| --- |
| 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} |
| } |
| ``` |
| |
