Prediction Error Minimization and Implications


slowimages This is the final of three posts on this subject. It reflects the work of Jakob Hohwy as referenced in the post Explaining Away and an interview in connection with his book: The Predictive Mind.

An interesting example of the hierarchical predictive coding model is binocular rivalry. Binocular rivalry is a form of visual experience that occurs when, using a special experimental set-up, each eye is presented (simultaneously) with a different visual stimulus. Thus, the right eye might be presented with an image of a house, while the left receives an image of a face. Under these albeit artificial conditions, subjective experience unfolds in a surprising, “bi-stable” manner. Instead of visually experiencing a confusing all-points merger of house and face information, subjects report a kind of perceptual alternation between seeing the house and seeing the face.

The driving (bottom-up) signals contain information that suggests two distinct, and incompatible, states of the visually presented world – for example, face at location X/house at location X. When one of these is selected as the best overall hypothesis, it will account for
all and only those elements of the driving input that the hypothesis predicts. As a result, prediction error for that hypothesis decreases. But prediction error associated with the elements of the driving signal suggestive of the alternative hypothesis is not suppressed; it is now propagated up the hierarchy. To suppress those prediction errors, the system needs to find another hypothesis. But having done so (and hence, having flipped the dominant hypothesis to the other interpretation), there will again emerge a large prediction error signal, this time deriving from those elements of the driving signal not accounted for by the flipped interpretation. No single hypothesis accounts for all the data, so the system alternates between the two semi-stable states. It behaves as a bi-stable system.

We do not experience a combined or interwoven image, because they do not constitute a viable hypothesis given our more general knowledge about the visual world. For it is part of that general knowledge that, for example, houses and faces are not present in the same place, at the same scale, at the same time. This, indeed, is the explanation of the existence of competition between certain higher-level hypotheses in the first place. They compete because the system has learned that “only one object can exist in the same place at the same time”.

hohwybinUntitledFigure 5 is from “Predictive coding explains binocular rivalry: an epistemological review.”

According to Hohwy, the messages that are passed around in the hierarchy are the sufficient statistics:  predictions and prediction errors concerning (1) the means of probability distributions associated with various sensory attributes or causes of sensory input out there in the world, and (2) the precisions (the inverse of variance) of those distributions. Hohwy suggests that the brain uses the normal (Gaussian) distribution. The hierarchy gives a deep and varied prediction error landscape, where prior probabilities are “empirical” in that they are learned and pulled down from higher levels, so they do not have to be extracted brand new from the current input. This reliance on higher levels means that processing at one level depends on processing at higher levels.

Different causal regularities in nature, working at different time scales, influence each other and thereby create non-linearities in the sensory input. Without such interactions, sensory input would be linear and fairly easy to predict both in detail and far into the future. So the temporal organization of the hierarchy reflects the causal order of the environment as well as the way the causes in the world interact with each other to produce the flow of sensory input that brains try to predict. Hohwy suggests that we make second order predictions or hypotheses about the accuracy of the input that comes from a noisy, uncertain non-linear world.

The brain actively changes itself and actively seeks out expected sensory input in an attempt to minimize prediction error. This means the brain seeks to expose itself to input that it can explain away. Attention through consciousness might be a way that the brain seeks input for testing certain hypotheses.

The brain maintains its own integrity in the onslaught of sensory input by slowing down and controlling the causal transition of the input through itself. If it had no means to slow down the input its states would be at the mercy of the world and would disperse quickly. Hohwy states that a good dam builder must slow down the inflow of water by slowing down and controlling it with a good system of dams, channels, and locks. This dam system must in some sense anticipate the flows of water in a way that makes sense in the long run and that manages flows well on average. The system will do this by minimizing “flow errors”, and it will do this by learning about the states of water flow in the world on the other side of the dam.

This means that other types of descriptions of mental processes must all come down to the way neurons manage to slow sensory input. Hohwy is studying autism as a disorder where the prediction hierarchy is stuck closer to the senses so the model of the world is not corrected through a great number of repetitions. Thus, things are not slowed down enough. Hohwy provides an example of trying to determine the mean of 20 numbers, but we are given them one at a time, and if things are working correctly, we maintain a running mean that in stepwise manner eventually can make the determination. However, in this example, an autistic person would be presented with a single number each time without the running mean. This makes prediction difficult.

Many of the technical, social and cultural ways we interact with the world can be characterized as attempts to make the link between sensory input and environmental causes less volatile–slowing them down. We see this in the benefits of the built environment that protect from the heat or cold, in radio that lets us hear things directly rather than through hearsay, and in language. This picture relies on the internal nature of the neural mechanism that minimizes prediction error, relative to which all our cultural and technological trappings are external. Culture and technology situate the mind closer to the world through improving the reliability of its sensory input. They help us to communicate with and predict other people’s behavior more accurately. An overlooked aspect  is that ritual, convention, music, and other shared practices help align our mental states with each other and further enhance mutual predictability.

Professional athletes talk about how the game slows down as they get used to a stiffer level of competition. Their predictive models get better and that slows things down. My budding football career burned out at age 14. Having progressed from backyard football to 11 men on a team football, I can recall carrying the ball and getting beyond the line of scrimmage and just seeing a blur–not knowing what to focus on. Slowness also seems to be the opposite of an anxiety attack where ideas spiral and move too quickly. That the brain exists to slow sensory input is an interesting idea.