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
└── <primary>/<task_id>/
├── 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/
├── <paper>.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:
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
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: {<metric>: 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: <number> # 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 <primary>/<task_id>
# score a submitted formula.py:
python harness/evaluation/evaluate.py score <primary>/<task_id> <submission.py>
# no submission → self-test: score each reference baseline as a submission
python harness/evaluation/evaluate.py score <primary>/<task_id>
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_descriptionprompt text (§4 slot 1) is not yet written. data_descriptionrendering fromtarget+inputsis not yet implemented in the harness (§4 slot 3).- LLM-judge channels (constant recovery, form match) are stubbed in
evaluate.py;totalcurrently equals the numeric score. - This README is now the authoritative v2 spec — the design proposals it
superseded have been removed.
CLAUDE.mdandtask_formulation.htmlstill reference the deleted v0.5 proposal and need reconciliation.