Nikolaj-K

Mappings out of V_6

input cardinality = 0

(#1)  []  ↦  []

input cardinality = 1

(#2)  [[]]  ↦  [[[]]]
(#3)  [[[]]]  ↦  [[]]

Nikolaj-K

Links of the pages in the video:

https://youtu.be/Q_c0n1d5x3I

########## ########## ########## ##########

• Paper:

Interpreting and Improving Diffusion Models from an Optimization Perspective >

Nikolaj-K

## Install hints for 
## https://github.com/yuanchenyang/smalldiffusion/
## as of July 2024. Produced via `pip freeze > requirements.txt`
## You may `pip install -r requirements.txt` this file for a numpy that worked for me.
## Small discussion at
## https://github.com/yuanchenyang/smalldiffusion/issues/1

# accelerate==0.31.0
# appnope==0.1.4
# asttokens==2.4.1

Nikolaj-K

Scirpt used in the video:
https://youtu.be/yx2xc9oHvkY

This video was a reaction to derivations such as:
re: https://community.deeplearning.ai/t/calculating-gradient-of-softmax-function/1897/3

----

For general $s\colon{\mathbb R}\to{\mathbb R}$, define the scaled vector ${\vec x}^s$: $i\mapsto \dfrac{s(x_i)}{\sum_{k=1}^n s(x_k)}$

Nikolaj-K

Video discussing pointing to text 'Diffusion Geometry' (May 2024, 49 pages) 
by Iolo Jones (Durham University)

https://www.youtube.com/watch?v=f2GJG7vMSZI

#### Links
* Paper:
https://arxiv.org/abs/2405.10858
https://arxiv.org/pdf/2405.10858

Nikolaj-K

Proofs discussed in the video:

https://youtu.be/h1Ikhh3J1vY

Legend and conventions:

$(P \to \bot) \lor P\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ ... $PEM$ ... Principle of excluded middle (a.k.a. $LEM$)
$((P \to \bot) \land P) \to Q\,\,\,$ ... $EXPL$ ... principle of explosion, a.k.a. ex falso
$((P \to Q) \to P) \to P$ ... $PP$ ... Pierce's principle
$((P \to \bot) \to P) \to P$ ... $CM$ ... consequentia mirabilis, a.k.a. Clavius's principle

Nikolaj-K

Shownotes to the video:
https://youtu.be/q-mjO9Uxvy0

For a related and relevant video constructive logic basics and upshots is at
https://youtu.be/-lPrjPHElik
For a related and relevant discussion on computably enumerable sets and their compliments, see this 4yo video
https://youtu.be/Ox0tD58DTG0
For some of the non-theorems in the list it helps to understand \Pi_0^2-complete sets.
The references video on how the Axiom of Choice and Regularity each imply LEM is at
https://youtu.be/2EOW23uVcRA

Nikolaj-K

"""
Script discussed in the video:

https://youtu.be/ndAmT8CYGDM

Links:
* https://en.wikipedia.org/wiki/Energy-based_model
* https://en.wikipedia.org/wiki/Brownian_motion
* https://www.extropic.ai/future
"""

Nikolaj-K

"""
Script discussed in the video

https://youtu.be/RltoGfNhex4

asyncio Enables (interleaved) sequences of functions execution within one thread.
Makes e.g. sense if you want less intensive computation results earlier (for IO) or
If some awaited computation is done in some external thread (e.g. info from a server).
"""
import asyncio

Nikolaj-K

"""
Script discussed in this videos:

* Video 1:
https://youtu.be/PApGm1TKFHQ

* Video 2:
https://youtu.be/1z2GRcaKSrA

==== Text for video 1 ====