2. Reasoning: Goal Trees and Problem Solving
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- Опубликовано: 25 авг 2024
- MIT 6.034 Artificial Intelligence, Fall 2010
View the complete course: ocw.mit.edu/6-0...
Instructor: Patrick Winston
This lecture covers a symbolic integration program from the early days of AI. We use safe and heuristic transformations to simplify the problem, and then consider broader questions of how much knowledge is involved, and how the knowledge is represented.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
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The difference between most universities and places like MIT isn't the curriculum, it's the instructors. And by some happy miracle, we've ended up in a world where these lectures are free to watch!
I wish those classes could be given in poor neighborhoods, so our youth could have a good education
From a person self-studying Artificial Intelligence, thank you so much for publishing this playlist! It is truly a great resource for me.
As someone who started self studying AI before me, what do you suggest? Books and courses
@@juliusolaifa5111 there are so many different fields within AI! I would say study all the basic Math needed for ML first like Calculus, Linear Algebra, maybe Optimization Theory, then studying some foundational Machine Learning ( you can try out Andrew Ng's Machine Learning course on Coursera for a non-math heavy introductoon, or go straight to books like Elements of Statistical Learning, and Learning from Data for more math-y theory). If you want a more hands-on coding introduction, I would suggest the Hands-on Machine Learning with Scikit-learn, Keras, and Tensorflow book.
Once, you have some intuition of foundational ML, you can explore other subfields like Computer Vision, NLP, Reinforcement Learning, Robotics, and so many more.
Personally, I have been studying a lot of Reinforcement Learning + Robotics this past year. I'm looking toward learning more NLP soon to work on some social robots 🤖 that can intelligently communicate with people!
Good luck on your journey in AI/ML!
@@khailai5204 Can you suggest materials on Robotics and Reinforcement Learning? I have gone through Andrew Ng course both ML and DL specialization. I bought ESL but haven't read much.
I am also self-studying ML (also taking a professional certificate class from Columbia). These videos are excellent. But I wish there was more programming in them.
Who else in quarantine and chilling with these lectures?
Learning never ends!
@@ericfitzgerald9214 aaye!!!
Yes broo
hell yea
Me🙋🏻♂️
Damn this course is good. My AI course began with "this is a node, this is a breadth first search, this is a..., you memorize this to pass the exam", this deals with the core concepts which I find more beneficial.
I can relate to this. Our course follows the same nonsense.
These lectures are awesome!
I dont know how integration and these transformations work, but I like the way Mr. Winston is teaching. Its all very clear, simple and structured that makes it easy to follow and its also very interesting how he is solving problems.
Another fact is that other instructors get lost even with notes, presentations and materials and hes just doing it out of mind and that show that he unterstood what hes talking about!
I wish I could be a student at MIT. Awesome education,thanks for sharing as we believe knowledge is freedom.
Thanks to OCW, we *all* are :-)
(Thanks MIT!)
@@RogerBarraud it doesnt give the vibes of getting a coffee attending to class and then chilling at the campus.. But its something
The calculus problem is much more interesting (and far less patronizing) than the typical "A traveler wants to get from city A to city C..." and I appreciate that about it.
So impressed. This robot professor is the best example of artificial intelligence I have ever seen!
Hopefully in the next version MIT will be able to create artificial emotions as well.
On the most fundamental level, you could kinda ask the same thing about us. I suppose.
you have no idea.
RIP Prof Patrick Winston :'(
Prof - "So this then, forms the core of an integration program, that will integrate almost nothing. But actually, almost nothing is integrable anyways, so it's a good head start." - 8:54
Yeah he got me good there :))
I'm literally sat here, open mouthed, trying to understand why nobody tried to teach calculus this way. Splitting into safe and heuristic operations, and formalising the approach to solving problems would have really helped back when I was studying mathematics.
To some extent that is because the purpose of a mathematics class is not to simply teach you how to solve mathematical problems via heuristic steps, but rather to give you an understanding of the underlying mathematical theory.
Perhaps one lesson or so of this could have been useful at some point to help bolster grades though...
Thanks a lot for the free content. Im one of those cases that cant go to college because of cronic illness, so this is the best type of content for self teaching. :D
Knowlegde about knowledge is power! -Professor
Second lecture and he knows everyone's name? Damn!
Read his post on why he decided to memorize all of his students' names. slice.mit.edu/2009/08/16/the-rumpelstiltskin-principle/
He knew everyone by name in the first lecture.
He actually knew their names by the first lecture.
the post's amzingly cool
Hahaha You know what? That is why he sat in this lecture in MIT, because ordain people just say " Hi" to you even you ever told him your name last time not long ago. And that is why there are countless the average dumb Joes around your daily life even now you have already out of campus into working life. And guess you couldn't agree me more about my remarks....................... Merry Xmas from Melbourne..........STF....................
This professor is a LEGEND.
Love the ending. Well said by the instructor.
I would like to add: "AI is whatever hasn't been done yet." - Douglas Hofstadter
Not quite agreeing here.
So intelligence is doing something someone else does't know how to do?
Fair point
" i take it back, it's not intelligent after all. It does integration the same way i do " best part of this video.
Jim Slagle's PhD thesis is here: dspace.mit.edu/bitstream/handle/1721.1/11997/31225400-MIT.pdf?sequence=2
For symbolic integration the paper by Ritt on Liouville's theory is pretty important
Thanks!
Thank you! I was looking for this.
Well this explains why there seem to be so many in AI that come from mathematics. As for the program, it simply automates a process that was derived from human thought.
43:33 This... professor.. knows what's up.
Wow ,great fun lectures. It's really changed my mind about what actually learning is about
19:08 pretty cool how he preempted their thoughts
What a good lecturer!
I see a some comments about being lost in the integrals. Well, as he said, he wanted us to witness the detailed process so we could understand how the "intelligence" works. The point of the lecture is that the computation is done with a set of rules and leads to a set of possible outcomes, as represented by the tree. Honestly, however, the calculus problem is quite basic. If you want to understand how to solve such problems I'd recommend watching a couple Khan Academy videos on simple integral calculus.
The point of the lecture was to take a hard problem that most of the students couldn't solve and show how a computer could solve those problems, in order to pose the question "Is this intelligence?"
I love this guy's stuff TOTALLY... Must watch his vids on teaching...
Im so mad that I had a terrible math teacher at my university! Teaching is a skill and I guess some profs just haven’t witnessed what it means to be good at teaching. I’m truly thankful for this resource
is there any text book accompanied the lecture???
Thanks for such an insightful presentation/Lecture. By the way, I am from Tanzania, East Africa
For those having their Math rusty like me here is why he substitute with sinx or cosx, it is simply because the function is defined in the domain [0,1[ that is because of (1-x2)^5/2=(sqrt(1-x2))^5 and anything under the sqrt should be positive so 1-x2 needs to be >=0 then 1>X2.....
I now know that after 30 years not doing it, I've completely forgotten how to do integration 😟
how i wish i got these methods of integration before my A-level exam
I don't understand any of this, but I'm watching lol.
Would love to learn more calc and trig to understand all this better.
Someone let me know if you have any suggestions on how I can teach my self!
Going to keep watching
We suggest you watch this playlist to get an overview of calculus: ruclips.net/p/PLBE9407EA64E2C318. There are a lot of channels on RUclips for calculus and trigonometry like Khan Academy or 3Blue1Brown. We recommend you look at those as well. Best wishes on your studies!
44:44 they solve some problem, they seem super smart. They tell you how they did it, and they don't seem so smart anymore! - words of wisdom
thanks for doing a calculus problem half the class. could easily made the point within 10 mins
I think you missed the point.
these transformations and stuff are human ideas. I wonder if we can make a machine with elementary ideas of what integration is and then can do any problem ( Alpha Zero in chess world is an example)
Last quote was amazing!
Out of curiosity: What level of mathematics should I have before watching these videos. I have never taken a calculus course, so I don't know why those transformations work. Do I need calculus, or can I get by without it? Or can I learn a certain calculus subjects without having to go into calculus in depth?
+Soulsphere001 The 6.034 MIT course page does list 18.02 as a prerequisite (as well as 6.01):
6.01-This is the only formal pre-requisite but we will depend on it strongly. In particular, we assume that you can programs in Python, that you understand search algorithms (depth-first, breadth-first, uniform-cost, A*) and basic probability and state estimation to the level covered in 6.01
18.02-We will assume that you know what the chain rule is and partial derivatives and dot products. If you have not taken 18.02 (or are not taking it concurrently), you should really wait to take 6.034 until you have.
*****
For some reason I cannot find the prerequisites anywhere on the course's webpages, so I really appreciate the reply. Thank you very much.
I did notice the Python prerequisite, and I started learning it two days ago. One of my cousins knows it and has been recommending, for years, that I learn it. Fortunately, programming isn't a new topic for me.
Bob Jones, I've been meaning to learn some calculus at some point, but I should go through my old precalculus book first. But, yes, I could probably just learn the specific calculus required for those equations.
"Bring the number down and lower the power" is a quote that my brother used to used a lot, and now I finally understand what it means.
Thanks for the information. I'll do as you suggest.
I wish I could like this 100 times.
There is one question, that when they apply x=sin(y), there is a subtle constraint of the range of x applied, which means abs(x) cannot be bigger than 1. But the original formula does not have the constraint of x value range. Are we losing something here?!
O the joy of being enlightened…
his notation is amazing!
The joke in the end is so interesting¡
I’m dumb and all, but what happened to the ^5/2 before transform c happened?
Anyone recommend symbolic integration prep videos/courses?
I noticed there has been a mistake on the integral ''\int sin^4 y/ cos^4 y dy''...it should be ...'' \int sin^4 y/ cos^3 y'' as long x=siny so dx= cos y dy...
Angelos Manglis Incorrect. The integral transformation he applied gave the integral of ((sin^4 y * cos y) / (cos^5 y))dy, which is the integral of (sin^4 y / cos^4 y)dy.
+James N How does the numerator become sin^4 y cos y, with direct substitution it shld be sin^4 y ?! Help !!
@@mayo7199 I suppose, as i expect, than you had solved your problem, but in case than a new visitor has the same question, then:
x = sen(y) --> dx = cos(y) dy;
int( sen4(y) * cos(y) dy / ( cos5(y) ) ) // Just is a replace. That's the cause of why there are a cos(y) in the enumerator;
int( sen4(y) dy / cos4(y) );
Impressed by the board.
I don't understand the explanation why the denominator became Cos^4 y as opposed to cos^5 y. How does the derivative of sin being equal to cos explain this? If anyone can assist in my understanding I would appreciate it very much.
+Ma Yo x=siny => dx=cosydy as was said a second later
+MrX5tech I heard him say just that, but As I mentioned I didn't understand his explanation
MrX5tech Got it, he's moving dx into the numerator in order to make the integral with respect to y... so the numerator becomes sin^4 y cos y and the cos y cancels one of cos's in the denominator DUUH ! sometimes the most obvious things get ya. Hey man Thanks !
Ma Yo Fluid theory (Reproduction/Feed/Reasoning) decanted selfmultidimentionalover...
The polydynamics of the movement generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...)
Simultaneous as my unidimensional variability...
unidimensional variability = live-beings
Why why why did they install the electronic chalkboard movers? What was wrong with the old system?
Was calling a Turkish student "the young Turk" not weird in 2010? 😂
The only thing about this program that seems strange to me is how it’s classified as artificially intelligent. I don’t see how it’s different from any other program. I do see how it “thinks” in the same way as I do while doing integration, but that “thinking” seems like pretty much the same control flow as any other program.
By the way very interesting lectures well taught and also atracts your interest to go through them!!
This course if for Comp sci. engineers or electrical engineers? Does this course coincide with Machine Learning and data Science?
We recommend checking out the EECS undergraduate curriculum to see how this course fits within all the other courses: www.eecs.mit.edu/academics-admissions/undergraduate-programs/course-6-2-electrical-eng-computer-science
You don't realize the difference between an MIT professor and a non-MIT professor until you watch MIT OCW.
I studied computer science but I never was a math guy. Can someone please explain me why this lectures of him matters for understanding ai?
Really fun lecture. Thanks.
What this Professor teaches is not just AI, but how to teach a subject as well...RIP `(-_-)'
Great Teacher!! Thanks for the material!!
Why did he chose those specific transformations as safe transformations?
can anyone tell me the name of integration model;Is it sleighel or slaygal or something else. that solved 54/56 Integration problems
How did he find functional composition depth at 34:45
Thank you for great series
How did he get to dz from 1/(1+y^2) dy at 31:07 ?
Tarun We're given y=tan(z) -> dy/dz = sec^2(z) -> dy = dz sec^2(z) = dz/cos^2(z) . Use this result to replace dy back in the problem qn. To get dz like what u hv asked, we just need to verify that 1/1+y^2 is indeed eql to cos^2(z). 1+y^2 = 1 + tan^2(z) = 1+sin^2(z)/cos^2(z) =(cos^2(z)+sin^2(z))/cos^2(z) = 1/cos^2(z). This 1/1+y^2 = cos^2(z).
@@jackedelic9188 thank you
R.I.P Patrick Winston
this is such an insanely cool topic!!!!!!!!!
can anyone tell me at 28:50 how did he get that division result
its synthetic devision, just look it up, or go to high school, either would work
Add 1 and subtract 1 on the numerator. Then split (y^4 - 1) into (y^2 - 1) * (y^2 + 1). Cancel out the common terms and that should be it. Writing on paper should make it more obvious if it is confusing.
substitute y=tanx=> dy=1/cos^2x*dx=(1+tan^2x)dx. then tan^4dx=>tan^4y*dy/(tan^2+1). Hope this can help!!!
@@muraliavarma That is one way to do it, but you could also go for polynomial long division, and for anybody reading this wanting to know how it works, take a look at this link: www.emathhelp.net/calculators/algebra-1/polynomial-long-division-calculator/?numer=y%5E4&denom=1+%2B+y%5E2&steps=on
hmm. This got advanced fast :(
I’m only on the second lecture as well, but I have heard that AI theory requires calculus and linear algebra so it might take some of that knowledge for the rest of the course, but this stuff actually isn’t too bad. If you want to learn it quickly, I’d just watch some videos on integration and then learn integration techniques. Being very good at it is pretty difficult, but understanding the basics is actually quite simple because it’s really algorithmic.
Where the heuristic transformations after 15:30 come from, what is this?
"feels?!"
Great lecture, thank you
AI was a hot topic in the 1980's. I did neural nets and troubleshooting and configuration expert systems. Some of those programs scared people. Now it's hot again. I'm somewhat surprised that so little progress has been made. I ultimately came around to the view the AI should be used to augment humans, not replace them. Doctors should be open to programs that help them make accurate diagnoses so they can spend their time caring for the person. How will we program non-local consciousness?
***** What do you mean by "non-local consciousness"?
thank you for this interesting course
It would be actually interesting if you can detect all the yawning persons in the audience. Hold the footage, look for someone who opens his mouth, if so he's yawning or speaking. People also sometimes hold the hand in front of the mouth. The difference can only tell a human. Not a simple task for a computer.
17:24 -> Her name is Sila :).
Her zaman bir önerisi mi varmış.
Hey could someone explain me why dx = cos y at about 19:25? that would be very nice. I cant finde an explanation online. A good link would help me too. Thanks
he just derived the x = sin y and he got dx = cos y dy
thank you! i wanst used to this nototation back then. :)
Cisco Ramon in the first row.
Finishing was awesome.. i loved it to the core
Spent whole time solving an integral problem to demonstrate a simple intuitive concept/approach.
Sanket Patole Fluid theory (Reproduction/Feed/Reasoning) decanted selfmultidimentionalover...
The polydynamics of the movement generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...)
Simultaneous as my unidimensional variability...
unidimensional variability = live-beings
awwww...23:00
red sweater with the muffler
Where can I find readings for the transformations mentioned at 14:30 ? I have taken calculus classes but I have never seen anything similar to that before and would like to learn.
+Erich Kramer See the course on MIT OpenCourseWare for the complete materials (including a list of readings) at ocw.mit.edu/6-034F10.
He's just pointing out that you can transform any of the trig functions into different trig functions using trig identities, demonstrated at 20:45
exciting and excited
I'm so lost
when do they start with the code ??
28:00 (tanx)^4 = y^4/(1 + y^2)^4 did he forget to put power 4 on the denominator
no, he was right, (tan(x))dx=1/cos(x)^2=1+tan(x)^2
I got lost when he apply C and got to sin^4y/cos^4y. can someone explain it in detail for me? thanks...
using x=siny,x^4 becomes sin^4(x),1-x^2 becomes cos^2(x),so cos^(2*5/2)(x) becomes cos^5(x) and then dx = cosy dy,so use all these transformations and you'll get it.
Hope it helps :)
How did a blind man write such a complex program?
funny coming from you, euler
I had these kind of problems in my university's Scheme course.
I wanna ask: Is this lecture for master or bachelor?
bachelors
When he wrote knowledge is power, how many of you got the remembrance of badass little finger-cersei scence..
Power is power
Why was tan4 chosen instead of cot4? I couldn't understand it.
+Attreya Bhatt It's because tan4 is a less complex composition of functions. You can think of tan4 (x) as a composition of 2 functions: tan x and x^4. Similarly, 1/cot4 (x) is a composition of 3 functions: cot x, x^4, and 1/x. Since it is generally simpler to integrate a composition of 2 functions than a composition of 3 functions, tan4 x was chosen
Oh thanks
is this how Wolfram Alpha works?
Thank you sir..
what's problem reduction? 03:35
Reducing the problem to the form that you are familiar with or have worked on before.
Uhh...The program ??..
18:00 33:00
love from nepal
22:52
we all will choose to ignore what was written on the board?
genius
Damn the ending........ Concludes the question that the program can not in fact be called intelligent
Great!
how is average depth of tree = 3
+imalive I believe he means, how many steps do I need to take before I reach the answer? For instance, take the problem Derivative(5x^2).
1) Factor out five. 5*Derivative(x^2)
2) Reference table of derivatives to find answer: 5*2*x.
As I understand, this problem has a depth of 2.
Thanks :-)
1 heuristic , 1 safe, 1 table lookup