric current. Within this elegantly simple framework, truly spectacular progress has been made in unravelling the intricate story of exactly how neurons work. In this century, and especially within the last three decades, an enormous amount has been learned about neurons: about their electrophysiology, microanatomy, connectivity, and development; about the large assortment of neurochemicals that mediate signaling from one neuron to the next; inside a neuron, about the cell's membrane, its roster of channel types, and their specific roles in receiving, integrating, and sending signals; about transmitter release, and about the range, structure, and mechanisms of receptors. Even the genetics of the proteins that constitute the various recep-tors is now steadily coming into view. (Nathans 1987, 1989, Gasic and Heine-mann, 1991, Heinemann et al. 1990). Figure -1: Drawing by Cajal based on his Golgi-stained sections of the superior part of the cerebral hemispheres and corpus callosum of a mouse of 20 days. A, corpus callosum; B, antero-posterior fibers; C, lateral ventricle;a, large pyramidal cell; b, callosal fiber bifurcating into a branch that is arborized in the gray matter and another that continues in the corpus callosum; c, callosal fiber that comes from an axon of the white matter; d, callosal fiber the originates in a pyramidal cell; e, axons of lateral pyramidal cells which follow a descending course in the corpus callosum without forming part of the commissure; f, f', the two final branches coming from a fiber of the corpus callosum and arborizing in the gray matter; g, epithelial cells; h, fiber from a large pyramid, giving off a fine collateral to the corpus callosum; i, fusiform cells whose axons ascend to the molecularlayer; j, terminal arborization of a callosal fiber originating on the opposite side. (With permission. Santiago Ram6n y Cajal, 1890. Reprinted in DeFelipe and Jones, eds., 1988, Cajal on the Cerebral Cortex. Oxford: Oxford University Press.) 2