[00:00:05] >> I am absolutely thrilled that we have Andrea blue here who is helper and professor of physics at the University of Pennsylvania Yes I've had the privilege of knowing Andrea for I think longer than probably both of us would care to admit but definitely since I was an undergrad so we can. [00:00:26] You can just guess. She has an absolutely stunning track record and has some amazing words and recognitions she is a Simons investigator and Simons fellow on theoretical physics she. Is a Fellow of the American Physical Society and the American Association for the Advancement of Science and she's also a fellow. [00:00:59] American Academy of Arts and Sciences and a member of the National Academy of Sciences and we are so happy that you are able to virtually visit us and she will be telling us about how materials can learn to function so I. So I want to talk to you today about some work that we're doing. [00:01:22] And this is where Judy designed systems that can learn how to perform biologically inspired functions and so that she cases of be looking at are and to design negative passant ratio so that you know usually when you stretch something right it shrinks in the other Earthlike not directions but in this case if you stretch it and make it a possum ratio means that if you stretch it it expands in the other direction that's that's one thing and the other one hat is a function call Alistair e.. [00:01:59] Which there's a mechanical version that proteins do and there's a slow version that the brain vascular networks do and I'll be talking about that those explain those when when the time comes and and show you that we actually have developed materials systems that can perform these functions so. [00:02:21] People I get started I just wanted to give a plug we just got approved in January for a center for slop in living matter and then. And it's it's really tennis repeal the astonishing for a soft matter soft and that matter we have over 60 faculty this stuff identifies working in. [00:02:43] Stop and or a living matter they come from more than 10 to prime cytology apartments in the sciences and engineering that doesn't include those who are in the medical school there are a few. And also doesn't that most people in the biology part of it because they say they view themselves as doing biology and not doing living matter settled so so this is really a lot of people who are actually not and by all it most stuff will run almost all of them are not in biology or in the medical school but really in the sciences and engineering. [00:03:18] And just you know we've got really quite amazing faculty so just since the center of what started in January it's a few months ago. Keep steady for example a select at the National Academy of Engineering and it's disher that's honored by medical insurance. And I want to highlight you know my physics colics pretty early arch and you know you got the Optical Society of America by a platonic so wired it just last week a lady kind of Corey was awarded the early career award for soft matter research by the p.s. settle. [00:03:59] Come and join us if you are an undergraduate comfort catches that is if your passions didn't apply proposed talk and no shock this coming. And so I don't sell her or haven't found I write so post some ratio. As I told you the person ratio tells tells you you know how much you expand or contract and that if you pull on the system right how much expand or contract in the other directions cork is a famous example the whole reason why it's useful is because it has a possible ratio or nearly 0 so that as you ram it into the into the. [00:04:39] Amount of the wine bottle right it doesn't expand or contract and there are fog in all directions that's what makes it so useful so the possible ratio is directly related to the ratio of the sugar modulus g.-d. to the bulk modulus be and it depends on the dimensionality spatial dimensions of Steve we're going to primarily work in 3 dimensions Ok. [00:05:05] And so it can range from minus one to. 3 House on in 3 dimensions and. We're interested in tuning systems so that they can be developed negative possible ratios between minus one and 0. And this is as I say. Motivated from biology turns out that tendencies do tend to have this property that they have negative possum regions. [00:05:36] And when we think about a negative Fossum ratio might be able to you know to net she get to that. Limit and let me just say that once the ship has a ratio this year to buck modulus exceeds 3 halves that's when the the positive ratio starts going negative Ok And when the racial issue to book my to list gets to the nitty Ok that's when the possum ratio reaches its minimal bounty of minus one. [00:06:07] Ok. When we think about cheating the possum ratio Ok because this is work that he did with said NATO and we've been working and jamming for many years you know what we actually started thinking about was jam packed nice because it turns out that the ratio of the shooter puck modulus is quite sure about Jack and Jackie not a negative possum ratio so it's all in the regime a positive person ratio but nevertheless it's quite you know full So so let me just talk a few minutes about Jam and Ok. [00:06:41] So jamming right is what happens if you take a bunch of particles there Pelly each other if they overlap if they don't overlap there's no interaction if they overlap they repel and if you look at the system to 0 temperature. You can see you know starting out from some random a national condition for example but you minimize the energy to get to search temperature you might find that if you're in a low enough density none of them overlap everybody's happy if the energy is 0 but if you're at your high of the density then there are these are last between particles Ok the red line just tells you then that you took the repulsive force that's pushing them apart. [00:07:25] And then the system is jammed so that's the way you know we talk about it as This Is Us. We did some of the same problem the way a computer scientists with with frame it though and that's helpful because at the back of our minds in the end I'm talking about learning and and you know the powerful machine learning methods that we have now be sample of deep neural networks work and in the way that in the way that I'm going to describe that you having problems Ok so if for example you've got a some deep neural network and it's trying to learn the difference between talks and cats right. [00:08:10] What you do is you feed it a bunch of pictures of dogs and cats right and then you say I want this known that work to spit out the word cap and it's he's a cat and the word dog going to see that doc but if it spits out the wrong word then you penalize the system I think construct a cost function where you pay if you give the wrong label for it for each example that you show are Ok And then what do you do you minimize the node weights you minimize the cost options sorry by adjusting the note weights you do a gradient descent or some kind of descent on the on the node weights to try to reach the minimum In other words you're trying to reach a constitution that is 0 the value of the cross which is 0 so that every label as identify correctly pay. [00:09:07] And so you are adjusting these degrees of freedom which I then don't weights in order to get there so that's that's the way you know. The learning works and in your own network so I could have phrased the general problem in exactly the same way Ok what I say is I don't want these particles to overlap as they overlap they have to pay a penalty. [00:09:32] Again which depends on how much they overlap. And that's my concentration in physics and called the energy right but it's because this is my cost function and then I just my degrees of freedom which in this case are the positions of the centers of the particles Ok in order to minimize that cost function the energy so we call that being as or temperature right but here we're just minimizing that cos I'm actually with respect to the degrees of freedom and we either end up with an i.j. abscessed I'm Ok or at low not density they are edgy I'm system and there if we have too many constraints compared to our to Greece of freedom Iraq so as I said we thought of jamming because we could tune the ratio this year to vote much a listen at what do I mean by that well if I look at just the same potential but the perfectly crystal an f.c.c. state Ok then if I look at the ratio of this year to vote much less as a function the pressure confining pressure Ok as I decrease that pressure. [00:10:43] The ratio remains absolutely constant doesn't change at all day until it reaches a precious 0 at that point the particles are just touching right and then both this year the book modulus drop to 0 but what happens. If I have the disorder state that you can state but as I decrease them complaining pressure the ratio they should have but much less struck such as a parallel Ok Which means that it goes to 00 pressure and. [00:11:17] And that spar more true nable right than what you'd have to the crystal So that's what we thought of that unit problem ratio we recently started thinking about that thank you and we remembered. Something that was funded out so the 1st before I get there it turns out that the properties of the g.m. packing Ok and linear response I tend to go to the properties of the Sprint network that I can construct for that that jam packing. [00:11:53] And so if I put a note of my network at the center of every particle and then I put a spring between every pair of overlapping particles Ok then but these 2 systems are equivalent in the response and then I think about what happens if I decrease the confining pressure in the case so I know in the chances that the relationship of folk modulus has struck me as I could crease it what's happening as a decrease that there are fewer and fewer overlaps particles that were overlapping now are no longer overlapping and in the spring now aren't that corresponds to removing those springs from the network so it's removing the edges of this network Ok So lowering that pressure or the density in g.m. packings is equivalent to pruning edges for this network. [00:12:46] And so we can think about what's the fact on this year in both modulus if we remove the pot so let me just take a spring an edge of the network every window and pull that out and asked how much has that changed the bulk modulus and how much that statues this year modulus Now the 1st a price list that that you are totally I don't currently get with each other how much you change the bulk modulus is totally and correlated with how much she had to share modulus and I'm going to make use of that Ok The 2nd thing is what it is distributions look like. [00:13:21] Well for the Crystal Wright for the perfect crystal. How much upon changes the book modulus will depend on where it is in that unit so rich which one it is that you that sell but I just have you know some delta function is the number delta function is just depends on the complexity of my unit stuff Ok. [00:13:41] And you would think Ok now right at the sorter that's just going to fuzz out these delta functions that's not what happens at off the distribution totally changes and it becomes a continuous distribution It stretched from starting out some high value and that's and then and then mistreated all the way down to 0 continuous And so what are the consequences and then how does that mean Ok and this plot at I have I normalized by that means the mean in the spot is here Ok I have some edges that are have to make a much bigger difference than you would expect in the mean and others that may get a smaller difference in the would expect I mean our Rick said Now I'm going to and she's 90 I'm Ok And this is the idea of edge demons so these are little demons that can go in and change the properties of any edge and for now let's just think about cutting that spring printing that spring and. [00:14:49] So that's what my little it's even does and I can go and I can pretty any answers that I want k. I suppose my platoon pretty completely at random Ok well then. Where the how much is what mom that list changed it's as if I remove a something from the mean they're removing the meat and for those Sure modulus that's the same thing you see is the same actual just repression for the book and share much alike so in fact the ratio of this year to book might have less is absolutely constant as I remove these bonds nothing happens. [00:15:30] If now I remove the bond that makes the biggest difference to the bulk modulus So I mean something at the top of the distribution for the bulk much less but the book change the book modulus is totally in correlated to change this year much less so for the sheer modulus that's really as if I remove the something from the meat Ok and so and that's smaller So that's a smaller change so the boat modulus a stropping much more than the share modulus and so that ratio shoots up Ok And this is incredibly efficient may find just by middling with. [00:16:11] You know one percent 2 percent 10 percent of the bonce I can change this thing by then a many orders of magnitude the scale is from tens of minus 8 percent of the well if there are 20 orders of magnitude on this critical scale so you see that we are changing the ratio of the folks of modulus to ship is sure to poke my hose experienced leaf or simply and remember this dashed line marks across under Schip 0 where the chip the ratio cheated over b.s. is 3 halves Ok so once you are above this the possum ratio is negative so we have very very fortunately driven the system to have a negative Fossum ratio at. [00:16:57] Right and I skip this. And just say that depending on which ones reproving we get different results we can print the bond that makes the smallest difference the sheer model as we can print the one that makes the smallest difference to the vote model is that turns out to be what you do with jamming Ok and then and you can get different results depending on your printing room but let's go back to this case this is the most interesting one where I prune the bond that changes the bulk modulus the most and that tries to be very strongly to art that behavior to make it across and Bishop behavior you think are what we're doing right by pretty the bond that changes the book modulus the most that lowers the most what we're doing is the same as doing gradient descent on the pulp modulus It's not like we're going downhill as fast as we can steep this descent on the book modulus and what are we doing well we're removing plants we've got we've got these learning I'm going to call learning degrees of freedom which means that each I'm allowing each edge of the network the degree of freedom that it can either be there or not there and I'm changing from there to not there by sending in this edge to him and to cut it Ok so what I'm doing is I'm adjusting these learning the degrees of freedom the presence or absence of the edge in order to do gradient descent deepest descent on the boat modulus that's exactly the strategy that a computer scientists would say to take Ok to cheat in the book module and once you realize that you know I was but I don't have to just do the presence or absence of bond I could say take out a barn and put it in some part else of the number upon states fixed or I could just. [00:18:58] Keep everybody there but I could see in how stiff the bond is what is the spring constant or I could change you know for some trick or springs that could change the equilibrium length of the spring it's a these are all possible learning degrees of freedom I could choose any one of these Ok I could choose any of these in order to minimize my cost function which is this case the bulk modulus and they realize wait a minute I don't have to just limit myself to a constitution which is the book modulus I could make my cost function I could tune it to beat any mechanical property any mechanical property that I can write as a sum over edge the properties of individual edges Ok Anything anyone of any mechanical property and that includes the plus one ratio it's going to include what I'm I'm going to tell you our stary I just need to construct the right cost function and then I can show you these are degrees of freedom and I can tune it Ok that's really powerful actually great right this is it really can basically take any mechanical network and essentially do machine learning on it Ok and given any property that we want any property that depends on the sum over edges the properties a bit has but there is a problem Ok this is not scalable wise enough scalable the bigger my system gets Ok I still have to know every single detail about my system so you know we have central core spring networks we have to know the stiffness of all the springs we have to know the positions of all the nodes perfectly we have to know we have to know that you can learn from lengths of all the springs you have to know all of these things in order to be able to calculate which Bond is going to change my cost function the most. [00:21:02] Right in order to degrade and it's sent we have to figure out which one to to fiddle with and that means we have to not only know everything about the the that network but we also have to be able to have an edge team and that goes in there and modifies that edge Ok that's gone on the computer and we do deep learning on the computers that's fine Ok but. [00:21:31] That's no good for designing a material Ok We want to be able to design the material without knowing all of the stuff in you know and all of the gory details. Is there a way that we can teach materials how to function or that they can learn how to function without using extremists and though it turns out that what we did initially was not to remove the bond that changes the book or share modulus the months that was a later innovation idea hacks there who realise that if we choose that then the other change the bulk and that changes share model s. are completely or correlated what current rich who worked with us initially did was different he actually print the fine that was that was the biggest contributor to the Focus your muscles and what that means and what that's equivalent to saying Suppose I take this is that and I put it under and isotopic compression or expansion Ok just very and then to talk more compression or expansion which Bond is under the biggest strengths Ok that's the one that we were cutting So now if you think that then you say well suppose I have a network that he does exactly like the network I have except that. [00:23:04] If it gets above some thrush in the pot and if my sperm gets above some threshold stripes if you can school too hard or compress your heart it breaks Ok then all I have to do is I can cheat the system and I can put it under isotropic stress and the ones that are into biggest isotropic stressed start popping 1st that goes pop up up up up and as it does that as these bonds break right the system will automatically tune itself to knocks at extinct because by each one that Hans is the one that is making at that moment the biggest contributions book modulus Ok which is almost the same as the one that changes the book much Alyson thus makes sense if I take this system now and I put it under shear strain then the ones that pop the print themselves Ok are the ones that make the biggest country share modulus which are on the same as the ones that changes your muscles the most and therefore I'm going to cheat myself to the opposite limit the biggest possible ratio that I can have Ok for the smallest Rishon the sure to book much less so when you think about that what's happening is that we're putting the system under stress by the way I'm sorry I forgot to say this if anybody has a question please as I meet your self and **** in. [00:24:44] Then that also I will know and I'm not shouting into the void. So. Does anybody have any questions yet Ok I think when I think about what's happening I put this thing under the stress and then the front start breaking right they start popping because they get up or something I feel stressed. [00:25:09] This but what's happening is that the system is evolving under that stress it's what is called Eating right it is changing its state according to the stress that it's under. And I just said that prune the bonds that are the greatest stress under an isotropic strain is almost the same as green bonds that change the book might just must look pretty in the ones that change but much less the model so it's like doing a gradient descent on the boat much less and but this is done naturally on its own this excuse wants to minimize the elastic energy right what the system wants a jewel is it wants it just the no positions. [00:25:57] It's going to break the course if it gets a person threshold stress but what it's doing it's going to just know positions so that each node is a mechanical cool Librium make the acceleration is 0 and so that's minimizing the lastic energy but what that saying is that the Comes function must be very similar to the elastic energy when you apply the proper strength. [00:26:26] And that's very powerful because then this icks is doing the minimisation for us if we can construct a cost function which is exactly the lastic energy when we apply the proper string you can't live with the proper boundary conditions then physics will minimize the cost function for us. [00:26:53] Now. And what's happening here each minute here is just responding this trust on it I just said Well Bond gets above some threshold Scrubs is going to power going to break Ok if you need to know what all the other bonds were doing to do that it just needed to know the stress on it and that's what's called a local rule Ok. [00:27:23] I didn't need to know everything about the rest of the system in order to do it. And just to prove that let me show you the results these are now real systems Ok they need to be machine just a terrific student incidentals for. Me So she took a solid foam Ok And she laser cut it Thank you I have to have one hit. [00:27:54] Parka because you can't. Yet say here is here is a piece of solid foam Ok it's like the center one Ok so what she did to get this was she put a note at the center every particle of a g.m. packing and she put that in a struct Ok in between every pair of overlapping particles to construct this thing that's sort of like this great network but of course it's nothing like a spring network it's kind of out of a solid bone it's very complicated to know what's actually happening what it is that you know but if you compress it so now you take this thing she takes this thing Ok And she puts it in this plastic frame which is smaller Ok. [00:28:36] That then compresses this thing it leaves it in there for an hour in the brain for an hour it takes it out and it says does this happen I get a possum Russia right because the idea is that the regions of the system if I compress it the regions that are under the biggest stress are going to deform the most Ok so the system is due to aging along this path some path that to put. [00:29:09] That is dictated by how much strain locally each region is under Ok and we say well that should give you a negative plus one ratio so does it end. And so here's the system this is called the blue the blue diamonds here are called the jam network and here's the plus on ratio as a function of the strains and which you age it so how how big is this the smaller it is right the bigger the strain. [00:29:40] The frame the bigger the strain that the system is and her Ok and what you see is that if you age it and in a small enough frame Ok big enough strain Ok the platinum ratio does and sorry blue diamonds the prosecution doesn't go negative Ok so this system just learned how to have a negative possum ratio and. [00:30:11] Now I can sort of mimic what's happening this is you know this is part of the central course spring network which is nice because that's saying that the idea is very robust but you know for a few people theorists brains. Let's think about it in terms of a a a central for Sprint network and those and that sense there's sort of 2 things that can be happening this spring constants could be changing in other words I could be changing the properties of the material by aging it in the frame Ok or the network geometry could be changing Ok it certain regions could be classing more than others etc and I'm going to in my case you know central for spring morrow I could say well that's like shooting the equilibrium likes and how important are these 2 effects changing and mature properties or so this changes the geometry of the system well she tested that by taking that compressed system Ok the system after it came out taking a picture of that and then laser cutting that network same geometry out of fresh all the foam and that's the green here. [00:31:26] What you can see is that still goes negative but that doesn't capture everything so part of it is the change of geometry that's caused by the green part of it is a change of the rich or no properties that's that's the difference between the green in the book Ok so because the green was it not because changing the geometry is actually not to drive it's negative plus some ratio we're going to just focus on that we're going to just say let's have a simple model of a central core spring network where they can have the in length of the bond it's under tension it wants to get bigger and if it's under compression it wants to get shorter Ok so it just has the some pull Ok We're going to call that the l. model and just look at the behavior of this system. [00:32:22] Right so the change of equilibrium length is just that proportional to the stress on it I think with this being pulled or being compressed and if you recall the total lastic energy right for spring escape times Al I'm going to sit secret live I mean squared might square for every edge and so this is equivalent to doing gradient descent on the elastic energy Ok under the conditions where it is in the frame Ok And when it's in the frame when am I doing what I I I can imagine to what I'm doing is like putting on a strain and the horizontal direction Ok a slight s.. [00:33:09] And the response I want is for to see the system deform in the protocol direction by exactly the same amount that would be a pos and ratio of minus one Ok if I I put a straight up sinus in the horizontal direction if in the vertical direction I get a strain which is compressing you know decrease the decrease in the size and it's exactly it's that amount that's a pos on racial minus one so what am I doing I'm putting it at frame where that's exactly what I'm doing I'm when I put it in this frame I'm compressing in the horizontal direction and the critical direction by the same amount and so I'm putting on the response that I want to get and I'm going to call that the clamps founder condition where I apply at the target which is the top and bottom. [00:34:04] Side top and bottom and boundaries apply the target pressure that I want at the same strain that that I want at the same time that I ply that source right I'm going to call that clamped Andrew conditions and we are doing precisely gradient descent we're just seeing the degrees of freedom which in this case of the room length of the springs in order to minimize a cost function which it is just that last a can or G.'s Ok but the claim that a condition and the system one just naturally do that on its own Ok. [00:34:43] And that works. Ok I showed you already that it works if I just compress it and hold it it also works if I do cycles of compression and expansion cycle compressed expand compressed expand I do that many times then that also works I can try that process on ratio if I have enough cycles I start out with this is them Ok and I apply more and more cycles that compression expansion in eventually the positive ratio gets very close to minus one and well even well into the non-linear regime. [00:35:16] And the range over which it's minus 20 is essentially get paid by the magnitude of my training stream. K. so. This is the cool thing right that we have edged events that works that works just fine but because the system is disordered I want to emphasize it's important that the systems disordered because if it were perfectly ordered every bond would be the same thing so because as this order because not everybody has the same we can use the stress the stress this year's distributed in with genius fully in the system different rates are under different amounts of stress and we can use that Clyde stress to direct the e.g. process in order for the system to learn the possum ratio even in the non-linear regime Ok well what else can we do and how can we parking we push this idea and said we can do you need property we want well what's an example of that so the other one that we focused on is Alice Terry and this is inspired by proteins so what is Alice Terry to Alister is a property that for example most and signs have. [00:36:38] Though if you have man made catalyst it will just go do its thing and till it gets fouled and then it will stop your pay but enzymes are much smarter than that you think they can be turned on and off depending on what you want and so here's a case where the enzyme which is this glue blob here the protein Ok gets turned off Ok so here's my molecule this red triangle is my molecule that wants to wants to buy into this protein and then get chemically altered by the protein and this is the molecule that the enzyme is working on it so it wants to bind and get chemically modified to go out but in this case it is unable to climb in still another kind of molecule called the regulatory my field finds to the protein somewhere else Ok once this thing is spent on it changes the conformation the protein way over here so that now this red triangle combined So this is how the enzyme is being turned on it's being turned on by this green molecule and and I think about this and mechanical terms what I'm doing is by binding this remark you I'm applying a strain to the protein here at this event and the response of the protein is to give rise to a strain year at the target Ok that now allows the substrate to public and because a symbolic binding of comparably sized molecules Ok what that saying is that the target strain that I get over here is about the same and magnitude it's a border one compared to the strain that is supplying here. [00:38:37] They say Ok a big deal elasticities long ranged right I can transmit about 6 signals a long way but in fact deprivation due to case very rapidly put distance and so to get an order one response here is pretty special for a typical pretty good sized object but you would expect us to have response over here on the other side the protein where where you know I was Terry usually is these juiced the source and the target sites are usually separated by by the sort of distance You would expect a response that's 2 or 3 orders of magnitude lower than what you got at the source so if you get a response a supporter one there is pressure 100 pretty used to that day and can we teach I mean chemical network to be able to do that well it might really have young collie the any kind of Tori heard about this and she got really excited and she said look you know the same thing happens in the brain Hey so the brain is a very small function a heart full of mass but it actually uses a huge amount of oxygen that comes into our minds and uses that that oxygen is used to support brain function Ok And what happens is that blood enters the brain right through the arteries so I have a big pressure drop at the arteries Ok I can I can think of the brain that then allergy would be a resistant network perhaps a large will switch drop across the. [00:40:24] The r.v. nice and then depending on what you're doing Ok the brain is going to send extra oxygen to support that So right now I'm talking a-K. in the brain if my brain is sending extra. Oxygen to my speech cortex to support it so that I can talk Ok. [00:40:49] Now. How does it do that it does it by sending extra blood flow there Ok because but is carrying oxygen some more put float means more oxygen that means I'm tuning. A pretty big pressure drop Ok at this speech cortex and how does it do that it actually contracts individual that's what's blood vessels in this network or it dilates them in order to send extra blood flow to that particular place and what that's doing is it's tuning the properties of individual edges of this network during the conductance is of the edge edges by dilating or are on contracting vessels changing the conductance has to direct extra pressure drop of a given magnitude to a given place to my speech cortex Ok so how does it do that thing question. [00:41:48] Mathematically that you systems turn out to be quite similar and you can see that because energy minimisation in the mechanical network means that every note should be a mechanical equipment no force 0 force and every node. And in the case of a closed network right the flows at just so that the network is at a minimum of the power dissipation and that gives you Kirchoff's law on every No Ok so mathematically there that these 2 problems are quite similar. [00:42:19] All right so now so there is actually a very healthy happy community of people who take. Crystal structure as opposed to proteins Ok and convert them into great networks Ok so I can think of a protein as a spring now you have. And then you can ask Ok does this have steri according to this free network or not that's not what we're going to do Ok we're not going to actually start with real proteins and then look at their spring networks and see if they have Alister but we're going to do is we're going to start with collections ensembles of just ordered networks in our case that came from jam packets because that's what we have lying around Ok And we're going to start out with these disorder networks and we're going to design them with Edge demons Ok Do you have Alister And so how do we do that well our constraint is that I want Suppose I place or strain which I'm going to call one going to choose units on my star stream as one Ok my constraint is I want my target strain to be at least as Delta from Delta Ok And so I construct a cost function which says If my target strain is less than Delta I pay a price. [00:43:57] Now and then I minimize the cost function with respect to for example the stiffness of the bond so the equilibrium like the bonds and the presence of assonance of upon those at my $30.00 degrees of freedom as I said before I think I just minimize my cost function but respect to these learning degrees of freedom using the set humans and so I'm doing this on the computer. [00:44:22] And I just want to show you that it works Ok so here it is and its network on the Left my to read notes here are those of the source notes and I'm applying a strain in between those notes which I'm calling one and then I read off the strain across that you target notes Ok and this case this is as as originally constructed here is my network and the starting target strain is point 005 Ok quite a bit smaller than my source tree now I'm going to start changing in this case the stiffness of each edge Ok I'm going to start treating it as a team the stiffness as the target straight is going up that only that blue dash wants corresponds to sprays that end up getting removed entirely Ok And at the end of the day but I'm it worked I was able to choose a strain of one Ok across this target Ok which is what I wanted so this network now as Alister Ok here's a slow network on the right Ok I'm applying a large pressure drop of one there to check calling one. [00:45:36] Across these 2 red notes and the pressure truck across these 2 green nodes starts out as point 003 I want to tune it Tapper pressure drop that is at least point to Ok so I'm going to start tuning out the conductance as each edge of the spring and matching dilating and contract ing each to change its conductance the blue dash ones are the ones that it gets to a very small value so they're almost entirely and at the end of the day I did get to the pressure point that this works well about 99 percent of the time why that is true this is an interesting question and so what you ask me like. [00:46:19] It's an interesting story in itself. But I just want to leave you that we can do it and do it and it essentially always works that almost always will but we don't just have to do it with Edge demons Ok we can do it directed e.g. to so. [00:46:42] Here it I'm using the element Ok Where remember if this frame gets stretched it wants to increase its equilibrium like that it gets compressed and wants to decrease it and when I'm doing is I'm applying the clenched boundary condition right where I'm a climb a strain and that at the source Ok and I'm applying the strain that the target that I want the system to keep to evolve to that I plant both of them and I do that I put on a bunch of cycles with this aging rule Ok this local rule and then I have a readout cycle where I say Ok let me just put the strain on the green one what is the strain on the red that comes out just when I put it on the green Ok And this is what this shows Ok so the green one there reading out the straight of the green when at each readout cycle it is you know what I put on it has it's about so as to restrain of amplitude one Ok but here's what's happening to the target bond over time Ok as it ages under this cloud boundary condition I'm doing both of them Ok if I take off the target straight and just at the source the red one is gradually that the target strain is gradually increasing over time and eventually reaches the same stream as the sort Ok I'm able to get a response of one compared to the source. [00:48:14] By doing repeated cycles of compression and expansion of the target source. So it works. But not always said case and now here's the dirty laundry that. The wrecked it aging requires that there's coupling between the source and target what can happen is if I play the source I ply the target Yeah they both go on but now I play the source maybe nothing happens at the target because that you are not coupled together and it turns out that they if you're close enough to the limit just having enough. [00:48:55] Springs per node just having an iconic to have any of each node so that the system is just barely mechanically stable that it's no problem to she cheated the sort of function but if you're way above it it doesn't work. And so. And so in fact this strategy did not work on floating arcs and. [00:49:21] This is now where my current post hoc knock Eastern comes into the picture so what he did was he took ideas from machine learning and for neuroscience Ok so contrastive learning. And it was seen that it's probably equilibrium propagation. But wish generalize this idea so the idea is the following I want to apply the clamp condition where I apply the source and I find the target response and I want and what I want is that under the 3 condition if I apply the source the target will do what I want right that's really what I want I want to just apply the source and get the right strain coming at the target it. [00:50:10] No way you do that is just you start with your network and you let it evolve for example according to the model but now you don't go downhill just with that last week energy from the class difference between the clamp in the 3 In other words you want to say I want to penalize the 3 case and I want to encourage the class kids. [00:50:34] And and that works Ok. So this just shows. The error function there the error goes down and these things are learning a lot stary I'm just going to just take my word for it works and the results are almost the same as what you eat it with from gradient descent Ok the directed agent corresponds leaving out this term Ok. [00:51:02] And what this does it is basically give you any cost function you want that you can construct as a property of the sum of the properties of edges you can now this gives you the local rules that you need to apply and order to mimic or directed aging to mimic. [00:51:24] Gradient descent on the concentration and the thing I just want to get you I know we started late and I just hope I can take a couple minutes show you where we can do it we and this is these are your experiments by Santo Subito and Dr Ian that I absolutely thrilled about where they constructed a network this is an electrical resistor an arc which is directly analogous the flow network that does it implements not he's couple turning rule and it works it can teach this network things Ok so the idea is that this network has edges that implement local learning. [00:52:07] And so each edge just response to the Baltic states across a. And here's the 16 network really tiny network and this shows that it can learn how to classify irises So this is the famous dataset we take for measurements of irises the pedal sizes and so forth and then and then there are 3 different species of viruses and the question is from these 4 measurements can you distinguish for a given picture which we're given set of measurements which Iris belongs to which species Ok And so this is a classification error over time so we're going to represent these measurements by 4 different voltages applied at the source notes and then the target notes there are 3 target notes that light up depending on whether it's species one species 2 or species 3 Ok And this is the error of classifying in the network you see the stars are rather large and then drops in the n.t. 97 it at 23 percent it gets 97 percent accuracy and classify and these irises and but just not like you know a neural network can do it with 100 percent but he now take 97 percent. [00:53:35] This just shows that they can learn different things so for us to learn how to classify the irises now it's going to learn Alice Terry I have one source known and I have to target notes that I want to have given both hitch and boom it learned it Ok the classification error dropped and you know if it's learned it Ok Now then I say No no I want these 2 source notes and these 2 target notes to have certain specific identities yet her that to then I want to test 3 we're now I have 3 sources and 3 targets. [00:54:11] And I have 4 sources and she targets and I'm going that to then then then say and said Ok well can you learn not her can you learn how to do linear regression can you solve 2 questions that you announce that figure out what that what that what the with the with the copious and should be and in these equations and yeah it could be that chip that's fine and then here's a different line your question problem it could be that chip that he said Ok Now go back and learn Alister again it was able to do that and so this thing is really learning it's very different things that as you get different influences learning different things Ok. [00:54:54] So it really is solving these problems. And if we think why is the so great why don't why am I so throat that they were able to do this it's because by thinking about a brain our brain is incredibly powerful and it's also incredibly robust to damage so that some people actually because a superior a policy need to have half their for ensuring that and they can still function Ok obviously you can't do that with a computer and say I've had this keep video of an i Phone that you saw it in half and stuff for t.v. it's like that. [00:55:34] But I don't know arts are like the brain they're incredibly resistant to damage so this is here's a network it has learned Alastair it Ok I would choose sources and she targets and now Sam removes the brown edge and is still learning yeah isto learn to do it now he's next. [00:55:55] The yellowish Ok than the purple it's a greenish the bluish as he snaps this network it still manages to learn Oster Ok so it's incredibly robust or damaged in the end sand is removed find out of 16 inches and it can still learn what we want to learn but it's really robust and so. [00:56:20] So so I'm excited so couple learning so what I want to leave you with is optimization of a consultation provides us with a way of deciding any desired mechanical or flow response that we want as well as it can be written as a sum of the properties of edges and that's that asterisk there. [00:56:43] And then couple of learning allows us to develop the right local rule that will mimic doing gradient descent on the cost function Ok so if we can. Design systems that implement that look at what they will be able to learn they will be able to learn anything we want Ok I don't think and we were able to do that in a real not with Sam and that great able to do this in a real system so I'm just. [00:57:15] You see this is recent I still just thrilled and so excited about this so just to show you the people to work side Mackie is the one who came up with this great couple earning grew up on sand and someone has implemented in an electrical network my terrific collaborators lady kind of Horry. [00:57:36] My collaborator of over 20 years so that said they go and don't carry and it worked with Sam to cut these now it's so thanks very much sorry I went and did take up almost all the time that I took by delaying at the beginning thank you so much Andrea. [00:58:04] That was really really fascinating. So do we have any questions from the audience. Yes since I'm on my own i Pod I'm not getting I can see your shot but I can't necessarily see all of your hands so if you do have a question why don't you know I'm mute and ask. [00:58:39] Ok. Michael because you have just I really like this last part with these with the small network Yeah and I'm just kind of curious whether you can speculate that this will be 2 better more efficient computers in some way. Yeah so. One of the things were working on is to see whether this we can turn this around and actually develop better machine learning algorithms and they could be implemented in neural networks 5 local rules Ok so that's that's that's one thing that we're actually exploring. [00:59:26] But but that idea this is not so so what are the advantages of this and disadvantages of this compared to at your own Well you know all that work is actually much better at it but. You know you get to much lower hers. But you don't and that's because it's non-linear and our network so far each is true we're just finding resistance is to resist her network we can make it not only here by using Di hits and so forth and that's something that we want you to see but that we can learn better so what are the pros and cons of these 2 ways of learning Well the one thing that if I keep this physical network. [01:00:10] Ok and I make it twice as big hey the time it takes for it to learn doesn't increase nearly as rapidly as it does should not Ok they think it's an squared as opposed to end Q. I'm sorry elsewhere to suppose system size system like squared as opposed to the number of nodes. [01:00:36] You so so it is much as it should be much more scalable and in fact it you know the problem with deep deep neural networks is that they take a long time to train and I don't know if you remember some of the Google Translate got a lot better just a few years ago. [01:00:56] Than it had been before and the reason why it did is it just took all that time to train and if you have an example since you train it and then once it was well trained it did great but it takes a lot of time to Cheney huge network to do that so that's that's one issue maybe that's good but the idea of this is not to compete when you're on the r. o. But let me just say another approach of this is that require spark less power than a c.p.u. this is the power of the electrical resistor network whereas a dealer will get to power the c.p.u. and sell it for press much less power so I think it's mighty nice ball is sport robotics. [01:01:35] Ok and if you know how some extra products you want to be able to look for environment to spawn who are. Even much less costly in terms of our. And also system size and do you have one of these there's a gun that works in there that learns the odds so they talk every Just wondering if you've got any more about To what degree you can predict non-linear response and additional when their response isn't as Muslims. [01:02:08] Yeah I mean the only response is not a problem right because I can still write down the response as a constitution and then minimize it yeah but is not sorry because it's hard to figure out like that on the responses well writing it down can be harder yeah that's right but you see we directed aging or the couple earning you get you get around that because you don't have to figure anything out right are you doing if you apply the strain you want as long as your edges have the right properties and it will it will develop a seed of response if you want to care but you're right it gets you know it gets harder to write down the cost option you know. [01:03:00] I'm still one is asking question but I can't see your name because it's currently covered by a bar I like blue jeans preference bar step just what I need an answer ask it be kept. Ok. Great talking throughout really enjoyed it. I question it is up so a lot of the results it is shown here are for I'm searching for a child limit so I wonder involuntary if those notes are somehow vibrate in. [01:03:36] Public outrage as to how what their results translated 3rd are systems. Yeah so so right real proteins you know are and answer temperature and cell and history is not necessarily their temperature response sometimes it is but sometimes it is not. And so do you know that inside Alice Terry Rhea from fluctuations is different if you have small enough thermal populations so that you have harmonic fluctuations from the minimum then nothing changes but if you have a big enough. [01:04:13] There are going fluctuations so that you're actually changing the current confirmation of your approach and you can have sort of induced Well sort of rearrangements In other words your Sprint network is actually changing which things are connected the effective screen network is changing where the edges are due to them for actuations then it's a really different story and that's one thing that we have not I have to say faced up to yet what happened can we can we to with it you know equal success or some success when you have what should be she's present and I think that's a that's a really interesting direction to go into this in our proposals that we have any other questions and not it's of the people who have their cameras on I don't see any hands I have a question as well awesome so enjoying the model that you have of the spare parameter which is basically telling you the rate at which you are intimate directed aging Yeah so I'm wondering if you have considered something at what you forget what you've been taught to or whether all the definitions you look at are going to be plastic and just last forever. [01:05:39] Yeah so that's a really interesting question and. So. So partner with we've just done them so that they last forever and this this realization. This what you call network this Sam and that built. This is like that and last for ever but it would be really interesting if you could forget on some time scale and we you know I'm pretty sure of science that forgetting is this is equally as important as money and you do want to be able to forget things and so to put in that high school is interesting the other thing I should say is that the time scale that comes from this learning will. [01:06:22] Ok but this time see it here that this is the rate of change right there so there's a there's a cook fish out in front here which is which is the time scale. We're assuming that that is long compared to the time that it takes to equilibrate the physical degrees of freedom and other words I have this eclipse agrees a freedom which are the currents on all the edges Ok that I have 30 degrees of freedom in this case which of the conductance is and the idea is that the convection says are changing on a much slower time scale than the actual current so that each instant right the the current cycle of rating. [01:07:08] For a given these given conducts its is and then I choose the conductance and then the currents adjust and so forth and they just instantly. And in and machine memory names are in. Neural burning actually you know in the brain those g. time scales are not so well separated so the question is can you slow down and. [01:07:37] Or came can't can you speed up that to slow down one time scale and speed up the other so that they're more comfortable and what is that due to learning and it turns out that that also works and and that is actually quite interesting in itself. And if we can do that if you don't have to use that the reason why the analog of this in Michigan there are any which is called equilibrium propagation has not been taken up is because it makes that approximation Ok that the quote and so the currents it could be very rapidly to the conductance us. [01:08:17] But if you release and release that condition. Then then this could actually become a practical thing for machine learning and and so that's something that we're working on now that's you thank you yeah. I think given that we've run a little bit late we're starting to eat into I think his abs time with you Andrea so it's Ok. [01:08:51] A great time for us to thank you all and think well I'd like to also think the audience for such wonderful questions they were yes. And primarily questions from students and post arts which I think is but just goes to show how awesome my students are postdocs are thank you all for being so perceptive and having such interesting ideas there but they're part of it when you're a direct thanks so much and everybody will talk.