# RealSR Benchmark v2 ## 1. Directory layout ``` hf_realsr_benchmark_v2/ ├── harness/evaluation/ # shared, generic — one copy for all tasks │ ├── eval_formula.py # execution engine: run a formula → raw metrics │ └── evaluate.py # driver: `reference` / `score` modes └── // ├── metadata.yaml # task definition (see §3) ├── prep_data.py # data_raw/ → data/ ├── data_raw/ # raw data + download.sh + parse script ├── reference/ # paper PDFs + .txt + summary_*.md ├── data/ # Type I : train.csv + test.csv │ # Type II: train.csv + test_fit.csv + test_test.csv └── formulas/ ├── .py # one reference-baseline formula per file ├── __init__.py # REGISTRY of the formula bank └── reference_metrics.json # GENERATED by `evaluate.py reference` ``` A task directory holds **no evaluation code** — only inputs (data, formulas, metadata). The harness is generic and takes a task directory as an argument. --- ## 2. The `formula.py` contract What a reference baseline — or an SR submission — exposes: ```python USED_INPUTS = ["x1", "x2", ...] # input column names actually used LAW_CONSTANTS = {"c_mu": 0.087, ...} # the scientific claim — paper-published, # frozen. The only field scored by the # LLM-judge constant channel. May be {}. OTHER_CONSTANTS = {"e2": 1.44, ...} # every other constant the formula consumes # (universal physics, unit factors, fixed # operator coefficients). Declared so audits # can count them; NOT scored. No bare `_FOO` # module constants — declare everything here. LOCAL_FITTABLE = {} # Type I: empty. # Type II: {"r": {"init": ...}, ...} # init = scalar (single start) # | list (multi-start seeds) # | None (closed-form fit) def fit(X_fit, y_fit, **law_constants): # Type II only — omit for Type I return {"r": ...} # keys MUST equal LOCAL_FITTABLE.keys() def predict(X, **params): # params = LAW_CONSTANTS ∪ this cluster's LOCAL # NO group_id argument — structurally prevents lookup-table cheating. # OTHER_CONSTANTS are read from the module namespace, not passed as kwargs. return y_pred ``` The harness performs **zero fitting on `train.csv`**. LAW_CONSTANTS are frozen paper values (reference) or LLM-submitted values (submission). LOCAL_FITTABLE parameters are fitted by the submission's own `fit()`, once per Type II cluster. --- ## 3. `metadata.yaml` fields ```yaml task_id / domain / license # identity type: typeI | typeII # drives the evaluation path has_group_id: bool context: >- … # prompt slot — background knowledge only # (no instructions, no columns, no priors) target: {name, symbol, unit, description, range} inputs: [{name, symbol, unit, description, range}, ...] # also the data_description source data_files: {train, test} or {train, test_fit, test_test} n_train / n_test / ... priors: # prompt slot — candidate constants - {name, value, unit, description, source, _role} # _role: candidate | distractor references: # the reference-baseline bank - {id, label, formula_file, reference_pdf, n_law_constants, n_other_constants, n_local_params, measured: {: value, ...}} # measured on test — hand-recorded caps: {max_law_constants, max_local_params, # mirror the reference bank max_init_size_per_param, fit_timeout_seconds} metric: rmse | r2 | mdape | ... # scoring metric (task-declared) best_baseline: # metric value of the strongest reference # — the 0.5 score anchor ``` **Not in metadata**: `task_description` (a global prompt, identical for every task) and `data_description` (rendered from `target` + `inputs` at prompt-assembly time). No `reference_baseline_id` / `naive_predictor` — the harness anchors scoring on the empirically best reference. --- ## 4. The prompt — a 4-slot template The prompt shown to an SR system is assembled from four slots, so any one can be dropped for ablation experiments: | Slot | Source | Content | |---|---|---| | `task_description` | global (not per-task) | contract instructions — what to submit | | `context` | `metadata.context` | domain background knowledge — the science | | `data_description` | rendered from `target` + `inputs` | what the data columns are | | `priors` | `metadata.priors` | candidate constants, genuine + distractors | `priors` lists genuinely useful constants mixed with distractors; both candidates and distractors must be traceable to the reference materials. The SR system must *select* which priors are relevant. --- ## 5. Train / test split | Type | Split | Data files | |---|---|---| | Type I | feature-axis OOD (e.g. nuclear: proton number Z ≤ 82 vs ≥ 83) | `train.csv`, `test.csv` | | Type II | cluster holdout — whole clusters held out — plus a within-cluster fit/test split | `train.csv`, `test_fit.csv`, `test_test.csv` | For Type II, `test_fit.csv` / `test_test.csv` both carry `group_id`; the harness groups by it. `submission.fit()` sees a cluster's `test_fit` rows; `submission.predict()` is scored on the disjoint `test_test` rows. All data must be real measurements (anti-fabrication: reference PDFs physically present, every cited constant locatable in its paper, data scripts actually run). --- ## 6. Evaluation — `evaluate.py` ``` # build the reference anchors (task setup, run once): python harness/evaluation/evaluate.py reference / # score a submitted formula.py: python harness/evaluation/evaluate.py score / # no submission → self-test: score each reference baseline as a submission python harness/evaluation/evaluate.py score / ``` `reference` mode runs the reference bank through `eval_formula`, writes `formulas/reference_metrics.json` (raw metrics + derived caps). `score` mode = contract check → `eval_formula` → reference-relative score. **Scoring model** — anchored on the empirically best reference baseline (no naive baseline): ``` lower-is-better metric: score = clip(1 - 0.5 * sub / best_ref, 0, 1) higher-is-better (r2) : score = clip(0.5 + 0.5 * (sub - ref)/(1 - ref), 0, 1) best reference baseline → 0.5 perfect prediction → 1.0 error = 2 × best ref → 0 ``` Type II computes the score per cluster and takes the equal-weight mean. The LLM-judge channels (constant recovery, form match) are not yet wired — `total` currently equals the numeric score. --- ## 7. Anti-dump caps A submission may be at most as complex as the most complex reference formula. The harness **derives** the caps from the reference bank (no hand-set values): ``` max_law_constants = max len(LAW_CONSTANTS) over the bank max_local_params = max len(LOCAL_FITTABLE) over the bank max_init_size_per_param = max init-array length (floor 1) fit_timeout_seconds = slowest reference fit × safety factor (Type II); None for Type I ``` Combined with the no-`group_id` `predict` signature, these block the regression-dump failure mode (a fitted lookup table masquerading as a formula). --- ## 8. Tasks present | Task | Type | Size | Reference bank | Status | |---|---|---|---|---| | `astronomy/nuclear_binding_energy_ame2020__BE_per_A` | I | 2078 train / 470 test | weizsacker_1935, duflo_1995, moller_1995, wang_2014 | complete | | `social_science/income_distribution_wid__pareto_alpha` | II | 47k rows / 40 test clusters | atkinson_2011, gabaix_2016, reed_2001 | metadata pending v2 convergence | --- ## 9. Known TODO - The global `task_description` prompt text (§4 slot 1) is not yet written. - `data_description` rendering from `target` + `inputs` is not yet implemented in the harness (§4 slot 3). - LLM-judge channels (constant recovery, form match) are stubbed in `evaluate.py`; `total` currently equals the numeric score. - This README is now the authoritative v2 spec — the design proposals it superseded have been removed. `CLAUDE.md` and `task_formulation.html` still reference the deleted v0.5 proposal and need reconciliation.