0:00:15a risk is switch to the second
0:00:17present a sent in this in this you in this a we we you present the fast they might those
0:00:22new with them
0:00:26and is
0:00:27this is a but you on what of well with a bit that's caff be and i C okay
0:00:32and uh
0:00:34so a
0:00:35i you already know that the um
0:00:38yeah are another
0:00:40kind of but with some for at the end and for C be that
0:00:43the the on a the on S one egg with um
0:00:45and one as the only one in some these
0:00:48yeah the dam goes you than it them
0:00:50but usually for them most new data can you we we on we need to compute the that be beyond
0:00:55oh the gradient and the hessian and and usually do they has and very very few already last
0:01:01uh it basically that's
0:01:04was up we need to in but very hot
0:01:06but a at that possibly has an and in in this
0:01:10in this present is that we we we to do how to
0:01:12avoid this problem
0:01:14how to how to avoid
0:01:15how to
0:01:16a lot but enough that has an and all so how to a the
0:01:21the lower the last
0:01:22in but up last
0:01:23has yeah
0:01:25and now is the a life
0:01:27might talk that we we you
0:01:29resent deeply side it press for the good
0:01:32the copy of method
0:01:33and we will find the
0:01:35the fast way to compare
0:01:36to compute looks
0:01:38the gradient
0:01:39i also to
0:01:40compute a process as N
0:01:42and it here we we
0:01:45with an
0:01:46the low rain and that's one for the a possibly has and
0:01:49and then by on this
0:01:52but you by on this low when it just when we we fight
0:01:55we we i
0:01:56we we we present
0:01:58a very it's so that need to
0:02:00to avoid
0:02:01the input of last has
0:02:05i skip this require already meant something
0:02:08reverse light
0:02:11a you know the to derive with that
0:02:12the the atlas electrics um we can see that the same the similar conversant robot whereabouts roy
0:02:18in nineteen seventy nine
0:02:20but here you see here this is a conference on
0:02:22two we to approximate the ten so by
0:02:25but extract the
0:02:28this the two
0:02:29to write really says that um is the
0:02:31okay this term
0:02:34is rest and it's right here and this time we present here
0:02:36this time is to inform the nonnegative trends on the front end
0:02:40i N
0:02:41and this time to an problems
0:02:43spice you can train
0:02:45and the car far and bit eyes
0:02:48zero are uh plus they've
0:02:52and is a see here
0:02:54to that
0:02:55the on as one of the lead that we have best
0:02:57all that on the fact that i the same time
0:03:00and he'll to be two two we before all this we use this
0:03:05but that's room
0:03:08with i we've fit i is that that's
0:03:10okay you C
0:03:12this the best the is a set up fact the i one
0:03:15and then you
0:03:16code for i on the on the but is a seven
0:03:19to very long for that
0:03:21but long list that and we employ this
0:03:23a back room
0:03:25do you best
0:03:26the fact
0:03:29you see here is we we need to compute the the copy and here i'm node that has sent the
0:03:34possibly may has sent here
0:03:35and also the gradient here
0:03:39and the
0:03:40a call we the also we of go we need to need to compute you
0:03:44the the cool and
0:03:46from the be and we compute the gradient
0:03:49for a for in this fall
0:03:50and also so be that has an approach me has an
0:03:53for in this fall
0:03:56a probably C come men
0:03:58i i a high computational cost
0:04:00and of course the of this but might is side
0:04:03you one here
0:04:06and a lot of time and also
0:04:11we we we present here than
0:04:12the way to avoid this problem
0:04:16it this line we'll
0:04:18so that how to
0:04:19compute the will be and matters
0:04:22this do though it the bustle
0:04:24the river a of the approximate ten so
0:04:27which search but only one come but
0:04:31we saw this this
0:04:34we be is spread in the very
0:04:36come come
0:04:39this one is that correct up
0:04:41correct upper up all the
0:04:44common a
0:04:45in in on the fact that it's that the the fact that and
0:04:49and B and is that the rotation matrix
0:04:52it better
0:04:53okay to say here this this breath the relation between
0:04:56the vector is a stand up
0:04:58okay so
0:04:59and vector is a
0:05:00and vector is a set of the most and
0:05:05my matrices a send up to time so
0:05:08quite complicated here
0:05:10you see if you were to i don't the data and
0:05:13and this one leader
0:05:14you where the wide the mode and
0:05:17methods and of the ten so
0:05:19and this italy's relation between
0:05:21two batteries and
0:05:25and we fine
0:05:26the compact form for that the the copy be and map so here
0:05:30and with few we we from this result we
0:05:33find the weighted method
0:05:38this one is the uh
0:05:40the final
0:05:41result for the gradient vectors
0:05:44and it with you see here this one is the gradient of the tensor with respect to the fact though
0:05:49the fact that one
0:05:50and this one is the right
0:05:52the great and
0:05:53of the
0:05:54a cross and tensor
0:05:56which are but to the fact the and
0:06:00and the got my mike this is press here the that the how to map product up
0:06:05this time
0:06:06what is that the fact the and
0:06:08is that the the something
0:06:11and of some this this crime matter
0:06:14at the nest
0:06:16we we present
0:06:17how to compute the
0:06:22the idea is this we we've split
0:06:25we can see that the the possibly has and that though
0:06:28and by and
0:06:30block might be
0:06:31and we we fight the plug i that is the press for for every block here
0:06:38this dist
0:06:39to and you with
0:06:41how to you
0:06:43that was sub just
0:06:44has us a but just
0:06:46like did you have a you
0:06:48if and by it
0:06:52say this is them
0:06:54the diagonal block this
0:06:56is and equal to M you you have to um the diagonal plot mattress and C
0:07:01compute by
0:07:02yeah my
0:07:04i am and go product up a got my
0:07:07with the and it it matters
0:07:09a a um of sci ice ice of N
0:07:13and is it that the diagonal vector
0:07:15and for that off diagonal my
0:07:17for the up
0:07:18diagonal diagonal method
0:07:20and you know in a equal to N
0:07:22we we we can decompose
0:07:24supp might in into
0:07:26this four
0:07:27this it is a diagonal matrix
0:07:29this the that block diagonal matrix enough for
0:07:31i i know what it
0:07:32is it problem
0:07:33i i matter and is also the block diagonal matter
0:07:36we be spread here
0:07:38in the next line
0:07:42a very in i property of that of possibly has an that that we can
0:07:45it's spread
0:07:46the approximate has an and that the low end
0:07:49and that one
0:07:51you see year
0:07:52so i say yeah that a i all method
0:07:55we we already defined though
0:07:57re slide
0:07:58and is that the point
0:07:59but but and method
0:08:02see here here that the right block low matter
0:08:06or within this fall
0:08:08i K yeah A the
0:08:10square matrix
0:08:10oh side and
0:08:13and ask way by and ask where
0:08:16and this well
0:08:17in the is the mac of the K method here even in this fall
0:08:22be here
0:08:28it in S like we you see here how to
0:08:31a which to like the case and
0:08:32and how
0:08:34how we can
0:08:34and to spend a little way that's one
0:08:36i just one for the prosody has and yeah
0:08:39the the has the a to my has an
0:08:42and it is a metric
0:08:43see you the plot like no mapping
0:08:45see you that the also plot that all method
0:08:48and case have where
0:08:51such that
0:08:53and of car yeah if we employ
0:08:56deep if we employ the by no
0:08:59it but to your we can it
0:09:01we can but we can of one
0:09:03the in but a blast scale
0:09:06a little the last has in method
0:09:08by this
0:09:10and if we compute here is that a compute the in but uh
0:09:13the approximate
0:09:14has and we
0:09:16all only compute it looked at the you might rate the came at rate and also in lot of this
0:09:21and this time have very
0:09:24the by some because this is this term is
0:09:26has i'll up and by K and
0:09:29and K
0:09:31and a
0:09:31and a square by and ask square
0:09:36and in but
0:09:37the same her
0:09:41we can quickly compute
0:09:44a because it brought no matrix
0:09:46so is slide up problem
0:09:47is that of compute the in of the whole that the whole take we compute in but it's
0:09:52sub method along the diagonal
0:09:54so do you have here
0:09:57and we also had how to compute the in but at that a least
0:10:01is have very is so uh
0:10:04it press here
0:10:07and finally from that them "'cause" new done of that room we fight with that
0:10:11we we formulate the fast them let's be learned with some that to we reply here
0:10:16i the approximation has has
0:10:18and we define you
0:10:21the fast them book use like
0:10:24the with uh okay this
0:10:26this term
0:10:27this term we that
0:10:29no this um
0:10:32i you see
0:10:33we so
0:10:34this them with that this this
0:10:36this a
0:10:43and the L make
0:10:45this border
0:10:47with uh this the
0:10:49okay also it's spread by the
0:10:51block diagonal i dunno method
0:10:54so finally
0:10:55you see here the the the true this
0:10:57most one
0:10:58with the of the
0:11:00the the five but to the much smaller than the this the approximation
0:11:03uh has and then and these K we can we do the at the clear do the commit
0:11:07so the of the
0:11:09in a of this method
0:11:11in the very don't to the in but that this
0:11:13the possibly has and
0:11:15and a call we don't need to control the to go beyond method
0:11:18we not only to compute the
0:11:20a possibly has an
0:11:24maybe a nice
0:11:27okay okay
0:11:29so in this snow the next slide you see here
0:11:32how to to the power with a how do to the the but but that in in the
0:11:37you know an increase um
0:11:39a very simple it and also very if if you soon that's a proposal were about rowing two thousand nine
0:11:44that's of and
0:11:44you nine
0:11:45uh that's but more like that it we it in line
0:11:49on the
0:11:50the low power by real met um but power what's so by the la
0:11:55enough a value and then we greater only
0:11:57we do
0:11:59you do the bar with and then we can
0:12:01after the fire ten iteration we can
0:12:04the can was and that the that's solution
0:12:08we don't use this approach
0:12:09we you are not a
0:12:10and this you this one T by on the cake Q T condition
0:12:14and this list to
0:12:16the medium i of this problem
0:12:18this for that's of that too
0:12:19this condition
0:12:23and as to the simulation
0:12:27is assume a some place and you see here for three dimensional tensor a with side what one and right
0:12:32by one hundred by one hundred combo by ten component
0:12:37the common
0:12:39we for to be collinear we the auto by this form
0:12:43and we see here
0:12:44with the
0:12:45multiplicative kl K with them what what deeply get the L
0:12:50the green light
0:12:52and that the i
0:12:54is from a up the
0:12:57one one right it ways that no one that fred
0:13:01i not yet and
0:13:02one ten held and B
0:13:04that's how the in twice and then the and with only
0:13:07get a convert to the solution and
0:13:09and i like that on the L
0:13:11the fast lm level and is them with quickly can what up the only
0:13:16one at right right
0:13:22but not case and not a that it we one that we
0:13:25test with one tell than by one column
0:13:27i want how than i with the common
0:13:29you to here one attract recommended
0:13:31it's really he'll
0:13:32and the
0:13:34fast and where make on is also quickly
0:13:36fit the data up the
0:13:38fifteen no sitting it weights and
0:13:41i and all right with some can of fit the data
0:13:45i is to to much but maybe i skip this like
0:13:49is used for to this prior to
0:13:51for of the method but maybe there with
0:13:56this you know uh an application with the leave at the faded the way that we
0:14:02we classified the data
0:14:06that's we from the data that we have forty four interest for a and that we put from the fight
0:14:11by the cable with flat it to this just kind of ten so C to by sitting
0:14:17that T two to T two because we have yeah i
0:14:20i orientation and for scale
0:14:22and of call we have yet the last of and is that number of plays
0:14:26for right
0:14:29it truck of from this
0:14:30ten so
0:14:33for the first
0:14:34first we track by
0:14:36thirty two
0:14:37and T F that we have here
0:14:40and the S like that we employ an an map to talk dove
0:14:43three too
0:14:44from the last
0:14:46the life factor
0:14:47and the but form we
0:14:48of and here you see
0:14:50but the K and it with on is only
0:14:52i was N
0:14:53with the us
0:14:54i T i percent
0:14:57maybe maybe though with the
0:14:58are you less
0:14:59with night night it's three was and but our and with need
0:15:02not for was a and if we employ this was can trying the ten i
0:15:06one as that was sent with ten
0:15:08face and all is not enough ten fate take class
0:15:11that's me we have one and right
0:15:17and we
0:15:19it to the good clothes and
0:15:21a you see here we already but both a fast and with them too
0:15:25for for et and a map the fast that was knew that for N
0:15:28and the M
0:15:29and that was don't we
0:15:31a you don't
0:15:32we to compare you are the last scale that will be and and also that scale
0:15:36has has C and
0:15:37the process may has them
0:15:39and we avoid
0:15:41they vote of the the last
0:15:46and it
0:15:47and you are virtually you see here would have the a into trend
0:15:50the fast them was new than
0:15:52we we the fast lemme i rammed
0:15:54and we term for canonical only
0:15:56um only to decompose and
0:15:59that these these two D dizzy
0:16:01similar to the one the one of the wooden and we can where you but row and
0:16:05and the mostly but
0:16:06oh and we is further
0:16:09thank you
0:16:38uh yeah think to the
0:16:40okay we we we we may the the net and also is similar to we man that the relative error
0:16:47you see here
0:16:48this is the right of the arrow
0:16:51but we we do is read how to compute this error of this is very simple that's we
0:16:57from the conference and you
0:17:06this so we compute this error and divide by norm up the so
0:17:13this your L T you ever
0:17:26no i i you these
0:17:27for from one is known so we don't you are not the kind of um is a one