LocaLeJEPA: Matching a uniform-ball prior within representation clusters¶

L1 regularizer and gradient mechanism; diagnostic only. Full visual representation training not reproduced.

Paper information¶

Field	Details
Paper	LocaLeJEPA: Maximum Entropy Representations under Geometric Priors
Affiliations	Co-first authors Kartik Tandon: University of Pennsylvania; Alessio Borgi: Sapienza University of Rome and University of Cambridge.
First public release	2026-10-20 16:15:06 UTC
Author code	alessioborgi/LocaLeJEPA, MIT, formula review at `771361c18d37e65df3dc188761ffb26751ce4e37`.
Local key	`locale-jepa`; no adapter
Local code	`src/auto_research/foundation_models/locale_jepa.py`
Local evidence	Local mechanism metrics; A100 validation receipt

What the paper changes¶

A global isotropic Gaussian can be unsuitable for manifold, hyperbolic or equivariant geometry. Cluster detached multiview means with cosine-like k-means, share labels across views and recenter each view within a cluster. Retain clusters of size at least four; if none qualify, use the whole batch and record fallback. Cluster centers need not approach one common origin.

Original paper figure¶

Original Figure 2: Multiview prediction and local matching

The figure labels clustering “KNN,” but the text and source use k-means. See figure provenance.

Core equations¶

\[ r_i^{(v)}=z_i^{(v)}-\mu_q^{(v)},\qquad \mu_q^{(v)}=|C_q|^{-1}\sum_{j\in C_q}z_j^{(v)}. \]

\[ D_{q,v}=|C_q|\,\mathbb E_u\int_{\mathbb R} |\widehat\phi_{q,v,u}(t)-\phi_Y(t)|^2e^{-t^2/2}\,dt, \qquad \mathcal L_{\mathrm{LocaLeReg}}= \frac{1}{|Q|V}\sum_{q\in Q}\sum_v D_{q,v}. \]

\[ \mathcal L=(1-\lambda)\frac{1}{NVd}\sum_{i,v}\|z_i^{(v)}-\bar z_i\|^2 +\lambda\mathcal L_{\mathrm{LocaLeReg}}. \]

The target is uniform on a ball of radius \(\sqrt{d+2}\), giving identity covariance. Compute projected characteristic functions from the ball cross-section; the Gaussian factor is only the integration window. Defaults: 256 directions, 17 nodes, trapezoids on [0,3] doubled by symmetry. Multiply each cluster's statistic by its own size then average clusters/views equally; changing K also changes effective strength.

Results reported by the authors¶

Fixed v1 Table 2 Euclidean ViT-S/8 ImageNet-1K linear top-1: LeJEPA 44.6±0.23%, matched optimization 51.6±0.28%, LocaLeJEPA 62.1±0.27% (\(\lambda=0.1,K=4\)). Upstream README values differ; these are paper results, not local or production A/B.

Local reproduction and limits¶

uniform_ball_cf, ballreg_loss, torch_kmeans_labels, local_ballreg_loss and locale_jepa_loss use pure Torch clustering. Only assignments are detached, not prediction means or residuals. Runner uses 64 width-eight vectors, two views and a small linear projector. Independent sinc, quadrature, translation-after-clustering, detachment, equal cluster reduction and fallback checks; clustering itself is not translation invariant or globally optimal. Record seed/gradient/cluster/source/data/device; no fallback from CUDA or benchmark/Evolve claim.

PYTHONPATH=src python scripts/run_oct21_locale_jepa.py \
  --device cpu --seeds 42,43,44 --steps 8 \
  --output runs/locale-jepa-cpu.json

Full experiment: not reproduced¶

ImageNet-1K 100 epochs, Imagenette 800-epoch topology study, eight-GPU ViT-L/14, seven transfer datasets and a probe grid. No weights/data, full run or retry.

Additional references¶

Paper PDF · Paper PDF, p. 3