0:00:14 | yeah |
---|---|

0:00:15 | a risk is switch to the second |

0:00:17 | present a sent in this in this you in this a we we you present the fast they might those |

0:00:22 | new with them |

0:00:24 | yes |

0:00:26 | and is |

0:00:27 | this is a but you on what of well with a bit that's caff be and i C okay |

0:00:32 | and uh |

0:00:34 | oh |

0:00:34 | so a |

0:00:35 | i you already know that the um |

0:00:38 | this |

0:00:38 | yeah are another |

0:00:40 | kind of but with some for at the end and for C be that |

0:00:43 | the the on a the on S one egg with um |

0:00:45 | and one as the only one in some these |

0:00:48 | yeah the dam goes you than it them |

0:00:50 | but usually for them most new data can you we we on we need to compute the that be beyond |

0:00:55 | oh the gradient and the hessian and and usually do they has and very very few already last |

0:01:00 | and |

0:01:01 | uh it basically that's |

0:01:03 | we |

0:01:04 | was up we need to in but very hot |

0:01:06 | but a at that possibly has an and in in this |

0:01:10 | in this present is that we we we to do how to |

0:01:12 | avoid this problem |

0:01:14 | how to how to avoid |

0:01:15 | how to |

0:01:16 | a lot but enough that has an and all so how to a the |

0:01:21 | the lower the last |

0:01:22 | in but up last |

0:01:23 | has yeah |

0:01:25 | and now is the a life |

0:01:26 | oh |

0:01:27 | might talk that we we you |

0:01:29 | resent deeply side it press for the good |

0:01:32 | the copy of method |

0:01:33 | and we will find the |

0:01:35 | the fast way to compare |

0:01:36 | to compute looks |

0:01:38 | the gradient |

0:01:39 | i also to |

0:01:40 | compute a process as N |

0:01:42 | and it here we we |

0:01:45 | with an |

0:01:46 | the low rain and that's one for the a possibly has and |

0:01:49 | and then by on this |

0:01:52 | but you by on this low when it just when we we fight |

0:01:55 | we we i |

0:01:56 | we we we present |

0:01:58 | a very it's so that need to |

0:02:00 | to avoid |

0:02:01 | the input of last has |

0:02:05 | i skip this require already meant something |

0:02:08 | for |

0:02:08 | reverse light |

0:02:10 | okay |

0:02:11 | a you know the to derive with that |

0:02:12 | the the atlas electrics um we can see that the same the similar conversant robot whereabouts roy |

0:02:18 | in nineteen seventy nine |

0:02:20 | but here you see here this is a conference on |

0:02:22 | two we to approximate the ten so by |

0:02:25 | but extract the |

0:02:27 | with |

0:02:28 | this the two |

0:02:29 | to write really says that um is the |

0:02:31 | okay this term |

0:02:34 | is rest and it's right here and this time we present here |

0:02:36 | this time is to inform the nonnegative trends on the front end |

0:02:40 | i N |

0:02:41 | and this time to an problems |

0:02:43 | spice you can train |

0:02:45 | and the car far and bit eyes |

0:02:48 | zero are uh plus they've |

0:02:52 | and is a see here |

0:02:54 | to that |

0:02:55 | the on as one of the lead that we have best |

0:02:57 | all that on the fact that i the same time |

0:03:00 | and he'll to be two two we before all this we use this |

0:03:05 | but that's room |

0:03:06 | with |

0:03:08 | with i we've fit i is that that's |

0:03:10 | okay you C |

0:03:12 | this the best the is a set up fact the i one |

0:03:15 | and then you |

0:03:16 | code for i on the on the but is a seven |

0:03:19 | to very long for that |

0:03:21 | but long list that and we employ this |

0:03:23 | a back room |

0:03:25 | do you best |

0:03:26 | the fact |

0:03:28 | but |

0:03:29 | you see here is we we need to compute the the copy and here i'm node that has sent the |

0:03:34 | possibly may has sent here |

0:03:35 | and also the gradient here |

0:03:39 | and the |

0:03:40 | a call we the also we of go we need to need to compute you |

0:03:44 | the the cool and |

0:03:46 | from the be and we compute the gradient |

0:03:49 | for a for in this fall |

0:03:50 | and also so be that has an approach me has an |

0:03:53 | for in this fall |

0:03:55 | and |

0:03:56 | a probably C come men |

0:03:58 | i i a high computational cost |

0:04:00 | and of course the of this but might is side |

0:04:03 | you one here |

0:04:06 | and a lot of time and also |

0:04:08 | yes |

0:04:10 | and |

0:04:11 | we we we present here than |

0:04:12 | the way to avoid this problem |

0:04:16 | it this line we'll |

0:04:18 | so that how to |

0:04:19 | compute the will be and matters |

0:04:22 | this do though it the bustle |

0:04:24 | the river a of the approximate ten so |

0:04:27 | which search but only one come but |

0:04:30 | and |

0:04:31 | we saw this this |

0:04:34 | we be is spread in the very |

0:04:36 | come come |

0:04:37 | vol |

0:04:39 | with |

0:04:39 | this one is that correct up |

0:04:41 | correct upper up all the |

0:04:44 | common a |

0:04:45 | in in on the fact that it's that the the fact that and |

0:04:49 | and B and is that the rotation matrix |

0:04:52 | it better |

0:04:53 | okay to say here this this breath the relation between |

0:04:56 | the vector is a stand up |

0:04:58 | okay so |

0:04:59 | and vector is a |

0:05:00 | and vector is a set of the most and |

0:05:05 | my matrices a send up to time so |

0:05:08 | quite complicated here |

0:05:10 | you see if you were to i don't the data and |

0:05:13 | and this one leader |

0:05:14 | you where the wide the mode and |

0:05:17 | methods and of the ten so |

0:05:19 | and this italy's relation between |

0:05:21 | two batteries and |

0:05:25 | and we fine |

0:05:26 | the compact form for that the the copy be and map so here |

0:05:30 | and with few we we from this result we |

0:05:33 | find the weighted method |

0:05:38 | this one is the uh |

0:05:40 | the final |

0:05:41 | result for the gradient vectors |

0:05:44 | and it with you see here this one is the gradient of the tensor with respect to the fact though |

0:05:48 | and |

0:05:49 | the fact that one |

0:05:50 | and this one is the right |

0:05:52 | the great and |

0:05:53 | of the |

0:05:54 | a cross and tensor |

0:05:56 | which are but to the fact the and |

0:06:00 | and the got my mike this is press here the that the how to map product up |

0:06:04 | on |

0:06:05 | this time |

0:06:06 | what is that the fact the and |

0:06:08 | is that the the something |

0:06:11 | and of some this this crime matter |

0:06:14 | at the nest |

0:06:15 | slide |

0:06:16 | we we present |

0:06:17 | how to compute the |

0:06:18 | approximate |

0:06:19 | yes |

0:06:22 | the idea is this we we've split |

0:06:25 | we can see that the the possibly has and that though |

0:06:28 | and by and |

0:06:30 | block might be |

0:06:31 | and we we fight the plug i that is the press for for every block here |

0:06:38 | is |

0:06:38 | this dist |

0:06:39 | to and you with |

0:06:41 | how to you |

0:06:43 | that was sub just |

0:06:44 | has us a but just |

0:06:46 | like did you have a you |

0:06:48 | if and by it |

0:06:49 | for |

0:06:52 | say this is them |

0:06:54 | the diagonal block this |

0:06:56 | is and equal to M you you have to um the diagonal plot mattress and C |

0:07:01 | compute by |

0:07:02 | yeah my |

0:07:03 | and |

0:07:04 | i am and go product up a got my |

0:07:07 | with the and it it matters |

0:07:09 | a a um of sci ice ice of N |

0:07:13 | and is it that the diagonal vector |

0:07:15 | and for that off diagonal my |

0:07:17 | for the up |

0:07:18 | diagonal diagonal method |

0:07:19 | when |

0:07:20 | and you know in a equal to N |

0:07:22 | we we we can decompose |

0:07:24 | this |

0:07:24 | supp might in into |

0:07:26 | this four |

0:07:27 | this it is a diagonal matrix |

0:07:29 | this the that block diagonal matrix enough for |

0:07:31 | i i know what it |

0:07:32 | is it problem |

0:07:33 | i i matter and is also the block diagonal matter |

0:07:36 | we be spread here |

0:07:38 | in the next line |

0:07:40 | so |

0:07:42 | a very in i property of that of possibly has an that that we can |

0:07:45 | it's spread |

0:07:46 | the approximate has an and that the low end |

0:07:49 | and that one |

0:07:51 | you see year |

0:07:52 | so i say yeah that a i all method |

0:07:55 | we we already defined though |

0:07:57 | re slide |

0:07:58 | and is that the point |

0:07:59 | but but and method |

0:08:01 | and |

0:08:02 | see here here that the right block low matter |

0:08:06 | or within this fall |

0:08:08 | i K yeah A the |

0:08:10 | square matrix |

0:08:10 | oh side and |

0:08:13 | and ask way by and ask where |

0:08:16 | and this well |

0:08:17 | in the is the mac of the K method here even in this fall |

0:08:22 | be here |

0:08:24 | okay |

0:08:25 | ah |

0:08:28 | it in S like we you see here how to |

0:08:31 | a which to like the case and |

0:08:32 | and how |

0:08:34 | how we can |

0:08:34 | and to spend a little way that's one |

0:08:36 | i just one for the prosody has and yeah |

0:08:39 | yeah |

0:08:39 | the the has the a to my has an |

0:08:42 | and it is a metric |

0:08:43 | see you the plot like no mapping |

0:08:45 | see you that the also plot that all method |

0:08:48 | and case have where |

0:08:49 | particular |

0:08:51 | such that |

0:08:53 | and of car yeah if we employ |

0:08:56 | deep if we employ the by no |

0:08:59 | binomial |

0:08:59 | it but to your we can it |

0:09:01 | we can but we can of one |

0:09:03 | the in but a blast scale |

0:09:06 | a little the last has in method |

0:09:08 | by this |

0:09:09 | for |

0:09:10 | and if we compute here is that a compute the in but uh |

0:09:13 | the approximate |

0:09:14 | has and we |

0:09:16 | all only compute it looked at the you might rate the came at rate and also in lot of this |

0:09:20 | style |

0:09:21 | and this time have very |

0:09:22 | small |

0:09:24 | the by some because this is this term is |

0:09:26 | has i'll up and by K and |

0:09:29 | and K |

0:09:31 | and a |

0:09:31 | and a square by and ask square |

0:09:36 | and in but |

0:09:37 | the same her |

0:09:41 | we can quickly compute |

0:09:43 | by |

0:09:44 | a because it brought no matrix |

0:09:46 | so is slide up problem |

0:09:47 | is that of compute the in of the whole that the whole take we compute in but it's |

0:09:52 | sub method along the diagonal |

0:09:54 | so do you have here |

0:09:57 | and we also had how to compute the in but at that a least |

0:10:01 | is have very is so uh |

0:10:03 | nine |

0:10:04 | it press here |

0:10:07 | and finally from that them "'cause" new done of that room we fight with that |

0:10:11 | we we formulate the fast them let's be learned with some that to we reply here |

0:10:16 | i the approximation has has |

0:10:18 | and we define you |

0:10:20 | this |

0:10:21 | the fast them book use like |

0:10:23 | which |

0:10:24 | the with uh okay this |

0:10:26 | this term |

0:10:27 | this term we that |

0:10:29 | no this um |

0:10:32 | i you see |

0:10:33 | we so |

0:10:34 | this them with that this this |

0:10:36 | this a |

0:10:41 | and |

0:10:43 | and the L make |

0:10:45 | it |

0:10:45 | this border |

0:10:47 | with uh this the |

0:10:49 | okay also it's spread by the |

0:10:51 | block diagonal i dunno method |

0:10:54 | so finally |

0:10:55 | you see here the the the true this |

0:10:57 | most one |

0:10:58 | with the of the |

0:11:00 | the the five but to the much smaller than the this the approximation |

0:11:03 | uh has and then and these K we can we do the at the clear do the commit |

0:11:07 | so the of the |

0:11:09 | in a of this method |

0:11:11 | in the very don't to the in but that this |

0:11:13 | the possibly has and |

0:11:15 | and a call we don't need to control the to go beyond method |

0:11:18 | we not only to compute the |

0:11:20 | a possibly has an |

0:11:24 | maybe a nice |

0:11:27 | okay okay |

0:11:29 | so in this snow the next slide you see here |

0:11:32 | how to to the power with a how do to the the but but that in in the |

0:11:37 | you know an increase um |

0:11:39 | a very simple it and also very if if you soon that's a proposal were about rowing two thousand nine |

0:11:44 | that's of and |

0:11:44 | you nine |

0:11:45 | uh that's but more like that it we it in line |

0:11:49 | on the |

0:11:50 | the low power by real met um but power what's so by the la |

0:11:53 | last |

0:11:55 | enough a value and then we greater only |

0:11:57 | we do |

0:11:59 | you do the bar with and then we can |

0:12:01 | after the fire ten iteration we can |

0:12:03 | yeah |

0:12:04 | the can was and that the that's solution |

0:12:06 | and |

0:12:07 | we |

0:12:08 | we don't use this approach |

0:12:09 | we you are not a |

0:12:10 | and this you this one T by on the cake Q T condition |

0:12:14 | and this list to |

0:12:16 | the medium i of this problem |

0:12:18 | this for that's of that too |

0:12:19 | this condition |

0:12:21 | okay |

0:12:23 | and as to the simulation |

0:12:27 | is assume a some place and you see here for three dimensional tensor a with side what one and right |

0:12:32 | by one hundred by one hundred combo by ten component |

0:12:36 | yeah |

0:12:37 | but |

0:12:37 | the common |

0:12:39 | we for to be collinear we the auto by this form |

0:12:43 | and we see here |

0:12:44 | with the |

0:12:45 | multiplicative kl K with them what what deeply get the L |

0:12:50 | the green light |

0:12:52 | and that the i |

0:12:54 | is from a up the |

0:12:56 | or |

0:12:57 | one one right it ways that no one that fred |

0:13:01 | i not yet and |

0:13:02 | one ten held and B |

0:13:04 | that's how the in twice and then the and with only |

0:13:07 | get a convert to the solution and |

0:13:09 | and i like that on the L |

0:13:11 | the fast lm level and is them with quickly can what up the only |

0:13:16 | one at right right |

0:13:22 | but not case and not a that it we one that we |

0:13:25 | test with one tell than by one column |

0:13:27 | i want how than i with the common |

0:13:29 | you to here one attract recommended |

0:13:31 | it's really he'll |

0:13:32 | and the |

0:13:34 | fast and where make on is also quickly |

0:13:36 | fit the data up the |

0:13:38 | fifteen no sitting it weights and |

0:13:41 | i and all right with some can of fit the data |

0:13:45 | i is to to much but maybe i skip this like |

0:13:49 | is used for to this prior to |

0:13:51 | for of the method but maybe there with |

0:13:54 | and |

0:13:54 | or |

0:13:56 | this you know uh an application with the leave at the faded the way that we |

0:14:02 | we classified the data |

0:14:06 | that's we from the data that we have forty four interest for a and that we put from the fight |

0:14:10 | label |

0:14:11 | by the cable with flat it to this just kind of ten so C to by sitting |

0:14:16 | by |

0:14:17 | that T two to T two because we have yeah i |

0:14:20 | i orientation and for scale |

0:14:22 | and of call we have yet the last of and is that number of plays |

0:14:26 | for right |

0:14:27 | and |

0:14:28 | we |

0:14:29 | it truck of from this |

0:14:30 | ten so |

0:14:33 | for the first |

0:14:34 | first we track by |

0:14:36 | thirty two |

0:14:37 | and T F that we have here |

0:14:40 | and the S like that we employ an an map to talk dove |

0:14:43 | three too |

0:14:44 | from the last |

0:14:45 | one |

0:14:46 | the life factor |

0:14:47 | and the but form we |

0:14:48 | of and here you see |

0:14:50 | but the K and it with on is only |

0:14:52 | i was N |

0:14:53 | with the us |

0:14:54 | i T i percent |

0:14:56 | is |

0:14:57 | maybe maybe though with the |

0:14:58 | are you less |

0:14:59 | with night night it's three was and but our and with need |

0:15:02 | not for was a and if we employ this was can trying the ten i |

0:15:06 | one as that was sent with ten |

0:15:08 | face and all is not enough ten fate take class |

0:15:11 | that's me we have one and right |

0:15:13 | for |

0:15:17 | and we |

0:15:19 | it to the good clothes and |

0:15:21 | a you see here we already but both a fast and with them too |

0:15:25 | for for et and a map the fast that was knew that for N |

0:15:28 | and the M |

0:15:29 | and that was don't we |

0:15:31 | a you don't |

0:15:32 | we to compare you are the last scale that will be and and also that scale |

0:15:36 | has has C and |

0:15:37 | the process may has them |

0:15:39 | and we avoid |

0:15:41 | they vote of the the last |

0:15:43 | has |

0:15:46 | and it |

0:15:47 | and you are virtually you see here would have the a into trend |

0:15:50 | the fast them was new than |

0:15:52 | we we the fast lemme i rammed |

0:15:54 | and we term for canonical only |

0:15:56 | um only to decompose and |

0:15:59 | that these these two D dizzy |

0:16:01 | similar to the one the one of the wooden and we can where you but row and |

0:16:05 | and the mostly but |

0:16:06 | oh and we is further |

0:16:09 | thank you |

0:16:26 | i |

0:16:38 | uh yeah think to the |

0:16:40 | okay we we we we may the the net and also is similar to we man that the relative error |

0:16:46 | two |

0:16:47 | you see here |

0:16:48 | this is the right of the arrow |

0:16:51 | but we we do is read how to compute this error of this is very simple that's we |

0:16:55 | we |

0:16:56 | okay |

0:16:57 | from the conference and you |

0:17:06 | this so we compute this error and divide by norm up the so |

0:17:12 | yeah |

0:17:13 | this your L T you ever |

0:17:17 | yes |

0:17:26 | no i i you these |

0:17:27 | for from one is known so we don't you are not the kind of um is a one |

0:17:34 | i |