Youtube comments of (@WelchLabsVideo).

  1. Huge thanks to grant for including me in this super fun video! It’s an honor to be edited back to back with some YouTube heroes!
    4500
  2. Woah, thanks 3Blue1Brown! I love your channel!
    1500
  3. uh, thanks?
    713
  4. +Anthony Trupiano Yeah - good point. It's just a question of how much I should break with convention here - lateral makes way more sense, but most people don't know what you're talking about when you say "lateral number".
    695
  5. That's absolutely incredible - thank you so much for sharing & best of luck in your PhD!!
    680
  6. +MindYourDecisions Thanks! I made this puzzle just for the video using an old puzzle, spray paint, and vinyl lettering.
    546
  7. Please have your homework turned in before the end of the day. :)
    500
  8. lol thanks 😁
    343
  9. Felt this same way shooting it!
    302
  10. +coltonHD Great question! This was an open question in mathematics (I believe in the early 19th century) - I can't recall the complete argument at the moment - but it was proven that 2 dimensions are it - we don't need more. Later in the series we'll talk about mathematical closure - which will realate to this. Thanks for watching!
    274
  11. Huge thanks to Grant for including Welch Labs here!
    263
  12. Thanks to KiwiCo for sponsoring today's video! Go to https://www.kiwico.com/welchlabs and use code WELCHLABS for 50% off your first month of monthly lines and/or for 20% off your first Panda Crate.
    196
  13. Haha - yess!
    168
  14. Well Done!
    162
  15. Yeah basically!
    157
  16. Haha true!
    148
  17. woohoo!
    145
  18. Ha! this was kinda my experience making the videos!
    137
  19. Thanks to PIA for helping make this video possible! Go to https://piavpn.com/WelchLabs to get 83% off Private Internet Access with 4 months free!
    129
  20. Thank you!
    124
  21. I don't know!
    113
  22. Yeah I originally thought this was going to be way shorter - but it got kinda deep!
    107
  23. Hadn't noticed that - cool!
    102
  24. Thank you!
    95
  25. Thank you for the kind words.
    92
  26. +Lorcan O'Brien Good question - that didn't actually take too long. Shooting with camera motion, however, takes FOREVER.
    91
  27. I know right!?
    87
  28. +Frasafrase Great question! I'll explain in detail as the series progresses, but yes, the function i show does have too many roots. This is because it's the only the real part of f(x) = x^2 +1 for complex x. In part 8 I'll show the real and imaginary parts together, and we'll see exactly 2 roots - I didn't want to overwhelm everyone in part 1. Thanks!
    76
  29. Good call, that's next! (Well, after a line...)
    71
  30. Thank you for the kind words!
    71
  31. Thank so much!!
    68
  32. haha yeah.
    68
  33. Very.
    66
  34. Amazing! That's funny I made that series b/c I had just finished writing my own neural network library - I think only Caffe was really available then for me (2013).
    65
  35. Awesome to see this translated!
    64
  36. I wish I could make them faster! :)
    63
  37. Thanks for watching!
    62
  38. Thanks for watching!
    62
  39. Woah interesting
    58
  40. My secret plot to hide subliminal messages in educational content has been revealed! Noooo!!!!!
    57
  41. Correction at 1:05 - derivative should read: 2(3x+2x^2)(3+4x). Thanks to Siddharth for pointing this out!
    52
  42. +Ilan Rodriguez Working on something like this now, can't wait to share! Thanks for watching!
    51
  43. Now is a great time to have a fresh look at this video’s sponsor KiwiCo - head to https://www.kiwico.com/welchlabs and use code WELCHLABS for 50% off your first monthly club crate or 20% off your first Panda Crate.
    50
  44. That is entirely too flattering a comparison, thank you for watching.
    47
  45. Agreed!
    45
  46. Noted! These are going into a playlist.
    43
  47. THank you!
    43
  48. Thanks for watching and for the kind words.
    42
  49. +Tomas Romas Thank you! I'm planning on getting to FFT sooner or later here, hopefully sooner. Thanks!
    41
  50. Haha, yeah this comment cracked me up too. It's funny, I was worried about the fire "getting out of control" and it turned out that my paper was really hard to burn!
    39
  51. Me too!
    39
  52. Thank you 😁
    39
  53. Sound fun!
    38
  54. +avatar098 woohoo!
    38
  55. Good Call! I'll fix this in the workbook.
    37
  56. Fascinating!
    37
  57. Printed it myself from this pdf: https://bildsuche.digitale-sammlungen.de/index.html?c=viewer&bandnummer=bsb00082065&pimage=8&v=100&nav=&l=de
    37
  58. Sign up for a 14-day free trial and enjoy all the amazing features MyHeritage has to offer: https://bit.ly/WelchLabs
    36
  59. Well this is one way to get better at spelling.
    35
  60. Take your personal data back with Incogni! Use code WELCHLABS and get 60% off an annual plan: http://incogni.com/welchlabs
    35
  61. it a good way I hope!
    34
  62. Thank you!
    32
  63. Great job! Now plot these guys and look for patterns!
    32
  64. Mostly adobe after effects, plus a custom motion rig to move the camera, plus lots of banging my head against the wall.
    31
  65. +Proto Great question! It turns out that the result is still a complex number. Richard Feynman introduces this in an interesting way: http://www.feynmanlectures.caltech.edu/I_22.html#Ch22-S6
    30
  66. Yes, this series got derailed pretty hard! I realized it was crazy ambitious - I'm sure I will cover lots of these topics eventually, and hopefully pick back up on this series. Thanks for watching!
    30
  67. Thanks for watching!
    30
  68. +Asim Deyaf Great intuition! This is how complex numbers are often represented - in polar form or using complex exponentials. https://en.wikipedia.org/wiki/Euler%27s_formula
    29
  69. Good luck!
    29
  70. I know right!?
    29
  71. Alright, it took a really long time, but I answered your question: https://youtu.be/4MmSZrAlqKc?t=10m41s
    27
  72. Me too! That series was tons of fun. I'm thinking the next series will be a little more in that direction.
    27
  73. haha - maybe one day.
    27
  74. Thank you!
    27
  75. Woohoo!
    27
  76. Thanks Dean! Thanks for taking the time to help with this series, your input was invaluable.
    27
  77. Thanks for watching!
    26
  78. Thank you!
    26
  79. https://www.amazon.com/Scotch-Magic-Tape-3105-Inches/dp/B0009F3P3U/ref=sr_1_4?ie=UTF8&qid=1479689065&sr=8-4&keywords=tape
    26
  80. Thank you! Will do!
    26
  81. Awesome!
    26
  82. Thanks for saying that - it took some work to figure out!
    25
  83. Thanks for watching - yes, I should have been more clear that this is an upper bound on the probability. For a much more elegant presentation, see my source: http://work.caltech.edu/slides/slides02.pdf. There's also a great video lecture that goes along: http://work.caltech.edu/lectures.html
    24
  84. HECK YES! I'd really like to do a series on it one of these days.
    24
  85. Woohoo!
    24
  86. 🤞🤞🤞
    24
  87. Awesome - hope you like it.
    23
  88. Thanks for watching!
    22
  89. Good point and great conversation here. I remember this bugging me too when Feynman took this step in Ch 22 of lectures vol 1. I didn't take the time to dig into it here - at least a footnote about it would have been a good idea. I'm working on this chapter of the Imaginary Numbers book now and will include something on it there!
    22
  90. Tycho Brahe!!!
    22
  91. +xerotolerant Nice explanation! This series became temporarily derailed - hoping to get back to in 2016. Thanks for watching!
    21
  92. Yeah I've bumped into this a few times - will but this on the idea list!
    21
  93. :)
    21
  94. Awesome, thanks for watching!
    20
  95. Woah that’s so cool!
    20
  96. Thanks for watching!
    19
  97. I have mixed feelings on it.
    19
  98. Great idea!
    19
  99. Awesome - thanks for sharing + watching!
    19
  100. Woohoo!
    19
  101. Thanks! This one took a little longer to get out than I wanted, but hopefully the extra details are worth it!
    19
  102. I noticed that too while editing! It's funny, I was going to make it grow, but for some reason it already appeared like it did - so I just left it alone.
    18
  103. THERE IS NO FORTE.
    18
  104. Thanks to KiwiCo for sponsoring today’s video! Go to https://www.kiwico.com/welchlabs and use code WELCHLABS for 50% off your first monthly club crate or for 20% off your first Panda Crate!
    18
  105. Thank you!
    17
  106. You Rock!
    17
  107. Thanks so much for the kind words, happy to help!
    17
  108. Working on it! Thanks for watching!
    17
  109. That's awesome!!
    17
  110. Yeah it's way more complicated/interesting than I realized!
    17
  111. +Mark G Great question! This should be become more clear towards the end of the series. Specifically, I'm planning an "applications" video - that will hopefully shed some light on this great question.
    16
  112. Double hedgehog internet. It's sick.
    16
  113. Thanks for watching - yes, I should have been more clear that this is an upper bound on the probability. For a much more elegant presentation, see my source: http://work.caltech.edu/slides/slides02.pdf. There's also a great video lecture that goes along: http://work.caltech.edu/lectures.html, checkout lecture two.
    15
  114. Haha, awesome. I should use that quote as a tagline: "Welch labs, exactly the kind of shit you always wanted to know." :)
    15
  115. Yes! You would need to scale it!
    15
  116. I was thinking straight to NIPS!
    15
  117. Philip Stuckey Great question! I think there is a connection, and I think it has to do with the fact that a circle is just a special case of an ellipse, where the major and minor axes have the same length. This is something I haven't tested, but it would be cool to make the same 3-D plot for values of k and m other than 1, I think the result may be an ellipse, which would explain why the equations are some similar. Thanks for watching!
    15
  118.  @marksmith8667  Good call! @pendragon7600 - shoot me your address here: https://www.welchlabs.com/contact
    15
  119. Yup! Self-Driving Cars was too big for one bite, I'll cover it in 3 seasons - hoping to get season 2 of SDCs out this summer, with some videos on other topic in between.
    15
  120. Thank you for the kind words and for watching!
    15
  121. Awesome, thanks for watching!
    14
  122. Thank you!
    14
  123. +Badnam3 yup, took way too long!
    14
  124. Word.
    14
  125. Haha, that's awesome!
    13
  126. Me too!
    13
  127. Erfan Noury Yes, you're absolutely right, thanks for pointing this out!
    13
  128. +Siddrameshwar Kadagad Thanks! Code is here: https://github.com/stephencwelch/Neural-Networks-Demystified
    13
  129. I should do a poster!
    13
  130. Awesome!
    13
  131. +Dennis Plotnik I haven't looked at this math in a little while, but I believe that if you don't transpose, you'll end up summing across synapses instead of examples. This would interfere with the backpropogation of errors - we would backpropogate to individual examples instead of to individual neurons. We need to know how much each weight contributes to the overall error (so we can update them!), not how much each example contributes. Let me know if that makes sense - if not, I'll have a closer look at the math. Thanks for watching!
    12
  132. Great question! It allows us to model non-linear things.
    12
  133. One day!
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  134. Haha yeah, only took me 10 months :/
    12
  135. Amazing - thank you!
    12
  136. Glad you enjoyed it!
    12
  137. Thank you!
    12
  138. wooohoo!
    12
  139. Oh no! Yeah, my handwriting isn't the best. Sorry for the confusion.
    11
  140. Woah - just saw that you commented! Awesome! Best of luck with the new script!
    11
  141. Just leave the cc field blank, thanks for watchin!
    11
  142. :)
    11
  143. Haha, good call. I guess I was hoping you guys hung out in like high school or something.
    11
  144. Aw man!
    11
  145. +Totally Awesome Nope, I wish.
    11
  146. Good Question! I left them out for clarity - here's a similar resources that uses biases: http://ufldl.stanford.edu/wiki/index.php/UFLDL_Tutorial
    11
  147. Thanks for watching!
    11
  148. Woohoo! Thanks for watching!
    10
  149. Thank you!
    10
  150. Awesome! It's crazy for me to think that these videos are 4 years old now!
    10
  151. Thank you!
    10
  152. Hype it.
    9
  153. Hey Francisco, thanks for watching. I believe your thinking of the fundamental theorem of arithmetic? And you're right that the surface visualization is not perfect - i treat this in more detail here: https://youtu.be/4MmSZrAlqKc?t=10m. Thanks for watching!
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  154. +Anr Daemon Added, thank you!
    9
  155. Awesome thanks for watching!
    9
  156. Let's gooooo!
    9
  157. Haha the helmet thing really made me laugh. I'll do my best, and thanks for watching!
    9
  158. Thank you!
    8
  159. http://www.premiumbeat.com/royalty_free_music/search/language
    8
  160. +No videos here I don't get into this to much in this series, but yes, other functions are possible and useful! Sigmoid is nice because it's nice and differentiable (which is important in gradient descent) - there are other activation functions out there though!
    8
  161. Haha - thanks for saying that - these song choices in my earlier videos aren't always so popular. Thanks for watching!
    8
  162. Thanks for watching and good call - I'll try to stay more up-to-date on the resources on the next series!
    8
  163. Hi Dan, I'm from Atlanta, Georgia, US. I imagine this has a lot more to do with me not being able to pronounce words correctly than any regional dialect stuff. Thanks for watching!
    8
  164. Here I'm defining imaginary numbers strictly as including a sqrt(-1) component - not that the complex number do include rational numbers. Thanks for watching!
    8
  165. +Andrew Blain Working on it!
    8
  166. That's exactly how I felt researching the series! Thanks for watching!
    8
  167. haha, thanks!
    8
  168. Michal Fašánek C would eat a massive amount of time. I've seen a couple of Java implementations, and I'm not sure about R here. I'm obviously VERY biased to Python - it's powerful, popular, and easy to learn. If you need some serious power,you may also want to consider Theano or the new tools for Torch from facebook:  https://research.facebook.com/blog/879898285375829/fair-open-sources-deep-learning-modules-for-torch/ best of luck!
    8
  169. Thanks for watching!
    8
  170. Do it! :)
    8
  171. Woohoo!
    8
  172. Awesome! Thanks for watching!
    8
  173. Hey Fabio, thanks for watching + commenting!
    8
  174. Hmm great point - not sure if there's a good answer or not!
    8
  175. I noticed that too, good eye!
    8
  176. Missed you too!
    8
  177. Glad you enjoyed it!
    8
  178. Thanks Brit!
    8
  179. I cover some of this here! https://youtu.be/Phscjl0u6TI
    8
  180. iPython notebook! http://ipython.org/notebook.html
    7
  181. Awesome, thanks for watching!
    7
  182. Thanks for watching! Working on it...
    7
  183. I've thought about this - not sure how popular it would be - it's on the maybe list for now!
    7
  184. +pizzahut3001 Great question! Complex numbers and vectors both have 2 components - however, complex number behave in a special why when multiplied or divided, that makes them useful in lots of cool ways. I'll explore this in parts 5 and 6. Thanks!
    7
  185. Coming later this year!
    7
  186. Thank you!
    7
  187. Thanks for watching! I'm a EE aswell. These are great questions - I'm hoping to cover applications of complex numbers in a future series.
    7
  188. Ah I know right! 🤦‍♂️
    7
  189. Woohoo!
    7
  190. Woohoo!
    7
  191. Confirmed
    7
  192. Thanks hope you like it!
    7
  193. Thanks for watching!
    7
  194. Fair point. I'm really aiming this series at middle + high school level and up, I see how it could feel slow! The following series should feel snappier - thanks for watching + commenting.
    7
  195. Thank you!
    7
  196. Thank you! You are too kind. Here's the music: http://www.premiumbeat.com/royalty_free_music/songs/a-girl-from-osaka
    6
  197. Interesting!
    6
  198. Nice!
    6
  199. +Jesse Wilburn Andrew Ng's Coursera course is a great place to start. Good luck!
    6
  200. Good question! Using nested for loops actually results in searching redundant rules - using itertools allows us to avoid these.
    6
  201. +kiyan arsh Yes, you shouldn't run into any issues with the code on data of this size. You probably need more layers for facial detection. Thanks!
    6
  202. Wow, thank you!
    6
  203. HAHAHAHAA YESSSSSSS. I'm so happy you recognized this.
    6
  204. No more in these series, but I definitely want to continue with more series in the historical mathematics "thread". Thanks for watching!
    6
  205. Thank you!
    6
  206. Nice!
    6
  207. Thank you!
    6
  208. Thank you!
    6
  209. Thank you!
    6
  210. Thank you!
    6
  211. Will be part of a longer playlist!
    6
  212. Excellent!
    5
  213. Nice Logic!
    5
  214. Thanks for watching! I'm hoping to move to a quicker cadence in the future.
    5
  215. Our universe couldn't support the 4 dimensions we needed, so it like...you know...blew up. And then burned for a while. Just one of the dangers of doing math :)
    5
  216. Thank you!
    5
  217. Thanks for watching! The editing for that final summary took soooo long, I'm glad you enjoyed it!
    5
  218. Thank you for watching and for the kind words.
    5
  219. I recommend using a library like sklearn. good luck!
    5
  220. Yesterday!
    5
  221. https://github.com/stephencwelch/Imaginary-Numbers-Are-Real
    5
  222. I'd love to - would you mind providing some sources?
    5
  223. Hahah, thank you!
    5
  224. Me too!
    5
  225. Wow, thanks!
    5
  226. https://www.premiumbeat.com/royalty_free_music/songs/language-2
    5
  227. haha both!
    5
  228. Woah, really?!
    5
  229. Great points! Any references you recommend?
    5
  230. Thank you!
    5
  231. Awesome thanks for watching!
    5
  232. Yeah I sadly didn't have time for ROPE - but it's so cool and uses COMPLEX NUMBERS! Maybe a future video.
    5
  233. Made my own copy from this pdf: https://bildsuche.digitale-sammlungen.de/index.html?c=viewer&bandnummer=bsb00082065&pimage=8&v=100&nav=&l=de Would be fun to do a reprinting if enough people wanted to buy it.
    5
  234. Thanks!
    5
  235. Oh Snap!
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  236. Madao Wow, hopefully the ad was bearable - thanks!
    5
  237. Amazing, thanks so much!
    5
  238. Will add to my list of potential topics!
    5
  239. haha, just 13.
    5
  240. Yes - this is something I'm definitely planning to do going forward, and perhaps retroactively once I have some time.
    4
  241. Yes.
    4
  242. +Rajit Venkatesh Good question! This is the one case I didn't explore here, because it would take (and deserves) a whole new series on calculus.
    4
  243. Haha awesome!
    4
  244. Thank you! Glad you enjoyed the series. 
    4
  245. Thanks for watching!
    4
  246. woohoo!
    4
  247. Try to figure out if it's capable of harming humans!
    4
  248. nice job!
    4
  249. Thank you!
    4
  250. Been reading to read about these for a while...they seem interesting.
    4
  251. Hey Richard, thanks for watching! Here's the piano song: https://www.premiumbeat.com/royalty_free_music/songs/language-2
    4
  252. Good call!
    4
  253. Haha , awesome, thanks for watching!
    4
  254. Nope, that's it. At lease when referring to the neurons in Artificial Neural Networks. The real things are apparently a bit more complicated.
    4
  255. I do have a book for sale: http://www.welchlabs.com/resources Thanks for watching!
    4
  256. https://www.amazon.com/Surely-Youre-Joking-Mr-Feynman-ebook/dp/B003V1WXKU
    4
  257. Thanks for watching! https://www.tunefruit.com/tracks/a-world-of-wonder-instrumental
    4
  258. Thanks for watching!
    4
  259. Wonderful - thank you!
    4
  260. Sweet! Thanks for watching.
    4
  261. Yes - this is on my to do list - should be available in the next 2 weeks. Thanks!
    4
  262. :)
    4
  263. Thanks! I'm using the iPython notebook. I recommend the anaconda distribution. https://store.continuum.io/cshop/anaconda/
    4
  264. You got it!
    4
  265. Well said!
    4
  266. Woohoo!
    4
  267. I try to "show the real thing" whenever I can, only thing that was really "effect" i think was showing the 96 kernels learning. I thought about actually doing a training run, but didn't have the time!
    4
  268. Yeah! I'm really excited for oppenheimer!
    4
  269. Thanks for watching!
    4
  270. haha no way.
    4
  271. Wow great points! I did the numerical simulation with QMSolve - they have other interesting simulations as well!
    4
  272. Thanks for watching!
    4
  273. Wow thank you for the kind words 😢
    4
  274. More of a prequel!
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  275. Yo! https://www.premiumbeat.com/royalty-free-tracks/dark-eyes-gypsy-jazz https://www.premiumbeat.com/royalty-free-tracks/supernatural https://www.premiumbeat.com/royalty-free-tracks/language-2
    4
  276. ugh I know - working on it, I promise!
    4
  277. Awesome, thanks for watching!
    4
  278. Hey Blake, thanks for watching - yeah, this was my first series, there's definitely a lot I could have done better - and I agree, this is definitely not a highschool friendly tutorial.
    4
  279. Thank you!
    4
  280. working on it!
    4
  281. Woohoo!
    4
  282. Fun question! I don't know - but I do like the name red numbers more than logarithms.
    4
  283. VPython
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  284. I know right!
    4
  285. Combination of buying old books and printing on old looking paper.
    4
  286. Really crappy VPython code I wrote.
    4
  287. Thanks for watching!
    4
  288. Woah. That's a long time. Thanks for watching.
    3
  289. +ehfo0 Use the " %pylab inline" or "%matplotlib inline" command before your code (in the ipython notebook!)
    3
  290. Damn! I can't believe I missed this! I really need to do some type of peer review on the next series.
    3
  291. Good question - it does! I didn't have time to fully address this here unfortunately.
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  292. Sorry about that - can't believe I missed it!
    3
  293. Great question - I've omitted the biases here for a couple reasons. 1. I wanted to eliminate everything that wasn't necessary to understanding the fundamentals. 2. Once you understand the fundamentals, implementing biases is pretty easy. For a similar implementation, with biases, check out: https://github.com/stephencwelch/Neural-Networks-For-Audio-Processing. Thanks!
    3
  294. Sorry?
    3
  295. Awesome, thank you!
    3
  296. Awesome, thank you!
    3
  297. Hahahaha
    3
  298. Good question - it's more about combining different combinations of weights. Thanks for watching!
    3
  299. Thanks for watching and for the kind words!
    3
  300. Thank you for watching and for the kind words.
    3
  301. Thanks for watching! I believe Quaternions were developed not to fill any gaps in algebra, but for specifically applications.
    3
  302. +Kyle McKenzie Thanks! I didn't test with Python 3 - thanks for pointing this out.
    3
  303. Thanks for watching!
    3
  304. ...compromises and writes songs about neural networks
    3
  305. +Vidwath Raj Yes - I think you only need to change dJdW2 and the cost function. Good luck!
    3
  306. Hi Alexander, this is on my to-do list! I should have all my code for this project available by the end of the year. Thanks!
    3
  307. Code is now available - linked in description, thanks!
    3
  308. Woohoo!
    3
  309. Thanks for watching and for the kind words! Stay tuned for a Patreon campaign later this year.
    3
  310. seriously bombelli
    3
  311. Good question! Technically it's a "double root", which, I promise, is less of a BS answer than it sounds.
    3
  312. Excellent point - I'm planning on publishing supporting code on Jan 1, but in the mean time:      def costFunction(self, X, y):         #Compute cost for given X,y, use weights already stored in class.         self.yHat = self.forward(X)         J = 0.5*sum((y-self.yHat)**2)         return J
    3
  313. Man, I've said it wrong all these years!
    3
  314. Thanks for watching! Decided to leave them out for simplicity.
    3
  315. Yup. I realized this right after releasing!
    3
  316. Hi Joseph, thanks for the kind words! I did have an error in my notebook, which I have just fixed, thanks so much for pointing this out, although I believe it's backwards form the way you've worded it.   According to David Mackay's Information Theory, Inference and Learning Algorithms book, activations are what goes into our activation functions, and activities are what comes out. So in this case a3 is an activity, and z3 is an activation. To make this more confusing, Mackay uses a to denote activation, rather than activity.  So, I think I've got this correct, but definitely let me know if this is not the case, thank you!
    3
  317. Code is now available - linked in description, thanks!
    3
  318. Awesome - I am definitely feeling pulled in that way!
    3
  319. #OnlyOneHaterMadeItThisFarYet
    3
  320. That would be fun! I'l keep it in mind!
    3
  321. Took ALOT of practice, but it's totally worth it.
    3
  322. Cool!
    3
  323. :)
    3
  324. Blue show fingers, red shows not fingers. Thanks for watching!
    3
  325. Thank you, and thanks for watching!
    3
  326. Woohoo!
    3
  327. Cool, thanks for watching!
    3
  328. Yeah I think that’s the move! Basically doing some experiments as I get back into YT.
    3
  329. Thanks for watching! I think my code is a good place to go if 1) You want to dig deeper 2) Something I've said doesn't make sense.
    3
  330. Will get there at some point! Ping me here and I'll add you to the international waitlist! https://www.welchlabs.com/contact
    3
  331. Awesome, thanks for watching!
    3
  332. I know right! I wanted to include that.
    3
  333. Used Manim for the first time on this one for the 3d animations!
    3
  334. Thanks!
    3
  335. yeah they are hard to get intuitive feels for - I think the transformers distill thread is probably the best thing I've seen.
    3
  336. Cool!
    3
  337. Thanks so much - will look at international shipping in the future - but not quite yet - sorry!
    3
  338. yeah, that July. The one in January. :)
    3
  339. Thank you!
    3
  340. Awesome let me know how it goes!
    3
  341. Build something with it!
    3
  342. Thank you!
    3
  343. It does just barely in the northern states.
    3
  344. Thank you!
    3
  345. I have some on TikTok!
    3
  346. Great point - I'll cover a bit more on this in the final episode (6) - but at the end of the day it's definitely a bit subjective!
    3
  347. Thank you!
    3
  348. Thank you!
    3
  349. Great question! This is exactly why Babbage proposed building the difference engine in the early 1800s - because it's so difficult to rid these books of errors.
    3
  350. Correct!
    3
  351. lol
    3
  352. Thank you!
    3
  353. Thanks for watching!
    3
  354. Namaste
    3
  355. But what topic 🤔
    3
  356. confirmed :)
    3
  357. You don’t like your documents SIFIED?
    3
  358. I've just crossed checked that, and yes, excited does have a c in it.
    3
  359. Thanks for watching!
    3
  360. Hello, I think I used google scholar or google books if I remember correctly.
    3
  361. I know right!?
    3
  362. Thanks! Will do!
    3
  363. Working on it!
    3
  364. Thank you sir!
    2
  365. +Dennis Plotnik This allows us to sum across examples when we do matrix multiplication. Hope that helps!
    2
  366. +TheDiscoMole Computing the transpose is just one of solving this specific part of the problem. Check out: http://deeplearning.stanford.edu/wiki/index.php/Backpropagation_Algorithm for a more rigorous implementation. While the math is presented more rigorously, it should be identical to the implementation presented here (without the biases). Let me know if you find otherwise. Thanks!
    2
  367. Check out part 13!
    2
  368. Maybe try it on your end and let me know how it goes?
    2
  369. Awesome, you should make videos! Thanks for watching.
    2
  370. Thanks! Happy Gnawing!
    2
  371. Haha, awesome. I should do mail time.
    2
  372. Good call! I'll see what I can do.
    2
  373. Thank you!
    2
  374. Awesome! Thanks for watching.
    2
  375. Just that I would like him to make more videos!
    2
  376. Awesome, thanks for watching, and great job experimenting!
    2
  377. Awesome! Thanks for watching - best of luck!
    2
  378. WOOHOO!
    2
  379. Hey Martin, good points! Yeah, I think I'll make my editing a bit snappier in the next series.I've just released supporting code: https://github.com/stephencwelch/LearningToSee. 3blue1brown is great! Thanks for watching.
    2
  380. I will take that as a huge compliment. Thanks for watching!
    2
  381. Awesome! Thanks for watching!
    2
  382. +Kyle McKenzie Thank you! The norm function I'm using is: numpy.linalg.linalg.norm. Thanks!
    2
  383. Thank you!
    2
  384. That would be fun! I'll keep it in mind.
    2
  385. I highly recommend 3blue1brown! https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw
    2
  386. Thank you!
    2
  387. woohoo!
    2
  388. Thanks for watching!
    2
  389. Sure!
    2
  390. Because the Matrix.
    2
  391. That's a great question! I believe the answer is no, but at the moment I don't have a very good reason why. You could ask this question on Quora or dig into the convex optimization literature - Stephen Boyd's classes and books are a good place to start (http://stanford.edu/~boyd/) - please share if you find a good answer!
    2
  392. That would be great! Hopefully one day.
    2
  393. Haha, thanks!
    2
  394. Appreciated! Thanks for watching!
    2
  395. Thank you!
    2
  396. Awesome! Thanks for watching!
    2
  397. Awesome, thanks for watching!
    2
  398. Thanks Daniel!
    2
  399. Wish I could say I planned that, just a happy accident though.
    2
  400. Ugh, way more than I thought! No sure yet, but at least 10. Brevity is unfortunately not one my strong suits.
    2
  401. Yeah, it ended up being WAY longer than I planned. There's just too much cool stuff to talk about.
    2
  402. Just to keep things simple!
    2
  403. Yes!
    2
  404. Jupyter notebook!
    2
  405. Meant to get to that last week, but that freaking final montage took way to long to edit - code should be available next week. Thanks for watching!
    2
  406. Hey Hunar, probably CNNs right now.
    2
  407. Thanks for watching!
    2
  408. Awesome, good luck!
    2
  409. Mostly Adobe Illustrator + In Design.
    2
  410. Thanks for watching!
    2
  411. Agreed!
    2
  412. Mostly Adobe Aftereffects and Cinema 4D.
    2
  413. Awesome, thanks for watching.
    2
  414. Thanks for watching!
    2
  415. Thank you!
    2
  416. FLAIR PENS! I have a serious addiction.
    2
  417. haha, yeah. But that would be kind of a boring series.
    2
  418. Thank you for watching and for the kind words!
    2
  419. jupyter notebook!
    2
  420. Great question - in a simple example, like the one presented here, the non-linear activation functions won't do that much. However as the number of layers and data becomes more complex, non-linear activation functions help give neural networks behavior that a linear model could not replicate. I haven't watched this series in a while, but the caltec ML lectures may go into more detail: https://work.caltech.edu/lectures.html Good luck!
    2
  421. Thanks!
    2
  422. Hahaha nope. Just trying to look like I knew what i was doing.
    2
  423. +Sanjaya Kumar Thank you! I'm working on the 3d graph explanation currently - should be out in the next few weeks!
    2
  424. https://github.com/stephencwelch/Imaginary-Numbers-Are-Real
    2
  425. Awesome, thanks for watching!
    2
  426. Really? Reference?
    2
  427. Thank you and thanks for watching!!
    2
  428. I tried vanilla gradient descent early on - seemed to complicate things unfortunately!
    2
  429. Interesting! I'll keep that in mind!
    2
  430. I wish I had done more CS and Math. I was an EE major.
    2
  431. Thanks!
    2
  432. https://www.premiumbeat.com/royalty_free_music/songs/language-2
    2
  433. Jupyter Notebook!
    2
  434. Awesome, thanks for watching!
    2
  435. +MOHSharpshooter You may want to look into the scale of the random numbers you're using to initialize your network. Have you tried the code I have on github? You could compare your results to it for different initializations. Thanks for watching!
    2
  436. Saw it! Thanks!
    2
  437. Awesome, thanks for watching!
    2
  438. you're welcome!
    2
  439. Sweet!
    2
  440. Thanks for watching! Any specific phrases/parts of the video you noticed this on? This is something I struggle with - striking the right balance between a "natural delivery" and clearly pronouncing everything.
    2
  441. Python! Mostly matplotlib. Thanks for watching!
    2
  442. Awesome - thank you!
    2
  443. http://www.premiumbeat.com/royalty_free_music/songs/language-2
    2
  444. Great question - this is going to sound like a BS answer, but it's got a "double" root at zero.
    2
  445. Thank you!
    2
  446. Thank you! Feel free to add your own subtitles!
    2
  447. jupyter notebook!
    2
  448. Aww man!
    2
  449. +gcgrabodan Thanks for watching and for the feedback. 1. Here I was just showing what a nueron does alone - you're right that we need to include weights - which I do later in the series for the whole network. 2. Great question - typically sigmoid parameters are not trained - it is possible to do so, but not very popular - we typically get better results by training weights, not sigmoid parameters. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.7016&rep=rep1&type=pdf 3. Yes! We need more data. I talk about this in parts 6 and 7. Thanks so much for watching and for the feedback!
    2
  450. Noted!
    2
  451. Nice
    2
  452. Yeah was going for historical accuracy!
    2
  453. Thank you!
    2
  454. Thanks!
    2
  455. Thank you!!
    2
  456. I would have completely agreed with you until I read Tom Mitchell's Machine learning while researching this series - specifically page 65.
    2
  457. Thank you!
    2
  458. Thanks! Leap Motion.
    2
  459. Thanks for watching!
    2
  460. Thank you!
    2
  461. Woohoo!
    2
  462. Thanks for watching!
    2
  463. Check out 3 blue 1 brown!
    2
  464. Thanks!
    2
  465. yeah!
    2
  466. I believe the Antikythera Mechanism effectively used the ptolemaic model. Would love to learn more about that.
    2
  467. Yep! I have light and dark versions :)
    2
  468. Great point! I'd love to include some further reading reference in the pdf - do you have any recommendations for this topic?
    2
  469. Thank you!!
    2
  470. Thank you!
    2
  471. I think it's from the 60s
    2
  472. Thanks for watching!
    2
  473. I think i used %pylab qt in the notebook to put the graph in an external window.
    2
  474. Lol was thinking the same thing when i did it wrong the first time and had to start over!
    2
  475. Thanks for watching!
    2
  476. Thanks for watching!
    2
  477. Google “Los Alamos reports” iirc this is 602
    2
  478. Ahhh yeah got catch
    2
  479. Thanks for watching!
    2
  480. Awesome, nice intuition!
    2
  481. Thanks for watching!
    2
  482. WOOHOO!
    2
  483. Thank you!
    2
  484. Haha nice
    2
  485. Finally catching up on these - such a nice progressive description of how these models work!
    2
  486. Interesting questions! I address these a little in part 6. Thanks for watching!w
    2
  487. Great idea - will put it on the list!
    2
  488. Thanks for watching!
    2
  489. Correct! Used illustrator for the “drawing over”
    2
  490. Will be back in stock by July 14!
    2
  491. Thank you!
    2
  492. Awesome thank so much!
    2
  493. Shade I think!
    2
  494. Awesome, thanks for watching!
    2
  495. nice
    2
  496. Thanks for watching!
    2
  497. Woohoo!
    2
  498. cinema 4d
    2
  499. Awesome! It's crazy how many great resources have come online since I made this!
    2
  500. Yup!
    2
  501. Will do my best
    2
  502. 🤗🤗🤗
    2
  503. Awesome thanks!
    2
  504. wohoo!
    2
  505. I am!!!!
    2
  506. If i remember correctly it's not always Ba and Kr.
    2
  507. Thanks, will do!
    2
  508. Wow, thanks!
    2
  509. 🤣
    2
  510. Reading list coming soon!
    2
  511. Thanks for watching! Georgia Tech + Berkeley. Go bearjackets!
    2
  512. haha awesome!
    2
  513. Right!
    2
  514. Thanks for watching!
    2
  515. There's some great references in the description! Good luck!
    2
  516. Haha awesome!
    2
  517. That's amazing!
    2
  518. Rhodes is the GOAT
    2
  519. Lol mostly true
    2
  520. Good Question!
    2
  521. Next Video release should be ~Dec 24.
    2
  522. Glad you enjoyed it!
    2
  523. Thank you! Will figure something out on that front!
    2
  524. That’s awesome thank you!!
    2
  525. gnossienne no. 1 by erik satie
    2
  526. Awesome thanks for watching!!
    2
  527. Wow, thank you!
    2
  528. Yes, good point. I'll have a look when I have a chance!
    2
  529. Thank you!
    2
  530. Girl from Osaka. Thanks for watching!
    2
  531. 3blue1brown is great! Thanks for watching.
    2
  532. I know right!
    2
  533. Wow - that's awesome. So glad I could be helpful.
    2
  534. It's the stupid heating system in my office - working on a solution. Thanks for watching!
    2
  535. Ran out time!
    2
  536. Printed them myself!
    2
  537. Working on it!
    2
  538. Thanks for watching!
    2
  539. Nice!
    2
  540. Thank you!
    2
  541. THank you!
    2
  542. Jupyter notebook! Thanks!
    2
  543. Thanks for watching!
    2
  544. Woohoo!
    2
  545. yeah, there turned out to be alot to say!
    2
  546. I think it’s just how my voice works
    2
  547. I know right!
    2
  548. Thanks for watching!
    2
  549. Crazy right?! I really want to explore the connection to the mathematics of relativity when I have time.
    2
  550. woohoo!
    2
  551. nice!
    2
  552. Thanks for watching!
    2
  553. Thank you!
    2
  554. Yeah, I realized this just as I was releasing this video. I've made a production note for next time. Sorry about that, and thanks for watching!
    2
  555. More on the way 😁
    2
  556. Haha sounds good
    2
  557. :)
    2
  558. I'll send your diploma.
    2
  559. Yup still in NC!
    2
  560. Thank you!
    2
  561. Fun Idea!
    2
  562. Thanks!
    2
  563. Hey what do you listen on? headphones? laptop speakers? Just curious - helps me optimize my mix.
    2
  564. More to come!
    2
  565. Wow, thanks for watching and for the kind words.
    2
  566. hahaha.
    2
  567. Awesome thanks for watching!
    2
  568. Woohoo!
    2
  569. Thanks for watching!
    2
  570. woohoo!
    2
  571. Awesome!
    2
  572. Good question! Uranium! But they didn’t have brought uranium to make multiple bombs.
    2
  573. Thanks for Watching Santosh!
    2
  574. That's an interesting point! One obvious difference is that the KV cache matrix is bigger than the original individual key and value matrices. It would be really interesting if MLA was equivalent to just collapsing the keys and values in traditional attention into a single larger matrix - I'm not sure if that's completely correct though - let me know if anyone has a good answer here!
    2
  575. Awesome, thanks for watching!
    2
  576. Thank you!
    2
  577. https://www.premiumbeat.com/royalty-free-tracks/among-the-hills
    2
  578. I need a pronunciation coach!
    2
  579. Same.
    2
  580. Good question!
    2
  581. Confirmed
    2
  582. Thanks for watching!
    2
  583. Thanks for watching!
    2
  584. Wow, thank you!
    2
  585. Thanks for watching!
    2
  586. Makes sense!
    2
  587. Glad you enjoyed it - getting the details right was a real pain! Especially the non uniform velocity of the moon around its orbit.
    2
  588. Thank you for the kind words and subsrcibing!
    2
  589. Haha, awesome. Thanks for watching!
    2
  590. yeah, this may have been a little overambitious...
    2
  591. Thanks for watching!
    2
  592. Thank you!
    2
  593. Thanks for watching!
    2
  594. Thank you!
    2
  595. Confirmed.
    2
  596. Thank for watching!
    2
  597. Thanks for watching!
    2
  598. lol - i should have used that for background music
    2
  599. That would be cool!
    2
  600. Yeah maybe I should slow down a little!
    2
  601. Yes.
    2
  602. :)
    2
  603. Thanks for watching! Noted.
    2
  604. Thank you!
    2
  605. Thanks for watching!
    2
  606. Thank you!
    2
  607. Thank you!
    2
  608. amazing!
    2
  609. Thanks! Yeah I love working on ending vibes.
    2
  610. What the heck?!
    2
  611. Awesome! Thank you!
    2
  612. Woohoo!
    2
  613. Bind them myself - wish I could buy them somewhere!
    2
  614. You are cool
    2
  615. woohoo!
    2
  616. lol
    2
  617. Thanks for watching!
    2
  618. Thank you for watching and for the kind words.
    2
  619. Yep my mistake!
    2
  620. Thanks for watching!
    2
  621. Thank you!
    2
  622. Thanks for watching!
    2
  623. Woah this is awesome! I think you win Ruben. Can I just "borrow" your google sheets for the next episode? :)
    2
  624. It goes a little fast at the end - I debated making the end longer, but struggled with an effective way to do it.
    2
  625. Coming super soon!
    2
  626. yes
    2
  627. Thanks for watching!
    2
  628. it goes hard right!?
    2
  629. Thank you!
    2
  630. 🤣
    2
  631. Haha fair.
    2
  632. Hmmm good question
    2
  633. lol. "let me just take the burgi of our value and..."
    2
  634. Thank you!
    2
  635. Thank you!
    2
  636. Good question!
    2
  637. Thanks! Sources in description.
    2
  638. Thanks for watching!
    2
  639. Thank you!
    2
  640. Awesome - I think you can watch in your browser without an account if you want!
    2
  641. Something like that I hope!
    2
  642. Definitely!
    2
  643. Woohoo!
    2
  644. yup, science = done. :)
    2
  645. Thank you!
    2
  646. Thanks for watching!
    2
  647. Great!
    2
  648. Glad you liked it!
    2
  649. Man I would love to
    2
  650. Wow awesome!
    2
  651. Yes that was one of my main sources!
    2
  652. Cool Idea! happy to be back!
    2
  653. It limits the model's confidence in any single answer.
    2
  654. Candy Heart
    2
  655. Awesome, thanks for watching!
    2
  656. Thanks for watching!
    2
  657. Thank you!
    2
  658. Let’s gooooo!
    2
  659. Thank you!
    2
  660. Thanks for watching!
    2
  661. New video this Saturday!!
    2
  662. Thanks for watching!
    2
  663. Woohoo!
    2
  664. Hired. :)
    2
  665. Awesome thank you for watching!
    2
  666. Woohoo!
    2
  667. :)
    2
  668. Thank you!
    2
  669. Amen!!
    2
  670. haha, thanks.
    2
  671. NICE
    2
  672. Should be next week - I'm doing status updates on Tiktok!
    2
  673. Thanks so much!
    2
  674. Haha awesome. Just heard 3blue1brown is making an FT video - should be awesome!
    2
  675. Glad it was helpful!
    2
  676. Wow, thank you!
    2
  677. I just learned that my pronunciation is less common! Hopefully not too distracting. https://english.stackexchange.com/questions/399942/how-do-you-pronounce-the-double-c-in-both-the-eccentricity-of-a-conic-section-an
    2
  678. Thanks! Fleisch's book was one of my main sources!!
    2
  679. :)
    2
  680. Didn’t originally plan that but worked out nicely!!
    2
  681. Confirmed
    2
  682. I think you're right!
    2
  683. Haha thanks!
    2
  684. Thanks!
    2
  685. Awesome!
    2
  686. I know right! It's like another dimension.
    2
  687. Thank you!
    2
  688. Awesome!
    2
  689. Woohoo!
    2
  690. Noted! Most of these videos do have Jupyter notebooks on by GitHub.
    2
  691. Thanks for watching!
    2
  692. Wow, thank you!
    2
  693. THAT BOOK IS DOPE.
    2
  694. Thanks to 3b1b for the referral, and thanks for watching!
    2
  695. Nope!
    2
  696. You're welcome!
    2
  697. Great question! I'm sure there are more relevant measurable quantities, but I'm not sure if the mathematical relationships would be as simple. I believe that stiffness for example introduces some non-linearity. Thanks for watching!
    2
  698. Thanks for watching! Math is better than chemistry anyway! ...but you should probably finish your chemistry.
    2
  699. Woohoo!!
    2
  700. Co-discoveries
    2
  701. Very cool!
    2
  702. Thank you!
    2
  703. I know right!?
    2
  704. woohoo!
    2
  705. Thanks for watching!
    2
  706. Thanks for watching!
    2
  707. Hey Scott!
    2
  708. Thanks for watching!
    2
  709. Thank you!
    2
  710. Not True!
    2
  711. I'm really excited for the movie!!
    2
  712. It’s from adobe stock - paywall :/
    2
  713. woohoo!
    1
  714. Agreed!
    1
  715. Thanks for watching! Should be out Saturday.
    1
  716. yeah...
    1
  717. Thank you!
    1
  718. Awesome, yes Stang is terrific!
    1
  719. Thank you for the kind words. I was trained in MATLAB as well, but have since (happily) made a full switch to python. The visualizations were made plotly.
    1
  720. Thank you!
    1
  721. Haha, i didn't think of that.
    1
  722. Good question! Sure, we could have stopped at brute force, but that method would not have scaled to bigger/harder/real problems.
    1
  723. Great questions! Hopefully I'll get to this in another series.
    1
  724. Awesome! Didn't even know this was possible. 
    1
  725. woohoo!
    1
  726. Calculus! :)
    1
  727. Thanks for the kind words.
    1
  728. hahaha awesome!
    1
  729. Check out part 13! Thanks for watching.
    1
  730. That's a hyperparameter that is up to the algorithm designer!
    1
  731. Thank you! Mostly just overhead time lapse images, and then I edit for timing.
    1
  732. Awesome, thank you!
    1
  733. Good point! I chose grids to be in line with the kind of data we would capture in most computer vision problems from a camera.
    1
  734. Wow, thank you!
    1
  735. Thanks for watching! Engineering.
    1
  736. Awesome, thanks for watching!
    1
  737. woah, cool!
    1
  738. Thanks for watching!
    1
  739. Thank you!
    1
  740. Me!
    1
  741. Aww man!
    1
  742. Thanks for watching!
    1
  743. Ouch!
    1
  744. Thanks for watching - I'm working on getting the code out soon!
    1
  745. Haha, thanks for watching!
    1
  746. Hell yeah indeed!
    1
  747. Awesome, thanks for watching!
    1
  748. Thanks for watching!
    1
  749. Agreed!
    1
  750. Thanks for watching, good catch!
    1
  751. HOW DID YOU KNOW?!?!?!?!
    1
  752. Thanks for watching! I highly recommend any book by Gilbert Strang on Linear Algebra.
    1
  753. Sounds amazing.
    1
  754. Woohoo!
    1
  755. Crazy right?!? Thanks for watching!
    1
  756. That's awesome! Thanks for watching!
    1
  757. Woohoo!
    1
  758. Holy crap. That's super humbling. Thank you for sharing and best of luck in your new endeavors.
    1
  759. Thanks for watching! Working on it, possible statistics or Euler's Formula.
    1
  760. As in "That tree is soooo lego!" ?
    1
  761. Thanks for watching!
    1
  762. Thanks for watching!
    1
  763. Working on parts 11 and 12 now! Thanks for watching!
    1
  764. Enjoy!
    1
  765. Thanks for watching!
    1
  766. Thank you!
    1
  767. Thanks for watching! Latin Modern Roman Italic
    1
  768. Thanks for watching!
    1
  769. Thank you!
    1
  770. Good question - it's more about putting all our different kinds of data on the same "normalized" scale.
    1
  771. Great question! We randomly initialize the weights, and later we train our network, allowing it to "learn" a better set of weights. There is a significant amount work that has been done on the way in which you should scale your random initializations, but that's a bit beyond the scope of this tutorial. Thanks!
    1
  772. Thanks for watching!
    1
  773. Awesome, thanks for watching!
    1
  774. Thanks for watching - I did make a real time version that I'm planning on sharing at some point - it works at like 3 fps on my old macbook.
    1
  775. Good question - we can't really measure precision for the baseline approach, but it's accuracy and recall are similar for our training and testing sets, meaning that it generalized beyond the training set.
    1
  776. Wow, thank you for your kind words! That's really great to hear.
    1
  777. Sleep = overrated.
    1
  778. awww man!
    1
  779. Awesome, thanks for watching!
    1
  780. Awesome! Thanks for watching!
    1
  781. Thanks!
    1
  782. Your welcome!
    1
  783. I like your definition too!
    1
  784. Thanks for watching!
    1
  785. good call on the XOR - I didn't think of that.
    1
  786. Working on it :)
    1
  787. Sounds fun! But gosh, how many freaking episodes would that take me..."Last time, in part 234..."
    1
  788. GREAT QUESTION! Not a coincidence. If you play around with the equations for the the real and imaginary parts of the function, I think you'll see why. Thanks for watching!
    1
  789. Woohoo!
    1
  790. Awesome, thanks for watching!
    1
  791. yeah, I'm hoping to get to some of these great questions in the next series. Thanks!
    1
  792. Woohoo!
    1
  793. Yeah, i was torn between blazing new trails and fitting in with the lexicon. Thanks for watching!
    1
  794. Wow, thanks for watching!
    1
  795. Aw man!
    1
  796. Thanks for watching!
    1
  797. thanks.
    1
  798. Woohoo!
    1
  799. Thanks!
    1
  800. Come back! :)
    1
  801. Gauss suggested "direct" for positive, and "inverse" for negative.
    1
  802. http://www.premiumbeat.com/royalty_free_music/songs/language-2
    1
  803. Hi Mario! Thanks for watching. You are correct, we could write 1<-120º or 1<240º, these are equivalent. We could also write 1<480º, or even 1<120º +/- 360k, where k is an integer. There's no universally preferred way to write these answers.
    1
  804. You got it!
    1
  805. I know! I'm a monster!
    1
  806. Yeah, there's a little handwaving going on there - these aren't quite the same bits as information storage bits. Check out David Mackay's book for a nice explanation! http://www.inference.phy.cam.ac.uk/itprnn/book.html
    1
  807. Thanks!
    1
  808. Thank you for watching this video!
    1
  809. Woohoo!
    1
  810. Thank you!
    1
  811. Awesome!
    1
  812. Thank you!
    1
  813. woohoo!
    1
  814. 1. Thank you! 2. Do it! Just get started!
    1
  815. Noted!
    1
  816. Agreed about Gauss! Thanks for watching.
    1
  817. Thanks for watching!
    1
  818. +dearaerin Thanks for watching! y and yHat are actually numpy two dimensional arrays - which are a bit different than numpy matrices.
    1
  819. Woohoo!
    1
  820. Yeah! Internet videos!
    1
  821. You would either need to 1. Normalize your output values first. 2. Use a different function. Thanks for subscribing!
    1
  822. For real.
    1
  823. Haha that would get INTENSE! But definitely interesting!
    1
  824. Oachkatzlan Schwoaf Great question - delta 3 is a 3 by 1 scalar, with one entry corresponding the each input example. Delta 3 is our backpropagating error, so it should make sense that we have one value error for each example. In this way, the error from each individual training example can be used to update the weights and train the network. The multiplication we perform in this step is scalar or element-wise. Hope this helps!
    1
  825. +JeevanAnand Anne Great question - I left the bias units out for the sake of simplicity. The tutorials from Andrew Ng are wonderful and include bias: http://ufldl.stanford.edu/wiki/index.php/Neural_Networks Thanks!
    1
  826. Hi Doug, I'm using the iPython notebook - by far my favorite way to do scientific programming. http://ipython.org/notebook.html
    1
  827. Awesome! Thanks for watching!
    1
  828. Awesome, thanks for watching!
    1
  829. Thank you!
    1
  830. Wow - thank you!
    1
  831. Haha, crap! I promise it is!
    1
  832. Thanks for watching!
    1
  833. Thanks! The wikipedia on AI is a great place to start!
    1
  834. https://www.premiumbeat.com/royalty_free_music/songs/benny-s-clarinet?auto thanks for watching!
    1
  835. woohoo!
    1
  836. Woah, that's a lot of thank you. 1000^(your welcome)!
    1
  837. Thanks for watching!
    1
  838. I think numpy.
    1
  839. Thank you!
    1
  840. Awesome, thanks for watching!
    1
  841. Thanks for watching!
    1
  842. Thanks for watching!
    1
  843. Maybe a future video!
    1
  844. Thanks for watching!
    1
  845. https://github.com/stephencwelch/LearningToSee
    1
  846. I'm sorry, I'm really not an expert on RBFs or Java. Best of luck!
    1
  847. Awesome, thanks for watching!
    1
  848. EPR?
    1
  849. :)
    1
  850. I'll put it on github tomorrow! https://github.com/stephencwelch/LearningToSee
    1
  851. You're very kind. Thank you.
    1
  852. Thanks for watching! Stay Tuned for a Patreon later this year.
    1
  853. Thanks for watching!
    1
  854. Oh no!
    1
  855. I just the jupyter notebook. And anaconda python.
    1
  856. Thank you for watching!
    1
  857. Jupyter notebook!
    1
  858. That would be cool! I'll keep that in mind
    1
  859. Thanks for watching! Quantum Mechanics would be a blast - maybe one day!
    1
  860. Thanks for watching!
    1
  861. I know! Working on it!
    1
  862. Awesome - thank you!
    1
  863. Thanks for watching! I believe you can put a monthly limit on your donations.
    1
  864. Wow, thanks!
    1
  865. Cool question!
    1
  866. Wow, thanks for watching!
    1
  867. Stay tuned!
    1
  868. Good Catch, yes there's an error in my table. I've added this to the description.
    1
  869. nice catch!
    1
  870. On my to-do list!
    1
  871. Thanks for watching! I believe this is scalar multiplication, but it might be worth verifying!
    1
  872. Agreed!
    1
  873. Woohoo!
    1
  874. Woohoo!
    1
  875. Thanks for watching!
    1
  876. I really wanted to get to this, but ran out of time! Maybe in a future series?
    1
  877. I'll make some specific recommendations in the next video on January 7. Thanks for watching!
    1
  878. hahaha - yes!
    1
  879. Thanks for watching! Hope you ate breakfast! it's the most important meal of the day.
    1
  880. yeah!
    1
  881. Great!
    1
  882. Thank you and thanks for watching!
    1
  883. +Frank Christiansen Thanks! Yes, there are lots of good intros to iPython notebook out there - I would start there, and come back to these after you're comfortable with basic iPython notebook workflow. You can fix your error by adding "import numpy as np" to your code. Should work fine on Windows 10. Good luck!
    1
  884. One day when I have more time! but not yet unfortunately :/
    1
  885. Interesting stuff, and good questions - thanks for watching!
    1
  886. I think 3blue1brown is about to come out with a really good calculus series!
    1
  887. Thank you!
    1
  888. Hahaha, good call! :)
    1
  889. Haha, thanks.
    1
  890. Not that I know of, but I hope someone makes one!
    1
  891. Thanks for watching!
    1
  892. Thanks for watching - I'm going to try to include more reference material in the next series!
    1
  893. Awesome! You're way ahead of me at your age - way to go!
    1
  894. I'm sorry I don't know arabic, but if your interested in translating, that would wonderful! Just click the gear icon!
    1
  895. Interesting question!
    1
  896. Awesome, thank you!
    1
  897. +Ahmad Al-Benali I agree! I talk about this in more detail in my blog post: http://www.welchlabs.com/blog/2015/9/4/imaginary-numbers-are-real-part-2-a-little-history It seems like Del Ferro just got lucky here, and found a solution that works sometimes. None of my sources really explain this, and I haven't found any that do. Let me know if you find anything I missed. Thanks!
    1
  898. Thank you!
    1
  899. At least it wasn't a real table!
    1
  900. Thanks for watching!
    1
  901. Your welcome! Thanks for watching!
    1
  902. Awesome, thanks!
    1
  903. Convert -i into polar (1<-90 degrees), and then take the square root! I think I do this in the book.
    1
  904. +Aniekan Umoren 2.x
    1
  905. Hahaha good call.
    1
  906. Awesome, thank you!
    1
  907. Woah - really good question! I don't know! Let me know if you figure it out.
    1
  908. Thanks!
    1
  909. Definitely!
    1
  910. aw man!
    1
  911. Aw man!
    1
  912. Thanks!
    1
  913. Hey Evyatar - we're splitting each time we want to add another pixel to our rule. Thanks for watching!
    1
  914. Thanks for watching!
    1
  915. Thanks for watching!
    1
  916. Good question - I try to touch on these questions in the series - for a deeper dive, check out: https://www.amazon.com/Imaginary-Tale-Princeton-Science-Library/dp/0691169241
    1
  917. Wow - thank you!
    1
  918. damn!
    1
  919. I'm hoping the new series has some intersection with that work! Thanks for watching.
    1
  920. Thanks!
    1
  921. Working on it, sorry for the delay!
    1
  922. Thanks for watching!
    1
  923. +fl645 Yeah, the music is a bit too loud on these early videos. I can provide a dropbox link to versions with lower music we've been using a conferences if you would like. Just send me a message with your email address, and I'll send over the link. Thanks for watching.
    1
  924. Great Question!
    1
  925. Thank you!
    1
  926. Googling Alexander Alexandrovich Antonov...found ...The astrophysical phenomenon of dark matter and dark energy proves the existence of the hidden Multiverse.
    1
  927. Thanks for watching! The Jupyter notebook.
    1
  928. Awesome, thanks for watching, and good points!
    1
  929. +Ross Boyd Great idea, I'll see if I can integrate these with future videos.
    1
  930. Thanks!
    1
  931. Sure, it's just with Knowledge engineering, we choose what fingers look like, where with the first ML approach, we let the data decide. Thanks for watching!
    1
  932. Haha, yeah - I was wondering if anyone would notice. Turns out my level-arm paper cutter thing is really sharp. Thanks for watching!
    1
  933. https://www.premiumbeat.com/royalty_free_music/songs/language-2
    1
  934. Thank you!
    1
  935. ff17x3 Thanks! The * does do element wise multiplication, I could have also used np.mulitply. I never really liked the way that numpy syntax worked. Thanks!
    1
  936. Awesome, thanks for watching!
    1
  937. :)
    1
  938. Woohoo!
    1
  939. +TheRipler Good question! I'm not sure - my main source here (An Imaginary Tale, by Nahin), only says "public contests".
    1
  940. 3blue1brown!
    1
  941. Hey Phillip - someone directed me to your work after I created this series - looks like you really pioneered the approach to complex function visualization I show here. Good stuff!
    1
  942. It's all on github - https://github.com/stephencwelch/Neural-Networks-Demysitifed Fork away!
    1
  943. I was thinking as all rules we can form from ands, ors, and nots.
    1
  944. Thank you for watching!
    1
  945. Haha, awesome. Thanks for watching.
    1
  946. Awesome, thanks for watching!
    1
  947. Sorry to here that! I try to build things up more carefully in my new material. Thanks for watching!
    1
  948. Thank you!
    1
  949. Yes!
    1
  950. print 'Thanks for watching!'
    1
  951. I guess that's better than understand and don't understand.
    1
  952. Wow, thank you!
    1
  953. God luck!
    1
  954. Wow, thank you!
    1
  955. Thanks for watching!
    1
  956. Thank you!
    1
  957. CRAP!
    1
  958. The Juypter Notebook. Thanks for watching!
    1
  959. Woah, thanks!
    1
  960. Didn't have time for this unfortunately - it's super heuristic based - https://github.com/stephencwelch/LearningToSee
    1
  961. Awesome!
    1
  962. Haha, that would have been funny. Thanks for watching!
    1
  963. Thank you!
    1
  964. https://github.com/stephencwelch/LearningToSee
    1
  965. Simply because a positive time a positive is defined to be positive. Thanks for watching!
    1
  966. I'm getting alot of requests for this - it could definitely be really cool!
    1
  967. You're welcome!
    1
  968. Thank you! Mathematica -> Cinema 4d -> after effects -> premiere.
    1
  969. Uh, thanks.
    1
  970. Word.
    1
  971. Yup! That's what I use professionally and to make these videos - highly recommend!
    1
  972. Thanks for watching!
    1
  973. Safety factor of 1.6 is reported in the paper - see reference! I feel that’s pretty close regardless of log/linear.
    1
  974. 3blue1brown!
    1
  975. :)
    1
  976. Thank you!
    1
  977. plotly!
    1
  978. Thanks for watching! https://www.patreon.com/welchlabs
    1
  979. 🤯
    1
  980. Wow, thank you!
    1
  981. #dedication 🤣
    1
  982. I've thought it would be fun to make and sell a small set -> if you're serious email me at stephen@welchlabs.com
    1
  983. Thanks for watching!
    1
  984. So close!
    1
  985. Woot!
    1
  986. Thanks!
    1
  987. Haha, thanks!
    1
  988. yeah, that really worked out nicely!
    1
  989. Thanks for watching!
    1
  990. You never know, the series could take a murderous turn...
    1
  991. Thanks for watching!
    1
  992. Awesome!
    1
  993. Thanks for watching!
    1
  994. Thanks for watching!
    1
  995. Thanks for watching!
    1
  996. Thank you!
    1
  997. awesome!
    1
  998. Thanks for watching!
    1
  999. For this series, I think just numpy and maybe opencv.
    1
  1000. woohoo!
    1
  1001. Check out note 2 in the pdf: http://www.welchlabs.com/guides
    1
  1002. Awesome!
    1
  1003. Ebay!
    1
  1004. Thanks for watching!
    1
  1005. Hurray!
    1
  1006. Amazing thanks for the info - that really is helpful.
    1
  1007. haha awesome
    1
  1008. Thanks for watching!
    1
  1009. Awesome!
    1
  1010. Awesome!
    1
  1011. Didn’t plan originally to line up with Oppenheimer, but realized it was probably a good idea a few months ago.
    1
  1012. me too!
    1
  1013. What are you listening on exactly? Will help me optimize my mix.
    1
  1014. Yeah boi! Now i just need to actually understand it...
    1
  1015. Yup!
    1
  1016. Great!
    1
  1017. Thank you!
    1
  1018. https://github.com/stephencwelch/Neural-Networks-Demystified
    1
  1019. Woohoo!
    1
  1020. Awesome!
    1
  1021. Thank you!
    1
  1022. Thanks - source please!
    1
  1023. Thank you!
    1
  1024. Thank you!
    1
  1025. Thanks!
    1
  1026. Much appreciated!
    1
  1027. Thanks for watching!
    1
  1028. Crap!
    1
  1029. yeah...
    1
  1030. Thank you!
    1
  1031. Hey Igor - I highly recommend 1) An Imaginary Tale by Nahin 2) Visual Complex Analysis by Needham.
    1
  1032. Thank you!
    1
  1033. Adding to my future topic idea list!
    1
  1034. It really feels like it, right?! But I promise, it's not.
    1
  1035. Haha wut
    1
  1036. Good catch, I didn't have time for this in this video - just added a little footnote.
    1
  1037. But how would it be mapped?!?!
    1
  1038. Stay tuned :)
    1
  1039. Fart
    1
  1040. Yeah didn’t quite have time for that rabbit hole!
    1
  1041. Good call - didn’t hear it that when I wrote it! Maybe “gather for Christmas” alone would have been better.
    1
  1042. Ah just as a I planned :)
    1
  1043. Woohoo!
    1
  1044. Just caught up on subtitle approvals - did you send through the youtube system?
    1
  1045. I know right - happy to be back.
    1
  1046. Thanks for watching!
    1
  1047. Thank you1
    1
  1048. Did I say the wrong number of zeros?
    1
  1049. Thank you!
    1
  1050. sqrt(2)/2 + i * sqrt(2)/2
    1
  1051. Hahaha!
    1
  1052. Thank you!
    1
  1053. Alright will see what I can do!
    1
  1054. Ah man
    1
  1055. NOICE
    1
  1056. 😢
    1
  1057. Thank you!
    1
  1058. Thank you
    1
  1059. Thanks for watching!
    1
  1060. hmmm, good point.
    1
  1061. Thank you!
    1
  1062. Big
    1
  1063. Yeah it didn't totally "turn off" as expected, just reduced.
    1
  1064. Thank you!
    1
  1065. Thanks for watching! I don't recall all the details - but I believe my source for this section is Paul Nahin's an imaginary tale.
    1
  1066. Thanks for watching!
    1
  1067. Awesome - what about tensions? :)
    1
  1068. haha - alot.
    1
  1069. Yeah, that's a little subjective - check out note two in the pdf: http://www.welchlabs.com/guides
    1
  1070. Thank you! Love Rhodes!
    1
  1071. Thanks for watching!
    1
  1072. Working on a reading list video!
    1
  1073. Thanks for watching!
    1
  1074. All Welch’s Welcome.
    1
  1075. Woohoo!
    1
  1076. Alison Young who let you guys on here? :)
    1
  1077. Awesome, thanks for watching!
    1
  1078. Thanks for watching!
    1
  1079. Thank you!
    1
  1080. Woohoo!
    1
  1081. Haha hype it
    1
  1082. Awesome!
    1
  1083. Thanks for watching!
    1
  1084. Awesome thank you!
    1
  1085. Thank you!
    1
  1086. Thats incredible thanks for the comment!
    1
  1087. Glad you enjoyed it!
    1
  1088. I've been reading that book off-and-on my myself. I'm definitely exciting to continue in this vein of mathematics, but it may take me some time. Thanks for watching!
    1
  1089. Thank you!
    1
  1090. Glad you liked it!
    1
  1091. Wow, thank you for watching and for supporting the channel!
    1
  1092. Thanks for watching - I recommend checking out https://www.amazon.com/Imaginary-Tale-Princeton-Science-Library/dp/0691169241
    1
  1093. Thanks for watching!
    1
  1094. Thank you!
    1
  1095. Thank you!!!
    1
  1096. Thanks!
    1
  1097. Thanks for watching!
    1
  1098. They didn’t think they could make enough uranium
    1
  1099. awesome!
    1
  1100. Cool!
    1
  1101. Thank you!
    1
  1102. Thanks for watching!
    1
  1103. Thank you!
    1
  1104. I know right!?
    1
  1105. Very fast
    1
  1106. word.
    1
  1107. Hmmm good question not sure!
    1
  1108. Thank you!!
    1
  1109. Thanks!
    1
  1110. Yayyy!
    1
  1111. Стас Бицько word!
    1
  1112. Thanks for watching!
    1
  1113. Good eye! I put a note about this in the description.
    1
  1114. Glad you enjoyed it!
    1
  1115. :)
    1
  1116. Woohoo!
    1
  1117. Deal.
    1
  1118. I know! I'm made some good progress on the next series - but I'm not there yet!
    1
  1119. Jupyter Notebook!
    1
  1120. Thanks for watching and for the kind words.
    1
  1121. Awesome thank you
    1
  1122. Negative
    1
  1123. Nice! Hard to play?
    1
  1124. Interesting right?
    1
  1125. Thanks for watching!
    1
  1126. Thanks for watching!
    1
  1127. Wow, thanks for watching!
    1
  1128. hmm good question!
    1
  1129. Adobe Premiere - thanks for watching!
    1
  1130. Haha wut
    1
  1131. Yeah, this video definitely crams a lot of calc into a short time period.
    1
  1132. Thanks!
    1
  1133. Thanks!
    1
  1134. :)
    1
  1135. Yeah we don't have any illustrations of him - so seemed like a good option.
    1
  1136. Not familiar with this will check it out!
    1
  1137. https://www.premiumbeat.com/royalty-free-tracks/language-2
    1
  1138. I know, lame! Working on it...
    1
  1139. Thanks for watching!
    1
  1140. Good point! The complex plane is useful for more than visualization - hopefully the next few episodes will clear this up!
    1
  1141. 🤞
    1
  1142. lol just posted errata in description.
    1
  1143. Sweet!
    1
  1144. Thanks for watching! I just used illustrator & premiere.
    1
  1145. I have a EE degree too -> yeah no one taught me this either!
    1
  1146. Thank you!
    1
  1147. Awesome!
    1
  1148. Thanks for watching!
    1
  1149. Happy to be back, thanks for watching!
    1
  1150. Woah, cool! Please do.
    1
  1151. Complex Analysis. Thanks for watching!
    1
  1152. woohoo!
    1
  1153. Thank you!
    1
  1154. Thank you!
    1
  1155. Thanks!
    1
  1156. Thanks for watching!
    1
  1157. Glad you liked it!
    1
  1158. Check out 3 blue 1 brown!
    1
  1159. ...yeah, what's that guys problem?
    1
  1160. Thanks for watching!
    1
  1161. Thanks for watching!
    1
  1162. Thanks!
    1
  1163. Wow thanks for watching!
    1
  1164. Cool idea!
    1
  1165. Thank you!
    1
  1166. Yeah, took me a while to get to this...you gotta go all the way to part 13!
    1
  1167. Yep just not for plutonium
    1
  1168. Me too!
    1
  1169. Thanks for watching!
    1
  1170. Woah - cool!
    1
  1171. IKEA!!
    1
  1172. Good Question! Usually you make an educated guess and then tune from there.
    1
  1173. Thank you!
    1
  1174. Thanks for watching!
    1
  1175. Thank you!
    1
  1176. Thanks for watching!
    1
  1177. Check out the description for references, best is probably: https://transformer-circuits.pub/
    1
  1178. Thank you!
    1
  1179. Thank you!
    1
  1180. Thank you!
    1
  1181. thanks for the vote of confidence!
    1
  1182. wow - thanks for watching!
    1
  1183. Glad you enjoyed it!
    1
  1184. Same!
    1
  1185. Wow, thank you!
    1
  1186. That's awesome!
    1
  1187. Should be up now - just tested.
    1
  1188. Nice!
    1
  1189. Same question!
    1
  1190. Thanks!
    1
  1191. Haha thanks!
    1
  1192. Thanks for watching!
    1
  1193. Thank you!
    1
  1194. Thank you!
    1
  1195. woohoo!
    1
  1196. Fairwell!
    1
  1197. Haha sounds good! 🤣
    1
  1198. Lots of great points here. I struggle with a few of these myself while writing. I definitely cannot prove your argument wrong, and I wasn't 100% convinced by Shashua's argument. However, after my research, as I say in the video, I don't believe that we're going to see production end-to-end any time soon, and maybe ever. I just don't believe that current deep learning techniques are going to scale that well with data. But, I could definitely be wrong! Thanks for watching + commenting, i'm happy to start a conversation about this stuff, I think it's important to talk about at SDCs become a reality.
    1
  1199. Sweet!
    1
  1200. Awesome!
    1
  1201. yeah, spelling = hard.
    1
  1202. Thanks for watching!
    1
  1203. Thank you!
    1
  1204. Thanks!
    1
  1205. Thank you!
    1
  1206. Thanks!
    1
  1207. Thanks for watching!
    1
  1208. THank you!
    1
  1209. Glad it was helpful!
    1
  1210. Thanks for watching!
    1
  1211. Another good question!
    1
  1212. Thanks for watching!
    1
  1213. Just an ikea countertop! I kinda like the character it adds.
    1
  1214. Working on it!
    1
  1215. Thanks for watching!
    1
  1216. Right! It takes me a while to resolve this - I think episode 13. :)
    1
  1217. :)
    1
  1218. Why thank you. It was a wedding gift.
    1
  1219. Thanks for watching!
    1
  1220. Thanks!
    1
  1221. Thanks so much!
    1
  1222. How's your homework going? :)
    1
  1223. Thank you!
    1
  1224. :)
    1
  1225. Thanks!
    1
  1226. Thanks you!
    1
  1227. Awesome thank you!
    1
  1228. Glad you enjoyed it!
    1
  1229. Glad you enjoyed it!
    1
  1230. Ahhhhh
    1
  1231. No specific reasoning - typically you have to experiment with hyperparameters like this!
    1
  1232. Thank you!
    1
  1233. Thanks!
    1
  1234. Thank you!
    1
  1235. Thanks for watching!
    1
  1236. Thanks for watching and for the kind words. It did take FOREVER.
    1
  1237. you can leave it blank!
    1
  1238. Totally
    1
  1239. That’s a great question - I didn’t find a good answer in my reading - beat account I’ve found is I’m the book critical assembly.
    1
  1240. Reading list coming soon!
    1
  1241. Thanks for watching!
    1
  1242. Thanks!
    1
  1243. Thank you!
    1
  1244. Thank you!
    1
  1245. Do it!
    1
  1246. Thank you! Cheers!
    1
  1247. Wow, thanks for watching!
    1
  1248. Thanks for watching!
    1
  1249. Thanks for watching!
    1
  1250. Woohoo!
    1
  1251. Haha thanks, glad someone noticed!
    1
  1252. Thanks for watching!
    1
  1253. Thank you1
    1
  1254. woohoo!
    1
  1255. Alright will see what I can do!
    1
  1256. Sweet.
    1
  1257. happy (late) birthday!
    1
  1258. Yeah wanted to include this but it didn’t fit - so crazy!!
    1
  1259. YES
    1
  1260. lol
    1
  1261. Haha actually yes!
    1
  1262. Rings a bell...
    1
  1263. Awesome thank you!
    1
  1264. Thanks for watching!
    1
  1265. Awesome, thanks for watching!
    1
  1266. Thanks!
    1
  1267. Welcome aboard!
    1
  1268. python, plotly, mathematica, cimena 4d, premiere pro.
    1
  1269. I’m back!
    1
  1270. Thanks for watching! Would you mind providing a source?
    1
  1271. Thank you!
    1
  1272. Thank you!
    1
  1273. Thanks for watching!
    1
  1274. Awesome thank you!
    1
  1275. Thanks for watching!
    1
  1276. Haha thanks!!
    1
  1277. yeah bro.
    1
  1278. Thanks for watching!
    1
  1279. Yeah he’s a really interesting charecter!
    1
  1280. :)
    1
  1281. Woohoo!
    1
  1282. Thanks for watching!
    1
  1283. Thanks for watching!
    1
  1284. Noted!
    1
  1285. That would be a bummer! Let me try a different title here…
    1
  1286. Awesome
    1
  1287. Jupyter Notebook + Adobe Premiere. Thanks for watching!
    1
  1288. You don't need permission, just approval after you translate!
    1
  1289. Woot!
    1
  1290. Yeah I love the look!
    1
  1291. 🤣
    1
  1292. Noted!
    1
  1293. Awesome!
    1
  1294. I was wondering the same thing - anthropic folks may have tried this
    1
  1295. Thanks!
    1
  1296. Thank you!
    1
  1297. What device are you playing on? Always trying to optimize my levels.
    1
  1298. 🥰
    1
  1299. Thank you!
    1
  1300. Thanks Adam!
    1
  1301. What?! :)
    1
  1302. Thanks!
    1
  1303. Thanks!
    1
  1304. I hope so too!
    1
  1305. Amazing thank you - hope you enjoy it!
    1
  1306. Haha thanks!
    1
  1307. usually i start from the author's repo or hugging face, and then take things apart step by step in jupyter notebooks - good luck!
    1
  1308. Might keep using it - I kinda like the charecter
    1
  1309. Lola!
    1
  1310. Thank you!
    1
  1311. Thanks for watching!
    1
  1312. :)
    1
  1313. That's ok!
    1
  1314. Thanks for watching!
    1
  1315. http://www.welchlabs.com/imaginarynumbersbook
    1
  1316. Thanks for watching!
    1
  1317. Thank you!
    1
  1318. Nice
    1
  1319. Awesome!
    1
  1320. That or the linear algebra!
    1
  1321. cool!
    1
  1322. THANKS!
    1
  1323. Working on it!
    1
  1324. Woah, cool! Thanks for watching/appreciating!
    1
  1325. I know right!
    1
  1326. Nice!
    1
  1327. Woohoo!
    1
  1328. Thanks for watching!
    1
  1329. agreed!
    1
  1330. Right!
    1
  1331. Thanks!
    1
  1332. Yessssss
    1
  1333. Yes!
    1
  1334. Thanks for watching!
    1
  1335. Thank you!
    1
  1336. Thanks for watching!
    1
  1337. Thanks for watching!
    1
  1338. Thanks for watching!
    1
  1339. Thank you!
    1
  1340. Thanks for watching!
    1
  1341. Great question - If I remember correctly, I believe that is this simple case (single layer, regression) it is - however for most neural networks this is definitely not true!
    1
  1342. Thanks!
    1
  1343. Wow - thank you for watching and for the kind words.
    1
  1344. They didn’t think they could make enough uranium
    1
  1345. wow, thanks!
    1
  1346. Thank you!
    1
  1347. Thanks!
    1
  1348. I know right!?
    1
  1349. Haha thank you!
    1
  1350. Awesome thanks for watching!
    1
  1351. NOICE
    1
  1352. Thank you!
    1
  1353. I did! Cutting out all those scraps of paper is dangerous!
    1
  1354. 😛
    1
  1355. That's amazing!!!
    1
  1356. Thank you!
    1
  1357. Thanks for watching! Language by Marvels on Mars.
    1
  1358. Where did you get your copy?
    1
  1359. Agreed!
    1
  1360. Thanks for watching!
    1
  1361. Woohoo!
    1
  1362. Woohoo!
    1
  1363. That's where I got the idea! :)
    1
  1364. :)
    1
  1365. Wait is only the UP called northern?
    1
  1366. Thanks for watching!
    1
  1367. Awesome!
    1
  1368. Agreed! Thanks for watching!
    1
  1369. it is?
    1
  1370. Thanks for your interest. Unfortunately shipping internationally is just too expensive right now - I recommend downloading the printable version. Thanks!
    1
  1371. Thanks 💯
    1
  1372. Haha yep
    1
  1373. Yeah i go kinda fast! If you want more chill pacing check out the book "The Daring Invention of Logarithms" -> it's great!
    1
  1374. Thanks for watching!
    1
  1375. Not sure!
    1
  1376. Thank you!
    1
  1377. Thanks!
    1
  1378. Thanks for watching!
    1
  1379. Woohoo! Thanks for watching!
    1
  1380. Thanks!
    1
  1381. Amazing! Best of luck on your journey!!
    1
  1382. Thanks for watching!
    1
  1383. Welcome!
    1
  1384. Hey Thomas - great point - yeah, I considered using more nuanced distinctions here, but I couldn't quite make it work while keeping things as simple as I wanted.
    1
  1385. One more quick thing - do you mind sharing references? I'd love to include some citations to more material like this in my supplementary materials.
    1
  1386. Good question - i left out bias for simplicity here - but it's definitely an important piece!
    1
  1387. Reading list coming!
    1
  1388. I will take that as a compliment :)
    1
  1389. Leap Motion.
    1
  1390. Hey bj - do you mind reference a source? Thanks!
    1
  1391. I think I need a pronunciation coach!
    1
  1392. Awesome, thanks for watching! I used python and plotly.
    1
  1393. Sortof? I kinda like the character though
    1
  1394. ❤
    1
  1395. Thanks?
    1
  1396. Thank you!
    1
  1397. Man I want to but AI is tough to make good videos about!! Will give it some thought.
    1
  1398. Thanks for watching!
    1
  1399. Thank you!
    1
  1400. 🤣
    1
  1401. Fair
    1
  1402. Awesome!
    1
  1403. Yeah that would have been cool to include!
    1
  1404. Thanks for watching! I would love to make that series, but I'm pretty sure it would take me 10^6 years to complete.
    1
  1405. Woohoo!
    1
  1406. Woohoo!
    1
  1407. Woohoo!
    1
  1408. What made you want to watch again?
    1
  1409. It's definitely on the list!
    1
  1410. Aww man!
    1
  1411. Thank you!
    1
  1412. Glad you enjoyed it!
    1
  1413. Woohooo!!
    1
  1414. Thanks!
    1
  1415. Thanks for watching!
    1
  1416. Good catch!
    1
  1417. Nope! :)
    1
  1418. Thanks! Working on it!
    1
  1419. Thank you!
    1
  1420. Good eye! Yeah I put a note about this in the description.
    1
  1421. I know, lame right?
    1
  1422. Oh woah haven't this - this one right? https://www.amazon.com/Worlds-See-Curiosity-Exploration-Discovery/dp/B0BSP29SQ4/ref=sr_1_1?dib=eyJ2IjoiMSJ9.WUldP9af9N0KDhw2t8hMREVU7hywO2A02fDWCcsJ7OuqSbEBnq7LZSl-4TcqP1PF2UgSBmh6Jx9VqHQa8DL87rwUKct1nycpSRRG3NthJ8qvJql2NDHVyBtWwPghFLZbl6uFmase1ybxxsxCTCKWCbvijW4zWKjGTxnAGNnk4T3DMoYsEuN1Buv2ve4o9fh4oYJIxG-QkvD28BmagZBlPoKYSxtQJ7XO5i_VhlUnzI4.toheypxIiOKOEbc-HeZRh1D13QynzYyNfVuQe8hvg7s&dib_tag=se&gad_source=1&hvadid=678801682541&hvdev=c&hvlocphy=9009566&hvnetw=g&hvqmt=e&hvrand=16912224946210263691&hvtargid=kwd-2246523272793&hydadcr=22534_13493212&keywords=fei+fei+li+book&qid=1720197297&sr=8-1 Ordering!
    1
  1423. Thank you!
    1
  1424. woohoo!
    1
  1425. Thanks for watching!
    1
  1426. Confirmed.
    1
  1427. Thank you!
    1
  1428. Woah cool!
    1
  1429. Thanks for watching!
    1
  1430. Thank you!
    1
  1431. Thank you!
    1
  1432. 🐈
    1
  1433. Thank you!
    1
  1434. Thank you!
    1
  1435. Thank you1
    1
  1436. Should all be there!
    1
  1437. Haha word
    1
  1438. Thank you!
    1
  1439. Thank you!
    1
  1440. Same - thanks so much!
    1
  1441. Pretty sure it’s totally separate
    1
  1442. Thank you!
    1
  1443. I know right!
    1
  1444. Precisely. :)
    1
  1445. Ah man I think i saw that forever ago, gotta watch it again!
    1
  1446. Electromorphous aw man!
    1
  1447. Great point Sebastian! We are starting off super subjective, if I'm doing my job right, this should definitely shift over the next 4 episodes!
    1
  1448. https://www.leapmotion.com/
    1
  1449. Legit log stuff coming in a few weeks!
    1
  1450. Thank you!
    1
  1451. Thanks! :)
    1
  1452. Haha I wish
    1
  1453. 🥰
    1
  1454. Awesome thanks for watching!
    1
  1455. 🥰
    1
  1456. :)
    1
  1457. Thanks for watching!
    1
  1458. Shoot me your email and I'll add you to my list to reach out to when I do offer international shipping: https://www.welchlabs.com/contact
    1
  1459. Thanks!! https://www.patreon.com/c/welchlabs
    1
  1460. Thanks for watching!
    1
  1461. Thank you so much!
    1
  1462. Hmm - interesting!
    1
  1463. Haha true.
    1
  1464. Thank you!
    1
  1465. Awesome - thanks for watching!
    1
  1466. Yeah, good question. I recommend Information Theory, Inference, and Learning Algorithms by David Mackay for more on information theory.
    1
  1467. Awesome thanks!
    1
  1468. Thanks! Girl from Osaka.
    1
  1469. Nice to see you too, thanks for watching!
    1
  1470. Awesome! That's ok - you don't have to get all of this at all - a library like Tensorflow will take care of most of this for you! Best of luck!
    1
  1471. awesome!
    1
  1472. I know!
    1
  1473. Agreed!
    1
  1474. Do you think a longer more detailed video would be better?
    1
  1475. Thank you!
    1
  1476. Thanks for watching!
    1
  1477. lol
    1
  1478. Thanks! for backprop!
    1
  1479. Great idea, I'll keep that in mind.
    1
  1480. Yeah I need to do more pronunciation home work!
    1
  1481. Couldn’t find any unfortunately!
    1
  1482. Maybe that's how we spells his name...
    1
  1483. Thanks for watching!
    1
  1484. It does get a tiny tiny cameo on screen - but yeah will have to be in a future one!
    1
  1485. Awesome!
    1
  1486. Interesting! Can you shoot me some references using the contact link at welchlabs.com?
    1
  1487. Yes right now
    1
  1488. Yup!
    1
  1489. Haha awesome.
    1
  1490. Woohoo!
    1
  1491. Woohoo!
    1
  1492. yeah...backprop gets really serious real fast. It's downhill from there though!
    1
  1493. Grant's stuff is incredible, thanks for the comparison!
    1
  1494. Thanks for watching!
    1
  1495. Hahah that's hilarious!
    1
  1496. Awesome - Thanks for watching!
    1
  1497. Glad you enjoyed it!
    1
  1498. Jupyter notebook! Thanks for watching.
    1
  1499. lol
    1
  1500. I agree that fatalities alone do not tell the whole story. My reference for this argument (https://www.rand.org/pubs/research_reports/RR1478.html) also does the math for injuries and accidents. When you factor in that SDCs do not drive perfectly, you still need a heck of a lot of data to validate these things. I think the fatality argument is a good starting point (that's why I picked it), but there's definitely more to it. Thanks for watching!
    1
  1501. Hoe about this: https://www.rand.org/pubs/research_reports/RR1478.html
    1
  1502. Awesome!
    1
  1503. Nice!
    1
  1504. Thanks for watching! "Time for Django" by Studio Le Bus. Cool avatar picture - where is it from?
    1
  1505. Maybe next semester?
    1
  1506. YES
    1
  1507. awesome!
    1
  1508. Woohoo!
    1
  1509. Haha awesome! Thanks for watching. Go to sleep.
    1
  1510. Thanks for watching and your support!
    1
  1511. Thanks for watching!
    1
  1512. Thank you!
    1
  1513. Ah good to know!
    1
  1514. My sincerest apologies - I regret everything
    1
  1515. Amen
    1
  1516. 😃
    1
  1517. Word :)
    1
  1518. Or do they... :)
    1
  1519. Thank you!
    1
  1520. Awe man!
    1
  1521. Woohoo!
    1
  1522. :)
    1
  1523. Hmmmm good point 🤔
    1
  1524. Big Thanks to Boris Vidal for the Translation!
    1
  1525. Thank you!
    1
  1526. woohoo!
    1
  1527. Yes will work on a reading list video!
    1
  1528. https://github.com/stephencwelch/Imaginary-Numbers-Are-Real
    1
  1529. Welcome aboard!
    1
  1530. Thanks for watching!
    1
  1531. woohoo!
    1
  1532. Haha yeah not my strong suit!
    1
  1533. Thank you!
    1
  1534. Thanks for watching! I recommend shooting in a lightbox to get started. I use python and the adobe creative suite for most visuals.
    1
  1535. No gradient descent!
    1
  1536. Thanks for watching!
    1
  1537. Thanks Matthew!
    1
  1538. lol
    1
  1539. Oh man that sounds awesome!
    1
  1540. Awesome!
    1
  1541. Fair point! Noted. Thanks for watching!
    1
  1542. I wish!
    1
  1543. Hey Dalton! Just curious what was unappealing about the title? Is it just the topic in general or something else? Were there things that you realized were interesting to you after you watched? Thanks!
    1
  1544. No worries - was wondering if any one would catch that - good eye!
    1
  1545. Cool!
    1
  1546. That's a good point!
    1
  1547. Thanks for watching!
    1
  1548. Glad it was helpful!
    1
  1549. Main research references are in the description!
    1
  1550. NOICE
    1
  1551. Thanks!
    1
  1552. Thank you!
    1
  1553. I know! I'm made some good progress on the next series - but I'm not there yet!
    1
  1554. woohoo!
    1
  1555. Thanks for watching!
    1
  1556. Ya!
    1
  1557. 🤣
    1
  1558. Thank you!
    1
  1559. Thanks for watching!
    1
  1560. Thanks for watching!
    1
  1561. aww shucks. :)
    1
  1562. Or maybe I've been pronouncing it wrong.... :)
    1
  1563. Gotcha! Thanks for watching! So my talking speed was a little too fast?
    1
  1564. Hahah thank you! Yes please pray to the algorithm gods for me 😆
    1
  1565. Bro
    1
  1566. :)
    1
  1567. Nice!
    1
  1568. They had the best science in the world!!
    1
  1569. https://www.premiumbeat.com/royalty-free-tracks/happy-french-guitar-2
    1
  1570. Woohoo!
    1
  1571. 🤔
    1
  1572. Woohoo!
    1
  1573. Yup - that's correct. Code: https://github.com/stephencwelch/Neural-Networks-Demystified Thanks for watching!
    1
  1574. Thanks!
    1
  1575. Thanks for watching!
    1
  1576. Nice observation - this will be resolved - it just takes some time!
    1
  1577. Woohoo!
    1
  1578. Thank you!
    1
  1579. The math!
    1
  1580. Glad you enjoyed it!
    1
  1581. Thank you!
    1
  1582. Thanks for watching!
    1
  1583. Thanks!
    1
  1584. You basically interploate between values on the table to get more accuracy.
    1
  1585. Thanks for watching!
    1
  1586. sure!
    1
  1587. Lol I agree (I think!)
    1
  1588. Random, eh?
    1
  1589. Woohoo!
    1
  1590. Thanks for watching!
    1
  1591. Woah interesting - thanks for sharing. Maybe your brain was kinda digesting in the background as we went?
    1
  1592. Thanks for watching!
    1
  1593. Thank you!
    1
  1594. Woohoo!!
    1
  1595. Nice!!
    1
  1596. Thanks for watching!
    1
  1597. Thank you so much 😀
    1
  1598. Good question - check out cross entropy loss. Thanks for watching!
    1
  1599. 😁
    1
  1600. Thanks! Yeah that was a bit tricky!!
    1
  1601. Wow - thank you for the kind words.
    1
  1602. Thanks for watching!
    1
  1603. I just overwhelmed by the scope I create for myself honestly. Would love to finish old series - we'll see!
    1
  1604. Thanks for watching!
    1
  1605. Thank you! Cheers!
    1
  1606. Yesssssssss!
    1
  1607. Thanks for watching!
    1
  1608. Amazing!
    1
  1609. Totally - hoping to cover another element in a couple weeks!
    1
  1610. I know right!
    1
  1611. Facts.
    1
  1612. Thanks for watching!
    1
  1613. Thanks for watching!
    1
  1614. Woah cool!
    1
  1615. Haha thanks!
    1
  1616. Agreed!
    1
  1617. Will look at this - thanks for the heads up!
    1
  1618. 🐈
    1
  1619. :)
    1
  1620. Thank you!
    1
  1621. Thank you!
    1
  1622. Cool right!?
    1
  1623. Thanks for watching!
    1
  1624. Yup! :)
    1
  1625. Thank you!
    1
  1626. Woohoo!
    1
  1627. I know right?!
    1
  1628. Thanks for watching!
    1
  1629. Thanks for watching!
    1
  1630. :)
    1
  1631. Great!
    1
  1632. Check out the pdf! :)
    1
  1633. Awesome - thanks for watching!
    1
  1634. Glad you enjoyed it!
    1
  1635. Thank you!
    1
  1636. Phanks!
    1
  1637. Thank you!
    1
  1638. Thanks for watching!
    1
  1639. Any point in particular, or just in general?
    1
  1640.  @dbartholemewfox  Cool, noted.
    1
  1641. 🤦‍♂️
    1
  1642. Cool - thanks for sharing!
    1
  1643. Welcome aboard!
    1
  1644. Thanks for watching!
    1
  1645. Mostly python and plotly. Thanks for watching!
    1
  1646. Thanks for watching!
    1
  1647. Woohoo!
    1
  1648. Yeah I feel like it was inevitable - it’s like latent in nature
    1
  1649. Interesting!
    1
  1650. Thanks!
    1
  1651. https://www.patreon.com/welchlabs Thanks!
    1
  1652. Thanks for watching!
    1
  1653. Good point!
    1
  1654. Hey Chirag! Hope all is well, thanks for watching!
    1
  1655. Awesome - thanks for watching!
    1
  1656. Me too!
    1
  1657. Thanks for watching!
    1
  1658. https://github.com/stephencwelch/Neural-Networks-Demystified
    1
  1659. Thanks for watching!
    1
  1660. Thanks for watching!
    1
  1661. Thanks!
    1
  1662. Thank you! Will see what I can do!
    1
  1663. Cool idea!
    1
  1664. We could use or, but we don't need it, since and and not form a functionally complete set.
    1
  1665. Thanks!
    1
  1666. Thanks for watching! At what time (s) does this happen?
    1
  1667. Agreed!
    1
  1668. Thank you! Cheers!
    1
  1669. Woohoo!
    1
  1670. Colab notebook in description!
    1
  1671. Thank you!
    1
  1672. :)
    1
  1673. Vpython and adobe illustrator
    1
  1674. Yeah - I'm made some good progress on the next series - but I'm not there yet!
    1
  1675. No way.
    1
  1676. Thanks 3b1B! and Thanks Iftakhar for watching!
    1
  1677. Thank you!
    1
  1678. Thank you Thank you Thank you
    1
  1679. Thanks for watching!
    1
  1680. Thanks for watching!
    1
  1681. Thanks for watching! Check out the pdfs for references!
    1
  1682. Thank you!
    1
  1683. Thanks!
    1
  1684. 🤓
    1
  1685. :)
    1
  1686. Thank you!
    1
  1687. mwhahahahahaha
    1
  1688. Amazing thank you!
    1
  1689. I know right!?
    1
  1690. lol thanks!
    1
  1691. Thanks for watching!
    1
  1692. Woohoo!
    1
  1693. Thanks for watching! Mathematica, Cinema 4D, after effects.
    1
  1694. Woo!
    1
  1695. haha awesome!
    1
  1696. Wow thanks so much!
    1
  1697. Thanks for watching!
    1
  1698. Thanks for watching! This link doesn't work for you? http://www.welchlabs.com/resources/freebook
    1
  1699. 2?
    1
  1700. Thank you!
    1
  1701. Welcome aboard!
    1
  1702. Thanks for watching!
    1
  1703. Awesome!
    1
  1704. Thanks!!
    1
  1705. Yeah the slide rule to the moon is cool! I couldn't quite find enough to make that it's own video - but i do refer to it some Tik Toks.
    1
  1706. Thanks 🔥
    1
  1707. :)
    1
  1708. Wow, thanks for watching!
    1
  1709. Hahaha that sound awesome.
    1
  1710. :)
    1
  1711. Thanks for watching!
    1
  1712. Thank you!
    1
  1713. Haha good point
    1
  1714. Demon core is on the list!
    1
  1715. Ehhh, maybe in a package like scikit learn, but not built into python. Thanks for watching!
    1
  1716. Oh no!
    1
  1717. Haha nice.
    1
  1718. No worries lol - I had a pretty long content gap.
    1
  1719. to see all the things!
    1
  1720. Thanks so much!
    1
  1721. Working on it!
    1
  1722. Thanks for watching!
    1
  1723. Interesting angle!
    1
  1724. Thanks so much! Grant is awesome
    1
  1725. Thanks!
    1
  1726. Not a dumb question at all! We have 9 weights to tune.
    1
  1727. Will have to try!
    1
  1728. Awesome - what about tension? :)
    1
  1729. :)
    1
  1730. Good call!
    1
  1731. Woohoo!
    1
  1732. awesome!
    1
  1733. Thanks for watching!
    1
  1734. Thank you so much!!
    1
  1735. Thank you for watching!
    1
  1736. I believe in you guys!
    1
  1737. Thank you!
    1
  1738. NICE
    1
  1739. Thanks!
    1
  1740. Good Question - keep watching! :)
    1
  1741. Mathematica + Cinema4d + After Effects
    1
  1742. Thank for watching!!
    1
  1743. Woohoo! Thanks for watching + commenting!
    1
  1744. THank you!
    1
  1745. Thank you!
    1
  1746. Thanks for watching! Language by marvels on mars.
    1
  1747. I hope so too!
    1
  1748. It’s in the description!
    1
  1749. Check out my TikTok!
    1
  1750. Yeah i want to cover these but am honestly lost on where to start - will give it some more thought!
    1
  1751. Yay! Thank you!
    1
  1752. I’ll see what I can do!
    1
  1753. jaf;lkdjds;akljfask lfdsa!
    1
  1754. Thanks for watching!
    1
  1755. Thanks for watching!
    1
  1756. I'm back!
    1
  1757. Awesome!
    1
  1758. Thanks for watching - great question - I have a footnote on this in the pdf!
    1
  1759. lol after working on this project for a while i started to see these patterns when i closed my eyes.
    1
  1760. Thanks for watching!
    1
  1761. Thanks for watching!
    1
  1762. Thanks for watching!
    1
  1763. Thanks for wathing!
    1
  1764. Thanks!
    1
  1765. Thank you! Considering doing some behind the scenes on patreon
    1
  1766. Thank for watching!
    1
  1767. Thanks for watching! 3Blue1Brown = awesome.
    1
  1768. Haha good to know
    1
  1769. True!
    1
  1770. Thank you!
    1
  1771. I’ll call nolan
    1
  1772. 🐕
    1
  1773. That's a fun question. Probably...
    1
  1774. Thanks for watching!
    1
  1775. Correct!
    1
  1776. Thanks for watching!
    1
  1777. 😁
    1
  1778. Sure will figure out a good way to do that!
    1
  1779. Ah man can’t wait to see it!
    1
  1780. Happy to be here!
    1
  1781. Awesome!
    1
  1782. Thanks for watching!
    1
  1783. Amazing thanks for the kind words
    1
  1784. Thanks for watching!
    1
  1785. Wow, awesome!
    1
  1786. Glad you enjoyed it!
    1
  1787. Thanks for the support!
    1
  1788. Nice!
    1
  1789. Thank you!
    1
  1790. Thanks for watching!
    1
  1791. Agreed! I own WAAAAAY to many.
    1
  1792. Thanks for watching!
    1
  1793. Nice!!
    1
  1794. Thanks for watching!
    1
  1795. woohoo!
    1
  1796. Amazing! What grade/year do you teach?
    1