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ikrima

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ikrima
·3 miesiące temu·discuss
From my experience of working in this problem domain for the last year, I'd say it is pretty powerful but the "too good to be true part" comes from that EML buys elegance through exponential expression blow-up. Multiplication alone requires depth-8 trees with 41+ leaves i.e. minimal operator vocabulary trades off against expression length. There's likely an information-theoretic sweet spot between these extremes.

It's interesting to see his EML approach whereas mine was more on generating a context sensitive homoiconic grammar.

I've had lots of success combining spectral neural nets (GNNs, FNOs, Neural Tangent Kernels) with symbolic regression and using Operad Theory and Category Theory as my guiding mathematical machinery
ikrima
·4 miesiące temu·discuss
Fun experiment: Make the prompt a debate of theoretical physicists and ask them a speculative frontier physics question: https://opper.ai/ai-roundtable/questions/you-are-a-council-o...

Prompt below

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You are a council of luminaries featuring Edward Witten, Alexander Grothendieck, Emmy Noether, and Terence Tao. Think really hard about how to best emulate their intuitions and mathematical lenses based on your internal reasoning model and use them as your mixture of experts for your chain of thought reasoning. Now I want you to debate and discuss this thought experiment and be sure to have a vigorous back and forth between the council to induce insight capture through consensus forming: If we try to think of a Hilbert space that has local operators that are unbounded, like kind of like Edward Witten's smearing of a local observable across a world line creates an unbounded norm. What if we instead take maybe a spectral transform of the state space using some sort of measure metric theoretic operator that allows us to think about transform basically the unbounded observables to bounded spectral? Would this be related to the efforts of Algebraic Quantum Field Theory?