| --- |
| pretty_name: RE-PoLar |
| license: cc-by-nc-4.0 |
| language: |
| - en |
| tags: |
| - llm |
| - layer-skipping |
| - layer-repetition |
| - programs-of-layers |
| - mcts |
| - routing |
| - reproduction |
| - math-reasoning |
| task_categories: |
| - text-generation |
| size_categories: |
| - 10M<n<100M |
| configs: |
| - config_name: programs_qwen15_moe_a27b |
| field: samples |
| data_files: |
| - split: seed42 |
| path: mcts_results/qwen15_moe_a27b/seed42/*/merged_mcts_samples.json.gz |
| - split: seed1 |
| path: mcts_results/qwen15_moe_a27b/seed1/*/merged_mcts_samples.json.gz |
| - split: seed7 |
| path: mcts_results/qwen15_moe_a27b/seed7/*/merged_mcts_samples.json.gz |
| - config_name: programs_qwen25_3b |
| field: samples |
| data_files: |
| - split: seed42 |
| path: mcts_results/qwen25_3b/seed42/*/merged_mcts_samples.json.gz |
| - split: seed1 |
| path: mcts_results/qwen25_3b/seed1/*/merged_mcts_samples.json.gz |
| - split: seed7 |
| path: mcts_results/qwen25_3b/seed7/*/merged_mcts_samples.json.gz |
| - config_name: programs_qwen25_7b |
| field: samples |
| data_files: |
| - split: seed42 |
| path: mcts_results/qwen25_7b/seed42/*/merged_mcts_samples.json.gz |
| - split: seed1 |
| path: mcts_results/qwen25_7b/seed1/*/merged_mcts_samples.json.gz |
| - split: seed7 |
| path: mcts_results/qwen25_7b/seed7/*/merged_mcts_samples.json.gz |
| - config_name: programs_qwen3_8b |
| field: samples |
| data_files: |
| - split: seed42 |
| path: mcts_results/qwen3_8b/seed42/*/merged_mcts_samples.json.gz |
| - split: seed1 |
| path: mcts_results/qwen3_8b/seed1/*/merged_mcts_samples.json.gz |
| - split: seed7 |
| path: mcts_results/qwen3_8b/seed7/*/merged_mcts_samples.json.gz |
| - config_name: programs_qwen3_32b |
| field: samples |
| data_files: |
| - split: seed42 |
| path: mcts_results/qwen3_32b/seed42/*/merged_mcts_samples.json.gz |
| - split: seed1 |
| path: mcts_results/qwen3_32b/seed1/*/merged_mcts_samples.json.gz |
| - split: seed7 |
| path: mcts_results/qwen3_32b/seed7/*/merged_mcts_samples.json.gz |
| - config_name: programs_llama32_3b |
| field: samples |
| data_files: |
| - split: seed42 |
| path: mcts_results/llama32_3b/seed42/*/merged_mcts_samples.json.gz |
| - split: seed1 |
| path: mcts_results/llama32_3b/seed1/*/merged_mcts_samples.json.gz |
| - split: seed7 |
| path: mcts_results/llama32_3b/seed7/*/merged_mcts_samples.json.gz |
| - config_name: answers_qwen15_moe_a27b |
| data_files: |
| - split: seed42 |
| path: generated_answers/qwen15_moe_a27b/seed42/*.jsonl.gz |
| - split: seed1 |
| path: generated_answers/qwen15_moe_a27b/seed1/*.jsonl.gz |
| - split: seed7 |
| path: generated_answers/qwen15_moe_a27b/seed7/*.jsonl.gz |
| - config_name: answers_qwen25_3b |
| data_files: |
| - split: seed42 |
| path: generated_answers/qwen25_3b/seed42/*.jsonl.gz |
| - split: seed1 |
| path: generated_answers/qwen25_3b/seed1/*.jsonl.gz |
| - split: seed7 |
| path: generated_answers/qwen25_3b/seed7/*.jsonl.gz |
| - config_name: answers_qwen25_7b |
| data_files: |
| - split: seed42 |
| path: generated_answers/qwen25_7b/seed42/*.jsonl.gz |
| - split: seed1 |
| path: generated_answers/qwen25_7b/seed1/*.jsonl.gz |
| - split: seed7 |
| path: generated_answers/qwen25_7b/seed7/*.jsonl.gz |
| - config_name: answers_qwen3_8b |
| data_files: |
| - split: seed42 |
| path: generated_answers/qwen3_8b/seed42/*.jsonl.gz |
| - split: seed1 |
| path: generated_answers/qwen3_8b/seed1/*.jsonl.gz |
| - split: seed7 |
| path: generated_answers/qwen3_8b/seed7/*.jsonl.gz |
| - config_name: answers_qwen3_32b |
| data_files: |
| - split: seed42 |
| path: generated_answers/qwen3_32b/seed42/*.jsonl.gz |
| - split: seed1 |
| path: generated_answers/qwen3_32b/seed1/*.jsonl.gz |
| - split: seed7 |
| path: generated_answers/qwen3_32b/seed7/*.jsonl.gz |
| - config_name: answers_llama32_3b |
| data_files: |
| - split: seed42 |
| path: generated_answers/llama32_3b/seed42/*.jsonl.gz |
| - split: seed1 |
| path: generated_answers/llama32_3b/seed1/*.jsonl.gz |
| - split: seed7 |
| path: generated_answers/llama32_3b/seed7/*.jsonl.gz |
| - config_name: polar_split_programs_qwen15_moe_a27b |
| field: samples |
| data_files: |
| - split: polar_default_seed42 |
| path: polar_split/mcts_results/qwen15_moe_a27b/polar_default/seed42/*/merged_mcts_samples.json.gz |
| - split: polar_default_seed1 |
| path: polar_split/mcts_results/qwen15_moe_a27b/polar_default/seed1/*/merged_mcts_samples.json.gz |
| - split: polar_default_seed7 |
| path: polar_split/mcts_results/qwen15_moe_a27b/polar_default/seed7/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed42 |
| path: polar_split/mcts_results/qwen15_moe_a27b/oneshot/seed42/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed1 |
| path: polar_split/mcts_results/qwen15_moe_a27b/oneshot/seed1/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed7 |
| path: polar_split/mcts_results/qwen15_moe_a27b/oneshot/seed7/*/merged_mcts_samples.json.gz |
| - config_name: polar_split_programs_qwen25_3b |
| field: samples |
| data_files: |
| - split: polar_default_seed42 |
| path: polar_split/mcts_results/qwen25_3b/polar_default/seed42/*/merged_mcts_samples.json.gz |
| - split: polar_default_seed1 |
| path: polar_split/mcts_results/qwen25_3b/polar_default/seed1/*/merged_mcts_samples.json.gz |
| - split: polar_default_seed7 |
| path: polar_split/mcts_results/qwen25_3b/polar_default/seed7/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed42 |
| path: polar_split/mcts_results/qwen25_3b/oneshot/seed42/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed1 |
| path: polar_split/mcts_results/qwen25_3b/oneshot/seed1/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed7 |
| path: polar_split/mcts_results/qwen25_3b/oneshot/seed7/*/merged_mcts_samples.json.gz |
| - config_name: polar_split_programs_qwen3_8b |
| field: samples |
| data_files: |
| - split: polar_default_seed42 |
| path: polar_split/mcts_results/qwen3_8b/polar_default/seed42/*/merged_mcts_samples.json.gz |
| - split: polar_default_seed1 |
| path: polar_split/mcts_results/qwen3_8b/polar_default/seed1/*/merged_mcts_samples.json.gz |
| - split: polar_default_seed7 |
| path: polar_split/mcts_results/qwen3_8b/polar_default/seed7/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed42 |
| path: polar_split/mcts_results/qwen3_8b/oneshot/seed42/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed1 |
| path: polar_split/mcts_results/qwen3_8b/oneshot/seed1/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed7 |
| path: polar_split/mcts_results/qwen3_8b/oneshot/seed7/*/merged_mcts_samples.json.gz |
| - config_name: polar_split_programs_llama32_3b |
| field: samples |
| data_files: |
| - split: polar_default_seed42 |
| path: polar_split/mcts_results/llama32_3b/polar_default/seed42/*/merged_mcts_samples.json.gz |
| - split: polar_default_seed1 |
| path: polar_split/mcts_results/llama32_3b/polar_default/seed1/*/merged_mcts_samples.json.gz |
| - split: polar_default_seed7 |
| path: polar_split/mcts_results/llama32_3b/polar_default/seed7/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed42 |
| path: polar_split/mcts_results/llama32_3b/oneshot/seed42/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed1 |
| path: polar_split/mcts_results/llama32_3b/oneshot/seed1/*/merged_mcts_samples.json.gz |
| - split: oneshot_seed7 |
| path: polar_split/mcts_results/llama32_3b/oneshot/seed7/*/merged_mcts_samples.json.gz |
| --- |
| |
| # RE-PoLar: every program-of-layers our searches evaluated |
|
|
| - **Authors:** Justus Westerhoff\*, Stephan Olbrich\*, Hatem Oraby, Walter Senn, Matthew E. Larkum, Felix Alexander Gers |
| - \*Shared first authorship; order chosen at random. |
| - **Affiliations:** Berliner Hochschule für Technik (BHT), Humboldt-Universität zu Berlin, University of Bern |
| - **Project page (interactive search-tree explorer):** https://datexis.github.io/RE-PoLar/ |
| - **Code:** https://github.com/DATEXIS/RE-PoLar |
| - **Paper:** [*Programs-of-Layers in LLMs through the Lens of Cortical Areas*](https://arxiv.org/abs/2609.31360) |
| - **Reproduced work:** [PoLar](https://arxiv.org/abs/2606.06574) (Li et al., ICML 2026) |
| |
| ## Overview |
| |
| A *program-of-layers* runs a transformer's layers in a different order than the standard |
| forward pass: some layers are skipped, some segments repeated. PoLar finds such programs per |
| question with a Monte Carlo Tree Search (MCTS) and trains a router that predicts one from the |
| question. This dataset holds everything our reproduction's searches, routers and fixed |
| programs produced: |
|
|
| - **Main track** (our DART-Math split, our search, `oneshot` prompt): 6 models × 3 search |
| seeds × 5 difficulty levels × 2,000 questions. Every program each search evaluated, with |
| its verdict (**56.6M programs in the whole dataset, 4.6M of them solving their question**), |
| the model's generated answer behind each verdict (53.2M answers), the trained routers |
| and their test results, the best fixed program per level, and the menu cross-execution. |
| - **PoLar split** (`polar_split/`, paper Appendix B): Li et al.'s released search on their own |
| MATH question sets, 4 models × 2 prompts (`polar_default`, `oneshot`) × 3 seeds, with |
| 4-fold cross-validated routers and fixed programs, and routers evaluated out of |
| distribution (ASDiv, MAWPS, MMLU-Pro). |
| - **Cross-checks** (`cross_checks/`): their search on our split and our search on theirs. |
|
|
| Models: Qwen1.5-MoE-A2.7B-Chat, Qwen2.5-3B-Instruct, Qwen2.5-7B-Instruct, Qwen3-8B, Qwen3-32B, |
| LLaMA-3.2-3B-Instruct. |
|
|
| <p align="center"><img src="assets/method_overview.png" width="720" alt="A router reads the prompt and picks a per-layer skip/keep/repeat program before the frozen transformer runs."></p> |
|
|
| ## Explore the search trees |
|
|
| The dataset viewer above shows the searches as tables: pick `programs_<model>` for the |
| programs and verdicts of each question (split = search seed), `answers_<model>` for the |
| generated answers, `polar_split_programs_<model>` for the PoLar split. The search trees |
| themselves, node by node, are on the |
| [project page's interactive explorer](https://datexis.github.io/RE-PoLar/). |
|
|
| ## Layout |
|
|
| ``` |
| mcts_results/<model>/seed<S>/dart-math-diff-<L>/merged_mcts_samples.json.gz programs + verdicts per question |
| generated_answers/<model>/seed<S>/diff<L>.jsonl.gz one generated answer per evaluation |
| router_checkpoints/<model>/seed<S>/diff<L>.pt trained routers (weights only) |
| router_results/<model>/seed<S>/diff<L>.json router test results, per question |
| fixed_program/<model>/seed<S>/diff<L>.json fixed-program baseline, per question |
| menu_crossexec/<model>/diff<L>.json.gz top-100 programs x 2,000 questions |
| menu_crossexec_heldout/<model>/diff<L>.json.gz top-100 by train+val, run on the 500 test questions |
| polar_split/... same artifacts under <model>/<prompt>/seed<S>/ |
| cross_checks/{their_search_our_split,our_search_polar_split}/... |
| DATA.md full schema of every file |
| ``` |
|
|
| `<model>`: `qwen15_moe_a27b`, `qwen25_3b`, `qwen25_7b`, `qwen3_8b`, `qwen3_32b`, `llama32_3b`; |
| `<S>`: search seed 42, 1, 7; `<L>`: difficulty level 1-5. [`DATA.md`](DATA.md) documents every |
| field, the search configurations and which runs have no answer texts. |
|
|
| ## Download and use |
|
|
| The code expects the files under `data/` of a clone of the repository: |
|
|
| ```bash |
| git clone https://github.com/DATEXIS/RE-PoLar && cd RE-PoLar |
| pip install -U huggingface_hub |
| hf download SWAMBIT/re-polar --repo-type dataset --local-dir data # everything, ~6 GB |
| hf download SWAMBIT/re-polar --repo-type dataset --local-dir data --include "router_results/*" "fixed_program/*" |
| ``` |
|
|
| One file with the `datasets` library, or directly: |
|
|
| ```python |
| from datasets import load_dataset |
| programs = load_dataset("SWAMBIT/re-polar", "programs_qwen3_8b", split="seed42") |
| print(programs[0]["sample_info"]["query_id"], len(programs[0]["final_valid_transitions"])) |
| |
| import gzip, json |
| router = json.load(open("data/router_results/qwen3_8b/seed42/diff1.json")) |
| print(router["overall"]) # Base tau=0, router p@1 and p@5 on the 500 test questions |
| with gzip.open("data/generated_answers/qwen3_8b/seed42/diff1.jsonl.gz", "rt") as f: |
| print(json.loads(next(f))) |
| ``` |
|
|
| ## Questions are not included |
|
|
| No file holds question text or reference answers, only `query_id`s. The MATH half of the |
| DART-Math pool traces back to the delisted `hendrycks/competition_math`, so the questions are |
| rebuilt locally from the public pool with the repository's code and joined on `query_id` |
| (`re_polar.datasets.dart_math`, `re_polar.datasets.polar_split`, |
| `re_polar.datasets.attach_mcts_questions`; see the repository README). The models sometimes |
| restate their question in a generated answer; such restatements are replaced by |
| `[question]` (DATA.md, "Generated text"). |
|
|
| ## Citation |
|
|
| ```bibtex |
| @article{westerhoff2026repolar, |
| title={Programs-of-Layers in LLMs through the Lens of Cortical Areas}, |
| author={Westerhoff, Justus and Olbrich, Stephan and Oraby, Hatem and Senn, Walter and Larkum, Matthew Evan and Gers, Felix Alexander}, |
| journal={arXiv preprint arXiv:2609.31360}, |
| year={2026} |
| } |
| ``` |
|
|
| ## License |
|
|
| **CC BY-NC 4.0.** The generated answers and verdicts are outputs of the models above and |
| also fall under their licenses: Qwen1.5-MoE-A2.7B-Chat (Tongyi Qianwen License), |
| Qwen2.5-3B-Instruct (Qwen Research License), Qwen2.5-7B-Instruct, Qwen3-8B and Qwen3-32B |
| (Apache 2.0), LLaMA-3.2-3B-Instruct (Llama 3.2 Community License; Built with Llama). The routers embed |
| questions with Qwen3-Embedding-0.6B (Apache 2.0). The code is MIT-licensed, see the repository. |
|
|
