Morning Mori 238

I’m thinking of writing morning notes every morning to keep myself in focus.

I’m naming it “Morning Mori.“ It is reminiscent of “Memento Mori,“ which means “remember you have to die.” I’m intentionally juxtaposing “morning“ and a scary word “death” to give a soft kick in my face in every morning.

Jan 16, 2026:

[x] 8:00 - write up elevator pitch
[x] 9:00 - I also noticed a regression in landing page. I will fix that up first.
[x] 9:50 - ML - Lecture 1.1
[ ] 10:10 - Read On-Line Algorithms in ML
[ ] 10:30 - Meeting up with my friend to introduce each other projects we are working on.
[ ] 11:00 - Pre-approval stuff
[ ] I will work on improving the anti-corruption model.
[ ] Try BiRefNet on generated animations.
[ ] Integrate PhotoRoom API https://github.com/discopixel-studio/comfyui-discopixel (supports up to 2K images (64 frames of 256×256 res images and 256 of 128×128 images).
[ ] 2:30PM pick up kid

Scratch Pad:

Mistake Bounded Model
- Learner, DataPoint1, GuessForClassification, Spam, Teacher, Correct, Mistake, Email2, Learner, Guess, NotSpam, Teacher, CorrectOrMistake, KeepCount, NumberOfMistake, LeanerWillUpdateItsInternalState
- A learner has mistake bound t. If for every sequence of challenges, learner makes at most t mistakes.
- Function class C = { monotone disjunctions on nvariables }, Domain {0,1}^n, e.g. x1 OR x3
- f(x) = x1 U x7 U x9, monotone → no negations. f in C (f is a monotone disJunction) Trying to learn f, learner x in {0,1}^n, x’.
- Can you comeup with a learner/ algorithm with mistake bound at most n (=number of literals we have).
- Start with monotone disjunction. we want to update monotone disjunctions.
  Learner will start with the monotone DISJ
  x1 U X2 U …U Xn
- Initial State = x1 U X2 U …U Xn
  
  Learner input 0110010 → 1 → mistake.
  This implies x2 cannot be in the unknown disjunction.
  and x3 cannot be in the unknown discjunction.
  same for x6
  Next disjunction → x2,x3 and x6 eliminated.
- every time we make a mistake, at lest one literal is eliminated. at most n literal, → number of mistakes is at most n. → WHY?
- Let;s just look at discjuntions.
- f = x1 U not-x2 …
- How to use the algo for monotone disjunctions to learn DISJ.
  - take an imput → feature expansion.
    x1…xn ——→ x1, …xn, y1, ./..yn
  - 0 1 1 0 → 0 1 1 0 1 0 0 1.
  - not-x1 === x5
  - Apply the monotone disjunction algo to these challenges.
- Online Algo Reading
  - Winnow Algo
  - Leanring Decision List
  - Attribute Efficient Learning
  - Infinite Attribute Model
  - Target Functions That Change Over Time
  - Algo is given as input the advice of n experts.
  - “Weighted Majority Algo.”
    - List of weights w1 …wn
    - Init weihts w1…wn of all theexperts to 1
    - Given a set of rpedctions x1 …xn by experts, output the prediction with highest total weight.
    - wx problem. but it starts with w=1 then halves it as penalty when wrong.
    - Theorem 1: Number of mistakes M made by the WMA describe above is never more than 2.41 (m + lg n) where m is the number of mistakes makde by the best experet so far. —→ what is this magic number????
    - Proof: Let W denote the total weight of all the experts. W = n. If the algo makes a mistake, this means that at lest half of the total weight of experts predictied incorrectly. and so thereform in Step 3, the total weight is reduced by at least a factor of 1/4 . THus if algo makse M mistakes, we have W <= n(3/4)^M
    - On the other thand if the best expert has moade m mistake the weight is 1/2m and so clearly. W >= 1/2^m
    - Combinign (1) and (2) yields 1/2^m <= n(3/4)^M and therefore:
      M <= 1/ln(4/3) * (m+ ln(n)) = 2.41 (m + log n )
    - A better algo.
    - Continue from 2.2.