LeCun Paper Proves JEPAs Converge to Same Representation

Randall Balestriero and Yann LeCun have published a formal proof that Joint-Embedding Predictive Architectures (JEPAs) trained on different modalities converge to identical representations up to a single rotation. The paper, posted to arXiv on October 29, 2026, transforms the Platonic Representation Hypothesis from speculation into a mathematical theorem under specific conditions.

Officially released on October 29, 2026, the research demonstrates that a 109-million-parameter text JEPA outperforms language models up to 72 billion parameters on alignment metrics while requiring 42 times fewer training samples than next-token prediction methods.

The Formal Proof

The theorem applies when positive pairs represent two observations of a single world state, what the authors term good views, with bounded misalignment between observations. Under these constraints, the paper argues that separate training problems across modalities reduce to the same optimization written in different coordinate systems. The solution spaces therefore coincide up to a rotation matrix.

This formalization addresses a question that has driven multi-modal research: whether neural networks trained on vision, language, and other modalities naturally discover the same underlying representation of reality. The authors provide mathematical conditions under which the answer is provably yes.

Sample Efficiency Results

The empirical companion to the proof reports that good views deliver equivalent cross-modal alignment with 1/42nd the training data required by next-token prediction. The authors reframe standard language model pretraining as a JEPA operating with bad views, observations that share minimal world-state information.

Their 109M-parameter text JEPA reportedly outperforms language models up to 72B parameters on alignment benchmarks. A single learned rotation matrix enables the trained encoder to function as an image captioner, achieving a CIDEr score of 0.838 on the COCO dataset according to the paper.

Architecture and Conditions

JEPAs predict representations of one view from another within a shared embedding space, rather than reconstructing pixel values or predicting next tokens. The architecture enforces alignment through contrastive learning on positive pairs.

The proof's conditions specify that positive pairs must observe the same world state through different sensors or perspectives. Misalignment between views must remain bounded. When these requirements hold, the theorem guarantees convergence to a common representation up to rotation, regardless of modality count.

Implications for LLM Training

The paper positions next-token prediction as a special case of JEPA training where consecutive text tokens form poor views of shared world states. This framing explains why language models align weakly with vision despite scale, according to the authors. Text tokens capture narrow linguistic patterns rather than the full observational context that good views require.

The 42x sample efficiency gap suggests that architecture choice, not just parameter count, determines how efficiently models learn cross-modal representations. The research argues that positive views, rather than scale alone, function as the primary lever for building platonic representations.

What This Means

The formalization provides theoretical grounding for multi-modal architectures and suggests a path toward more sample-efficient training. If good views can be constructed systematically across domains, the approach may reduce the data requirements for models that align multiple modalities. The proof also clarifies why certain training objectives produce better cross-modal alignment than others, offering design principles for next-generation architectures.