README.md

ORMs are trained to predict the correctness of the whole solution on the position of "\<eos\>".
But they are actually trained to forcast the correctness of the whole solution on each token (i.e., token-level loss).

Usage:

```python
import torch
from transformers import AutoTokenizer, AutoModelForCausalLM

model_name = "ScalableMath/llemma-7b-orm-prm800k-level-1to3-hf"
model = AutoModelForCausalLM.from_pretrained(model_name, torch_dtype=torch.bfloat16, device_map="auto")

tokenizer = AutoTokenizer.from_pretrained("EleutherAI/llemma_7b")

qa_example = """# Question

Convert the point $(0,3)$ in rectangular coordinates to polar coordinates.  Enter your answer in the form $(r,\theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$

# Solution

To convert from rectangular to polar coordinates, I need to use the formulas $r = \sqrt{x^2 + y^2}$ and $\theta = \tan^{-1}(y/x).$

In this case, $x = 0$ and $y = 3,$ so I can plug them into the formulas.

For $r,$ I get $r = \sqrt{0^2 + 3^2} = \sqrt{9} = 3.$

For $\theta,$ I get $\theta = \tan^{-1}(3/0).$

This is undefined, since the tangent function is not defined at $0.$

However, I can use the fact that the point $(0,3)$ lies on the positive $y$-axis, which has an angle of $\pi/2$ radians or $90^\circ.$

Therefore, I can choose any angle in the range $(0,\pi/2)$ as the value of $\theta.$

I will choose $\theta = \pi/2,$ since it is the simplest and most natural choice.

Therefore, the polar coordinates of the point $(0,3)$ are $(3,\pi/2).$

# Answer

(3,\pi/2)"""

begin_solution_tokens = tokenizer.encode("\n\n# Solution", add_special_tokens=False)[1:]
scoring_tokens = tokenizer.encode("\n\n", add_special_tokens=False)[1:]
eos_token = tokenizer.eos_token_id

input_ids = tokenizer.encode(qa_example)

begin_solution_flag = False

candidate_positions = []

for start_idx in range(len(input_ids)):
    if tuple(input_ids[start_idx:start_idx+len(begin_solution_tokens)]) == tuple(begin_solution_tokens):
        begin_solution_flag = True

    if begin_solution_flag and tuple(input_ids[start_idx:start_idx+len(scoring_tokens)]) == tuple(scoring_tokens):
        candidate_positions.append(start_idx)

    if input_ids[start_idx] == eos_token:
        candidate_positions.append(start_idx)
        break

# maybe delete the first and the second to last candidate_positions
# because they are "\n\n" after "# Solution" and after "# Answer"
del candidate_positions[0]
del candidate_positions[-2]

input_tensor = torch.tensor([input_ids])
candidate_positions = torch.tensor(candidate_positions)

with torch.no_grad():
    logits = model(input_tensor).logits
    scores =logits.mean(dim=-1)
    step_scores = scores[0][candidate_positions]
    step_probs = torch.sigmoid(step_scores)

print(step_probs)

# only the last logprob is orm's output
# tensor([0.4531, 0.3882, 0.3748, 0.4785, 0.4087, 0.3166, 0.3040, 0.2295, 0.2628, 0.2568])
```