amorarc/func-jepa-data

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

Contents

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).