Neurophysiology and Information: Theory of Brain Function Christopher Fiorillo BiS 527, Spring 2013 042 350 4326,
[email protected]
Lecture 7: The Brain’s Perspective: Application of
Probability to the Brain
Fiorillo CD (2012) Beyond Bayes: On the need for a unified and Jaynesian definition of probability and information within neuroscience. Information 3: 175-203.
http://www.mdpi.com/2078-2489/3/2/175
Assistants: Sunil Kim, 이주영 Ju-Young Lee,
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
Perspectives in Physics
• In order to apply the rules of physics (Newton’s laws, conservation of energy, etc.), we must choose a “frame of reference” • The rules of physics are followed for each observer, but the observers will not agree with one another (about values such as velocity) This is the principle of relativity. – The perspective of one observer can be related to that of another (for example, through the “Lorentz transformation”)
• We would like to be able to understand our perspective of a neuron’s inputs and outputs, and also the neuron’s perspective, and how they relate to each other
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?
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) • 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.”
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.
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.
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
Behaviorism • Behaviorism views an animal from the perspective of a third-person observer • Skinner’s views, and “behaviorism” were extremely influential in psychology (especially ~ 1950 - 1980). • 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
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.
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)
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
Skinner’s Xenocentric Approach
Neurocentric Inference in 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, and motor control, as we discussed in a previous lecture
• Studies have identified the information that the brain uses, even though they know nothing about the neural mechanisms
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?
What information does a neuron possess?
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?
Information is causation, and flows with energy
The Information in an Ion Channel • An ion channel is a protein that is sensitive to a “stimulus,” which is either a particular chemical, or voltage across the cell membrane • It can exist in two or more conformations • It knows its own state and its intrinsic properties – Temperature – Conformation – How its conformation depends on its “stimulus” (this is an intrinsic property of the molecule)
The Information in a Simple Molecular Sensor Boltzmann’s Equation
1 P2 = ⎛ E2 − E1 ⎞ 1+ exp⎜ ⎟ k T ⎝ B ⎠ 0.04 0.035
6 UP, 2 DOWN
0.03
Likelihood
Sensor Sensor “on” “on” “off”
0.025
3 UP, 1 DOWN
0.02 0.015
No Sensors
0.01 0.005
Voltage
0 ï0.08
ï0.07
ï0.06
ï0.05
ï0.04
ï0.03
ï0.02
ï0.01
0
The Information in an Ion Channel • The probabilities distributions on the previous slide cannot be correct – A probability distribution can never have a sigmoid shape over an infinite state space – There was no prior distribution, which is essential – Boltzmann’s distribution was not derived for this problem and is probably inappropriate
• But the ion channel clearly has information, and the basic idea on the previous slide is correct
Physical Inference • Even in the absence of any sensors, in the absence of any interaction with the external world, it is still possible to estimate its state • This is because all of the basic aspects of the external world have internal analogs • In statistical mechanics, temperature alone is sufficient to derive probability distributions for some quantities (such as velocity) • Given only internal mass M, the external mass would follow an exponential distribution with expected value equal to M. – This would be prior information, because it always available, even without any sensory evidence • There is always some information. A state of complete ignorance does not exist
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.
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.