Create README.md

README.md

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+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])
+```