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

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:

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

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

Configuration

Default matches the LeJEPA reference implementation:

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

Feature flag

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