Predicting the next character alone cannot achieve this kind of compression, because the probability distribution obtained from the training results is related to the corpus, and multi-scale compression and alignment cannot be fully learned by the backpropagation of this model
Key insight is the finiteness of reasoning parts in planar geometry that can be quickly solved by the SAT, which often does not exist in most first-order and second-order logics, such as number theory, algebra, or functional analysis
The problem is that using LLM as a role for drawing auxiliary lines is too inefficient. It is hard to imagine people deploying a large number of machines to solve a simple IMO problem. This field must be in the early stage of development, and much work remains unfinished. A reasonable point of view is that the search part should be replaced by a small neural network, and the reasoning part should not be difficult, and does not require much improvement. Now is the time to use self-play to improve performance, treating the conclusions that need to be proved in plane geometry problems as a point in the diagram and the conditions as another point in the diagram. Then two players try to move towards each other as much as possible and share data, so that the contribution made by each player in this process can be used as an analogy for calculating wins and losses in Go, and thus improve performance through self-play.
The problem is that LLM as a role for drawing auxiliary lines is too inefficient. It is hard to imagine people deploying a large number of machines to solve a simple IMO problem. This field must be in the early stage of development, and much work remains unfinished
Most of Dynamic programming is just a method of reducing computational complexity by changing the noun objects in first-order logic (or second-order logic, advanced version) to walk through the answers of unfinished tasks using completed tasks. Only in very few cases is it necessary to extract and match the completed parts from the unfinished objects in the above process, which often involves optimizing a function f(A,B). However, most of the time, this process is futile.
mixtral 7*8B does indeed have this characteristic. It tends to disregard the requirement for structured output and often outputs unnecessary things in a very casual manner. However, I have found that models like qwen 72b or others have better controllability in this aspect, at least reaching the level of gpt 3.5.
Temperature and light may create illusions in LLM. A potential available solution to this is to establish a knowledge graph based on sensor signals, where LLM is used to understand the speech signals given by humans and then interpret these signals as operations on the graph using similarity calculations.
No matter what n is, the answer to this problem on an n*n chessboard is basically cn^2. Due to the finitness of this problem, the optimal solution will repeat in a certain pattern in two directions. Additionally, c should be slightly smaller than 3/4, between 5/8 and 3/4.
