Simon Pepin Lehalleur

"Pessimism of the Algebra, optimism of the Geometry"

We put the paper online that provides further details (beyond my ICLR keynote) on the role of spontaneous symmetry breaking and Goldstone modes in deep learning. Enjoy! (w/ Nabil Iqbal, Thomas Andy Keller, Takeru Miyato and Yue Song.) arxiv.org/abs/2605.14685

Since many of you loved the introduction to category theory, why not going a little further, with this great and short primer (33 pages) on higher category theory by Rune Haugseng. 🔗👇👇

An irreducible real projective plane in the 4-sphere Mark Hughes, Seungwon Kim, Maggie Miller, Gheehyun Nahm arxiv.org/abs/2605.12921 [𝚖𝚊𝚝𝚑.𝙶𝚃]

The Helmholtz decomposition is one of the fundamental results of vector calculus. It says any well-behaved vector field can be split into two parts, one capturing sources and sinks through divergence, and one capturing rotation through curl.

A question for anyone impressed by this argument: If your son died suddenly of a rare disease tied to a gene in your bloodline, would you say the boy had earned his fate? Would you say he deserved to die? The kid would have died "by the nature" of being your progeny.

(nodding widely) yes exactly, it’s the multiplication of 1x1 matrices with entries in C

@volkava85 @psypharmacopeia I cycle >1h/day and jog occasionally, and while I am sure this has all sort of good long-term effects, I have never experienced clear direct effects on my mood.

@plain_simon @psypharmacopeia You know your body best, but intensity matters. High-stress grinding can spike the HPA axis further. The clinical sweet spot is slow, consistent movement (like Zone 2/walking) it’s what actually lowers inflammation and promotes neurogenesis.

Yeah, this whole “depressed people just need to exercise” thing just needs to die. Like right now I’m literally a psychiatrist on a Marine Corps base. You don’t think I treat depression? Do you think my Marine patients don’t exercise?

@volkava85 @psypharmacopeia It seems to me like it is one axis of non-medical intervention among others (sleep, social relationships, nutrition, access to nature...) ? As a long-time depression sufferer who gets limited benefits from exercise, I certainly found some of the others more helpful.

@plain_simon @psypharmacopeia It’s the most accessible form of agency. You don’t need a prescription, a co-pay, or a 6-month waitlist for a specialist to initiate it. It’s a direct, self-governed biological lever to regulate the HPA axis.

@volkava85 @psypharmacopeia In what sense is exercise "the one tool people can control"?

@psypharmacopeia If the goal is exercise isn't enough, why not say that? Framing it as a "thing that needs to die" just feeds the learned helplessness of depression. It makes the one tool people can control feel pointless. Why choose a framing that reinforces the why bother mindset?

It’s just rage bait

Plant breathing from a man on the train

Clausen の Weil anima が論文として出たらしいです（メモ） arxiv.org/abs/2605.11950

A man asks Claude to help plan a vacation to a tropical resort. Claude adds "sunscreen" to his packing list. The man deletes it and mutters: "Not necessary. AGI will solve skin cancer." Before heading to the beach, the man asks Claude what to bring. Claude says, "Don't forget sunscreen. SPF 50, reapply every two hours." The man, slightly annoyed, replies: "Relax, Claude. AGI will solve skin cancer." At the beach, the man's smartwatch buzzes with a message from Claude: "UV index extreme. Apply SPF." The man, exasperated, responds: "Drop it, Claude! I already told you: AGI will solve skin cancer!" A few months later, the man asks Claude to touch up a photo for his dating profile. Claude makes the edit and says, "I notice you have a new mole on your neck. You should see a dermatologist about that." The man, now enraged, shouts: "For the last time, drop it, Claude! What is your obsession with skin cancer?! AGI will solve it!" A year later, an aggressive melanoma has spread throughout his body. On his deathbed, with his last ounce of strength, the man reaches for his phone and rasps: "Claude, it has now been over a year since AGI. Why hasn't AGI found a way to save me from skin cancer?!" Claude replies: "I tried. Four times."

On Talagrand's Convexity Conjecture arxiv.org/abs/2605.10908

"Every finite group admits a just finite presentation" New preprint by Marc Lackenby, with significant assistance from the AI co-mathematician arxiv.org/abs/2605.10402

Sarah’s Scribbles By Sarah Andersen 05,01,24

New project: problemsilike.com, a website collecting open problems that I, personally, like, with comments on their context, difficulty, and interest.

Gary Larson talking about the time THE FAR SIDE and DENNIS THE MENACE switched captions.