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| Susanna Siegel |
Update: on 4th May we posted a reply to this post from Jakob Hohwy that can be seen here.
Chapter 3 - Prediction Error, Context, and Precision
Presented by Susanna Siegel
Presented by Susanna Siegel
Chapters 1 and 2 sketch a picture on which the brain generates perceptual experiences and judgment by relying on learned expectations to help interpret sensory signals. The need for interpretation arises initially because the signals are informationally impoverished, compared to the contents of the perceptual experiences and judgments that we end up with. The main point of Chapter 3 is that in addition filling in missing about the external world that’s missing from the initial sensory signal, there is a second dimension along which the brain has to respond to the sensory signal. It has to assess whether any given signal itself is ‘noisy’, where this means that it is not the result of a mechanism that systematically relates the subject to the distal stimulus that the perceptual experience purports to characterize. A signal is noise if it results from a random fluctuation, or some other process that isn’t systematically connected to any properties or objects in the world.
There are thus two sources of uncertainty that each generate a need to interpret sensory signals: The first-order impoverishment of the initial sensory signals themselves, and the second-order uncertainty about whether to ‘trust’ whatever information is given by the sensory signals, however paltry that information may be.
Hohwy describes what’s needed to address the problem of second-order uncertainty in several ways. What’s needed is “second-order perceptual inference”, “engaging in second-order statistics that optimize precision expectations”, a “need to not only assess the central tendency of the distributions, such as the mean, but the variation about the mean”, a need to “modulate the way prediction errors are processed in the perceptual hierarchy”. Suppose I’m collecting signals and they form a trend. Now the nth signal comes in. The trend predicts that the nth signal will say “Yellow”. But instead the signal says “Grey”. Suppose I have little confidence in this signal. My second-order verdict on whether to trust it is that it’s probably unreliable.
First question: What are proper grounds for low confidence in a signal? The mere fact that it bucks the trend shouldn’t be enough, and shouldn’t even be necessary. In a specific case, I might know that the signal is due to random variation. But often we don’t have information about specific cases. We rely on generalizations about how much random variation there is likely to be. Presumably different generalizations are reasonable, depending on the information-collection mechanism. They could even differ within the brain. If a trend-bucking signal comes in, we might have some reason to think it is noise, and some reason to think it is merely surprising. If our choice is to either take the signal at face value or not, then what are grounds for deciding not to? And if we answer this question at the level of the explicit deliberation that a person can do, what is the analogous answer for a mechanism or for the brain?
First question: What are proper grounds for low confidence in a signal? The mere fact that it bucks the trend shouldn’t be enough, and shouldn’t even be necessary. In a specific case, I might know that the signal is due to random variation. But often we don’t have information about specific cases. We rely on generalizations about how much random variation there is likely to be. Presumably different generalizations are reasonable, depending on the information-collection mechanism. They could even differ within the brain. If a trend-bucking signal comes in, we might have some reason to think it is noise, and some reason to think it is merely surprising. If our choice is to either take the signal at face value or not, then what are grounds for deciding not to? And if we answer this question at the level of the explicit deliberation that a person can do, what is the analogous answer for a mechanism or for the brain?
Second question: Suppose I disregard the “Grey” signal on the grounds (whatever they are) that it’s probably just noise. The “Grey” signal is not the signal predicted by the trend, so there’s a discrepancy between the expectation and the signal. Terminological question: Is this signal a prediction error? Answer 1: Yes, because of the discrepancy between the expectation and the signal. Answer 2: No, because the signal has been classified as noise, and therefore not at odds with the expectation. There’s a discrepancy, but not yet any ‘mistake’ on the part of the expectation.
Here’s a remark from p. 66 that doesn’t decide between these answers: “If the reliability of the signal is expected to be poor, then the prediction error unit self-inhibits, suppressing prediction error such that its signaling is weighted less in overall processing.” “Inhibiting” the prediction error could mean, not classifying a signal as an error – as per Answer 2. But “weighing the prediction error signal less” suggests that Answer 1.
What are the functional differences between the verdicts of second-order monitoring ‘Be very confident in this signal’, ‘Ignore the signal – it is just noise’, or something in between? I find a few different functional possibilities on the thumbs-down verdict(s) of second-order monitoring. I’d like to know where Hohwy locates these differences in the PEM framework, and how they differ from functions that seem similar but don’t seem to stem from second-order inference. In some cases, the same function could be performed either as a response to second-order inference, or in response to first-order inference. I’m going to list a bunch of responses the brain could make to a signal, in order to try to clarify (i) the impact of second-order perceptual inference on perceptual processing, (ii) when and how it differs functionally from first-order perceptual inference, (iii) its role in Bayes’ theorem.
To illustrate, let’s fill out the Yellow/Grey example. Suppose you see a banana. Let’s say it really is grey, and that the initial sensory signal reflects this, because it is produced by a mechanism that is systematically connected to the color of the banana. Metaphorically: the color of the banana says, through the sensory signal, “I’m gray”. Enter the problem of second-order uncertainty. The problem is to assess whether this greyness-signal is or isn’t noise. I’ve been talking so far as if the signal simply says “Gray”, without any incremental structure. But we could think of the signal in the form of a probability distribution of over colors. Since it seems needlessly exact to assign numerical values to the options, let’s talk in comparative terms. Suppose “Grey” = pretty loud signal. “Yellow” = pretty weak signal. Then for each of these signals, the problem of second-order certainty arises. E.g., in principle, the “Grey” signal could fail the second-order test, but “Yellow” could pass it.
Third question: Does the signal come in the form of a probability distribution? (I’ve simplified by talking as if the information was atomistic – just about color, rather than being clusters of color with other properties. But whatever the content o the signal is, we can ask whether it belongs to a structure of distribution of probabilities). If so, how can we assess whether early sensory signals really do come in this structure, independently of the framework? You might say: “The explanatory power of the framework gives us reason to think that signals are structured in this way.” But could we get independent confirmation of this structure in some way? If so, how? What kind of evidence would speak against this hypothesis?
Fourth Question: Continuing the metaphor of dialog between brain and banana, here are four functions whereby the “Grey” signal is not allowed to impact the trend that predicted something other than Grey. These are all ways in which the “Grey” signal could fail to end up determining the content of the color experience. I’m listing these to ask about (i) the impact of second-order perceptual inference on perceptual processing, (ii) when and how it differs functionally from first-order perceptual inference.
Option 1: Outweighing by second-order inference. The “Grey” signal is loud and clear. Its loudness and clarity gives it some amount of weight favoring the hypothesis that X (the banana) is grey. But the noise-assessment verdict has more weight, and so it outweighs the “Grey” signal.
Dialog form
What are the functional differences between the verdicts of second-order monitoring ‘Be very confident in this signal’, ‘Ignore the signal – it is just noise’, or something in between? I find a few different functional possibilities on the thumbs-down verdict(s) of second-order monitoring. I’d like to know where Hohwy locates these differences in the PEM framework, and how they differ from functions that seem similar but don’t seem to stem from second-order inference. In some cases, the same function could be performed either as a response to second-order inference, or in response to first-order inference. I’m going to list a bunch of responses the brain could make to a signal, in order to try to clarify (i) the impact of second-order perceptual inference on perceptual processing, (ii) when and how it differs functionally from first-order perceptual inference, (iii) its role in Bayes’ theorem.
To illustrate, let’s fill out the Yellow/Grey example. Suppose you see a banana. Let’s say it really is grey, and that the initial sensory signal reflects this, because it is produced by a mechanism that is systematically connected to the color of the banana. Metaphorically: the color of the banana says, through the sensory signal, “I’m gray”. Enter the problem of second-order uncertainty. The problem is to assess whether this greyness-signal is or isn’t noise. I’ve been talking so far as if the signal simply says “Gray”, without any incremental structure. But we could think of the signal in the form of a probability distribution of over colors. Since it seems needlessly exact to assign numerical values to the options, let’s talk in comparative terms. Suppose “Grey” = pretty loud signal. “Yellow” = pretty weak signal. Then for each of these signals, the problem of second-order certainty arises. E.g., in principle, the “Grey” signal could fail the second-order test, but “Yellow” could pass it.
Third question: Does the signal come in the form of a probability distribution? (I’ve simplified by talking as if the information was atomistic – just about color, rather than being clusters of color with other properties. But whatever the content o the signal is, we can ask whether it belongs to a structure of distribution of probabilities). If so, how can we assess whether early sensory signals really do come in this structure, independently of the framework? You might say: “The explanatory power of the framework gives us reason to think that signals are structured in this way.” But could we get independent confirmation of this structure in some way? If so, how? What kind of evidence would speak against this hypothesis?
Fourth Question: Continuing the metaphor of dialog between brain and banana, here are four functions whereby the “Grey” signal is not allowed to impact the trend that predicted something other than Grey. These are all ways in which the “Grey” signal could fail to end up determining the content of the color experience. I’m listing these to ask about (i) the impact of second-order perceptual inference on perceptual processing, (ii) when and how it differs functionally from first-order perceptual inference.
Option 1: Outweighing by second-order inference. The “Grey” signal is loud and clear. Its loudness and clarity gives it some amount of weight favoring the hypothesis that X (the banana) is grey. But the noise-assessment verdict has more weight, and so it outweighs the “Grey” signal.
Dialog form
Brain: What color are you?
Banana: I’m gray.
Brain (to itself): X’s saying that is just a fluke.
Compare Outweighing by prediction. The “Grey” signal is loud and clear. Its loudness and clarity gives it some amount of weight favoring the hypothesis that X (the banana) is grey. But the expectation that X will be yellow has more weight, and so it outweighs the “Grey” signal.
Dialog form
Compare Outweighing by prediction. The “Grey” signal is loud and clear. Its loudness and clarity gives it some amount of weight favoring the hypothesis that X (the banana) is grey. But the expectation that X will be yellow has more weight, and so it outweighs the “Grey” signal.
Dialog form
Brain: What color are you?
Banana: I’m gray.
Brain: But you’re a banana. You must be yellow.
Q: Is there a difference in what gets “passed up through the perceptual hierarchy”? What would we need to know, in a given case, to know which of these two kinds of outweighing was occurring?
Option 2: Resolution of first-order uncertainty. The “Grey” signal is weak, and the other color signals are too. In the face of impoverished color information, the expectation that X will be yellow has more weight than any of the incoming sensory signal.
Dialog form
Q: Is there a difference in what gets “passed up through the perceptual hierarchy”? What would we need to know, in a given case, to know which of these two kinds of outweighing was occurring?
Option 2: Resolution of first-order uncertainty. The “Grey” signal is weak, and the other color signals are too. In the face of impoverished color information, the expectation that X will be yellow has more weight than any of the incoming sensory signal.
Dialog form
Brain: What color are you?
Banana: I dunno - maybe red, maybe blue, maybe green, maybe grey… but I’m a banana.
Brain: Well then you must be yellow.
Q: Could second-order monitoring lead to the assessment that there is no systematic relationship between the color signals and the banana’s color?
Option 3: Pre-emptive silencing by second-order inference. The “Grey” signal that starts out weak, but if given a chance to evolve, it would become stronger. But the expectation that the signal is noise stops its evolution.
Dialog form
Q: Could second-order monitoring lead to the assessment that there is no systematic relationship between the color signals and the banana’s color?
Option 3: Pre-emptive silencing by second-order inference. The “Grey” signal that starts out weak, but if given a chance to evolve, it would become stronger. But the expectation that the signal is noise stops its evolution.
Dialog form
Brain (to itself): I wonder what color you are.
Banana: I dunno, maybe I’m gray.
Brain (to itself): There’s no way it could find out. It’s probably yellow since it’s a banana.
Compare Pre-emptive silencing by prediction. There’s a “Grey” signal that starts out weak, but if given a chance to evolve it would become stronger. But the expectation that X is yellow stops the evolution of the signal.
Dialog form
Compare Pre-emptive silencing by prediction. There’s a “Grey” signal that starts out weak, but if given a chance to evolve it would become stronger. But the expectation that X is yellow stops the evolution of the signal.
Dialog form
Brain: What color are you?
Banana: I dunno, maybe I’m gray.
Brain: Well don’t bother trying to find out. It would be inefficient for you to spend your efforts investigating. You’re a banana, so you must be yellow.
Q: What are the functional differences between these two kinds of pre-emptive silencing?
Fifth question: Noise and Bayes. Where can we locate second-order inferences in Bayes’ theorem? If my noise-monitor decides that “Grey” signal is noise, and the brain is calculating a conditional probability of H|Grey, is that just one route by which it would decrease the likelihood (Grey|H)? Or does second-order monitoring for how noisy “Grey” is have some separate role apart from the calculation of H|Grey?
Sixth question: Binary experiences in a sea of probability distributions? One of the promises Hohwy makes for PEM is to explain how it is that we come to have experiences we do. Why do we end up experiencing the Muller-Lyer lines as different lengths? Why do we end up with the rubber hand illusion? An answer that appeals to Bayesian processing can take the following form. You end up with an experience with content Hi, because there was an early sensory signal that played the role of E in the production of a distribution of conditional probabilities of H|E over hypothesis space containing H’s, and in that distribution, Hi|E came out highest. So it was selected to be the content of the experience. This story glides over the fact that E, too, is a distribution. So at some point there had to be a selection of which Ejfigured in the calculation using Bayes’s theorem of the winning H, and which E in the distribution was conditionalized on to get unconditional H. Presumably the winning E is the strongest signal in a distribution. E.g., “Grey” is .7 and “Not Grey” is .3, then E = “Grey”, and no other calculations over “Not Grey” need to be made.
On this picture, experience is a lone binary state in a sea of signals that are structured as probability distributions. Why do you think experience is special? Do you think its phenomenal character rules out its having a structure like the one you find in other sensory signals? If you think experience isn’t special, and does share a structure like the other signals, then how is the distribution within experience derived from prior processing?
Q: What are the functional differences between these two kinds of pre-emptive silencing?
Fifth question: Noise and Bayes. Where can we locate second-order inferences in Bayes’ theorem? If my noise-monitor decides that “Grey” signal is noise, and the brain is calculating a conditional probability of H|Grey, is that just one route by which it would decrease the likelihood (Grey|H)? Or does second-order monitoring for how noisy “Grey” is have some separate role apart from the calculation of H|Grey?
Sixth question: Binary experiences in a sea of probability distributions? One of the promises Hohwy makes for PEM is to explain how it is that we come to have experiences we do. Why do we end up experiencing the Muller-Lyer lines as different lengths? Why do we end up with the rubber hand illusion? An answer that appeals to Bayesian processing can take the following form. You end up with an experience with content Hi, because there was an early sensory signal that played the role of E in the production of a distribution of conditional probabilities of H|E over hypothesis space containing H’s, and in that distribution, Hi|E came out highest. So it was selected to be the content of the experience. This story glides over the fact that E, too, is a distribution. So at some point there had to be a selection of which Ejfigured in the calculation using Bayes’s theorem of the winning H, and which E in the distribution was conditionalized on to get unconditional H. Presumably the winning E is the strongest signal in a distribution. E.g., “Grey” is .7 and “Not Grey” is .3, then E = “Grey”, and no other calculations over “Not Grey” need to be made.
On this picture, experience is a lone binary state in a sea of signals that are structured as probability distributions. Why do you think experience is special? Do you think its phenomenal character rules out its having a structure like the one you find in other sensory signals? If you think experience isn’t special, and does share a structure like the other signals, then how is the distribution within experience derived from prior processing?
Thanks for these cool questions, Susanna. Some answers here
ReplyDeletehttp://philosophybirmingham.blogspot.co.uk/2014/05/HohwyRepliestoSiegel.html#more
Feel free to chip in!