About the synthetic data generation

[yeppp27]

Hi, thanks for your great work. And I observe that the synthetic data is generate though ``a simple breadth-first-search (BFS) manner" in the appendix B.1:
(i) a simple breadth-first-search (BFS) manner, obtaining a search tree Tq similar to the one of the (i)
self-training process. Subsequently, we verify the obtained answers of all leaf nodes of Tq according to a(i). The verified search trees are then used to derive data samples with target values for D .

Can you provide the code for this process?

[zhoubiansining]

This process is almost the same as the generation process in self_train/generation/generate_both_samples_MATH.py except that you don't need a vm or the MCTS* algorithm. This means you may simply do expansion layer by layer like bfs and randomly select some nodes to further do expansion. The verification process is identical. You can refer to self_train/generation/generate_both_samples_MATH.py for replication.

[yeppp27]

Thanks for your response! Does the 'PVM' mode in the Monte Carlo Tree Search (MCTS) process omit the rollout phase?

[zhoubiansining]

In fact, we retain the rollout phase to ensure accurate value estimation. But since we have a vm, we only simulate a few steps and estimate the value with the vm. You can adjust the number of rollout steps using the argument roll_forward_steps. If you want to increase efficiency, you may also remove this process.