Neurophysiology and Information: Theory of Brain Function

Transcription

1 Neurophysiology and Information: Theory of Brain Function Christopher Fiorillo BiS 527, Spring , Part 5: The Brain s Perspective: Application of Probability to the Brain Fiorillo CD, Beyond Bayes: On the need for a unified and Jaynesian definition of probability and information within neuroscience Information (currently being revised for reviewers). Assistants: Sora Yun, <ysl0142@kaist.ac.kr>, Ju-Young Lee, <hohojy29@kaist.ac.kr>

2 Jaynesian Observers Probabilities characterize the information of an observer (which must correspond to a physical system) Different observers have different information In principle, we can use probabilities to describe the information of any observer, not just our own We must be very careful to distinguish what information we are using, and to which observer it belongs We must choose a perspective

3 Perspectives in Physics In the field of mechanics, in order to apply the rules of physics (Newton s laws, conservation of energy, etc.), we must choose a frame of reference Einstein is the one most famous for demonstrating the importance of perspective, in his relativity For example, according to Einstein, one must measure time using a clock. As a practical matter, scientists cannot pretend to be an omniscient God. The rules of physics are followed for each observer, but the observers will not agree about specific values, such as velocity The perspective of one observer is related to that of another, and can be converted through a process known as a Lorentz transformation

4 Where are the Probabilities and Information? Frequentist Object Third-Person Jaynesian Observer First-Person Jaynesian Observer

5 2 Jaynesian Approaches to the Nervous System The Scientist s Point of View: Scientists describe their knowledge of the nervous system. They may use knowledge of inputs to predict outputs, or vice versa This is the conventional approach. The problem with this approach is that the relationship between inputs and outputs tends to be extremely complex. Jaynesian theory provides an objective and quantitative means to describe the world from different perspectives (different sets of information) What information does a nervous system have about its world?

6 First versus Third-Person Approaches In grammar First-person: I, we Second-person: you Third-person: it, he, she, they In literature These terms are often used to describe whether the story is told from the perspective of a character (firstperson) or by an omniscient narrator (third-person) These terms are not commonly used in science. The perspective of the brain would be first-person, which I have sometimes called neurocentric. The perspective of the scientist is third-person, which I have sometimes called xenocentric.

7 Three Approaches to Information and Probability Frequentist, Third-person Bayesian, and First-Person Bayesian The conventional approach is an ill-defined mixture of frequentist and third-person approaches The frequentist approach is really just a misguided and rather incoherent third-person approach in which scientists pretend that probabilities correspond to frequencies The third-person Bayesian perspective is perfectly legitimate This is the conventional perspective of scientists, and it may be the best perspective for most science and engineering problems But for biological and artificial nervous systems, it leads to very complex descriptions and limited insight. A first-person Bayesian perspective may be simpler and more useful It might be simpler to understand the nervous system from the first-person perspective A first-person approach to the nervous system has been used for high levels of the nervous system, but almost not at all for understanding lower levels.

8 B.F. Skinner and Behaviorism Skinner viewed animals and people as a black box. He argued that we can understand behavior without understanding the contents of the black box. We just need to observe the relationship between inputs and outputs Behavior depends strongly on the environment (inputs), and especially reward and punishment (reinforcement) He did not argue that brain mechanisms were unimportant, but rather that we do not or cannot know what is happening in the brain. Therefore it is not an appropriate basis for scientific study of behavior.

9 The Conventional Xenocentric Approach The input-output (IO) function describes what the scientist knows about the system The scientist is an external observer of the system The internal physics and information of the black box determine the IO function, but we do not, and perhaps cannot, know about the contents of the black box So we ignore it

10 Behaviorism Behaviorism views an animal from the perspective of a third-person observer Skinner s views, and behaviorism were extremely influential in psychology (especially ~ ). Behaviorism eventually was rejected by most psychologists and neuroscientists. Most people now view behavior as the result of brain mechanisms, and they seek to understand psychology from the firstperson perspective of the brain. One first-person school of thought is sometimes called cognitivist In our personal lives, we almost never use Skinner s approach. We use a first-person approach to understand the people whom we know

11 A Theory of Mind In psychology, a theory of mind refers to the understanding that another person is likely to have different information from oneself. Young children (less than ~4 or 5 years) do not have a theory of mind Non-human adult apes may or may not have a theory of mind, but other animals are not thought to have a theory of mind. Without a theory of mind, it is not possible to understand another person s perspective In our daily lives, we almost always use a theory of mind to understand other people (or pet animals). We do not use a theory of mind to understand other types of objects.

12 Test for A Theory of Mind A young girl and her mother are in a kitchen with an experimenter The experimenter puts a spoon in drawer A, while the mother and daughter watch The mother leaves the kitchen and is out of sight. The experimenter then removes the spoon and places it in drawer B, while the girl watches The mother then returns to the kitchen, and the experimenter asks the girl where will your mother look for the spoon? Young children will answer drawer B. They do not possess a theory of mind. The girl cannot distinguish her knowledge from her mother s knowledge. Scientists have made analogous errors, and have attributed their knowledge to the neural systems they study (probably due to frequentist notions)

13 Perspectives in Contemporary Neuroscience There is no unified approach in neuroscience today. Some fields use a neurocentric approach, and others, xenocentric Studies of higher-level or cognitive brain regions use a neurocentric (first-person) approach. Studies of sensory and motor regions use a combination of approaches, but mostly xenocentric. Studies of single neurons always use a xenocentric approach. Thus we treat higher parts of the brain like a person, and lower or smaller parts like an object. There is no scientific basis for this distinction, and most people are unaware of the distinction. The distinction is natural and intuitive to our minds. The new approach that I will advocate is to apply a firstperson, neurocentric perspective to all the neurons in the brain

14 Skinner s Xenocentric Approach

15 Neurocentric Inference at the Level of Perception and Behavior There has been tremendous progress in the last decade in applying Bayesian principles to understand high-level phenomena, mostly in humans This includes perception, language, motor control Studies have identified the information that the brain uses, even though they know nothing about the neural mechanisms

16 The Aperture Problem The direction of motion of a large object is ambiguous when viewed in a small region of space (an aperture ) Given the current sensory evidence, motion could be in any direction over a range of 180 degrees What is the relevant prior information (what are the most common patterns in the world)? There is more likely to be one object moving with one velocity rather than multiple objects moving with multiple velocities. Objects tend to move slower rather than faster. It has been shown that the brian has this prior information, which it must have learned (through development or evolution) A Detailed Study Weiss, Simoncelli, and Adelson. Motion illusions as optimal percepts. Nature Neuroscience 2002

17 Bayesian Integration in Sensorimotor Learning Kording and Wolpert, Nature 2004 As in studies of visual illusions, this study provided evidence of Bayesian integration In the case of visual illusions, the prior information comes from a lifetime of experience with the visual world. Prior information is not controlled by the experimenters In this experiment, they manipulated a frequency distribution, and they showed that subjects were able to learn about that distribution and use that knowledge as their prior in Bayesian integration.

18 The Physical Basis of Inference Studies have not identified the neural basis of inference How is it possible for one physical system (the observer) to infer the state of another physical system (the object) No one has ever explained this in any detail. Is inference unique to the human brain, or animal brains, or cells, or biochemistry, or is it a universal property of matter and energy?

19 What information does a neuron possess?

20 The Neuron s Point of View What information does a neuron have about its world? Information must have a biophysical basis We know a lot about the biophysical properties of neurons. We can quantify the information of a neuron by combining our knowledge of its biophysical properties with Jaynesian probability theory. A neuron has sensors that are coupled to ion channels, and they therefore alter membrane voltage. What information is in a single sensor? A population of sensors? The neuron s membrane voltage?

21 The Information in a Simple Molecular Sensor Boltzmann s Equation 1 P 2 = 1 + exp E 2 E 1 k B T UP, 2 DOWN 0.03 Likelihood Sensor on off UP, 1 DOWN No Sensors Voltage

22 A Neuron s Information By reducing uncertainty, the sensors in a single neuron contribute to the general goal of the nervous system. But if the information is about light intensity, it is of limited use. In order to make decisions, the system needs to have information about future reward (biological fitness). Getting reward information from external sensory quantities like light intensity is difficult. That is the main problem that is solved at the network level, not at the single neuron level. We will address it in later lectures.

23 The Computational Goal of the Brain Precisely quantifying a neuron s information may be useful to us in understanding things like the properties of ion channels and synapses However, for most of the things that we would like to know about the nervous system, quantifying information precisely is not very useful. Usually, we would just like to know what information a neuron has, in a qualitative sense. The important reason for introducing Jaynesian (Bayesian) theory is that it allows us to describe the computational goal of the nervous system very clearly. The goal is to reduce uncertainty, and we can state precisely and quantitatively how that happens, at least in principle. We can then start to investigate how the nervous system achieves that goal.