Comment by narrator

So this shows you have a basic understanding of how CNNs represent data for classification tasks. This is excellent!

However, you might not be aware of the current research into "Emergent Phenomena in Large Language Models"[1].

Work such as PaLM[2] show that language models evolve the ability to "reason" over the internal data representation. Minerva explicitly breaks down that ability by "comb[ining] several techniques, including few-shot prompting, chain of thought or scratchpad prompting, and majority voting, to achieve state-of-the-art performance on STEM reasoning tasks."

This lets it solve novel problems such as "Assume that the variance of the first n natural numbers is 10, and the variance of the first m even natural numbers is 16. Compute m + n".

To preempt the "oh it is in the training set" issues, I'd note this (on a different problem): The model correctly takes the derivative of a position vector to compute the velocity. It then computes the norm of the resulting vector, and uses a trigonometric identity to obtain a final numerical answer. Minerva takes a completely different approach from the ground truth solution."

I'd encourage you to read the Minerva paper[4] and update your understanding on what large neural networks are doing. These reasoning abilities are not* as simply as "compressed data representation + reconstruction" - the chain-of-reasoning approaches partially use that of course, but also appear to a form of lemma chaining, similar what something like Prolog does.

As a specific demonstration for their ability to generate novel outputs that make sense:

Prompt: explain Algorithm X in the style of a Kayne rap

Response: Alright, here's a rap about Algorithm X[5], the famous algorithm for solving the exact cover problem:

  `Alright, here's a rap about Algorithm X, the famous algorithm for solving the exact cover problem:

  Verse 1:
  I'm Algorithm X, the greatest of them all
  I'll solve any exact cover problem, big or small
  My steps are simple, my logic is sound
  Just give me your matrix, and I'll give you the answer you found

  Chorus:
  Algorithm X, the master of the game
  I'll solve your problem, and do it by name
  Exact cover, no problem for me
  I'm Algorithm X, the MVP

  Verse 2:
  First, I'll start by selecting a column
  Then I'll look for a row with a one in that column
  Once I find a match, I'll mark the row and column
  And repeat the process until the matrix is gone

  Chorus:
  Algorithm X, the master of the game
  I'll solve your problem, and do it by name
  Exact cover, no problem for me
  I'm Algorithm X, the MVP

  Verse 3:
  But sometimes the matrix is too big to solve
  That's when I use my dancing moves
  I'll shuffle and prune, until the solution is clear
  And in the end, I'll have your answer, my dear

  Chorus:
  Algorithm X, the master of the game
  I'll solve your problem, and do it by name
  Exact cover, no problem for me
  I'm Algorithm X, the MVP.`

Now I entirely concede that it has read things on how Algorithm X works, and that it seems to use a template for "rap" responses. But:

  But sometimes the matrix is too big to solve
  That's when I use my dancing moves
  I'll shuffle and prune, until the solution is clear
  And in the end, I'll have your answer, my dear

I refuse to believe that anywhere, at any point has someone written an explanation of the use of dancing links[6] in Knuth's Algorithm X like that.

[1] https://ai.googleblog.com/2022/11/characterizing-emergent-ph...

[2] https://arxiv.org/abs/2204.02311

[3] https://ai.googleblog.com/2022/06/minerva-solving-quantitati...

[4] https://arxiv.org/pdf/2206.14858.pdf

[5] https://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X

[6] https://en.wikipedia.org/wiki/Dancing_Links