Neurophysiology and Information: Theory of Brain Function

Transcription

1 Neurophysiology and Information: Theory of Brain Function Christopher Fiorillo BiS 527, Spring , Part 1: Inference in Perception, Cognition, and Motor Control Reading: Students should visit some websites where they can experience and learn about illusions. Addresses are given in later slides.

2 What is the function of the brain? We would like to state this in terms that are as general as possible, while also being quantitative If it is possible to develop a general theory of how the brain works, then we must first identify a general computational goal

3 The function of the brain is to produce motor outputs Plants do not have a nervous system Tunicates (sea squirts) have a nervous system early in development. They swim until they find a good place to live. Then they eat (digest) all of their brain and never move again. This general point has been described eloquently by Daniel Wolpert, a neuroscientist who studies motor systems. Animals must select some motor actions over others. This is decisionmaking

4 Uncertainty is the Problem in Making Decisions If I knew everything, then I would have no uncertainty I would always know exactly what I should do, and I would make perfect decisions The more information I have about the world, the better my decisions, and the more successful I am (in terms of biology) Uncertainty is the only problem in making decisions The function of the brain is to get as much information as possible (about aspects of the world that are of biological importance) In other words, the function of the brain is to minimize its uncertainty about the world

5 Inference Rene Descartes ( ) famously wrote: Cogito ergo sum, I think therefore I am. He argued (very persuasively) that he could be certain of his own existence, but that everything else that he knew was uncertain This was among the most important arguments ever made in epistemology, the study of knowledge Inference refers to knowledge of the world, which is necessarily characterized by uncertainty. I use inference as a synonym of estimate or predict or hypothesis or guess. I also use knowledge and information as synonyms Inference is quantitatively described through probabilities, which we will discuss in later lectures

6 Why is everything uncertain? For any particular aspect of the world that one wants to know about, there are other aspects that interfere. The world consists of many things, and they interfere with one another. Any event could have more than one possible cause. Hermann von Helmholz gave the example of being punched in the eye and seeing a flash of light Obviously that does not happen often. But when you see light, you cannot be certain whether it comes from photons, or from mechanical pressure on your eye. von Helmholz was also a founder of what is now known as thermodynamics, a branch of physics that deals especially with heat Thermodynamics and statistical mechanics gives a more general answer to the question of why everything is uncertain

7 Energy Information A B Perception Inference Information Flows through A Series of Molecular Sensors C Retinal the light sensor in rhodopsin

8 Heat Makes Inference More Difficult Retinal is used by the eye because it is sensitive to light. But like all other sensors, it is also sensitive to heat. Heat is the movement of molecules. The rhodopsin molecule, including retinal, has internal movement in the absence of any external force. Other molecules collide with rhodopsin These microscopic mechanical forces can also change the conformation of retinal The conformation of a sensor is influenced by light, chemical concentration, etc. But it is also influenced by heat, and sometimes by other events, such as being punched in the eye All of the information of the brain (and the universe) relies upon molecular sensors such as this. There is nothing else in the brain. Thus there is always at least a small amount of uncertainty.

9 Everything the Brain Does is Inference Every function of the brain can be understood as inference (or prediction) Performing inference simply means have the right information at the right time Bayesian methods are being used to try to quantify inference using probabilities However, there are many aspects of brain function that can be understood as inference even without careful quantitative methods We will next discuss examples, starting with perception.

10 Perceptual Bistability These images exhibit perceptual bistability There are two ways in which they are perceived, and they alternate There are numerous objects that are consistent with these images. The sensory evidence is ambiguous. The brain guesses that one of two objects is the most probable given knowledge of objects in the real world. Perception corresponds to the best guess. For example, the lower image is seen as a 3-D cube, rather than as an unusual combination of 1-D lines In the visual system, there are neurons for faces and vases and cubes of various orientations, but not for objects that have not been learned through experience. We expect to see faces and vases and cubes, but other possibilities are improbable

11 Binocular Rivalry When different images are presented to the two eyes, one image is seen (usually for a few seconds), and then the other One does not see a superposition (mixture) of the two, or an average To observe rivalry, view the images from a short distance, but allow your eyes to relax as though you are looking at something far away Rivalry demonstrates that some of the information that is present at low levels of the visual system is suppressed and does not advance to the high levels Since the two images are not compatible with one another, the high levels see only one or the other This is a rational inference When the two images differ quantitatively rather than qualitatively, then one observes an average of the two The alternation could be explained by adaptation of neurons at higher levels of cortex Rivalry is not seen at all in LGN. It is weakly present in neurons of striate cortex, and becomes stronger at higher levels. It is essentially complete in IT cortex.

12 Illusions Many illusions are the result of rational inference The sensory evidence coming into the brain is ambiguous There are many possible interpretations of what is the true state of the world. To guess, the brain combines prior information with new sensory information Prior information is already in the brain as the result of learning about patterns in the sensory world Some patterns are common, and these are the patterns that the brain expects to see Illusions occur when sensory patterns are unusual (in a statistical sense). The rational, best guess is that the pattern is similar to the pattens that have been experienced in the past (based on the prior information). But in some rare circumstances, our best guess is wrong, and we experience an illusion. The critical point is that when we experience an illusion, we are doing the best we possibly can with our limited information. Our brains are working perfectly.

13 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. A Detailed Study Weiss, Simoncelli, and Adelson. Motion illusions as optimal percepts. Nature Neuroscience 2002

14 An Audiovisual Illusion The McGurk Effect v=t4fui0eg1x4&feature=related When we watch someone speak, our perception of their words depends on both auditory and visual information Conscious perception corresponds to high-level multisensory neurons, not lowlevel monosensory neurons

15 Inference in Language Language comprehension relies on knowledge of the statistical structure of language Grammar specifies rules, and knowledge of these rules is important for comprehension. The probability of a particular word depends strongly on the preceding words, and on the context (subject matter) Seidenberg, Language acquisition and use: learning and applying probabilistic constraints Science, 1997.

16 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. 2 types of information were used: information about past target locations, and visual information about current finger (and cursor) location. Finger movement depended on both of these (in an optimal manner)

17 Prediction in Motor Control Prediction of external forces is necessary to maintain posture and for many aspects of motor control Multiple types of information are important. Proprioceptive information about relative position of body parts Visual information Information of about self-generated motor outputs These can be illustrated by a simple experiment that we will attempt to perform in class When I remove a weight from my own hand, I can predict the precise time of the change in force and I can therefore adjust the contraction of my muscles (unconsciously) so that my hand does not move. When someone else removes a weight from my hand, I cannot predict the precise time of the change in force, and therefore I cannot keep my hand still, even if I try.

18 Bayes s Theorem Posterior distribution = prior X likelihood Best guess = combination of prior knowledge with current sensory evidence Information can be separated in various ways prior knowledge, current visual evidence, current auditory evidence, etc. Examples: The aperture problem McGurk Effect Sensorimotor task P(B AC) P(A BC) = P(A C) x P(B C)