WEBVTT 00:00:00.000 --> 00:00:02.620 You know when you're prepping for a major exam, 00:00:02.799 --> 00:00:05.080 right? Yeah. And instead of actually learning 00:00:05.080 --> 00:00:06.919 the material, you just... You just completely 00:00:06.919 --> 00:00:09.160 memorize the practice test. Yes, exactly. You 00:00:09.160 --> 00:00:10.699 just memorize... You sit down and you know the 00:00:10.699 --> 00:00:13.779 answer to question four is C, but you don't actually 00:00:13.779 --> 00:00:17.600 know, you know, why it's C. Right. And then the 00:00:17.600 --> 00:00:19.899 professor tweaks the real exam questions just 00:00:19.899 --> 00:00:22.480 a tiny bit and you completely bomb it. You just 00:00:22.480 --> 00:00:25.589 score zero. Because you didn't learn the underlying 00:00:25.589 --> 00:00:27.710 subject. I mean, you learned a highly specific 00:00:27.710 --> 00:00:31.010 set of past conditions that are, well, they're 00:00:31.010 --> 00:00:33.710 never going to repeat exactly the same way. Welcome 00:00:33.710 --> 00:00:35.590 to the deep dive. I'm so glad you're joining 00:00:35.590 --> 00:00:38.329 us. Today we're looking at a fundamental flaw 00:00:38.329 --> 00:00:40.890 in artificial intelligence and statistical modeling 00:00:40.890 --> 00:00:44.250 called overfitting. It's a really pervasive issue. 00:00:44.369 --> 00:00:47.090 It really is. We're pulling from some comprehensive 00:00:47.090 --> 00:00:50.289 source breakdowns of why AI sometimes fails, 00:00:50.689 --> 00:00:53.289 precisely because it tries to be Like, too perfect. 00:00:53.810 --> 00:00:55.429 Our mission today is to figure out how these 00:00:55.429 --> 00:00:58.369 complex models break down and how engineers actually 00:00:58.369 --> 00:01:01.350 find the sweet spot of learning. Right. And if 00:01:01.350 --> 00:01:05.489 you can, just picture a massive complex star 00:01:05.489 --> 00:01:08.629 chart of data clusters. In a world of absolute 00:01:08.629 --> 00:01:11.409 information overload, the hardest part of predicting 00:01:11.409 --> 00:01:13.989 the future isn't gathering the data. Yeah, we 00:01:13.989 --> 00:01:15.890 have plenty of the data. Exactly. The hardest 00:01:15.890 --> 00:01:18.590 part is figuring out which data to ignore. OK, 00:01:18.590 --> 00:01:21.739 let's unpack this. The core irony here is that 00:01:21.739 --> 00:01:24.180 building a highly complex model that perfectly 00:01:24.180 --> 00:01:27.060 memorizes its training data almost guarantees 00:01:27.060 --> 00:01:29.180 it will fail in the real world. It's totally 00:01:29.180 --> 00:01:31.959 counterintuitive. It is. And to understand how 00:01:31.959 --> 00:01:34.319 these models break down, we really have to look 00:01:34.319 --> 00:01:36.420 at the difference between extracting a meaningful 00:01:36.420 --> 00:01:39.099 trend and just blindly memorizing a textbook. 00:01:39.519 --> 00:01:41.659 Right. The foundational definition of overfitting, 00:01:41.879 --> 00:01:44.379 at least from our source text, is a situation 00:01:44.379 --> 00:01:46.640 where a mathematical model contains more parameters 00:01:46.640 --> 00:01:49.459 than can be justified by the data. And the essence 00:01:49.459 --> 00:01:53.400 of the problem is when a model unknowingly extracts 00:01:53.400 --> 00:01:56.400 residual variation, as if that variation represents 00:01:56.400 --> 00:01:59.400 the real underlying model structure. Let's pause 00:01:59.400 --> 00:02:01.620 there. Residual variation. What does that actually 00:02:01.620 --> 00:02:04.560 look like in practice? It's the noise. It is 00:02:04.560 --> 00:02:08.360 the random fluctuations, the totally irrelevant 00:02:08.360 --> 00:02:10.840 details that just happen to be present in the 00:02:10.840 --> 00:02:13.250 specific data set you're analyzing. OK, I want 00:02:13.250 --> 00:02:16.629 to bring up a brilliant, relatable analogy for 00:02:16.629 --> 00:02:19.810 this from the source material involving a database 00:02:19.810 --> 00:02:22.069 of retail purchases. Oh, this is a great one. 00:02:22.210 --> 00:02:25.689 Right. So imagine a data set that tracks the 00:02:25.689 --> 00:02:28.729 item bought, who bought it, and the exact date 00:02:28.729 --> 00:02:31.030 and time of the purchase. Got it. If you want 00:02:31.030 --> 00:02:33.419 to predict what someone will buy next. It is 00:02:33.419 --> 00:02:35.580 incredibly easy to construct a model that fits 00:02:35.580 --> 00:02:37.699 your training set perfectly. You just use the 00:02:37.699 --> 00:02:39.500 exact date and time to predict the purchase. 00:02:39.620 --> 00:02:42.439 Because it's a unique identifier. Exactly. The 00:02:42.439 --> 00:02:44.860 model says, oh, John bought sneakers on Tuesday, 00:02:44.900 --> 00:02:49.060 October 12th at exactly 2 .04 p .m. The model 00:02:49.060 --> 00:02:52.460 perfectly maps that past event, but as a predictive 00:02:52.460 --> 00:02:54.819 tool for the future. It's entirely useless. Completely 00:02:54.819 --> 00:02:57.439 useless. Because that specific time stamp Tuesday 00:02:57.439 --> 00:03:00.680 at 2 .04 p .m. on that specific date, it's never 00:03:00.680 --> 00:03:02.849 going to exist again. The algorithm learned the 00:03:02.849 --> 00:03:05.710 noise, not the signal. What's fascinating here 00:03:05.710 --> 00:03:08.189 is the mathematical tipping point of this problem. 00:03:08.810 --> 00:03:11.310 If the number of parameters, meaning the variables 00:03:11.310 --> 00:03:14.629 your model's tracking, is the same as or greater 00:03:14.629 --> 00:03:17.889 than the number of observations you have, your 00:03:17.889 --> 00:03:19.770 model doesn't even have to look for a trend. 00:03:19.949 --> 00:03:22.689 It can perfectly predict the training data simply 00:03:22.689 --> 00:03:25.909 by memorizing it in its entirety. Wow. So it's 00:03:25.909 --> 00:03:28.530 like having a puzzle where every single piece 00:03:28.530 --> 00:03:33.080 is cut. to fit only one incredibly specific microscopic 00:03:33.080 --> 00:03:36.080 groove instead of forming an actual picture. 00:03:36.259 --> 00:03:38.180 That's a really good way to visualize it. And 00:03:38.180 --> 00:03:40.199 the terminology used to describe this in machine 00:03:40.199 --> 00:03:42.560 learning paints a really clear picture. Which 00:03:42.560 --> 00:03:45.060 is what, exactly? A learning algorithm is said 00:03:45.060 --> 00:03:48.120 to overfit if it is highly accurate in hindsight. 00:03:48.280 --> 00:03:50.219 Meaning it perfectly fits the known training 00:03:50.219 --> 00:03:53.979 data. Right. But it's less accurate in foresight 00:03:53.979 --> 00:03:57.659 when it actually has to predict new unseen data. 00:03:57.819 --> 00:04:00.400 It's just a fundamental failure of generalization. 00:04:00.539 --> 00:04:02.740 That makes so much sense. And for you listening, 00:04:03.060 --> 00:04:06.020 think about your own learning processes. When 00:04:06.020 --> 00:04:08.439 you are confronted with a massive new subject, 00:04:08.900 --> 00:04:11.780 are you memorizing disconnected facts or are 00:04:11.780 --> 00:04:13.759 you looking for the underlying rules that let 00:04:13.759 --> 00:04:16.040 you solve problems you've never even seen before? 00:04:16.839 --> 00:04:20.300 That is the big question. So, okay, if looking 00:04:20.300 --> 00:04:23.100 too closely at the data creates a fragile model, 00:04:23.560 --> 00:04:26.730 the obvious temptation is to just like... Just 00:04:26.730 --> 00:04:29.290 simplify it. Yeah. Draw a straight line, ignore 00:04:29.290 --> 00:04:31.069 the nuance, and keep everything as simple as 00:04:31.069 --> 00:04:33.410 possible. But that comes with its own trap, doesn't 00:04:33.410 --> 00:04:35.350 it? Oh, absolutely. That leads straight into 00:04:35.350 --> 00:04:37.230 the opposite extreme, which is underfitting. 00:04:37.329 --> 00:04:40.490 Underfitting. Yeah. This occurs when a statistical 00:04:40.490 --> 00:04:42.769 model or a machine learning algorithm is simply 00:04:42.769 --> 00:04:45.410 too rigid to capture the underlying structure 00:04:45.410 --> 00:04:48.360 of the data. Imagine your data points actually 00:04:48.360 --> 00:04:51.279 form a geometric curve, like specifically a parabola. 00:04:51.319 --> 00:04:53.720 Right, a U -shape. Exactly. And we try to fit 00:04:53.720 --> 00:04:56.579 a straight linear model to that core. A straight 00:04:56.579 --> 00:04:58.959 line can never fit a parabola. It can't. The 00:04:58.959 --> 00:05:01.660 model is missing the necessary parameters or 00:05:01.660 --> 00:05:04.439 the mathematical terms that would appear in a 00:05:04.439 --> 00:05:07.139 correctly specified model. It is fundamentally 00:05:07.139 --> 00:05:09.740 incapable of understanding the underlying structure 00:05:09.740 --> 00:05:13.699 because it's too simplistic. OK, so underfitting 00:05:13.899 --> 00:05:17.319 is being too stubborn to see the nuance, and 00:05:17.319 --> 00:05:19.420 overfitting is being so obsessed with the nuance 00:05:19.420 --> 00:05:22.160 that you completely lose the plot. That is exactly 00:05:22.160 --> 00:05:25.540 it. And finding that balance brings us to a foundational 00:05:25.540 --> 00:05:28.759 concept in statistical learning, the bias -variance 00:05:28.759 --> 00:05:30.620 tradeoff. The bias -variance tradeoff, okay. 00:05:30.639 --> 00:05:33.199 Yeah, this is how experts analyze a model for 00:05:33.199 --> 00:05:35.660 different types of error, and understanding the 00:05:35.660 --> 00:05:37.740 mechanics of it is just crucial for anyone looking 00:05:37.740 --> 00:05:40.660 at data. So let's break down both terms. Sure. 00:05:40.939 --> 00:05:43.319 When a model is underfitting, like our straight 00:05:43.319 --> 00:05:46.279 line trying to measure a curve, it has high bias 00:05:46.279 --> 00:05:49.279 and low variance. Let's define what we mean by 00:05:49.279 --> 00:05:51.360 bias in a purely mathematical sense here, so 00:05:51.360 --> 00:05:53.839 we don't confuse it with human bias. Good point. 00:05:54.160 --> 00:05:56.639 It has high bias because it is stubbornly biased 00:05:56.639 --> 00:05:59.519 toward its own simplistic assumption. The assumption 00:05:59.519 --> 00:06:01.480 that the data must be a straight line, regardless 00:06:01.480 --> 00:06:03.480 of what the data actually looks like. Okay, got 00:06:03.480 --> 00:06:06.439 it. Yes, and it has low variance because that 00:06:06.439 --> 00:06:08.819 straight line doesn't change or wiggle much from 00:06:08.819 --> 00:06:11.379 sample to sample. If you feed it five different 00:06:11.379 --> 00:06:14.279 datasets, it will keep drawing the same rigid 00:06:14.279 --> 00:06:17.439 straight line. It is consistently, predictably 00:06:17.439 --> 00:06:19.800 wrong. Right. It's very stable, but it's useless. 00:06:20.160 --> 00:06:23.439 Exactly. Now on the flip side, an overfitted 00:06:23.439 --> 00:06:26.699 model has low bias. It drops all assumptions 00:06:26.699 --> 00:06:29.959 and is highly flexible. It's willing to bend 00:06:29.959 --> 00:06:32.810 to every single data point. But it suffers from 00:06:32.810 --> 00:06:35.949 high variance. Yes. Its estimated sampling variances 00:06:35.949 --> 00:06:39.170 become needlessly large. It swings wildly to 00:06:39.170 --> 00:06:41.490 hit every random piece of noise. Which means 00:06:41.490 --> 00:06:43.670 if you give it a slightly different data set, 00:06:43.930 --> 00:06:46.269 the model's shape will change dramatically, right? 00:06:46.370 --> 00:06:48.709 It's far too sensitive. Exactly. So the ultimate 00:06:48.709 --> 00:06:51.269 goal in mathematical modeling isn't just to blindly 00:06:51.269 --> 00:06:53.990 reduce errors on your training data down to zero. 00:06:54.069 --> 00:06:56.029 Right, because that just leads to memorization. 00:06:56.240 --> 00:06:58.959 Correct. The best approximating model is achieved 00:06:58.959 --> 00:07:01.680 by carefully balancing the errors of both underfitting 00:07:01.680 --> 00:07:04.319 and overfitting. You have to find the exact point 00:07:04.319 --> 00:07:06.300 where the model is complex enough to capture 00:07:06.300 --> 00:07:08.959 the real trend, but restrained enough to ignore 00:07:08.959 --> 00:07:11.000 the random wiggles. OK, here's where it gets 00:07:11.000 --> 00:07:13.699 really interesting to me. Finding that balance 00:07:13.699 --> 00:07:16.860 feels less like a strict math problem and more 00:07:16.860 --> 00:07:20.579 like a like a philosophical debate about how 00:07:20.579 --> 00:07:22.740 we view complexity in the universe. It really 00:07:22.740 --> 00:07:25.220 is. So let me push back on this restraint idea. 00:07:25.360 --> 00:07:28.639 We live in an era of supercomputers and massive 00:07:28.639 --> 00:07:31.839 data centers. If we have the computational power, 00:07:32.439 --> 00:07:35.579 why can't we just test thousands of complex variables 00:07:35.579 --> 00:07:38.220 just to be safe? Throw everything at it. Yeah. 00:07:38.459 --> 00:07:40.100 Why not throw everything at the wall and let 00:07:40.100 --> 00:07:42.800 the machine sort out what's a real trend and 00:07:42.800 --> 00:07:45.980 what's a wiggle? Well, because of a deeply held 00:07:45.980 --> 00:07:48.540 philosophical principle that underpins basically 00:07:48.540 --> 00:07:51.579 all of science. the principle of parsimony. Also 00:07:51.579 --> 00:07:54.339 known as Occam's razor. Exactly. In the context 00:07:54.339 --> 00:07:57.100 of mathematical modeling, Occam's razor implies 00:07:57.100 --> 00:08:00.540 that any given complex function is a priori less 00:08:00.540 --> 00:08:02.779 probable than any given simple function. Less 00:08:02.779 --> 00:08:05.220 probable just by its very nature of being complicated. 00:08:05.439 --> 00:08:07.579 Right. If you replace a simple linear function 00:08:07.579 --> 00:08:10.180 that requires, say, three parameters with a highly 00:08:10.180 --> 00:08:13.279 complex one that has dozens, you carry a massive 00:08:13.279 --> 00:08:16.379 statistical risk. Unless you get an undeniable 00:08:16.379 --> 00:08:19.759 game in how well it fits the data to offset that 00:08:19.759 --> 00:08:22.899 huge jump in complexity, you are almost certainly 00:08:22.899 --> 00:08:25.420 overfitting. That makes sense. And if you just 00:08:25.420 --> 00:08:28.160 throw thousands of random variables at a machine 00:08:28.160 --> 00:08:31.079 like you suggested, you run head first into a 00:08:31.079 --> 00:08:33.299 mathematical trap called Friedman's paradox. 00:08:33.539 --> 00:08:35.720 Oh, Friedman's paradox. Yeah. Let's unpack the 00:08:35.720 --> 00:08:37.960 mechanics of that. What actually happens inside 00:08:37.960 --> 00:08:40.879 the model when we do that? It's what happens 00:08:40.879 --> 00:08:44.889 when you introduce a huge set of explanatory 00:08:44.889 --> 00:08:47.929 variables that have absolutely no relation to 00:08:47.929 --> 00:08:49.970 the thing you were trying to predict. Like total 00:08:49.970 --> 00:08:52.090 nonsense variables. Right. Let's say you're trying 00:08:52.090 --> 00:08:54.990 to predict the stock market and you feed a model, 00:08:55.309 --> 00:08:57.690 the daily temperature in London, the number of 00:08:57.690 --> 00:09:00.269 letters in his CEO's name, and I don't know, 00:09:00.289 --> 00:09:01.750 the color of the building across the street. 00:09:02.190 --> 00:09:04.429 Okay. Pure mathematical probability dictates 00:09:04.429 --> 00:09:06.970 that some of those random variables will falsely 00:09:06.970 --> 00:09:09.309 appear to be statistically significant just by 00:09:09.309 --> 00:09:11.370 sheer chance. Ah, I see. So if you flip enough 00:09:11.370 --> 00:09:13.730 coins, eventually you'll get heads 10 times in 00:09:13.730 --> 00:09:16.730 a row and a model that doesn't understand context 00:09:16.730 --> 00:09:19.330 will conclude that the coin is rigged or that 00:09:19.330 --> 00:09:23.230 the specific sequence of coin flips is this brilliant 00:09:23.230 --> 00:09:26.129 predictor of the future. It doesn't realize it's 00:09:26.129 --> 00:09:29.190 just random chance over a massive sample size. 00:09:29.710 --> 00:09:32.370 That is the trap. You think you're building a 00:09:32.370 --> 00:09:34.730 smarter model because it found a pattern, but 00:09:34.730 --> 00:09:36.970 you're actually building a more fragile one based 00:09:36.970 --> 00:09:39.649 on an illusion. Wow. The literature on model 00:09:39.649 --> 00:09:42.110 selection captures this danger beautifully with 00:09:42.110 --> 00:09:44.370 a classic thought experiment. It goes like this. 00:09:44.970 --> 00:09:47.850 Given a data set, you can fit thousands of models 00:09:47.850 --> 00:09:50.769 at the push of a button. With so many candidate 00:09:50.769 --> 00:09:53.230 models, overfitting is a real danger. Right. 00:09:53.409 --> 00:09:56.629 And then it asks, Is the monkey who typed Hamlet 00:09:56.629 --> 00:09:59.909 actually a good writer? Ah. The classic infinite 00:09:59.909 --> 00:10:02.289 monkeys on infinite typewriters. Yes. If one 00:10:02.289 --> 00:10:04.210 of them randomly types out a Shakespeare play, 00:10:04.490 --> 00:10:06.009 you don't hire the monkey as a screenwriter. 00:10:06.070 --> 00:10:07.830 Definitely not. It didn't learn how to write. 00:10:07.889 --> 00:10:09.990 It just generated a random output that happened 00:10:09.990 --> 00:10:12.529 to match a known pattern perfectly. It's the 00:10:12.529 --> 00:10:16.389 ultimate confusion of random chance with genuine 00:10:16.389 --> 00:10:20.070 underlying structure. OK. But as much as we are 00:10:20.070 --> 00:10:22.809 talking about typing monkeys in geometry, getting 00:10:22.809 --> 00:10:26.200 the fit wrong has massive tangible consequences 00:10:26.200 --> 00:10:28.639 in the real world. Whoa, absolutely. Let's look 00:10:28.639 --> 00:10:31.000 at the practical headaches engineers deal with 00:10:31.000 --> 00:10:34.399 when a model overfits. Our source points out 00:10:34.399 --> 00:10:38.759 a major issue. Overfitted models are significantly 00:10:38.759 --> 00:10:42.159 less portable. Yes, that's a big one. Think about 00:10:42.159 --> 00:10:45.820 the practical headache here. A simple one -variable 00:10:45.820 --> 00:10:48.879 linear regression is so portable you could literally 00:10:48.879 --> 00:10:51.240 do the math by hand on a napkin. Right, anyone 00:10:51.240 --> 00:10:54.120 can use it anywhere. But an overfitted model 00:10:54.120 --> 00:10:56.980 becomes hopelessly tied to its original environment. 00:10:57.159 --> 00:11:00.240 It's too needy. Exactly. It becomes so complex 00:11:00.240 --> 00:11:03.139 that the only way to reproduce it is to exactly 00:11:03.139 --> 00:11:05.799 duplicate the original modeler's entire setup. 00:11:06.039 --> 00:11:08.659 It makes scientific reproduction incredibly difficult. 00:11:09.080 --> 00:11:11.639 It also demands too much unnecessary information. 00:11:12.080 --> 00:11:14.000 Like, if your model is hopelessly complex, you 00:11:14.000 --> 00:11:16.799 have to feed it all these useless variables every 00:11:16.799 --> 00:11:18.379 single time you run it. Which takes time and 00:11:18.379 --> 00:11:21.230 money. Right. Gathering this unneeded data is 00:11:21.230 --> 00:11:23.269 expensive and it's error prone, especially if 00:11:23.269 --> 00:11:25.070 humans have to gather the information manually 00:11:25.070 --> 00:11:28.210 and enter the data into the system. But the stakes 00:11:28.210 --> 00:11:30.769 get even higher when we look at the intersection 00:11:30.769 --> 00:11:33.629 of machine learning, privacy, and law. Oh man, 00:11:33.909 --> 00:11:36.129 yeah. Remember the core mechanism we discussed 00:11:36.129 --> 00:11:39.990 earlier? An overfitted model essentially memorizes 00:11:39.990 --> 00:11:43.289 its training set. Like memorizing the exact timestamp 00:11:43.289 --> 00:11:45.669 of the retail purchase instead of the purchasing 00:11:45.669 --> 00:11:48.070 trend. Right. And because of that memorization, 00:11:48.389 --> 00:11:51.549 it may actually be possible to reconstruct details 00:11:51.549 --> 00:11:54.509 of individual training instances directly from 00:11:54.509 --> 00:11:56.649 the machine learning model. Wait, really? It 00:11:56.649 --> 00:11:59.250 could just spit the data back out. Yes. If that 00:11:59.250 --> 00:12:01.750 training data includes sensitive, personally 00:12:01.750 --> 00:12:05.269 identifiable information PII, you have a major 00:12:05.269 --> 00:12:08.059 privacy leak on your hands. That's terrifying. 00:12:08.559 --> 00:12:10.779 The model could spit out someone's private data 00:12:10.779 --> 00:12:13.919 because it mistakenly coded that specific private 00:12:13.919 --> 00:12:16.240 data point as a necessary rule for predicting 00:12:16.240 --> 00:12:18.950 the future. It's a massive legal liability for 00:12:18.950 --> 00:12:20.830 artificial intelligence right now, especially 00:12:20.830 --> 00:12:23.429 when it comes to copyright. Huge liability. Developers 00:12:23.429 --> 00:12:25.970 of generative deep learning models, specifically 00:12:25.970 --> 00:12:28.769 systems like GitHub Copilot and Stable Diffusion, 00:12:29.429 --> 00:12:31.690 are facing copyright infringement lawsuits over 00:12:31.690 --> 00:12:33.909 this exact thing. Yeah, the core of the argument 00:12:33.909 --> 00:12:36.289 is that their models are so overfitted, they 00:12:36.289 --> 00:12:38.710 are capable of reproducing copyrighted items 00:12:38.710 --> 00:12:41.470 verbatim from their training data. Just regurgitating 00:12:41.470 --> 00:12:44.590 it. Exactly. Generative models that are overfitted 00:12:44.590 --> 00:12:46.950 aren't just learning the abstract style of an 00:12:46.950 --> 00:12:49.330 image or a block of code. They are spitting out 00:12:49.330 --> 00:12:51.809 outputs that are virtually identical to specific 00:12:51.809 --> 00:12:54.870 instances from the training set. There is a very 00:12:54.870 --> 00:12:57.669 striking visual example documented in our source. 00:12:57.970 --> 00:13:00.830 An original photograph of the author Anne Graham 00:13:00.830 --> 00:13:04.289 Lotz was placed alongside an image generated 00:13:04.289 --> 00:13:06.950 by the AI stable diffusion when prompted with 00:13:06.950 --> 00:13:09.389 her name. And what was the result? The generated 00:13:09.389 --> 00:13:12.090 image and the copyrighted photograph were virtually 00:13:12.090 --> 00:13:15.029 identical. Wow. The AI didn't learn what a human 00:13:15.029 --> 00:13:17.570 face looks like and generate a novel one. It 00:13:17.570 --> 00:13:19.669 had memorized her specific photograph during 00:13:19.669 --> 00:13:21.450 its training phase and just spat it back out. 00:13:21.590 --> 00:13:24.409 Which demonstrates exactly how an abstract mathematical 00:13:24.409 --> 00:13:27.250 flaw, failing to penalize complexity, can lead 00:13:27.250 --> 00:13:30.029 straight to a courtroom. It really does. So with 00:13:30.029 --> 00:13:32.629 broken models, privacy leaks, and copyright lawsuits 00:13:32.629 --> 00:13:35.169 on the line, how do engineers actually fix this? 00:13:35.289 --> 00:13:37.149 If I have a broken fit, what is in the toolbox? 00:13:37.639 --> 00:13:40.700 Well, for underfitting, the remedies make intuitive 00:13:40.700 --> 00:13:43.320 sense. Right. You can increase the model's complexity 00:13:43.320 --> 00:13:46.360 or just increase the training data. Exactly. 00:13:46.720 --> 00:13:49.039 There's also ensemble methods, which combine 00:13:49.039 --> 00:13:51.340 multiple models so they can work together to 00:13:51.340 --> 00:13:53.360 capture the pattern. And feature engineering. 00:13:53.419 --> 00:13:56.279 Right. Where you create new relevant features 00:13:56.279 --> 00:13:58.299 from the existing ones. You've got it. But what 00:13:58.299 --> 00:14:00.860 about the overfitting side? What are the remedies 00:14:00.860 --> 00:14:04.120 for a model that has memorized too much? That's 00:14:04.120 --> 00:14:06.580 what I want to know. There are a variety of techniques 00:14:06.580 --> 00:14:10.519 to test a model's ability to generalize, like 00:14:10.519 --> 00:14:12.539 evaluating it on a validation data set it has 00:14:12.539 --> 00:14:16.399 never seen before. But structurally, there are 00:14:16.399 --> 00:14:18.960 two incredibly interesting mechanisms engineers 00:14:18.960 --> 00:14:22.720 use to force a neural network to stop overfitting, 00:14:23.139 --> 00:14:25.639 dropout and pruning. Ooh, dropout and pruning. 00:14:25.879 --> 00:14:28.860 Let's explore the mechanics of dropout regularization 00:14:28.860 --> 00:14:32.519 first. Sure. It involves the probabilistic random 00:14:32.519 --> 00:14:35.509 removal of inputs to a layer. or the random removal 00:14:35.509 --> 00:14:38.570 of training set data. So you are purposely hiding 00:14:38.570 --> 00:14:40.629 information from the algorithm while it tries 00:14:40.629 --> 00:14:44.330 to learn. Yes, exactly. By forcing the model 00:14:44.330 --> 00:14:47.309 to make predictions while randomly missing pieces 00:14:47.309 --> 00:14:49.830 of information, you prevent it from becoming 00:14:49.830 --> 00:14:53.570 overly reliant on any single highly specific 00:14:53.570 --> 00:14:56.230 data point. That's brilliant. A great way to 00:14:56.230 --> 00:14:59.149 visualize this is to think of a business that 00:14:59.149 --> 00:15:02.370 forces its employees to constantly rotate roles, 00:15:03.350 --> 00:15:05.830 or randomly gives people days off. Oh, I like 00:15:05.830 --> 00:15:08.470 that analogy. Yeah. It forces the whole team, 00:15:08.730 --> 00:15:10.830 which is the neural network, to learn how the 00:15:10.830 --> 00:15:13.230 business actually runs. It prevents the company 00:15:13.230 --> 00:15:16.730 from relying entirely on one star employee or 00:15:16.730 --> 00:15:19.190 one specific heavily weighted node to do all 00:15:19.190 --> 00:15:21.450 the work. So if the star employee is out, the 00:15:21.450 --> 00:15:23.690 system doesn't collapse. Exactly. That analogy 00:15:23.690 --> 00:15:25.909 perfectly highlights the mechanism. It improves 00:15:25.909 --> 00:15:27.990 the robustness of the model because it forces 00:15:27.990 --> 00:15:31.269 the network to find the deeper generalized patterns 00:15:31.269 --> 00:15:34.070 that hold true, even when some of the noise or 00:15:34.070 --> 00:15:35.889 some of the specific nodes are stripped away. 00:15:36.110 --> 00:15:38.600 OK, so that's dropout. What about pruning? Pruning 00:15:38.600 --> 00:15:41.419 is the process of identifying a sparse optimal 00:15:41.419 --> 00:15:43.720 structure within the neural network and essentially 00:15:43.720 --> 00:15:46.240 cutting away the unnecessary parameters. Think 00:15:46.240 --> 00:15:48.649 of it as trimming the dead weight. Right. And 00:15:48.649 --> 00:15:51.629 not only does this mitigate overfitting by enforcing 00:15:51.629 --> 00:15:54.450 Occam's razor and enhancing generalization, but 00:15:54.450 --> 00:15:56.909 it also significantly reduces the computational 00:15:56.909 --> 00:15:59.370 cost of running the model. You get a leaner, 00:15:59.529 --> 00:16:02.610 faster, and more accurate system. Exactly. OK, 00:16:02.629 --> 00:16:04.830 so we've established the rules of the road. Keep 00:16:04.830 --> 00:16:07.610 it simple, penalize complexity, don't let it 00:16:07.610 --> 00:16:10.330 memorize the noise, and randomly drop out data 00:16:10.330 --> 00:16:13.139 to force robustness. Those are the golden rules. 00:16:13.279 --> 00:16:16.240 But there is a massive curveball in modern machine 00:16:16.240 --> 00:16:18.720 learning research mentioned in our source. Is 00:16:18.720 --> 00:16:21.240 there ever a scenario where breaking all of these 00:16:21.240 --> 00:16:23.799 rules actually works? This raises an important 00:16:23.799 --> 00:16:26.460 question, and it introduces a paradox that researchers 00:16:26.460 --> 00:16:30.159 call benign overfitting. Benign overfitting. 00:16:30.279 --> 00:16:33.360 Yeah. It essentially turns the traditional bias 00:16:33.360 --> 00:16:35.480 -variance trade -off we just discussed completely 00:16:35.480 --> 00:16:38.220 on its head. I'm intrigued. The phenomenon describes 00:16:38.220 --> 00:16:40.860 a situation where a statistical model seems to 00:16:40.860 --> 00:16:43.759 generalize perfectly well to unseen data, even 00:16:43.759 --> 00:16:46.340 when it has been fit perfectly to noisy training 00:16:46.340 --> 00:16:49.539 data. Wait, what? How is that logically possible? 00:16:49.840 --> 00:16:52.340 We just spent 10 minutes establishing that Occam's 00:16:52.340 --> 00:16:55.799 razor canalizes complexity and that fitting perfectly 00:16:55.799 --> 00:16:58.620 to noisy data destroys a model's ability to predict 00:16:58.620 --> 00:17:01.120 the future. I know, it sounds impossible. How 00:17:01.120 --> 00:17:03.820 can a model that memorizes noise suddenly become 00:17:03.820 --> 00:17:06.349 functional again? Well, it is a phenomenon of 00:17:06.349 --> 00:17:08.809 particular interest in deep neural networks. 00:17:09.430 --> 00:17:11.630 Theoretical studies show that in this specific 00:17:11.630 --> 00:17:14.609 setting, something called overparameterization 00:17:14.609 --> 00:17:18.289 is actually essential for benign overfitting 00:17:18.289 --> 00:17:22.019 to occur. Overparameterization meaning having 00:17:22.019 --> 00:17:24.680 way too many parameters. Yeah. Far more than 00:17:24.680 --> 00:17:27.799 the data could possibly justify. Yes. The math 00:17:27.799 --> 00:17:30.220 shows that if the number of directions in the 00:17:30.220 --> 00:17:32.160 parameter space that are completely unimportant 00:17:32.160 --> 00:17:34.680 for predictions significantly exceeds your sample 00:17:34.680 --> 00:17:37.700 size, the model can safely absorb all the noise 00:17:37.700 --> 00:17:40.400 into those useless dimensions. Let's unpack what 00:17:40.400 --> 00:17:42.339 a parameter space actually looks like in this 00:17:42.339 --> 00:17:44.799 context. It's almost like having a massive, highly 00:17:44.799 --> 00:17:47.220 porous sponge. A sponge, okay. Yeah, the actual 00:17:47.220 --> 00:17:49.980 structure of the sponge, the core network, absorbs 00:17:49.980 --> 00:17:53.109 the real water. which is the true signal. And 00:17:53.109 --> 00:17:56.910 all the thousands of tiny empty pores, the excess 00:17:56.910 --> 00:18:00.869 parameters, they just trap the dust and the noise 00:18:00.869 --> 00:18:03.029 harmlessly. That is a fantastic way to picture 00:18:03.029 --> 00:18:05.170 it. Because there is so much excess capacity, 00:18:05.630 --> 00:18:08.009 the noise dissipates into those empty dimensions 00:18:08.009 --> 00:18:10.490 without warping the core predictive structure. 00:18:10.609 --> 00:18:13.450 Wow. The model technically memorizes the training 00:18:13.450 --> 00:18:16.109 data, fulfilling the definition of overfitting, 00:18:16.329 --> 00:18:18.730 but the noise doesn't interfere with its ability 00:18:18.730 --> 00:18:21.950 to generalize to new data. The rules of simple 00:18:21.950 --> 00:18:24.009 statistics just stretch and warp when the models 00:18:24.009 --> 00:18:27.539 get massively complex. The noise just... dissipates 00:18:27.539 --> 00:18:30.039 into the void, leaving the true signal intact 00:18:30.039 --> 00:18:32.559 for the actual prediction. It's wild. It is a 00:18:32.559 --> 00:18:34.440 frontier of machine learning that experts are 00:18:34.440 --> 00:18:36.460 still working to fully map out from a theoretical 00:18:36.460 --> 00:18:39.059 perspective, but it shows just how nuanced the 00:18:39.059 --> 00:18:41.339 concept of learning becomes at massive scale. 00:18:41.440 --> 00:18:43.480 So what does this all mean? We started with the 00:18:43.480 --> 00:18:47.079 idea of a practice test and ended up with algorithms 00:18:47.079 --> 00:18:49.900 absorbing noise into infinite dimensions. It's 00:18:49.900 --> 00:18:52.920 been quite a journey. It has. But at its core, 00:18:53.359 --> 00:18:55.319 whether we're talking about a simple statistical 00:18:55.319 --> 00:18:58.529 regression drawn napkin or a massively complex 00:18:58.529 --> 00:19:01.829 machine learning deep neural network, the overarching 00:19:01.829 --> 00:19:04.650 goal remains the same. Absolutely. The best models 00:19:04.650 --> 00:19:07.529 are achieved by balancing the errors of underfitting 00:19:07.529 --> 00:19:10.230 and overfitting. You have to be flexible enough 00:19:10.230 --> 00:19:13.609 to capture the real trend, but skeptical enough 00:19:13.609 --> 00:19:17.049 to ignore the random noise. And, you know, that 00:19:17.049 --> 00:19:19.349 balance isn't just a requirement for machines, 00:19:19.410 --> 00:19:21.269 it's a requirement for human critical thinking 00:19:21.269 --> 00:19:23.509 as well. Which is a perfect takeaway for you 00:19:23.509 --> 00:19:26.190 listening. Being well -informed in a world of 00:19:26.190 --> 00:19:28.750 endless data isn't about memorizing every single 00:19:28.750 --> 00:19:31.490 fact. It's about finding your own signal in the 00:19:31.490 --> 00:19:34.029 noise. Thank you so much for joining us on this 00:19:34.029 --> 00:19:37.009 deep dive. But before we go, there's one final 00:19:37.009 --> 00:19:39.430 provocative concept about robustness that we 00:19:39.430 --> 00:19:41.869 want to leave you with. Oh, yes. We intuitively 00:19:41.869 --> 00:19:44.170 understand that information from all of our past 00:19:44.170 --> 00:19:47.089 experience is divided into two groups. Information 00:19:47.089 --> 00:19:49.589 that is relevant for the future and irrelevant 00:19:49.589 --> 00:19:52.329 noise that we should discard. But the higher 00:19:52.329 --> 00:19:55.150 the uncertainty of a future event, the more noise 00:19:55.150 --> 00:19:57.150 exists in the past that needs to be ignored. 00:19:57.670 --> 00:20:00.769 It leaves us with a profound question. How do 00:20:00.769 --> 00:20:04.130 we, or any machine we build, ever truly know 00:20:04.130 --> 00:20:06.410 which part of our past experience was just random 00:20:06.410 --> 00:20:09.089 noise until the future actually arrives? You 00:20:09.089 --> 00:20:11.349 can't just memorize the past if the future is 00:20:11.349 --> 00:20:13.390 a completely different test. Something to think 00:20:13.390 --> 00:20:15.190 about next time you try to predict what happens 00:20:15.190 --> 00:20:17.670 next. Until then, keep questioning the data.