1 00:00:00,000 --> 00:00:02,930 Welcome to the Deep Dive. Today we're tackling 2 00:00:02,930 --> 00:00:06,690 something huge, really one of the biggest scientific 3 00:00:06,690 --> 00:00:10,470 goals out there, trying to, well, reverse engineer 4 00:00:10,470 --> 00:00:13,449 the human mind. It's a massive undertaking. And 5 00:00:13,449 --> 00:00:16,050 it's not just talk, right? This is where serious 6 00:00:16,050 --> 00:00:18,269 computational thinking meets, you know, cognitive 7 00:00:18,269 --> 00:00:20,829 psychology head on. And it feels especially relevant 8 00:00:20,829 --> 00:00:22,890 right now. I mean, look at AI today. You've got 9 00:00:22,890 --> 00:00:25,570 these enormous systems trained on unbelievable 10 00:00:25,570 --> 00:00:28,129 amounts of data, very structured data usually. 11 00:00:28,269 --> 00:00:30,589 Right. They can do amazing specific things, but 12 00:00:30,589 --> 00:00:34,240 they often feel a bit brittle. They don't generalize 13 00:00:34,240 --> 00:00:37,179 like we do. They need so much data. They're data 14 00:00:37,179 --> 00:00:39,520 -hungry giants, exactly. And then there's us, 15 00:00:39,700 --> 00:00:41,899 humans. We seem to be the ultimate general -purpose 16 00:00:41,899 --> 00:00:44,320 learners. Totally. Think about a kid just messing 17 00:00:44,320 --> 00:00:47,560 around, learning concepts from maybe one or two 18 00:00:47,560 --> 00:00:50,020 examples, messy examples often. How do we do 19 00:00:50,020 --> 00:00:52,340 that? That huge gap between the data -hungry 20 00:00:52,340 --> 00:00:55,179 algorithm and the incredibly efficient, flexible 21 00:00:55,179 --> 00:00:57,179 human brain, that's the puzzle we're digging 22 00:00:57,179 --> 00:01:00,520 into. And our guide for this deep dive is the 23 00:01:00,520 --> 00:01:03,579 book, Bayesian Models of Cognition. Reverse engineering 24 00:01:03,579 --> 00:01:07,920 the mind. The core argument, the big idea, is 25 00:01:07,920 --> 00:01:10,620 that this Bayesian framework, it might just be 26 00:01:10,620 --> 00:01:12,739 the key. It offers a kind of computational language, 27 00:01:12,819 --> 00:01:14,400 a way to bridge that gap we were just talking 28 00:01:14,400 --> 00:01:16,519 about. The idea is really compelling, isn't it? 29 00:01:16,540 --> 00:01:18,939 That we can maybe build models that capture the 30 00:01:18,939 --> 00:01:21,519 best bits of how cognitive science has thought 31 00:01:21,519 --> 00:01:24,180 about the mind over the years. You know, combining 32 00:01:24,180 --> 00:01:27,170 that structured logical knowledge with... powerful 33 00:01:27,170 --> 00:01:29,189 statistical learning. Yeah, it's about putting 34 00:01:29,189 --> 00:01:31,469 together the rules and the probabilities, the 35 00:01:31,469 --> 00:01:34,790 symbols and the stats in a principled way. It 36 00:01:34,790 --> 00:01:37,269 sounds like a roadmap, almost, for understanding 37 00:01:37,269 --> 00:01:39,969 how we learn abstract stuff, figure out cause 38 00:01:39,969 --> 00:01:42,090 and effect, make decisions when things aren't 39 00:01:42,090 --> 00:01:44,569 certain. It really is. Some argue it's maybe 40 00:01:44,569 --> 00:01:47,030 the most unifying theoretical framework cognitive 41 00:01:47,030 --> 00:01:49,950 science has had in, well, decades. It touches 42 00:01:49,950 --> 00:01:52,069 everything. Okay, so that's our mission for today. 43 00:01:52,189 --> 00:01:54,329 We're going to explore the basics of this Bayesian 44 00:01:54,329 --> 00:01:56,739 approach. look at the tools it gives us for thinking 45 00:01:56,739 --> 00:01:59,099 about mental structures, and then really focus 46 00:01:59,099 --> 00:02:00,659 in on how it applies to things like learning 47 00:02:00,659 --> 00:02:02,879 concepts and understanding language. Let's get 48 00:02:02,879 --> 00:02:08,629 started. So where do we begin? Well, right at 49 00:02:08,629 --> 00:02:10,930 the heart of it all is this classic philosophical 50 00:02:10,930 --> 00:02:14,330 problem, but it's also a deep computational one, 51 00:02:14,469 --> 00:02:18,229 the problem of induction. Basically, how does 52 00:02:18,229 --> 00:02:20,469 your mind manage to go beyond the information 53 00:02:20,469 --> 00:02:23,020 you actually get? How do you generalize? This 54 00:02:23,020 --> 00:02:25,280 is absolutely central, and it really throws the 55 00:02:25,280 --> 00:02:28,340 difference between us and current AI into sharp 56 00:02:28,340 --> 00:02:30,719 relief. Think about that child learning a word 57 00:02:30,719 --> 00:02:34,080 like horse. They might see just one horse, maybe 58 00:02:34,080 --> 00:02:37,000 two, hear the word, and boom. They often get 59 00:02:37,000 --> 00:02:38,699 the concept this applies to other four -legged 60 00:02:38,699 --> 00:02:40,560 neighing animals, not just that specific one 61 00:02:40,560 --> 00:02:42,699 or all animals. That's incredible generalization 62 00:02:42,699 --> 00:02:45,639 from almost nothing data -wise. And you compare 63 00:02:45,639 --> 00:02:49,759 that to, say, a standard machine learning system. 64 00:02:50,039 --> 00:02:54,039 You'd need potentially hundreds, maybe thousands 65 00:02:54,039 --> 00:02:57,300 of labeled pictures of horses for it to reliably 66 00:02:57,300 --> 00:03:00,639 classify them, let alone grasp the concept in 67 00:03:00,639 --> 00:03:03,180 a flexible way. The speed and efficiency of human 68 00:03:03,180 --> 00:03:06,039 learning is just staggering sometimes. So the 69 00:03:06,039 --> 00:03:08,639 unavoidable conclusion is if the data we get 70 00:03:08,639 --> 00:03:11,199 from the world is often so sparse, something 71 00:03:11,199 --> 00:03:13,419 inside the mind must be filling in the gaps. 72 00:03:13,580 --> 00:03:15,620 There has to be some kind of prior knowledge, 73 00:03:15,740 --> 00:03:18,099 some structure that limits the possibilities 74 00:03:18,099 --> 00:03:20,099 the learner even considers. Right. You can't 75 00:03:20,099 --> 00:03:22,060 just learn from scratch with so little data. 76 00:03:22,120 --> 00:03:24,550 There must be some. Built -in assumptions or 77 00:03:24,550 --> 00:03:27,110 biases. Exactly. And it's interesting the book 78 00:03:27,110 --> 00:03:29,270 points out that different fields wrestling with 79 00:03:29,270 --> 00:03:30,770 this have come up with different names for the 80 00:03:30,770 --> 00:03:33,289 same basic idea. Oh, yeah. Psychologists and 81 00:03:33,289 --> 00:03:36,069 linguists might talk about constraints. AI and 82 00:03:36,069 --> 00:03:38,069 machine learning people call it inductive bias. 83 00:03:38,349 --> 00:03:40,889 And statisticians, especially Bayesians, call 84 00:03:40,889 --> 00:03:44,689 it the prior. Constraints, inductive bias, priors, 85 00:03:44,689 --> 00:03:46,849 all getting at the same necessary ingredient. 86 00:03:47,229 --> 00:03:49,409 You need some background knowledge to make sense 87 00:03:49,409 --> 00:03:52,659 of limited data. Precisely. And needing this 88 00:03:52,659 --> 00:03:55,159 kind of structure, this prior knowledge, is what 89 00:03:55,159 --> 00:03:57,400 led cognitive science to try and reconcile its 90 00:03:57,400 --> 00:03:59,919 own history. For a long time, there were these 91 00:03:59,919 --> 00:04:02,000 different camps, different ways of thinking about 92 00:04:02,000 --> 00:04:04,699 the mind. Right. The book talks about three main 93 00:04:04,699 --> 00:04:07,860 traditions, didn't it? Yes, and they often didn't 94 00:04:07,860 --> 00:04:10,120 talk to each other very well. First, you had 95 00:04:10,120 --> 00:04:14,099 the symbolic tradition. That's like logic rules, 96 00:04:14,539 --> 00:04:18,300 allenteering, thinking is computation. Pretty 97 00:04:18,300 --> 00:04:21,519 much mid -20th century stuff. focused on formal 98 00:04:21,519 --> 00:04:24,319 logic, structured representations, think language 99 00:04:24,319 --> 00:04:27,180 of thought. Its big strength was handling abstraction 100 00:04:27,180 --> 00:04:29,779 and compositionality, combining concepts using 101 00:04:29,779 --> 00:04:32,399 rules, but... But it wasn't great at learning, 102 00:04:32,480 --> 00:04:35,189 maybe? Or dealing with uncertainty? Exactly. 103 00:04:35,250 --> 00:04:37,310 How do those rules get there in the first place? 104 00:04:37,470 --> 00:04:40,029 And how do they handle messy, probabilistic, 105 00:04:40,050 --> 00:04:42,490 real -world stuff? That was the weakness. Okay, 106 00:04:42,529 --> 00:04:44,569 so tradition number two. The connectionist tradition. 107 00:04:44,670 --> 00:04:46,870 This is sort of the ancestor of today's deep 108 00:04:46,870 --> 00:04:49,310 learning. Think neural networks, even simple 109 00:04:49,310 --> 00:04:51,910 ones. Ah, so less about explicit rules, more 110 00:04:51,910 --> 00:04:54,439 about connections and weights. Right. Simple 111 00:04:54,439 --> 00:04:57,160 processing units, learning by strengthening connections 112 00:04:57,160 --> 00:05:00,600 based on statistical patterns in the data. Very 113 00:05:00,600 --> 00:05:02,819 good at handling noisy input, finding subtle 114 00:05:02,819 --> 00:05:05,120 patterns, but... But maybe struggled with that 115 00:05:05,120 --> 00:05:07,639 high -level abstract structure, like grammar 116 00:05:07,639 --> 00:05:10,620 or explicit causal reasoning. That was the challenge, 117 00:05:10,699 --> 00:05:14,019 yeah. Representing things like if A, then B wasn't 118 00:05:14,019 --> 00:05:16,439 as natural. And the third one, the rational tradition. 119 00:05:16,850 --> 00:05:19,509 This one came a bit more from economics and philosophy, 120 00:05:19,850 --> 00:05:22,889 championed by folks like John Anderson. The focus 121 00:05:22,889 --> 00:05:26,569 here was on optimality. Meaning? Meaning, forget 122 00:05:26,569 --> 00:05:28,829 the specific mechanism for a second. Ask what 123 00:05:28,829 --> 00:05:31,310 the ideal solution is to the problem the mind 124 00:05:31,310 --> 00:05:33,769 is trying to solve. What would a perfectly rational 125 00:05:33,769 --> 00:05:36,430 agent do, given its goals and the environment? 126 00:05:36,769 --> 00:05:39,689 It provided a powerful benchmark, but maybe less 127 00:05:39,689 --> 00:05:43,370 of a concrete how -to. Okay, so symbolic rules, 128 00:05:43,610 --> 00:05:48,180 connectionist, stats. Rational optimality. Three 129 00:05:48,180 --> 00:05:50,040 different angles. And the big claim in the book 130 00:05:50,040 --> 00:05:52,139 is that the Bayesian framework provides a way 131 00:05:52,139 --> 00:05:53,920 to finally bring these together. It offers a 132 00:05:53,920 --> 00:05:55,959 common language. How so? How does it merge them? 133 00:05:56,079 --> 00:05:58,740 It allows that rich, structured knowledge from 134 00:05:58,740 --> 00:06:01,160 the symbolic tradition, the rules, the concepts, 135 00:06:01,180 --> 00:06:04,579 to be formally represented as the prior. That's 136 00:06:04,579 --> 00:06:06,899 your starting point, your inductive bias. Okay, 137 00:06:06,980 --> 00:06:09,399 so the symbolic stuff becomes the prior belief. 138 00:06:09,639 --> 00:06:11,459 And then you use a powerful statistical engine, 139 00:06:11,560 --> 00:06:13,980 kind of like the connectionist approach, to update 140 00:06:13,980 --> 00:06:16,360 that prior based on the data you actually observe. 141 00:06:16,860 --> 00:06:19,720 The structure isn't rigid. It's a probabilistic 142 00:06:19,720 --> 00:06:21,980 starting point that learning refines. That makes 143 00:06:21,980 --> 00:06:24,600 sense. The structure guides the statistical learning. 144 00:06:24,740 --> 00:06:26,399 And the tool that makes this marriage happen 145 00:06:26,399 --> 00:06:29,560 is Bayes' rule. It looks simple, that little 146 00:06:29,560 --> 00:06:33,120 equation, propto, PDH, PhD, but wow, the implications 147 00:06:33,120 --> 00:06:35,449 run deep. Okay, let's break that down again, 148 00:06:35,490 --> 00:06:37,410 make it super intuitive. PhD is the answer we 149 00:06:37,410 --> 00:06:42,050 want, right? The posterior belief. Ah. How likely 150 00:06:42,050 --> 00:06:45,189 is my hypothesis after I've seen the data? Correct. 151 00:06:45,290 --> 00:06:47,509 And it's proportional to two things multiplied 152 00:06:47,509 --> 00:06:50,410 together. First, PhDers. That's the likelihood. 153 00:06:50,649 --> 00:06:52,910 Which answers the question. If my hypothesis 154 00:06:52,910 --> 00:06:55,209 were true, how likely is it that I would have 155 00:06:55,209 --> 00:06:57,490 seen this specific data? It's about how well 156 00:06:57,490 --> 00:06:59,889 the hypothesis explains the evidence. Got it. 157 00:07:00,089 --> 00:07:02,800 If I think the coin is fair... How likely was 158 00:07:02,800 --> 00:07:04,839 it to get eight heads out of ten flips, Dee? 159 00:07:05,279 --> 00:07:07,899 Exactly. And the second piece is pH. That's the 160 00:07:07,899 --> 00:07:09,959 prior. This is your belief in the hypothesis 161 00:07:09,959 --> 00:07:12,420 before you saw any new data. It's all your background 162 00:07:12,420 --> 00:07:14,180 knowledge, your assumptions, your inductive bias. 163 00:07:14,680 --> 00:07:17,100 Ah, okay. So the prior is where that symbolic 164 00:07:17,100 --> 00:07:18,920 structure, those constraints we talked about, 165 00:07:19,000 --> 00:07:21,639 actually plug into the math. Precisely. That's 166 00:07:21,639 --> 00:07:24,180 the synthesis. Now, let's use that medical example 167 00:07:24,180 --> 00:07:26,620 again. It makes it really clear. John is coughing. 168 00:07:26,699 --> 00:07:29,079 That's our data. Right. And hypotheses. Let's 169 00:07:29,079 --> 00:07:31,689 say H dollar one dollars. He has a cold. Two 170 00:07:31,689 --> 00:07:34,509 H -dollars size. He has something serious like 171 00:07:34,509 --> 00:07:37,410 lung disease, $3 .83. Maybe it's just heartburn 172 00:07:37,410 --> 00:07:40,670 acting up. Okay. Now, the likelihood, PT -dollars, 173 00:07:40,689 --> 00:07:43,269 how well do these explain the cough? Well, coughing 174 00:07:43,269 --> 00:07:45,370 is pretty likely given a cold, H -dollar -dollar, 175 00:07:45,490 --> 00:07:48,189 or lung disease, much less likely given heartburn, 176 00:07:48,269 --> 00:07:51,069 three show -to -ones -two. So, $8 and $2 -dollars 177 00:07:51,069 --> 00:07:53,209 -two have high likelihoods. Makes sense. But 178 00:07:53,209 --> 00:07:55,329 what about the prior? Okay. Our background knowledge. 179 00:07:55,490 --> 00:07:58,629 That's where things shift. Colds, H -dollar -one, 180 00:07:58,750 --> 00:08:01,589 are incredibly common. High prior. Heartburn, 181 00:08:01,689 --> 00:08:04,089 the H111, is also fairly common. Moderate type 182 00:08:04,089 --> 00:08:06,649 prior. But serious lung disease, thankfully, 183 00:08:06,750 --> 00:08:10,029 is rare. Very low prior. Okay, so H -dollar bold 184 00:08:10,029 --> 00:08:14,790 has high likelihood AD high prior. 2H2 -dollar 185 00:08:14,790 --> 00:08:17,569 lung disease has high likelihood but low W prior. 186 00:08:18,449 --> 00:08:21,949 3H2 -dollar heartburn has low likelihood but 187 00:08:21,949 --> 00:08:24,949 maybe a decent prior. Exactly. Now, multiply 188 00:08:24,949 --> 00:08:27,410 likelihood times prior for each one. The cold 189 00:08:27,410 --> 00:08:29,470 scores high on both counts, so its posterior 190 00:08:29,470 --> 00:08:32,850 probability skyrockets. Lung disease scores well 191 00:08:32,850 --> 00:08:34,789 on likelihood, but gets dragged down massively 192 00:08:34,789 --> 00:08:38,509 by its low prior. Heartburn, 5H3O, gets penalized 193 00:08:38,509 --> 00:08:41,110 by the low likelihood. So the most rational conclusion, 194 00:08:41,370 --> 00:08:43,509 the one Bayes' rule spits out, is the cold. It 195 00:08:43,509 --> 00:08:45,909 balances explaining the symptom with how common 196 00:08:45,909 --> 00:08:47,769 the cause is. Yes, it does it automatically. 197 00:08:47,909 --> 00:08:50,110 It's intuitive reasoning, formalized. And this 198 00:08:50,110 --> 00:08:51,809 machinery also gives us something incredibly 199 00:08:51,809 --> 00:08:54,169 powerful. A way to avoid just memorizing the 200 00:08:54,169 --> 00:08:56,190 data, to avoid... overfitting it's called the 201 00:08:56,190 --> 00:08:58,169 bayesian occam's razor okay this sounds important 202 00:08:58,169 --> 00:09:00,269 occam's razor the idea that simpler explanations 203 00:09:00,269 --> 00:09:02,610 are better how does bay's rule enforce that it's 204 00:09:02,610 --> 00:09:04,669 baked into the mathematics of comparing models 205 00:09:04,669 --> 00:09:07,690 especially when one model is more complex than 206 00:09:07,690 --> 00:09:09,990 another let's use the coin example again okay 207 00:09:09,990 --> 00:09:12,190 hypothesis ten of dollars the coin is perfectly 208 00:09:12,190 --> 00:09:15,210 fair simple fixed parameter three dollars and 209 00:09:15,210 --> 00:09:18,250 five five hypothesis hive dollars the coin is 210 00:09:18,250 --> 00:09:21,200 biased but we don't know how Its bias, theta, 211 00:09:21,340 --> 00:09:23,559 could be any value between 0 and 1. That's a 212 00:09:23,559 --> 00:09:25,659 much more complex hypothesis. Right. X -Gene 213 00:09:25,659 --> 00:09:28,000 can explain anything. If I get 10 heads, theta 214 00:09:28,000 --> 00:09:29,720 could say maybe 10 to the dollar. If I get 10 215 00:09:29,720 --> 00:09:32,379 tails, maybe that X to the dollar. It seems more 216 00:09:32,379 --> 00:09:35,409 flexible. But that flexibility comes at a cost. 217 00:09:35,570 --> 00:09:38,070 When the Bayesian system evaluates how likely 218 00:09:38,070 --> 00:09:41,309 the overall model H $ is, it doesn't just pick 219 00:09:41,309 --> 00:09:43,549 the best parameter. It has to consider all the 220 00:09:43,549 --> 00:09:46,070 possible parameters the model allows. It calculates 221 00:09:46,070 --> 00:09:48,190 something called the marginal likelihood. Marginal 222 00:09:48,190 --> 00:09:49,929 likelihood? Yeah. What's that averaging over? 223 00:09:50,029 --> 00:09:53,009 It averages the likelihood of the data over all 224 00:09:53,009 --> 00:09:55,789 possible values of the parameter theta, weighted 225 00:09:55,789 --> 00:09:58,049 by the prior probability of those parameters. 226 00:09:58,789 --> 00:10:01,049 Basically, how well does the complex model explain 227 00:10:01,049 --> 00:10:03,629 the data on average, considering all its possible 228 00:10:03,629 --> 00:10:06,450 internal settings? Ah, I think I see. Because 229 00:10:06,450 --> 00:10:09,269 odd of dollars spreads its bets across all possible 230 00:10:09,269 --> 00:10:12,429 biases, all theta from dollar to one, it doesn't 231 00:10:12,429 --> 00:10:14,889 predict any specific outcome very strongly. Exactly. 232 00:10:14,889 --> 00:10:17,990 It has to dilute its predictive power. The simple 233 00:10:17,990 --> 00:10:20,549 model odd of dollar dollars puts all its predictive 234 00:10:20,549 --> 00:10:23,710 chips on outcomes near 50 -50. If the data actually 235 00:10:23,710 --> 00:10:27,440 is near 50 -50, say five heads, five tails. Totterdaller 236 00:10:27,440 --> 00:10:30,120 looks great. Otterdaller looks weak because it 237 00:10:30,120 --> 00:10:32,500 wasted predictive power on extreme outcomes that 238 00:10:32,500 --> 00:10:35,039 didn't happen. So the complex model gets penalized 239 00:10:35,039 --> 00:10:37,539 for its flexibility unless... Unless the data 240 00:10:37,539 --> 00:10:40,539 is so extreme, so far from what the simple model 241 00:10:40,539 --> 00:10:43,419 predicts, like nine heads out of ten flips, that 242 00:10:43,419 --> 00:10:45,320 the simple model just can't explain it anymore. 243 00:10:45,539 --> 00:10:47,919 Only then does the data provide enough evidence 244 00:10:47,919 --> 00:10:50,559 to justify paying the complexity cost of HE dollars. 245 00:10:51,000 --> 00:10:53,139 Wow. So the preference for simplicity isn't just 246 00:10:53,139 --> 00:10:55,240 a philosophical guideline. It's a mathematical 247 00:10:55,240 --> 00:10:58,120 consequence of... probability theory. It automatically 248 00:10:58,120 --> 00:11:01,139 balances model fit with model complexity. That's 249 00:11:01,139 --> 00:11:03,539 the beauty of it. It helps the system generalize 250 00:11:03,539 --> 00:11:05,539 better because it prevents chasing noise in the 251 00:11:05,539 --> 00:11:08,539 data with overly complicated explanations. It's 252 00:11:08,539 --> 00:11:10,779 fundamental to how we learn efficiently. Okay, 253 00:11:10,860 --> 00:11:14,100 so we have Bayes' rule for updating beliefs and 254 00:11:14,100 --> 00:11:17,679 this built -in Occam's razor, but how do we represent 255 00:11:17,679 --> 00:11:20,220 complex knowledge about the world, especially 256 00:11:20,220 --> 00:11:22,980 relationships like cause and effect? Chapter 257 00:11:22,980 --> 00:11:26,039 4 brings in graphical models. Yes, specifically 258 00:11:26,039 --> 00:11:29,840 Bayesian networks or Bayesnets. These are incredibly 259 00:11:29,840 --> 00:11:32,600 useful. They provide a visual way to represent 260 00:11:32,600 --> 00:11:35,639 the dependencies or lack thereof between lots 261 00:11:35,639 --> 00:11:38,220 of variables. Like a map of how things influence 262 00:11:38,220 --> 00:11:41,399 each other. Kind of, but more importantly, they 263 00:11:41,399 --> 00:11:43,980 define the generative model. The arrows in the 264 00:11:43,980 --> 00:11:46,960 graph show you the assumed causal story, the 265 00:11:46,960 --> 00:11:48,960 sequence of probabilistic steps that could have 266 00:11:48,960 --> 00:11:51,500 generated the data you're seeing. This aligns 267 00:11:51,500 --> 00:11:53,679 really well with how humans seem to build intuitive 268 00:11:53,679 --> 00:11:56,110 theories about how things work. Thinking in terms 269 00:11:56,110 --> 00:11:58,950 of how did this come about feels very natural. 270 00:11:59,110 --> 00:12:02,029 It is. And this generative view is key for modeling 271 00:12:02,029 --> 00:12:04,690 causality, which is such a powerful inductive 272 00:12:04,690 --> 00:12:07,330 bias we humans have. It also leads to some really 273 00:12:07,330 --> 00:12:09,769 interesting patterns of inference, like the explaining 274 00:12:09,769 --> 00:12:12,029 away effect. Oh, yeah. The book used a fun example 275 00:12:12,029 --> 00:12:14,110 for this. Let's try to unpack it. It involves 276 00:12:14,110 --> 00:12:17,649 psychic powers and a dodgy coin. That's the one. 277 00:12:18,190 --> 00:12:20,549 Imagine you see your friend flip a coin and it 278 00:12:20,549 --> 00:12:24,399 lands heads. Call that observation $6. Now, you 279 00:12:24,399 --> 00:12:27,240 might entertain two possible explanations. $6, 280 00:12:27,240 --> 00:12:29,080 double the two dollars, your friend has psychic 281 00:12:29,080 --> 00:12:32,460 powers and influenced the flip. Or $6, three, 282 00:12:32,639 --> 00:12:35,200 maybe the coin is secretly two -headed. Okay, 283 00:12:35,259 --> 00:12:38,379 so observing heads makes me slightly increase 284 00:12:38,379 --> 00:12:41,740 my belief in both the psychic hypothesis. and 285 00:12:41,740 --> 00:12:44,679 the two -headed coin hypothesis by 833, assuming 286 00:12:44,679 --> 00:12:46,740 I didn't know anything else. Right. The single 287 00:12:46,740 --> 00:12:49,480 piece of evidence supports, to some degree, both 288 00:12:49,480 --> 00:12:52,299 potential causes. But now someone tells you, 289 00:12:52,360 --> 00:12:54,279 hey, just so you know, that coin is actually 290 00:12:54,279 --> 00:12:56,899 two -headed. So $6 D is now known to be true. 291 00:12:57,039 --> 00:12:59,679 Right. What happens to your belief in your friend's 292 00:12:59,679 --> 00:13:01,600 psychic powers? But the reason I believe in them 293 00:13:01,600 --> 00:13:03,980 more, the coin landing heads is now perfectly 294 00:13:03,980 --> 00:13:05,580 explained by the fact the coin is two -headed 295 00:13:05,580 --> 00:13:08,980 by $23. Yeah. My belief in the psychic powers 296 00:13:08,980 --> 00:13:10,879 should probably drop back down to whatever it 297 00:13:10,879 --> 00:13:13,320 was before I saw the flip. Exactly. The known 298 00:13:13,320 --> 00:13:16,740 cause by 3332 explains away the evidence by the 299 00:13:16,740 --> 00:13:19,379 alternative cause by ever 22. The information 300 00:13:19,379 --> 00:13:21,120 fleet changes because knowing the state of one 301 00:13:21,120 --> 00:13:24,139 cause makes the evidence. about the other cause. 302 00:13:24,399 --> 00:13:26,779 That's subtle, but makes total sense when you 303 00:13:26,779 --> 00:13:28,399 think about the causal structure. It wouldn't 304 00:13:28,399 --> 00:13:30,639 happen if you just looked at correlations. Precisely. 305 00:13:30,639 --> 00:13:33,480 The structure of the graph dictates how evidence 306 00:13:33,480 --> 00:13:36,159 propagates. And these models aren't just for 307 00:13:36,159 --> 00:13:38,860 passive observation. They're crucial for modeling 308 00:13:38,860 --> 00:13:41,399 intervention. What we do in the world. What happens 309 00:13:41,399 --> 00:13:44,440 if I push this? Yes. The framework incorporates 310 00:13:44,440 --> 00:13:47,820 Judea Pearl's do operator, which allows us to 311 00:13:47,820 --> 00:13:50,440 represent actually intervening in the system, 312 00:13:50,500 --> 00:13:54,440 not just observing it. This lets us model counterfactuals 313 00:13:54,440 --> 00:13:56,100 and compare different theories of how humans 314 00:13:56,100 --> 00:13:58,460 judge causal strength, like comparing simple 315 00:13:58,460 --> 00:14:01,639 probability changes, delta p, with more nuanced 316 00:14:01,639 --> 00:14:03,860 causal power models that account for background 317 00:14:03,860 --> 00:14:06,299 causes. Okay, so we have the basic update rule, 318 00:14:06,500 --> 00:14:09,440 Bayes, the complexity control, Occam's razor, 319 00:14:09,620 --> 00:14:12,379 and the structure for causal knowledge, graphical 320 00:14:12,379 --> 00:14:15,980 models. Now, Chapter 7 takes the next step. How 321 00:14:15,980 --> 00:14:18,580 do these beliefs actually lead to actions, from 322 00:14:18,580 --> 00:14:20,960 belief to behavior? This brings in Bayesian decision 323 00:14:20,960 --> 00:14:23,789 theory. It's the link between knowing and doing. 324 00:14:23,889 --> 00:14:26,590 The idea is that a rational agent should act 325 00:14:26,590 --> 00:14:29,690 to maximize its expected utility. Expected utility. 326 00:14:30,570 --> 00:14:33,490 So you weigh the goodness or badness, utility, 327 00:14:33,730 --> 00:14:36,590 of each possible outcome by how likely you think 328 00:14:36,590 --> 00:14:38,490 that outcome is, your posterior probability, 329 00:14:38,889 --> 00:14:41,470 and choose the action that gives the highest 330 00:14:41,470 --> 00:14:44,200 average score. That's the core idea for a perfectly 331 00:14:44,200 --> 00:14:46,620 rational agent. But of course, humans don't always 332 00:14:46,620 --> 00:14:48,700 seem perfectly rational in this classical sense. 333 00:14:49,000 --> 00:14:52,220 The book discusses deviations like probability 334 00:14:52,220 --> 00:14:55,299 matching. Ah, right. If a light flashes on the 335 00:14:55,299 --> 00:14:58,200 left 70 % of the time and the right 30 % of the 336 00:14:58,200 --> 00:15:00,600 time, the optimal thing is to always guess left. 337 00:15:00,779 --> 00:15:03,360 But people often guess left 70 % of the time 338 00:15:03,360 --> 00:15:06,279 and right 30 % of the time. They match the probabilities. 339 00:15:06,480 --> 00:15:08,360 Exactly. And for a long time, that was held up 340 00:15:08,360 --> 00:15:10,220 as evidence that humans are just irrational, 341 00:15:10,460 --> 00:15:13,120 not maximizing utility. But the Bayesian perspective 342 00:15:13,120 --> 00:15:15,519 offers a different lens, maybe. It does. Instead 343 00:15:15,519 --> 00:15:18,259 of just saying irrational, we can ask why people 344 00:15:18,259 --> 00:15:21,120 might do this. Maybe probability matching is 345 00:15:21,120 --> 00:15:23,159 actually a rational strategy under certain constraints. 346 00:15:23,320 --> 00:15:26,179 For example, if you model the decision not as 347 00:15:26,179 --> 00:15:28,779 one big optimization, but as a series of quick 348 00:15:28,779 --> 00:15:31,919 independent choices where exploring occasionally. 349 00:15:32,740 --> 00:15:34,899 guessing right sometimes, might have long -term 350 00:15:34,899 --> 00:15:37,360 benefits, or if you're trying to approximate 351 00:15:37,360 --> 00:15:40,179 the optimal solution with limited cognitive resources. 352 00:15:40,600 --> 00:15:43,580 So the behavior might look suboptimal if you 353 00:15:43,580 --> 00:15:46,649 ignore the constraints, but rational given those 354 00:15:46,649 --> 00:15:49,289 constraints. Precisely. It opens the door to 355 00:15:49,289 --> 00:15:51,789 analyzing these seemingly irrational behaviors 356 00:15:51,789 --> 00:15:54,629 within a broader rational framework, considering 357 00:15:54,629 --> 00:15:56,750 things like cognitive costs and approximation 358 00:15:56,750 --> 00:15:59,470 strategies. This hints towards the idea of resource 359 00:15:59,470 --> 00:16:01,610 rationality, which we'll likely come back to. 360 00:16:01,789 --> 00:16:03,529 All right, let's delve deeper now into some core 361 00:16:03,529 --> 00:16:05,769 human abilities, starting with how we handle 362 00:16:05,769 --> 00:16:08,570 concepts and categorization. Chapter 9 tackles 363 00:16:08,570 --> 00:16:11,539 this. Psychologists have argued for ages about 364 00:16:11,539 --> 00:16:14,179 how we represent categories. Is it like an average 365 00:16:14,179 --> 00:16:16,120 prototype? Or is it a collection of specific 366 00:16:16,120 --> 00:16:19,059 exemplars we've seen? Yeah, that prototype versus 367 00:16:19,059 --> 00:16:22,460 exemplar debate was a big one. Prototype models 368 00:16:22,460 --> 00:16:25,059 are good for typicality effects, but struggle 369 00:16:25,059 --> 00:16:27,299 with categories that seem to have multiple clusters. 370 00:16:28,120 --> 00:16:30,600 Exemplar models handle weird distributions better, 371 00:16:30,679 --> 00:16:33,659 but seem less efficient. Traditional models often 372 00:16:33,659 --> 00:16:35,940 made you pick one or the other. So how does the 373 00:16:35,940 --> 00:16:38,340 Bayesian approach help here? Does it force a 374 00:16:38,340 --> 00:16:41,129 choice? No, and that's the clever part. It uses 375 00:16:41,129 --> 00:16:43,769 something called nonparametric Bayesian models. 376 00:16:43,950 --> 00:16:46,210 Okay, nonparametric Bayesian sounds intimidating. 377 00:16:46,549 --> 00:16:49,850 The book also calls them infinite models. How 378 00:16:49,850 --> 00:16:52,610 can my finite brain use an infinite model? That 379 00:16:52,610 --> 00:16:55,169 seems like a problem. It sounds paradoxical, 380 00:16:55,169 --> 00:16:57,789 but the infinite part refers to the potential 381 00:16:57,789 --> 00:17:00,230 complexity and not the actual complexity used 382 00:17:00,230 --> 00:17:02,690 at any given time. These models assume there 383 00:17:02,690 --> 00:17:05,230 could be, in principle, an infinite number of 384 00:17:05,230 --> 00:17:07,670 categories or clusters available. But we obviously 385 00:17:07,670 --> 00:17:10,049 don't use infinitely many categories. Right. 386 00:17:10,150 --> 00:17:13,089 The magic is that the inference process itself, 387 00:17:13,250 --> 00:17:15,609 driven by the data and that Bayesian Occam's 388 00:17:15,609 --> 00:17:18,349 razor we talked about, only activates a finite 389 00:17:18,349 --> 00:17:20,950 number of these potential categories just enough 390 00:17:20,950 --> 00:17:24,369 to explain the beta well. It doesn't posit infinite 391 00:17:24,369 --> 00:17:26,769 structure needlessly. It discovers the necessary 392 00:17:26,769 --> 00:17:29,950 structure. So the complexity grows only if the 393 00:17:29,950 --> 00:17:33,059 data really demands it. Exactly. And the most 394 00:17:33,059 --> 00:17:35,740 famous way to visualize this is the Chinese restaurant 395 00:17:35,740 --> 00:17:38,799 process, or CRP. It's a beautiful metaphor. Okay, 396 00:17:38,859 --> 00:17:41,039 I'm intrigued. Lay out the Chinese restaurant 397 00:17:41,039 --> 00:17:43,400 process for us. Imagine a Chinese restaurant 398 00:17:43,400 --> 00:17:46,359 with theoretically infinitely many empty round 399 00:17:46,359 --> 00:17:49,559 tables. Each table represents a potential category 400 00:17:49,559 --> 00:17:53,099 or cluster. Now, customers, or data points, the 401 00:17:53,099 --> 00:17:54,960 things we're categorizing, start arriving one 402 00:17:54,960 --> 00:17:57,420 by one. The first customer walks in, picks an 403 00:17:57,420 --> 00:17:59,539 empty table, and sits down. Starts the first 404 00:17:59,539 --> 00:18:01,660 category. The second customer comes in, they 405 00:18:01,660 --> 00:18:03,380 have a choice. What's the choice? They can either 406 00:18:03,380 --> 00:18:05,720 sit at the already occupied table, joining that 407 00:18:05,720 --> 00:18:08,240 category, or start a new table, a new category. 408 00:18:08,880 --> 00:18:11,440 The probability of joining an existing table 409 00:18:11,440 --> 00:18:13,779 is proportional to how many people are already 410 00:18:13,779 --> 00:18:16,619 sitting there. Ah, so popular tables get more 411 00:18:16,619 --> 00:18:19,670 popular, like a rich get richer effect. Exactly. 412 00:18:19,789 --> 00:18:22,910 That creates pressure towards forming large central 413 00:18:22,910 --> 00:18:26,230 clusters like prototypes. But there's also always 414 00:18:26,230 --> 00:18:28,289 a chance the customer will choose to start a 415 00:18:28,289 --> 00:18:31,130 new table. The probability of starting a new 416 00:18:31,130 --> 00:18:33,269 table is proportional to a parameter, usually 417 00:18:33,269 --> 00:18:36,009 called alpha. Alpha. And what does alpha control? 418 00:18:36,369 --> 00:18:39,769 Alpha controls the sociability. or the tendency 419 00:18:39,769 --> 00:18:42,990 to create new categories. If alpha is low, customers 420 00:18:42,990 --> 00:18:45,410 strongly prefer existing tables, and you end 421 00:18:45,410 --> 00:18:47,930 up with just a few large clusters, very prototype 422 00:18:47,930 --> 00:18:51,029 -like. If alpha is high, customers are more adventurous, 423 00:18:51,250 --> 00:18:53,490 start lots of new tables, and you get many small 424 00:18:53,490 --> 00:18:56,069 clusters, more like an exemplar model. So the 425 00:18:56,069 --> 00:18:58,390 model doesn't choose prototype or exemplar beforehand. 426 00:18:58,769 --> 00:19:02,009 It can behave like either or something in between, 427 00:19:02,170 --> 00:19:03,970 depending on the data pattern and that alpha 428 00:19:03,970 --> 00:19:06,960 parameter. Precisely. The CRP acts as a prior 429 00:19:06,960 --> 00:19:09,220 over how data should be partitioned, automatically 430 00:19:09,220 --> 00:19:11,579 inferring the right number and type of clusters. 431 00:19:11,660 --> 00:19:13,700 It gives you that needed flexibility. That's 432 00:19:13,700 --> 00:19:16,000 really elegant. Okay, let's switch gears to language 433 00:19:16,000 --> 00:19:17,740 acquisition and processing covered in Chapter 434 00:19:17,740 --> 00:19:20,859 16. How does the Bayesian lens apply here? It 435 00:19:20,859 --> 00:19:23,380 reframes things like understanding a sentence 436 00:19:23,380 --> 00:19:26,680 parsing as an inverse inference problem. Inverse 437 00:19:26,680 --> 00:19:29,059 inference. Yeah. Meaning working backward from 438 00:19:29,059 --> 00:19:31,539 the data. Yeah. When you hear a sentence, what 439 00:19:31,539 --> 00:19:34,160 you get is just a string of words. The underlying 440 00:19:34,160 --> 00:19:37,279 grammatical structure, the parse tree, is hidden. 441 00:19:37,880 --> 00:19:40,140 Parsing is the process of inferring the most 442 00:19:40,140 --> 00:19:42,299 likely hidden structure that could have generated 443 00:19:42,299 --> 00:19:44,500 the word string you heard. So it's like you're 444 00:19:44,500 --> 00:19:47,180 implicitly asking, what set of grammar rules 445 00:19:47,180 --> 00:19:50,599 applied probabilistically best explains this 446 00:19:50,599 --> 00:19:53,200 sequence of words? Exactly. And that's why you 447 00:19:53,200 --> 00:19:55,960 need probabilistic grammars, like probabilistic 448 00:19:55,960 --> 00:19:59,819 context -free grammars, PCFGs. They assign probabilities 449 00:19:59,819 --> 00:20:01,940 to different grammatical rules or structures, 450 00:20:02,099 --> 00:20:04,819 allowing the listener to resolve ambiguity. Think 451 00:20:04,819 --> 00:20:06,779 about a sentence like, the old man, the boat. 452 00:20:07,019 --> 00:20:09,480 Oh, yeah, that's a classic garden path sentence. 453 00:20:09,759 --> 00:20:12,200 Hard to parse. Your brain tries different parses, 454 00:20:12,200 --> 00:20:14,140 different structures, and usually settles on 455 00:20:14,140 --> 00:20:16,259 the most probable one, given the grammar and 456 00:20:16,259 --> 00:20:19,299 context. The Bayesian approach formalizes the 457 00:20:19,299 --> 00:20:22,099 search for the best explanation. And this inverse 458 00:20:22,099 --> 00:20:24,460 logic applies even at lower levels, like just 459 00:20:24,460 --> 00:20:26,920 hearing sounds. The book mentioned the perceptual 460 00:20:26,920 --> 00:20:29,470 magnet effect. Yes, another fantastic example. 461 00:20:29,670 --> 00:20:32,329 This is about how we perceive speak sounds, like 462 00:20:32,329 --> 00:20:34,970 vowels. We don't hear them exactly as they are 463 00:20:34,970 --> 00:20:37,710 acoustically. Sounds that are acoustically near 464 00:20:37,710 --> 00:20:40,549 a category prototype tend to get perceived as 465 00:20:40,549 --> 00:20:42,549 being even closer to that prototype than they 466 00:20:42,549 --> 00:20:44,730 really are. So the ideal E sound, for example, 467 00:20:44,890 --> 00:20:49,170 pulls nearby A -ish sounds towards it perceptually, 468 00:20:49,210 --> 00:20:52,150 like a magnet. That's the idea. The Bayesian 469 00:20:52,150 --> 00:20:54,750 explanation treats the sound you actually hear 470 00:20:54,750 --> 00:20:58,029 as a noisy version of an intended clean phonetic 471 00:20:58,029 --> 00:21:00,849 category, the prototype. Your brain performs 472 00:21:00,849 --> 00:21:03,910 inverse inference. What underlying clean vowel 473 00:21:03,910 --> 00:21:06,190 sound was most likely to have generated this 474 00:21:06,190 --> 00:21:08,410 noisy acoustic signal I just heard? And because 475 00:21:08,410 --> 00:21:11,309 the prototype is, by definition, the most common 476 00:21:11,309 --> 00:21:13,930 or probable realization of that category. The 477 00:21:13,930 --> 00:21:16,789 inference process rationally biases your perception 478 00:21:16,789 --> 00:21:19,049 towards that prototype, effectively compensating 479 00:21:19,049 --> 00:21:21,670 for the assumed noise. The magnet effect falls 480 00:21:21,670 --> 00:21:24,230 out naturally from rational inference under uncertainty 481 00:21:24,230 --> 00:21:26,750 about noise. Wow, okay, so parsing is inverse 482 00:21:26,750 --> 00:21:29,009 inference, perception is inverse inference. What 483 00:21:29,009 --> 00:21:30,930 about understanding meaning beyond the literal 484 00:21:30,930 --> 00:21:35,559 words? That too. This uses the Rational Speech 485 00:21:35,559 --> 00:21:39,079 Act, RSA, framework. It models conversation as 486 00:21:39,079 --> 00:21:41,200 a kind of cooperative game between a speaker 487 00:21:41,200 --> 00:21:44,180 and a listener, both trying to be rational. How 488 00:21:44,180 --> 00:21:46,680 does that help with inferring implied meaning? 489 00:21:47,130 --> 00:21:49,950 The listener basically performs inverse inference 490 00:21:49,950 --> 00:21:52,809 on the speaker's intentions. You assume the speaker 491 00:21:52,809 --> 00:21:54,730 chose their words rationally and efficiently 492 00:21:54,730 --> 00:21:57,740 to convey a particular meaning. Let's use that 493 00:21:57,740 --> 00:22:01,400 some versus all example again. If I say some 494 00:22:01,400 --> 00:22:04,079 of the cookies are gone. You, the listener, immediately 495 00:22:04,079 --> 00:22:06,819 infer, I mean, not all of the cookies are gone, 496 00:22:06,900 --> 00:22:09,980 even though logically some could include all. 497 00:22:10,220 --> 00:22:13,259 Right. How does RSA explain that inference? The 498 00:22:13,259 --> 00:22:15,640 listener reasons. OK, the speaker said some. 499 00:22:15,740 --> 00:22:17,519 If all the cookies were gone, they could have 500 00:22:17,519 --> 00:22:20,589 said all. All is just as easy to say, and it's 501 00:22:20,589 --> 00:22:22,930 more informative. Since they didn't say all, 502 00:22:23,269 --> 00:22:26,730 they must believe all is false. Ah, so it's reasoning 503 00:22:26,730 --> 00:22:28,829 about the speaker's choice of utterance compared 504 00:22:28,829 --> 00:22:31,109 to other utterances they could have made. It's 505 00:22:31,109 --> 00:22:32,869 like inverse planning applied to communication. 506 00:22:33,369 --> 00:22:35,490 Exactly. You assume the speaker is trying to 507 00:22:35,490 --> 00:22:38,150 be helpful and informative, following Gratian 508 00:22:38,150 --> 00:22:40,869 maxims, essentially, and you work backward from 509 00:22:40,869 --> 00:22:43,210 what they said to what they likely meant. It's 510 00:22:43,210 --> 00:22:45,990 a computational way to handle those subtle conversational 511 00:22:45,990 --> 00:22:48,250 inferences. This really feels like it's bringing 512 00:22:48,250 --> 00:22:50,990 everything together, logic, probability, intention, 513 00:22:51,250 --> 00:22:55,029 which leads nicely into chapters 18 and 19, and 514 00:22:55,029 --> 00:22:57,269 this grand idea of the probabilistic language 515 00:22:57,269 --> 00:23:00,119 of thought, PLID. That sounds like the ultimate 516 00:23:00,119 --> 00:23:02,640 synthesis. It's a very ambitious and exciting 517 00:23:02,640 --> 00:23:05,819 hypothesis. The core idea is that human concepts 518 00:23:05,819 --> 00:23:07,680 and knowledge aren't just static data structures. 519 00:23:08,000 --> 00:23:10,359 They are best thought of as stochastic functions 520 00:23:10,359 --> 00:23:13,079 or little programs written in a universal probabilistic 521 00:23:13,079 --> 00:23:16,019 programming language, PPL, like the language 522 00:23:16,019 --> 00:23:19,339 church developed by Goodman, Mansinka, Roy, Bonowitz, 523 00:23:19,559 --> 00:23:22,559 and Tenenbaum. Okay, hold on. Concept is programs. 524 00:23:23,200 --> 00:23:25,019 Probabilistic programs. What does that mean practically? 525 00:23:25,440 --> 00:23:28,039 It means a concept defines a generative process, 526 00:23:28,180 --> 00:23:30,720 for examples of that concept, including the uncertainty 527 00:23:30,720 --> 00:23:32,880 involved. Think about the concept of strength. 528 00:23:33,079 --> 00:23:35,359 It's not just a number. It might be represented 529 00:23:35,359 --> 00:23:38,519 as a program that, when run, samples a value 530 00:23:38,519 --> 00:23:41,579 from a probability distribution, say a Gaussian, 531 00:23:41,839 --> 00:23:44,180 representing typical human strengths. So the 532 00:23:44,180 --> 00:23:46,839 program itself defines the variability and likelihood 533 00:23:46,839 --> 00:23:49,960 of different strengths. Yes. And the power comes 534 00:23:49,960 --> 00:23:52,579 from composing these programs. The book uses 535 00:23:52,579 --> 00:23:55,380 a great example. reasoning about a tug -of -war 536 00:23:55,380 --> 00:23:58,099 game. You can have concepts like player strength, 537 00:23:58,400 --> 00:24:00,980 a probabilistic program sampling a strength value, 538 00:24:01,319 --> 00:24:04,460 team strength, a program that sums the strengths 539 00:24:04,460 --> 00:24:06,799 of players on the team, maybe even eyes lazy, 540 00:24:06,960 --> 00:24:09,200 a program that sometimes reduces a player's effective 541 00:24:09,200 --> 00:24:12,200 strength. The PPL framework lets you build a 542 00:24:12,200 --> 00:24:14,400 model of the entire tug -of -war situation by 543 00:24:14,400 --> 00:24:16,420 combining these conceptual programs. And then 544 00:24:16,420 --> 00:24:19,319 you can run this model. How? You can run it forward 545 00:24:19,319 --> 00:24:22,579 to simulate likely outcomes. Or, more powerfully, 546 00:24:22,680 --> 00:24:24,859 you can run it backward using Bayesian inference. 547 00:24:25,460 --> 00:24:28,480 Suppose you observe a surprising outcome. A small 548 00:24:28,480 --> 00:24:32,079 team, Team A, beat a much larger team, Team B. 549 00:24:32,180 --> 00:24:35,220 You can ask the PPL system, given this outcome, 550 00:24:35,759 --> 00:24:38,000 What were the likely latent properties, like 551 00:24:38,000 --> 00:24:40,220 the individual strengths or laziness factors 552 00:24:40,220 --> 00:24:43,140 of the players? The system effectively runs many 553 00:24:43,140 --> 00:24:45,720 simulations, tweaking the hidden variables according 554 00:24:45,720 --> 00:24:48,339 to Bay's rule until it finds the scenarios most 555 00:24:48,339 --> 00:24:50,299 likely to have produced that surprising win. 556 00:24:50,660 --> 00:24:52,839 Maybe the players on Team A were just incredibly 557 00:24:52,839 --> 00:24:56,240 strong, or maybe key players on Team B were having 558 00:24:56,240 --> 00:24:59,460 an off day or lazy. So it lets you infer hidden 559 00:24:59,460 --> 00:25:02,140 causes and properties by inverting the generative 560 00:25:02,140 --> 00:25:04,619 model defined by these programs. That seems incredibly 561 00:25:04,619 --> 00:25:07,279 powerful for reasoning. It is. And it connects 562 00:25:07,279 --> 00:25:09,599 directly to learning. If concepts are programs, 563 00:25:09,960 --> 00:25:12,359 then learning a concept is like inferring the 564 00:25:12,359 --> 00:25:14,799 program. Chapter 19. How do you infer a program? 565 00:25:14,900 --> 00:25:17,099 There must be infinitely many possible programs. 566 00:25:17,299 --> 00:25:20,019 There are. But this is where the prior overprograms 567 00:25:20,019 --> 00:25:22,259 comes back in, linking to Bayesian -Ockham's 568 00:25:22,259 --> 00:25:24,960 razor again. The prior distribution overprograms 569 00:25:24,960 --> 00:25:27,299 heavily favors simpler programs, those that are 570 00:25:27,299 --> 00:25:30,420 shorter or have lower complexity, like Kolmogorov 571 00:25:30,420 --> 00:25:32,859 complexity, discussed later in the book. Ah. 572 00:25:33,359 --> 00:25:36,319 So when a child learns a concept like even number 573 00:25:36,319 --> 00:25:40,039 from just a few examples, 2, 4, 8, 10, they aren't 574 00:25:40,039 --> 00:25:43,579 just finding any program that fits. They're implicitly 575 00:25:43,579 --> 00:25:46,019 searching for the simplest, most elegant program 576 00:25:46,019 --> 00:25:48,880 consistent with those examples. The strong prior 577 00:25:48,880 --> 00:25:51,640 favoring simplicity allows them to jump to the 578 00:25:51,640 --> 00:25:55,019 correct general definition divisible by two incredibly 579 00:25:55,019 --> 00:25:57,619 quickly without needing thousands of examples. 580 00:25:57,859 --> 00:26:00,160 It explains how we learn abstract structures 581 00:26:00,160 --> 00:26:03,059 so efficiently. This idea of structured knowledge, 582 00:26:03,279 --> 00:26:05,859 especially structured priors, seems absolutely 583 00:26:05,859 --> 00:26:09,079 key to how humans build deep understanding. We 584 00:26:09,079 --> 00:26:11,339 don't just learn isolated facts. We build intuitive 585 00:26:11,339 --> 00:26:13,940 theories about domains like physics, biology, 586 00:26:14,319 --> 00:26:16,720 or other people's minds. Chapter 8 introduces 587 00:26:16,720 --> 00:26:19,299 hierarchical Bayesian models, HBMs, as a way 588 00:26:19,299 --> 00:26:21,380 to capture this. HBMs are perfect for this. They 589 00:26:21,380 --> 00:26:23,740 explicitly model knowledge at multiple levels 590 00:26:23,740 --> 00:26:26,019 of abstraction. Think of it like layers. Layers. 591 00:26:26,079 --> 00:26:28,000 How does that work? At the bottom layer, you 592 00:26:28,000 --> 00:26:29,880 have the raw data, the specific observations. 593 00:26:30,500 --> 00:26:32,859 In the middle layers, you might have parameters 594 00:26:32,859 --> 00:26:35,019 or structures related to specific categories 595 00:26:35,019 --> 00:26:38,180 or items. And crucially, at the top layer, you 596 00:26:38,180 --> 00:26:40,779 have hyperparameters that represent abstract 597 00:26:40,779 --> 00:26:43,579 principles or overarching theories about the 598 00:26:43,579 --> 00:26:46,259 domain itself. So the top layer influences the 599 00:26:46,259 --> 00:26:48,359 learning happening at the lower layers. Exactly. 600 00:26:48,420 --> 00:26:50,880 The top layer basically learns the inductive 601 00:26:50,880 --> 00:26:53,940 bias for the layers below it. This is how HBMs 602 00:26:53,940 --> 00:26:57,029 model learning to learn. You don't just learn 603 00:26:57,029 --> 00:26:59,369 facts, you learn the structure of the domain, 604 00:26:59,589 --> 00:27:01,829 which then makes learning new facts within that 605 00:27:01,829 --> 00:27:03,910 domain much faster. The book had a really compelling 606 00:27:03,910 --> 00:27:05,869 example of this with medical reasoning, right? 607 00:27:06,210 --> 00:27:08,769 Discovering the disease symptom structure. Yes, 608 00:27:08,849 --> 00:27:11,750 a classic study by Kemp, Tenenbaum, Griffiths, 609 00:27:11,750 --> 00:27:14,150 and others. Participants had to figure out causal 610 00:27:14,150 --> 00:27:17,769 links between, say, 16 variables. Some were potential 611 00:27:17,769 --> 00:27:20,930 hidden causes, diseases, C1, and others were 612 00:27:20,930 --> 00:27:23,950 observable effects, symptoms, C2. And a simple 613 00:27:23,950 --> 00:27:27,089 flat model struggled. A standard two -level Bayesian 614 00:27:27,089 --> 00:27:29,930 network treating all 16 variables as potentially 615 00:27:29,930 --> 00:27:33,509 equal did very poorly. It needed lots of data 616 00:27:33,509 --> 00:27:35,670 to even start seeing the patterns because it 617 00:27:35,670 --> 00:27:38,329 had no higher -level structure to guide it. But 618 00:27:38,329 --> 00:27:40,970 the hierarchical Bayesian model... The HBM had 619 00:27:40,970 --> 00:27:43,589 a top layer designed to discover abstract types 620 00:27:43,589 --> 00:27:45,630 of variables and common patterns of connection 621 00:27:45,630 --> 00:27:48,049 between them. This top layer quickly figured 622 00:27:48,049 --> 00:27:51,039 out... Uh -huh. Variables 1 through 6 consistently 623 00:27:51,039 --> 00:27:54,299 act like causes, and variables 7 through 16 act 624 00:27:54,299 --> 00:27:56,940 like effects, and the dominant pattern is links 625 00:27:56,940 --> 00:27:58,880 going from the first group to the second group. 626 00:27:59,099 --> 00:28:02,630 C1, Ted Toulon. It learned the schema. Diseases 627 00:28:02,630 --> 00:28:05,569 cause symptoms. Precisely. And once it learned 628 00:28:05,569 --> 00:28:08,329 that abstract schema at the top level, it provided 629 00:28:08,329 --> 00:28:10,970 a powerful inductive bias to the lower level. 630 00:28:11,130 --> 00:28:13,509 The model could then learn the specific disease 631 00:28:13,509 --> 00:28:16,589 symptom links much, much faster and more accurately, 632 00:28:16,849 --> 00:28:19,130 even with the same limited data that baffled 633 00:28:19,130 --> 00:28:21,170 the flat model. That's a beautiful demonstration 634 00:28:21,170 --> 00:28:23,109 of learning the structure of knowledge itself. 635 00:28:23,190 --> 00:28:25,309 It feels very much like how a child develops 636 00:28:25,309 --> 00:28:27,930 expertise in a domain. It really does capture 637 00:28:27,930 --> 00:28:30,549 that transition from slow, data -driven learning 638 00:28:30,549 --> 00:28:33,940 to... faster, theory -driven learning that we 639 00:28:33,940 --> 00:28:36,220 see in development. Okay, another core intuitive 640 00:28:36,220 --> 00:28:38,339 theory we have is about other people's theory 641 00:28:38,339 --> 00:28:42,059 of mind. Tom, chapter 14. How do we figure out 642 00:28:42,059 --> 00:28:44,779 what others believe or want? The Bayesian approach 643 00:28:44,779 --> 00:28:47,259 models this primarily through inverse planning. 644 00:28:47,480 --> 00:28:49,839 It's similar to the Rational Speech Act idea, 645 00:28:50,000 --> 00:28:53,000 but applied more broadly to actions. So I see 646 00:28:53,000 --> 00:28:55,299 someone do something, and I work backward to 647 00:28:55,299 --> 00:28:57,420 figure out the beliefs and desires that likely 648 00:28:57,420 --> 00:29:00,039 led to that action. Exactly. You essentially 649 00:29:00,039 --> 00:29:02,299 assume the other person is acting approximately, 650 00:29:02,480 --> 00:29:04,559 rationally, to achieve their goals given their 651 00:29:04,559 --> 00:29:07,279 beliefs about the world. You invert their presumed 652 00:29:07,279 --> 00:29:09,779 planning process. And this lets us do more than 653 00:29:09,779 --> 00:29:12,180 just guess one thing, right? Like, we can figure 654 00:29:12,180 --> 00:29:14,740 out preferences and costs. Let's use that ice 655 00:29:14,740 --> 00:29:17,400 cream versus cake example. Okay. You see your 656 00:29:17,400 --> 00:29:20,200 friend walk past a delicious looking cake, $10, 657 00:29:20,200 --> 00:29:22,859 and choose a simple ice cream, $8 instead. My 658 00:29:22,859 --> 00:29:24,779 first thought might be, wow, they must really 659 00:29:24,779 --> 00:29:27,119 like ice cream more than cake. High reward for 660 00:29:27,119 --> 00:29:29,789 $8 one. But then you consider the context, the 661 00:29:29,789 --> 00:29:33,230 costs. Maybe the cake shop, $8 .02, was across 662 00:29:33,230 --> 00:29:36,529 the street, requiring effort, a cost to get to, 663 00:29:36,690 --> 00:29:38,789 while the ice cream stand, $8 .01, was right 664 00:29:38,789 --> 00:29:42,490 there, zero cost. Ah. So even if they slightly 665 00:29:42,490 --> 00:29:45,390 prefer the taste of cake, higher intrinsic reward 666 00:29:45,390 --> 00:29:48,589 for $8 .02, the effort involved might make choosing 667 00:29:48,589 --> 00:29:51,609 the easily accessible ice cream, $8 .01, the 668 00:29:51,609 --> 00:29:54,779 more rational action overall. Precisely. Inverse 669 00:29:54,779 --> 00:29:56,980 planning allows you to jointly infer both the 670 00:29:56,980 --> 00:30:00,240 likely rewards, preferences, and the likely costs, 671 00:30:00,619 --> 00:30:03,680 effort, obstacles that best explain the observed 672 00:30:03,680 --> 00:30:06,369 action. You might conclude they slightly prefer 673 00:30:06,369 --> 00:30:08,829 cake but aren't willing to pay the cost, which 674 00:30:08,829 --> 00:30:10,990 is a much more nuanced understanding than just 675 00:30:10,990 --> 00:30:12,990 saying they prefer ice cream. It captures that 676 00:30:12,990 --> 00:30:15,609 sophisticated social calculus we seem to do constantly. 677 00:30:15,849 --> 00:30:17,930 Yes, inferring these hidden mental states from 678 00:30:17,930 --> 00:30:20,529 sparse behavioral data is a hallmark of human 679 00:30:20,529 --> 00:30:22,990 social intelligence, and inverse planning provides 680 00:30:22,990 --> 00:30:25,730 a formal model for it. Now let's shift from intuitive 681 00:30:25,730 --> 00:30:28,650 psychology to intuitive physics, IPE. In Chapter 682 00:30:28,650 --> 00:30:31,130 15. We seem to have a pretty good feel for how 683 00:30:31,130 --> 00:30:33,349 physical objects behave, even without knowing 684 00:30:33,349 --> 00:30:36,529 Newtonian equations. Right. The proposal here 685 00:30:36,529 --> 00:30:38,490 is that we have something like an intuitive physics 686 00:30:38,490 --> 00:30:42,210 engine in our heads, a mental simulator. But 687 00:30:42,210 --> 00:30:44,210 it's not just deterministic. Physical reasoning 688 00:30:44,210 --> 00:30:47,470 is treated as probabilistic inference using this 689 00:30:47,470 --> 00:30:50,190 engine. So we can run simulations, like if I 690 00:30:50,190 --> 00:30:53,250 stack these blocks this way, will the tower likely 691 00:30:53,250 --> 00:30:55,490 fall? Yes, we can run it forward for prediction. 692 00:30:56,420 --> 00:30:59,160 But critically, like with Tom, the real power 693 00:30:59,160 --> 00:31:01,900 comes from running it backward for inverse inference 694 00:31:01,900 --> 00:31:04,440 and also using it for counterfactual reasoning. 695 00:31:04,680 --> 00:31:07,140 Meaning we can infer hidden properties or reason 696 00:31:07,140 --> 00:31:10,799 about what if. Exactly. You see a tower of blocks 697 00:31:10,799 --> 00:31:13,019 standing stably. You can infer things about the 698 00:31:13,019 --> 00:31:15,859 hidden properties like the likely mass or friction 699 00:31:15,859 --> 00:31:18,339 of the blocks needed for it to be stable. Or 700 00:31:18,339 --> 00:31:21,000 you can perform counterfactuals. The tower is 701 00:31:21,000 --> 00:31:22,980 standing, but what would have happened if I had 702 00:31:22,980 --> 00:31:25,839 removed that one specific block near the bottom? 703 00:31:26,059 --> 00:31:27,900 And running that simulation tells you how crucial 704 00:31:27,900 --> 00:31:31,059 that block was. Yes. If the simulation shows 705 00:31:31,059 --> 00:31:33,240 the tower would have collapsed without that block, 706 00:31:33,500 --> 00:31:36,000 you attribute high causal responsibility to that 707 00:31:36,000 --> 00:31:39,190 block for the tower's stability. This kind of 708 00:31:39,190 --> 00:31:41,890 probabilistic simulation and counterfactual reasoning 709 00:31:41,890 --> 00:31:45,549 using the IPE aligns remarkably well with people's 710 00:31:45,549 --> 00:31:47,569 judgments about physical causality, stability, 711 00:31:47,829 --> 00:31:50,750 and blame things that go way beyond simple prediction. 712 00:31:51,009 --> 00:31:53,250 Okay, let's tie these threads together now by 713 00:31:53,250 --> 00:31:56,150 looking explicitly at Bayesian models of cognitive 714 00:31:56,150 --> 00:31:59,309 development in Chapter 20. How does this framework 715 00:31:59,309 --> 00:32:01,450 account for how children learn these intuitive 716 00:32:01,450 --> 00:32:04,069 theories? It starts with core knowledge, right? 717 00:32:04,190 --> 00:32:07,130 Yes. The idea is that infants aren't blank slates. 718 00:32:07,190 --> 00:32:09,589 They come equipped with some initial foundational 719 00:32:09,589 --> 00:32:13,230 core knowledge systems. Things like understanding 720 00:32:13,230 --> 00:32:16,230 that objects persist even when hidden, that agents 721 00:32:16,230 --> 00:32:19,069 act purposefully and efficiently, basic number 722 00:32:19,069 --> 00:32:22,109 sense, basic spatial reasoning. So in the Bayesian 723 00:32:22,109 --> 00:32:25,029 or PPL framework, this core knowledge acts as 724 00:32:25,029 --> 00:32:27,150 the initial high -level priors, the starting 725 00:32:27,150 --> 00:32:29,230 code. That's a great way to put it. These are 726 00:32:29,230 --> 00:32:30,849 the built -in assumptions that get the learning 727 00:32:30,849 --> 00:32:33,140 process off the ground. providing the initial 728 00:32:33,140 --> 00:32:35,420 structure needed to interpret the sparse data 729 00:32:35,420 --> 00:32:37,960 infants receive. But development isn't always 730 00:32:37,960 --> 00:32:41,200 smooth. Kids sometimes seem to jump suddenly 731 00:32:41,200 --> 00:32:44,440 from one way of thinking to another. How is that 732 00:32:44,440 --> 00:32:46,839 captured? The models address this by focusing 733 00:32:46,839 --> 00:32:49,119 not just on the endpoint, the ideal rational 734 00:32:49,119 --> 00:32:51,799 model, but also on the process of learning and 735 00:32:51,799 --> 00:32:54,970 belief revision. They often use stochastic search 736 00:32:54,970 --> 00:32:58,089 algorithms as plausible process models. Stochastic 737 00:32:58,089 --> 00:33:01,049 search. Like randomly trying things out. Sort 738 00:33:01,049 --> 00:33:03,670 of, but in a structured way. Think about algorithms 739 00:33:03,670 --> 00:33:07,130 like Markov Chain Monte Carlo, MCMC, which sample 740 00:33:07,130 --> 00:33:09,910 hypotheses in proportion to their posterior probability. 741 00:33:10,430 --> 00:33:13,490 Or even simpler heuristics like Wednesday Loose 742 00:33:13,490 --> 00:33:16,329 Switch, WSLS. Wednesday Loose Switch. How does 743 00:33:16,329 --> 00:33:18,490 that work in development? Imagine a child trying 744 00:33:18,490 --> 00:33:20,930 to figure out which button on a toy makes a light 745 00:33:20,930 --> 00:33:23,559 flash. They might try the red button, their current 746 00:33:23,559 --> 00:33:27,039 hypothesis. If the light flashes, win. They stick 747 00:33:27,039 --> 00:33:29,579 with that hypothesis, stay. If they press red 748 00:33:29,579 --> 00:33:31,579 and nothing happens, lose. They're likely to 749 00:33:31,579 --> 00:33:33,619 randomly try something else, switch. Maybe the 750 00:33:33,619 --> 00:33:36,079 blue button, maybe shaking the toy. Ah, so it's 751 00:33:36,079 --> 00:33:38,059 a simple rule for exploring different hypotheses 752 00:33:38,059 --> 00:33:42,250 based on immediate feedback. Yes. And crucially, 753 00:33:42,349 --> 00:33:44,970 because of the random switch step, two children 754 00:33:44,970 --> 00:33:47,309 seeing the exact same evidence might temporarily 755 00:33:47,309 --> 00:33:50,349 explore different hypotheses or jump to different 756 00:33:50,349 --> 00:33:53,029 conclusions. It captures some of the trial and 757 00:33:53,029 --> 00:33:55,390 error feel and the variability we see in children's 758 00:33:55,390 --> 00:33:58,029 reasoning as they revise their beliefs. It's 759 00:33:58,029 --> 00:34:00,150 not always a perfectly smooth update. Sometimes 760 00:34:00,150 --> 00:34:02,650 they just try something new. So the big picture 761 00:34:02,650 --> 00:34:04,829 of development is maybe starting with core knowledge 762 00:34:04,829 --> 00:34:07,680 priors. using these stochastic search processes 763 00:34:07,680 --> 00:34:10,320 to explore, and gradually building up more complex 764 00:34:10,320 --> 00:34:13,480 hierarchical models, HPMs, as the data accumulates 765 00:34:13,480 --> 00:34:15,679 and demands better, more abstract explanations. 766 00:34:16,079 --> 00:34:18,059 That's a really good summary. Development is 767 00:34:18,059 --> 00:34:20,539 seen as this interplay between innate structure, 768 00:34:20,800 --> 00:34:24,139 statistical learning, and noisy exploratory hypothesis 769 00:34:24,139 --> 00:34:27,380 testing, eventually converging on richer, more 770 00:34:27,380 --> 00:34:30,199 abstract, and more predictably powerful intuitive 771 00:34:30,199 --> 00:34:32,440 theories. Okay, we've built up this impressive 772 00:34:32,440 --> 00:34:35,179 picture of the mind as a Bayesian engine, using 773 00:34:35,179 --> 00:34:37,920 priors, likelihoods, graphical models, HBMs. 774 00:34:37,940 --> 00:34:41,719 But let's face reality. Calculating exact Bayesian 775 00:34:41,719 --> 00:34:43,980 probabilities for complex real -world problems 776 00:34:43,980 --> 00:34:46,420 is often computationally intractable, right? 777 00:34:46,559 --> 00:34:49,199 Chapter 11 talks about approximation. Absolutely 778 00:34:49,199 --> 00:34:52,519 critical point. Exact Bayesian inference is often 779 00:34:52,519 --> 00:34:55,900 NP -hard. The brain, whatever it's doing, can't 780 00:34:55,900 --> 00:34:58,280 possibly be performing exact calculations for 781 00:34:58,280 --> 00:35:00,699 everything. So we need approximation algorithms. 782 00:35:01,139 --> 00:35:02,900 Like Monte Carlo methods where you draw samples. 783 00:35:03,429 --> 00:35:06,590 Or variational inference. Yes. Those are standard 784 00:35:06,590 --> 00:35:08,630 techniques in machine learning to approximate 785 00:35:08,630 --> 00:35:10,829 Bayesian inference when the exact calculation 786 00:35:10,829 --> 00:35:13,909 is too hard. But here's the really cool cognitive 787 00:35:13,909 --> 00:35:17,250 twist. The book argues these approximation methods 788 00:35:17,250 --> 00:35:20,050 aren't just engineering hacks. They might actually 789 00:35:20,050 --> 00:35:22,730 be good rational process models of how human 790 00:35:22,730 --> 00:35:25,449 cognition works, including its limitations and 791 00:35:25,449 --> 00:35:27,949 biases. So the way these algorithms cut corners 792 00:35:27,949 --> 00:35:30,469 might actually explain some quirks of human thinking. 793 00:35:30,730 --> 00:35:33,380 That's the proposal. Take particle filters, for 794 00:35:33,380 --> 00:35:35,679 example. They're a type of sequential Monte Carlo 795 00:35:35,679 --> 00:35:38,139 method often used for tracking changing states 796 00:35:38,139 --> 00:35:40,860 over time. They work by maintaining a set of 797 00:35:40,860 --> 00:35:43,260 particles, each representing a hypothesis about 798 00:35:43,260 --> 00:35:45,639 the current state. But crucially, you can only 799 00:35:45,639 --> 00:35:48,980 maintain a finite, often small number of particles 800 00:35:48,980 --> 00:35:51,840 due to computational limits, like our limited 801 00:35:51,840 --> 00:35:54,960 working memory or attention. When new data comes 802 00:35:54,960 --> 00:35:57,539 in, you update the probabilities of your particles, 803 00:35:57,659 --> 00:36:00,429 and then you have to resample. You preferentially 804 00:36:00,429 --> 00:36:02,670 replicate the high probability particles and 805 00:36:02,670 --> 00:36:05,190 discard the low probability ones. What does that 806 00:36:05,190 --> 00:36:07,429 limitation, the finite number of particles, lead 807 00:36:07,429 --> 00:36:10,050 to? It naturally leads to effects like primacy 808 00:36:10,050 --> 00:36:13,590 and recency and learning and memory tasks. The 809 00:36:13,590 --> 00:36:15,730 particles that got established early on, primacy, 810 00:36:15,789 --> 00:36:18,369 might persist longer than they should. And the 811 00:36:18,369 --> 00:36:21,329 most recent updates, recency, get disproportionate 812 00:36:21,329 --> 00:36:23,409 weight because they've just been resampled. Wow. 813 00:36:23,909 --> 00:36:26,210 So these classic memory biases, which some might 814 00:36:26,210 --> 00:36:28,590 see as flaws, could actually be signatures of 815 00:36:28,590 --> 00:36:30,650 the brain using a resource -limited approximation 816 00:36:30,650 --> 00:36:33,429 algorithm, like a particle filter, to try and 817 00:36:33,429 --> 00:36:37,010 perform Bayesian inference. Exactly. The error 818 00:36:37,010 --> 00:36:40,070 is actually evidence for a specific type of rational 819 00:36:40,070 --> 00:36:42,809 approximation strategy. The approximation itself 820 00:36:42,809 --> 00:36:45,230 becomes part of the cognitive model. That's a 821 00:36:45,230 --> 00:36:48,690 powerful idea. Now, Chapter 12 tackles the other 822 00:36:48,690 --> 00:36:52,880 giant in the room. Neural networks. How does 823 00:36:52,880 --> 00:36:56,840 this Bayesian view connect with modern deep learning? 824 00:36:57,079 --> 00:36:59,579 Are they fundamentally different paradigms? It's 825 00:36:59,579 --> 00:37:02,019 a fascinating relationship and the book argues 826 00:37:02,019 --> 00:37:04,639 there are deep connections, maybe deeper than 827 00:37:04,639 --> 00:37:08,119 often assumed. On a basic level, some simple 828 00:37:08,119 --> 00:37:10,880 neural networks are actually mathematically equivalent 829 00:37:10,880 --> 00:37:14,199 to certain simple Bayesian models. Really? Like 830 00:37:14,199 --> 00:37:16,860 what? For instance, logistic regression, a common 831 00:37:16,860 --> 00:37:19,099 building block in neural nets, can be shown to 832 00:37:19,099 --> 00:37:22,000 be equivalent to a naive Bayes classifier under 833 00:37:22,000 --> 00:37:24,500 certain assumptions. So neural nets can implement 834 00:37:24,500 --> 00:37:26,920 Bayesian computations. Okay, for simple cases, 835 00:37:27,099 --> 00:37:29,440 what about the big, complex, deep learning models 836 00:37:29,440 --> 00:37:32,119 and how they're trained? Even there, the connections 837 00:37:32,119 --> 00:37:34,880 emerge. The way we train neural networks often 838 00:37:34,880 --> 00:37:37,199 implicitly corresponds to making Bayesian assumptions. 839 00:37:37,900 --> 00:37:39,659 Think about standard training techniques like 840 00:37:39,659 --> 00:37:42,179 weight decay or L2 regularization. Yeah, where 841 00:37:42,179 --> 00:37:44,079 you penalize large weights in the network to 842 00:37:44,079 --> 00:37:46,519 prevent overfitting. Well, it turns out that 843 00:37:46,519 --> 00:37:48,619 adding a weight decay term during training is 844 00:37:48,619 --> 00:37:51,000 mathematically identical to performing maximum 845 00:37:51,000 --> 00:37:55,219 A posteriori. MAP inference on the weights, assuming 846 00:37:55,219 --> 00:37:57,900 a Gaussian prior centered at zero for those weights. 847 00:37:58,079 --> 00:38:00,960 Whoa! So telling the network don't let your weights 848 00:38:00,960 --> 00:38:03,980 get too big is the same as telling a Bayesian 849 00:38:03,980 --> 00:38:06,960 model assume, a priori, that the weights are 850 00:38:06,960 --> 00:38:10,619 probably small, close to zero. Precisely. The 851 00:38:10,619 --> 00:38:13,639 regularization acts as a prior, biasing the learning 852 00:38:13,639 --> 00:38:16,860 towards simpler solutions. It suggests that even 853 00:38:16,860 --> 00:38:19,320 in these massive data -driven systems, principles 854 00:38:19,320 --> 00:38:22,019 of Bayesian inference, like imposing priors to 855 00:38:22,019 --> 00:38:25,019 control complexity, are still operating, even 856 00:38:25,019 --> 00:38:26,820 if they're implemented through engineering choices 857 00:38:26,820 --> 00:38:29,380 rather than explicit probabilistic modeling. 858 00:38:29,719 --> 00:38:32,099 So maybe the divide isn't as sharp as it seems. 859 00:38:32,239 --> 00:38:34,360 Neural nets might be discovering or implementing 860 00:38:34,360 --> 00:38:37,070 Bayesian principles in their own way. That's 861 00:38:37,070 --> 00:38:38,949 one perspective. The relationship is complex 862 00:38:38,949 --> 00:38:41,110 and still being actively researched, but the 863 00:38:41,110 --> 00:38:42,909 idea that they are complementary rather than 864 00:38:42,909 --> 00:38:45,570 competing frameworks is gaining traction. This 865 00:38:45,570 --> 00:38:48,090 leads us to maybe the most encompassing idea 866 00:38:48,090 --> 00:38:51,510 in the later parts of the book. Resource rationality, 867 00:38:51,550 --> 00:38:54,550 chapter 13. This feels like it ties together 868 00:38:54,550 --> 00:38:58,050 the optimality of Bayes with the reality of limitations. 869 00:38:58,650 --> 00:39:00,869 It does. It's an extension of the rational analysis 870 00:39:00,869 --> 00:39:02,789 approach we mentioned earlier. Instead of just 871 00:39:02,789 --> 00:39:05,369 asking, what's the optimal behavior to maximize 872 00:39:05,369 --> 00:39:08,860 utility? Resource rationality asks, what's the 873 00:39:08,860 --> 00:39:11,739 optimal behavior to maximize utility minus the 874 00:39:11,739 --> 00:39:14,179 cost of the computation needed to figure out 875 00:39:14,179 --> 00:39:16,460 that behavior? So thinking itself has a cost 876 00:39:16,460 --> 00:39:20,039 time, mental effort, and a truly rational agent 877 00:39:20,039 --> 00:39:23,699 has to factor that cost into its decisions. Exactly. 878 00:39:23,699 --> 00:39:26,179 You have to rationally decide how much to think. 879 00:39:26,559 --> 00:39:29,400 This provides a powerful explanation for many 880 00:39:29,400 --> 00:39:31,679 cognitive biases that look irrational from a 881 00:39:31,679 --> 00:39:34,440 purely classical perspective. Take the anchoring 882 00:39:34,440 --> 00:39:36,219 and adjustment heuristic. Right, where you start 883 00:39:36,219 --> 00:39:38,739 with some initial number, the anchor, and then 884 00:39:38,739 --> 00:39:40,659 adjust away from it, but often you don't adjust 885 00:39:40,659 --> 00:39:42,760 enough so your final estimate is biased towards 886 00:39:42,760 --> 00:39:44,880 the anchor. Classically, stopping adjustment 887 00:39:44,880 --> 00:39:47,900 too early is an error, but why might a resource 888 00:39:47,900 --> 00:39:51,179 -rational agent do it? Hmm. Maybe the first bits 889 00:39:51,179 --> 00:39:53,460 of adjustment give you big improvements in accuracy, 890 00:39:53,679 --> 00:39:56,500 but further adjustments... yields smaller and 891 00:39:56,500 --> 00:39:59,599 smaller gains. Precisely. The potential improvement 892 00:39:59,599 --> 00:40:02,400 in your answer diminishes, maybe geometrically, 893 00:40:02,539 --> 00:40:05,780 with each extra step of mental effort. But the 894 00:40:05,780 --> 00:40:08,860 cost of that effort, time, cognitive load, might 895 00:40:08,860 --> 00:40:11,400 remain constant. At some point, the marginal 896 00:40:11,400 --> 00:40:13,860 benefit of one more adjustment step is no longer 897 00:40:13,860 --> 00:40:16,519 worth the marginal cost. So the resource rational 898 00:40:16,519 --> 00:40:19,630 agent rationally stops adjusting early. Accepting 899 00:40:19,630 --> 00:40:21,889 a slightly biased answer because further refinement 900 00:40:21,889 --> 00:40:24,889 would cost more in thinking time than it's worth 901 00:40:24,889 --> 00:40:27,250 in improved accuracy. That's the core idea. The 902 00:40:27,250 --> 00:40:29,809 bias isn't a bug. It's an optimal adaptation 903 00:40:29,809 --> 00:40:32,510 to cognitive limitations. It's the best you can 904 00:40:32,510 --> 00:40:35,230 do given finite resources. That really reframes 905 00:40:35,230 --> 00:40:37,690 how we think about cognitive biases, not as failures 906 00:40:37,690 --> 00:40:40,389 of rationality, but as potentially optimal solutions 907 00:40:40,389 --> 00:40:43,030 under computational constraints. It does. And 908 00:40:43,030 --> 00:40:44,829 it brings the whole Bayesian program into closer 909 00:40:44,829 --> 00:40:47,590 contact with psychological reality. The overall 910 00:40:47,590 --> 00:40:57,360 picture is... So wrapping this all up, after 911 00:40:57,360 --> 00:41:00,199 this deep dive into Bayesian models of cognition, 912 00:41:00,599 --> 00:41:02,739 what's the big takeaway? What does it all mean, 913 00:41:02,820 --> 00:41:04,760 especially looking forward? I think the biggest 914 00:41:04,760 --> 00:41:06,739 takeaway is that the Bayesian framework offers 915 00:41:06,739 --> 00:41:09,869 this incredibly rich... precise and unifying 916 00:41:09,869 --> 00:41:12,469 language for talking about the mind. It connects 917 00:41:12,469 --> 00:41:15,349 perception, learning, reasoning, language, social 918 00:41:15,349 --> 00:41:17,989 cognition, all these different areas back to 919 00:41:17,989 --> 00:41:19,829 fundamental principles of how an intelligent 920 00:41:19,829 --> 00:41:21,969 system should handle uncertainty and structure. 921 00:41:22,170 --> 00:41:24,949 It links knowledge representations, statistical 922 00:41:24,949 --> 00:41:27,769 learning, and rational action in a way no other 923 00:41:27,769 --> 00:41:30,030 framework really has. But where does that leave 924 00:41:30,030 --> 00:41:32,989 us with the current AI landscape? Will giant 925 00:41:32,989 --> 00:41:35,610 models like LLMs just figure all this out on 926 00:41:35,610 --> 00:41:37,469 their own by scaling up? Or is there something 927 00:41:37,469 --> 00:41:39,510 fundamental missing? That's the million dollar 928 00:41:39,510 --> 00:41:41,710 question, isn't it? Will these massive networks 929 00:41:41,710 --> 00:41:44,030 simultaneously learn the kind of compositional, 930 00:41:44,170 --> 00:41:47,349 causal, structured representations that seem 931 00:41:47,349 --> 00:41:50,090 core to human thought and that the Bayesian framework 932 00:41:50,090 --> 00:41:53,550 models so naturally? Or will we find that building 933 00:41:53,550 --> 00:41:56,769 truly human -like AI, flexible, data efficient, 934 00:41:57,070 --> 00:41:59,949 capable of deep understanding requires explicitly 935 00:41:59,949 --> 00:42:02,630 incorporating the principles of Bayesian inference, 936 00:42:02,929 --> 00:42:05,630 hierarchical structure, intuitive theories, and 937 00:42:05,630 --> 00:42:07,909 maybe even resource rationality into their design? 938 00:42:08,170 --> 00:42:11,309 A fundamental tension. Emergent structure versus 939 00:42:11,309 --> 00:42:14,210 engineered structure guided by cognitive principles. 940 00:42:14,449 --> 00:42:17,190 Exactly. It's likely the future lies in some 941 00:42:17,190 --> 00:42:19,309 synthesis, but the principles laid out in this 942 00:42:19,309 --> 00:42:21,809 Bayesian approach to cognition seem like essential 943 00:42:21,809 --> 00:42:24,130 guideposts for understanding what human intelligence 944 00:42:24,130 --> 00:42:26,469 is and how we might eventually replicate it. 945 00:42:26,570 --> 00:42:28,530 That's a really provocative thought to end on. 946 00:42:28,590 --> 00:42:30,949 For listeners who are captivated by these ideas 947 00:42:30,949 --> 00:42:33,130 and want to dig deeper into the sources, what 948 00:42:33,130 --> 00:42:35,380 would you recommend? Well, besides the main book 949 00:42:35,380 --> 00:42:37,139 we've been discussing, going back to some of 950 00:42:37,139 --> 00:42:39,539 the foundational work is always valuable. John 951 00:42:39,539 --> 00:42:41,619 Anderson's writings on rational analysis are 952 00:42:41,619 --> 00:42:44,860 key. Judea Pearl's work, especially Causality, 953 00:42:45,059 --> 00:42:48,460 is fundamental for graphical models. And of course, 954 00:42:48,480 --> 00:42:50,699 exploring the primary research papers by the 955 00:42:50,699 --> 00:42:53,059 authors of Bayesian models of cognition themselves, 956 00:42:53,159 --> 00:42:56,639 people like Josh Tenenbaum, Tom Griffiths, Charles 957 00:42:56,639 --> 00:42:59,840 Kemp, Noah Goodman, on topics like hierarchical 958 00:42:59,840 --> 00:43:02,280 Bayesian models, the probabilistic language of 959 00:43:02,280 --> 00:43:05,039 thought. and intuitive theories would be incredibly 960 00:43:05,039 --> 00:43:07,719 rewarding. Excellent suggestions. It really feels 961 00:43:07,719 --> 00:43:10,239 like understanding the mind requires grappling 962 00:43:10,239 --> 00:43:12,780 with these ideas about probability, structure, 963 00:43:13,059 --> 00:43:15,579 and rational inference in an uncertain world. 964 00:43:15,719 --> 00:43:17,739 It certainly seems that way. It's a challenging 965 00:43:17,739 --> 00:43:19,260 but incredibly exciting frontier.