Does it mean coding tools making use of MDLMs can more precisely edit code chunks without prompting hacks? Seems like there is absolutely no downside, looking forward to all SOTA models switching to this technique soon!
I like Inverse types! While it's not novel idea, this seems like a very concise implementation of it.
Inverse types are also known as negative types (https://legacy.cs.indiana.edu/~sabry/papers/rational.pdf) or holes. This concept is what needed to make a concrete category for computation compact (highly recommend: http://arxiv.org/abs/0903.0340) and make the connection to how our physical universe actually works on a quantum level, with antiparticles performing backward computation.
I'm pretty sure this model of computation of filling holes with inference would allow us to understand advantages of quantum computation much better.
Do you have any thoughts on HVM's SupGen for program synthesis? I would love to understand how interaction nets makes the notion of inverse types and filling holes more natural and efficient.
I got "The scatter plot appears to be arranged to resemble the character "Pepe the Frog," a popular internet meme ... " lol
Not sure whether multimodal embeddings have such a good pattern recognition accuracy in this case, probably most of information goes into attending to plot related features, like its labels and ticks.
This is very cool! I'm wondering how does it compare to classical ATPs like Waldmeister or Vampire, can SupGen compete in CASC (https://tptp.org/CASC/)?
Right, these are different questions indeed. Scott wonders what happens to amplitudes as they already appear in the theory but with numbers being no longer complex. But those lifted representations effectively change to a specific basis in higher dimensions (think qubit's 2x2 density matrix becoming a 4-dimensional distribution vector, with the same 3 real degrees of freedom) where everything is real and interpreted as probabilities.
That's not what I'm saying. Bell or any CHSH-like experiment can be equivalently described using random variables and quasi-stochastic processes instead of quantum states, unitaries, and measurements. It would still involve non-local correlations and inequality violations, but without mentioning the Born rule, phases, and interference with imaginary numbers. It is just an equivalent mathematical framework.
These alternate theories that use quaternions and whatnot are just mathematical marvels that have nothing to do with physics, QM can be well explained with conventional probability theory already (even without generalized probability theories that people also study). Seems like negative conditional probabilities governing quantum processes can be understood as intrinsic Bayesian inference or Particle filter estimators. I wish there were more research in this direction ...
Complex numbers are not a QM feature; they are just more convenient to use in computations. There are equivalent formulations, like Wigner's phase-space with quasi-probabilities and MIC-POVMs that don't have any complex numbers. The weird part is the negative probabilities, not imaginary numbers.