Nikolaj-K
/ Consequentia_Mirabilis.txt
Last active
April 13, 2024 11:24
Pierce's law, Consequentia Mirabilis, ¬¬-Elimination and LEM without Explosion
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| 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
/ subcountability.tex
Last active
April 8, 2024 00:04
ℕ surjects onto ℝ. Subsets of ℕ surject onto ℕ^ℕ. ℕ^ℕ injects into ℕ. All that.
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| 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
/ manual_sampling.py
Created
March 12, 2024 22:44
Manually sampling from any given 1D histogram
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| """ | |
| 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 | |
| """ |
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| """ | |
| 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
/ ReLU_square.py
Last active
January 16, 2024 05:00
Computing all polynomials via just ReLU activations (no learning needed)
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| """ | |
| Script discussed in this videos: | |
| * Video 1: | |
| https://youtu.be/PApGm1TKFHQ | |
| * Video 2: | |
| https://youtu.be/1z2GRcaKSrA | |
| ==== Text for video 1 ==== |
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| Below is the sketch of my script for the video at: | |
| https://youtu.be/ZSmORp3Bm2c | |
| Paper discussed: | |
| - https://arxiv.org/pdf/2307.03223.pdf | |
| Large width network theory: | |
| - https://en.wikipedia.org/wiki/Universal_approximation_theorem | |
| - https://en.wikipedia.org/wiki/Gaussian_process |
Nikolaj-K
/ scalargrad.py
Last active
October 23, 2023 21:31
A simple implementation of reverse accumulation (back-propagation)
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| """ | |
| Impelmentation of reverse accumulation (backpropagation), discussed in | |
| https://youtu.be/BcCk8I6YAqw | |
| Most of this script is exposition code. The reverse accumulation code still runs if you delete everything except the following 5 classes | |
| * ValAndDVal, ExprBaseRevAcc, VarExprRevAcc, PlusExprRevAcc, MultExprRevAcc | |
| validated using the following 2 functions: | |
| * p, run_VarExprRevAcc_gradient_decent_demo |
Nikolaj-K
/ bandit_strategies.py
Last active
October 10, 2023 15:59
A small pytorch routine approaching the n-armed bandit problem
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| """ | |
| Casino strategies and some pytorch. The code is explained in the video | |
| https://youtu.be/VUVVVi9CgbI | |
| I think you can install pytorch via `pip` or `pip3` through | |
| `pip3 install torch torchvision` | |
| Some mathy reading material: | |
| * http://yuanz.web.illinois.edu/teaching/IE498fa19/ |
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| """ | |
| Code discussed in the video: | |
| https://youtu.be/0A3mAUGFUow | |
| * Motivation: | |
| - Relation between Legendre symbol and quadratic equations on ZxZ | |
| + See https://en.wikipedia.org/wiki/Legendre_symbol#Table_of_values | |
| * For any fixed number, validate |
Nikolaj-K
/ copious_secret_santa.py
Last active
August 19, 2023 18:01
Copious Secret Santa / Voting assignment
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| """ | |
| Script used in the video | |
| https://youtu.be/2b9fOpX0zKY | |
| Formal structure: balanced simple digraph | |
| (Important special properties out-degrees equals the in-degrees, no self-loops, no parallel arrows) | |
| 1. Proof task: Count them, given any assginment of out-degrees. | |
| How does it compare to just random disgraphs with that those out-degrees? | |
| 1. Coding task: Generate one given the out-degrees, fast. (I have a bad, probabilistic solution) |
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