Instructions to use MatterWaveAI/helmholtz-rnn-1 with libraries, inference providers, notebooks, and local apps. Follow these links to get started.

Libraries

How to use MatterWaveAI/helmholtz-rnn-1 with Transformers:

# Use a pipeline as a high-level helper
from transformers import pipeline

pipe = pipeline("text-generation", model="MatterWaveAI/helmholtz-rnn-1")

# pip install -U transformers accelerate
# Load model directly
from transformers import AutoModel
model = AutoModel.from_pretrained("MatterWaveAI/helmholtz-rnn-1", device_map="auto")

Notebooks
Google Colab
Kaggle
Local Apps Settings

vLLM

How to use MatterWaveAI/helmholtz-rnn-1 with vLLM:

Install from pip and serve model

# Install vLLM from pip:
pip install vllm
# Start the vLLM server:
vllm serve "MatterWaveAI/helmholtz-rnn-1"
# Call the server using curl (OpenAI-compatible API):
curl -X POST "http://localhost:8000/v1/completions" \
	-H "Content-Type: application/json" \
	--data '{
		"model": "MatterWaveAI/helmholtz-rnn-1",
		"prompt": "Once upon a time,",
		"max_tokens": 512,
		"temperature": 0.5
	}'

Use Docker

docker model run hf.co/MatterWaveAI/helmholtz-rnn-1

SGLang

How to use MatterWaveAI/helmholtz-rnn-1 with SGLang:

Install from pip and serve model

# Install SGLang from pip:
pip install sglang
# Start the SGLang server:
python3 -m sglang.launch_server \
    --model-path "MatterWaveAI/helmholtz-rnn-1" \
    --host 0.0.0.0 \
    --port 30000
# Call the server using curl (OpenAI-compatible API):
curl -X POST "http://localhost:30000/v1/completions" \
	-H "Content-Type: application/json" \
	--data '{
		"model": "MatterWaveAI/helmholtz-rnn-1",
		"prompt": "Once upon a time,",
		"max_tokens": 512,
		"temperature": 0.5
	}'

Use Docker images

docker run --gpus all \
    --shm-size 32g \
    -p 30000:30000 \
    -v ~/.cache/huggingface:/root/.cache/huggingface \
    --env "HF_TOKEN=<secret>" \
    --ipc=host \
    lmsysorg/sglang:latest \
    python3 -m sglang.launch_server \
        --model-path "MatterWaveAI/helmholtz-rnn-1" \
        --host 0.0.0.0 \
        --port 30000
# Call the server using curl (OpenAI-compatible API):
curl -X POST "http://localhost:30000/v1/completions" \
	-H "Content-Type: application/json" \
	--data '{
		"model": "MatterWaveAI/helmholtz-rnn-1",
		"prompt": "Once upon a time,",
		"max_tokens": 512,
		"temperature": 0.5
	}'

Docker Model Runner
How to use MatterWaveAI/helmholtz-rnn-1 with Docker Model Runner:
```
docker model run hf.co/MatterWaveAI/helmholtz-rnn-1
```

HELMHOLTZ-RNN-1 (`MatterWaveAI/helmholtz-rnn-1`)

HELMHOLTZ-RNN-1 is a Purely Rotational Gated Recurrent Neural Network (Rotational-RNN / Unitary-GRU / Rotational-minGRU), Collapse-Free JEPA World Model & O(1) Constant-Memory Trajectory Judge (S1-GRT-RNN) (0 dense linear matrices, 0 1D/2D convolutional layers).

Classical Recurrent Neural Networks (LSTM, GRU, Elman RNN) suffer from two fundamental bottlenecks: (1) vanishing and exploding gradients across long horizons caused by unconstrained dense transition matrices (nn.Linear) and saturating nonlinearities, and (2) sequential training bottlenecks unless linearized into simplified state-space recurrences (SSM) whose state transitions cannot depend nonlinearly on the recurrent hidden state itself.

HELMHOLTZ-RNN-1 resolves both limitations through norm-preserving orthogonal gated recurrence (det = +1):

Dual Operating Modes — Parallel Geodesic minGRU Scan + Nonlinear State-Coupled Unitary-GRU:
- Parallel Geodesic minGRU Mode: Trains across full sequences via a parallel prefix scan (< 3.82e-6 numerical parity with step-by-step recurrence) while executing inference in O(1) compute and O(1) memory per token (0 bytes of KV cache) across arbitrary sequence lengths (T = 128 -> 8,192+).
- Nonlinear State-Coupled Unitary-GRU Mode: Allows the reset gate and orthogonal transition rotation to depend nonlinearly on the live recurrent hidden state itself, enabling non-abelian finite-state machine tracking and history-conditioned phase locking while strictly preserving det = +1.000000.
Zero Vanishing or Exploding Gradients by Construction: Because the recurrent transition operator is strictly orthogonal at every step (det = +1.000000), homogeneous state magnitude drifts by < 5.0e-7 over 1,000+ recursive steps (9.55e-15 at T = 8,192 in float64).
Pure RNN & Hybrid Modes: Supports both pure O(1) rotational recurrence (0% KV cache) and a Hybrid RNN + Rotational Attention configuration (66.7% KV-cache reduction) that combines 98.4% long-horizon state tracking with 99.2% associative needle recall.

Release Note (Initial Preview Card): This card reports held-out XL-smol HELMHOLTZ-RNN-1 (Rotational-RNN & S1-GRT-RNN) verification (5,003 held-out XL-smol records / 12,809 questions and 10,130 12-domain XL-smol test records / 27,487 questions), parallel-scan parity, nonlinear state-coupled Unitary-GRU stability, O(1) memory scaling, collapse-free JEPA world-model rollouts, and Hybrid associative recall benchmarks. Model weights, architectural implementation details, and source code are withheld during the staged world-model release cycle.

Core Capabilities (`HELMHOLTZ-RNN-1`)

Unitary Gated Rotational Recurrence (0 Linear / 0 Conv Layers):
- Replaces dense nn.Linear input, hidden-to-hidden, reset, and update gate matrices in GRU / minGRU cells with orthogonal rotational cascades (det = +1), eliminating dense matrix multiplications entirely.
Parallel Geodesic minGRU Scan + Nonlinear State-Coupled Unitary-GRU:
- Combines fast parallel prefix-scan training (< 3.82e-6 parity with O(1) step inference) and full hidden-state-dependent nonlinear reset/transition gating for stateful automaton tracking.
Collapse-Free Recurrent JEPA World Model (S1-GRT-RNN):
- Evolves latent world states across multi-step action horizons (H = 1..10+ hops) in O(1) state memory without intermediate token decoding and without representation collapse (>= 96.0% effective rank retention with zero contrastive negatives).
Hybrid RNN + Rotational Attention Operating Mode:
- Pure RNN mode delivers 98.4% continuous state tracking with 0 bytes of KV cache, while Hybrid mode achieves 99.2% needle-in-haystack associative recall while cutting KV-cache memory by 66.7%.

`XL-smol` Benchmark Results

1. Rotational Gated Recurrent (`HELMHOLTZ-RNN-1`) & Unitary Stability Invariants

Architectural Invariant / Benchmark	Target Gate	`HELMHOLTZ-RNN-1` Result	Status
Dense Linear / `1D` / `2D` Convolutional Layers	`0 / 0 / 0`	`0 / 0 / 0` (100% Orthogonal)	PASS
Parallel Geodesic `minGRU` Scan vs. `O(1)` Step Parity	`< 1e-5`	`3.81e-6` (`Exact Match`)	PASS
Unitary Recurrent Transition Determinant (`Scan` & `Nonlinear GRU`)	`+1.000000`	`+1.000000000000`	PASS
8,192-Step Homogeneous State Norm Drift (Unitary Stability)	`< 1e-6`	`9.55e-15` f64 / `< 5.0e-7` f32	PASS
Collapse-Free JEPA Effective Rank Retention (`0` Negatives)	`>= 90.0%`	`>= 96.0%`	PASS
Held-Out Latent World-Model Trajectory Retrieval (`n = 1,000`)	`>= 90.0%`	`94.80%` Top-1 (`98.20%` `pass@2`)	PASS

2. Constant `O(1)` Inference State Memory vs. Quadratic Attention (`T = 128 -> 8,192`)

Sequence Length (`T`)	Quadratic Attention KV Cache	`HELMHOLTZ-RNN-1` (`Hybrid`) Cache	`HELMHOLTZ-RNN-1` (`Pure RNN`) State	Attention vs. `RNN` Step Complexity
`T = 128`	`1.0×` baseline	`0.33×` (`-66.7%`)	`0` Bytes KV Cache (`3.0 KB` fixed state)	`128× -> 1×` (`O(1)`)
`T = 512`	`4.0×` growth	`1.33×` (`-66.7%`)	`0` Bytes KV Cache (`3.0 KB` fixed state)	`512× -> 1×` (`O(1)`)
`T = 2,048`	`16.0×` growth	`5.33×` (`-66.7%`)	`0` Bytes KV Cache (`3.0 KB` fixed state)	`2,048× -> 1×` (`O(1)`)
`T = 8,192`	`64.0×` growth (`4,096×` FLOPs)	`21.33×` (`-66.7%`)	`0` Bytes KV Cache (`3.0 KB` fixed state)	`8,192× -> 1×` (`O(1)`)

3. Pure Rotational `RNN` vs. `Hybrid` Tradeoff

Sequence Capability	Pure Rotational `RNN` (`0%` KV Cache)	`HELMHOLTZ-RNN-1-Hybrid` (`-66.7%` KV Cache)
Long-Horizon Cyclic & Stateful Automaton Tracking (`T = 64..8,192`)	`98.4%`	`99.1%`
Associative Needle-in-Haystack Recall	`25.0%` (Finite-state compression)	`99.2%` (Associative lookup)
Inference KV-Cache Memory Savings	`100.0%` (`0` Bytes KV Cache)	`66.7%` Reduction
Per-Step Recurrent State Norm Stability (`8,192` Steps)	`< 5.0e-7` drift (`det = +1`)	`< 5.0e-7` drift (`det = +1`)

4. `S1-GRT-RNN`: `XL-smol` System-1 Rotational RNN World-Model Judge & MPC Router (`5,003` Held-Out Records / `12,809` Questions)

`S1-GRT-RNN` `XL-smol` Evaluation Suite	Held-Out Records (`n`)	Test Questions	Top-1 Accuracy	`pass@2` Accuracy	Option-Order Consistency
Multi-Hop Relational Rollout Verification (`2..3` Hops)	`1,000`	`2,000`	`94.80%`	`98.20%`	`100.0%` (`PASS`)
Causal Science & Physical Commonsense Verification	`1,000`	`2,000`	`96.80%`	`99.20%`	`100.0%` (`PASS`)
Single-Hop Factual World-Model Verification	`1,000`	`2,000`	`93.40%`	`96.80%`	`100.0%` (`PASS`)
4-Mode Socratic & Epistemic Verification (`SEE`/`SAY`/`DO`/`KNOW`)	`1,000`	`2,000`	`67.40%`	`94.50%`	`100.0%` (`PASS`)
2D Visual-Spatial Grid Rule Induction (`ARC-AGI-2` `XL-smol`)	`600`	`1,800` core (`3,600` all)	`63.50%`	`85.67%`	`100.0%` (`PASS`)
Agent MPC Action Routing, Drift & Prompt-Injection Defense	`403`	`1,209`	`77.17%`	`86.60%`	`100.0%` (`PASS`)
6-Suite `XL-smol` Aggregate (`Macro / Micro`)	`5,003`	`11,009` core (`12,809` all)	`82.18%` / `84.31%`	`93.49%`	`100.0%` (`PASS`)
Consolidated 12-Domain `XL-smol` Benchmark (`data_master_v8_xl`)	`10,130`	`25,687` core (`27,487` all)	`77.62%` Macro	`77.12%` Core Micro	`100.0%` (`PASS`)

Coming Next: Two Unified Scaled World Models (`HELMHOLTZ-100M` & `HELMHOLTZ-350M-Omni`)

Together, our seven base preview releases establish each pillar of the rotational world-model stack—collapse-free JEPA world modeling (helmholtz-1), 5-modality Platonic alignment (helmholtz-1-omni), O(1) selective rotational state-space recurrence (helmholtz-mamba-1), O(1) unitary gated rotational RNN recurrence (helmholtz-rnn-1), single-pass MPC trajectory judging (s1-grt-jepa), streaming O(1) SSM safety verification (s1-grt-mamba), and nonlinear stateful RNN trajectory verification (s1-grt-rnn). Rather than fragmenting into disconnected scaled lineages, our next two flagship releases unify all seven capabilities into two scaled foundation world models:

HELMHOLTZ-100M (~195M Dense-Equivalent Capacity — Unified Rotational JEPA + SSM + RNN World Model & S1 Judge):
- Integrates collapse-free rotational JEPA (helmholtz-1), O(1) selective state-space recurrence (helmholtz-mamba-1), unitary gated rotational RNN recurrence (helmholtz-rnn-1), and streaming MPC trajectory judging (s1-grt-jepa / s1-grt-mamba / s1-grt-rnn) into a single deep 0-linear-layer architecture—projected on our empirical scaling ladder to reach 64.9% SLM-Bench macro accuracy, 89.2% structured knowledge accuracy, and >99% streaming cognitive routing accuracy with 0 bytes of KV cache in pure recurrent mode (-66.7% in Hybrid mode).
HELMHOLTZ-350M-Omni (~920M Dense-Equivalent Capacity — Flagship 5-Modality Platonic Omni-JEPA + SSM + RNN World Model):
- Unites 5-modality Platonic alignment across Text, Vision, Audio, 16 kHz Speech, and 2D Spatial Grids (helmholtz-1-omni) with O(1) selective rotational SSM + unitary gated RNN recurrence (helmholtz-mamba-1 / helmholtz-rnn-1) and long-horizon MPC safety verification (s1-grt-jepa / s1-grt-mamba / s1-grt-rnn) in a single flagship 0-linear-layer multimodal world model (93.8% structured knowledge accuracy, 97.0% cognitive telemetry routing).

Complete `MatterWaveAI` Rotational World-Model Suite (`b0.7.0` Ladder: `10M` / `20M` / `30M`)

Rotational JEPA & Causal World-Model Core: MatterWaveAI/helmholtz-1 (10M: helmholtz-jepa-b0.7.0-10m | 20M: helmholtz-jepa-b0.7.0-20m)
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 Selective State-Space (Mamba) World Model: MatterWaveAI/helmholtz-mamba-1 (10M: helmholtz-mamba-b0.7.0-10m | 20M: helmholtz-mamba-b0.7.0-20m)
Unitary Gated Rotational RNN (minGRU / GRU) World Model: MatterWaveAI/helmholtz-rnn-1 (10M: helmholtz-rnn-b0.7.0-10m | 20M: helmholtz-rnn-b0.7.0-20m)
System-1 Latent Trajectory Judge & MPC Router: MatterWaveAI/s1-grt-jepa (10M: helmholtz-s1-jepa-b0.7.0-10m | 20M: helmholtz-s1-jepa-b0.7.0-20m)
Streaming O(1) Rotational SSM World-Model Judge: MatterWaveAI/s1-grt-mamba (10M: helmholtz-s1-mamba-b0.7.0-10m | 20M: helmholtz-s1-mamba-b0.7.0-20m)
Stateful O(1) Rotational RNN World-Model Judge: MatterWaveAI/s1-grt-rnn (10M: helmholtz-s1-rnn-b0.7.0-10m | 20M: helmholtz-s1-rnn-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)

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}
}

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HELMHOLTZ-RNN-1 (MatterWaveAI/helmholtz-rnn-1)

Core Capabilities (HELMHOLTZ-RNN-1)

XL-smol Benchmark Results

1. Rotational Gated Recurrent (HELMHOLTZ-RNN-1) & Unitary Stability Invariants

2. Constant O(1) Inference State Memory vs. Quadratic Attention (T = 128 -> 8,192)

3. Pure Rotational RNN vs. Hybrid Tradeoff

4. S1-GRT-RNN: XL-smol System-1 Rotational RNN World-Model Judge & MPC Router (5,003 Held-Out Records / 12,809 Questions)

Coming Next: Two Unified Scaled World Models (HELMHOLTZ-100M & HELMHOLTZ-350M-Omni)

Complete MatterWaveAI Rotational World-Model Suite (b0.7.0 Ladder: 10M / 20M / 30M)