---
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:

```bash
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:

```python
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`).