Added gpt-4o baseline tutorial

Author: jamesbraza

README.md

@@ -128,3 +128,70 @@ or in your terminal via `chafa valid_molecule.svg`
 ([chafa docs](https://hpjansson.org/chafa/)).
 
 ![valid molecule](docs/assets/valid_molecule.svg)
+
+### Benchmark
+
+Here is a sample baseline of
+[`ether0-benchmark`](https://huggingface.co/datasets/futurehouse/ether0-benchmark)
+on `gpt-4o` using [`lmi`](https://github.com/Future-House/ldp/tree/main/packages/lmi).
+To install `lmi`, please install `ether0` with the `baselines` extra
+(for example `uv sync --extra baselines`).
+
+We also need to run our remote rewards server via `ether0-serve`
+(for more information, see [`ether0.remotes` docs](packages/remotes/README.md)):
+
+```bash
+ETHER0_REMOTES_API_TOKEN=abc123 ether0-serve
+```
+
+Next, start `ipython`: with the relevant environment variables set:
+
+```bash
+ETHER0_REMOTES_API_BASE_URL="http://127.0.0.1:8000" ETHER0_REMOTES_API_TOKEN=abc123 ipython
+```
+
+And run the following Python code:
+
+```python
+import itertools
+import statistics
+from collections import defaultdict
+
+from aviary.core import Message
+from datasets import load_dataset
+from lmi import LiteLLMModel
+from tqdm.asyncio import tqdm_asyncio as asyncio
+
+from ether0.data import get_problem_category
+from ether0.model_prompts import LOOSE_XML_ANSWER_USER_PROMPT, extract_answer_loose
+from ether0.models import RewardFunctionInfo
+from ether0.rewards import EVAL_FUNCTIONS
+
+# Add LLM prompt of your making to the dataset
+test_ds = load_dataset("futurehouse/ether0-benchmark", split="test").map(
+    lambda x: {"prompt": "\n\n".join((LOOSE_XML_ANSWER_USER_PROMPT, x["problem"]))}
+)
+
+# Prompt to LLM
+model = LiteLLMModel(name="gpt-4o")
+results = await asyncio.gather(
+    *(model.acompletion([Message(content=row["prompt"])]) for row in test_ds),
+    desc="Running evaluation",
+)
+
+# Compute rewards
+per_category_rewards = defaultdict(list)
+for row, result in zip(test_ds, results, strict=True):
+    reward_info = RewardFunctionInfo.model_validate(row["solution"])
+    yhat = extract_answer_loose(result[0].text)
+    reward = EVAL_FUNCTIONS[reward_info.fxn_name](yhat=yhat, y=reward_info.answer_info)
+    per_category_rewards[get_problem_category(reward_info.problem_type)].append(reward)
+
+for category, rewards in sorted(per_category_rewards.items()):
+    print(
+        f"In category {category!r} of {len(rewards)} questions,"
+        f" average reward was {statistics.mean(rewards):.3f}."
+    )
+accuracy = statistics.mean(itertools.chain.from_iterable(per_category_rewards.values()))
+print(f"Cumulative average reward across {len(test_ds)} questions was {accuracy:.3f}.")
+```