Are our brains Bayesian? (2016)
rss.onlinelibrary.wiley.com
rss.onlinelibrary.wiley.com
In the 90s we finally switched it up, and developed computing paradigms based on human biology, and came up with applying neural nets to brain science. Then someone had the idea to create a Bayesian NN.
Each iteration we get closer to explaining how the brain works, but showing that each iteration is closer to workable based on our knowledge of the biology of the brain.
But we still have no idea how we get from brain biology to rational (and irrational) thought. I'd be excited if we solved this within my lifetime.
People are taught in school that a sufficient response to the question "how do we hear things?" is to talk about sound waves, the shape of the outer ear, the tympanic membrane, malleus, incus, stapes, cochlea, etc. At some point you arrive at: "and then the brain processes the signal in the auditory cortex and stuff." We have become accustomed to this sort of answer, but it really doesn't even begin to answer the real (and interesting) question: why does all that processing result in the felt experience of hearing, rather than the nervous system just bubbling up and causing a behavior with no feelings? Why does it "feel" that way and not some other way? Is there a different kind of hearing that "feels" fundamentally different from our experience?
My point is that, we are closer to explaining some functional aspects of the brain, but when it comes to explaining the nature and character of our qualitative experience, we are at the same place as the ancient Eastern philosophers - we've really gotten nowhere.
Fortunately, it is a question, which can stay unanswered with no practical consequences. It is a subjective counterpart of "Why is there something rather than nothing?", and we aren't answering either anytime soon.
> Is there a different kind of hearing that "feels" fundamentally different from our experience?
Even if there is, we will need different brain hardware to experience it first-hand, otherwise we'd have to do with analogies or, for more precision, with functional descriptions of perceptual processing.
Utterly absurd and completely false. An explanation for the question of why pain feels the why it does, for example, has enormous practical implications and consequences. The current neurological and medical approaches to pain management are poorly understood and often dangerous in extreme cases. We literally don't know why or how Tylenol works. That is a huge problem. The current best-case scenario, absent an explanation of the nature of the character of pain experiences, is that we find some neural activities that we can alter with advanced medical techniques which reliably suppress pain experiences. But it's not clear that 1) we will ever find such techniques, 2) that such techniques would exhaustively alter all the kinds of physical pain a human might experience, 3) that such techniques wouldn't negatively alter other aspects of a person's mind. If we had a fuller explanation of the nature of the character of the experience itself (rather than just treating consciousness like a black box), we might be able to alter the experiences more precisely and appropriately.
I was talking about the question "why does all that processing result in the felt experience [...]?"
Even if we had the answer for the second question (say, "There is immaterial soul which is responsible for our felt experiences and that's why we feel"), it will not help with pain treatment.
Theories of mind have been going back thousands of years from before the time computers were dreamed of. This idea of a technological paradigm of neuroscience falls apart quite easily when you consider the far longer exploration into human consciousness and neurophysiological function, both fields of inquiry are far older than computer science.
Never mind the fact, those that study neuroscience, they speak of neurochemical signaling pathways, of pre- and post-synapatic chemical reaction, or of the functional imaging of the brain's different regions. There is a great deal of genetic analysis, of pharmaceutical interest, and of genuine biological mysteries. I'm sorry but I just don't agree that neuroscientists are couching their field in terms of computers.
The we refers to computer scientists.
And even before computers, we still had technology. But we didn't really have an understanding of brain physiology thousands of years ago, so the statement really only applies to theories on how we get from brain physiology to computing, not theory of mind.
Well of course computer scientists compare the brain to whatever the most advanced AI is. That's how they pitch grant applications!
Hell, I'm doing it right now in this application I've got on Overleaf in another tab, though I guess in reverse: I describe what we know functionally about the brain, then propose to build computational models to study it.
https://en.wikipedia.org/wiki/Perceptron
Leslie Valiant proposed a mathematical model for human learning (and mostly applied to machine learning theory) in the 1980s, and it's been been refined to more explicftly Bayesian models recently:
https://en.wikipedia.org/wiki/Probably_approximately_correct...
http://web.mit.edu/6.435/www/Valiant84.pdf
Anyway, these aren't intended to be faithful models of hmuan brains, but more loosely inspired by functions observed in human brains. There's on good reasoning that an naturally evolved human brain would operate under one simple, sound, fundamental computing principle. It's far more likely to be a mishmash of unsound models, like all evolved physical characteristics of animals.
Quite the opposite, actually. Anything essential to survival and reproduction is optimized for its design constraints quite heavily, resulting in many attributes of observed organisms being physiologically optimal.
You should look into the "rational analysis" paradigm in cognitive science.
The problem there is that "rational" has dual meanings:
* The a priori kind of "rational", as in "optimal according to some equation", where that equation is often Bayesian or RL-related
* The a posteriori kind of "rational", where we decide that science and math are better than intuition and so on.
I pretty much support the Bayesian brain assumption, and the labs I work with follow it in a few different forms, but I suspect that the cognitive science of rationality will some day be a pretty fruitful field. That is, I suspect that a posteriori rationality can't be neatly reduced to a priori optimality[1].
[1] -- http://www.saet.illinois.edu/papers_and_talks/event-07/nolea...
source: Lecture to the London Mathematical Society on 20 February 1947, pdf: http://www.vordenker.de/downloads/turing-vorlesung.pdf, also see this Quora answer for details: https://www.quora.com/What-did-Alan-Turing-mean-by-his-state...). Actually his exact phrasing is the reverse (on pg 13): "... if a machine is expected to be infallible, it cannot also be intelligent. "
How does the Bayesian brain hypothesis deal with this fallacy? It seems to me that nothing based on classical probability can explain this fallacy. So either the observation that humans can assign higher probability to joint events is wrong or human decision making isn't exactly probabilistic (in the classical sense, can't rule out exotic probabilistic approaches).
EDIT: As several folks have commented that the conjunction fallacy can be explained away by different arguments based on interpretation and semantic issues. Indeed, the original Linda problem was susceptible to these issues. However, since then several researchers have tried to study this effect more carefully and it seems to still persist. An example that I'm aware of is the following https://link.springer.com/article/10.3758/BF03195280 where the authors used unambiguous language and a betting paradigm, but still found the effect. Again, this is most likely not fool proof. Regardless, I do not think the fallacy can be trivially explained away as an effect of ambiguous language.
There are other ways the brain could be Bayesian though. For example, at the lowest level our neurons could use Bayesian inference. How this manifests itself at much higher levels such as with language and planning might be difficult to predict.
Instead of choosing from options:
1) Linda is A
2) Linda is A and B
they might actually understand the first statement in the context of the second statement as:
1) Linda is A and not B
[1] https://www.lesswrong.com/posts/QAK43nNCTQQycAcYe/conjunctio...
However, not everybody, you can be trained against that. I've heard that police interrogators are less prone to this fallacy because they know that liars who had time to prepare often add dozens of details to their story that no ordinary person would remember.
Anecdotic: Somebody asked: "Why do I feel often that angry, when I get a 'Typ5-Answer'?" (With the background an TYp5-Answer is located in the field of the manipulation of (someones) reality.
HINT: Typ1-Answer: labeling of 'Objects' / Type2-Answer: naming of coherencies / Ty ....(-;
The crux I think is that when
A. bank teller
is juxtaposed with
B. bank teller and feminist,
we vaguely and falsely interpret A as "bank teller and not feminist", while the correct explicit interpretation is "bank teller and possibly feminist, but possibly not".
Rather than a fallacy of some kind, people may actually be so good at correct inferences that they are bad at leaving that intuition out of their reasoning process when thinking about a weird, outlying theoretical world.
To study how accurately Bayesian some animals are, I think you need to find ways to pose them questions which are relevant to them, and read off their inferences from their behaviour. This is obviously harder to do, and you have to worry a great deal about the animal optimising for something that differs from your first guess (e.g. it doesn't want maximum food on a good day, it wants not to starve on a bad day). I don't have references to hand but I think that when we can do this, the results are quite good.
The Bayesian machinery tells you how to update your beliefs given evidence. It doesn't tell you what shape those beliefs should be in the first place.
My theory is that we carry around a deck of personas or sterotypes. We hear of a new person, and some behaviour of theirs. We then predict which persona was likely to generate that behaviour. Conditional on the distribution over personas we answer the questions about that person's predicted behaviour.
In the `Linda` example the theory above suggests we take the background information about all their political commitments at college, which from the description would seem to give strong evidence about their persona.
The common and wrong answer to the question stems from predicting, based on the persona, that the person would continue with their political commitments.
The 'shape being wrong' issue here is that maybe personas are not the right way to structure the problem. But Bayes's theorem doesn't tell you that. That's a whole load of extra machinery that people have additionally developed and should deploy when using Bayes's theorem.
Back to the word problem. An issue is that the options:
- A
- A&B
Both include A. In a world where A always happens the only non-trivial way to read the question is that the first option must implicitly mean (A&!B).
If A is assumed to be true, the question then becomes is B more likely to be true or not true. The background information given is a reasonable explanation for the common answer of people selecting (A&B).
Using the KL divergence of the posterior predictive distribution as a target to optimize does a bit better, but still isn't a "solution".
A topology on U is a system of subsets of U that's closed under union and finite intersections and containing the empty set and U itself. Go!
The simple answer is: the graph topology of the resulting program traces, equivalent to the topology of a graphical model sampled from a distribution over graphical models. The complicated answer is: the Scott topology of the program-trace space.
I realise both are implemented using neural networks, but as an analogy digital computers can implement bayesian algorithms, boolean algorithms, predicate logic, etc. It's quite possible our neural systems have optimised to different behaviours to solve different problems, and in _some_ cases these implement or approximate to Bayesian methods.
Maybe brain operates here on a syntactical level: which sentence is more likely to be present in a narrative about a subject and system 2 ([0]) fails to preempt the answer.
[0]: https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow Two systems
Haven't finished yet, he gets into artificial intelligence in the next few chapters, but he seems to make the claim that our brains work by doing a number of computations involved in causal inference beyond just Bayesian inference, such as subconsciously constructing causal diagrams and using them for causal inference including asking questions about counterfactual scenarios.
Would be interested to hear if anyone else who has read this book can help elaborate on this some.
Another way of thinking is to form new beliefs that are a function of prior evidence plus new evidence, e.g., by setting all old beliefs aside and starting afresh with the complete body of available evidence.
It's not clear to me that these two methods produce the same results, though I can't think of a counterexample. But to the extent that our brains probably remember both beliefs and evidence, we are not probably not fully Bayesian.
1990s Internet debater #1: "The plural of anecdote is not data"
2010s Internet debater #2: "True, but it does make a good bayesian prior"
LSD and sticky notes were invented by accident -- as were tons of other things.
Sure, one could add several pedantic reservations here, if they wanted to be thick on purpose, but the meaning of the parent's statement is clear. This series of passive aggressive counter-questions seems to violate the principle of charity.
It's pretty obvious that evolution didn't "invent" anything because accident or not, to invent requires an originator or discoverer which is to say an entity with agency. It's as absurd as saying relativity invented black holes.
And yet everybody understood what the parent means, which is that it was created by an evolutionary process.
And also everybody understands that the pedantic minutiae of whether "invent" can be used here is beside the actual point the parent makes.
It's enough that it exists in the real world.
The "concrete", real-world biological systems, including our brains, however employs frequencies and "weights", which corresponds to wideness of a pathway, which does not require any numbers or counting.
Mother Nature Does Not Count (and it does not compute any probabilities, of course). Higher level intellect does.
Math and logic are superimposed on the Universe and Nature. It is naive to assume that the Universe and Nature is based on math and logic, as ancient Greek views suppose.
Yes, there is basis behind Modus Ponens - in a certain conditions having Hs and Os inevitably leads to H2Os because universe has its laws, and because it has its laws it produces certain regularities and certain patterns which could be matched and even generalized by an intelligent observer, but it is not the other way around.
I think it’s more naive to think that the question has been settled..
https://en.m.wikipedia.org/wiki/Mathematical_universe_hypoth...
If, however, you are fond of joggling with abstractions and of studying of philosophers themselves and various philosophical systems (instead of what is) then, of course, you could put together yet another pile of abstractions and even systematically compare it with another pile of abstractions, and so on. Lots of people do.
Universe is one (at least we and everything else is bound by this one single unfolding process we call Universe) while abstractions are infinite, and most of them are disconnected from what is - they generalize nothing but other disconnected abstractions.
In the same way Voltage = Current x Resistance describes the behaviour of an electrical circuit and we can evaluate it numerically, but electrical circuits are analog and don't encapsulate or express those values numerically at all.
The brain might exhibit Bayesian behaviour without encoding or evaluating anything numerically. After all the values in Bayesian formulae are probabilities on a continuous scale, so there's nothing inherently discrete about their values.