Welcome to the Deep Dive. Today we're tackling something huge, really one of the biggest scientific goals out there, trying to, well, reverse engineer the human mind. It's a massive undertaking. And it's not just talk, right? This is where serious computational thinking meets, you know, cognitive psychology head on. And it feels especially relevant right now. I mean, look at AI today. You've got these enormous systems trained on unbelievable amounts of data, very structured data usually. Right. They can do amazing specific things, but they often feel a bit brittle. They don't generalize like we do. They need so much data. They're data -hungry giants, exactly. And then there's us, humans. We seem to be the ultimate general -purpose learners. Totally. Think about a kid just messing around, learning concepts from maybe one or two examples, messy examples often. How do we do that? That huge gap between the data -hungry algorithm and the incredibly efficient, flexible human brain, that's the puzzle we're digging into. And our guide for this deep dive is the book, Bayesian Models of Cognition. Reverse engineering the mind. The core argument, the big idea, is that this Bayesian framework, it might just be the key. It offers a kind of computational language, a way to bridge that gap we were just talking about. The idea is really compelling, isn't it? That we can maybe build models that capture the best bits of how cognitive science has thought about the mind over the years. You know, combining that structured logical knowledge with... powerful statistical learning. Yeah, it's about putting together the rules and the probabilities, the symbols and the stats in a principled way. It sounds like a roadmap, almost, for understanding how we learn abstract stuff, figure out cause and effect, make decisions when things aren't certain. It really is. Some argue it's maybe the most unifying theoretical framework cognitive science has had in, well, decades. It touches everything. Okay, so that's our mission for today. We're going to explore the basics of this Bayesian approach. look at the tools it gives us for thinking about mental structures, and then really focus in on how it applies to things like learning concepts and understanding language. Let's get started. So where do we begin? Well, right at the heart of it all is this classic philosophical problem, but it's also a deep computational one, the problem of induction. Basically, how does your mind manage to go beyond the information you actually get? How do you generalize? This is absolutely central, and it really throws the difference between us and current AI into sharp relief. Think about that child learning a word like horse. They might see just one horse, maybe two, hear the word, and boom. They often get the concept this applies to other four -legged neighing animals, not just that specific one or all animals. That's incredible generalization from almost nothing data -wise. And you compare that to, say, a standard machine learning system. You'd need potentially hundreds, maybe thousands of labeled pictures of horses for it to reliably classify them, let alone grasp the concept in a flexible way. The speed and efficiency of human learning is just staggering sometimes. So the unavoidable conclusion is if the data we get from the world is often so sparse, something inside the mind must be filling in the gaps. There has to be some kind of prior knowledge, some structure that limits the possibilities the learner even considers. Right. You can't just learn from scratch with so little data. There must be some. Built -in assumptions or biases. Exactly. And it's interesting the book points out that different fields wrestling with this have come up with different names for the same basic idea. Oh, yeah. Psychologists and linguists might talk about constraints. AI and machine learning people call it inductive bias. And statisticians, especially Bayesians, call it the prior. Constraints, inductive bias, priors, all getting at the same necessary ingredient. You need some background knowledge to make sense of limited data. Precisely. And needing this kind of structure, this prior knowledge, is what led cognitive science to try and reconcile its own history. For a long time, there were these different camps, different ways of thinking about the mind. Right. The book talks about three main traditions, didn't it? Yes, and they often didn't talk to each other very well. First, you had the symbolic tradition. That's like logic rules, allenteering, thinking is computation. Pretty much mid -20th century stuff. focused on formal logic, structured representations, think language of thought. Its big strength was handling abstraction and compositionality, combining concepts using rules, but... But it wasn't great at learning, maybe? Or dealing with uncertainty? Exactly. How do those rules get there in the first place? And how do they handle messy, probabilistic, real -world stuff? That was the weakness. Okay, so tradition number two. The connectionist tradition. This is sort of the ancestor of today's deep learning. Think neural networks, even simple ones. Ah, so less about explicit rules, more about connections and weights. Right. Simple processing units, learning by strengthening connections based on statistical patterns in the data. Very good at handling noisy input, finding subtle patterns, but... But maybe struggled with that high -level abstract structure, like grammar or explicit causal reasoning. That was the challenge, yeah. Representing things like if A, then B wasn't as natural. And the third one, the rational tradition. This one came a bit more from economics and philosophy, championed by folks like John Anderson. The focus here was on optimality. Meaning? Meaning, forget the specific mechanism for a second. Ask what the ideal solution is to the problem the mind is trying to solve. What would a perfectly rational agent do, given its goals and the environment? It provided a powerful benchmark, but maybe less of a concrete how -to. Okay, so symbolic rules, connectionist, stats. Rational optimality. Three different angles. And the big claim in the book is that the Bayesian framework provides a way to finally bring these together. It offers a common language. How so? How does it merge them? It allows that rich, structured knowledge from the symbolic tradition, the rules, the concepts, to be formally represented as the prior. That's your starting point, your inductive bias. Okay, so the symbolic stuff becomes the prior belief. And then you use a powerful statistical engine, kind of like the connectionist approach, to update that prior based on the data you actually observe. The structure isn't rigid. It's a probabilistic starting point that learning refines. That makes sense. The structure guides the statistical learning. And the tool that makes this marriage happen is Bayes' rule. It looks simple, that little equation, propto, PDH, PhD, but wow, the implications run deep. Okay, let's break that down again, make it super intuitive. PhD is the answer we want, right? The posterior belief. Ah. How likely is my hypothesis after I've seen the data? Correct. And it's proportional to two things multiplied together. First, PhDers. That's the likelihood. Which answers the question. If my hypothesis were true, how likely is it that I would have seen this specific data? It's about how well the hypothesis explains the evidence. Got it. If I think the coin is fair... How likely was it to get eight heads out of ten flips, Dee? Exactly. And the second piece is pH. That's the prior. This is your belief in the hypothesis before you saw any new data. It's all your background knowledge, your assumptions, your inductive bias. Ah, okay. So the prior is where that symbolic structure, those constraints we talked about, actually plug into the math. Precisely. That's the synthesis. Now, let's use that medical example again. It makes it really clear. John is coughing. That's our data. Right. And hypotheses. Let's say H dollar one dollars. He has a cold. Two H -dollars size. He has something serious like lung disease, $3 .83. Maybe it's just heartburn acting up. Okay. Now, the likelihood, PT -dollars, how well do these explain the cough? Well, coughing is pretty likely given a cold, H -dollar -dollar, or lung disease, much less likely given heartburn, three show -to -ones -two. So, $8 and $2 -dollars -two have high likelihoods. Makes sense. But what about the prior? Okay. Our background knowledge. That's where things shift. Colds, H -dollar -one, are incredibly common. High prior. Heartburn, the H111, is also fairly common. Moderate type prior. But serious lung disease, thankfully, is rare. Very low prior. Okay, so H -dollar bold has high likelihood AD high prior. 2H2 -dollar lung disease has high likelihood but low W prior. 3H2 -dollar heartburn has low likelihood but maybe a decent prior. Exactly. Now, multiply likelihood times prior for each one. The cold scores high on both counts, so its posterior probability skyrockets. Lung disease scores well on likelihood, but gets dragged down massively by its low prior. Heartburn, 5H3O, gets penalized by the low likelihood. So the most rational conclusion, the one Bayes' rule spits out, is the cold. It balances explaining the symptom with how common the cause is. Yes, it does it automatically. It's intuitive reasoning, formalized. And this machinery also gives us something incredibly powerful. A way to avoid just memorizing the data, to avoid... overfitting it's called the bayesian occam's razor okay this sounds important occam's razor the idea that simpler explanations are better how does bay's rule enforce that it's baked into the mathematics of comparing models especially when one model is more complex than another let's use the coin example again okay hypothesis ten of dollars the coin is perfectly fair simple fixed parameter three dollars and five five hypothesis hive dollars the coin is biased but we don't know how Its bias, theta, could be any value between 0 and 1. That's a much more complex hypothesis. Right. X -Gene can explain anything. If I get 10 heads, theta could say maybe 10 to the dollar. If I get 10 tails, maybe that X to the dollar. It seems more flexible. But that flexibility comes at a cost. When the Bayesian system evaluates how likely the overall model H $ is, it doesn't just pick the best parameter. It has to consider all the possible parameters the model allows. It calculates something called the marginal likelihood. Marginal likelihood? Yeah. What's that averaging over? It averages the likelihood of the data over all possible values of the parameter theta, weighted by the prior probability of those parameters. Basically, how well does the complex model explain the data on average, considering all its possible internal settings? Ah, I think I see. Because odd of dollars spreads its bets across all possible biases, all theta from dollar to one, it doesn't predict any specific outcome very strongly. Exactly. It has to dilute its predictive power. The simple model odd of dollar dollars puts all its predictive chips on outcomes near 50 -50. If the data actually is near 50 -50, say five heads, five tails. Totterdaller looks great. Otterdaller looks weak because it wasted predictive power on extreme outcomes that didn't happen. So the complex model gets penalized for its flexibility unless... Unless the data is so extreme, so far from what the simple model predicts, like nine heads out of ten flips, that the simple model just can't explain it anymore. Only then does the data provide enough evidence to justify paying the complexity cost of HE dollars. Wow. So the preference for simplicity isn't just a philosophical guideline. It's a mathematical consequence of... probability theory. It automatically balances model fit with model complexity. That's the beauty of it. It helps the system generalize better because it prevents chasing noise in the data with overly complicated explanations. It's fundamental to how we learn efficiently. Okay, so we have Bayes' rule for updating beliefs and this built -in Occam's razor, but how do we represent complex knowledge about the world, especially relationships like cause and effect? Chapter 4 brings in graphical models. Yes, specifically Bayesian networks or Bayesnets. These are incredibly useful. They provide a visual way to represent the dependencies or lack thereof between lots of variables. Like a map of how things influence each other. Kind of, but more importantly, they define the generative model. The arrows in the graph show you the assumed causal story, the sequence of probabilistic steps that could have generated the data you're seeing. This aligns really well with how humans seem to build intuitive theories about how things work. Thinking in terms of how did this come about feels very natural. It is. And this generative view is key for modeling causality, which is such a powerful inductive bias we humans have. It also leads to some really interesting patterns of inference, like the explaining away effect. Oh, yeah. The book used a fun example for this. Let's try to unpack it. It involves psychic powers and a dodgy coin. That's the one. Imagine you see your friend flip a coin and it lands heads. Call that observation $6. Now, you might entertain two possible explanations. $6, double the two dollars, your friend has psychic powers and influenced the flip. Or $6, three, maybe the coin is secretly two -headed. Okay, so observing heads makes me slightly increase my belief in both the psychic hypothesis. and the two -headed coin hypothesis by 833, assuming I didn't know anything else. Right. The single piece of evidence supports, to some degree, both potential causes. But now someone tells you, hey, just so you know, that coin is actually two -headed. So $6 D is now known to be true. Right. What happens to your belief in your friend's psychic powers? But the reason I believe in them more, the coin landing heads is now perfectly explained by the fact the coin is two -headed by $23. Yeah. My belief in the psychic powers should probably drop back down to whatever it was before I saw the flip. Exactly. The known cause by 3332 explains away the evidence by the alternative cause by ever 22. The information fleet changes because knowing the state of one cause makes the evidence. about the other cause. That's subtle, but makes total sense when you think about the causal structure. It wouldn't happen if you just looked at correlations. Precisely. The structure of the graph dictates how evidence propagates. And these models aren't just for passive observation. They're crucial for modeling intervention. What we do in the world. What happens if I push this? Yes. The framework incorporates Judea Pearl's do operator, which allows us to represent actually intervening in the system, not just observing it. This lets us model counterfactuals and compare different theories of how humans judge causal strength, like comparing simple probability changes, delta p, with more nuanced causal power models that account for background causes. Okay, so we have the basic update rule, Bayes, the complexity control, Occam's razor, and the structure for causal knowledge, graphical models. Now, Chapter 7 takes the next step. How do these beliefs actually lead to actions, from belief to behavior? This brings in Bayesian decision theory. It's the link between knowing and doing. The idea is that a rational agent should act to maximize its expected utility. Expected utility. So you weigh the goodness or badness, utility, of each possible outcome by how likely you think that outcome is, your posterior probability, and choose the action that gives the highest average score. That's the core idea for a perfectly rational agent. But of course, humans don't always seem perfectly rational in this classical sense. The book discusses deviations like probability matching. Ah, right. If a light flashes on the left 70 % of the time and the right 30 % of the time, the optimal thing is to always guess left. But people often guess left 70 % of the time and right 30 % of the time. They match the probabilities. Exactly. And for a long time, that was held up as evidence that humans are just irrational, not maximizing utility. But the Bayesian perspective offers a different lens, maybe. It does. Instead of just saying irrational, we can ask why people might do this. Maybe probability matching is actually a rational strategy under certain constraints. For example, if you model the decision not as one big optimization, but as a series of quick independent choices where exploring occasionally. guessing right sometimes, might have long -term benefits, or if you're trying to approximate the optimal solution with limited cognitive resources. So the behavior might look suboptimal if you ignore the constraints, but rational given those constraints. Precisely. It opens the door to analyzing these seemingly irrational behaviors within a broader rational framework, considering things like cognitive costs and approximation strategies. This hints towards the idea of resource rationality, which we'll likely come back to. All right, let's delve deeper now into some core human abilities, starting with how we handle concepts and categorization. Chapter 9 tackles this. Psychologists have argued for ages about how we represent categories. Is it like an average prototype? Or is it a collection of specific exemplars we've seen? Yeah, that prototype versus exemplar debate was a big one. Prototype models are good for typicality effects, but struggle with categories that seem to have multiple clusters. Exemplar models handle weird distributions better, but seem less efficient. Traditional models often made you pick one or the other. So how does the Bayesian approach help here? Does it force a choice? No, and that's the clever part. It uses something called nonparametric Bayesian models. Okay, nonparametric Bayesian sounds intimidating. The book also calls them infinite models. How can my finite brain use an infinite model? That seems like a problem. It sounds paradoxical, but the infinite part refers to the potential complexity and not the actual complexity used at any given time. These models assume there could be, in principle, an infinite number of categories or clusters available. But we obviously don't use infinitely many categories. Right. The magic is that the inference process itself, driven by the data and that Bayesian Occam's razor we talked about, only activates a finite number of these potential categories just enough to explain the beta well. It doesn't posit infinite structure needlessly. It discovers the necessary structure. So the complexity grows only if the data really demands it. Exactly. And the most famous way to visualize this is the Chinese restaurant process, or CRP. It's a beautiful metaphor. Okay, I'm intrigued. Lay out the Chinese restaurant process for us. Imagine a Chinese restaurant with theoretically infinitely many empty round tables. Each table represents a potential category or cluster. Now, customers, or data points, the things we're categorizing, start arriving one by one. The first customer walks in, picks an empty table, and sits down. Starts the first category. The second customer comes in, they have a choice. What's the choice? They can either sit at the already occupied table, joining that category, or start a new table, a new category. The probability of joining an existing table is proportional to how many people are already sitting there. Ah, so popular tables get more popular, like a rich get richer effect. Exactly. That creates pressure towards forming large central clusters like prototypes. But there's also always a chance the customer will choose to start a new table. The probability of starting a new table is proportional to a parameter, usually called alpha. Alpha. And what does alpha control? Alpha controls the sociability. or the tendency to create new categories. If alpha is low, customers strongly prefer existing tables, and you end up with just a few large clusters, very prototype -like. If alpha is high, customers are more adventurous, start lots of new tables, and you get many small clusters, more like an exemplar model. So the model doesn't choose prototype or exemplar beforehand. It can behave like either or something in between, depending on the data pattern and that alpha parameter. Precisely. The CRP acts as a prior over how data should be partitioned, automatically inferring the right number and type of clusters. It gives you that needed flexibility. That's really elegant. Okay, let's switch gears to language acquisition and processing covered in Chapter 16. How does the Bayesian lens apply here? It reframes things like understanding a sentence parsing as an inverse inference problem. Inverse inference. Yeah. Meaning working backward from the data. Yeah. When you hear a sentence, what you get is just a string of words. The underlying grammatical structure, the parse tree, is hidden. Parsing is the process of inferring the most likely hidden structure that could have generated the word string you heard. So it's like you're implicitly asking, what set of grammar rules applied probabilistically best explains this sequence of words? Exactly. And that's why you need probabilistic grammars, like probabilistic context -free grammars, PCFGs. They assign probabilities to different grammatical rules or structures, allowing the listener to resolve ambiguity. Think about a sentence like, the old man, the boat. Oh, yeah, that's a classic garden path sentence. Hard to parse. Your brain tries different parses, different structures, and usually settles on the most probable one, given the grammar and context. The Bayesian approach formalizes the search for the best explanation. And this inverse logic applies even at lower levels, like just hearing sounds. The book mentioned the perceptual magnet effect. Yes, another fantastic example. This is about how we perceive speak sounds, like vowels. We don't hear them exactly as they are acoustically. Sounds that are acoustically near a category prototype tend to get perceived as being even closer to that prototype than they really are. So the ideal E sound, for example, pulls nearby A -ish sounds towards it perceptually, like a magnet. That's the idea. The Bayesian explanation treats the sound you actually hear as a noisy version of an intended clean phonetic category, the prototype. Your brain performs inverse inference. What underlying clean vowel sound was most likely to have generated this noisy acoustic signal I just heard? And because the prototype is, by definition, the most common or probable realization of that category. The inference process rationally biases your perception towards that prototype, effectively compensating for the assumed noise. The magnet effect falls out naturally from rational inference under uncertainty about noise. Wow, okay, so parsing is inverse inference, perception is inverse inference. What about understanding meaning beyond the literal words? That too. This uses the Rational Speech Act, RSA, framework. It models conversation as a kind of cooperative game between a speaker and a listener, both trying to be rational. How does that help with inferring implied meaning? The listener basically performs inverse inference on the speaker's intentions. You assume the speaker chose their words rationally and efficiently to convey a particular meaning. Let's use that some versus all example again. If I say some of the cookies are gone. You, the listener, immediately infer, I mean, not all of the cookies are gone, even though logically some could include all. Right. How does RSA explain that inference? The listener reasons. OK, the speaker said some. If all the cookies were gone, they could have said all. All is just as easy to say, and it's more informative. Since they didn't say all, they must believe all is false. Ah, so it's reasoning about the speaker's choice of utterance compared to other utterances they could have made. It's like inverse planning applied to communication. Exactly. You assume the speaker is trying to be helpful and informative, following Gratian maxims, essentially, and you work backward from what they said to what they likely meant. It's a computational way to handle those subtle conversational inferences. This really feels like it's bringing everything together, logic, probability, intention, which leads nicely into chapters 18 and 19, and this grand idea of the probabilistic language of thought, PLID. That sounds like the ultimate synthesis. It's a very ambitious and exciting hypothesis. The core idea is that human concepts and knowledge aren't just static data structures. They are best thought of as stochastic functions or little programs written in a universal probabilistic programming language, PPL, like the language church developed by Goodman, Mansinka, Roy, Bonowitz, and Tenenbaum. Okay, hold on. Concept is programs. Probabilistic programs. What does that mean practically? It means a concept defines a generative process, for examples of that concept, including the uncertainty involved. Think about the concept of strength. It's not just a number. It might be represented as a program that, when run, samples a value from a probability distribution, say a Gaussian, representing typical human strengths. So the program itself defines the variability and likelihood of different strengths. Yes. And the power comes from composing these programs. The book uses a great example. reasoning about a tug -of -war game. You can have concepts like player strength, a probabilistic program sampling a strength value, team strength, a program that sums the strengths of players on the team, maybe even eyes lazy, a program that sometimes reduces a player's effective strength. The PPL framework lets you build a model of the entire tug -of -war situation by combining these conceptual programs. And then you can run this model. How? You can run it forward to simulate likely outcomes. Or, more powerfully, you can run it backward using Bayesian inference. Suppose you observe a surprising outcome. A small team, Team A, beat a much larger team, Team B. You can ask the PPL system, given this outcome, What were the likely latent properties, like the individual strengths or laziness factors of the players? The system effectively runs many simulations, tweaking the hidden variables according to Bay's rule until it finds the scenarios most likely to have produced that surprising win. Maybe the players on Team A were just incredibly strong, or maybe key players on Team B were having an off day or lazy. So it lets you infer hidden causes and properties by inverting the generative model defined by these programs. That seems incredibly powerful for reasoning. It is. And it connects directly to learning. If concepts are programs, then learning a concept is like inferring the program. Chapter 19. How do you infer a program? There must be infinitely many possible programs. There are. But this is where the prior overprograms comes back in, linking to Bayesian -Ockham's razor again. The prior distribution overprograms heavily favors simpler programs, those that are shorter or have lower complexity, like Kolmogorov complexity, discussed later in the book. Ah. So when a child learns a concept like even number from just a few examples, 2, 4, 8, 10, they aren't just finding any program that fits. They're implicitly searching for the simplest, most elegant program consistent with those examples. The strong prior favoring simplicity allows them to jump to the correct general definition divisible by two incredibly quickly without needing thousands of examples. It explains how we learn abstract structures so efficiently. This idea of structured knowledge, especially structured priors, seems absolutely key to how humans build deep understanding. We don't just learn isolated facts. We build intuitive theories about domains like physics, biology, or other people's minds. Chapter 8 introduces hierarchical Bayesian models, HBMs, as a way to capture this. HBMs are perfect for this. They explicitly model knowledge at multiple levels of abstraction. Think of it like layers. Layers. How does that work? At the bottom layer, you have the raw data, the specific observations. In the middle layers, you might have parameters or structures related to specific categories or items. And crucially, at the top layer, you have hyperparameters that represent abstract principles or overarching theories about the domain itself. So the top layer influences the learning happening at the lower layers. Exactly. The top layer basically learns the inductive bias for the layers below it. This is how HBMs model learning to learn. You don't just learn facts, you learn the structure of the domain, which then makes learning new facts within that domain much faster. The book had a really compelling example of this with medical reasoning, right? Discovering the disease symptom structure. Yes, a classic study by Kemp, Tenenbaum, Griffiths, and others. Participants had to figure out causal links between, say, 16 variables. Some were potential hidden causes, diseases, C1, and others were observable effects, symptoms, C2. And a simple flat model struggled. A standard two -level Bayesian network treating all 16 variables as potentially equal did very poorly. It needed lots of data to even start seeing the patterns because it had no higher -level structure to guide it. But the hierarchical Bayesian model... The HBM had a top layer designed to discover abstract types of variables and common patterns of connection between them. This top layer quickly figured out... Uh -huh. Variables 1 through 6 consistently act like causes, and variables 7 through 16 act like effects, and the dominant pattern is links going from the first group to the second group. C1, Ted Toulon. It learned the schema. Diseases cause symptoms. Precisely. And once it learned that abstract schema at the top level, it provided a powerful inductive bias to the lower level. The model could then learn the specific disease symptom links much, much faster and more accurately, even with the same limited data that baffled the flat model. That's a beautiful demonstration of learning the structure of knowledge itself. It feels very much like how a child develops expertise in a domain. It really does capture that transition from slow, data -driven learning to... faster, theory -driven learning that we see in development. Okay, another core intuitive theory we have is about other people's theory of mind. Tom, chapter 14. How do we figure out what others believe or want? The Bayesian approach models this primarily through inverse planning. It's similar to the Rational Speech Act idea, but applied more broadly to actions. So I see someone do something, and I work backward to figure out the beliefs and desires that likely led to that action. Exactly. You essentially assume the other person is acting approximately, rationally, to achieve their goals given their beliefs about the world. You invert their presumed planning process. And this lets us do more than just guess one thing, right? Like, we can figure out preferences and costs. Let's use that ice cream versus cake example. Okay. You see your friend walk past a delicious looking cake, $10, and choose a simple ice cream, $8 instead. My first thought might be, wow, they must really like ice cream more than cake. High reward for $8 one. But then you consider the context, the costs. Maybe the cake shop, $8 .02, was across the street, requiring effort, a cost to get to, while the ice cream stand, $8 .01, was right there, zero cost. Ah. So even if they slightly prefer the taste of cake, higher intrinsic reward for $8 .02, the effort involved might make choosing the easily accessible ice cream, $8 .01, the more rational action overall. Precisely. Inverse planning allows you to jointly infer both the likely rewards, preferences, and the likely costs, effort, obstacles that best explain the observed action. You might conclude they slightly prefer cake but aren't willing to pay the cost, which is a much more nuanced understanding than just saying they prefer ice cream. It captures that sophisticated social calculus we seem to do constantly. Yes, inferring these hidden mental states from sparse behavioral data is a hallmark of human social intelligence, and inverse planning provides a formal model for it. Now let's shift from intuitive psychology to intuitive physics, IPE. In Chapter 15. We seem to have a pretty good feel for how physical objects behave, even without knowing Newtonian equations. Right. The proposal here is that we have something like an intuitive physics engine in our heads, a mental simulator. But it's not just deterministic. Physical reasoning is treated as probabilistic inference using this engine. So we can run simulations, like if I stack these blocks this way, will the tower likely fall? Yes, we can run it forward for prediction. But critically, like with Tom, the real power comes from running it backward for inverse inference and also using it for counterfactual reasoning. Meaning we can infer hidden properties or reason about what if. Exactly. You see a tower of blocks standing stably. You can infer things about the hidden properties like the likely mass or friction of the blocks needed for it to be stable. Or you can perform counterfactuals. The tower is standing, but what would have happened if I had removed that one specific block near the bottom? And running that simulation tells you how crucial that block was. Yes. If the simulation shows the tower would have collapsed without that block, you attribute high causal responsibility to that block for the tower's stability. This kind of probabilistic simulation and counterfactual reasoning using the IPE aligns remarkably well with people's judgments about physical causality, stability, and blame things that go way beyond simple prediction. Okay, let's tie these threads together now by looking explicitly at Bayesian models of cognitive development in Chapter 20. How does this framework account for how children learn these intuitive theories? It starts with core knowledge, right? Yes. The idea is that infants aren't blank slates. They come equipped with some initial foundational core knowledge systems. Things like understanding that objects persist even when hidden, that agents act purposefully and efficiently, basic number sense, basic spatial reasoning. So in the Bayesian or PPL framework, this core knowledge acts as the initial high -level priors, the starting code. That's a great way to put it. These are the built -in assumptions that get the learning process off the ground. providing the initial structure needed to interpret the sparse data infants receive. But development isn't always smooth. Kids sometimes seem to jump suddenly from one way of thinking to another. How is that captured? The models address this by focusing not just on the endpoint, the ideal rational model, but also on the process of learning and belief revision. They often use stochastic search algorithms as plausible process models. Stochastic search. Like randomly trying things out. Sort of, but in a structured way. Think about algorithms like Markov Chain Monte Carlo, MCMC, which sample hypotheses in proportion to their posterior probability. Or even simpler heuristics like Wednesday Loose Switch, WSLS. Wednesday Loose Switch. How does that work in development? Imagine a child trying to figure out which button on a toy makes a light flash. They might try the red button, their current hypothesis. If the light flashes, win. They stick with that hypothesis, stay. If they press red and nothing happens, lose. They're likely to randomly try something else, switch. Maybe the blue button, maybe shaking the toy. Ah, so it's a simple rule for exploring different hypotheses based on immediate feedback. Yes. And crucially, because of the random switch step, two children seeing the exact same evidence might temporarily explore different hypotheses or jump to different conclusions. It captures some of the trial and error feel and the variability we see in children's reasoning as they revise their beliefs. It's not always a perfectly smooth update. Sometimes they just try something new. So the big picture of development is maybe starting with core knowledge priors. using these stochastic search processes to explore, and gradually building up more complex hierarchical models, HPMs, as the data accumulates and demands better, more abstract explanations. That's a really good summary. Development is seen as this interplay between innate structure, statistical learning, and noisy exploratory hypothesis testing, eventually converging on richer, more abstract, and more predictably powerful intuitive theories. Okay, we've built up this impressive picture of the mind as a Bayesian engine, using priors, likelihoods, graphical models, HBMs. But let's face reality. Calculating exact Bayesian probabilities for complex real -world problems is often computationally intractable, right? Chapter 11 talks about approximation. Absolutely critical point. Exact Bayesian inference is often NP -hard. The brain, whatever it's doing, can't possibly be performing exact calculations for everything. So we need approximation algorithms. Like Monte Carlo methods where you draw samples. Or variational inference. Yes. Those are standard techniques in machine learning to approximate Bayesian inference when the exact calculation is too hard. But here's the really cool cognitive twist. The book argues these approximation methods aren't just engineering hacks. They might actually be good rational process models of how human cognition works, including its limitations and biases. So the way these algorithms cut corners might actually explain some quirks of human thinking. That's the proposal. Take particle filters, for example. They're a type of sequential Monte Carlo method often used for tracking changing states over time. They work by maintaining a set of particles, each representing a hypothesis about the current state. But crucially, you can only maintain a finite, often small number of particles due to computational limits, like our limited working memory or attention. When new data comes in, you update the probabilities of your particles, and then you have to resample. You preferentially replicate the high probability particles and discard the low probability ones. What does that limitation, the finite number of particles, lead to? It naturally leads to effects like primacy and recency and learning and memory tasks. The particles that got established early on, primacy, might persist longer than they should. And the most recent updates, recency, get disproportionate weight because they've just been resampled. Wow. So these classic memory biases, which some might see as flaws, could actually be signatures of the brain using a resource -limited approximation algorithm, like a particle filter, to try and perform Bayesian inference. Exactly. The error is actually evidence for a specific type of rational approximation strategy. The approximation itself becomes part of the cognitive model. That's a powerful idea. Now, Chapter 12 tackles the other giant in the room. Neural networks. How does this Bayesian view connect with modern deep learning? Are they fundamentally different paradigms? It's a fascinating relationship and the book argues there are deep connections, maybe deeper than often assumed. On a basic level, some simple neural networks are actually mathematically equivalent to certain simple Bayesian models. Really? Like what? For instance, logistic regression, a common building block in neural nets, can be shown to be equivalent to a naive Bayes classifier under certain assumptions. So neural nets can implement Bayesian computations. Okay, for simple cases, what about the big, complex, deep learning models and how they're trained? Even there, the connections emerge. The way we train neural networks often implicitly corresponds to making Bayesian assumptions. Think about standard training techniques like weight decay or L2 regularization. Yeah, where you penalize large weights in the network to prevent overfitting. Well, it turns out that adding a weight decay term during training is mathematically identical to performing maximum A posteriori. MAP inference on the weights, assuming a Gaussian prior centered at zero for those weights. Whoa! So telling the network don't let your weights get too big is the same as telling a Bayesian model assume, a priori, that the weights are probably small, close to zero. Precisely. The regularization acts as a prior, biasing the learning towards simpler solutions. It suggests that even in these massive data -driven systems, principles of Bayesian inference, like imposing priors to control complexity, are still operating, even if they're implemented through engineering choices rather than explicit probabilistic modeling. So maybe the divide isn't as sharp as it seems. Neural nets might be discovering or implementing Bayesian principles in their own way. That's one perspective. The relationship is complex and still being actively researched, but the idea that they are complementary rather than competing frameworks is gaining traction. This leads us to maybe the most encompassing idea in the later parts of the book. Resource rationality, chapter 13. This feels like it ties together the optimality of Bayes with the reality of limitations. It does. It's an extension of the rational analysis approach we mentioned earlier. Instead of just asking, what's the optimal behavior to maximize utility? Resource rationality asks, what's the optimal behavior to maximize utility minus the cost of the computation needed to figure out that behavior? So thinking itself has a cost time, mental effort, and a truly rational agent has to factor that cost into its decisions. Exactly. You have to rationally decide how much to think. This provides a powerful explanation for many cognitive biases that look irrational from a purely classical perspective. Take the anchoring and adjustment heuristic. Right, where you start with some initial number, the anchor, and then adjust away from it, but often you don't adjust enough so your final estimate is biased towards the anchor. Classically, stopping adjustment too early is an error, but why might a resource -rational agent do it? Hmm. Maybe the first bits of adjustment give you big improvements in accuracy, but further adjustments... yields smaller and smaller gains. Precisely. The potential improvement in your answer diminishes, maybe geometrically, with each extra step of mental effort. But the cost of that effort, time, cognitive load, might remain constant. At some point, the marginal benefit of one more adjustment step is no longer worth the marginal cost. So the resource rational agent rationally stops adjusting early. Accepting a slightly biased answer because further refinement would cost more in thinking time than it's worth in improved accuracy. That's the core idea. The bias isn't a bug. It's an optimal adaptation to cognitive limitations. It's the best you can do given finite resources. That really reframes how we think about cognitive biases, not as failures of rationality, but as potentially optimal solutions under computational constraints. It does. And it brings the whole Bayesian program into closer contact with psychological reality. The overall picture is... So wrapping this all up, after this deep dive into Bayesian models of cognition, what's the big takeaway? What does it all mean, especially looking forward? I think the biggest takeaway is that the Bayesian framework offers this incredibly rich... precise and unifying language for talking about the mind. It connects perception, learning, reasoning, language, social cognition, all these different areas back to fundamental principles of how an intelligent system should handle uncertainty and structure. It links knowledge representations, statistical learning, and rational action in a way no other framework really has. But where does that leave us with the current AI landscape? Will giant models like LLMs just figure all this out on their own by scaling up? Or is there something fundamental missing? That's the million dollar question, isn't it? Will these massive networks simultaneously learn the kind of compositional, causal, structured representations that seem core to human thought and that the Bayesian framework models so naturally? Or will we find that building truly human -like AI, flexible, data efficient, capable of deep understanding requires explicitly incorporating the principles of Bayesian inference, hierarchical structure, intuitive theories, and maybe even resource rationality into their design? A fundamental tension. Emergent structure versus engineered structure guided by cognitive principles. Exactly. It's likely the future lies in some synthesis, but the principles laid out in this Bayesian approach to cognition seem like essential guideposts for understanding what human intelligence is and how we might eventually replicate it. That's a really provocative thought to end on. For listeners who are captivated by these ideas and want to dig deeper into the sources, what would you recommend? Well, besides the main book we've been discussing, going back to some of the foundational work is always valuable. John Anderson's writings on rational analysis are key. Judea Pearl's work, especially Causality, is fundamental for graphical models. And of course, exploring the primary research papers by the authors of Bayesian models of cognition themselves, people like Josh Tenenbaum, Tom Griffiths, Charles Kemp, Noah Goodman, on topics like hierarchical Bayesian models, the probabilistic language of thought. and intuitive theories would be incredibly rewarding. Excellent suggestions. It really feels like understanding the mind requires grappling with these ideas about probability, structure, and rational inference in an uncertain world. It certainly seems that way. It's a challenging but incredibly exciting frontier.