Intensive Teaching · September 2026

The most important things

Before: Join the Iliad Discord and check you can see #intensive-september. That is where you post any material you need to share with participants. If you can't see it, tell Leonard (@leonardbereska on Discord).
During: At 17:40, make sure everyone fills out the feedback form.
After: Fill out the end-of-day log: rate the day and tell us anything that went wrong.
Fill out Who stood out: name anyone who made a positive impression.

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57 project proposals are open for review. Stars, a sentence, or both. Read them.

Your days

[B.3]Singular Learning Theory · Thu 17 Sep Thu 17 Sep, leading 37 responses · energy 4.0/5

Overall -0.06 as expected n = 36

Content +0.17 as expected n = 36

Clarity +0.39 better than expected n = 36

Motivation 0.00 as expected n = 36

Exercises +0.28 better than expected n = 36

Readings -0.38 below expected n = 8

Other activities -0.18 as expected n = 11

Pace -0.83 too slow n = 36

Difficulty -0.78 too easy n = 36

Novelty +1.08 mostly new n = 36

Read what they wrote58

Worked well19

Excellent pedagogy and big picture motivation.
I liked that it was on a whiteboard, it made it much easier to follow. The teachers could explain things really understandably. I liked that they worked through some toy examples on the board. I also really respected their epistemic humility and it helped create a great atmosphere for asking questions, admitting confusion etc.
I think the short lecture followed by exercises system was quite good, but everything was a bit too slow - could have done several of these blocks probably rather than just three.
I liked the pace and especially the whiteboard lecturing. I follow better when new concepts are thought using a whiteboard vs slides.
The exercises well well chosen.
I really liked the bite-sized sections of lecture+exercises!
the long discussion at the start of today about how the theory today fits within ai safety, what the hopes are how it could help etc before even going into the theory details. every lecturer should do this!!
The whiteboard -- I did like the format a lot, reminded me of Uni lectures and the "How to Speak" lecture by Patrick Winston https://ocw.mit.edu/courses/res-tll-005-how-to-speak-january-iap-2018/ where he claims that comprehension speed is about the pace of writing on the board. Previous lectures weren't as easy to follow because of slides, while here you can write along and digest more slowly. I also liked that the motivation for devoting so much time to singularities specifically was given. The lecturers today had a vision that most of the time should be spent on singularities and implemented it. The exercises were also quite fun, I enjoyed them a lot. As well as the format, aka lecture-exercise-lecture-exercise.
The willingness of the lecturers to help during the exercises to make sure nobody would fall behind
i kind of liked the blackboard lecture style a lot (compared to a presentation with slides)
Recap of exercise 3.4 on the board was very useful to get insight.
my favorite day so far, the flow between teaching, exercises is quite good with the teaching sessions not too long and well designed exercises to gain some insights to the material hands on.
Discussion of the solution on whiteboard
I think the lecturers were good and engaged well.
Geometric intuition for local learning coefficient.
Short lecture, dive into exercises
Discussing with the lecturers in the off time clarified most of my questions , they were very helpful!
Kai is fantastic. He's an excellent communicator and clearly has some mastery of the topic. Matthew as well was very easy to ask questions.
Whiteboard is the best. Makes the pace perfect.

Would improve27

I think the class was pitched at the wrong level. Too much time was spent on trivial things like curve sketching and computing derivatives. On the whole, I feel that very few concepts were covered today. This was very pedagogical and I was able to follow everything. However, the level of this class was more appropriate to an undergraduate class rather than a class of PhDs and postdocs.
The intro & motivation was a bit too long. I think the pace could have been a bit faster, and this would have allowed us to cover more material.
I think the first two lectures were slow in terms of delivery of new concepts, and I think it would have made sense to have slides so that walking through the examples more seamless than it ended up being. The content was interesting overall and some of the exercises were good.
Some of the explanations at the whiteboard were not very clear and some others were a bit too elemental. At some points I think that the questions of the participants were not really relevant to the explanation, so I think the speaker should not be afraid to delay the answer and continue with what he wants to explain.
The initial discussion was great. However, the lecturer wasn't comfortable with a lot of the maths involved- which is in principle okay (maybe less okay in something like SLT though). The problem was that people kept asking irrelevant technical questions about some of the constructions. A lecturer with more mathematical maturity maybe would have cut off these discussions (they were mostly useless and pedantic) and would've continued with the intuitive explanations he was giving. Despite this, the materials were really good!
I think the day wasn't dense enough in material -- most of the time we just practiced differentiation and multiplying jacobians by fixed vectors. It's fun, but not for too long. Increasing the density of material and covering certain corner cases, where things break overall, could be valuable no matter what the second day covers. Adding examples of models from standard statistical courses and discussing where we could break them for SLT and what does it allow us to analyze could be interesting. E.g. showing some key non-identifiability results + LLC for these models as a comparison. If for them, unlike neural networks we discuss later in the course, things start to break, that justifies an additional discussion.
I think the pace was rather slow and would have liked to see more of SLT or more technicalities. We looked at examples of losses that were fine theoretically, but would have liked to see some of this formalism applied to real networks, even though just with approximation.
I was happy with how today went.
Lectures only covered a general overview, and hinged on too simple cases. The exercises were useful, but it would be useful to see some deeper and technical results during lectures as well.
The discussion at the start of the day was nice, I think having more time to discuss these broader questions would be nice, not necessarily on this day. There seemed to have been a misunderstanding in what the point of the lectures was, as I believe they were meant to provide a schematic overview with exercises going into the more specific details. Many participants seem to have expected more formal details during the lecture, and clarifying this disctinction at the start would probably have made everyone accept some level of glossing over details more than they did. This time could for example be spent on going into more detail on the particularly complicated stuff, like the volume scaling law. I think the content of the first block about singularities could've been condensed more, as most people are familiar with the underlying maths.
Add the usage of https://www.geogebra.org/calculator or similar (say contour plots) when we want to discuss surfaces and landscapes for the ease of visualization of valleys etc. The day started with the oral motivation for SLT (no math), and I found it not too easy to follow given that there were no slides. I think that part would benefit from slides. Also, I hope it's gonna be addressed on Day 2, but if not, I'd say that an "empowering example" or a success of SLT to be shown would be a nice point to start. Actually, applies for every topic we cover at the intensive. The lecture would've benefitted from more preparation of the whiteboard lecturing itself, as Matthew was sometimes unsure of what he was going to show, or at least that was an impression. Also, I am against any lecturing right before lunch -- too intense for hungry brains. The whiteboard would've benefitted from elevation, as writing on the lower part was not visible to the participants in the back. Also hope it would be addressed tomorrow, but showing how specifically statistical learning theory fails that we need SLT would be very helpful and motivating.
Having short slides on top of the drawings on the board during the oral presentations to help the audience following
- I felt like the talks often lacked structure, which contributed for the unnecessarily slow pace; also, more content would be nice - some exercises were too much undergraduate Calculus-like and the "insight density that they offered" was small - also, I appreciate the presentation + exercise structure of the notes but feel like given the small extent of the presentation part, it would help to clearly separate which results I should retain from something I learn from an exercise which has a particular context; (also maybe some plots would be a nice addition)
Generally was good. However, SLT seems to be a combination of (1) conceptual insights into loss landscapes and learning dynamics and (2) rather technical mathematical results and conditions that are useful for understanding, deriving, and evaluating the conceptual insights, but aren't necessarily otherwise important. It might've been nice for the teaching to distinguish more clearly between these. Which parts are technical waypoints and which are the big ideas?
I had quite low expectations, but overall the material was quite clear. It is, unfortunately, mostly undergrad calculus and algebra, hopefully the next day will give better perspective on things.
Most exercises were warm ups, very quick to finish and far from realistic settings. The lectures were not as substansive as I would have hoped. A lot of discussion that was tangent to the goal of the day. The lectures felt a bit unprepared. Definitely use varied pedagogical supports (slides + white board) to improve teaching. Too much hand waving without visual support to structure and ground the arguments
honestly today
Visual aids, slide wth the visualisations of the graph
I think some of the material could be better motivated, and also some pre-reqs could be assumed
Pacing on resolution of singularities.
The beginning felt too easy and the first exercises also easy. I would have liked more motivation and more difficulty.
I would make the material a bit higher level. Possibly also the connection to statistical physics could be highlighted more. Motivation/introduction went a bit overtime.
First half of the day with Mathew was fine but it didn't seem as prepared.
We should have more coding exercises.
Today was a really nice day. I loved that it was at the whiteboard, was great for setting the pace.
I think some of the mathematical formalism could have been made a bit more rigorous for clarity, although I think the overall ideas were intuitively conveyed. The pace was also a bit too slow and wecovered relatively little content vs. most of the time on exercises.
I found the pace too slow and too easily disrailed by questions that were not really important. Overall it was set at a level not appropriate for the course. The material was in principle new, but it over emphasied low level concepts and progressed very slowly for someone with 'mathematical maturity'. Some of the digressions were brought about by participants

Changed my mind9

SLT looks like the String Theory -- lots of math, some captivating some complicated, but with no practical utility. I have asked Matthew whether SLT made one apriori prediction and if it was successful and he told me he knows none. He did say though that SLT helped him see the things differently and in a richer manner -- more emphasis on that should've been made.
SLT is interesting, i need to learn more calculus
Nothing, we did not get very far into SLT.
SLT is very cool and i want to know more about it
n/a
Degeneracies are features, not bugs, in learning.
Perhaps SLT may be useful
I discussed with other participants about EA Global New York. I learned how algebraic geometry can be useful for AI safety.
nop

Other thoughts3

The schedule format in the google doc works well.
n/a
Excited for day 2.

[B.3]Singular Learning Theory · Fri 18 Sep Fri 18 Sep, leading 37 responses · energy 3.4/5

Overall 0.00 as expected n = 30

Content +0.07 as expected n = 30

Clarity +0.07 as expected n = 30

Motivation -0.03 as expected n = 30

Exercises +0.13 as expected n = 30

Readings +0.11 as expected n = 9

Other activities -0.31 below expected n = 16

Pace -0.37 too slow n = 30

Difficulty -0.13 about right n = 30

Novelty +1.03 mostly new n = 30

Read what they wrote40

Worked well9

The online presentation we got was quite good. It put a lot of the material into perspective.
I really like having two days on the same topic. Really helped with retention.
- Having two days on it, gave time for things to settle - Grounded in actual papers (Watanabe, the LLC estimation papers)
I think the discussion at the end was interesting - a lot of people asked good questions. I also had the doubt about how eliminating data is much easier to treat in Bayesian learning than SGD learning.
Kai is a fantastic teacher, Mathew was also good but felt a slight bit unprepared at times.
Lectures were clear.
Connecting LLC drops to phase transitions in models.
The online lecture -- it finally provided the megapromise for SLT showing that SLT predicts stuff that the actual learning ends up doing. This belongs to the morning of Day 1, like this should be the starting point. The lecture content was great as well, but for the improvement suggestions see above (such as should've been twice shorter). The exercises do not disappoint, they were nice, I liked them. The structure -- I think I should stop praising lecture-exercises-lecture-exercises because I have been doing that, so I'd just say keep it up. The essential points of maintaining "no lecturing before lunch" and "lecture under an hour, better 30 mins perhaps", as it was today (30 mins was great) were observed too. And I liked that exercises were given with suggested extensions, such that you could either do just the 3 core ones, or all 7. Keep that structure up.
exercises on phase transitions were nice because they were simple.

Would improve21

I would have loved to hear more about open problems and research directions. This is something that occurred to me and also applies to the other topics and lectures.
I would add coding demos for exercises.
- Some of the notation was really unfamiliar and not introduced much, a notation sheet or sticking closer to day 1 / Watanabe's notation would help a lot - Making the LLC estimation exercise part of the main day, to see the theory in practice
Too many graphs on the slide, better to have less and explore in detail. Write a bit bigger on whiteboard.
The remote contribution to the lecture did not work as well as the in person part. The material was more advanced than last time, which was very much appreciated.
I think there is probably too much focus on the mathematics in the lectures, which has generally been quite easy and posed no issue in exercises. I've found it significantly more difficult to get enough conceptual understanding, and I think the lectures should prioritise this much more. I think this debt made following the last lecture - which seemed very interesting! - quite punishing. I think many of the exercises were not particularly insightful as they felt like simple algebraic manipulations or computations in multivariable calculus. Exceptions included the exercises on why d/2 and not d and Ex. 4.2.
More context about how this relates to AI safety.
The pacing was a bit slow. Too much time was spent on basic mathematics and a few important results were just briefly sketched.
In fact, the second day of SLT was much better and more engaging in comparison to the first one. Potentially, some additional exercises on computations of degeneracies -- at least in common statistical models and explicitly seeing their implications could be really fun.
An almost 2h remote presentation, followed by discussion, with no scheduled breaks, at the end of the day was quite heavy. Great content otherwise!
It was good to get the applications of yesterday's basics. I believe some of this could be joined into the previous day to strectch the buildup of theory shorter.
I think the material should be given in a different order so that the main theory is presented (rather than elucidated in the exercised and focusing on basic definitions in the lecture). At points certain knowledge could have safely been assumed (e.g. basics of Bayesian statistics)
More practical code examples for estimating lambda.
feels like not enough new material for an entire day and the lecture times today were a bit too long to be effective
Regarding yesterday I said: "- I felt like the talks often lacked structure, which contributed for the unnecessarily slow pace; also, more content would be nice - some (not all) of the exercises were too much undergraduate Calculus-like and the "insight density that they offered" was small - also, I appreciate the presentation + exercise structure of the notes but feel like given the small extent of the presentation part, it would help to clearly separate which results I should retain from something I learn from an exercise which has a particular context; (also maybe some plots would be a nice addition)" These things still apply to today. I'll just add that the talk by Miguel was too long and the slides had too much information which made it difficult to follow. (I would have liked to hear about the papers he mentioned in a more comprehensive manner). Also, it would be nice if some of the things he presented were the integrated as a continuation of the main talk/notes material.
Adding a group activity would be cool I think
Exercises were useful, but the ratio of symbol manipulation to conceptual insight wasn't great. I think it might be possible to construct more examples that make things more visual/build more intuition. The phase transition problem was pretty good, for example. I also spent some time playing around with posteriors and V(epsilon) functions in Desmos and found it quite useful.
I don't feel that I obtained much insight from solving the exercises. I found the talk at the end a bit too dense. I found it very convenient to have written detailed notes. I think one of yesterday's exercises 2.16 was a bit confusing. It is given an example of a reparametrisation that introduces degeneracy on loss landscape. If I understand correctly, this can be made more precise in a general setting. Namely, at a critical point, reparametrization by a diffeomorphism must preserve the Hessian as a bilinear form. In the example the parametrization is not a diffeo at the origin, so it is expected that the signature of the Hessian is not preserved.
More preparation before the lecture suggested for lecturers: say running it between themselves before running it in front of the participants. This suggestion comes from the fact that sometimes Matthew was lost in what he was saying, but I can't recall his specific phrase. Smth along the lines of "Okay this actually does not belong here." I think if this is done he'll be great! For the online lecture, the soundcheck and other stuff better be run before to avoid fixing problems during the allocated timeslot. Also the lecture itself was quite long (2 hours) which inevitably leads to losing focus without a break. If we don't wanna be doing a break, perhaps a Veritasium approach (two plot lines, the movie aka lecture switching between the two to keep engagement, the trick Derek borrowed from cinematography school) would help. In fact, lots of cool stuff was in the end, where the concentration was already lost, so perhaps the talk could've been twice as short without the need to go into details early on. I'd say Julian was quite a master in this: he had like 160 slides in his MechInterp day, but it actually felt extremely engaging and not tiring at all, as each paper had one single figure from it on the slide and was covered quite briefly, with a single idea behind it, illustrated with that figure. Quite an exemplary approach.
The lectures need a bit more structure (dual support using slides is very pedagogical). I feel like these two days could have been condensed in about 1.5 days, giving time to read and discuss papers in the last hours of each day. This way, Miguel's lecture would have hit the target better and conveyed more meaningful questions and discussions.
There should be no remote presentations during the intensive. Pace can be a bit faster.

Changed my mind7

SLT has quite a few compelling ideas and it seems like it could use a lot more active researchers! But I'm still not sure how clear the link to AI safety is. Not just in terms of differential advancement of safety - I'm not sure what the theory of impact is for positive differential impact at all.
Not particularly
n/a
SLT provides a rigorous foundation for developmental stages.
became a bit less sure about if im convinced by SLT, but will spend some time doing more reading to make sure!
I realized that maybe chasing the strict minimum of the loss function landscape is not really needed. Maybe the landscapes is the wrong thing to study. The secret to generalization might be hiding in a different thing altogether (the early stopping generalization had a point, just like other methods like random deactivations). Btw the demo that, unlike GD/SGD, Adam and Muon first learn smaller components, which might be "noise," was quite surprising and exciting.
SLT during training could be interesting but needs improvement in LLC estimators.

Other thoughts3

Today and yesterday was very tough because my calculus is rusty. As a computer scientist I’m much more familiar and comfortable with discrete math
n/a
Outstanding two-day deep dive.

The day

10:00 Lecture starts

12:30 Lunch at LISA

13:30 Afternoon session

17:40 Feedback form

18:00 Day ends. Dinner at LISA

When	Where
Mon 7 Sep	LISA, 25 Holywell Row, London EC2A 4XE
Tue 8 – Mon 14 Sep	23 Curtain Road, London EC2A 3LT
From Tue 15 Sep	69 Wilson Street, Moorgate, London EC2A 2BB

Resources

Elsewhere