---
license: apache-2.0
library_name: transformers
pipeline_tag: text-to-image
tags:
  - grt
  - grt-image
  - text-to-image
  - vision
  - rotational-transformer
  - givens-rotations
  - sophia-torus
  - matterwave
base_model: MatterWaveAI/grt-30m
---

# GRT-30M-Image (`MatterWaveAI/grt-30m-image`)

**GRT-30M-Image** is a **100% Native Rotational Text-to-Image & Visual Patch Synthesis Language Model** (`29,371,239` total parameters, **zero `nn.Linear` layers**, **zero `nn.Conv2d` layers**) built on top of [`MatterWaveAI/grt-30m`](https://huggingface.co/MatterWaveAI/grt-30m). Completing the bidirectional Vision symmetry alongside [`MatterWaveAI/grt-30m-vl`](https://huggingface.co/MatterWaveAI/grt-30m-vl) (`Image → Text`), `GRT-30M-Image` synthesizes `(B, 3, 224, 224)` RGB images and discrete 4-codebook visual patch tokens directly from causal text representations through a purely rotational inverse Givens butterfly patch decoder (`GRTPolarImageDecoderHead`).

## Architecture Summary

| Component | Module | Parameters | Geometry |
| :--- | :--- | :---: | :--- |
| **Language Backbone** | `GRTModel` + `GRTCosineHead` | `29,305,498` | 12-layer causal Givens Rotational Transformer (`MatterWaveAI/grt-30m`, frozen to preserve 100% text fluency) |
| **Polar Image Decoder Head** | `GRTPolarImageDecoderHead` (`model.image_head`) | `65,741` | 15-stage Givens butterfly expand (`d_model=256 → 1024`) → `GRTRadialGELU` → 15-stage butterfly contract (`1024 → 4×256` sub-patches) → 11-stage inverse patch cascade (`256 → 1024 → 588 = 3×14×14`) → spatial fold `(B, 3, 224, 224)` |
| **Total (`GRT-30M-Image`)** | `GRTImageForConditionalGeneration` (`GRTForTextToImage`) | **`29,371,239`** | **0 `nn.Linear`, 0 `nn.Conv2d`** |
| **4-Codebook Visual RVQ Bank** | `GRTVisualRVQCodecBank` (benchmark evaluation head) | `32,772` | 4 planar-pair polar cosine codebooks (`K = 64` entries × `128` pairs per codebook) over RGB spatial-spectral sub-bands |

## Visual Synthesis Alignment Metrics (`HuygensAdam` / Circular Order Parameter `R_p` Splay Torque)

- **Held-Out Visual RVQ Perplexity**: `81.17` (unaligned) → **`16.98`** (aligned, `4.78×` reduction)
- **Visual RVQ Mean Top-1 Accuracy (4 Codebooks)**: `1.48%` → **`25.19%`** (`[20.86%, 25.63%, 26.04%, 28.23%]`, `16.1×` over random chance)
- **Text-Conditioned Prompt Margin (`ΔL` vs. Shuffled Prompts)**: `-0.0074` → **`+0.6440` nats**
- **Patch Polar Cosine Similarity**: `0.1004` → **`0.6737`**
- **2D Spectral Magnitude Cosine Similarity**: `0.1782` → **`0.7857`**
- **Reconstruction PSNR / Spectral SNR**: `11.38 dB` / `-8.20 dB` → **`19.14 dB` PSNR / `+2.31 dB` SNR** (`+10.51 dB` gain)

---

## 8-Way Classical Geometric Optimizer Ablation (`Intel Arc 140T XPU`)

We benchmarked all 8 classical geometric, symplectic, and gyroscopic optimizers from `transformers.models.grt.optimization_grt` on `MatterWaveAI/grt-30m-image` (`GRTPolarImageDecoderHead` + 4-codebook visual RVQ polar cosine codec bank `GRTVisualRVQCodecBank`, `K = 64` per codebook, `200` steps per optimizer, `batch_size = 36`, `seed = 42`, across a 144-concept procedural text-to-image benchmark of 6 colors × 6 geometric shapes × 4 spatial layouts):

| Rank | Optimizer (`optimizer_type`) | Final Train Loss | Held-Out RVQ Val Loss | Held-Out RVQ Val PPL | RVQ Mean Top-1 Acc (4 Codebooks) | Codebook-0 Primary Acc | Text-Conditioned Margin (`ΔL`) | Patch Polar Cosine Sim | Spectral SNR / PSNR (dB) | Time (s) |
| :---: | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| **1** | **`HuygensAdam` (`huygens_adam`)** | **`2.8188`** | **`2.8317`** | **`16.9750`** | **`25.19%`** | `20.86%` | **`+0.6440`** | **`0.6737`** | **`2.31` / `19.14 dB`** | `55.59s` |
| **2** | **`PolarNaturalAdam` (`polar_natural_adam`)** | `2.8244` | `2.8368` | `17.0605` | `25.08%` | `20.85%` | `+0.6333` | `0.6717` | `2.29` / `19.13 dB` | `185.71s` |
| **3** | **`HessianPairAdam` (`hessian_pair_adam`)** | `2.8260` | `2.8382` | `17.0850` | `25.04%` | `20.67%` | `+0.6341` | `0.6723` | `2.30` / `19.13 dB` | `172.73s` |
| **4** | **`PairAdam` (`pair_adam`)** | `2.8306` | `2.8417` | `17.1447` | `25.04%` | `20.48%` | `+0.6356` | `0.6731` | **`2.31` / `19.14 dB`** | `196.00s` |
| **5** | **`CyclideAdam` (`cyclide_adam`)** | `2.8337` | `2.8454` | `17.2093` | `25.02%` | **`20.87%`** | `+0.6292` | `0.6701` | `2.28` / `19.12 dB` | `85.62s` |
| **6** | **`GyricAdam` (`gyric_adam`)** | `2.8520` | `2.8651` | `17.5505` | `24.64%` | `20.04%` | `+0.6298` | `0.6608` | `2.21` / `19.04 dB` | **`47.46s`** |
| **7** | **`HuygensSymplecticAdam` (`huygens_symplectic_adam`)** | `2.8962` | `2.9087` | `18.3322` | `24.01%` | `19.65%` | `+0.6061` | `0.6508` | `2.14` / `18.97 dB` | `55.41s` |
| **8** | **`SymplecticAdam` (`symplectic_adam`)** | `2.8965` | `2.9089` | `18.3370` | `24.01%` | `19.65%` | `+0.6056` | `0.6508` | `2.14` / `18.97 dB` | `65.04s` |

### Key Geometric Findings on Rotational Text-to-Image (`GRTImage`)
- **`HuygensAdam` Sweeps #1 Across Visual RVQ Perplexity, Accuracy, Text-Conditioning Margin & Polar Cosine Similarity**: On 2D spatial patch synthesis (`256` patches of `14×14×3` unfolded across 41 Givens butterfly stages), Kuramoto–Huygens circular order-parameter splay torque (`R_p = |(1/P) ∑_p exp(i θ_p)|`) prevents angular phase collapse across spatial sub-patches, achieving **#1 held-out RVQ validation loss (`2.8317`, `val_ppl = 16.9750`)**, **#1 4-codebook visual RVQ accuracy (`25.19%`)**, **#1 text-conditioning margin (`+0.6440` nats)**, and **#1 patch polar cosine similarity (`0.6737`, `19.14 dB` PSNR)**.
- **`PolarNaturalAdam` (#2) & `HessianPairAdam` (#3) Excel on Multi-Stage Butterfly Curvature**: Scaling angular updates by the Riemannian polar metric `1 / (r² + ε)` and Cauchy–Riemann toroidal curvature outperforms first-order `PairAdam` (`2.8368` and `2.8382` vs. `2.8417` validation loss).
- **`CyclideAdam` Achieves #1 Primary Codebook-0 Accuracy (`20.87%`)**: Dupin cyclide conic metric preconditioning with deviatoric twist attains the highest primary RGB chromatic codebook accuracy (`20.87%`).

---

## Quickstart (`transformers`)

```python
import torch
from transformers import AutoTokenizer, GRTImageForConditionalGeneration

model_id = "MatterWaveAI/grt-30m-image"
tokenizer = AutoTokenizer.from_pretrained(model_id)
model = GRTImageForConditionalGeneration.from_pretrained(model_id, dtype=torch.float32)

prompt = "<|im_start|>user\nGenerate image (color=gold, shape=ring, layout=center): render a gold ring in the center region<|im_end|>\n<|im_start|>assistant\n"
inputs = tokenizer(prompt, return_tensors="pt", add_special_tokens=False)
outputs = model(**inputs)
print("Synthesized RGB image shape:", outputs.pixel_values.shape)  # (1, 3, 224, 224)
print("Synthesized polar patches shape:", outputs.image_patches.shape)   # (1, 256, 588)
```

---

## Complete `MatterWaveAI/grt-30m*` Research Suite on Hugging Face

1. **Base Causal LM**: [`MatterWaveAI/grt-30m`](https://huggingface.co/MatterWaveAI/grt-30m)
2. **Chat Fine-Tune**: [`MatterWaveAI/grt-30m-chat`](https://huggingface.co/MatterWaveAI/grt-30m-chat)
3. **4-Expert Mixture-of-Rotations (`MoR`)**: [`MatterWaveAI/grt-30m-mor`](https://huggingface.co/MatterWaveAI/grt-30m-mor)
4. **Circular-Pooled Sentence Embedding**: [`MatterWaveAI/grt-30m-embedding`](https://huggingface.co/MatterWaveAI/grt-30m-embedding)
5. **Cross-Encoder Reranker**: [`MatterWaveAI/grt-30m-reranker`](https://huggingface.co/MatterWaveAI/grt-30m-reranker)
6. **Vision-Language (`GRTVL`)**: [`MatterWaveAI/grt-30m-vl`](https://huggingface.co/MatterWaveAI/grt-30m-vl)
7. **Rotational Text-to-Image (`GRTImage`)**: [`MatterWaveAI/grt-30m-image`](https://huggingface.co/MatterWaveAI/grt-30m-image)
8. **Canonical Tokenizer & Polar Embedding Bank**: [`MatterWaveAI/grt-30m-tokenizer`](https://huggingface.co/MatterWaveAI/grt-30m-tokenizer)
9. **Rotational Text-to-Speech (`GRTTTS`)**: [`MatterWaveAI/grt-30m-tts`](https://huggingface.co/MatterWaveAI/grt-30m-tts)
10. **Rotational Speech Recognition (`GRTASR`)**: [`MatterWaveAI/grt-30m-asr`](https://huggingface.co/MatterWaveAI/grt-30m-asr)
11. **Multimodal Vision-Audio-Language-Speech-Image (`GRTOmni`)**: [`MatterWaveAI/grt-30m-omni`](https://huggingface.co/MatterWaveAI/grt-30m-omni)

- **Whitepaper**: [**The Geometric Rotation Transformer (GRT): A Purely Rotational Foundation Architecture (`GRT_Whitepaper.pdf`)**](https://huggingface.co/MatterWaveAI/grt-30m/resolve/main/GRT_Whitepaper.pdf)

---

## License

Apache 2.0

---

## Citation

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