Memory and the Computational Brain E-Book

C. R. Gallistel

• Herausgeber: John Wiley & Sons
• Kategorie: Geisteswissenschaft
• Serie: Blackwell/Maryland Lectures in Language and Cognition
• Sprache: Englisch

Seitenzahl: 799

Veröffentlichungsjahr: 2011

Beschreibung

Memory and the Computational Brain offers a provocative argument that goes to the heart of neuroscience, proposing that the field can and should benefit from the recent advances of cognitive science and the development of information theory over the course of the last several decades. 

• A provocative argument that impacts across the fields of linguistics, cognitive science, and neuroscience, suggesting new perspectives on learning mechanisms in the brain
• Proposes that the field of neuroscience can and should benefit from the recent advances of cognitive science and the development of information theory
• Suggests that the architecture of the brain is structured precisely for learning and for memory, and integrates the concept of an addressable read/write memory mechanism into the foundations of neuroscience
• Based on lectures in the prestigious Blackwell-Maryland Lectures in Language and Cognition, and now significantly reworked and expanded to make it ideal for students and faculty

Leseprobe

Contents

Preface

1 Information

Shannon’s Theory of Communication

Measuring Information

Efficient Coding

Information and the Brain

Digital and Analog Signals

Appendix: The Information Content of Rare Versus Common Events and Signals

2 Bayesian Updating

Bayes’ Theorem and Our Intuitions about Evidence

Using Bayes’ Rule

Summary

3 Functions

Functions of One Argument

Composition and Decomposition of Functions

Functions of More than One Argument

The Limits to Functional Decomposition

Functions Can Map to Multi-Part Outputs

Mapping to Multiple-Element Outputs Does Not Increase Expressive Power

Defining Particular Functions

Summary: Physical/Neurobiological Implications of Facts about Functions

4 Representations

Some Simple Examples

Notation

The Algebraic Representation of Geometry

5 Symbols

Physical Properties of Good Symbols

Symbol Taxonomy

Summary

6 Procedures

Algorithms

Procedures, Computation, and Symbols

Coding and Procedures

Two Senses of Knowing

A Geometric Example

7 Computation

Formalizing Procedures

The Turing Machine

Turing Machine for the Successor Function

Turing Machines for fis_even

Turing Machines for f+

Minimal Memory Structure

General Purpose Computer

Summary

8 Architectures

One-Dimensional Look-Up Tables (If-Then Implementation)

Adding State Memory: Finite-State Machines

Adding Register Memory

Summary

9 Data Structures

Finding Information in Memory

An Illustrative Example

Procedures and the Coding of Data Structures

The Structure of the Read-Only Biological Memory

10 Computing with Neurons

Transducers and Conductors

Synapses and the Logic Gates

The Slowness of It All

The Time-Scale Problem

Synaptic Plasticity

Recurrent Loops in Which Activity Reverberates

11 The Nature of Learning

Learning As Rewiring

Synaptic Plasticity and the Associative Theory of Learning

Why Associations Are Not Symbols

Distributed Coding

Learning As the Extraction and Preservation of Useful Information

Updating an Estimate of One’s Location

12 Learning Time and Space

Computational Accessibility

Learning the Time of Day

Learning Durations

Episodic Memory

13 The Modularity of Learning

Example 1: Path Integration

Example 2: Learning the Solar Ephemeris

Example 3: “Associative” Learning

Summary

14 Dead Reckoning in a Neural Network

Reverberating Circuits as Read/Write Memory Mechanisms

Implementing Combinatorial Operations by Table-Look-Up

The Full Model

The Ontogeny of the Connections?

How Realistic Is the Model?

Lessons to Be Drawn

Summary

15 Nural Models of Interval Timing

Timing an Interval on First Encounter

Dworkin’s Paradox

Neurally Inspired Models

The Deeper Problems

16 The Molecular Basis of Memory

The Need to Separate Theory of Memory from Theory of Learning

The Coding Question

A Cautionary Tale

Why Not Synaptic Conductance?

A Molecular or Sub-Molecular Mechanism?

Bringing the Data to the Computational Machinery

Is It Universal?

References

Glossary

Index

This edition first published 2010

© 2010 C. R. Gallistel and Adam Philip King

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Library of Congress Cataloging-in-Publication Data

Gallistel, C. R., 1941−

Memory and the computational brain : why cognitive science will transform neuroscience / C. R. Gallistel and Adam Philip King.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-4051-2287-0 (alk. paper) — ISBN 978-1-4051-2288-7 (pbk. : alk. paper)

1. Cognitive neuroscience. 2. Cognitive science. I. King, Adam Philip. II. Title.

QP360.5G35 2009

612.8′2—dc22

2008044683

Preface

This is a long book with a simple message: there must be an addressable read/write memory mechanism in brains that encodes information received by the brain into symbols (writes), locates the information when needed (addresses), and transports it to computational machinery that makes productive use of the information (reads).

Such a memory mechanism is indispensable in powerful computing devices, and the behavioral data imply that brains are powerful organs of computation. Computational cognitive scientists presume the existence of an addressable read/write memory mechanism, yet neuroscientists do not know of, and are not looking for, such a mechanism. The truths the cognitive scientists know about information processing, when integrated into neuroscience, will transform our understanding of how the brain works.

An example of such a transformation is the effect that the molecular identification of the gene had on biochemistry. It brought to biochemistry a new conceptual framework. The foundation for this new framework was the concept of a code written into the structure of the DNA molecule. The code concept, which had no place in the old framework, was foundational in the new one. On this foundation, there arose an entire framework in which the duplication, transcription, translation, and correction of the code were basic concepts.

As in biochemistry prior to 1953, one can search through the literature on the neurobiology of memory in vain for a discussion of the coding question: How do the changes wrought by experience in the physical structure of the memory mechanism encode information about the experience? When experience writes to memory the distance and direction of a food source from a nest or hive, how are that distance and that direction represented in the experientially altered structure of the memory mechanism? And how can that encoded information be retrieved and transcribed from that enduring structure into the transient signals that carry that same information to the computational machinery that acts on this information? The answers to these questions must be at the core of our understanding of the physical basis of memory in nervous tissue. In the voluminous contemporary literature on the neurobiology of memory, there is no discussion of these questions. We have written this book in the hope of getting the scientific community that is interested in how brains compute to focus on finding the answers to these critical questions.

In elaborating our argument, we walk the reader through the concepts at the heart of the scientific understanding of information technology. Although most students know the terminology, the level of their understanding of the conceptual framework from which it comes is often superficial. Computer scientists are, in our view, to some extent to be faulted for this state of affairs. Computer science has been central to cognitive science from the beginning, because it was through computer science that the scientific community came to understand how it was possible to physically realize computations. In our view, the basic insights taught in computer science courses on, for example, automata theory, are a more secure basis for considering what the functional architecture of a computational brain must be than are the speculations in neuroscience about how brains compute. We believe that computer science has identified the essential components of a powerful computing machine, whereas neuroscience has yet to establish an empirically secured understanding of how the brain computes. The neuroscience literature contains many conjectures about how the brain computes, but none is well established. Unfortunately, computer scientists sometimes forget what they know about the foundations of physically realizable computation when they begin to think about brains. This is particularly true within the neural network or connectionist modeling framework. The work done in that tradition pays too much attention to neuroscientific speculations about the neural mechanisms that supposedly mediate computation and not enough to well-established results in theoretical and practical computer science concerning the architecture required in a powerful computing machine, whether instantiated with silicone chips or with neurons. Connectionists draw their computational conclusions from architectural commitments, whereas computationalists draw their architectural conclusions from their computational commitments.

In the first chapter, we explicate Shannon’s concept of communication and the definition of information that arises out of it. If the function of memory is to carry information forward in time, then we have to be clear about what information is. Here, as in all of our chapters on the foundational concepts in computation, we call attention to lessons of fundamental importance to understanding how brains work. One such lesson is that Shannon’s conception of the communication process requires that the receiver, that is, the brain, have a representation of the set of possible messages and a probability distribution over that set. Absent such a representation, it is impossible for the world to communicate information to the brain, at least information as defined by Shannon, which is the only rigorous definition that we have and the foundation on which the immensely powerful theory of information has been built. In this same chapter, we also review Shannon’s ideas about efficient codes, ideas that we believe will inform the neuroscience of the future, for reasons that we touch on repeatedly in this book.

Informative signals change the receiver’s probability distribution, the probability of the different states of the world (different messages in a set of possible messages). The receiver’s representation after an information-bearing signal has been received is the receiver’s posterior probability distribution over the possible values of an empirical variable, such as, for example, the distance from the nest to a food source or the rate at which food has been found in a given location. This conception puts Bayes’ theorem at the heart of the communication process, because it is a theorem about the normative (correct) way in which to update the receiver’s representation of the probable state of the world. In Chapter 2, we take the reader through the Bayesian updating process, both because of its close connection to Shannon’s conception of the communication process, and because of the ever growing role of Bayesian models in contemporary cognitive science (Chater, Tenenbaum, & Yuille, 2006). For those less mathematically inclined, Chapter 2 can be skipped or skimmed without loss of continuity.

Because communication between the brain and the world is only possible, in a rigorous sense, if the brain is assumed to have a representation of possible states of the world and their probabilities, the concept of a representation is another critical concept. Before we can explicate this concept, we have to explicate a concept on which it (and many other concepts) depends, the concept of a function. Chapter 3 explains the concept of a function, while Chapter 4 explains the concept of a representation.

Computations are the compositions of functions. A truth about functions of far-reaching significance for our understanding of the functional architecture of the brain is that functions of arbitrarily many arguments may be realized by the composition of functions that have only two arguments, but they cannot be realized by the composition of one-argument functions. The symbols that carry the two values that serve as the arguments of a two-argument function cannot occupy physically adjacent locations, generally speaking. Thus, the functional architecture of any powerful computing device, including the brain, must make provision for bringing symbols from their different locations to the machinery that effects the primitive two-argument functions, out of which the functions with many arguments are constructed by composition.

A representation with wide-ranging power requires computations, because the information the brain needs to know in order to act effectively is not explicit in the sensory signals on which it depends for its knowledge of the world. A read/write memory frees the composition of functions from the constraints of real time by making the empirically specified values for the arguments of functions available at any time, regardless of the time at which past experience specified them.

Representations are functioning homomorphisms. They require structure-preserving mappings (homomorphisms) from states of the world (the represented system) to symbols in the brain (the representing system). These mappings preserve aspects of the formal structure of the world. In a functioning homomorphism, the similarity of formal structure between symbolic processes in the representing system and aspects of the represented system is exploited by the representing system to inform the actions that it takes within the represented system. This is a fancy way of saying that the brain uses its representations to direct its actions.

Symbols are the physical stuff of computation and representation. They are the physical entities in memory that carry information forward in time. They become, either directly or by transcription into signals, the arguments of the procedures that implement functions. And they embody the results of those computations; they carry forward in explicit, computationally accessible form the information that has been extracted from transient signals by means of those computations. To achieve a physical understanding of a representational system like the brain, it is essential to understand its symbols as physical entities. Good symbols must be distinguishable, constructible, compact, and efficacious. Chapter 5 is devoted to explicating and illustrating these attributes of good symbols.

Procedures, or in more contemporary parlance algorithms, are realized through the composition of functions. We make a critical distinction between procedures implemented by means of look-up tables and what we call compact procedures. The essence of the distinction is that the specification of the physical structure of a look-up table requires more information than will ever be extracted by the use of that table. By contrast, the information required to specify the structure of a mechanism that implements a compact procedure may be hundreds of orders of magnitude less than the information that can be extracted using that mechanism. In the table-look-up realization of a function, all of the singletons, pairs, triplets, etc. of values that might ever serve as arguments are explicitly represented in the physical structure of the machinery that implements the function, as are all the values that the function could ever return. This places the table-look-up approach at the mercy of what we call the infinitude of the possible. This infinitude is merciless, a point we return to repeatedly.

By contrast, a compact procedure is a composition of functions that is guaranteed to generate (rather than retrieve, as in table look-up) the symbol for the value of an n-argument function, for any arguments in the domain of the function. The distinction between a look-up table and a compact generative procedure is critical for students of the functional architecture of the brain. One widely entertained functional architecture, the neural network architecture, implements arithmetic and other basic functions by table look-up of nominal symbols rather than by mechanisms that implement compact procedures on compactly encoded symbols. In Chapter 6, we review the intimate connection between compact procedures and compactly encoded symbols. A symbol is compact if its physical magnitude grows only as the logarithm of the number of distinct values that it can represent. A symbol is an encoding symbol if its structure is dictated by a coding algorithm applied to its referent.

With these many preliminaries attended to, we come in Chapter 7 to the exposition of the computer scientist’s understanding of computation, Turing computabil-ity. Here, we introduce the standard distinction between the finite-state component of a computing machine (the transition table) and the memory (the tape). The distinction is critical, because contemporary thinking about the neurobiological mechanism of memory tries to dispense with the tape and place all of the memory in the transition table (state memory). We review well-known results in computer science about why this cannot be a generally satisfactory solution, emphasizing the infinitude of possible experience, as opposed to the finitude of the actual experience. We revisit the question of how the symbols are brought to the machinery that returns the values of the functions of which those symbols are arguments. In doing so, we explain the considerations that lead to the so-called von Neumann architecture (the central processor).

In Chapter 8, we consider different suggestions about the functional architecture of a computing machine. This discussion addresses three questions seldom addressed by cognitive neuroscientists, let alone by neuroscientists in general: What are the functional building blocks of a computing machine? How must they be configured? How can they be physically realized? We approach these questions by considering the capabilities of machines with increasingly complex functional structure, showing at each stage mechanical implementations for the functional components. We use mechanical implementations because of their physical transparency, the ease with which one can understand how and why they do what they do. In considering these implementations, we are trying to strengthen the reader’s understanding of how abstract descriptions of computation become physically realized. Our point in this exercise is to develop, through a series of machines and formalisms, a step-by-step argument leading up to a computational mechanism with the power of a Turing machine. Our purpose is primarily to show that to get machines that can do computations of reasonable complexity, a specific, minimal functional architecture is demanded. One of its indispensable components is a read/write memory. Secondarily, we show that the physical realization of what is required is not all that complex. And thirdly, we show the relation between descriptions of the structure of a computational mechanism at various levels of abstraction from its physical realization.

In Chapter 9, we take up the critical role of the addressability of the symbols in memory. Every symbol has both a content component, the component of the symbol that carries the information, and an address component, which is the component by which the system gains access to that information. This bipartite structure of the elements of memory provides the physical basis for distinguishing between a variable and its value and for binding the value to the variable. The address of a value becomes the symbol for the variable of which it is the value. Because the addresses are composed in the same symbolic currency as the symbols themselves, they can themselves be symbols. Addresses can–and very frequently do–appear in the symbol fields of other memory locations. This makes the variables themselves accessible to computation, on the same terms as their values. We show how this makes it possible to create data structures in memory. These data structures encode the relations between variables by the arrangement of their symbols in memory. The ability to distinguish between a variable and its value, the ability to bind the latter to the former, and the ability to create data structures that encode relations between variables are critical features of a powerful representational system. All of these capabilities come simply from making memories addressable. All of these capabilities are absent–or only very awkwardly made present–in a neural network architecture, because this architecture lacks addressable symbolic memories.

To bolster our argument that addressable symbolic memories are required by the logic of a system whose function is to carry information forward in an accessible form, we call attention to the fact that the memory elements in the genetic code have this same bipartite structure: A gene has two components, one of which, the coding component, carries information about the sequence of amino acids in a protein; the other of which, the promoter, gives the system access to that information.

In Chapter 10, we consider current conjectures about how the elements of a computing machine can be physically realized using neurons. Because the suggestion that the computational models considered by cognitive scientists ought to be neurobiologically transparent1 has been so influential in cognitive neuroscience, we emphasize just how conjectural our current understanding of the neural mechanisms of computation is. There is, for example, no consensus about such a basic question as how information is encoded in spike trains. If we liken the flow of information between locations in the nervous system to the flow of information over a telegraph network, then electrophysiologists have been tapping into this flow for almost a century. One might expect that after all this listening in, they would have reached a consensus about what it is about the pulses that conveys the information. But in fact, no such consensus has been reached. This implies that neuroscientists understand as much about information processing in the nervous system as computer scientists would understand about information processing in a computer if they were unable to say how the current pulses on the data bus encoded the information that enters into the CPU’s computations.

In Chapter 10, we review conventional material on how it is that synapses can implement elementary logic functions (AND, OR, NOT, NAND). We take note of the painful slowness of both synaptic processes and the long-distance information transmission mechanism (the action potential), relative to their counterparts in an electronic computing machine. We ponder, without coming to any conclusions, how it is possible for the brain to compute as fast as it manifestly does.

Mostly, however, in Chapter 10 we return to the coding question. We point out that the physical change that embodies the creation of a memory must have three aspects, only one of which is considered in contemporary discussions of the mechanism of memory formation in neural tissue, which is always assumed to be an enduring change in synaptic conductance. The change that mediates memory formation must, indeed, be an enduring change. No one doubts that. But it must also be capable of encoding information, just as the molecular structure of a gene endows it with the capacity to encode information. And, it must encode information in a readable way. There must be a mechanism that can transcribe the encoded information, making it accessible to computational machinery. DNA would have no function if the information it encodes could not be transcribed.

We consider at length why enduring changes in synaptic conductance, at least as they are currently conceived, are ill suited both to encode information and, assuming that they did somehow encode it, make it available to computation. The essence of our argument is that changes in synaptic conductance are the physiologists’ conception of how the brain realizes the changes in the strengths of associative bonds. Hypothesized changes in the strengths of associative bonds have been at the foundation of psychological and philosophical theorizing about learning for centuries. It is important to realize this, because it is widely recognized that associative bonds make poor symbols: changes in associative strength do not readily encode facts about the state of the experienced world (such as, for example, the distance from a hive to food source or the duration of an interval). It is, thus, no accident that associative theories of learning have generally been anti-representational (P. M. Church-land, 1989; Edelman & Gally, 2001; Hoeffner, McClelland, & Seidenberg, 1996; Hull, 1930; Rumelhart & McClelland, 1986; Skinner, 1938, 1957; Smolensky, 1991). If one’s conception of the basic element of memory makes that element ill-suited to play the role of a symbol, then one’s story about learning and memory is not going to be a story in which representations figure prominently.

In Chapter 11, we take up this theme: the influence of theories of learning on our conception of the neurobiological mechanism of memory, and vice versa. Psychologists, cognitive scientists, and neuroscientists currently entertain two very different stories about the nature of learning. On one story, learning is the process or processes by which experience rewires a plastic brain. This is one or another version of the associative theory of learning. On the second story, learning is the extraction from experience of information about the state of the world, which information is carried forward in memory to inform subsequent behavior. Put another way, learning is the process of extracting by computation the values of variables, the variables that play a critical role in the direction of behavior.

We review the mutually reinforcing fit between the first view of the nature of learning and the neurobiologists’ conception of the physiological basis of memory. We take up again the explanation of why it is that associations cannot readily be made to function as symbols. In doing so, we consider the issue of distributed codes, because arguments about representations or the lack thereof in neural networks often turn on issues of distributed coding.

In the second half of Chapter 11, we expand on the view of learning as the extraction from experience of facts about the world and the animal’s relation to it, by means of computations. Our focus here is on the phenomenon of dead reckoning, a computational process that is universally agreed to play a fundamental role in animal navigation. In the vast literature on symbolic versus connectionist approaches to computation and representation, most of the focus is on phenomena for which we have no good computational models. We believe that the focus ought to be on the many well-documented behavioral phenomena for which computational models with clear first-order adequacy are readily to hand. Dead reckoning is a prime example. It has been computationally well understood and explicitly taught for centuries. And, there is an extensive experimental literature on its use by animals in navigation, a literature in which ants and bees figure prominently. Here, we have a computation that we believe we understand, with excellent experimental evidence that it occurs in nervous systems that are far removed from our own on the evolutionary bush and many orders of magnitude smaller.

In Chapter 12, we review some of the behavioral evidence that animals routinely represent their location in time and space, that they remember the spatial locations of many significant features of their experienced environment, and they remember the temporal locations of many significant events in their past. One of us reviewed this diverse and large literature at greater length in an earlier book (Gallistel, 1990). In Chapter 12, we revisit some of the material covered there, but our focus is on more recent experimental findings. We review at some length the evidence for episodic memory that has been obtained from the ingenious experimental study of food caching and retrieval in a species of bird that, in the wild, makes and retrieves food from tens of thousands of caches. The importance of this work for our argument is that it demonstrates clearly the existence of complex experience-derived, computationally accessible data structures in brains much smaller than our own and far removed from ours in their location on the evolutionary bush. It is data like these that motivate our focus in an earlier chapter (Chapter 9) on the architecture that a memory system must have in order to encode data structures, because these data are hard to understand within the associative framework in which animal learning has traditionally been treated (Clayton, Emery, & Dickinson, 2006).

In Chapter 13, we review the computational considerations that make learning processes modular. The view that there are only one or a very few quite generally applicable learning processes (the general process view, see, for example, Domjan, 1998, pp. 17ff.) has long dominated discussions of learning. It has particularly dominated the treatment of animal learning, most particularly when the focus is on the underlying neurobiological mechanism. Such a view is consonant with a non-representational framework. In this framework, the behavioral modifications wrought by experience sometimes make animals look as if they know what it is about the world that makes their actions rational, but this appearance of symbolic knowledge is an illusion; in fact, they have simply learned to behave more effectively (Clayton, Emery, & Dickinson, 2006). However, if we believe with Marr (1982) that brains really do compute the values of distal variables and that learning is this extraction from experience of the values of variables (Gallistel, 1990), then learning processes are inescapably modular. They are modular because it takes different computations to extract different representations from different data, as was first pointed out by Chomsky (1975). We illustrate this point by a renewed discussion of dead reckoning (aka path integration), by a discussion of the mechanism by which bees learn the solar ephemeris, and by a discussion of the special computations that are required to explain the many fundamental aspects of classical (Pavlovian) conditioning that are unexplained by the traditional associative approach to the understanding of conditioning.2

In Chapter 14, we take up again the question of how the nervous system might carry information forward in time in a computationally accessible form in the absence of a read/write memory mechanism. Having explained in earlier chapters why plastic synapses cannot perform this function, we now consider in detail one of the leading neural network models of dead reckoning (Samsonovich & McNaughton, 1997). This model relies on the only widely conjectured mechanism for performing the essential memory function, reverberatory loops. We review this model in detail because it illustrates so dramatically the points we have made earlier about the price that is paid when one dispenses with a read/write memory. To our mind, what this model proves is that the price is too high.

In Chapter 15, we return to the interval timing phenomena that we reviewed in Chapter 12 (and, at greater length, in Gallistel, 1990; Gallistel & Gibbon, 2000; Gallistel & Gibbon, 2002), but now we do so in order to consider neural models of interval timing. Here, again, we show the price that is paid by dispensing with a read/write memory. Given a read/write memory, it is easy to model, at least to a first approximation, the data on interval timing (Gallistel & Gibbon, 2002; Gibbon, Church, & Meck, 1984; Gibbon, 1977). Without such a mechanism, modeling these phenomena is very hard. Because the representational burden is thrown onto the conjectured dynamic properties of neurons, the models become prey to the problem of the infinitude of the possible. Basically, you need too many neurons, because you have to allocate resources to all possible intervals rather than just to those that have actually been observed. Moreover, these models all fail to provide computational access to the information about previously experienced durations, because the information resides not in the activity of the neurons, nor in the associations between them, but rather in the intrinsic properties of the neurons in the arrays used to represent durations. The rest of the system has no access to those intrinsic properties.

Finally, in Chapter 16, we take up the question that will have been pressing on the minds of many readers ever since it became clear that we are profoundly skeptical about the hypothesis that the physical basis of memory is some form of synaptic plasticity, the only hypothesis that has ever been seriously considered by the neuroscience community. The obvious question is: Well, if it’s not synaptic plasticity, what is it? Here, we refuse to be drawn. We do not think we know what the mechanism of an addressable read/write memory is, and we have no faith in our ability to conjecture a correct answer. We do, however, raise a number of considerations that we believe should guide thinking about possible mechanisms. Almost all of these considerations lead us to think that the answer is most likely to be found deep within neurons, at the molecular or sub-molecular level of structure. It is easier and less demanding of physical resources to implement a read/write memory at the level of molecular or sub-molecular structure. Indeed, most of what is needed is already implemented at the sub-molecular level in the structure of DNA and RNA.

1 That is, they ought to rest on what we understand about how the brain computes.

2 This is the within-field jargon for the learning that occurs in “associative” learning paradigms. It is revelatory of the anti-representational foundations of traditional thinking about learning. It is called conditioning because experience is not assumed to give rise to symbolic knowledge of the world. Rather, it “conditions” (rewires) the nervous system so that it generates more effective behavior.