Ok, after re-realizing the “triangle inequality” is so darned ‘everything’ when it comes to defining ‘metric spaces’, I looked for any recent “triangle inequality” stuff in scholar.
2017: Improving compiler efficiency by thousands of times by implementing triangle inequality logic that uses VECTORS (the angles of the triangle) instead of the SIDES (lengths).
(What it’s doing is figuring out lowest + highest search space in loops, restricting search space to ONLY what’s needed. (instead of 0 -> 100000, if all it needs is 5000 < x < 6000 the checking will be a heck of a lot faster.
Generalizations of the Theory and Deployment of Triangular
Inequality for Compiler-Based Strength Reduction
Yufei Ding, Lin Ning, Hui Guan, Xipeng Shen
I post things that inspire me. This is related to AI and clustering (or “making categories”) which has always got me thinking.
Oooh: “Start from where you are”. Ghost landmark. I Like it.
oh NOOOO – it’s start from where last WERE to figure out where you’re GOING, including where you are.
“Ghosts In many iterative algorithms, the locations of the
points or the values of the vectors in question get incremental
updates across iterations. We call their locations/values in
the previous iteration their ghosts. Because a ghost of a point
is often close to that point, it can often serve as a good
“Property II: Landmark Preference. Unlike ETI, which
prefers landmarks close to either point in the question, ATI
prefers landmarks that form small angles from either of the
vectors in question. It is easy to see, from the deﬁnition of
ATI, that such landmarks give tighter bounds than those with
large angles from both vectors.”
_To get there, go as straight as possible with fewest dramatic turns_ – like Great Circle in flying. Ah!
• Cosine Similarity:
On the other hand, for cosine similarity, the group bounds
from ATI depend only on the largest angle from the target
vectors to the landmark (e.g., max(θ ~
)), which stays
the same across different query points. But the group
bounds from ETI depend on multiple factors
OHOHOHOH… because NARROW ANGLES is equivalent to a NARROW LIGHT CONE.
In a narrow light cone, you can find what you want more quickly than if you had a WIDE light cone!!
Ha ha — PHYSICS…
Ok. I’m finally going to have to give respect to Euclid,100 AD.