I've recently gotten a new appreciation for these beaut's. Some of the baddest higher-order functions since {fmap, >>=, <*>}! Quite a clear and general framework for recursion and corecursion
In physical systems, symmetries can create long-lived waves (Goldstone modes) that carry information over long distances. Does the same thing happen inside equivariant neural networks?
Turns out yes -- and models learn to use them for memory! Such a fun project to be part of.
The work of people to formalise mathematics is the real deal. Forget all the nonsense with LLMs blundering about stringing together mathy-sounding things that might or might not be true; it’s formalisation that will allow humans & computers to lean on each other’s strengths here.
@CIOEquitile @martinmbauer About 1: Electrons dont interact with strong force. Neutrinos dont with EM, etc. Its all about which fields are coupled together, and there is no reason that “everything must couple with EM”. One more non-EM-charged field is not even a surprise, its the generic expectation.
A secret weapon indeed. Like programmers, physicists learned well the virtues of laziness. And for some incredible examples, I have to again recommend ‘Scale’ by Geoffrey West
Want to learn one of theoretical physicists' most important secret weapons? A simple consistency condition, applied wisely, can be used to guess the answers to many problems with barely any work -- such as the ratio of the Sun's mass to the Earth's https://t.co/nlfnewvu7f
The elegance of ML is the elegance of biology, not the elegance of math or physics.
Simple gradient descent creates mind-boggling structure and behavior, just as evolution creates the awe inspiring complexity of nature.
@skdh@BartoszMilewski Im familiar with a lot of your writings and statements, but i was open to being shown if you had said something else. But if not we can just conclude this very unpleasant interaction and Ill let my original comment to Bartosz stand
@skdh@BartoszMilewski Playing games? All i did was disagree with you and explain why i do. Im happy to elaborate even further, if you were genuinely open to engaging (preferably not on twitter) but the immediate descent into accusations isnt likely to help…
@skdh@BartoszMilewski Do i understand correctly that youre agreeing with my statements ? So you agree with me that extreme fine-tunings represent a mystery we need to solve, and that pretty math is *not* the primary reason behind the activity in SUSY and string theory?
@skdh@BartoszMilewski I dont think our disagreement is about the LHC. i think our disagreement is about 1) whether we can just disregard fine tunings or accept they represent a mystery to be understood 2) the idea that “beauty” is somehow the main motivation for ideas like susy or string theory
@TheMichaelBurge im not sure i follow the point you’re making… are you suggesting a problem with the halting problem or another kind of unexpected computational power due to QM determinism? Determinism in the PDE sense doesn’t necessarily imply computability
@TheMichaelBurge Right total number of particles can change (in quantum field theory) but that’s different from changing the fundamental degrees of freedom…
@TheMichaelBurge The overall number of degrees of freedom cant change dynamically in QM. This gets subtle in the context of the whole universe, but we dont yet have reason to doubt this continues to hold…
@TheMichaelBurge tricky to answer in a tweet, lol. allocation and de allocation are only possible for specific subsystems under study and require use of an “environment”. The more general thing you might want violates no-cloning / no-deleting thms (qm is not cartesian closed)
@TheMichaelBurge Right, the evolution due to Schrödinger’s equation is completely deterministic. Non-determinism enters due to the extra collapse postulate. (& an Everettian like myself would argue thats only an epiphenomenon caused by the system becoming entangled with the observer/environment.
@TheMichaelBurge There is a field like that. Electromagnetism! Its described by a U(1) gauge group, which amounts to what you’re describing. And there could be other U(1)s too.