printing a bunch of whitespace is a way of entering into a new state ( I am thinking about a state machine), so the LLM can use that whitespace as a new token that can be used later to refine the state of the system. In math terms, whitespace is a tag for a class (or state) in the LLM. I think that perhaps RL can take advantage of such tags. For example whitespace could indicate a point of low gradient (indetermination) or a branching point, the LLM in some way would learn to enhance the learning rate parameter, so the message in the head of the LLM is: be ready to learn from RL because in your actual state you need to take a branch from a branching point that can enhance your capabilities. This is similar to tossing a coin or a die. The rule could be: when whitespace do increase the learning rate parameter to escape from zero gradient points. Caveat emptor: This is just an speculation, I don't have any data to support this hypothesis. Also this suggests that whitespace could be a "token that reflects the state of previous layers" and is not contained in the vocabulary used to train the model, so I should say that whitespace is a macro-token or neurotoken. If this hypothesis has some ground then it could also be plausible that whitespace could be an enumerate neural tag in the sense that the length of whitespace reflects or is related to the layer in which the zero gradient or branching point occurs.
Finally, my throwaway user need whitespace so I will change the password to a random one to force myself to avoid adding new ideas.
You are correct, but the real problem is that copyright needs complete reform.
Let's not forget the basis:
> [The Congress shall have Power . . . ] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.
Is our current implementation of copyright promoting the progress of science and useful arts?
Or will science and the useful arts be accelerated by culling back the current cruft of copyright laws?
For example, imagine if copyright were non-transferable and did not permit exclusive licensing agreements.
Interesting. I understand that you draw the line that separate workflow from agents as the exploitation exploration trade-off. This could allow a dynamic environment in which a parameter depending of each task control the workflow-agent planning. So there is not a clear cut off, the difference depends of the task, the priors, and the posterior experience.
I just tried the chat and asked the LLM to compute the double integral of 6*y on the interior of a triangle given the vertices. There were many trials all incorrect, then I asked to compute a python program to solve this, again incorrect. I know math computation is a weak point for LLM specially on a chat. In one of the programs it used a hardcoded number 10 to branch, this suggests that the program generated was fitted to give a good result for the test (I did give it the correct result before). This suggests that you should be careful when testing the generated programs, they could be fitted to pass your simple tests.
Edited: Also I tried to compute the integral of 6y on the triangle with vertices A(8, 8), B(15, 29), C(10, 12) and it yield a wrong result of 2341, then I suggested computing that using the formula for the barycenter of the triangle, that is, 6Area*(Mean of y-coordinates) and it returned the correct value of 686.
To summarize: It seems that LLM are not able to give correct result for simple math problems (here a double integral on a triangle). So students should not rely on them since nowaday they are not able to perform simple task without many errors.
Here is an even easier one, ask llms to take the integral from 0 to 3 of 1/(x-1)^3. It fails to notice it's an improper integral and just gives an answer.
