Datasets:

amorarc
/

func-jepa-data

license: mit
pretty_name: Func-JEPA data
tags:
  - symbolic-mathematics
  - synthetic
  - functions
  - symbolic-regression
size_categories:
  - 1M<n<10M

Func-JEPA data

Synthetic datasets of univariate mathematical functions used in Func-JEPA: Learning a Sobolev Space of Functions as Latent Vectors (Alejandro Moreno Arcas, 2026). Code: https://github.com/amorarc/Func-JEPA · Model: https://huggingface.co/amorarc/func-jepa

All functions were generated with SymPy by the code of the repository (docs/DATA.md there describes the generator, the families, and the build sequence). Download into the layout that the scripts expect:

huggingface-cli download amorarc/func-jepa-data --repo-type dataset --local-dir data

Folder	Train / val / test	Interval	Used for
`v4/`	2,000,001 / 20,410 / 20,406	`[-π, π]`	pretraining corpus of the encoder `encoder_pi`, training data of every module
`v3_test_clean/`	– / – / 12,146	`[-π, π]`	test set of every table in the paper (no function of it is in `v4` train)
`compose_v3/`	4,166,692 / 20,009 / 19,975 pairs	`[-π, π]`	composition pairs `(g, h(g))` for `h` in sin, cos, log, sqrt, square, cube, quadratic
`v05/`	2,000,001 / 20,410 / 20,410	`[0, 5]`	pretraining corpus of the second encoder `encoder_05`

Format

NumPy .npz files (no pickled objects) plus a meta.json with the vocabulary, the generator configuration, and the sizes. In the function datasets, row i holds a function f and its first two derivatives:

Array	Shape	Content
`tokens`, `lens`	`(N, 3, 128)` uint8, `(N, 3)`	prefix token ids of `f`, `f'`, `f''`, padded; vocabulary in `meta.json`
`vals`	`(N, 3, 64)` float32	values at the 64 Gauss–Legendre nodes of the interval
`norms`	`(N, 3)` float32	L² norms, with quadrature weights normalised to sum 1
`family`	`(N,)`	generating family (id order in `meta.json["families"]`)
`group`, `sweep`, `sweep_param`, `sweep_value`	`(N,)`	equivalence group (rewritings of one function), coefficient sweep and swept value; `-1` = none
`ode`	`(N, 5)`	integer coefficients of the linear ODE the function solves (ODE family), else zeros
`edeg`, `has_d2`	`(N,)`	effective Legendre degree; whether `f''` is stored

compose_v3 files hold, per pair, the operator id op, the inner function (g_tokens, g_lens, g_idx = row in the first corpus), the composed function (tokens, lens, vals, norms), the coefficients coef of the quadratic, and g_lift (the inner function was shifted by a constant to keep log g and sqrt g defined).

Read a row with the repository:

from fjepa.data import FunctionDataset
ds = FunctionDataset("data/v3_test_clean", "test")
ds.prefix(0, 0)            # prefix tokens of f (use 1 for f')

Notes

Only f and f' are used for pretraining; f'' is used for zero-shot tests.
v4 is a length- and class-resampled re-split of a merged pool; its validation and test splits are not disjoint from the earlier corpus v3, which is why the paper reports on v3_test_clean.
The latent caches used by the training scripts are not included; they are recomputed from these files with the frozen encoder (python -m fjepa.decoder_data, python -m fjepa.compose_data encode).

Func-JEPA data

Contents

Format

Notes