Matsuki Metropolis

[Matsuki Metropolis @matto31415]

@jeffreyNgodfrey the last solution on that last link is super similar to the "almost solution" you proposed earlier today!

[Matsuki Metropolis @matto31415]

#probability question: is there an "intuitive" reason why one cannot construct (d+2) #random vectors in R^d that are strictly negatively correlated?

[Matsuki Metropolis @matto31415]

@jeffreyNgodfrey Oh, it seems like it's a classic!!
https://t.co/eSWQlvpuKd

[Matsuki Metropolis @matto31415]

@RHeirene @KrzakalaF

[Matsuki Metropolis @matto31415]

@jeffreyNgodfrey Since the d+1 vectors are strictly negatively correlated with the (d+2)-th vector, it seems like, writing down the formula for dot product taking the (d+2)-th vector as one of the basis vector, that after projection the vectors are even more negatively correlated, no?

[Matsuki Metropolis @matto31415]

@jeffreyNgodfrey actually, now I wonder if this apparently too simple solution works: suppose the d+2 vectors exist. Project the d+1 first vectors to the space orthogonal to the (d+2)-th vector. The d+1 vectors remain strictly neg. correlated, but on a space of dim d+1. Conclude by induction??

[Matsuki Metropolis @matto31415]

@jeffreyNgodfrey my bad!

[Matsuki Metropolis @matto31415]

@jeffreyNgodfrey Nice reasoning! It feels so close to having a full proof. (although you meant 2^d and not 2d, right ?)

[Matsuki Metropolis @matto31415]

@jeffreyNgodfrey Yes, exactly! I kinda can do the algebra, but it feels like there should be some nice geometric reason. But maybe not..

[Matsuki Metropolis @matto31415]

@jeffreyNgodfrey Actually, thinking more about it, one can do without the randomness. Prove that there is no (d+2) vectors in R^d whose pairwise dot product is strictly negative.

[Matsuki Metropolis @matto31415]

@mslapointe oh, wow! Also true for science entrance exam?

[Matsuki Metropolis @matto31415]

@Tweetermeyer We all know it's a fraud, but why is nobody doing anything about that!

[Matsuki Metropolis @matto31415]

@celestelabedz Making cheese

[Heiga Zen (全 炳河) @heiga_zen]

Google Research Tokyo page is now live!

https://t.co/n350p6s8LM

[Ryan Adams @ryan_p_adams]

PSA from your neighborhood @NeurIPSConf SAC:

Reviewers: We write papers to advance knowledge. The purpose of experiments is to empirically evaluate hypotheses. If you ask for an experiment on a particular benchmark, please be clear about what hypothesis you want investigated.

[Matsuki Metropolis @matto31415]

@astro_jje the virus travels through 5G, did you wear a mask?

[Matsuki Metropolis @matto31415]

@uPicchini "imagine a world where [...] you say, ‘our university is thinking of promoting x from this position to this position on the basis of his or her research activity’ and then everybody in the world is invited to comment." - - > probably much better than the current system 😅

[Matsuki Metropolis @matto31415]

@GabriellBirchak @BullshitQuantum ?

[Matsuki Metropolis @matto31415]

@hardmaru they switched back to the previous keyboard model, but my 2015 keyboard still feels way better...