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

[C.3]Computational Mechanics Thu 10 Sep, leading 41 responses · energy 4.0/5

Overall +0.92 better than expected n = 39

Content +0.67 better than expected n = 39

Clarity +0.51 better than expected n = 39

Motivation +0.10 as expected n = 39

Exercises +0.51 better than expected n = 39

Readings +0.63 better than expected n = 35

Other activities +0.25 better than expected n = 32

Pace +0.03 about right n = 39

Difficulty +0.03 about right n = 39

Novelty +1.05 mostly new n = 39

Read what they wrote65

Worked well23

I really enjoyed the pacing and intuition / explanations of the lecturer
Described above.
The progressivity of the concepts presented, also the article with a short summary and a guide to point out the most important sections to read.
Slides were very clear, and the exercises fun and instructive.
Good explanation of generative models, linear embeddings, sufficient stats; good discussions.
Learning new ideas
It was great.
Long exercise sessions, with exercises not being too hard, so it was possible to get a grasp of all the concepts covered
really enjoyed the python exercises for computing belief states and the quiz (good check). also easy to follow "story" of going from hmms to belief states to the transformer result
Clear build-up of definition.
The answers given by the teacher and conversations with him and other participants
Lectures were well structured. I could clearly follow how the ideas were building up. The readings were relevant, and I was impressed I could understand a technical paper on a completely new topic after only a few hours of lectures.
Exercises
Xavier was the best lecturer so far. Found him very easy to follow.
The clear structure with the timetable, it was paced very well with plenty of time for questions. The exercises were at a good level and very clearly linked to the slides and the paper we read at the end.
The structure announced in advance: a 30 min intro lecture with two follow-up deep-dives. Having an intro lecture really helps. The slide numbering -- makes it easy to do notes and refer later with the questions. The exercises -- really drove the point home and assisted with understanding a lot, as it felt a bit abstract at times. Finishing with reading and discussing a paper was a top notch, just like yesterday with Tudor on Physics of Deep Learning. I love this structure so far.
the exercises are very well chosen. The presenter was very good.
I liked how the day was broken up into lectures and exercises/reading
As opposed the past three days, the material, while advanced, seemed more targeted and far more clearly presented in the slides and the problem sheets. The problem sheets themselves were more helpful than those of the past three days as they were detail-oriented and low-level, catered towards enhancing our understanding of the very basics of the new techniques introduced today. I did not feel overwhelmed by them and came away feeling like I measurably learnt something new. The larger amount of time allocated to doing them was also very welcome and made the day feel far more productive than previous ones.
Xavier did a really great job of explaining mathematically challenging concepts clearly in limited time, and also in giving broader motivations for the field.
the exercises were awesome. They really helped me understand the material.
The day was very well structured and it was clear what we were doing when. The exercises were clear and helpful.
Both the presentation structure and lecturing by Xavier were great.

Would improve24

This day was really really good. The pace was fantastic- you could follow everything whilst being slightly challenged. The exercises were good too, and at the end of the session we were able to fully understand a paper (not just superficially) and be able to discuss its merits and limitations.
Maybe adding some animations and some proofs for the most important results in the appendix
Perhaps one example could have been presented inside the joint class. The lecture was clear! Perhaps it would be possible to compound the python exercises to try and reproduce the findings of https://arxiv.org/pdf/2405.15943 in a small transformer. More comments about open problem in the field would also have been useful to give more direction! Overall very good lecture and the topic fits well in the allocated time.
We spent a lot of time introducing and defining GHMMs, minimal sufficient stats etc. This material was very clear and pedagogical, but it might have been nice to spend more time talking about how this relates to learning, how it cashes out in LLMs, and what the important open questions are. I now know a lot about the data-generating process, but still have only a fuzzy understanding of why or when we should expect it to be embedded nicely in transformer activations and what implications this has for behavior and learnability.
I thought the teaching was very good, in fact I wanted more of it! Felt like there was a lot of time towards the end of the day for reading that could have been filled with an additional lecture / some other activity.
The exercises 1 and 2 were really easy. But maybe that's actually a good thing
- more time on the mixed state presentation, it went quite fast relative to how central it is - link the exercises more directly to the Shai et al. paper i.e show how the belief states from the HMM exercises end up in the residual stream
I think at points the material was quite abstract and I didn't really connect it to the feature analysis from say mech interp. Maybe also the applications to steering and how these tools can be applied felt fuzzy.
very nice lectures and exercises, maybe make more time for coding?
More time for exercises, as they were fun and useful.
Commenting more on the limitations and future goals
I would add more coding exercises and show resulting plots as outputs and explain concepts by interpreting them.
The lectures were overall clear. I think it would be beneficial to go through exercise and examples in the classroom.
Nothing really good day
a short explanation of IID, clear definition of hidden markov model at the start.
Hard to say honestly, such a great lecture, structure, the material and the day. Three things though: 1. Exercises -- maybe it's just me, but they required a lot of pretty simple compute, which becomes tedious at some point because you do not feel like you are learning or understanding smth new with the new exercise. Maybe makes sense to have a pointer like "if you do not have time to do the computations, take the resulting matrices from Solutions and proceed to the next steps." 2. Given that I have been catching (although maybe it's just me being unsure about the hidden state of mind of surrounding students) the "we can find the belief state geometry, so what?" vibe slightly, maybe makes sense to provide an empowering example, however small. The paper was incredible, don't get me wrong, but it does not look like it was found too promising of the research direction that necessitated the entire startup established under it. Smth to think about rather than just a suggestion, as that's the problem that was present in "physics of Deep Learning" as well -- people are like "So what?" forgetting that Quantum Mechanics and GTR was also pretty much "We know the deflection of light by Sun and additional 5% of precession of Mercury's orbit, so what?" and then we had precise GPS and gravitational waves. Nice to be showing that "So what?" is not a question to be asking. 3. it would be nice to make the intro lecture somewhat more connected to reality, as it feels quite abstract in the beginning. Say compare this with the hidden states of mind: we do not know the mood of the person, and we infer it from what they say. So we have this "mundane" problem familiar to pretty much everyone and then put the math behind it. Otherwise the beginning might read too abstract, and my brain gets lost when it does.
- Don't assume we've gone through the full exercise sheet when starting off the next lecture (he made a lot of references "as we saw in the exercises", but a lot of us didn't get this far, so it felt really out of context). - Spend 5-10 mins in the beginning reviewing expected knowledge (e.g. HMM for today, "beliefs", "belief system")
second part was a little too dense
I thought the material was very interesting, but I think I'm still missing a bit of information about how this could be applied / used for AI safety/alignment work.
I think this topic could do with two days instead of one.
Maybe a bit more on the foundational math.
- Adding more pictures, - introducing the definitions a bit gentler, I felt that other participants might not have enough relevant background to quickly grasp what's happening (i.e. physicist don't know Chomsky hierarchy)
The lectures we too fast. Make significant pauses before going from one slide to another. It gives time to take notes, digest the material and come up with questions about things that are misunderstood. The language in the exercises was hard to understand coming from a physics background.
I think perhaps the exercises. I found them very easy and often not very illuminating. I also struggled a bit to understand the applicability of computational mechanics to AI safety from the slides, but this became much clearer after a discussion with Xavier and reading the paper. Probably the day could have had more content - I think it is an interesting subfield!

Changed my mind14

I was not aware of computational mechanics and where it fits into the interpretability/alignment world - I would consider this as a potential area of research I would like to eventually contribute to.
I am more aware of the utility to study toy models to assess the learning capabilities of large models.
Somewhat more persuaded that this geometry of learned representations stuff is worth pursuing, although still seems unclear if it will extend to representations of the concepts we care about in the networks we care about.
Very interested to learn about belief state geometry and would be interested to think about theoretical guarantees in this area.
- interp on toy processes with known "ground truth" seems a lot more of an approachable problem than I thought, ended up picking this area for my proposal
I understand better the connection between computational mechanics and theory of world models.
Discovered a really interesting project at simplex.pub, and got interested on computational mechanics
I think computational mechanics is a very interesting field that I didn't know about until today. I will definitely dig deeper.
The reading felt a bit 'numerological' or like astrology but maybe it's just that I didn't understand it well enough. Will think about this.
I am sceptical about this being able to help AI Safety in the next 5 years but appreciate its value in scientific understanding for the future.
Hidden states wow. I knew that HMMs were used for financial markets in the second half of XX century and Renaissance Tech made a lot of money from that, and it's wonderful to see that they apply here too. I also realized that the states of mind reflect very well upon the material. We can be listening to the person / reading the text and be unsure whether they are passive aggressive or sarcastic or normal / whatever.
"pretrained models should learn more than the hidden structure of the data generating process—they must also learn how to update their beliefs about the hidden state of the world as they synchronize to it in context" that's crazy
It was interesting to learn about computational mechanics, although from the readings, it seems unclear how scalable it is.
I have been encouraged to think more about computational mechanics. When I first started thinking about understanding LLMs my first thoughts were a (very) naive version of this approach. I am considering looking into this area further and possibly pursuing research in this direction.

Other thoughts4

Thanks to Xavier for his time and cheerfulness!
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I'm having some personal problems that were making it difficult to focus. But the lectures today seemed great - pace, difficulty, teaching, exercises, everything was really good.
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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

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