# Sigreg

> Sketched Isotropic Gaussian Regularization primitive. Scalar loss matching the embedding distribution to a standard-normal target via Cramér-Wold slicing and the Epps-Pulley empirical characteristic function test. Port of rbalestr-lab/lejepa (MIT). Default-off in v1.49.571.

- Skill: `majiayu000/sigreg` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds add majiayu000/sigreg`
- Raw SKILL.md: https://api.skillmd.com/api/skills/majiayu000/sigreg/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: majiayu000 (https://skillmd.com/u/majiayu000)
- Updated: 2026-09-09
- Page: https://skillmd.com/skills/majiayu000/sigreg

---


# SIGReg — Sketched Isotropic Gaussian Regularization

Port of SIGReg from Balestriero & LeCun (2025, *LeJEPA*) arXiv:2511.08544v3. The
primitive computes a scalar loss measuring how far an embedding distribution is
from the standard-normal target, using Cramér-Wold slicing plus the Epps-Pulley
empirical characteristic function test. Linear O(N·M·K) time, naturally
differentiable, multi-GPU friendly (all_reduce over ECF averages).

## Public API

```typescript
import { sigreg } from './src/sigreg/index.js';

const loss = sigreg(embeddings);  // embeddings: number[num_samples][num_dims]
// scalar loss; use as L_total = L_pred + λ · loss
```

For telemetry:

```typescript
import { sigregWithBreakdown } from './src/sigreg/index.js';

const { loss, perSliceStatistic, maxSliceStatistic, runTag } = sigregWithBreakdown(embeddings);
```

## Configuration

Default matches the LeJEPA reference implementation:

```typescript
const LEJEPA_DEFAULT_CONFIG = {
  numSlices: 1024,
  univariateTest: { numPoints: 17, sigma: 1.0 },
};
```

## Feature flag

Default-off. Opt-in via `.claude/gsd-skill-creator.json`:

```json
{
  "heuristics-free-skill-space": {
    "sigreg": { "enabled": true }
  }
}
```

## Attribution

Ported from https://github.com/rbalestr-lab/lejepa under the MIT license.
© Randall Balestriero and LeJEPA Contributors. See `../../license_notices.md`.

## Related modules

- `src/skill-isotropy/` — Skill Space Isotropy Audit (Phase 728) — read-only audit use case
- `src/intrinsic-telemetry/` — Phase 733 — SIGReg-on-embeddings is a candidate signal