Massachusetts Institute Of Technology Faculty

"It cannot be a complete coincidence that several outstanding logicians of the twentieth century found shelter in s at some time in their lives: Cantor, , Gödel, Peano, and are some. was one of the saner among them, though in some ways his behavior must be classified as strange, even by mathematicians' standards. He looked like a cross between a and a large owl. He spoke softly in complete paragraphs which seemed to have been read out of a book, evenly and slowly enunciated, as by a . When interrupted, he would pause for an uncomfortably long period to recover the thread of the argument. He never made casual remarks: they did not belong in the baggage of ."

"The more experimental scientists and s are, the more common sense they have, and so on until you get to the mathematicians, who are totally devoid of common sense."

"The spectacular results in the fluctuation theory of sums of independent random variables, obtained in the last 15 years by , , , , , , and others, have gradually led to the realization that the nature of the problem, as well as that of the methods of solution, is algebraic and combinatorial. After Baxter showed that the crux of the problem lay in simplifying a certain operator identity, several algebraic proofs (, , Wendel) followed. It is the present purpose to carry this algebraization to the limit: the result we present amounts to a solution of the for s. The solution is not presented as an algorithm, but by showing that every identity in a Baxter algebra is effectively equivalent to an identity of symmetric functions independent of the number of variables. Remarkably, the identities used so far in the combinatorics of fluctuation theory "translate" by the present method into classical identities of easy verification. The present method is nevertheless also useful for guessing and proving new combinatorial identities: by way of example, it will be shown in the second part of this note how it leads to a generalization of the Bohnenblust-Spitzer formula for the action of arbitrary ."

"It has been observed that whereas s and s are likely to be embarrassed by references to the beauty in their work, mathematicians instead like to engage in discussions of the beauty of mathematics. Professional artists are more likely to stress the technical rather than the aesthetic aspects of their work. Mathematicians, instead, are fond of passing judgment on the beauty of their favored pieces of mathematics. Even a cursory observation shows that the characteristics of mathematical beauty are at variance with those of artistic beauty. For example, courses in “art appreciation” are fairly common; it is however unthinkable to find any “mathematical beauty appreciation” courses taught anywhere. The purpose of the present paper is to try to uncover the sense of the term “beauty” as it is currently used by mathematicians."

"Friends may come and go, but enemies accumulate."

"Integrity is essential. It's the inner voice, the source of self-control, the basis for the trust that is imperative in today's military. It's doing the right thing when nobody's looking."

"If women don't belong in engineering, then engineering, as a profession, is irrelevant to the needs of our society. If engineering doesn't make welcome space for them, then engineering will become marginalized as other fields expand their turf to seek out and make a place for women."

"It's not easy being a pioneer. It's not easy having to prove every day that you belong. It's not easy being invisible or having your ideas credited to someone else."

"Aircraft trailing vortices have little waves that are generated and then break up....If another aircraft intercepts that trailing vortex, someone can be killed, because it’s a swirling flow....People now know that if you land airplanes three minutes apart, that’s going to be safer."

"In cabin sensing is such a hot topic because it allows OEMs to not only meet regulatory and rating requirements that are on the horizon, but also sets them up to differentiate their brands in a very competitive market. Also, car manufacturers can expand on cameras, other sensors and machine learning-based algorithms that are already deployed for DMS. Building on that as a foundation, they can often, cost effectively, add advanced safety features and engaging mobility experiences to existing platforms."

"Our focus should always be on advancing automotive technologies to save lives and I love how interior sensing enables several advanced safety features. One important functionality is child and child seat detection, which helps determine if a child is left behind in a vehicle unattended. I am hopeful that this can help avoid tragic deaths due to vehicular heatstroke. And, as anyone who has driven around with kids or for that matter, pets will know, they often cause distraction, so child and pet detection can provide important inputs to promote safer driving behavior."

"Every step in my career has served a purpose. Of course, each step provided me with a particular level of training. But the steps also bought me time to figure out what I like and what I don’t like professionally and personally. If I had to end with some advice, I would say: Take each of these steps seriously and not to rush ahead to the next one."

"I grew up not having any clue what a Mathematician was… so I looked up and wrote to random Math Professors. It sounds silly, but this actually helped shape my career path. Doing math for a living is a sweet gig, and I am deeply grateful to be a part of the mathematics community."

"I am also very interested in the experience features that in cabin sensing will enable. The Emotion AI technology that we created at Affectiva, now part of Smart Eye, also unlocks massively interesting personalization. By understanding the emotional and cognitive states of people in a vehicle we can adapt the environment to their needs in the moment. For example, if someone is getting drowsy, the lighting dims, the heating turns up and soothing music plays quietly in the background, creating a comfortable and restorative environment."

"I have always been very interested in the intersection of healthcare and automotive. So, I am glad to see that, for example through Euro NCAP, attention is being given to sudden sickness. What if interior sensing AI could detect driver impairment due to a medical event? For example, we already have early stage capabilities for detecting heart rate variability using computer vision, and I am eager to see these types of technologies advance so that they can actually be deployed in vehicles."

"When you don't feel valued, you feel like sh*t. When you feel like sh*t, you don't do good math."

"There are also fascinating backseat use cases around content recommendations and monetization of advertising data, even. Understanding passenger reactions and emotional engagement with music and video content can help refine content recommendations, making these more relevant to the user and their experience. Where advertising is deployed, understanding viewer engagement with that content provides OEMs and advertisers with very valuable data. I think users will be interested in opting in to that, if there is an incentive for them. Imagine a scenario where you and your friends take a rideshare to a concert and engage with advertising in the back of a car. In return, since the system knows you are taking a ride to a concert, it offers you a discount coupon for a band t-shirt or such. And, to wrap this up, a fun use case often requested by OEMS, is trip highlights where the Emotion AI detects smiles and joy, so that an interior camera can take cool pictures just at the right moment there’s a lot of fun we can add to the overall experience considering the right applications of this technology."

"In cabin sensing is the natural evolution of DMS and is seeing increased demand because of its many important applications in safety as well as entertainment, comfort, wellness and beyond. Instead of just focusing on the driver, interior sensing solutions have a full view of the entire cabin. With a camera and other sensors, these systems provide human-centric insight into what’s happening in a vehicle, by detecting the state of the cabin and that of the driver and passengers in it."

"Occupancy detection, which determines how many people are in the cabin and where they are sitting, is another interesting area of functionality. This too can help improve existing safety functionality, as it helps determine proper seat position and seat belt usage and can provide important analysis for airbag deployment."

"Over the past several years, we’ve seen Driver Monitoring Systems (DMS) go from nice to have to must have technology in cars."

"We can have our econ ‘hats’ on with some theory in mind, but without a deep understanding of the context and constraints in the particular environment you're working in, it's hard to design interventions that might be useful"

"Everyone has their own path to finding their passion and, for some, that may be longer than for others."

"Yeah, absolutely. I’m actually Kenyan, by the way. So I was born and raised there, which is why I do research there. But yes, I’ve been to them several times. In fact, I was just there, I was there in February. Yeah. I mean, they’re not rich people, right? This is rural Kenya. They’re pretty poor. They’re mostly growing and eating maize. That’s the main staple of the whole country. A lot of them might not eat much meat a year, maybe at Christmas."

"I didn’t allow myself to work on it during the day,” she said, “because I didn’t consider it to be real math. I thought it was, like, my homework."

"It’s really [three- and four-dimensional shapes] that are exciting for me, but the study of these things is deeply linked with knot theory."

"Fundamentally, the way we think about it is that we decompose the computation that's in the robot's head now into two parts. The first part is in charge of taking the sequence, the history of actions and observations, and trying to synthesize them into some representation of a belief for a probability distribution about the way the world might be and then another module that takes that belief and decides how to behave."

"So the dimensionality of the space is kind of unthinkably high. It's also not exactly clear what constitutes an object here. If you were going to behave in this world, it would be a very long sequence of primitive actions that you would take in order to clean this kitchen. And also there's just a fundamental amount of uncertainty in this problem, right? So you don't know what's in the blue bowl or what will happen if you try to pull out a certain thing. You don't know when the people are coming home or what they want for dinner all sorts of stuff you don't know."

"And so any approach that works effectively in a domain like this is going to have to handle very large spaces, very long horizons, and really lots of uncertainty. So we have kind of a standard structural decomposition to this problem. We call this belief space hierarchical planning in the now. I'll decode what that means a little bit."

"Invoking the simple principle of translational symmetry — which in nature gives rise to conservation of momentum — led to dramatic improvements in image recognition"

"Computational biology is the art of developing and applying computational methods to answer questions in biology, such as studying how proteins fold, identifying genes that are associated with diseases, or inferring human population histories from genetic data."

"So imagine that you have some kind of probability distribution over the worlds that the robot could actually end up operating in. I want to find a program that's going to behave well, let's say get a lot of reward in expectation on average over all the environments that it could possibly find itself in. So that's, I would say, kind of a reasonable formal objective for a robot. And one thing that's good about this as an objective is that we don't have to argue about it, right? It doesn't say whether there should be learning in there or what kind of learning or should it be a genetic algorithm or should it have planning. In some sense, you could say, "I just want to make the program that's going to be the best that can be on average over these environments.""

"OK, I'll keep going. I'll surely be able to offend some people soon. And I'll work harder at that. OK. so if we kind of accept this idea that we're going to build in some structure, then what? And the thing that my colleague and I have done recently. Well, now, maybe not super recently, but recent. In order to test out the idea that there's a set of mechanisms that would work well, what we did is we hand built the rest of the system. So we hand-built some transition models, inference rules, ways of doing search control and so on and connected them up to these general mechanisms and made a system."

"So just as convolution gives us a great leverage when you apply it to the right part of the problem, then the intuition as well, hopefully there there's a few mechanisms, hopefully not like 100 mechanisms, but maybe 10. And then if we figure out how to use those mechanisms to bias learning and to structure behavior that we could learn robust ways of behaving that are efficient and so on."

"So one set of possible kind of general ideas includes convolution in space also and time. Maybe understanding the kinematics of the system that it's connected together in joints and segments, a notion of planning to move through space, being able to do causal reasoning-- if I were to do this, what would happen? -- Abstracting over individual objects, various kinds of state and temporal abstraction and so on. So our view-- I don't want to commit to a particular list-- but is that there's a list of structural principles that are pretty generic and very broadly useful and we should build them in."

"But the problem is now I've written down an objective function. I've said, "Oh, if you could tell me a distribution over possible worlds that you'd like this program to work well in, then I know in a certain mathematical sense with the best program is." But now my problem as the engineer, as the person who is in the robot factory, which is again, the kind of maybe analogous to the problem of nature, is I have to figure out how do I how do I find this program that's going to be good and all these situations?"

"And just again, to kind of give you the motivation. I really want a robot. This isn't my kitchen, by the way, just in case you were worried, my kitchen. But imagine that you had to clean this kitchen or make breakfast in it or something. It would be very hard. And imagine programming a robot to do it. It's extremely hard. And so one thing that's useful to do is to think about what makes this problem hard. So one of the things that makes it hard is that there are lots of objects."

"Then I sort of reinvented reinforcement learning in a not very good way, really. But it was kind of entertaining. And I this is a slide by the way for those young people in the audience. You might know, but back in the day, we used to write with colored depends on pieces of clear plastic. And that's what we used to give talks. So I had this kind of pseudo reinforcement learning thing. And by 1990, I actually had this little robot called Spanky that did actual reinforcement learning during my actual defense. So it didn't learn anything too complicated. But it did do it in real time. So that was kind of fun."

"So I'll just tell you some story because people usually like stories, and it's kind of the afternoon. So and this is related to the question about reinforcement learning, probably, right? So how did I get into this whole thing? When I just finished my undergraduate degree, which actually was in philosophy, weirdly enough, I went to work at a research institute while I was starting my PhD. And they had this robot nobody really knew actually very much about robotics. So And it was my job as the brand new person to try to get the robot to drive down the hallway."

"So OK, I finished my PhD. And I thought, OK, I know something about robot learning now. But I really want to make robots that can do complicated things. And I couldn't figure out how to get basic reinforcement learning methods to really scale up to problems that I cared about. And so this is one last flight. I'll show you from some talk that I gave in 1995. And I kind of complained that the ideal that you could take just a big bunch of what I like to call neural goo now, just a big bunch of generic neural network stuff, and train it to be an intelligent agent all by itself. But that wasn't going to be feasible. And instead, we needed some kind of compositional structure. And that would give us more efficient learning and more robust behavior and so on."

"So if humans have to engineer a very complicated system, then it has to be the engineering process has to have some modularity to it because humans are really bad at understanding one big messy system. They're good at understanding pieces and parts that work together. So it may be that we have to take a modular design approach in our engineering efforts for intelligence, not because the intelligence needs to have that architecture, but because we, the human engineers, need those tools for actually building a system."

"So one way to think about the whole problem set up then is that I, as the robotics engineer, have to do for my robots the job that nature did for you. That is to say, I have to think about I'm a robot factory. I'm going to make these robots. And the robots are going to go out in the world. Maybe they're going to go and work in people's Kitchens or something. And every kitchen is going to be different. So there's going to be a lot that I don't know about the world. But somehow, I have to figure out the best program, what program, to put in the head of all my robots, so that when they go out in the world to behave, they can do a good job so that's the way I think about the problem that I face. And in order to think about what would be the best program, I kind of think about it this way."

"So all these constraints need to somehow come together into a way of building intelligence systems. Actually, I would stop here for a minute just because it's a convenient spot and see if there are questions. I see some red Q&A button. So maybe someone can ask."

"OK, so what's my research goal? I come from the machines end of this world, roughly. And what I really want to do is figure out how it is that we can make intelligent robots. And I do this mostly because I'm interested in intelligence more than I'm interested actually in robots. But I think that trying to make a physical agent who goes out and interacts in the world is a really good test bed for understanding what kinds of reasoning and perception and control we need in order to make it an intelligent system."

"And so what we want to do is think about first of all, what's the best-- what would be the best pi to put inside the robot. How can we think about that? And then we have to think about the problem of how is it that we, in my case, as me, as an engineer, I'm going to find that pi that I should put in my robot."

"So the way I want to think about this, the job of this program. So I'm going to make a robot. I'm going to put a program in the head of the robot. So let's say, I'm not going to worry about hardware. I'm just going to read about the software. And so the program that I'm going to put in the head of my robot, it has to do this job that's written in the formula up here. And what this is just shorthand for saying is that it has to represent some kind of mapping from observation and actions that it's had in the past. So o, a star means the whole history of observations and actions that it's ever had. Based on that, it has to pick the next action. So that's not really saying much of anything at all. That's just a description of every single robot control program basically that's been written. You have to take your history of actions and observations, compute the next action."

"And so what happened was I programmed the robot. And it would run into the wall. And I would bring it back. And I would fix the programming. And it would run into the wall again, hopefully for a slightly different reason. And over the course of a couple of weeks, I managed to write a program that would use these funny sonar sensors on the robot and make it drive down the hall without crashing into the walls. And so that was good. And I was happy, in a way, at the end of that, that I had gotten it to work. But I reflected on that a bit more. And what I decided was that I had learned how to navigate down the hallway using the sonar sensors. And what I thought was that-- and it had taken a long time. And I was kind of a hassle. And really, the system should have been doing the learning, not me. So my view was that I should figure out a way to get out of the loop to build systems that could learn on their own to do stuff. And then I could just wait for them to do that. And that would be better. So that was flaky."

"The problems require interdisciplinary dexterity and involve not only management of large data sets but also the development of novel abstract frameworks for understanding their structure."

"So the way I think about the problems-- this is kind of a definitely a computer scientist way to think about the problem-- is to think about the robot as a transducer, as some kind of a system that's connected up to the world. And it makes observations of the world. And it takes actions that change the state of the world. And presumably, there's some objective, right? We want to take actions that change the state of the world in some way that we think will be good."

"So there are a bunch of ways you can think about the problem. I mean, one would be to say, "Oh, I'm really lazy. I don't really want to think very much about working in the factory. It seems awfully hard. I will just make a robot that has roughly an empty head. It doesn't really know very much at all. And then it just has to interact in the world and learn everything by interacting." But of course, you don't really want a robot that comes to your kitchen and begins to learn about physics, right? That would break a lot of dishes."

"Yeah, actually. For years there has been. So a more typical formalization would be in terms of predictive models and planning or reasoning. So reinforcement learning. Also, it depends. The phrase unfortunately, the phrase, "reinforcement learning," grows and stretches too. And sometimes for many people and in many discourses, it's come to mean all of intelligent behavior, in which case, I would say, well, no it's all reinforcement learning. But that's vacuous. Other formulations involve reasoning about objects and their relationships and thinking about the long term consequences of taking actions in the world and so on. So there's really different ways of framing and formalizing the problem. And they give you very different computational profiles and different learning strategies. OK, good."