Pow what's up everybody once again it's Brandon and Shawn and today I'm going over three branding elements that play significant parts in Chief Keef's rise to success meteoric rise at that and y'all can thank KD Black for this video appreciate you asking bruh so let's get to number one. Chief Keef had a unique style and flow I think that's pretty obvious for the people who heard him during that age before people started copying and things like that but that whole yeah that sort of mumble and even his style of mumble is different from most people's style of mumble and he didn't always rap that way by the way. So when he changed to that style cut through the noise. Number two his hardcore street persona and I know a lot of people are like how could that really differentiate Chief Keef how could that make him different well a lot of people underestimate the fact that thugs don't exist to the extent or gangsters or street people or whatever you want to call them they don't really exist in hip hop to the extent they used to nowhere near people underestimate the takeover of the backpack or I'm weird or I'm so different I'm artsy or I'm hippy type rappers since Kanye West has really started that way back in the early 2000s. The hardcore thug thing doesn't really exist anymore and even when you see a lot of them they will be so fake and they will be so you know made up and done up his was so wrong where you're like this dude he really don't care he don't even know better he should be flashier and have all these jewels this is just straight authentic and genuine when you're watching those first videos of Chief Keef and him being in the streets I can't forget to mention that he really started to create a wave and bubble locally at first which actually makes for a great launch pad for a career once people on the outside start to discover you specifically if it's through the internet and just other general media and those elements alone actually in most normal cases would explain someone who blows up in the game and becomes popular and gets a wave or attention for a certain period of time but they don't account for Chief Keef's meteoric rise that he had so much and so suddenly as it seemed and what the cause that was yes yes no Chicago Chief Keef's rise got accelerated and amplified because he was from Chicago in a time where Chicago as a whole was trending nationally on news it was starting to be branded as one of the most dangerous places in the United States news outside of music completely just regular news networks so you've got the city getting attention and then when you have this guy who comes and starts to get attention himself alone but he's coming from this lifestyle that's representative of what is already getting attention the type of danger and things that's getting attention from the city he becomes a poster boy so now when you hear danger and violence of people getting shot in Chicago the people from the outside Chicago who aren't fully familiar which is most people right most people in the world aren't from Chicago they start to think Chief Keef when they hear Chicago they'll hear Chicago then they'll think danger then they'll think Chief Keef and then when people hear Chief Keef they think hey Chicago so now you have these mental associations which is so powerful in marketing and branding if you can position yourself next to something that's already trending or take responsibility of something that has legs on its own that's getting pushed as a concept and you become a poster boy or girl for whatever that vibe and wave is you're getting a lot of work done for you with very little effort because yes you spend time marketing and pushing yourself but that other thing is already creating conversation which by association creates conversation for you and that's a huge thing that you know it was kind of just timing you really couldn't have planned it to happen or Chief Keef that way so you know sometimes we have those luck of a draw once in a lifetime situations it's not they didn't have what it took to blow up but to blow up to that scale was like 50 cent level of not only am I a street dude and rapping but now I get shot nine times and survive and now I'm coming out with more music it's like oh you really are from that lifestyle Chief Keef is similarly like oh not only is this like the worst city and they're always and they're always putting like hey 600 people died in this panel time and 30 people died in this span of time well I'm from that lifestyle so it's real real real and people are attracted to things that seem real and dangerous when it comes to that specific type of brand anyway please share this if you found it helpful any kind of way and you know what to do hit that subscribe button


Today, my friends, I'm making a gumbo that nobody's gonna be able to complain about. Check it out.  Take your three andouilles and we're just gonna toss them in. Now that's your andouilles, just let it cook. Our andouilles is done, but look at that natural oil down in there and that real flavor. We're gonna leave that right there and we're gonna add to that sausage grease a half cup of canola oil, then about three-fourths of a cup of all-purpose flour. All right, so one of the most important things when stirring your roux, keep it on low and you must have a wooden spoon because plastic will just melt away into your roux. So we got our roux right where we want it. Notice it's not smoking, so you can't complain about it. Going with our whole eternity. That's green pepper, celery, and onion. Now we add us a couple tablespoons of minced garlic. Pour that in, that keeps cooking. After a few minutes of slow cooking, we crank it up. Now we add one big container of chicken stock, six cups. Now get your andouilles, put a little dantos on it, and now it's dandouille. If anybody can do it, dandouille can. Cut up our andouille. And add your andouille into the pot. Add in one and a half pound of cut up, boneless, skinless chicken thighs. I got some of my special Cajun blend here that I'm gonna add to it. Now you know if you're cooking gumbo and you wanna do it right, you gotta do this. Reach for a bottle of that dantos spicy. That's the red top. I got about that much in there and you know we're gonna add all that flavor. Get that mixed in. That's dantastic, dantomite. So this has been simmering for at least 30 minutes now. And the last thing that I do right before we serve, we put in some frozen cut okra. We cut the heat off, we're gonna let this sit for five minutes and then we eat. And if you're wondering why I use frozen okra, well it's because if you use the fresh okra and put it in here, sometimes it just gets a little too slimy. If you use the frozen, it's never gonna be too slimy.  Turn it upside down.  That right there my friends is how you do it. Now let's give it a try. All right, so now it's time to eat. I brought in my salesman Tyler because he likes to complain about everything. So Tyler, here's a spork. Let us know what you think about that. All right, you know I love a good complaint.  Only thing, can't get this cadence season in anywhere. Not yet. Yum yum, get you some.


Alright, I have a feeling things are about to get, uh, complicated. Ladies and gentlemen, welcome back to the channel. My name is Jack the Buster, I, Shinobi. Today we have episodes 66 and 67 of our One Piece Watchthrough. The last one kind of dropping a bombshell at the end, revealing that this woman is Princess Vivi. Again, if you didn't catch the outro of the last one, I have the figure of her. It's a long story. But nonetheless, things are not as they seem with these two groups that Vivi and her group was, like, infiltrating the Baroque works. I'm not really sure. I'm guessing we're gonna get answers this episode of these next two episodes. There's only one way to find out. If you knew the channel drop a sub, hit that big one. Bells from the future episodes. Let's get started with episode 66 of One Piece. I mean, if you guys have enough confidence, you can take on Zoro. I think by they means, like, Vivi in them? Yeah, VIP, that's Vivi. Okay. So he's her bodyguard? Makes sense. Squad captain, security. Okay, yeah. So they found out a little bit too much about Baroque works and the boss's secret. No time, baby. And the question is that aside that Luffy, Zoro, and all of them are gonna want to be on or not? Yeah, Luffy's just still asleep. Just chillin' in the middle of the battlefield. Oh, no. Oh, I thought it was gonna be precise. That was a whole explosion. Oh, no. Egorom. Oh, shoot. What is happening? That was so slick. I know she used that already once, but why did she cut her hair bit or her hair tie? He doesn't know? What? He's just dragging Luffy. I love how they didn't question it either. Hey, this is a good bodyguard, bro. Given his life for her. Oh, kingdom of alabaster. Okay. So she's like the princess of alabaster? Do not tell me his power. Is that he flicks boogers, bro? Don't tell me that. Please. You've been a pair for a long time and you didn't know?  Hey, this is so sad. He's gonna get rolled. Explosive boogers. Are you sure? Show. Are you sure this is what you want to do? Wait, he's gonna bat it? Oh, no. He's just gonna take it to the face. Okay. Mr. Nine, we didn't know you long. That's a rough way to go, bud. Please protect her. Oh, okay. They both have devil fruit powers. I feel like that's going to be very common here in the grand line. Just randos with devil fruit powers. Just making a run for it. Stop laughing. Hey, that sounds pretty nice to me. Yeah, I'm very confused by all the like alignments here. I love how Nami is the one to step in and say yes. Is that worth it? Okay, at least some of us have some kind of plan here. Zoro and Nami being responsible. They're negotiating. He has no time to negotiate. He's just gonna say yes. That's kind of fair. Yeah. The most he can say is he can try. I would say this is shameless, but yeah, they were trying to kill them a minute ago. But why is the princess involved in like a very dangerous mission like this? This doesn't seem correct. She's just the middle man, bro. He's just laying there listening to the bite. Good morning, Luffy. Oh my gosh. Oh, wait, wait, he does. Yeah. Oh, I don't remember that. A ruthless business woman. Hey, you agreed to a different contract, brother. Oh my God. Dang, son. Oh my gosh. Go, Zoro. He's run. You tried your best, buddy. Yeah. Zoro will try his best. Again, if her dying would be the falling of the kingdom, why is she here? Run, Vivi. I don't think you're getting out without help. Is that Luffy? Oh my goodness. Why is he still so large? Yeah, Luffy has absolutely zero contacts of what's going on. Man's just about to go back to sleep. Uh-oh, there he is. Boogerman. Run, Karu. Who is this? Oh, Miss Monday is on her side. Oh no. Everybody's giving their life. Oh my gosh. Oh, this is so sad. She's right. She is. Let's go, Miss Monday. Okay, why is he going in melee range, though? Oh shoot, never mind. Oh my gosh. What a clothesline. And then a booger to top it off, bro. He's kind of cracked. Miss Monday is dead. Bom-bom fruit. Stop this laughing. Hello, Kilo. Does she like dive bomb? Oh, I see. And then she... Yeah, she does dive bomb. She just like insanely increases her weight. That is terrifying. Low key. Okay, that's so overkill, dude.  They are a very dynamic duo. Straight buried her. That's a really cool name for a kingdom, though. Alabasta. Go, Zoro! You better dodge, Vivi. Split the booger. Hahaha. Wait, what? Was she about to, yeah, attack Zoro? Why else would he have stopped the booger, bro? You got the lore, bud? I love how much confidence she has in Zoro to take them down. She's not even gonna go. Oh. Okay. Your classic crime group. I have a feeling that like someone found out who's the identity. That seems like the main thing. Oh, we'll have a high ranking whenever the said ideal nation is founded. They're all fighting for it now. Mr. Zero. The stronger they are. I always was to know Mr. Zero is even as strong if we don't even know what his face looks like. Sounds to me like he's a poser. I don't know. I owe someone money. I hate that so much. Oh, Luffy! What? Why is he still large? Is it because he ate so much food? Can he actually not change? What is he doing? What? Oh, my gosh. Luffy thinks he just murdered all these people? What? Oh, my gosh. You can't be serious. Does he think Zoro just snapped and went on a killing spree? Luffy, no. Ay, ay, ay. Are they even going to get in the way or just let Luffy try to attack Zoro? Look at him. He's the one who went over. Oh, no. You're not even going to listen to him? Oh, my gosh, bro. Luffy, please. You're not enemies. He's enraged. He's like, yeah, I want to see how this plays out. And now VV is just unguarded. Uh, Nami, can you get in here, please?  That's going to hurt because typically he would have more faith in his friends like this and not just immediately think that Zoro is just evil.  Oh, my gosh, he's flattening the town. I'm going to be honest, the whole kilo kilo first kind of cool. Oh, oh, my. Oh, my. He worked off the food. Well, Mr. Vives down like nothing too. Luffy, please stop. She's up there. Please, someone. Dodge. Oh, my gosh. Oh, shoot. It's go time now.  I mean Luffy more than Zoro, but oh, my gosh. This is so frustrating, bro. I mean, Zoro isn't actually fighting to kill. I think he just wants to put Luffy down to unstoppable forces, to immovable objects. At least he took down Mr. Vives first. Oh, shoot. Oh, no. Luffy, you lack critical information, brother. I mean, Nami could actually clear it up if she were here. She could just yell at Luffy and be like, no, listen to Zoro. But again, I think Luffy is still a little tipsy. I want to look at those wanted posters. I need to go back. Oh, no. She's right in the middle of it.   Why would you get in the middle of this? It's like a tornado. Oh, no. The fear of God. I need to go back real quick and see these posters because I think it showed our lungs like really early on. All right. Who do we got? We have D-Jot, Schupeel, Gloss. D-R. Does that say hit, man? Okay. I feel like at least one of those is a good chance of them popping up in the future. Dude, Luffy can be so frustrating sometimes, man. I get that's who he is. But again, I thought the whole thing was that he just trusts his friends. Like he knew Nami was going through it, but didn't even want to know why he just knew that he was fighting for her. Episode 67, I guess. Let's get it. The pure rage in their eyes. That's a cool shot. Getting in the way of a fair fight. VV space. Jot on the floor, bro. These two Baroque works agents are just like laid out and one to hit each. Oh my guys. Chill this energy. They're like radiating. I love how VV isn't even using this opportunity to escape. She's so so entranced by this. Thank goodness. My goodness. That's what they needed. Again, not a confirmed billion. She's like billion berries. You're still trying to put each other. It's like two kids, bro. You make the contract or you die. Oh my ideals meal. Why he tried? VV is just so over it. Did that other guy actually die? Yeah, you probably got so much money. Oh no, this is going to be a sad backstory. Isn't it? Alabaster is like hella poor or something. Oh shoot. Don't have money to spare. Oh, Baroque works. Are they the ones that incited the civil war? Oh, so that's why. She wanted to find the boss. Yeah. Oh, is he okay? Yeah. You couldn't send anyone else? Or did she just take it into her own hands? I can respect that. She's like he told me to. They just want to. Oh, they don't want to overthrow him. Yeah, just take over. Okay. And just have whoever this boss at Mr. Zero rule around Alabaster. Yeah. All the money's being used on troops weapons, etc. Luffy's intrigued. Why? Who's listening? Luffy's upset. Oh, shoot. Rock-a-dial? Like the animal? Oh my God. Oh, no. Oh, warlord. Why is his name Crocodile? Nami's like, we're doomed. Dude, that's sick. No wonder Luffy's hype.  Wait, so is he Mr. Zero? Oh my God. Legit inspector has her images now or detective. Yeah.  That's not even close to a billion. Who's are those? They're going to be like on him. Poor Nami looks so depressed over there. Oh, a thousand. Oh, he's disguised as her.  Oh my gosh. What a beast. They really want to check on Usopp and Sanji. I really hope that crocodile is an actual crocodile. Oh, that's right. 80 million. How much is Luffy? I forgot Luffy is lucky. 80 million when he did have one. He's a warlord. There's only seven of them. Dude, this man actually sacrificing himself. My goodness. Journal pose. Is it like a log pose? Oh, shoot. Wow. That's pretty OP. Oh, I see. I see. I see. The set GPS. This is low key. So sad. Two or three islands away. Okay. He's a G, dude. You're not going to make it out. Oh, he's talking to them. Oh, he's about to have like a thousand people after him. Oh, seven, Igarum. Oh, seven. I hope he makes it, man. That dude is fearless. It's all for the kingdom. There goes our hero. Watch him as he goes. I had a slight feeling that they would see the ship in the background just blow up. Oh, my God. Oh, my God. That was sitcom level timing, bro. Igarum, no. Bro. Crocodiles crew, don't waste time. Oh, my gosh. Dog, that was a whole new, like actually not compared to them. Oh, my gosh. That's so sad. It was just the timing of like how you can see it in the background while they were talking. I was like, something's going to happen to it, man. They have a lot to be filled in on. The plot has thickened. God dang. My boy is moving. Oh, that's her bird. Oh, no. Oh, no. They already know, dude. Oh, no. The answer cut card is a duck. It showed it as like a little baby, so she's had them for a while. Oh, my gosh.  I mean, they clearly have firepower, too. You guys don't understand. Everybody's dead. Smacking them. They'll figure it out. You got to get out of there in the thick of the fog. And they should have some kind of lead, the fact that they deported on a different part of the island. Oh, no. Was what? She on board! Did she fly? So which day of the week is she? All Sunday? Why is that all before it? Oh, my gosh. Oh, she's got to be like cracked. She wanted them to know her trail. What? It's brave.  I mean, it's dangerous. Oh, my. I mean, she got on the ship without anyone knowing. I don't know if this is going to work out. I'm sorry. What are these powers? Is this like telekinesis? Yeah, devil fruit. I'm not shocked. She just pushed them away. I was about to say I'm surprised he hasn't said anything about it yet. Wait, what? Oh, cool.  Who's this guy talking to? She's just like toying with them. Little garden. Does that carry weight? Oh, little garden doesn't sound very dangerous. I'm going to be honest. Oh, she's giving the hat back. Nice. Oh, thank you. Miss all Sunday. Nothing at all island. Why is she doing this? I don't understand. Does she just have respect for Luffy since she's heard so much about him? She's kind of cheeky, bro. They don't have many options. I mean, weigh the options first. Luffy's like, I didn't think of that. The captain does. She has to gain a little bit of respect for Luffy for that. Hey, that's fair. Actually true. Yeah. No. Bunchy. What is this? Oh, the sea kings are like just the big creatures, right? Oh, she's got a turtle. That's sick. Gets on board, gives them directions, refuses to elaborate leaves. Gigachat miss all Sunday. She just wants to get back to her kingdom, bro. That was such a weird interaction. Oh, baby's so nice. Little garden is the next destination. From how she presented it. No. Back to her. Is she going there too? Oh. Oh. Does Bigfoot reside in Little Garden? A very interesting interaction at the end of that episode. I thought Miss All Sunday would actually try to fight all of them. I mean, considering the fact that we don't know the whole motives, I guess the motives is like to overthrow albasta. But why let Princess Vivi get away if she's so pivotal in overturning that overthrow? Unless Miss All Sunday is so confident in her both herself and Crocodile that they can take care of them later. That's my only guess. Either that or like I said, she's just cocky and it just thinks that they won't pose a threat at all or that is she just wanted to check out all this that she's heard about about Luffy. But nonetheless, a very interesting turn. Not anywhere near how I expected all of this to go, but it is kind of confirmed that Vivi, I think, is on the good side of things. But who knows? I mean, maybe they're trying to overthrow albasta for good reason and Vivi actually isn't on the good side of things. But I think we'll have to make it to albasta to actually find out why things are being overthrown and why Civil War actually broke out in the first place. But that's the end for episode 66 and 67. I hope you did enjoy. As always, drop a sub if you're new and I'll catch you in the next one. Peace, peace.


Assalamu alaikum warahmatullahi wabarakatuh, now I chose Asmaa bint Abu Bakr because when I was thinking about you know who do I want to learn from and there's so many incredible women in our in our tradition but I realized I had very limited knowledge about her and I thought like what do I know about her as you know someone who's clearly a figure in our tradition and she and I thought there's only a handful maybe two stories that I can think of so I intentionally chose her because I wanted to learn more about her and this is where you know for all of you to keep in mind we are students of knowledge you know we we sit up here we might seem like we're you know in this position of teaching but we are actually always learning and I know that we're always learning so for me I'm so grateful for these programs because they allow me the opportunity to also learn so I am excited to share what I have learned about this extraordinary example for all of us so she is Asmaa of course the daughter of Sayyidina Abu Bakr as well as Qutayla bin Abdul Azza and she was the first wife of Sayyidina Abu Bakr she did not become Muslim so they actually divorced before the Prophet's license mission began so she's the half sister of of course our mother Sayyidina Ayesha of Allah and whose mother was Umrah man so just important things to know because sometimes you hear that they're sisters but that distinction is important now according to Ibn Qatiyar Asmaa of Allah was about 10 years older than Ayesha of Allah and but others like Imam of the Habib say that it was a much bigger wide wider age gap between 13 and 19 years so Allah knows but she embraced Islam at 11 years old are there any 11 year olds here anybody 11 10 in that range anybody has a daughter that's 10 11 I just think about I mean I have a 10 year old soon to be 11 think about what a precious time that is and that you know subhanAllah through her father of course she embraced this faith and I just thought wow she you know it's such a young tender age she um the faith you know entered her heart she's considered again there's a difference of opinion to be the 15th some say 17th some say 18th person to become Muslim in the earlier community so she was prominent from the very beginning she was there and she was like all the earlier converts they would gather in Dar al-Arqam and study with the Prophet's life Salaam and in those earlier years we don't know much about her life but we do know that she marries another very important person who is and who is he he is the son of Ibn Khuelid who is the brother of Sayyidina Khadija our mother so making him her nephew Sayyidina Khadija's nephew and then his mother is Safiyah who is the Prophet's wife's aunt so that makes him the first cousin to the Prophet's life Salaam so she marries someone again from this incredibly noble from both mother and father her lineage is very noble and he is also considered the fourth or fifth male adult to become Muslim in that earlier community so just an amazing pairing and of course he just FYI he goes on to be part of the ashara mubashara the ten who are promised jannah so her husband is again an incredible and he has his own story which one day inshallah maybe we can go into but the Sayyidina Mubakat also brought him by by the way also to Islam so it's kind of it's really sweet right like the man who would go on to be his daughter's husband came to Islam through him as well really beautiful now their beginnings as a couple were were difficult like many of that earlier generation they didn't have very much and Zubair al Awam was known for having just one possession when he came to ask for her hand which was a horse he didn't have much else other than this horse but of course his character and that's why Sayyidina Mubakat gave him his daughter because of his incredible character so they had very humble beginnings and asma talks about that in her you know in her hadith that she she related some hadith which we'll get to but in some of those hadiths she talks about the challenges that she had as his wife and just you know the struggles of the life that they had the hardships and the poverty that they endured so during right before the hijra or at that time she becomes pregnant with her first son another very notable in our tradition of the life and as Zubair al Adi Allah and so she becomes pregnant with him and this is when the Prophet said him and said Nabubakar flee right we know the story that they go to seek protection in Thor and for three days and three nights and so they're looking to keep this obviously under wrap with only trusted people and you know it's a very you know secret mission but she steps up to the plate of taking on the responsibility as a pregnant woman in her third trimester anybody here in their third trimester anybody oh mashallah so we have one a couple of sisters now I want you to think about this you know we those of us who have had children we know what the third trimester is like you can barely walk you know a few steps without needing a break right your back is hurting you've got a lot of things going on so just I just was floored when you read the description of what she did in that state we have to remember I mean we're talking about the middle of the desert Mecca leaving the outskirts with people seeking to kill the Prophet said him and her father but she steps up knowing that she is also with child and she clearly is in her act showing where her love and her priorities and her hearts are she wants to protect the messenger of Allah and she wants to protect her father even at the risk of her own life and her own child's life so this is an extraordinary woman who goes out I want you to take a guess does anyone know how far Ghadr Thor is from Mecca how far anybody get take a guess and use miles you know everything I read was like kilometers I'm like I'm an American I don't I don't know kilometers so miles please anybody miles what do you think how many miles how many 20 miles mashallah anybody else any other guesses 10 very close close seven miles seven miles she would walk it took her about two hours in the blazing sun as a third as a pregnant woman in her third trimester and this is where you know she again stepped up to the challenge and what was her purpose she she took them provisions and she acquired this beautiful nickname because when she was putting together the provisions she didn't have anything this is again to show you how little they had she had nothing else to tie the water you know the water what is it called the the leather water pouch there's a term for it but she didn't have anything to tie that or the food so what did she do at that time the women used to wear a waistband that would you know prevent their dresses from falling so she took that waistband and she tore it into two and this is where she got the nickname that that's when the taqeen right which is referring to the the woman of two waistbands because when the Prophet saw what she had done when he when she came and she's you know to untie her you know waistbands and giving them the provisions he made a beautiful dot for her and he said indeed Allah has given you so the words are important to to pay attention to indeed Allah has given you in exchange for these waistbands two waistbands in paradise so he is indicating to her that she is in jannah she is guaranteed jannah which is a again an extraordinary gift so subhanAllah this is her sacrifice and she was again willing to take that you know that trek into the desert risking her own life two hours two hours there two hours coming back four hours for three days right now fast forward she alhamdulillah you know makes hijrah as well and on her way to medina she delivers her baby that's how close to delivery she was and she delivers in quba and this was a really great extraordinary moment for the muslims there because at that point the jews were you know they were they had spread this rumor that they were cursing the muslims so that they would nobody would ever have a baby in medina so she was her son Abdullah ibn Zubayr was the first infant to be born in medina as a muslim so again another great honor for her and so the muslims are of course celebrating his birth now again for those of us who have had children before instinctually we know immediately you get the baby whether you're at the hospital or at home or however the birth is and your instinct as a mother is to latch on nurse so i want you to imagine how much strength it takes for a mother to again think of like what is best for my baby instinctually i feel like i need to nurse him but she was aware that what was better for her infant was to send him to who none other than rasulullah sallallahu alayhi wa sallam for him to perform tahneek which is the process of taking a date and mixing it with his saliva and breaking off a piece and putting it in the mouth of the infant so that it promotes well-being and health and of course any any mixture of his noble mubarak mubarak saliva is is she fast for him so she did that and you know again just put yourself in her place like to to know these things and to separate yourself from your child upon birth it's not easy to do for everybody but of course these are people who had a greater understanding subhanAllah so she goes on in medina to become again a devoted wife a devoted mother she bears seven more children subhanAllah i mean i have two and to me i i'm like when i see anybody with two or more i really i'm just like in awe but to imagine seven subhanAllah and again in a time of immense difficulty but she went on and she did it mashaAllah and she spent her time just serving serving her family she was known to be incredibly charitable this is one of her qualities that even her own son Abdullah and he in a hadith noted about her he said that i have never known two more generous women other than my aunt aisha radiAllah and her and my own mother asma now he made a really great observation and how they were different in their charity and again i want you to think about who matches your style more so i said radiAllah anha she was the type that would collect a good amount of money right so it's like she's saving saving saving and then once she saved or whatever it was maybe it was food then she would go and distribute it but she had this habit of wanting to save it first and then at once give it away right so think are you do you follow that or do you follow asma's example radiAllah anha which was to give it away immediately so she didn't hold on to anything that was given to her if it was an excess she wanted to always give it away right away so some of us you know we we operate differently but it's really nice to try to connect like where would i be in this spectrum right and so um her uh situation as she you know lived with a zubair and madina and they you know grew their family actually turned around completely he became one of the wealthiest men of madina and then later mecca after the fatah so she was known then for feeding the poor and anytime she got sick which is a really good tip for us to think about i remember my mother allel hamha anytime there was anything that happened to the family her instinct was always sadaqa she always had shed we had a you know on the mantle um above the fireplace in her previous home she had a quran and then she would have a place right next to it that she would put her money that she was going to give for sadaqa but it was her habit anybody's sick anything happens uh god forbid a car accident and this was the way um and so how many of us do that and how many of us think again as soon as something befalls us that we need to look to purifying our our wealth and and seeking allah subhanAllah's help and also thinking of other people benefiting other people right it's very natural to think of yourself and want to preserve yourself in those situations but subhanAllah um you know people of a greater understanding again knew that no you want to take care of others so this was her way as well and she would feed the sick and she would free the slaves so this was her habit if she was ever sick she was also known for teaching fiqh of hajj for the uh during the hajj season and these are the facts that just you know for your information she narrated a total of five hadith alhamdulillah um and you can you know if you're ever reading books you might see you know narrated by asma which is an incredible honor we really have to think about the fact that you know there are so many people around the process of them but not everybody is in the hadith collections and here she is narrating five hadith she also is a warrior on top of all of this she's fought in the battle of yarmouk uh later on in life subhanAllah so she was an she was actually on the battlefield and they said she was a fierce warrior and anybody want to take a guess what age she reached before she passed just throw out a number an idea older older than 90 years old a hundred years old and subhanAllah the climax of her story and right before she passed away is one of the most incredible things i've ever read her exchange with her own son i just you just can't help but just be so in awe and humbled by these women because again we live in a time where where we don't have these living examples i mean i'm sure there's beautiful women everywhere but these stories these epic stories uh bat fighting battles you know raising seven children suffering through famine and so many other things um sanctions and then to also live to a hundred years old but i'll get to that point in a moment about her her end of her life so there are few really key lessons from her life that i just felt were really important to know in addition to all that we just shared the first as was mentioned in the description of this talk was the hadith that a lot of us may associate with asma bintabi bakr radi allah which is the narration where she entered the prophet sallallahu alayhi wasallam's home this is according to aisha radi allah hannah her sister and she was wearing a thin garment okay a see through garment and at that time the prophet sallallahu alayhi wasallam this was again before the aya of hijab was revealed but she the prophet turned away from her and then he said to her oh asma when a woman reaches the age of maturity it is not proper for her to show anything but this and this and that was referring to her hands and her face so this hadith is really important for us to think about as women for obviously the context because we live in a time as we know women are exploited constantly and women's fashion even what has been introduced in the you know fashion of muhajjabat many things would be considered inappropriate and we have to just be real we have very clear boundaries in our sharia about what is acceptable and what isn't and this is why this hadith is something we have to pay attention to so when you get dressed you have to think about would i be someone that the prophet sallallahu alayhi wasallam would turn away from based on what i'm wearing right now i i mean i would i think that would be the most mortifying thing ever i would do anything for him to have a one glance of his so is it worth it to wear the yoga pants no sisters it is not is it worth it to wear the see through things that show your shape just because you want to keep up with the fashion trends and look really this or that no if it compromises you're standing with allah subhanahu wa ta'ala and the messenger of allah sallallahu alayhi wasallam it is not worth it and that is why i so appreciate the grace and the beauty that asmaa she said she was in submission she was in submission she accepted it she didn't challenge the prophet sallallahu alayhi wasallam and that's why we have to pay attention to the language of today of the modern zeitgeist it's all around these themes that are alien to our tradition she wasn't triggered when he said that she didn't take offense and personalize it and you know say oh the patriarchy she understood this is the messenger of allah sallallahu alayhi wasallam he his entire life is for my salvation so if he's going to tell me something to do or not to do i will accept it and she accepted it and then you know the the the mufasirin say that shortly after um the the verse of uh you know hijab was revealed and the specific hadith relates to verse 31 where allah subhanahu wa ta'ala says except for what is apparent he goes you know tell the believing women to lower their gaze and guard their chastity and not to reveal their adornments except for what is apparent so it's she's she had you know subhanallah apart in this beautiful verse being revealed to us so she's again an extraordinary example for us and so we want to think about that when we are if our spouses or if our parents are challenging the way we dress we have to think about what is their intention sometimes it could be control and there's no real you know noble intention it's just control but other times it actually is for your betterment and it's good to question why not just what they're saying but why are they saying that to me you know is it for some ulterior motive or is it really because they're looking out for me and nine times out of ten is shala because you have we we want to always have the best of opinion of our parents and our family members and our loved ones they are looking out for us we just need to accept that and not question and have you know these doubts about everyone which is what again the modern zeitgeist does it just promotes this you know constant you know friction between us so really powerful story about that and there's there's more but for the sake of time i'll go to the next point which is her this is also another really incredible lesson we can take from asma asma was amazingly brave and courageous she had real courage she spoke out when whenever there was you know i mean we already saw mashallah what she did in terms of protecting the process but even speaking to people and having the emotional intelligence and wisdom to know how to say certain things effectively which is a tool something we all need to learn this is why grammar matters rhetoric matters our liberal arts matter because we have to be empowered with language to be able to say things effectively and she and her discourse and her dialogue she was incredibly wise so there's a story of her grandfather so who is the father of sainab abu bakr his name is abu khaafa so he did had not yet accepted islam when the process of abu bakr migrated to medina he was still a non-muslim so he was really hurt that they fled because his grandchildren are left in in his son's home without in his estimation any care and he kind of came into the house and said to his grandchildren oh your father's left you in a really terrible situation he's taken all his money at that point abu bakr took all of his money which some say was around six thousand dirham or dinar to help the muslims so he took his wealth with him and so when her grandfather walks in seeing the situation of his grandchildren he immediately you know says these things in a way to bring doubt into their hearts about you know the what their father did but she had so much later for her father as well as the image of islam and the muslims that what did she do he was blind okay so he was blind so she went and she quickly gathered a little bag and she put pebbles in it like stones and then she put it in an area and covered it and she took her grandfather by the hand she said no grandfather he didn't leave us without anything look touch this this is all the money he left us so he was like oh okay in that case then there's no blame if he left all of that for you but she had this beautiful reda again to protect the image of her father protect the image of the prophet said and the muslims to do that and then another story comes out of when she was in medina so now fast forward seven years after she's uh she's left and she is in medina she's an established mother has her own family what happens her own mother remember her own mother potato who had not yet accepted islam she's still and she dies in that state all the but i was she visits the visits her and she brings with her all of these treats and food and like ghee and raisins and other foods and she wants to give all of these gifts to her daughter now it smells conflicted right she's like wait a second even though you're my mother you're still on the other side of this and i need to make sure this is okay for me to even accept you as my guest and accept your gifts so she had again that wisdom and that um raida deep raida for for her faith to go and ask the prophet through her sister isha can i accept my mother even though she is not a muslim and she's brought me all of these gifts and this is also really relevant okay how many of you are converts in this room now allahu akbar may allah protect and preserve all of you and inshallah bring hidaya to all of your loved ones we had a sister here i don't know if she's here i don't want to call her out but she was here yesterday for our liquor that we did and her heart was really heavy she's a convert and she said i have no support system and this is the situation of many of our convert sisters which is why it's so important that we hold space with one another and that we bring our convert sisters and brothers into our communities and make sure that they never ever in their life feel that they have no support system but we all of us and especially our converts you owe asma bin sabi bakar a lot for what she's did in this exchange because because of her and this situation with her mother and seeking the advice of the prophet sallallahu alaihi wa sallam the ayah was revealed which is allah does not forbid you from dealing kindly and fairly with those who have neither fought nor driven you out of your homes surely allah loves those who are fair this is chapter 60 verse 8 this ayah was revealed to reassure everyone whose family and loved ones have not yet adopted the faith that you can still have them in your life you can still have a beautiful relationship with them as long as they're not forcing you out of their homes or torturing you or doing anything like that to you know again bring them into your homes and and treat them with the same love and dignity and respect he gave that permission and so she was relieved and she accepted her mother but another again incredible story that we get from asma the third is the story that she had with um just such a powerful story subhanallah so again we're going to rewind a little bit when she didn't have a lot and you know her husband was struggling and they had this horse at that time in her life she did a lot she was the she would go out early and get water for the horse feed the horse bring it fodder she would walk it she would go and get um date seeds and they would they would at that time crush it and it was a very labor intensive life and um at one point she had to walk about two miles to do this process of crushing these date stones and then they would carry these massive things on their head so again try to visualize this she's walking two miles exhausted she's been laboring all day just trying to make it survive and who comes and crosses her path none other than the beloved sallallahu alayhi wasallam and this is his sister-in-law so you know sometimes and this is again something that we should just really appreciate that is lost unfortunately today in the nonverbal communication that can sometimes be really powerful not everything always has to be said sometimes the states and the hearts are communicating so the prophet sallallahu alayhi wasallam sees his sister-in-law in this state without a single word he stops his camel and orders the camel to kneel and then he's he makes a sound or if something to that effect which was an indication to her like come on i got you sit sit on the camel i'm gonna take you the rest of the way he had this compassion for his sister-in-law seeing her in this state but subhanAllah and i want you to see what she does this is again emotional intelligence of a wife and a woman who is using her intellect to assess the situation there's all these men here the prophet systems here i could really use a ride right but my husband is jealous i can't do it without words without any words what does she do she just stands there and the prophet sallallahu alayhi wasallam again he knows the hearts no communication they just understood each other he understood that her shyness meant she wasn't going to get on and he just proceeded forward and she went home rushed home to tell her husband about this whole incident what happened because she wanted to be transparent we and we have to again apply this in the modern context a lot of things are happening in spaces private and marriages and lives all over the place and everybody's all about privacy now give me a break you're married transparency you should have you know access to to one another's you know whatever is is public right but this idea that no i can do my own thing and i don't have to share so just let's learn from her she wanted to again show her husband that i honored you in your absence so she tells him what happened and his response is also really beautiful because it just gives us insight that they actually cared about one another and it wasn't this whole you know power game all the time like i want this and i want that they weren't about that they were about the hearts so he told her he said by Allah you're carrying the date stones and you being seen by the prophets that i'm on with that you know with it on your head in such a state is more shameful to me than you having taken a ride with him so he's letting her know like i'm pained that you were in this that i've put you in this situation i don't care about that but they were so considerate of one another's feelings so we have to think about that in the context of you know who are we um are we you know again not sharing certain things with our spouses or are we taking these positions that are not really thoughtful about one another's feelings and this applies to the brothers too i hope they're watching this it's or will watch it at some point but you know if your wife asks you not to uh socialize with certain people it's respect that you honor that request and vice versa and i think we just have to you know uh take take that uh you know nasiha from this but she prioritized her husband's feelings in that incident and then quickly because i know we have um oh sure thank you just like to often know set the father myself she's awesome she reminded me to define the word ghayra ghayra is a type of jealousy but it is a beautiful jealousy right it's feeling that you know you're to want to protect the honor of something or someone so that's what what that word means i'm in it applied to the story before but she had immense aid and she was known for that um i'm sorry what how much time do i have i just don't want to just so i know what is it like am i done five minutes okay well i'll try to finish this up as quickly as i can um that it's just she's got so many gems from her stories upon a lot but we received two really important hadith from her that warned about ingratitude so that's why i think she's such a great role model for all of us she this is from her own narration so she reports that the prophet sallallahu alaihi wa sallam passed by a group of women in the mosque one day we're a group of women okay just imagine this we're all here we're remembering all of us and the prophet sallallahu alaihi wa sallam walks by and he waves so beautiful what probably with the right hand he waved with his hand to greet them with peace and then he said this is his nasiha to the women beware of ingratitude to those who bless you beware of ingratitude to those who bless you and we know that the prophet sallallahu alaihi wa sallam when he repeated something he was driving a point home he was trying to penetrate the hearts and one of the women said oh messenger of Allah i seek refuge in Allah o prophet of Allah from being ungrateful to Allah and you know she's seeking like what explain and he says rather one of you will be widowed for a long time throughout her middle years then Allah provides her with a husband and he benefits her with a child the joy of her life then she gets very angry and she swears by Allah saying i've never one good i've never had one good moment with you that is in gratitude to the blessings of Allah that is in gratitude to those who bless her that's one and then another hadith she also narrates that the messenger of Allah sallallahu alaihi wa sallam said spend in charity and do not count it lest Allah counted against you do not hoard it lest Allah withhold you from from you so we learned again her way according to her son was she would just give it away so she's teaching us be in a state of gratitude don't deny blessings don't magnify incidents because these are shapeonic you know thoughts when you magnify an incident and it overshadows a lifetime or years of experiences this is what thank you thank you this is in gratitude directly because shaitan wants you to hyper again focus on one thing that was said to you one thing that was done to you and that you negate everything else may Allah protect us from that we never want to fall under the category of those who are ungrateful in fact we want the opposite we always want because you know the opposite of gratitude is kufr so may Allah protect us from that and then to spend in charity and to give away without counting so this is really great nasiha sometimes you know we are in positions where we might have to give and if you're the type who is worried about giving away your wealth this comes from again a lack of understanding may Allah increase us and understanding that never are we losing when we give for the sake of that never is it a loss it is always a gain it is always an investment so we want to you know really fight do that much ahead enough that we give if it if you feel the impulse just give and don't think twice about it don't let that internal conversation have well maybe i'll just do half this time and i can do it another time and no nafs shaitan work together to try to you know prevent you from getting the maximum reward so she's teaching us right spend don't count it because then Allah will count it against you and then finally and this is what i wanted to end on um i mentioned one incident where she spoke to a tyrant of her time they call him the fraun of our umma abu jahl right um or i might i might not have given you the detail sorry i think i mentioned it but i didn't get the detail so here's the detail of what happened abu jahl during the time when the Prophet said and said nabbu bakr were missing he stormed into her house and he demanded from her where are they tell me where are they and i want you to again imagine she's a pregnant woman pregnant so vulnerable there's no protector her father is not there she stands up to him says i'm not telling you anything i don't know anything he slapped her so hard on her face that her earring fell off and she still stood firm in front of him and he realized i can't get anything out of her and he left so that's one incident earlier in her life at a hundred years old her son abdel ebn subair was uh executed and crucified by al-hajjaj ibn yusuf at hundred years old and right before this incident happened where he was executed they have this beautiful exchange her mother and son he actually goes to her seeking counsel on what to do because he knew that if he fights al-hajjaj he's going to be killed so he didn't know should he surrender should he fight him and this is a mother talking to her son knowing that she's sending him to certain death and she basically says to him i would much rather you die a noble death than go and you know basically be beholden to this tyrant so she it gives him this encouragement and this nasiha and it's his beautiful back and forth and then he says to her you know about being afraid he's vulnerable this is his mother and he says to her i'm scared about being crucified after death and she says skinning a slaughtered goat does not bring it pain off you go and seek Allah's help a hundred years old sending her son to do the right thing and he she noticed that he was wearing armor and she said what what are you wearing take that off that's not the clothing of someone who's going in to martyrdom you have to stand firm so she gave her son that encouragement because she knew that that was you know his he was already promised jannah she knew where he was going and she wanted to give him that you know fight like end his life in the in this beautiful way and not to cower to this tyrant now al-hajjaj of course being who he was he wanted to taunt her so he did he taunted her and he called he went and send one of his minions to go get her and said come face me you know what did i do to your son basically taunting this a hundred year old woman and she refused to see him and then he doubled down and said if you don't come i'm gonna drag you by your two braids and again she was firm and defiant she's not gonna capitulate to him finally he had no choice but to go to her and you know again he's trying to taunt her and she says to him something so powerful remember this she says you may have ruined my son's dunya but he has ruined your akhara allahu akbar allahu akbar allahu akbar that is who asma bint ebi bakar was she was an incredible force a loving mother a devoted wife daughter sister-in-law everything and she had this life of a hundred years Allah gave her and now alhamdulillah here we are celebrating her life inshallah i'm so honored again to have learned about her life with all of you and i hope you'll learn more about her and all of the other wonderful sahabiya and women around our prophet sallallahu alayhi wa sallam as we usher in this mubarak month of rabbi al-awwal jaza kumallahu khayran wa salaamu alaykum wa rahmatullahi wa barakatuh look it's so good


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And we also heard from Secau Barkley yesterday. He confirmed that he will not be at Giants' mandatory mini camp. He says the following to summarize basically, he says he's not trying to reset the running back market. He wants a fair deal and it doesn't sound like the Giants have met his expectations there yet. But the part that sort of stands out to me here is that he mentions how he wants to be compensated for his contributions to the team on the field and in the locker room. And that's a reasonable ask, okay? Because there has been no one that you can point to in the NFL that has been more crucial to any or on that team rather, more crucial to any of the success that they have had over the last five years than Secau on. Look any winny has a hand in and when he's not out there, it's not pretty. And this is where it gets tricky because the Giants can't negotiate this next contract for what he's done in the past. That's what he's done. What are you going to be in the future? This deal has to be based on the value that they think he's going to have and bring them going forward. Now he is and I will remind everyone because everyone thinks Sequan's played in the league for 10 years. He's a baby. He's 26 years old still, 26. And he's got a whole time, okay, over the devaluing of the position, okay?  Sequan means so much to this team and this organization. I think he'll continue for years to come to be that guy and I really hope that they can come to terms on something that works for everyone. But the Giants front office is already in the process of digging itself out of a hole from the previous regime and one misstep here and how they sort of structure this deal could put them right back at the bottom of it. Because it might be the toughest deal to navigate in the entire league this year and I do not envy either side. And people are split. Like I have a lot of Giants fans in my life and half of them are saying I love Sequan. They recognize everything he's done but they're like do not pay him. Do not give him, it's the ruthlessness of the business and I'm curious, like Golden Tate and Darius Butler's takes on this. And then the other half is like give him what, is that an emotional decision to give him tons of money? What is the in between and can they get there in a hurry? They have till mid July to sort of figure it out, I think. So Godspeed to both sides. And of course I say Hamilton, you know, in the words of the great Nate Burleson, pay the man. Oh my God. Yeah. Kind of pay everybody. Hamilton? No, that's it. Go ahead. Yes. Please. Please my friend. No, yeah, with Sequan it's, you know, he doesn't mean so much to that organization. It is different than most running backs that you have to deal with because he does so much as he mentions in the locker room and on the field and his versatility and all that. It has to be taken into consideration. I don't envy Joe Shane here at all because it's going to be tough.


who's gonna talk about the next speaker is Mark Selke who's finishing up at Stanford and then we'll join IAS and Harvard recording in progress now we need the recorded music okay okay so mark is gonna talk about robustness and isoperimetry take it away okay thanks so much for inviting me and coming today so people can hear me okay okay great so yeah so I'll talk today about universal law of robustness via isoprimetry and this is joint with one of my advisors Sebastian Mubeck who's at Microsoft so the purpose of this talk is to say something about very large machine learning models so just to give a sense of why this is a pertinent topic you know machine learning models have been getting extremely large very quickly it's probably most of us are aware and to just say a bit of comparison with kind of the statistic story from 10 or 15 years ago classically when we think about how large our statistical model should be we think that the number of parameters should be kind of just right so maybe if there are too many parameters we're going to overfit if there's too few parameters we want to underfit and there should be some kind of Goldilocks zone and if we think about kind of the extreme of choosing too many parameters in a way that would be sensible we would think that well if we're fitting and data points then at most we're solving an equation so we should need and parameters and this is really not the case for for large modern neural networks so just to show some numbers if you look at the MNIST data set these are these digits here there's like 60,000 images a pixel an image has a thousand pixels maybe and typical model will use something on the order of a million parameters so it's a lot more than 60,000 a similar story for image net all the numbers are bigger the parameter number is even way bigger and okay if you look at these recent large language models it's even up to almost a trillion so there's a pretty prominent and successful story that has shed some light on this which is not what I'm going to talk about today but I want to just mention it first so so just as I contrast so this story is saying that when I have a lot of data points and they're in high dimension maybe these two large numbers are comparable then it's kind of fine to have mild over parametrization so there's quite a few works on this the last one was talked about a few days ago so there's these curves where if you look at a larger and larger model size then you improve then you overfit and then you you go back down again what I'm going to talk about today is a specific setting in which it seems like extreme over parametrization may be mandatory so for example in double descent often theoretical analyses will say that well if you over parametrize by a factor of 10 that's that's fine that's good and here we're going to really want to over parametrize by a sumber constant factor okay so let me say what the setting is and what the result is and what's going on now so I'll give a informal statement and kind of it's trying to reconcile the following three phenomena of neural networks the first is that they're over parametrized the second is that they often memorize their trading data almost perfectly and the third is that they generalize well to the same type of test data but they are brittle against adversarial perturbations at test time so if I if I add a little bit of adversarial label noise to this image I can't tell it apart but it gets classified very differently so our result says that if you want to memorize and you want to be robust then you need over parametrization in some theoretical model so to give an informal statement which I'll then explain more carefully for the next few slides we're going to fix a reasonable function class described by some number P of parameters so this is something like a deep neural network with some fixed architecture so every trainable weight in the network is a parameter we're going to sample and data points ID from a d-dimensional distribution so it can be fairly general but should be truly d-dimensional so it shouldn't be like a line living in d-dimensions but it can be some kind of Gaussian not necessarily spherical and then we're going to add label noise we're going to have some maybe deterministic labels and we're going to add some noise and then we're going to try to memorize the labels and we're going to try to do this using a function in our function class that we fixed beforehand and we're going to want this function to be Lipschitz which is our proxy for robustness and the result is that we're going to need at least order n times d parameters in order to do this so if our function class does not have enough parameters it will not contain a robust memorizer so in short over parameterization may be necessary for a robust memorization okay so let me now explain in a bit more detail what I'm talking about with all these things and you know please ask questions as I go through this technical setup so so we're going to be living in d-dimensions for now we'll just say we have data on the unit sphere as we'll see it can be relaxed and you should think the number of data points is something of polynomial order in the dimension so pretty flexible linear is fine cubic is also fine the labels are something deterministic this function g which we don't really care about and crucially we're going to have some noise so each label yi will have some noise zi and the noises need to have some average variance sigma squared so the noise distribution can even depend on the input xi it doesn't it's pretty unrestrictive so we're going to think about memorization so we'll say a function a classifier f fits the labels perfectly that means it's a perfect memorizer right so that makes sense and we'll also be even fine with partial memorization which means that you fit the labels including some of the noise so you you fit the labels better than just ignoring the noise so for example if our mean squared error is less than half the noise level then then that that counts as memorization okay next what is robustness I'm going to say a classifier is robust if it has a small options constant okay so this is sufficient condition for any sort of robustness it certainly implies that if I change my input a little bit then my classifier won't move very much it's a bit of a strong condition but it's convenient mathematically so we're going to define robustness this way for the purposes of this talk and I want to point out that the scale here is constant so our inputs are on the unit sphere our labels are constant order and so it makes sense to hope for a dimension free lip shits constant here so this this has caused some occasional confusion so let me just say if you're thinking about a real image maybe you think it has d pixels and each pixel is an order one number so the scaling seems a little strange but if you just rescale down all this is saying is that if I change 1 percent of my pixels then my classifier should not change very much it's it's kind of it's saying you know a small relative change in my input should should be benign there's no there's no funny games going on okay now a fact is that if I have some random data set some random x I y I pairs generated this way then there's going to exist a perfect memorizer which is O of 1 lip shits and the reason is just that all of my inputs are separated because I have random inputs in high dimension and so I can I can just do something very simple I can take a sum of bumps so for each input point x I I can put a bump function supported right around it and just just fit x I but no other points and just do this for each input separately okay so very simple very silly not what we want to be interested in and okay so the simple construction is lip shits because the the points are separated it's a perfect memorizer but it uses a lot of parameters it uses n times D real parameters because to specify this function f here I have to tell you every single coordinate of every single input point x I so in terms of parameters it's it's you know much less efficient than you would think should be possible and what we're going to see is that you know this is the the best parameter efficiency you can get already this silly construction so I don't I certainly don't want you to think oh sorry yeah yeah so so each x I is a point in D dimensions and in this function f we were using all the points x 1 through x n to construct the function f so so that's N D real numbers and they the input points of your problem yeah but but the the idea is um we want to think of fixing a function class with some number of free parameters before we see our data set so so we need to right so so in order to be able to find such a function like this in our in our function class we need to have all the functions of this form for all possible points x I does that make sense okay okay great yeah thanks for the question it's a it's a bit it's a bit subtle the the setup any other questions okay great okay so yeah it turns out no function class is more parameter efficient and let me now say what I mean when I talking about parameter efficiency a bit more precisely so when I have a function class specified by p parameters what I mean is abstractly there's some parameter vector in p dimensions and each function of my class corresponds to some parameter vector okay and I need some regularity conditions for this to make sense otherwise my parameter could vector could just be one-dimensional because I can biject it with any set so we're going to require first that the parameters are bounded in norm by some constant I'll call J and a second that the parametrization is J Lipschitz in the sense that if I change the parametrization vector then the classifier changes in L infinity norm by a most J times this amount of change okay so the eventual dependence on J is going to be logarithmic so so if J is D to the 10 that's completely fine so so I think of these conditions as being quite benign and on the other hand these conditions do let us prevent silly pathologies because I can't extract infinitely many bits from a single real parameter when I have these kinds of regularity conditions there so just as a simple first example if I'm looking at linear regression then my functions are going to look like this they're just inner products and the number of parameters is going to be the dimension of the original space again okay let's look at a more realistic example of this setup so let's look at feedforward neural networks with so so these are given by linear maps composed alternatively with nonlinearities alpha for example the ReLU and in our setup the parameter vector W is going to encode all the entries in all of these weight matrices here and some very nice thing about our setup is that if you have a structured matrix like a convolution there are a lot of repeated entries this correspondingly decreases the number of parameters I can just treat it as one coordinated my parameter vector and if we think about the Lipschitz constants in this case both the Lipschitz constants in the parameterization and the Lipschitz constant of the classifier itself are going to be upper bounded by a natural quantity which is the product of the operator norms of the weight matrices so the Lipschitz constant in W is kind of what we need to be reasonable that's this number j but as I mentioned the dependence is logarithmic so so basically you can think that as long as the log of this product of norms is reasonably sized we're in good shape so so in particular as long as the depth is not insanely large this is very well handled by our setup and often this norm project is also explicitly controlled for other reasons like to ensure training stability any questions about this or anything else I've said in the past couple minutes okay great yeah so it turns out there's a there's a trade-off here so if you if you don't care about robustness you just want to memorize in the setting I've described you just need n parameters even with a two-layer neural network but as I've said you need n d parameters to robustly memorize which is achieved by this sum of bumps a very simple function and it if you try to improve it's not clear how so the general trade-off here was first conjectured for two-layer networks in this previous paper by Bubeck Lee and Nagaraj and our main result is a very general form of this trade-off so the setup is that we're going to fix a function class described by p parameters let me just say they have poly d size in general there's a log j and we're going to have a data set with noisy labels so as a reminder this means the the x i's are i i d say on the sphere and the y i's have some noise in there then for any memorizer in my function class its Lipschitz constant has to be at least of order sigma root and d over p so again sigma is the noise level in the labels and is the number of examples d is the dimension p is the number of parameters in particular to get a dimension free Lipschitz constant I need to have at least and d parameters so that's the main takeaway in my setup before I said that the x i should be a uniform on the unit sphere but they can actually be a lot more general first you can have any distribution satisfying isoprimetry something like a log so below inequality I'll say what that is on the next slide and also you can have a mixture of like almost and different distributions and it's still fine and you can also have data dependent label noise you just need some like expected noise level so it's some like half your data set can be no noise and it's fine too this trade-off is also tied in general not just at the end points but but at any number of parameters basically and the reason is that you can project down to some intermediate dimension and use the same kind of some of bumps construction there so let me now say what I mean by isoprimetry so this is a key property of high-dimensional space and the basic definition is that any Lipschitz function concentrates extremely well with Gaussian tails right sorry I think the minus sign is merged in with the fraction bar in the numerator anyway so this is a common property of high-dimensional distributions so spheres gaussians some slightly more exotic distributions and it's implied by having a good log constant so it's a it's a strong property but it's it's sort of generic issue in high dimensions it's not it's not like a very rigid property okay so as you can maybe tell us this we tried to make this theorem kind of realistic and not not such a spherical car result so let me now try to say a bit about what how you could try to tie it into practice so certainly real data sets are going to be mixture so maybe uniform on the sphere is not very realistic but I can think my data set has a cat component a dog component maybe some slightly more specific versions of these components seems fine and in order to you know we're not going to know what the dimension is that's a that's kind of a tricky thing in trying to think about how to how to apply this in practice right you have some number of pixels in your image that's obviously a very bad notion of dimension but you could hope to say that there's some effective dimension there's some data manifold and and the result would hold with that effective dimension and this leads to some possibilities of extrapolating from large to large scales from small scales and so on in various ways what is the noise so so in theory in the setup if there's no noise there was nothing for us to learn so if I had if I had this problem with no noise then I would just need one function in my function class because there would be there would be no memorization to do and yeah so so we wanted to fix a function class beforehand and then see our random data set so if our end of data set had no noise in the labels then we could just we would just know what function to use so like kind of like this is really looking at memorization so so and one one interpretation of what memorization is is like memorizing noise that's kind of the setup so so you know I'm not I'm not trying to argue that memorizing noise is good but I think it's a it's a good way to get a theoretical problem and if you if you don't have a good understanding of like a priori of what your data set is gonna look like it may be a reasonable way to think about you know modeling it so so for example just one story that's related is the called the long tail hypothesis it says that in a large data set a significant fraction of the points will be kind of isolated so there's kind of a long tail in the the cluster distribution in your data set so a lot of the the images will be kind of unrelated to other images and maybe their labels can be thought of as noise from kind of a learning point of view but it's certainly an assumption that would be nice to remove and maybe with a slightly different setup in there's let me just quickly say that for if you look at the scale that this type of prediction leads to you do get something realistic so this is very naive it you shouldn't trust any of these numbers I just want to show that they're kind of on the right order of magnitude so what you can do to try to extrapolate is you can look at MNIST this is a relatively small model their small data set and so empirically good robust accuracy is achieved at something like a million parameters for this model and what we can do if we want to extrapolate is we can say this means the effective dimension should actually be 10 even though the naive dimension the number of pixels was a thousand and there's this so the the discrepancy between a thousand and ten is a hundred so maybe we try to just port this over and we say for image net we're gonna use the same constant a hundred we're gonna scale everything up so you could think of many other ways to do this extrapolation but I just want to say that this does give something up the right scale for current practice so so this is like a relevant scaling that we're looking at okay let me just briefly say something about the proof and then wrap up so I'll give a proof in a very simple setting where the labels are pure noise and they're just ID plus minus ones so the first step is we're going to assume that the labels end up being balanced so they're not too biased and this is going to hold with high probability and it's only going to be assumed once so we're going to use a union bound later but we're just going to assume this once and it won't get amplified so what does isoprimetry tell me it tells me that for any fixed function in my class which is lip shits either the function is unlikely to be minus one or it's unlikely to be one so one of these is so either minus one or one is achieved by my classifier on a very small fraction of my total state space so just you know concentration of measure on a sphere if I have some like linear function on the sphere this will be true for example and this means that if I fix this function f first and then I look at my random data set it's quite unlikely to output both labels in kind of a balanced way on my data set it's going to have a e to the minus nd scale probability to do so because one of the labels is achieved on a very small fraction of the state space okay so this means that when we just union bound over our function class we need at least e to the nd labels in order to be able to memorize these noisy labels we need at least e to the nd parameters and roughly speaking a p parameter function class is like an e to the p sized discrete function class so based on the way things were set up you just do a union bound over an epsilon out of your function class so it's actually not a very technically sophisticated just to mention if you want to do mixtures here you just assume balanced labels within each component and if you want to do partial memorization you just use you just think of adding sub Gaussian variables in the right way instead of instead of kind of their combinatorial way of thinking about it yeah um yeah let me just skip to the end maybe and mention a few open directions that I think are interesting so one is to think about non Euclidean geometries so kind of abstractly the the result still goes through but it's much less clear to me like in what cases it's reasonable to think of this isoprimetry property defined in terms of concentration of elliptic functions as kind of a realistic or reasonable thing um it would also be very interesting to understand what changes for different notions of robustness maybe the elliptic constant can be weakened so what one natural thing to think about naively is the sobolev norm so the l2 norm of the gradient but this doesn't lead to anything interesting at all for this setting because even this silly sum of bumps function it has an extremely small sobolev norm because it's only supported on a very small fraction of the state space so it's important that we're using the elliptic constant and not a sobolev norm but there may be other ways of getting around this finally it would be interesting to see what happens with different architectures maybe it's possible to prove different more refined laws to compare with with you know with how how the state of the art evolves as models continue to grow and to try to prove maybe a result that takes training dynamics into account instead of just a uniform bound over a function class so thanks very much for your attention let me know if there are any final questions any questions thank you and thank you for representation so if you consider the the effective dimension of the manifold as you were suggesting you you will expect that you further degrees a lot to the number of data point that you have in your in your set so what it seems to me that nowadays we are able to so the number of parameters we have is the way above the limit that you need to have this robust classification so I was wondering if do you think it is a dynamical problem so are we reaching the solution or we are ending up somewhere in the space of parameters yeah that's a good question I mean I'm really not sure I yeah I think it's true that if you especially if you think of maybe also an effective data set size as well as an effective dimension even this lower bound might you know still not be getting up to realistic levels so I think on one level you can just think of it as a philosophical result saying maybe it's not crazy to use lots of parameters maybe there's some justification I think but it's also you know even a better or more refined lower bounds might be possible with training dynamics so one thing is there's this phenomenon that often you want to train a very large model but then you can remove a lot of the parameters afterwards so what we have here the the lower bound applies also to the number of parameters you end up after sparsifying so so it it doesn't distinguish between the number of parameters used during training and the number of parameters in the final model at all but yeah potentially a version that is taking training into account might be able to do that that would be extremely interesting any other questions yes I have is it audible from zoom sorry we could you repeat that can you hear me is it clear yeah yeah from zoom there was a parameter called also non-linear can you please go to that slide once yeah here yes in this actually what is the stability condition because if we are trying to introduce the non-linear non-linearity in the system it holds for some bounds right what is the upper bound and the lower bound for this so maybe you're saying that I'm I'm assuming that my non-linearity is one lip shits here when I write this product of matrix norms what is the condition it holds actually to be a valid to be in the same data set sorry I don't understand the question okay I'll just try to be very precise because we are trying to multiply here with non-linearity values right if I am correct yeah are you talking about the product of norms on the bottom or the definition of the function f or the f of x f of x okay okay great so wd multiplied by alpha and wd minus one multiplied by alpha so what is the condition for stability for the non-linear signal non-linearity or it's just a function which we are just so it's composition it's not multiplication first off because I was thinking that it is being multiplied okay it is a composition yeah sorry yeah it's it's composition so you're multiplying by matrix and then you're applying a non-linearity to every entry and then you're multiplying by another matrix what what kind of nonlinearity is being considered in this scenario actually it's kind of anything that's let's say one lip shits that so there are a lot of standard non-linearity is used in practice I mean the relu is the most common but you can make up all sorts of variations as well but I mean they're all nice lip shits functions thank you thank you thanks for the talk concerning this effective dimension if you have a kind of hidden manifold you need this effective dimension to scale linearly with the ambient dimension or like can it be a little oh it can be anything and yeah just because it's just the log sobo of constant that enters in okay and does your result say anything when the perturbation is at the level of the examples rather than the label or is it like much harder to look at and do you think that the same final result would apply or is it specific to label noise yeah that's a good question and I'm not sure yeah if the if the noise is on the inputs thank you mark quick question so you you saw the double descent care of me in the beginning I was just a little confused could you comment a little bit on the how you see the connection of the of your result to that literature that I was just trying to say that there's a lot of work on you know over parameters project over parameterization at large this is a flagship example and I I think I mostly unique feature of what I was talking about is that it's looking at a much larger amount of over parameterization so most of these results you're thinking about over parameterization where the there's just a constant factor or something and maybe quick follow up could you comment a little bit on your last point on how you think that sgd training could be taken into account in this framework I don't have any proof ideas if that's what you're asking yeah I mean I would expect that you want to start with some very specific model and stuff and you know like when we were thinking about this we were also starting with a very specific model but somehow things became much more general but it's hard to imagine that for a result on sgd training I think thanks I do have also one I'm so this is about scale of the data so what happens if you actually consider data that lies on the still the dimension sphere but as norm square root of D and say you also scale up norm what the square root of D say yeah sure so that everything as every component is t of one yeah and also you scale up the label noise would you so I'm wondering how the result changes just need the you know you just need to blow up the lip sheets constant by root D or if you still insist on having t of one what would happen yeah so I guess the way I'm thinking about it maybe let me find the slide the way I'm thinking about it there's kind of a natural choice of lip sheets constant scale to aim for once I give you the scale of the inputs and the outputs right so what I want for robustness is if I change my input by a small amount like relatively to its norm then the label should change by a small amount also relative to its scale so so you know that that's a that's kind of a very clean way to just describe what's happening and everything will go through if you just use that scaling thanks any other questions yes thank you so you had some examples at the end of realistic real networks and comparing Amnist and ImageNet so were these networks also robustly trained yeah yeah so the the result I was looking at for Amnist is this paper by Madri and his lab on robust classification and they used you know projected gradient descent training and yeah I mean that you know they did not verify the lip sheets constant or anything like this they just found that it was difficult to find adversarial examples right more questions do you know how to compare this result with the result of the previous talk in the sense you have lots of regimes in which you have this kind of clustering phenomena between some new ones or parameters which in the end might you know you you enter the upper heavy level parameters regime but then you end up not being able to do it anymore because training effectively reduces the number of parameters are you think that connects with what you discussed yeah I'm let's see so yeah I'm really not sure I haven't thought about this but maybe we can talk afterwards if you'd like I feel like I shouldn't try to make up things right now that I think about it final question and then group picture I was trying to understand your result compared to the double descent curve because in that case even you go to the optimal a generalizing arrow the regime is the sample size is proportional to the number of parameter so from this robustness concern do you know in that regime this model is not robust because you have a lower bound this parameter size but that's not a regime for double descent curves so I want to see is there any explanation for that I think when you are doing so so yeah so maybe we just think about linear regression for double descent so if you if you're doing linear regression over the sphere then kind of the natural scale of a classifier is is going to have ellipsis constant that's like square D for me right because I want a typical point on the sphere to get a non-trivial label yeah so so I think the it's a bit strange but if you if you think about linear regression in the context I was talking about then it's kind of not robust if you want a random point to get a good label but I mean even in that setup when you increase the number of parameter you won't get any robust classifier I mean you'd have to always keep the constant at other root and in that case yeah that's right so this is just I think this model is not very suited for linear regression on the sphere yeah okay thank you right so let's thank the speakers once again


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