Everybody forest here rip at 20 23 top sterling baseball hobby 4 box case number 12 random hit style We got eight hits in the case eight spots in the break. Well type him in as we go random off at the very end See who gets what thank you all very much for joining. Let's pull a let's pull a cut auto or like a baton odd or something or Both do both of those things drop in chat Tell him I I'll tell Brad you say what's up All time this is that good bubble wrap, too. Oh, yeah, it's that good stuff Jason Serena Yeet. Yeah legal killed it in almanac, man. Nice. Nice illegal Well, Shane if you were to buy the last 18 spots, I probably won't tweet out that link I won't drop that link anymore case number 13 of top sterling is next Case number 13 at top. So I think we're behind a little bit. Yeah about what 10 minutes behind now Retired numbers and postseason performers. That's a thick card. It's a thickie. Got here. Who we got here retired numbers? Oh, yeah, two of five Nolan Ryan quad patch auto Two color two color three color one color on the Nolan Ryan Express to a five all-time strikeout leader sweet Nolan Five postseason performers. Oh, wow, that's awesome. Yachty Molina one-of-one jumbo letter patch Yachty air Molina the oh and Molina Hello, Kyle. How many more how many but how many more packs you got? Only 30 more almanac packs you guys they're flying. They're flying Gotta go to drip shop dot live slash lane sports Get your almanac pack 150 a pop Any chases left any preview cards left Yeah, yeah, Shane told me an illegal came in here asking for Brad Like you still talk to the guy pull the Luca logo man It's like tell him I said hi if he still allows you to speak to him Fielding award winners in 80s all-stars Fielding award winners you got called Mr. Layton at the bank I That's ridiculous Vladimir Guerrero, Jr. Dual relic auto 16 of 25 Vladimir Guerrero, Jr. 16 of 25 Dual relic auto again 80s all-stars See a prior Ricky Henderson. I'm say Ricky Henderson Barry Larkin dual relic auto numbered 8 of 25 Barry Larkin very underrated all-time in My opinion I didn't get to see him play His numbers are crazy. It was very consistent to Barry Larkin dual relic auto. I mean, it's the Hall of Fame. He's not underrated. He's literally a Hall of Famer 8 of 25 Dual relic auto four more hits world series champs in 70s all-stars Cows like a hidden camera TV show World Series champions Can't wait to see all the more golf content Chipper triple jersey auto two of ten sweet chipper Makes you want the ice cream sandwich the big chipper So I live literally like across street from like a 7-eleven essentially. Oh, I'll go there sometimes get Yeah, like a chip which or something It's too easy man, yeah, the M&M the M&M was pretty good too. Yeah Sometimes if I'm feeling chocolatey, they'll have like chocolate cookie and chocolate ice cream one I'm like, yeah, I need the chocolate. I got to get that So house one's pretty unbeatable. Yeah, although the Mayfield big chipper is good too though 70s all-stars.  I don't care. Oh, that's cool Fisk Carlton Fisk dual relic auto six of 25 red Sox Fisk probably feels like you're watching the shop security cameras legal Watching Kyle walk around All right, 2023 rookies and MVP award winners. Let's see a banger here First box is really good Kind of cooled off a little bit since then 2023 rookies will do that first. I'm ready to pull a one-of-one rookie Think Sam pulled what a Gorman one-of-one Christopher Morell rookie dual jersey auto six of 25 Kids been unreal strikes out a lot, but also hit a ton of bombs Christopher Morell six 25 Ricky dual jersey auto VP award winners. Oh, that's a redemption. Okay, then most redemption I've seen him in dual so far. Let's see what this one is triple Sterling said triple auto relic red parallel that should be to five on the red of each row Hideki Matsui Oh, I know what the other one is Shohei ohtani Monster red to five triple auto redemption each row Matsui ohtani Well, well, well good luck on that and a red. Yep, that should be to five I think all the reds and sterling her to five. Good Lord. That's gonna be a pretty good case Middle not the best when we ended with the Morell the triple redemption the Nolan Ryan to five was really nice And the Molina one-of-one patch was pretty nice too All right. Good luck everybody or anonymize the names and hit same amount of times, which is 10 Put them side by side. That's how we know who's got what names first here one two three four five six seven eight nine and ten John a down at Brittany G and on the hits one two three four five six seven eight nine and ten Chipper down to Yachty Little it's a little Yachty. All right, John a with a chipper and the Fisk John N a Christopher Morell Christopher S. Nolan Ryan on the quad patch auto Edward E their redemption Yep, each row Matsui ohtani big congrats to Edward E Brittany G with a flat junior to 25 Jonathan L the Barry Larkin and Brittany also with the one-of-one Yachty Molina. Thanks again everybody I'll get the results posted to the site and we're on to case number 13


This is covering the spread part of the Fandall podcast network The NFL schedule release for 2023 is tonight and frankly It's kind of dull the fact they have like a full show and a full thing leading up to the release of the schedule is Pretty annoying, but it does matter for us is better because we can decide When we want to bet futures markets and different teams based on when they play certain teams based on if their schedule is front Loaded being tough back load or whatever it may be and you know rest travel all that stuff does matters It doesn't matter for us as betters but I also think it's a good excuse to talk about strength of schedule and I think that a lot of times when we discuss this we discuss in a Very flawed manner what I do for today is use my power rankings to Lay out which teams have the toughest schedules for this year talk through what that means to their wind totals And hopefully try to give you a better metric for that than what you'll see typically when schedules are discussed for Tonight welcome on in to covering the spread. That's right here on the Fandall podcast network and number fire calm My name is Jim Sonness. I am a senior writer and analyst for number fire talking here about some NFL Strength as schedule numbers based on what my numbers are showing we'll talk through the three teams with the toughest schedules this year The three of the easiest schedules again based on just my numbers Hopefully trying to dissect whether that makes sense whether that's a flawed way to look at it and much more to give some insight into the schedules and hopefully a better way of looking at it then looking at Opposing teams record from the previous year will also dig into some NASCAR and Garlington talking through cup series Exiting series truck series all at the same time giving you where my numbers are showing value for this week Over at Fandall sportsbook But first a reminder to make sure you're subscribed to covering the spread wherever you get your podcast tomorrow I will not be here. I'm gonna have Tom Vecchio feeling for me on Friday and Monday My wife's PhD hooding is coming up on Friday. So I'll be at that So thank you to Tom for filling in for me while I'll be gone there as a result No video version of the show Friday and Monday over on the Fandall YouTube page But there will be a an audio version on the covering the spread podcast feed So make sure you're subscribed there and if you like what you hear leave us a five star rating as well Thank you to advance to Tom for filling in for me The NBA playoffs are in full swing and you can get on the action right now over at Fandall sportsbook right now all customers Not just new customers getting no sweats same game parlay every weekend of the NBA playoffs That's right Just play say three plus legs same game parlay or same game parlay plus on any NBA playoff game You'll get bonus bets back if you don't win There's no better place to bet all the playoff action than America's number one sports book head to the Fandall app and getting no sweats Same game parlay every weekend of the NBA playoffs Fandall official sports betting partner of the NBA must be 21 plus and president select states Fandall is offering online sports wagering in Kansas under an agreement with Kansas dark Sino LLC Bonus issued is not the trouble bonus bets that expire seven days after receipt Restrictions applies the terms at sportsbook.fandall.com gambling problem call 1 800 gambler or visit fandall.com Slash RG and Massachusetts hope is here gambling helpline ma. Or or call you 800 327 50 50 or 24 7 support in New York 1877 8 hope and wire text open wide in Arizona 1 800 next step or text next step to 533 42 in Connecticut<PHONE_NUMBER> or visit ccpg.org fast chat in Indiana 1809 with it in Wyoming in Kansas 1805 224 700 or in Kansas KS gambling help calm Louisiana is 1807 7 770 stop in Maryland MD gambling help that org and in West Virginia go to 1 800 gambler net Now let's talk here about the NFL strength of schedule and as mentioned you're gonna see a lot of tweets I've already seen them about Strength of schedule and how tough a team schedule is and a lot of those at least the ones released from NFL Communications for some reason are based on the opposing teams record the previous year They will caveat it saying that it's flawed and it is so I think the simplest solution is if it's that flawed Just don't use it, but you will see it out there for sure others are smarter I've seen this past couple years where they will use betting markets to tell you the strength of schedule and that's awesome that is a lot smarter way because markets are more efficient than Last year's schedule the jets in 2023 are very different than the jets in 2022 So using markets to decide that much smarter the one flaw there is that The wind totals for teams facing the chiefs are inherently lower because the chiefs are on their schedule That's going to in a way make the chiefs schedule look easier than it is. So It is a much better route than using last year's numbers I think I respect this route a lot for sure, but that is that one flaw is that It already kind of factors in they're like, oh, they're facing these teams So it makes the good teams look like they have easier schedules and they may actually have So I wanted to run through what I've got in this regard I have a power rating for each team that accounts for all season moves and projects What I expect them to be like this upcoming year I can take that power rating and then look at the wind total for each team That will give me an expected wind total based on each team's power rating and based on their power rating alone If a team has a much lower wind total projected by my numbers Then you'd expect based on their power rating and implies their schedule is difficult So a team is rated at x and they're projected to win y games if they are projected to win Actually win projected y minus one games that implies that their schedule is very tough One win less than you'd expect based on their power rating their verse would be true as well So this is also flawed because it assumes my model is correct and that's obviously not the case I would love for that to be the case, but it's flawed But I do think that this is a good way of looking at things And it's better than looking at last year's schedule I do think the market angle is probably correct too, but you know, this is a hopefully unique way to look at it Once buys are announced I can add that in and stuff But this is accounting for opponents faced where they'll face them and things like that So for today wanted to run through the teams the toughest schedules. Those are the easiest to outline What that means as far as What my numbers say I'll run through the expected win total based on the team's power rating The actual projected wins my numbers and their win total over at fan dual sports book When I dig into my numbers the team with the expected Toughest schedule so far this year is the new england patriots because right now if you take Just the power rating that my numbers have for the patriots their win total will be 7.8 But when you plug in their actual schedule, their projected win totals by my numbers is 6.9 It's almost a full win lower than you'd expect based on their team's strength in my model Their win total at fan dual sports book is seven and a half. The under is even money I think there is value on the under here as a result of this and the reason the patriot schedule is so tough is because the afc east itself Is very tough. You got the bills there. I think the jets as much as we can joke about them Will be significantly better with Aaron Rodgers in town versus Zach Wilson Rodgers played through a thumb injury all of last year Comes over here. I think the offensive line They've got a lot of depth that tackled despite not being very strong there And then you have Garrett Wilson and competent pass catchers beyond him as well So the jets are tough dolphins if two is healthy or tough But also there even if two a does miss time that defense should be good with Vic Fangio in town as well Outside of the afc east the patriots also facing the afc west so facing the chiefs facing the chargers teams like that My numbers don't hate the raiders or the broncos as well. So that's a tough road and the nfc east So you get the eagles you get the cowboys Giants and commanders not as big of a tough of a task, but It's a really difficult schedule here for new england I do not have the patriots favored in any of their road games as of right now So I think they'll be better this year. I like what they did in the draft Taking three offensive linemen pretty late to try to give themselves swipes at high upside positions And I like that a lot. I think that approach was good bringing in bill o'brien should help them a lot too But it's a very tough schedule It's tough to be super jazzed about this passing offense in terms of efficiency So I think when you look at the schedule for the patriots the under seven and a half and even money Does make a lot of sense. That's what I'd be willing to make Based largely on the schedule they'll face this year The number two toughest schedule across the nfl for this season based on my numbers is the washington commanders If you look at their power rating, they'd be expected to win seven point three games I hadn't been projected for six point eight now this one is actually in line with what the market has because the market has the Commanders win total at six point five with the over at minus one twenty two So if I've got six point eight wins, I won't say exactly a lot at the market there Uh at six and a half over at minus one twenty two big thing here is obviously the nfc east that is a a tough Path for them. They're facing the ascs too. So similar pathway here as the patriots Now the commander is the difference for them is they do get some pretty good matchups at home They'll face the bears at home. They'll face the cardinals who may or may not be tanking And that's part of why even with a tough schedule I have them projected a hair above their actual win total for this year But it is a tough road part of this too is I've got them projected decently high because of their defense But also I don't think Sam Howells and like the worst position to succeed. I did like Howell coming out of the draft it's hard to have high expectations for a guy who was a fifth round pick but Had good collegiate efficiency numbers outside of being sacked a lot Um, you know, he's young. He was decently efficient pretty experience coming out checks a lot of box in that regard So I don't mind the commanders this year, but that's schedule very very tough And it keeps me away from taking the over six and a half Uh at minus one twenty two Despite the fact based on their actual strength their wind hole for me should be seven point three So they could bump down half a win based on the schedule. They'll face the third toughest schedule for this year It's just uh, then data against all patriots associated teams It seems like because the las vegas raiders have the third toughest schedule I think that might be why their wind total came down. It was seven and a half It was um, I think plus money on the over It's now six and a half with minus 144 on the over and similar to washington I think this is in line the market is correct on this one because I've got The raiders expected wins based on their power rating at seven point six Their projected wins are seven point ones so down a half win based on their schedule And the wind total is six and a half with minus 144 on the over I think with the schedule they're facing that's enough to push me away from taking over six and a half Despite the fact that jimmy groplos fine. Um, they've got davante adams got some decent infrastructure I still think that we can stay away from the over here As a result of the schedule they're facing the asc west obviously given they are in the asc west and they're facing asc east too Uh, so they get the the the bills jets dolphins patriots Their nsc matchup is the north so that's not bad because the only team i'm super high on there is the lions and The vikings are fine packers fine bearers below average So the nsc portion is not that bad But when you're facing the cheese twice facing the chargers twice I don't again. I don't mind the broncos all that much It's a pretty tough road So I do have them projected above their wind total But once you account for the juice at minus 144 or they become a stay away Because the schedule for the raiders is very tough So the three toughest schedules that my numbers are the patriots commanders and raiders And I think that there is some value in taking the under on the patriots at seven and a half wins That is even money right now at fangirls sportsbook other tough schedules to this year by my numbers are the cardinals therefore The nsc west is not great, but it's still a tough schedule Followed by the giants the chargers and the broncos. So those are the top seven as far as toughest schedules for this year On the flip side the easiest schedule for 2023 based on just my numbers I don't think it'll be a shock to anybody given the division they play in but it belongs to the new orland saints The new orland saints if you just take You know Derek Carr in this offense with a pretty good defense I'd have them projected for 8.7 wins. That's not bad. That's an okay number for sure But when you add in their schedule, I have them projected for 10 wins So they get a a bump of 1.3 wins based on the schedule They will face alone that is a huge bump their wind total at fangirls sportsbook is nine and a half with the over at plus 106 So even though that number is high when you look at it It is like kind of like startling how high that number is for the saints I do still think there are some appeal In potentially taking the over there because of the route they will face the saints this year facing the nsc south so Facing a rookie quarterback in the panthers either Baker mayfuel or Kyle Trask and They get the falcons. My numbers are not super enthusiastic about as we'll discuss here in a second They also face the nsc north. So as mentioned not a super tough division as Producers and this is the key part here for the nsc south. So they face the afc south I think that the cults could be fun this year. I don't think the cults would be good though Like they're gonna be fun to watch doesn't mean I think they'll be great get the texans You know a rookie quarterback there as well The titans are a very odd team And then you get the jags. I like the jags plenty, but the afc south is a good draw for sure So the saints Again, if you go just based on their power rating projected for 8.7 wins But I've got them at 10 as a result of the schedule they will face massive massive boost so despite the fact i'm not I think the saints are about an average team based on my numbers I do still think there is appeal in over nine nav wins at plus 106 right now Over at fandal sports.  It might feel gross But there is potentially some value there as of right now The second easiest schedule is also in the nfc south However, this is what i'm not going to be taking the over on their wind total despite the fact their schedule is very very easy That team is the atlanta falcons The falcons their wind total of fandal sports book is eight and a half with the under at minus 110 If you just take the falcons power rating in my model and plug it out there Their expected wind total would be 6.6 two wins below their total When you add in their schedule it bumps up to 7.3 So they gain 0.7 wins based on the schedule they will face which is a good number, but it's still 1.2 wins below their total. So even with an easy schedule I think that there is value in the under here on the falcons. So they get the same route as The saints get where they're facing the nfc south the nsc north and the asc south They do have a lot of winnable games at home. They've got green bay at home houston indian washington But the road schedule is very very tough So the falcons have the second easiest schedule in the league I still think there is value in the under on eight and a half wins at minus 110 desmond ridder Played decent last year. I thought that he was pretty fun coming out of Cincinnati. So it's not really a ridder thing It's a the defense Has a long way to go. They've made a ton of swipes that defense, you know, especially late in the draft They took a lot of swipes there a lot of ads and free agency, but they had a long way to go So i'm still a bit pessimistic here. I understand why this wind total is high and i'm not like Jumping to take the under but I do think there is value in the under at eight and a half wins in minus 110 Despite the fact the falcons have the second easiest schedule by my numbers this year The 30 easiest schedule going back to the nsc north and its team that is going to be playing an opening day in the nfl Against the can city chiefs. That is the detroit lions their wind total nine and a half over as minus 122 I've got that about right based on their strength because the lion's strength has them as a 9.8 win team based on my power rating But once you plug in their schedule their wind total for me is 10.4 So almost a full win over the total at nine and a half So I think there is value in the over here for the lions at uh minus 122 over nine and a half If you look at the home games for detroit, those are largely super winnable Obviously all the nfc north teams at home, but also they get atlanta at home carolina and las vegas The schedule is pretty easy here despite facing the afc west again They get the chiefs an opening day dolls left face the chargers the raiders and the broncos But they also do get the nfc south So they benefit from the nfc south being very very poor They benefit from facing a lot of very soft teams at home which jacks up their their expected wind total or their Expected win odds in those games quite a bit and gives them some pretty steady baselines for wins I do tend to like jared golf. So maybe this is me just being too high on him But this is even with their wind total or their projected passing efficiency being lower for 2023 that it was in 2022 This will change their wind total will change based on uh the schedule being released tonight because we'll know When james and williams is suspended. I have it just kind of baked in as if he's playing 11 out of 17 games right now But if they have a super tough uh first six games before williams is back Then that will lower their wind total or if their easier games are coming in the first six that may actually increase their wind total from where it is So this number will change I'd be okay waiting to take the over nine and a half right now because again, I got them a 10.4 Over nine and a half minus 122 not a ton of wiggle room there. So I'd wait until the line schedule is released, but Assuming they don't get just totally skewered In their schedule release with a lot of tough teams early on I think there could be some value in the lines over nine and a half winds at minus 122 So Situations of monitoring. I do like the lions over nine half winds I do like the falcons under eight and a half despite needs the schedule Don't mind the saints over nine and a half at plus one of six as far as the tougher schedules Do you like the patriots under seven and a half at even money as of right now other easy schedules? I would note the panthers of course in the nfc south The the cults in the antsy south and the jags in the antsy south and the 49ers in the nfc west Given the weakness of the rands and the cardinals not a huge shock to see the 49ers there so Again, easiest schedules this year saints falcons lions panthers cults jags and 49ers Hopefully that makes a lot of sense. Hopefully it's not too self flattering to use my power ratings to judge Strength the schedule, but again, you know, I think there are flaws other ways There are flaws every way in measuring strength the schedule So hopefully this has been a useful exercise for you and trying to project out scheduling strength Let's shift gears now and talk about some nascar because we got a lot of nascar coming up this week It is in darlington throwback weekend for the nascar cup series where they're running a lot of old school paint schemes always a fun time We had three races coming up with the trucks Xfinity and the cup series all running in darlington for this weekend As far as the cup series goes I'm not seeing a ton of value as of right now at fan dual sports book I have kyle larson at 15 to win this race His implied odds at five to one are 16.7 percent So if you are able to get access to larson at six to one or longer, I'd fire away That's a pretty good bet But at five to one I can't quite get there I do think there is a route to betting on kyle larson this weekend Which we'll talk about later on But I can't quite get there on the outright market at fan dual sports book for this week I have very close to showing valian ross chest 8 and 11 to 1 I have met 7.5 percent to win so 1300 or longer would probably be a good number there at 13 to 1 or longer William Byron has 10 to 1 some places plus 850 at fan dual sports book I'd have fair value in him is uh plus 11 20 is i odds me 8.2 percent So i'm watching larson to see if I can get a six I'm watching chastain to see if I can get 13 to 1 or longer Then watching Byron to see if I can get 12 to 1 or longer on him Fan dual does not have top 10 odds up yet for the nascar cups Here's let me just check here one last time to see If those have been posting in the past couple of minutes. Oh, they have okay. How about that? So fan duals posted top 10 odds I'm going to run through these right now and see if there is any value and Oh, there is a little bit. Okay So the guy i'm focusing on right now as far as being an out a value to finish top 10 Is corey lejoy. He is 11 to 1 to finish top 10 at fan dual sports book You can actually get 15 to 1 elsewhere and I show value even at 11 to 1 So I think lejoy is a good bet. I have corey lejoy in the top 10 At 12 percent of the time that seems like a grotesque number his implied odds at 11 to 1 are Lower than that. They'd be under 10 percent 11 to 1 8.3 percent. So implied odds 8.3 percent I have lejoy at 12 percent to finish top 10 The reason he is there is because his form has been much better this year ran pretty well in fontana another high tire wear track With a lot of speed. So that was encouraging because spire's big issue is speed But lejoy actually did hang pretty well in that one We went to las vegas. Lejoy is also competent there had good speed in dover was solid last week in uh, kansas And darwin does a track where he's actually been good in the past. He had a run here back in 2021 I believe where he ran top 15 pretty much the entire night didn't finish top 10 But he was good. So we've seen lejoy pop at this track before His current form is the best it has ever been by a wide margin I think 11 to 1 is a really good number. So if you can get 15 to 1 go take that It's a great number But even at 11 to 1 at fan dual sports book I do still think core lejoy is a value for this race I also would add I want to give like the biggest of caveats here Please don't like, you know dump a lot of money on this because I have value in core lejoy to win elsewhere. He's a thousand to one to win the implied odds that are 0.1 I have my 0.36 to win. So It's a bet that loses 99.6 percent of the time. I want to be very clear about that But I did bet it myself. I took the 1000 to 1 on lejoy to win. It's not going to happen. It happens one out of every 100 and something times but Worth a shot one. I've already like 200 times actually, but I think it was worth a shot for me. So I did take lejoy A thousand to one to win.  I'm not saying you should follow it But I did show value there. So core lejoy 11 to 1 the more sound bets over a fan dual sports book for this week I mentioned before that you can bet kyle larson this weekend without taking the 5 to 1 in the cup series That's because he is also running in the Xfinity series And I do show value on him at 2 to 1 at fan dual sports But you can't get plus 225. I believe out there still But I have larson at 37.4 to win so value at both these numbers 2 to 1 or 225 Larson is driving for colleague racing in this event. That's not the same equipment as junior motorsports car So it's not the best equipment But it's fine equipment that can win at this track. Were they good enough driver and kyle larson very good at darwinton he's a little bit erratic he can be kind of Maybe get out over his skis a little bit at times, but I think that he is a very talented race car driver. You put him up against this kind of field I do respect a lot of the drivers in this field in the Xfinity But I think kyle larson is still the best So he has not won darwinton in the cup series before I think he could get a win on saturday in xfinity I would not be shocked if he did it on sunday in the cup series as well 2 to 1 for darwinton For larson at darwinton is a fine number on the xfinity side of things Even with larson sucking up 37 of the win equity in my model I also have austin hill as a value. He is 28 to 1 at fan dual sports book I got him at 35 elsewhere earlier this week So shop around on austin hill see what number you can get but Even at 28 to 1 would be a slight value for me at fan dual sports book I have him at 4.2 to win his implied odds at 28 to 1 or 3.4 percent implied odds at 35 to 1 I think are 2.8 percent, but Either way good value on austin hill here. He won los vegas. It's not the best track comp for darwinton, but He has a higher speed track does have at least some tire fall off hill Not the best track record in darwinton specifically either in Xfinity or in the truck series, but this number is very very long So I would be okay taking that. I do think it's okay to shop around on hill for a top five as well He is plus 375 there at other books. So I don't mind that but uh 28 to 1 to win also okay for austin hill other top five bets I like elsewhere. Chandler smith is plus 275 I think with what he's done in In richman's another track with a lot of tire fall off Not a great comp for darwinton, but it's also again the heavy tire fall off thing does matter So he destroys that track plus 275 for a top five to me makes a lot of sense Brandon jones is plus 375. My numbers tend to be a bit too high at him, but You know, it's a jrn car He has experience at darwinton. So plus 375 for a top five makes sense and fine Finally daniel hemrick at plus 750. So every single college car showing value in some Some market for me with larson to win a two to one smith plus 275 top five and then hemrick plus 750 I just think it's a long number. So top five bets I like for xinni chant or austin hill to 375 Chandler smith 275 Brandon jones 375 and daniel hemrick at plus 750 Fandall does not have truck odds up yet. I guess they posted top 10 Maybe I can see no no truck odds yet up yet for a fan duel In darwinton, but you can look elsewhere and I also show some value in a favorite elsewhere for the truck series And that's in a william byron. You can get plus 250 the implied odds there are 29 percent I have byron at 33.6 to win byron is in a kyle bush motorsports truck Which means he will have absurd speed this weekend when you put kyle bush in that truck He can get win odds north of 50 percent But byron there 33 by my model seems pretty reasonable. So Byron at plus 250. I'm very on board of that I think that uh Is weird to bet two super short numbers that a track that does have some chaos like darwinton, but Given how good william byron is how good that equipment is plus 250 I'm very on board of that and very on board with larson a two to one in the xinni series I do also show value in steward freason at 40 to 1 and parker quickerman at 50 to 1 if and will sports book or other books For this race freason's top five mark is plus 450 clickerman is five to one Those are both also values for me. So I don't mind taking swipes at the outripes of 40 and 50 to 1 respectively on freason and clickerman But I think the top five bets are better the better route given that we got Byron in this field chastain's in this field bubble wall is in this field in the very good truck You got coreyla joy here too. Um, not the I'm not sure really what to think of the spire equipment, but There are some good drivers here. So I prefer to go the top five routes with freason at plus 450 clickerman five to one I think both those are good values But if you want to go the outrides, I will not talk you out of it So overall a lot of fun value for this weekend in darwinton We'll see how things play out But what could go wrong with tying your horse to coreyla joy in the cup series a thousand to one to win But 11 to 1 for a top 10 at fandall. I think that makes a lot of sense That's gonna be all we have here for today and for me this week on covering the spread as mentioned Tom becky. Oh filling in for me tomorrow and monday big. Thank you to tom for doing that You can find that on the covering the spread podcast feed wherever you get your podcast and as I thank you to tom Make sure you leave a rating a five star rating over at podcast at thank tom for his time filling in for me If you've got any questions for me, I am on twitter at jim saunas j i m s a n n e s You can also follow the fandall podcast network at fandall podcast I want to thank you all for tuning in for today Enjoy the schedule release for tonight if you hate your life enough to watch that just kidding. It's great Have fun. Enjoy that. We'll talk to you all next week. This has been covering the spread right here on the fandall podcast network


Recognized by the distinctive white ring around its eyes, the Adeli penguin is only one of two species of penguin whose only home is Antarctica. While Adeli numbers have been observed to decline in some regions amid a changing climate, the truth is, surprisingly little is known about the penguin's actual distribution along Antarctica's coastline. A 2015 land and air survey explored previously unreported colonies of Adeli here in a cluster of ice-choked islands called the Danger Islands. The discovery could mark an important technological turning point in species tracking that would have clear implications for preserving biodiversity. Researchers conducted their survey from aboard a research vessel and on the grounds of several of the Danger Islands, only one of which had ever been inspected for Adeli penguins. They counted nests manually from panoramic photos and from imagery captured by drones. In all, the team tallied 751,527 pairs of Adeli penguins in the Danger Islands. That's more than the rest of the Antarctic Peninsula combined, and at a region scale, the new count boosts the previous population estimate by nearly 70%. The researchers compared their findings with aerial imagery captured in the 1950s and satellite imagery gathered since the 90s. The analysis revealed that, overall, Adeli numbers have remained roughly stable in stark contrast to the declines observed along the Western Antarctic Peninsula. These findings are consistent with recent modeling work showing that the warming pattern of the peninsula has perhaps spared the Danger Islands from large environmental changes, at least from a penguin's perspective. That conclusion, of course, is limited by the lack of imagery between the late 1950s and 1990. But it points to the potential power of medium-resolution satellite imagery. Combined with drone-based photography, such imagery could enable researchers to discover further penguin colonies and chart their biogeography over time. Additionally, the results make a strong case for increased species protection in the Danger Islands. The islands are large and likely to remain a vital hotspot for avian abundance under projected climate change. As such, the team argues that they deserve special consideration in the negotiation and design of marine protected areas in this region.


Alright, so a lot of you have seen my last video that I put out on Wednesday and I was talking about just the job perspective for the PA profession over the course of the next 10 years and I wanted you guys to just kind of take a really good look at that statistic that they were throwing out there just so that you can be making the most informed decision when it comes to the career that you're trying to get into. I had a question from that video and I wanted to touch on that because it specifically talks about job satisfaction and you know what's going on in the PA profession. So I will talk to you about that from my perspective in this video.  This is Adana. Welcome back to my channel. Okay, thank you guys so much for joining me again. If you are new to my channel, I make PA related videos amongst other videos just about my life as a mom, wife, and PA. So if you're interested in that, take a look around. If you like what you see, go ahead and subscribe, okay? I have this comment that was made by Courtney Foster and she said, I've been having a bit of a crisis because all of the PA's I work with and follow are saying that they are extremely overwhelmed and burnt out and it's making me wonder if this field is something I want to do and is worth it or if people reach their career goals and realize that things aren't not quite what they had hoped. I also cannot tell how much of this is work-life balance in general or COVID related. Do you have any input on that? Thank you so much for your videos. All right, Courtney, so yes, I do have some input on that and I mean I just want to start off by saying like honestly it's not just PA's like the physicians are burnt out, the nurses are burnt out, the techs are burnt out, like legit everybody in healthcare is burnt out. And I think that it's largely because of COVID. So I know when I first started it was in 2020, kind of really at the height of COVID, I started in like April of 2020 and it was bad and when I'm telling you bad it was just like there were not as many providers working like in hospital. We had to cover so many different service lines. It was really just like overwhelming first and foremost as a new grad PA but also just as a PA going into a new specialty that you weren't necessarily really familiar with. It was super just overwhelming and inundating the amount of work that we had to do. And at the same time, you know, you are fighting off this virus that you are still trying to figure out like how it works and you know what works in terms of treatment and all of that stuff. So it was pretty bad. Now obviously a year later it's a little bit better in terms of what we know about the virus and how it works and therefore when treating patients with COVID it's a lot less stressful I guess you can say. However, it's still, there's still a lot of like build over or like spill over I guess you can say from 2020 in terms of just how tired people are, okay. Like my nurses, I have nurses that every week that I go to work it's like oh somebody news quitting just because it's they're tired you know they're being asked to do a lot and it's the same from the PA perspective. They're putting a lot on us as you know APPs and I don't know if we're always like as appreciated and I think that's part of what the issue is in healthcare in general like be it from the physicians or the PAs or the nurses that feel like they're burnt out. I think a lot of it stems from a lack of feeling like they are appreciated you know if you get like thank yous and things like that from your higher ups your bosses or hey you know you guys are doing a good job we understand that this is not easy but we appreciate you all I think those that goes a long way you know just a little sign of appreciation so that is my thoughts with respect to if it's COVID related or work life balance I mean I think as PAs we really have the opportunity to truly have a good work life balance and if you don't have a good work life balance I think that's kind of on you like you can decide the type of job that you want the type of hours that you want there's so many different job structures and hour structures be it 4-10s or 3-12s or 3-24s in two weeks which is what I do or you know you're working five days a week eight hours a day or you're working five on or six on and seven off or whatever the case may be like there are structures that you can choose so that you're able to actually fulfill that work life balance and so if you're not feeling like your work life balance is where it needs to be then that is something that you can take a really good look at and can change now in terms of them being overwhelmed like I said I think it's a lot of it has to do with COVID but honestly like when you get into I've had some friends some people that have said you know like the PA profession is not necessarily what they thought that they would were getting into I guess you could say you know like they they want something where they feel like they're making a difference in terms of like the long run and then there are others that are like this is absolutely what I wanted to do which is me you know like I'm happy seeing patients I'm happy you know treating patients I think that it's something that I've wanted to do for a while and obviously you know I'm not necessarily in the specialty that I thought that I wanted to be in originally but I'm having a great time being a trauma PA I'm learning a lot and I'm very excited that I'm afforded the opportunity to be in this field and be in this specialty and learn all the various different procedures and and advanced practice skills that I'm allowed you know to learn through this specialty so I think it just depends on you and the specialty that you want to get into be it you know primary care or a surgical subspecialty or something different like pediatrics whatever it may be you can make that decision and I think that is the beauty of you know the APP model especially when you have this this way of kind of doing this lateral movement if you get into something that you don't really like that you're not really feeling so if you know you were in urgent care and you're like nah I'm not feeling this or and let me go to primary care or vice versa you can and you don't have to get a new certification and you literally just have to look for a job and be like hey let me interview and you know hopefully you get the job and so I think that is that's something that can help stem some of this like oh I don't know if this is what it was all cracked up to be or if it's as fulfilling as I want it to be because if you want to follow patients long term then you know get into Peds and see them until they're 21 if you want to not follow patients at all then you know get into emergency medicine or urgent care and and just kind of treat them acutely but there is a space for you and there's an opportunity for you to kind of look into all of that and just get what's best for you so hopefully this answers your question Courtney I mean I again I think that different strokes for different folks right you know there are different things that may be kind of fueling this overwhelmed feeling but I think overall it's COVID related so have no fear just keep pushing through keep asking questions to various different PAs and get all of their input and then see what that means for you and your future and then make your decision based on that okay thank you guys so much for watching thank you Courtney for this question if you guys have any other questions for me please leave them in comment section below go ahead and like this video I still have a little something in my throat you guys but go ahead and like this video subscribe to my channel and follow me on Instagram and on the PA and on Instagram and get that C University thank you guys so much for watching I will talk to you guys next time


Do you ever wonder what happens when the police leave? Crime scene cleaners are private companies that handle the cleanup after the police are gone. Spalling Decon is one of the nation's largest cleanup companies handling the aftermath of homicides, suicides, decompositions, hoarding, and much more. These are our stories. We are doing a hoard from drug addicts and homeless who had broken into the rental and have completely, completely destroyed it. So we found the sharps container. It's actually your analysis container that they're using as a sharps container. You can hear alcohol pads and things like that all the way around this room. So I'm pretty sure this is the room where they were having their fun. We are in Tampa just five minutes away from our office, which is really, really convenient. It's really awesome because we never get jobs like this. So we are doing a hoard from drug addicts and homeless who had broken into the rental and have completely, completely destroyed it. Today's goal is to do one trailer and try to get as much stuff from the first and second floor in that trailer. Should be good to go. All right, guys. So the weather outside is looking quite frightful, not in a winter wonderland kind of way. But we had a tropical storm in the Gulf of Mexico that has recently broken up. I feel sad for it because we all hate breakups. But we're getting all of the rain. It was going really, really, really fast. So yeah, we're getting all of the rain from that and it should be hitting in about an hour. Oh, if it rains on a job, we just keep going. Just be a little wet. We know some of you guys like it wet. It's not a bad looking house, though. I mean, from the outside. Can't really tell much about the inside just yet. We're going to focus solely on downstairs right now. That's an old RCA from like 1921. There's no electricity. You can't open up the windows. But we got this. That was a really good run, Nick. We got mice over there. Dad? No. There's a lot. Where? I don't do mice or breakfast that are alive. All right, Nick. Yeah, so it's an old house. Dodging weave. Dodging weave. That's it. Oh, yay.  I didn't know you were like, oops. Everything is a total trash. Nick, what? You want to see Clam? Giant Norman. Look who showed up to the job site. Not on purpose. I didn't know I was coming here. Yeah. I was dropping off my mini-me. You got a baseball swing? A little bit, but mainly not for baseball. You want to see? No. You want to check? No, I'm good. That's just an embarrassment. I just didn't take my gloves off. I didn't want to give Jack Jack a hug with my dirty glove. Am I thirsty? Those are cool. Those are old. Let me see the year. They're all there, too. Not broken. Just the box. 1997 national champions. Clam inherited it from her father. Yeah, so she had to walk and talk. Walk and talk, guys. So she inherited the house, and she kind of just left it vacant until she figured out what she wanted to do with it. And that's when she noticed the drug addicts and things like that were living in here and actually just trashed the whole place. Oh my God. This stuff we're going to set aside. Anything personal like that? She said she'd like this to keep it. Yeah, she's actually going to renovate it and turn it into a rental. There he is. What's going on? Leaving? Oh! Get lonely, Lonnie. What are you doing? Hey, how are you feeling? You going swimming today? Take him here. Squeeze his arm and take Squishy. I'm going to take that. Squeeze his arm. Take Squishy. Squishy. Yeah. He's walking around and grabbing everybody saying Squishy. All right, man. You have a good day. He's the only non-Squishy one here. It's Muscle One! Super Gecko Muscle! His side gave out. And my side.  The handle just broke. Then when his side gave out, my side dropped and just popped my shoulder out of place and then back in. Bye, Jack Jack! Bye, Jack Jack! Oh God. Do it again.  It's not too bad. That's not too bad. That's Ashcrack territory. Uh-uh. I ain't about that. I knew going into it, it was a friend of a friend, but I love the fact that it's an actual friend of Lauren and Laura. And I got to see my little buddy today, Jack Jack. So, all around, it is an awesome Friday evening. My inner 90-year-old lady was screaming. Screaming. I hate seeing beautiful glass destroyed. I hate it. Kills me. Sorry. I'm doing, like, the finishing touches on each room. It's a historic place. It's gonna end up being gutted and then rebuilt. And I'm hoping to God that she'll keep, like, a character that's still in here because I love houses. Like, 1914 is when this house was built. 1920s. There you go. 1914. You were way off, Nick. Just don't. He was off. 1924 years. He was off. Six years. Wow. Go back to kindergarten. Make me. Give me the trash like that. Trash that I am. Freakin' phenomenal. Original hardwood floors out there. Crown molding around the top here. You have the crown molding there. Betty White is older than sliced bread. Betty White was born in 1922. Sliced bread was started in 1928 and this house was built in 1914. So, Betty White might be older than sliced bread, but this house definitely beats both of them. Period. Show us what you're really hiding there. Not a good enough camera. It doesn't magnify. No, it doesn't. Us carnies have to stick together. Oh my God, yes.  And we'll see who walks out at 35 years old with back problems. Me. Grab that. That's handmade. Somebody made that for somebody. You want to see this? Yeah. Yeah. Okay, that's my weak arm. This is my masturbation arm. Oh, that's one. Yeah. So, we found the sharps container. It's actually your analysis container that they're using as a sharps container. So, because it's already being used as a sharps container, I'm going to go ahead and the caps are not on these, or the caps are on these guys. So, I'm good to just safely pick them up and drop them in. If the caps were not on them, obviously I'm not going to stick my hand in it, but if the cap was not on them, you can hear the whole bottle full. I would actually grab a pair of pliers and put those guys in there that are safe than sorry. Good thing is, is the caps were on them, so I didn't have to go get a pair of pliers, but there's alcohol pads and things like that all the way around this room. So, I'm pretty sure this is the room where they were having their fun. So, at this point, by state law, we're not allowed to go over the side walls of the trailer. Obvious reasons and safety. We want to turn a corner and a whole bunch of stuff fall out. So, when the trailer is full, and it reaches its full capacity, which means that we're up to the side walls, which on this guy we have eight, eight foot side walls, I think, then we're good to go. He said he found his white beater. Nah, you're throwing those away, actually. The white beaters. Table lights. I am so tired with you. 25, exactly. Now that the downstairs is completely cleared out, I'm going to go ahead and start taking photos of the upstairs because we're actually going to be able to start the upstairs today, which is wicked awesome. I'm assuming, it used to be an apartment up here in an apartment down here. Yeah. And in 1914, when it was originally built, it was probably one whole house and the staircase was probably somewhere back here. What do you say that? Or right up here on the side, because it's just how old houses are normally built. Sure. The floor upstairs is a little sketchy, so we sent the, uh, the carny upstairs, and he's just dropping stuff downstairs. We'll see how it goes, but you can see, got a little bit of room left. Got it? Now the landing is super small, plus there's a lot of soft spots, so I don't want a lot of people in this front room safety issue-wise. I've already had that one cleared up. So apparently the front room is already, or the front bedroom is already cleared out, and we just have this stairway area, voyeur, voyeur area. It's almost complete. We probably have to take a couple more loads here in the next couple days. Step with one foot first, and then put your weight on it. There we go, there we go. Lower, lower, lower. Drop it. And drop it like it's hot. That is called redneck engineering. Brush the shoulders. But that's all the, the wood grain and everything that they've chewed. We're good in here, Carl. That's an understatement. Like dying here. Cool us down. But it did not help with the humidity, which made it even worse. So that is not from the rain. That is from where? My shirt. So we have the owner here, Brock, who is going to tell us a little bit of history. So this is something that doesn't happen very often, but she was more than welcome to help us out today. Yes. The house was built in 1929. It has had several owners. My family acquired it in the early 90s, I think. And so my father got it. It was a demolition property or something along those lines. There's a story behind that. But, you know, anyway, that's how he acquired it. He did some work on it. And it's been in the family for a very long time. He left it to me. I have a sister and he has four grandchildren that I would like to let them decide what they want to do with it because I don't have the heart to do it. I just need to get it livable or rentable and see if what the four grandkids would like to do with it. Because each of the kids, myself and my sister, have their own house property. Which is Canadian. Very close. I don't want it to sit vacant any longer and the grandchildren have gotten older. So if ever they needed some place to live, they could always be assured that they would be able to live from their grandfather. So let me see what you guys see today. Yeah, that's perfect. And then I'll just set this one right here. Okay, from the bedroom. So you remember this room? Couldn't hardly walk. You couldn't even see up the window. And this room was pretty much the same. There was a giant changing table in here and the mattress and things like that. So we had the carpet padding. It was super easy. It was already lifted so I just rolled it up and we took it out for you. So here's a couple of pieces of furniture that were requested to be saved for refinishing. We have the kitchen. Wow. Kitchen is completely empty. Fantastic. We named the room behind you the back room. Because this was full. Full of bags. So we cleared everything out of here as well. Oh nice. So you're pretty much the first floor 100% as a clean slate. So the goal today was to fill one trailer. We have everything out of here. Okay. Like I said on our second round about we'll do a scrapper for you. Set everything out by the road. So let's take a walk upstairs. So this is all termite throw. The house is very active with termites. Oh really? So all of the furniture that we have found up here actually completely fell apart. So you remember we could hardly get up the stairs. Exactly. This is completely clean as well. Oh awesome. I guess I should close these windows now. Yeah so now that we're up here and we're able to we can actually close the windows that are open. Everything else is cleared out. Wow that is nice. Look at all the... This was actually from one piece of furniture. Wow. One piece. It was from all of this from that one entertainment center. Wow. Yikes. Yes they were. Awesome. I appreciate everything you guys did. It looks great. Thank you. Absolutely. That's what we're here for. So would you say that's another dumpster? I would say that's probably a small dump. So we have our big one which we call Big Bertha. And then we have our small dump trailer. Looking around through here. You have a lot of books. We do have some furniture back here. But I would say that this would be equivalent to our small dump trailer. And that right there is really bad. There's a couple of other really soft spots over here. So you want to try to avoid going stepping on this one. That one there. I guess I should do the... Yeah let's do these windows. Which one is it that's really really soft you say? I have your trash can over it.  Perfect. So I'm going to go ahead and just leave these garbage bags here for the next time. Yes sir. We'll see you on the next go round. Alrighty. Alrighty. Thank you guys. I appreciate it. Today we are finished with the first portion. Filled the whole dump trailer. I'm glad Nick is just chilling out for a second because we all need to brake pads on the back of the truck. Nick's there. It was kind of intense. We're all done with this first portion. We weren't able to fill completely the trailer to completely fill the trailer. I don't know. You guys know it's kind of weird sometimes. We got the entire first floor done. The client is super super super happy with what we've done. And we've got almost almost the whole upstairs. We have three rooms left upstairs so stay tuned for the part two of this guy. Hey guys thanks for watching and don't forget to like, comment, share and subscribe. Pause for the cause and ring that bell to get notifications when we launch our new episodes every Thursday. Have a good day guys. Peace. For more information visit any of our locations. That's it guys. On to the next.


JD Vance, a so-called populist outsider who worked in private equity and benefited from tax loopholes designed for the rich, will now be a U.S. Senator, thanks to his billionaire benefactor Peter Thiel. Thiel alone was one of the largest individual donors in the midterm elections, doling out at least $32 million, with most of his campaign cash spent on two super PACs created to support his Silicon Valley protégés. Thiel wasn't the only billionaire to bed big in 2022 either. 465 billionaires pumped $881 million into the 2022 midterm elections before October in support of both political parties, although a majority of those donations went to Republicans. When we get fourth quarter campaign finance disclosures next January, their donations will easily climb over $1 billion, with the 2022 election set to be the most expensive midterm in history. Even though many extremist big-money candidates, aside from Vance, lost their elections, they still received millions of votes collectively, with some races ending on razor-thin margins. The fact that many races between pro-democracy candidates and nasty neo-fascist candidates were so close is a major indictment of our entire electoral system, and the influence that big-money wields billionaires like Peter Thiel have created a deep cynicism about our democracy, which they continue to exploit for their economic benefit, propping up faux-populous politicians who seek to distract us from their ultimate agenda, tax cuts for the rich, and the continued transfer of wealth from working people into the pockets of the top 1%. Now be warned, as long as billionaires can manipulate elections like this, our democracy, our rights, and our livelihoods will be on the line. We must continue our fight to vanquish the corrupting influence of big-money on our system.


We're ready for the last session. And the first speaker is Eric Bonsera from MIT. Eric, take it away. Hi, can you hear me? Thanks so much for having me here, and it's been great. I can understand that it's the last session, so please bear with me. You're probably tired at this point, but it's the last one. OK, so thanks for coming. I'm going to talk about the staircase property and the leap complexity, which, despite the name, is about neural networks. And this is work with my really wonderful co-authors, Emmanuel and Theodore, especially for the last two works, which are what I'm going to be focusing on, and then the initial explorations were with Matt, with Guy, Gerdg, and Emmanuel. So we know that deep learning works. That's why we're studying it. And why does it work? Because we have some neural network architecture. We're training it with some optimizer, and we have some structure in the data. So this suggests the theoretical problem. Given some structure in the data, can we characterize when SGD trains our own network or what? And that's what I'm going to be talking about today. And what's the structure in the data? We're going to assume that the target function is multi-index. So I'll tell you what this means. We're going to first see that classical learning algorithms, so kernel algorithms, need a number of samples, which depends on the degree of this multi-index function. And then we're going to see that deep learning can solve. And we argue the complexity of deep learning is characterized by a quantity called the leap of the function, which is going to be much smaller than this degree. And so deep learning is going to beat out like these classical methods. And I'll define these terms, multi-index degree, and leap as we get along. So it's a very basic setting. We have data samples xi, yi, where xi is in rd, and yi is in r, these are the labels. And for the purpose of this talk, we're going to consider xi, which are uniform in the hyperbine or hypercube. You can also do this for Gaussian. You should see our paper, and I can say more about this if you have questions. But this is easier for notation. And but the assumption that the data is isotropic, so all of the coordinates are kind of drawn from the sum iid distribution is important here. And then the labels are going to be given by some target function f star, and we have some noise, which is 0 and E. So what's the main assumption we're making? But the target function is multi-index. So we have our target function f star is going to be equal to h star on some subset of the coordinates i1 through ip, where that subset of the coordinates is unknown. So h star is a function that depends only on p coordinates. It's also unknown, and those p coordinates are unknown. So there's like d choose p choices for these coordinates. We should think of p as being order 1. So the function f star depends on a small number of the coordinates of its input. But the input dimension grows. I'll give you some examples and you can ask some questions. So these are some whimsical examples I came up with. And the assumptions are not met in these examples, but bear with me. So it's just illustrative. So f star of x could be whether some patient with some symptoms, which you can view as a vector in plus 1 minus 1 to the d, each coordinate is whether that patient has that symptom or doesn't, has a disease. And so you're given data, which are the symptoms of the patient and whether the patient has the disease. And it turns out that disease depends on a very small number of symptoms, but you don't know which one's ahead of time. And so the machine learning algorithm kind of has to figure out which are the important symptoms and then fit a function. OK, or whether a person has some phenotype and depends maybe on a small number of genes that are expressed. So maybe these are not very clarifying examples, but please ask questions now about the setting because this will be, if you don't understand it, because this will be kind of the setting of the data. It's clear? OK. I was told wait 30 seconds, make it awkward, and then somebody will always, yeah. I was going to wait. OK, so the question is, are all these multi-index functions created equal? So in the question of representation by neural networks, can I find a neural network that kind of approximates a certain multi-index function? The answer is yes, because you can just take the network and make it depend only on those p coordinates that matter. But you pay 2 to the p, but this is much less than 2 to the d, which would be the curse of the machine. From the point of view of generalization, the answer is also yes. You can, if you take the minimum norm network that fits the data, so this is kind of like minimizing the norm of the parameters, but fitting the training data, then you'll avoid this curse of dimensionality. But this is not an efficient algorithm, because you can't, it's like an NP-hard problem to find the minimum norm network that fits the data. But in practice, what are the networks, how the networks optimize, they're optimized with SG. And so some, I think it's like L2 norm of the weight, so. OK. I think if you take like a, what? Yeah? Yeah, so I think if you have some neural networks, two layers that are bounded norming do some class of functions. I think it's called the baron norm. You should read the Bach paper. I think so, yeah. Yeah, it should be L2 norm. So if you were able to find the minimum L2 norm weight neural network, you would be able to fit the data with that, that fits the data. Then it would generalize. Because kind of what would happen is you would have zero weight on the coordinates that are not I1 through IP, that are the ones you don't know. But SGD training, so all multi-index functions are created equal, but some are more equal than others. Some are significantly easier to learn than others. As an experiment, you can run when we ran. So just to take a function on the binary hypercube with input dimension 30, you train with MSc, so squared loss. And if you try to train X1 versus try to learn the product of X1 through X10, which is going to be in plus 1, minus 1, because this is plus 1, minus 1, input space, you see that the loss really decreases very fast for learning X1, but it kind of gets stuck. And here I've trained it for 100 times more than the left-hand plot, 100 times more samples, and same hyperparameters. This is like some five-layer resinet, and it didn't succeed. OK, so you can say, well, maybe what's determining how hard this function is, is the degree of this function. But that's not quite true, because you can also train on this function we call the staircase function. So what this staircase function looks like, I'll just write it here. I'll just expand the sum. It's a high degree function, because it's got in this case 10 terms of increasing degree with one degree 10 term, but it's still efficiently learned by neural networks with the same hyperparameters as in the parity case. So somehow adding these extra terms has let you learn the high degree terms. Adding these lower degree terms somehow mysteriously, yeah, improve it for a squirrel. I think they don't have anything for a non-squirrel. We only ran on the squared line. So actually, I haven't really thought about how to define it for the non-squirrel. Good open question. Yeah, so somehow these lower degree components are helping you learn this high degree component, which by itself is not being learned. So there's some hierarchical structure in this function. You can think about it that magically gives you this behavior, where the test loss decreases. So this is for uniform on the binary hypercube input. OK, so what are we going to do? We're going to try to. Are you going to do online? This was the, I have the details written somewhere, but you get the same behavior with batch or with many batch with online with ERM with a fixed number of samples. The specific experiment, I could tell you the details, but I can't tell you the details. OK, yeah? So actually, here I'm plotting 1 over the square root of 10 times this. I normalize it. So the L2 norm of these is the same, and this gets to much smaller than 1 over square root of 10. 1 over 10 L2 norm. So 1 over square root of 10 L2 norm. So because you get to 0 error by Parseval's theorem, you know that you've actually learned the high degree term, because you can write any function on the binary hypercube, but uniquely as a polynomial. So you kind of are learning all the coefficients. And I have another plot, which I forgot to put in this, where you can see actually that the Fourier coefficients associated with each of these terms are learned in order, where x1 is learned first, and then x1, x2, and so on. So this is kind of a toy setting, but it inspired these investigations. And basically, what I'm going to tell you is that why can we learn this high degree function? Because you have a question? Yeah. So if you do one pass, the train loss is equal to the test in this case, because the input space is so large. If you do ERM, then the train loss goes to 0 also. But I was plotting the test loss. So this is generalization on outside of your sample. So the number of samples you need depends on the degree of the functions as d to the degree, where d is the input dimension, for classical machine learning, and then kernel machine learning, and then deep learning, we argue we pay d to the leap. We prove this in some cases, and there are some cases that are still contractually open, but we have evidence. OK, so let's do the d to the degree first. So a popular tool to analyze training dynamics of neural networks is so-called NTK. And under this NTK parametrization, which is a specific parametrization of your neural network initialization learning rate, as you take the width to infinity, you're basically training with SGD, or it's as powerful as using a kernel method. So anything you can do with, so there's a specific kernel that's associated with a certain neural network initialization and architecture. And as the width goes to infinity, SGD may make or will be the same as training with a kernel method. So this is good because we understand kernel methods well. Actually, I'm not going to define what they are because this is not the subject of this talk, but there's something where you can really get a good grasp on how you're going to generalize. But it's bad because it doesn't capture our experiments. So it turns out, as I mentioned before, you can write any function on the binary hypercube uniquely as some polynomial where these coefficients, called the Fourier coefficients, are unique. There's 2 to the p of these coefficients, h hat of s, each associated with one subset of the inputs. And so you can define the degree of the, you can define the degree of h star as the maximum non-zero Fourier coefficient, like the maximum size of the set where the Fourier coefficient is non-zero. And it turns out that the degree of h star controls the sample complexity when you take the NTK of a two-layer polyconnected network and the NTK parameterization. And this is previously known. In fact, we prove it's not very complicated, but one can prove that any kernel method needs any kernel method, not just the one for this neural network, but any neural network you choose. The corresponding NTK will always need these are the degree samples to learn. In this setting where you're trying to learn f star of x, and it's equal to h star of xi to the xi p, and you don't know why I want the right p. So I could get into more detail about that, but I think I should move on to the meat of this talk. Any questions? I can give you an intuition. Basically what happens is that if you can learn the class of any kernel method can only output functions that lie within an n dimensional subspace, where n is the number of training samples. And somehow the class of f star that you could make with any choice of i1 through ip, that's d to the degree different possible functions. And they lie in the d. They don't lie in smaller than a d to the degree subspace. So they wouldn't lie in the sub-space of classes. Functions you can learn with the kernel. So this is the first attempt is NTK. So you pay d to the degree. Now the meat is why can we do better with deep learning? And it's like kind of independent of what I've said before. So now if you zone that, you can still come back in. OK. So recall this experiment, parity versus staircase. So we're going to argue that we're going to find this notion of leap. I'm going to say a parity has a large leap and the staircase has a small leap. OK. So now let's write down what the networked architecture we're going to do it. Take this. I'm going to take a two-layer network architecture. So this is the first layers, the second layer is A. And this is in R to the M, where M is the width of the architecture. And then the, I should not have drawn this. OK, so all right. OK, so the first layer is W. And here you apply some non-linearity sigma. So this is your input X. You feed it through the network architecture. You apply non-linearity sigma, then you add up the neurons weighted by A. OK, so why did the N2K analysis fail? Well, because you have isotropic initialization. So the coordinates, so here I fixed X, I want through IP to be 1 through P, since your initialization is a permutation invariant. This is just as hard as learning an unknown I1 through IP. So the coordinates 1 through P are not especially favored. Each row, for each neuron, there's an equal weight on each of the inputs. And so this kind of turns out that if we just trained the second layer, we would need D to the degree sample. But so OK, let's do a thought experiment. What if instead we initialized each row of your first-layer matrix with the first coordinates, first P coordinates of order 1, so much larger, and then we initialized the last coordinates of order 1 over D, smaller. Now this favors learning functions of the first P coordinates and actually turns out that if you have such an initialization, then you can learn any function of the X1 through XP just by training the second layer. Of course, we don't have this magical initialization. We don't know what the right coordinates are. So then the hypothesis is SGD works by making the neurons, so the weights large, on these first P coordinates. So this would be the cat. So this is a heuristic intuition, so a good question. So imagine we were to freeze W and we were just training A. This is kind of the dynamics here are well understood. It's just a random features model. And so we can understand the generalization, how many samples you need to generalize easily. It turns out that if you had much sufficiently diverse, but much larger weight on the first P coordinates, then you would be able to learn with 2 to the P samples, which is much smaller than D to the degree. Because remember, P is constant and the D is growing. So the hypothesis is that this magical initialization is actually being provided by SGD. And this is actually, I'm going to show you an experiment now. So this is some other function which I've plotted because it'll give you a nice plot. You don't have to look too much at the form of this function. It just depends on the first eight coordinates. Let me show you a video I can't do it on Beamer, so I'm going to switch to Keynote. This is like a very hybrid talk with Beamer and the Keynote and the Blackboard. So what I'm plotting on this left-hand side, the test loss during training for this function. And on the right-hand side, I've plotted W transpose W, where W the first layer of weight. And the input dimension is 30. It's just for visualization. You see this effect even more if you take the larger D. And so you have the 30 by 30 matrix here. And after training, the W transpose W is basically 0 everywhere except for this 8 by 8 block, which corresponds to the first eight coordinates. So after training, you have your like, this is just out of the box, SGD on this neural network. After training, you see this 8 by 8 matrix does have the kind of the property. So for our theory, we take infinite. Here, I think I took 40 neurons. I didn't take too many. Actually, I think this is a resonant. I'm even just plotting the first layer in all of the resonance. Yeah. Yeah. Here? Sorry, you're looking at this screen. Sorry. OK, this is training like step, like number of samples. So it go from 0 to 500,000. And this is the test loss. And then this here is the W transpose W, the absolute value of the weights. So I'm going to show you a video. It's very cool. You get a different plot. The theory will make it. I have an odd degree term here, so I have x1. So this is kind of what you see here is the initial decrease in the loss is due to picking up x1. The initial decrease in the loss is because it learns x1. And then afterwards, it plateaus for a bit while it tries to find 2, 3, 4. Once it figures out 2, 3, 4 are important, weights align, and it learns. And then plateaus while it tries to learn 5, 6, 7, 8. And when it figures out those are important, it decreases again. So the length of the plateau will depend on the leap. So this is kind of maybe you're already starting to see the definition. So the difference between the variables in each of the monomials is you pick them up sequentially. OK, so I'm going to show you a video. So here on the, I'll play it a few times, but you see as the training progresses, the loss kind of decreases. And I'm plotting the evolution of the W transpose W at the same time. So you can see when the loss is plateaued here, it totally depends on the first four coordinates. It falls, and now it depends on the first eight coordinates. So you kind of see inside the weights of the matrix that it's putting more attention in some sense onto the variables that matter for the term it's trying to learn. OK, tell me when you get bored of seeing it. So now I have the first four, and now it falls at first eight. So you can see, and you can do this with other functions. And the first, now the first four, and it's when this is plateauing, and now the first eight falls. OK, now operation successful. I'm back here. OK, so all right, so the observation is that you learn there's phases in this learning. And in each phase, you have D to the order 1 steps, which is large. And you're picking up some coordinates in the support. And then you have the smaller number, like it's 2 to the order p, where basically if you were just training the second layer, you would be able to fit the function to the coordinates to which the first layer weights have already picked up. So the key question is, why do the first layer weights grow in the direction of the support? And what governs the complexity of finding the coordinates in the support? This is the leap complexity, which is this. So it'll take D to the order of leap steps to find the length of the plateau where you're trying to find the new chord. Any questions? And I'll go into a calculation. No, that's why I put in quotes. I haven't defined it yet. First to give intuition. Yeah? I have a question. Yes? Yeah, yeah. OK, so here in my initial, this is a thought experiment. Are you talking about this? So this is a thought experiment. I actually initialize each of the rows. So this is like, if I had this, then I would be done, basically, because I could just train the second layer weights. Then the thing is that actually, this is found automatically by SGD. So this magical initialization is kind of how the dynamics proceed to find them. Isotropic. So if you look at the video, let me pause, see? Here, it didn't pause fast enough, but here you have x1 has been picked up already. But yeah, the rest is isotropic. And it picks up. Yeah, so then it grows to the first four. Yeah, OK, all right. Let's move on. OK. Good, so yeah, so you have this leap. I'm going to find it. OK, so we want to understand how training these networks works. You train the first layer with one pass SGD with some mini batch size, just for simplicity for these slides. You can do also with bit mini batch size equals 1, but you get a different limit. And so in the, this is hard to understand. You have stochasticity because of the small width or the finite width and finite sample size. But you can approximate the dynamics. If you take large width, mini batch size, and small step size, you can approximate the dynamics by this kind of thing, this expression where I've taken the population expectation. And I've taken, what else have I done? And also all the neurons are kind of interacting in a mean field way. So this is kind of what you get in the mean field, in the mean field limit. I've simplified a bit, even, but OK. So you have some expression which tells you how the first layer weights are evolving on each step. So let's give an intuitive picture. Yeah? Yeah, large. But in practice, you don't need it that large. Infinite width, but actually it's like, OK. Order one width with large enough constant width. Doesn't depend on the input length. It does not depend on the input length. Like 100 width for any, it depends on the final accuracy you want to achieve in theoretical results. So yeah, but it does not depend on the, sure, p is constant. So yes, it depends on p actually. Pretty bad thing. So yes. So OK, so you're actually reading it. So here. So OK, for constant time of training, you can maintain this approximation as long as it's a small constant time. When you have a larger amount of time, then you also need to add in the current. This becomes the residual. But for what actually in the result on beam field training, we first train the first layer while keeping the second fixed, and then we train the second layer while keeping the first fixed. And so we train for a small amount of time, the first layer. So then this is still valid. And then the second layer, we just use the kernel analogy. Let me give you some intuition. So OK, so I just made that picture. And now I'm looking at one individual neuron. So let's say this neuron, OK? And the weights of this neuron are going to evolve according to this formula. So what are the weights at initialization? These are Gaussian. And then after one step, OK, here I've plotted the projection to the first two coordinates, kind of the distribution of the overall neurons of the weights protected first two coordinates. After one step, you see kind of like the coordinates in the direction one grow a lot. OK, why is this? I'll give you the calculation. You want to see the calculation? I think you do. So OK, so what? No, it makes it more awkward if I don't. And I've told this is how you give a talk. I don't know. OK, so also, yeah, this is not a one. This is my cursor. OK, so what is this? What is how I'm perpetuating the weights? Taking the step size times this expectation over x of x1, this is my target function, times sigma prime of x transpose w times x. This here is a vector. I mean, these are vector, OK? This is kind of the direction of perturbation. So now let me do a Taylor expansion of the sigma prime. And this is roughly the eta times the expectation of x1 times, OK, let's just put some constants which are the derivatives. I don't know. So OK, so OK, so the point is this is close. This is small to begin with. And so we can do a Taylor expansion. This is small. This is going to be on the, yeah, so OK. This is roughly sigma prime of 0 plus sigma prime prime of 0 times x transpose w plus sigma prime prime prime of 0 times x transpose w squared divided by 2, all times x, OK? So what does this expression look like? So this is actually going to be, it's going to depend on the coordinate. So if I look at the first coordinate, which is the first coordinate of x here, this expression will be roughly the expectation over x of x1 times x1 times sigma prime of 0, which is equal to order of 1, OK? And if I look at the other coordinates, which are not equal to the one coordinate, this would be the expectation of x of x1 times xi sigma prime of 0 times plus sigma prime prime of 0 times x transpose w plus lower order terms. And this is going to be much, much smaller than 1 because this first term will cancel because the expectation of x1 times xi is 0.  And then the other terms are the ones that are going to contribute, but they're small. So this is much smaller than 1. OK, so basically, the coordinates in the direction of x1 are going to move, so I should be wrapping up soon. So what happens if you do x1 times x2 instead? It's the same thing. I could do the same calculation. But actually, because you're x1 times x2, you're high degree parity, you're going to be stuck in a saddle point. So after one step, you still have coordinates 1 over square root of d for all the first-layer weights. And after any constant number of steps, you're still going to be stuck at the saddle point. So actually, it's much harder to learn. You need more than a constant number of steps. You'd log d steps. But then what happens with the magic of this function x1 plus x2, x1 x2, which is the staircase? Well, the first step, you're same after one step, only the x1 term matters. So you kind of grow in the direction of x1. After another step, the x2 term can grow, because the x1 term actually has grown. So you can escape the saddle. It allows you to escape the saddle when you have the w1, which is large. So after only two steps, now you've basically have the magnitude of the coordinates that you want on all the weight. OK. So I think I have four more minutes, and then it'll be questions. So do you have questions now? I'm going to tell you what the leap is. But do you have questions about these calculations? Yes. The first, what? The first term. Yes. This term. OK. So OK. So x is in plus 1 minus 1 to the d. And this is so the norm of x is equal to square root of d. And w is drown Gaussian i d over d. So the norm of w is equal to order 1. So then the dot product of this, x transpose w, is going to be order 1. So actually, we take this initialization that's like some constant times this, so it's small. So then this is some small constant so we can do the Taylor expansion. Yeah, we multiply for the theoretical analysis. Yeah, in practice, it's all standard. So yeah, so you're right, you've got me. So there's some sigma, there's some c here. OK, it's small. OK. All right, good. So back to this experiment, the first layer of weights have grown successfully for x1 and for this staircase, but they stuck at the saddle for x1 times x2. So let's go back to what happens in parity in the staircase. Well, somehow, the weights are stuck at the saddle, which is actually of higher order here. And then they escape the saddle by climbing the staircase, so to speak, in the staircase starting. We have the first two to learn x1 and learn x1, x2, and so on. OK. So now you can define the leap complexity. So again, we're writing the function h star, we write it as a polynomial. And let's consider it set of non-zero Fourier coefficients. The leap of h star is less than or equal to l. If there's some ordering of these non-zero Fourier coefficients such that you can kind of grow the size of the support that you haven't previously seen by most l on each iteration. OK, it's kind of like you can think of it as first you're going to learn the Fourier coefficient corresponding kS1, and all those coordinates will grow. And then s1 and s2, and you only really pay for the coordinates you haven't learned so far. OK. So there's some examples. The parity has leap k, because it's one Fourier coefficient of order of k. And the staircase has leap 1. And this conjecture is that for any set S of non-zero Fourier coefficients to almost all h star that have those non-zero Fourier coefficients, you're going to need d to the maximum of leap of h star minus 1 comma 1 samples. So this is a conjecture, and I said almost all, because there are some degenerate cases we can prove. But there's a measure theoretic sense in which you can define almost all. OK, and also why this here? Because this is based off of the complexity of escaping the saddle point corresponding to learning that monomial. So this is a paper of Reza and Benardus and others. So Reza is in the audience. Yeah, because it's one pass SGD. So we're really doing one sample per step. So yeah, for ERM, I think it's different. Also, there's some paper recently that says that if you smooth the loss, then you can actually get a slightly different bound. It's like leap over 2, or it would be leap over 2. So I can talk to you about that. Yeah. Yeah. OK, so any questions? I'll tell you what we've proven, and then it's over. Yeah. OK, yeah. You have to be careful, yeah. So you can take a small step in the first step. The first step can be small. So it's a small constant still. Yeah, it's still constant. It doesn't go to 0 as d goes infinity. So I mean, we don't know of any other way of analyzing first-layer training dynamics, because it's nonlinear. So basically, we train it for very small time, so the Taylor expansion is still valid. And it requires some type analysis, or some technical type analysis. But then when you train the second layer, you can train it for a lot of time, which is still constant. But it's a big constant, yeah. It doesn't grow in d. So this is, yeah. The only depends on h star, on p, really, on the number of coordinates. Yes? Yes? Yes. Yes, because of one pass. Yes. So there's, I can, OK, so I have, literally right here, I have an extra slide, which I copied from keynote. There is an, so we have also like some, so how do we prove this stuff? I haven't told you how we prove. We analyze some PDEs, and we can prove that they're kind of stuck in certain cases, like degenerate cases. And you can construct a degenerate case, but if you perturb it slightly, then you escape. And so we have, yeah. We don't, so in the extension to Gaussian, which I didn't talk about, we don't believe that there are degenerate cases. But, you know, we don't actually know. So let me tell you what we have, what progress we made on this conjecture. I copied here, I put in gray, so you don't get distracted too much. So the case of leap equals to one, I believe, is mostly resolved. We have this paper, which shows that if you take a mean field network, with sufficiently large, like infinitely large width, but really order one width doesn't depend on d is enough, and you train it for order d, order one time, which corresponds to basically order d samples, if you want to play fast and loose. Meaning that you can order one time, you can simulate with order d samples. But it's not necessarily true that you can't do more with order samples. We don't know that. But OK, if you look at the mean field networks trained in order one time, they can learn, if and only if, leap of h star is equal to one. And this is star here because of these degenerate cases. OK? And this is required using the mean field approximation, then saying because the target function depends on a small number of coordinates, you can get like a PDE, which is equivalent, but which is simpler to analyze. And then you analyze it. So we analyze it for any p. So it's like, let me do the Taylor expansion trick. OK, so what happens with the leap more than one? This is mostly open. We do have CS, we can prove that this d to the least order leap should be hard for CSQ algorithms. And then we also have some special cases in which SGD can learn a family of leap staircase functions. So basically these would be staircase functions where I remove kind of a race coefficient or remove terms. And also, in the Gaussian case, you have Hermit polynomials of higher degree. So yeah, so this is our, yeah, this is it. Any questions? And then I'll put the summary slide. Yes? Yeah, so it's this staircase functions that look like this except I've erased some of the terms. Or in the Gaussian case, I have like Hermit k instead of, yeah. OK, yes. So in the paper we only do, in the ABM 23 paper, we only do Gaussian. But the same will hold for uniform on the hypercube. So I've kind of lied. One of the papers is for hypercube. The other one is for hypercube and Gaussian, but we only really show for Gaussian. Yeah, so it turns out the leap, so OK, this is my summary slide. So you define an isotropic leap. So you define it. It's a slight variation of the leap, which is so you have a slightly different definition of multi-index function, where it's not some p coordinates that matter, it's some p directions of the input that matter. So basically, f star of x is equal to h star of mx, where m is in r to the d times p, p times d, OK? And that's kind of the appropriate definition for Gaussian, because it now has a symmetry. And you have to define a corresponding isotropically, which can depend on the expansion of h star in the Hermite basis. Now you pay more, actually, for high degree Hermite, even though if they only depend on one direction. And then you also, so that adds a complication. Because even with one coordinate, now you have many different possible leaps. Partly why the first paper was only for Gaussian. And it was more like rigorous. And then this one, it's rigorous, but it's only special set. OK, yeah, that's it. Good. Good. Good. Good. Good. Good. I'll just assume that here I respond to sort of the 10 dimensional update that they like to do the interpolation of the first one case. It was in that case. In this case, but there's also, I mean, this is for general, you're talking about 2 to the p versus poly of p dependence on the samples? Or what? Yeah. I don't know if you need extra structure with GD, because otherwise you're solving an NP-hard problem. Like learning the support. If you have a staircase, I'm not sure. I don't know. So we didn't talk about it. I'm not sure whether it's strictly better or worse than those bounds. This is also one pass. The GD is a slightly different setting computationally. Whether you do ERM, OK. So for the leap one result, for example, so you can do it for batch GD with a constant number of steps where the batches are ordered D. And it's independently drawn each time. So the mini batch SGD, where order D mini batch size each time for a constant number of steps. I don't know if you can do it for the full, but maybe. So the main difficulty is, OK, yeah, sure. You show that the weights adapt to the directions of the support. But then you have to show they're still diverse. So this requires you have to show that some kernel is non-singular, and this is a kernel that's generated by the train dynamics. So you actually use some algebraic facts to do this. And I don't know how this all interfaces. Yeah, I'm not sure. Yes. If I understand correctly, the greedy low-rank learning dynamics are generally when you have very small initialization. So this is not the setting we're assuming here. So it's a different reason for the low-rank to occur. It's also not a degeneracy problem. It's because we can't prove that the mean field PDE is valid for those timescales, for longer timescales than order one. So the limiting dynamics, you would actually exponential in time samples for those to be valid. So and here we're trading for poly number steps, so poly time. So you would need e to the poly dynamics, poly samples. So actually, this analysis is not this, more than one, is not for using the mean field PDE. But it's using a martingale argument, kind of like the one in the Ben-Aruz paper, and Reza is here too, I think. And then we have the modification where we show that you do go from tattle to tattle. Oh, I also forgot to mention, the achievability result here is we train the first layer and then the second layer, and then here we even cheat more. So we train the first layer and the second layer, and we also have a projection down to a ball kind of thing on each step, just to control it. So there's a lot to be done. Yeah, OK. Does that answer your question? I think I'm probably out of time, but people keep on saying, yeah, asking. The learn the parity? Yeah. Yes, so because the mechanism is such that the weights grow in the direction of the relevant coordinates, you can fit any function that depends on those weights, by training the second layer. So kind of after training the first layer, now you can train the second layer in your, so basically kind of like learn the subspace, yeah. OK.