symbolic_data

The model-agnostic symbolic-regression data layer, carved out of flash-ansr: skeleton/expression sampling, priors, (X, y) support sampling, holdout management, and dataset construction.

Both symbolic-regression methods (for training holdout) and the srbf eval framework depend on it, so training, holdout, and evaluation draw from one source of truth. Its only heavy dependency is simplipy; otherwise just numpy/sklearn plus huggingface_hub (for resolving versioned catalogs from the HF asset repo).

Publications

• Saegert & Köthe 2026, Breaking the Simplification Bottleneck in Amortized Neural Symbolic Regression (ICML 2026) https://arxiv.org/abs/2602.08885

Install

pip install symbolic-data

Quick start

import symbolic_data

# 1. Load a curated catalog (level 1: expressions + their intrinsic per-variable sampling). The
#    curated sets are Hugging Face artifacts (not bundled in the wheel): a bare `name` needs network
#    on first use, then caches; pass an explicit local path for offline use. `load_catalog("name@version")`
#    resolves a versioned catalog from the HF manifest, and `load_catalog("user/repo:name")` loads a
#    third party's published catalog.
feynman = symbolic_data.load_catalog("feynman")            # 100 equations (Udrescu & Tegmark 2020)
entry = feynman["I.6.2a"]
entry.prepared, entry.variables                            # expression + intrinsic per-variable sampling

# 2. Draw (X, y) Problems from a ProblemSource (level 2). Mode is inferred from the config:
#    a declarative/frozen `catalog` ref (set), a generative `catalog` ref (generate, on-the-fly),
#    or inline `problems` (fixed).
src = symbolic_data.ProblemSource({"catalog": "feynman",
                                   "sampling": {"n_support": 32, "n_validation": 32, "noise": 0.01}})
for problem in src:
    if problem.is_placeholder:                                                        # a slot the source could not fill (recorded, not skipped)
        continue
    problem.x_support, problem.y_support, problem.y_support_noisy, problem.expression  # fit / tokenize

# 3. Freeze for exact reproduction (no seeds): materialize() -> a fixed source that re-iterates
#    byte-identical Problems, identical across models/runs.
frozen = src.materialize()

Extensibility

Distributions are pluggable via a registry: in-process with @symbolic_data.DISTRIBUTIONS.register("name"), or across packages via an importlib.metadata entry point in the symbolic_data.distributions group. A registered name drops into the same {"name": ..., "kwargs": ...} config slot as a builtin (e.g. the fastsrb distribution).

Catalogs are extensible through the resolver: publish your own to a Hugging Face dataset repo with a manifest.json, then symbolic_data.load_catalog("your-user/your-repo:name@version").

Versioning / reproducibility

Reproducibility comes from fixed data, not seeds: sampling draws from a threaded numpy.random.Generator (entropy by default), and exact reproduction across runs/models is obtained from a fixed (materialized) catalog rather than by re-seeding. Versioned catalogs resolve from Hugging Face with a pinned revision and a sha256 integrity check. Catalogs are HF artifacts (not bundled in the wheel): a bare name needs network on first use, then caches; pass an explicit local path for fully offline operation.

The public stack: Problem, the unified distribution framework (incl. the fastsrb distribution), and the Catalog a ProblemSource samples from -- either a declarative ProblemCatalog (+ load_catalog + the versioned HF resolver) or an on-the-fly GenerativeCatalog (LampleChartonCatalog: random unary-binary operator trees; build_catalog dispatches a catalog: {type: ...} config). ProblemSource adds the usage policy (draw method, support/validation counts, noise, holdouts/filters, problems_per_expression, unbounded streaming, materialize() + to_catalog() for frozen, byte-reproducible catalogs). Generate-mode is fully Generator-driven (no global np.random); the public generative face is LampleChartonCatalog. Curated catalogs (FastSRB, Feynman, Nguyen) are published to the HF assets repo and resolved by name (not bundled in the wheel). CLI: symbolic-data materialize.

Deferred: a frozen holdout grid; functional-equivalence exclude (currently exact normalized-expression match).

Licensing

The repository is MIT-licensed (see LICENSE) with one carve-out: everything under assets_sa/ is CC BY-SA 4.0 (OEIS-/Wikipedia-derived benchmark catalogs; see assets_sa/LICENSE for the full legal code + derivation statement). Vendored upstream data under assets/upstream/*/ carries per-directory NOTICE + license files; THIRD_PARTY_LICENSES has the summary table. The share-alike catalogs publish to a separate HF repo (psaegert/symbolic-data-assets-sa), never mixed into the permissive artifact repo.