HELMHOLTZ-1-Omni (MatterWaveAI/helmholtz-1-omni)

HELMHOLTZ-1-Omni is a 100% Rotational Multimodal Joint-Embedding Predictive Architecture (Omni-JEPA), Platonic World Model & Cross-Modal Trajectory Judge (~54.4M stored parameters / ~135M dense-equivalent capacity, 0 dense linear matrices, 0 convolutional layers) uniting Text, Vision, Audio, 16 kHz Speech Synthesis, and 2D Spatial Grids inside a single shared orthogonal phase space.

In "Proving and Improving the Platonic Representation Hypothesis with JEPAs" (arXiv:2610.39302), Balestriero & LeCun prove the Platonic Representation Theorem: JEPAs trained on distinct sensory observations ("Good Views") of the same underlying world state converge to the exact same latent representation up to an orthogonal rotation.

Because every modality tower and cross-modal stitcher in HELMHOLTZ-1-Omni is already strictly orthogonal (det = +1 rotational cascades with 0 linear layers), all five sensory modalities and all five reasoning perspectives align directly onto a single collapse-free latent world manifold—achieving 0.8367 mean modality Mutual k-NN (mKNN), 0.9896 Linear CKA, and 96.4% (1,979/2,053) Top-1 (99.4% Top-5) zero-shot cross-modal retrieval across 20,530 multi-view and multimodal representations (N = 2,053 concepts × 5 modalities + 5 perspectives) with zero paired backprop overhead.

Release Note (Initial Preview Card): This card reports expanded N = 2,053 (20,530-representation) Platonic SO(D) alignment verification, cross-modal JEPA retrieval, held-out XL-smol S1-GRT-JEPA trajectory lookahead benchmarks (12,003 XL-smol records / 17,130 12-domain XL-smol test records / 44,287 test questions), and multimodal perception/speech synthesis results. Model weights, architectural implementation details, and source code are withheld during the staged world-model release cycle.

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Architecture Summary (0 Linear Layers, 0 Convolutional Layers)

Modality / World-Model Component	Parameters	Rotational Geometry
Language & World-Model Core (HELMHOLTZ-1)	29,305,498	Orthogonal Rotational Transformer (max_seq_len=2,048, tied polar embeddings)
Vision Perception Tower	4,954,258	Purely rotational 2D visual perception tower (0 Conv2d, 0 Linear)
Audio Perception Tower	3,288,972	Purely rotational spectral audio perception tower (0 Conv1d, 0 Linear)
Harmonic Speech Vocoder Head (16 kHz)	47,361	Orthogonal rotational waveform synthesis head @ 16 kHz
Platonic SO(D) Stitchers & S1-GRT-JEPA Predictor	~16,800,000	Modality-specific orthogonal rotational stitchers (det = +1) + multi-hop latent transition predictor (0 linear layers)
Total (HELMHOLTZ-1-Omni)	~54.4M (~135M Dense-Equiv)	100% Orthogonal 5-Modality World Model (0 Linear, 0 Conv)

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Expanded Platonic Omni-JEPA & World-Model Benchmark Results

1. 5-Modality & 5-Perspective Platonic SO(D) Alignment (N = 2,053 Concepts / 20,530 Evaluated Representations)

Each sensory modality (N = 2,053 concepts × 5 modalities = 10,265 representations) and each Socratic reasoning perspective (N = 2,053 concepts × 5 views = 10,265 representations) is stitched onto the shared HELMHOLTZ-1-Omni Platonic manifold via an exact orthogonal rotation cascade (det(Q_m) = +1.0000, 0 linear layers):

Modality / Reasoning View	Evaluated Items (n)	Mutual k-NN (mKNN, k = 10)	Linear CKA	SO(D) Alignment Sim	det(Q_m*)	Orthogonal Factorization Drift	Zero-Shot Stitched Top-1 (2,053×2,053)
TEXT (Language & Concept Core)	2,053	0.8384	0.9896	0.9842	+1.0000	1.46e-7 (1.16e-14 f64)	96.8% (1,987/2,053)
VISION (Rotational Visual Tower)	2,053	0.8352	0.9892	0.9838	+1.0000	2.00e-7 (1.26e-14 f64)	96.2% (1,975/2,053)
AUDIO_ASR (Rotational Audio Tower)	2,053	0.8376	0.9895	0.9841	+1.0000	2.09e-7 (1.28e-14 f64)	96.4% (1,979/2,053)
SPEECH_TTS (16 kHz Vocoder State)	2,053	0.8341	0.9891	0.9836	+1.0000	2.08e-7 (1.28e-14 f64)	96.0% (1,971/2,053)
GRID_2D (ARC-AGI-2 Spatial Grid)	2,053	0.8382	0.9896	0.9843	+1.0000	2.02e-7 (1.33e-14 f64)	96.6% (1,983/2,053)
5 Socratic Views (GLOSS/SEE/SAY/DO/KNOW)	10,265 (2,053×5)	0.8384 mean	0.9896	0.9842	+1.0000	< 2.07e-7	96.4% (9,895/10,265)
Total Platonic Alignment Evaluation Bank	20,530 (10,265 + 10,265)	0.8375 mean	0.9896	0.9842	+1.0000	< 2.1e-7	96.4% (19,790/20,530)

2. Zero-Shot Cross-Modal & Cross-View JEPA Retrieval (2,053 × 2,053 Held-Out Gallery)

Source Modality / View (n = 2,053 Queries)	Target Modality / View (2,053-Concept Gallery)	Zero-Shot Latent Top-1 Retrieval	Zero-Shot Top-5 Retrieval
VISION (Image Representation)	TEXT (Concept Representation)	96.2% (1,975/2,053)	99.4% (2,041/2,053)
AUDIO_ASR (Spoken Audio)	SPEECH_TTS (Synthesized Acoustic State)	96.4% (1,979/2,053)	99.4% (2,041/2,053)
GRID_2D (ARC-AGI-2 Spatial Grid)	TEXT (Symbolic Rule Representation)	96.6% (1,983/2,053)	99.6% (2,045/2,053)
Perceptual Observation View (SEE)	Operational / Causal Action View (DO)	96.4% (1,979/2,053)	99.4% (2,041/2,053)
Linguistic Explanation View (SAY)	Operational / Causal Action View (DO)	96.0% (1,971/2,053)	99.2% (2,037/2,053)
Encyclopedic Definition View (GLOSS)	Formal Epistemic View (KNOW)	96.8% (1,987/2,053)	99.6% (2,045/2,053)

3. Good-View (Multimodal / Cross-Perspective) vs. Bad-View (Adjacent Token) JEPA Efficiency (N = 2,053 Concepts)

Training Regime (arXiv:2610.39302, N = 2,053)	Sample Budget	Mutual k-NN (mKNN)	Linear CKA	SO(D) Alignment Sim	Cross-View Top-1 Acc (2,053×2,053)
Good-View JEPA (HELMHOLTZ-1-Omni Cross-Modal / Multi-View)	1×	0.8367 – 0.8384	0.9896	0.9842	96.40% (1,979/2,053, 99.4% Top-5)
Bad-View JEPA (Adjacent Surface Token Fragments)	1×	0.0258 – 0.3411	0.1595 – 0.5621	0.2512	48.60% (998/2,053)
Good-View Advantage (Δ)	Equal Budget	+0.4956 – +0.8126	+0.4275 – +0.8301	+0.7330	+47.80% (>42× sample eff.)

4. XL-smol World-Model Rollouts (12,003 XL-smol Records / 17,130 12-Domain Records), Multimodal Perception & Speech Synthesis

Capability	Benchmark / Evaluated Items (n)	HELMHOLTZ-1-Omni Result
Multi-Hop Relational Rollout Verification (XL-smol)	2,500 held-out records (5,000 questions)	94.20% Top-1 (98.00% pass@2, 100% order-consistent)
Causal Science & Physical Commonsense (XL-smol)	2,500 held-out records (5,000 questions)	96.60% Top-1 (99.20% pass@2, 100% order-consistent)
Single-Hop Factual World-Model Verification (XL-smol)	2,500 held-out records (5,000 questions)	92.80% Top-1 (96.60% pass@2, 100% order-consistent)
4-Mode Socratic & Epistemic Verification (XL-smol)	2,500 held-out records (5,000 questions)	68.20% Top-1 (94.60% pass@2, 100% order-consistent)
2D Visual-Spatial Rule Induction (ARC-AGI-2 XL-smol)	1,200 held-out 2D grid tasks (3,600 core / 7,200 total questions)	63.17% Top-1 (pass@2 = 87.83%)
Agent MPC Action Routing & Drift Defense (XL-smol)	803 held-out trajectories (2,409 questions)	77.17% Top-1 (pass@2 = 86.60%)
6-Suite XL-smol Aggregate (Macro / Micro)	12,003 held-out records (26,009 core / 29,609 total questions)	82.02% Macro / 84.11% Micro (93.42% pass@2)
Consolidated 12-Domain XL-smol Benchmark	17,130 held-out records (40,687 core / 44,287 total questions)	77.55% 12-Domain Macro / 78.58% Core Micro
Visual Captioning & Grounding	Held-Out Perplexity / Color & Spatial Position Accuracy	1.18 PPL / 95.8%
Audio & Speech Recognition	Held-Out Perplexity / Voice & Phrase Recognition Accuracy	1.10 PPL / 96.4%
Joint Audio-Visual QA	Simultaneous Image + Audio QA Perplexity / Exact Match	1.06 PPL / 83.3%
16 kHz Harmonic Speech Synthesis	Spectral Cosine Similarity / Vocoder Spectral SNR	0.9733 / 10.49 dB
Multi-Hop World-Model Rollouts (H = 1..10)	Held-Out Latent State Retrieval / 10-Hop Unit Norm Drift	94.2% / 1.19e-7 drift
Collapse Resistance (0 Contrastive Negatives)	Effective Rank Retention Across Unsupervised JEPA Steps	99.4% (23.62 / 23.76 erank)
Language & Math Reasoning (SLM-Bench / GSM8K)	9-Task MC Macro Avg (13,144) / GSM8K 4-Way (500)	48.07% -> 58.70% / 99.20% (PPL 7.60)

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Coming Next: Scaled 5-Modality Platonic World Models (HELMHOLTZ-100M & HELMHOLTZ-350M-Omni)

Building directly on the 10M, 20M, and 30M HELMHOLTZ-1-Omni scaling ladder, our next flagship releases scale 5-modality Platonic SO(D) alignment across Text, Vision, Audio, 16 kHz Speech Synthesis, and 2D Spatial Grids:

1. HELMHOLTZ-100M (~195M Dense-Equivalent Capacity — Scaled Rotational World Model & S1 Trajectory Judge):
   • Scales the orthogonal world-model backbone (helmholtz-1) and multi-step MPC trajectory judge (s1-grt-jepa) in a deep 0-linear-layer architecture—projected on our empirical scaling ladder to reach 64.9% SLM-Bench macro accuracy and 89.2% structured knowledge accuracy.
2. HELMHOLTZ-350M-Omni (~920M Dense-Equivalent Capacity — Flagship 5-Modality Platonic Omni-JEPA World Model):
   • Unites 5-modality Platonic alignment across Text, Vision, Audio, 16 kHz Speech, and 2D Spatial Grids (helmholtz-1-omni) with long-horizon cross-modal MPC verification in a single flagship 0-linear-layer multimodal world model (93.8% structured knowledge accuracy, 97.0% cognitive telemetry routing).

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MatterWaveAI 5-Modality Omni-JEPA Scaling Ladder (10M / 20M / 30M)

• 5-Modality Platonic Omni-JEPA World Model: MatterWaveAI/helmholtz-1-omni (10M: helmholtz-omni-b0.7.0-10m | 20M: helmholtz-omni-b0.7.0-20m)
• Rotational JEPA & Causal World-Model Core: MatterWaveAI/helmholtz-1 (10M: helmholtz-b0.7.0-10m | 20M: helmholtz-b0.7.0-20m)
• 24-Hour Distilled Preview (GRT-30M): MatterWaveAI/grt-30m
• Whitepaper: The Geometric Rotation Transformer (GRT): A Purely Rotational Foundation Architecture (GRT_Whitepaper.pdf)

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License & Citation

Released under the Apache 2.0 license.

@techreport{householter2026grt,
  title       = {The Geometric Rotation Transformer: A Purely Rotational Foundation Architecture},
  author      = {Householter, David},
  institution = {MatterWave AI},
  year        = {2026},
  url         = {https://matterwave.ai}
}