Nikolaj-K

Script discussed in the video:

https://youtu.be/tqmtZ82WHJc

==== Bayesian calculus vs Propositional logic ==== Idea: Logical implications are akin to Conditional probabilities. Reading: $P(B \vert A)=1 \iff A\to B$ $P(B \vert A)=0 \iff \neg(A\to B)$ "$P(B \vert A)$ ... $P(A\to B)$"

Nikolaj-K

import random
from scipy import special
import matplotlib.pyplot as plt
import numpy as np


def l1_normalize(finite_stream):
    lst = list(finite_stream)
    return np.array(lst) / sum(lst)

Nikolaj-K

==== Integration by parts ====

$\int_a^b (p\cdot f)' dx = (p\cdot f)_a^b = (p\cdot f)(b) - (p\cdot f)(a)$

$\implies$

$\int_a^b p\cdot f', dx = -\int_a^b p'\cdot f, dx + (p\cdot f)(b) - (p\cdot f)(a)$

=== Score ===

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