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title: README
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</style>
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_**Purely Rotational Foundation Models & Geometric Optimization**_
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**MatterWave AI** researches and builds **[Geometric Rotation Transformers (GRT)](https://huggingface.co/MatterWaveAI/grt-30m/resolve/main/GRT_Whitepaper.pdf)** — a foundation architecture that replaces dense linear weight matrices (`nn.Linear`) in attention (`Q, K, V, O`) and feed-forward (`expand, contract`) blocks with cascades of content-modulated 2×2 Givens rotations on `SO(D)` interleaved with butterfly permutations.
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## Build and Scale with Geometric Rotation Transformers
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Because every transform in the GRT residual path is an orthogonal rotation cascade, hidden-state norms are preserved by construction rather than by post-hoc rescaling. GRT checkpoints execute deterministically with bit-for-bit greedy generation parity across **PyTorch** (CUDA, ROCm, Intel XPU), **vLLM**, and **llama.cpp** (CPU AVX2, Vulkan, and ROCm HIP).
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Starting from the exact same pretrained checkpoints built for our NeurIPS submission with first-generation **PairAdam**, replacing the optimizer with **[HuygensSymplecticAdam](https://huggingface.co/MatterWaveAI/grt-20m-curriculum)** and training across a multi-round curriculum delivers substantial improvements across the 10-task **SLM-Bench** evaluation suite (13,144 held-out multiple-choice examples across BoolQ, ARC-Easy, ARC-Challenge, OpenBookQA, PIQA, WinoGrande, HellaSwag, QNLI, and CommonsenseQA, plus 500 held-out GSM8K mathematical reasoning problems):
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* **[GRT-10M-Curriculum (8.7M total / 2.2M backbone)](https://huggingface.co/MatterWaveAI/grt-10m-curriculum)** — Lifts 9-task multiple-choice accuracy from **37.61%** (PairAdam) to **41.71%** (Single-Pass) to **44.57%** (Multi-Round Curriculum, **+6.96%**), while GSM8K 4-way verification reaches **95.80%** (perplexity reduced **5.77×** from 145.85 to **25.28**).
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* **[GRT-20M-Curriculum (16.7M total / 10.3M backbone)](https://huggingface.co/MatterWaveAI/grt-20m-curriculum)** — Lifts 9-task multiple-choice accuracy from **38.63%** (PairAdam) to **45.03%** (Single-Pass) to **47.36%** (Multi-Round Curriculum, **+8.73%**), while GSM8K 4-way verification reaches **97.60%** (perplexity reduced **7.86×** from 60.12 to **7.65**).
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* **[GRT-30M-Curriculum (29.3M total / 9.74M backbone)](https://huggingface.co/MatterWaveAI/grt-30m-curriculum)** — Lifts 9-task multiple-choice accuracy from **39.61%** (PairAdam) to **43.86%** (Single-Pass) to **47.16%** (Multi-Round Curriculum, **+7.55%**), while GSM8K 4-way verification reaches **99.20%** (perplexity reduced **3.68×** from 28.00 to **7.60**).
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## System-1 Cognitive Telemetry & Multimodal Specialists
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Beyond base causal language modeling, the **[GRT-30M](https://huggingface.co/MatterWaveAI/grt-30m)** backbone powers specialized reasoning routers, retrieval encoders, and unified multimodal checkpoints:
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* **[Open-S1-GRT-30M](https://huggingface.co/MatterWaveAI/open-s1-grt-30m)** — 5-head System-1 cognitive telemetry router (action routing, escalation, loop guard, specification support, and verification gating) reaching **98.06%** held-out accuracy (**ECE = 0.0095**).
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* **[GRT Architecture Whitepaper (PDF)](https://huggingface.co/MatterWaveAI/grt-30m/resolve/main/GRT_Whitepaper.pdf)** — Full mathematical formulation, kernel design, and multi-backend verification report.
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## Explore the MatterWave AI Model Suite
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Browse our open-weights repositories by category:
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<div class="grid lg:grid-cols-2 gap-x-4 gap-y-7 p2">
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<div class="col-span-1 p2">
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<p><strong>Foundation & Curriculum LMs</strong></p>
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<ul class="social">
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M184 0c30.9 0 56 25.1 56 56l0 400c0 30.9-25.1 56-56 56c-28.9 0-52.7-21.9-55.7-50.1c-5.2 1.4-10.7 2.1-16.3 2.1c-35.3 0-64-28.7-64-64c0-7.4 1.3-14.6 3.6-21.2C21.4 367.4 0 338.2 0 304c0-31.9 18.7-59.5 45.8-72.3C37.1 220.8 32 207 32 192c0-30.7 21.6-56.3 50.4-62.6C80.8 123.9 80 118 80 112c0-29.9 20.6-55.1 48.3-62.1C131.3 21.9 155.1 0 184 0zM328 0c28.9 0 52.6 21.9 55.7 49.9c27.8 7 48.3 32.1 48.3 62.1c0 6-.8 11.9-2.4 17.4c28.8 6.2 50.4 31.9 50.4 62.6c0 15-5.1 28.8-13.8 39.7C493.3 244.5 512 272.1 512 304c0 34.2-21.4 63.4-51.6 74.8c2.3 6.6 3.6 13.8 3.6 21.2c0 35.3-28.7 64-64 64c-5.6 0-11.1-.7-16.3-2.1c-3 28.2-26.8 50.1-55.7 50.1c-30.9 0-56-25.1-56-56l0-400c0-30.9 25.1-56 56-56z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-curriculum">GRT-30M-Curriculum (47.16% MC / 99.2% GSM8K)</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M184 0c30.9 0 56 25.1 56 56l0 400c0 30.9-25.1 56-56 56c-28.9 0-52.7-21.9-55.7-50.1c-5.2 1.4-10.7 2.1-16.3 2.1c-35.3 0-64-28.7-64-64c0-7.4 1.3-14.6 3.6-21.2C21.4 367.4 0 338.2 0 304c0-31.9 18.7-59.5 45.8-72.3C37.1 220.8 32 207 32 192c0-30.7 21.6-56.3 50.4-62.6C80.8 123.9 80 118 80 112c0-29.9 20.6-55.1 48.3-62.1C131.3 21.9 155.1 0 184 0zM328 0c28.9 0 52.6 21.9 55.7 49.9c27.8 7 48.3 32.1 48.3 62.1c0 6-.8 11.9-2.4 17.4c28.8 6.2 50.4 31.9 50.4 62.6c0 15-5.1 28.8-13.8 39.7C493.3 244.5 512 272.1 512 304c0 34.2-21.4 63.4-51.6 74.8c2.3 6.6 3.6 13.8 3.6 21.2c0 35.3-28.7 64-64 64c-5.6 0-11.1-.7-16.3-2.1c-3 28.2-26.8 50.1-55.7 50.1c-30.9 0-56-25.1-56-56l0-400c0-30.9 25.1-56 56-56z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-20m-curriculum">GRT-20M-Curriculum (47.36% MC / 97.6% GSM8K)</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M184 0c30.9 0 56 25.1 56 56l0 400c0 30.9-25.1 56-56 56c-28.9 0-52.7-21.9-55.7-50.1c-5.2 1.4-10.7 2.1-16.3 2.1c-35.3 0-64-28.7-64-64c0-7.4 1.3-14.6 3.6-21.2C21.4 367.4 0 338.2 0 304c0-31.9 18.7-59.5 45.8-72.3C37.1 220.8 32 207 32 192c0-30.7 21.6-56.3 50.4-62.6C80.8 123.9 80 118 80 112c0-29.9 20.6-55.1 48.3-62.1C131.3 21.9 155.1 0 184 0zM328 0c28.9 0 52.6 21.9 55.7 49.9c27.8 7 48.3 32.1 48.3 62.1c0 6-.8 11.9-2.4 17.4c28.8 6.2 50.4 31.9 50.4 62.6c0 15-5.1 28.8-13.8 39.7C493.3 244.5 512 272.1 512 304c0 34.2-21.4 63.4-51.6 74.8c2.3 6.6 3.6 13.8 3.6 21.2c0 35.3-28.7 64-64 64c-5.6 0-11.1-.7-16.3-2.1c-3 28.2-26.8 50.1-55.7 50.1c-30.9 0-56-25.1-56-56l0-400c0-30.9 25.1-56 56-56z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-10m-curriculum">GRT-10M-Curriculum (44.57% MC / 95.8% GSM8K)</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon"><path fill="currentColor" d="M448 80l0 48c0 44.2-100.3 80-224 80S0 172.2 0 128L0 80C0 35.8 100.3 0 224 0S448 35.8 448 80zM393.2 214.7c20.8-7.4 39.9-16.9 54.8-28.6L448 288c0 44.2-100.3 80-224 80S0 332.2 0 288L0 186.1c14.9 11.8 34 21.2 54.8 28.6C99.7 230.7 159.5 240 224 240s124.3-9.3 169.2-25.3zM0 346.1c14.9 11.8 34 21.2 54.8 28.6C99.7 390.7 159.5 400 224 400s124.3-9.3 169.2-25.3c20.8-7.4 39.9-16.9 54.8-28.6l0 85.9c0 44.2-100.3 80-224 80S0 476.2 0 432l0-85.9z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m">GRT-30M (Qwen 3 Distilled Base + GGUF)</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon"><path fill="currentColor" d="M448 80l0 48c0 44.2-100.3 80-224 80S0 172.2 0 128L0 80C0 35.8 100.3 0 224 0S448 35.8 448 80zM393.2 214.7c20.8-7.4 39.9-16.9 54.8-28.6L448 288c0 44.2-100.3 80-224 80S0 332.2 0 288L0 186.1c14.9 11.8 34 21.2 54.8 28.6C99.7 230.7 159.5 240 224 240s124.3-9.3 169.2-25.3zM0 346.1c14.9 11.8 34 21.2 54.8 28.6C99.7 390.7 159.5 400 224 400s124.3-9.3 169.2-25.3c20.8-7.4 39.9-16.9 54.8-28.6l0 85.9c0 44.2-100.3 80-224 80S0 476.2 0 432l0-85.9z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-20m">GRT-20M</a> | <a href="https://huggingface.co/MatterWaveAI/grt-10m">GRT-10M</a></li>
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</ul>
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</div>
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<div class="col-span-1 p2">
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<p><strong>Reasoning, Routing & NLP Specialists</strong></p>
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<ul class="social">
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M176 24c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40c-35.3 0-64 28.7-64 64l-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0c0 35.3 28.7 64 64 64l0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40c35.3 0 64-28.7 64-64l40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0c0-35.3-28.7-64-64-64l0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40zM160 128l192 0c17.7 0 32 14.3 32 32l0 192c0 17.7-14.3 32-32 32l-192 0c-17.7 0-32-14.3-32-32l0-192c0-17.7 14.3-32 32-32zm192 32l-192 0 0 192 192 0 0-192z"/></svg><a href="https://huggingface.co/MatterWaveAI/open-s1-grt-30m">Open-S1-GRT-30M (System-1 Router)</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M176 24c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40c-35.3 0-64 28.7-64 64l-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0c0 35.3 28.7 64 64 64l0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40c35.3 0 64-28.7 64-64l40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0c0-35.3-28.7-64-64-64l0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40zM160 128l192 0c17.7 0 32 14.3 32 32l0 192c0 17.7-14.3 32-32 32l-192 0c-17.7 0-32-14.3-32-32l0-192c0-17.7 14.3-32 32-32zm192 32l-192 0 0 192 192 0 0-192z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-chat">GRT-30M-Chat</a> | <a href="https://huggingface.co/MatterWaveAI/grt-30m-mor">GRT-30M-MoR</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M176 24c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40c-35.3 0-64 28.7-64 64l-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0c0 35.3 28.7 64 64 64l0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40c35.3 0 64-28.7 64-64l40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0c0-35.3-28.7-64-64-64l0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40zM160 128l192 0c17.7 0 32 14.3 32 32l0 192c0 17.7-14.3 32-32 32l-192 0c-17.7 0-32-14.3-32-32l0-192c0-17.7 14.3-32 32-32zm192 32l-192 0 0 192 192 0 0-192z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-code">GRT-30M-Code</a> | <a href="https://huggingface.co/MatterWaveAI/grt-30m-prm">GRT-30M-PRM</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M176 24c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40c-35.3 0-64 28.7-64 64l-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0c0 35.3 28.7 64 64 64l0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40c35.3 0 64-28.7 64-64l40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0c0-35.3-28.7-64-64-64l0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40zM160 128l192 0c17.7 0 32 14.3 32 32l0 192c0 17.7-14.3 32-32 32l-192 0c-17.7 0-32-14.3-32-32l0-192c0-17.7 14.3-32 32-32zm192 32l-192 0 0 192 192 0 0-192z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-qa">GRT-30M-QA</a> | <a href="https://huggingface.co/MatterWaveAI/grt-30m-ner">GRT-30M-NER</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M176 24c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40c-35.3 0-64 28.7-64 64l-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0 0 56-40 0c-13.3 0-24 10.7-24 24s10.7 24 24 24l40 0c0 35.3 28.7 64 64 64l0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40 56 0 0 40c0 13.3 10.7 24 24 24s24-10.7 24-24l0-40c35.3 0 64-28.7 64-64l40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0 0-56 40 0c13.3 0 24-10.7 24-24s-10.7-24-24-24l-40 0c0-35.3-28.7-64-64-64l0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40c0-13.3-10.7-24-24-24s-24 10.7-24 24l0 40-56 0 0-40zM160 128l192 0c17.7 0 32 14.3 32 32l0 192c0 17.7-14.3 32-32 32l-192 0c-17.7 0-32-14.3-32-32l0-192c0-17.7 14.3-32 32-32zm192 32l-192 0 0 192 192 0 0-192z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-lora">GRT-30M-LoRA</a></li>
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</ul>
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</div>
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<div class="col-span-1 p2">
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<p><strong>Retrieval, Embeddings & Tokenizer</strong></p>
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<ul class="social">
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 512" class="icon"><path fill="currentColor" d="M175 389.4c-9.8 16-15 34.3-15 53.1c-10 3.5-20.8 5.5-32 5.5c-53 0-96-43-96-96L32 64C14.3 64 0 49.7 0 32S14.3 0 32 0L96 0l64 0 64 0c17.7 0 32 14.3 32 32s-14.3 32-32 32l0 245.9-49 79.6zM96 64l0 96 64 0 0-96L96 64zM352 0L480 0l32 0c17.7 0 32 14.3 32 32s-14.3 32-32 32l0 150.9L629.7 406.2c6.7 10.9 10.3 23.5 10.3 36.4c0 38.3-31.1 69.4-69.4 69.4l-309.2 0c-38.3 0-69.4-31.1-69.4-69.4c0-12.8 3.6-25.4 10.3-36.4L320 214.9 320 64c-17.7 0-32-14.3-32-32s14.3-32 32-32l32 0zm32 64l0 160c0 5.9-1.6 11.7-4.7 16.8L330.5 320l171 0-48.8-79.2c-3.1-5-4.7-10.8-4.7-16.8l0-160-64 0z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-embedding">GRT-30M-Embedding (Circular-Pooled)</a></li>
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| 79 |
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 512" class="icon"><path fill="currentColor" d="M175 389.4c-9.8 16-15 34.3-15 53.1c-10 3.5-20.8 5.5-32 5.5c-53 0-96-43-96-96L32 64C14.3 64 0 49.7 0 32S14.3 0 32 0L96 0l64 0 64 0c17.7 0 32 14.3 32 32s-14.3 32-32 32l0 245.9-49 79.6zM96 64l0 96 64 0 0-96L96 64zM352 0L480 0l32 0c17.7 0 32 14.3 32 32s-14.3 32-32 32l0 150.9L629.7 406.2c6.7 10.9 10.3 23.5 10.3 36.4c0 38.3-31.1 69.4-69.4 69.4l-309.2 0c-38.3 0-69.4-31.1-69.4-69.4c0-12.8 3.6-25.4 10.3-36.4L320 214.9 320 64c-17.7 0-32-14.3-32-32s14.3-32 32-32l32 0zm32 64l0 160c0 5.9-1.6 11.7-4.7 16.8L330.5 320l171 0-48.8-79.2c-3.1-5-4.7-10.8-4.7-16.8l0-160-64 0z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-reranker">GRT-30M-Reranker</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 512" class="icon"><path fill="currentColor" d="M175 389.4c-9.8 16-15 34.3-15 53.1c-10 3.5-20.8 5.5-32 5.5c-53 0-96-43-96-96L32 64C14.3 64 0 49.7 0 32S14.3 0 32 0L96 0l64 0 64 0c17.7 0 32 14.3 32 32s-14.3 32-32 32l0 245.9-49 79.6zM96 64l0 96 64 0 0-96L96 64zM352 0L480 0l32 0c17.7 0 32 14.3 32 32s-14.3 32-32 32l0 150.9L629.7 406.2c6.7 10.9 10.3 23.5 10.3 36.4c0 38.3-31.1 69.4-69.4 69.4l-309.2 0c-38.3 0-69.4-31.1-69.4-69.4c0-12.8 3.6-25.4 10.3-36.4L320 214.9 320 64c-17.7 0-32-14.3-32-32s14.3-32 32-32l32 0zm32 64l0 160c0 5.9-1.6 11.7-4.7 16.8L330.5 320l171 0-48.8-79.2c-3.1-5-4.7-10.8-4.7-16.8l0-160-64 0z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-tokenizer">GRT-30M-Tokenizer & Polar Bank</a></li>
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</ul>
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</div>
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<div class="col-span-1 p2">
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<p><strong>Multimodal (Omni, Vision, Speech, Audio)</strong></p>
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| 85 |
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<ul class="social">
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M208.5 62.3l28.1-36.9C248.8 9.4 267.8 0 288 0c28.5 0 53.6 18.7 61.8 46l17.8 59.4c10.3 34.4 36.1 62 69.8 74.6l39.8 14.9c20.9 7.9 34.8 27.9 34.8 50.2c0 16.9-7.9 32.8-21.5 42.9l-67.3 50.5c-24.3 18.2-37.2 47.9-33.8 78.1l2.5 22.7c4.3 38.7-26 72.6-65 72.6c-14.8 0-29.3-5.1-40.8-14.3l-55.4-44.3c-4.5-3.6-9.3-6.7-14.5-9.2c-15.8-7.9-33.7-10.4-51-7.3L82.4 451.9C47.8 458.2 16 431.6 16 396.5c0-13.2 4.7-26 13.1-36.2l11.2-13.4c14.6-17.4 22.6-39.4 22.6-62.1c0-18.8-5.5-37.2-15.8-53L8.8 173.5C3.1 164.7 0 154.4 0 143.9c0-33.4 30.1-58.8 63-53.2l51.3 8.7c35.9 6.1 72.2-8.2 94.2-37.1z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-omni">GRT-30M-Omni (Vision + Audio + Speech + Text)</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M208.5 62.3l28.1-36.9C248.8 9.4 267.8 0 288 0c28.5 0 53.6 18.7 61.8 46l17.8 59.4c10.3 34.4 36.1 62 69.8 74.6l39.8 14.9c20.9 7.9 34.8 27.9 34.8 50.2c0 16.9-7.9 32.8-21.5 42.9l-67.3 50.5c-24.3 18.2-37.2 47.9-33.8 78.1l2.5 22.7c4.3 38.7-26 72.6-65 72.6c-14.8 0-29.3-5.1-40.8-14.3l-55.4-44.3c-4.5-3.6-9.3-6.7-14.5-9.2c-15.8-7.9-33.7-10.4-51-7.3L82.4 451.9C47.8 458.2 16 431.6 16 396.5c0-13.2 4.7-26 13.1-36.2l11.2-13.4c14.6-17.4 22.6-39.4 22.6-62.1c0-18.8-5.5-37.2-15.8-53L8.8 173.5C3.1 164.7 0 154.4 0 143.9c0-33.4 30.1-58.8 63-53.2l51.3 8.7c35.9 6.1 72.2-8.2 94.2-37.1z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-vl">GRT-30M-VL</a> | <a href="https://huggingface.co/MatterWaveAI/grt-30m-image">GRT-30M-Image</a></li>
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<li><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon"><path fill="currentColor" d="M208.5 62.3l28.1-36.9C248.8 9.4 267.8 0 288 0c28.5 0 53.6 18.7 61.8 46l17.8 59.4c10.3 34.4 36.1 62 69.8 74.6l39.8 14.9c20.9 7.9 34.8 27.9 34.8 50.2c0 16.9-7.9 32.8-21.5 42.9l-67.3 50.5c-24.3 18.2-37.2 47.9-33.8 78.1l2.5 22.7c4.3 38.7-26 72.6-65 72.6c-14.8 0-29.3-5.1-40.8-14.3l-55.4-44.3c-4.5-3.6-9.3-6.7-14.5-9.2c-15.8-7.9-33.7-10.4-51-7.3L82.4 451.9C47.8 458.2 16 431.6 16 396.5c0-13.2 4.7-26 13.1-36.2l11.2-13.4c14.6-17.4 22.6-39.4 22.6-62.1c0-18.8-5.5-37.2-15.8-53L8.8 173.5C3.1 164.7 0 154.4 0 143.9c0-33.4 30.1-58.8 63-53.2l51.3 8.7c35.9 6.1 72.2-8.2 94.2-37.1z"/></svg><a href="https://huggingface.co/MatterWaveAI/grt-30m-asr">GRT-30M-ASR</a> | <a href="https://huggingface.co/MatterWaveAI/grt-30m-tts">GRT-30M-TTS</a></li>
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<title>MatterWave AI — Geometric Rotation Transformer (GRT) Suite</title>
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<h1>MatterWave AI</h1>
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<p><strong>MatterWave AI</strong> researches and builds <strong>Geometric Rotation Transformers (<code>GRT</code>)</strong> — a purely rotational foundation architecture that replaces dense linear weight matrices (<code>nn.Linear</code>) in attention (<code>Q, K, V, O</code>) and feed-forward (<code>expand, contract</code>) blocks with cascades of content-modulated <code>2×2</code> Givens rotations on <code>SO(D)</code> interleaved with butterfly permutations.</p>
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<p>Every transform in the GRT residual path is norm-preserving by construction (<code>||R(theta) x||_2 = ||x||_2</code>), enabling deterministic multi-backend execution (<code>PyTorch</code> CUDA / ROCm / Intel XPU, <code>vLLM</code>, and <code>llama.cpp</code> CPU / Vulkan / HIP) and multi-round geometric optimization (<code>PairAdam</code>, <code>SymplecticAdam</code>, and <code>HuygensSymplecticAdam</code>).</p>
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<p>• <strong>Whitepaper:</strong> <a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m/resolve/main/GRT_Whitepaper.pdf"><strong>The Geometric Rotation Transformer (GRT): A Purely Rotational Foundation Architecture (<code>GRT_Whitepaper.pdf</code>)</strong></a></p>
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<hr/>
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<h2>1. Foundation Scale Tiers (<code>10M</code> / <code>20M</code> / <code>30M</code>) & Curriculum Progression</h2>
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<p>Starting from the exact same pretrained checkpoints built for our NeurIPS submission with first-generation <code>PairAdam</code>, replacing the optimizer with <strong><code>HuygensSymplecticAdam</code></strong> and training across a <strong>Multi-Round Curriculum (<code>-curriculum</code>)</strong> delivers large gains across the 10-task <code>SLM-Bench</code> evaluation suite (<code>13,144</code> held-out multiple-choice examples + <code>500</code> held-out <code>GSM8K</code> mathematical reasoning problems):</p>
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<h3>9-Task Multiple-Choice Macro Average (<code>BoolQ</code>, <code>ARC-E</code>, <code>ARC-C</code>, <code>OpenBookQA</code>, <code>PIQA</code>, <code>WinoGrande</code>, <code>HellaSwag</code>, <code>QNLI</code>, <code>CommonsenseQA</code>)</h3>
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<div class="table-wrap"><table><thead><tr><th>Scale Tier</th><th>Total / Non-Emb Params</th><th>Pre-Fine-Tune Base</th><th>NeurIPS Baseline (<code>PairAdam</code>)</th><th>Single-Pass (<code>HuygensSymplecticAdam</code>)</th><th>Multi-Round Curriculum (<code>-curriculum</code>)</th><th>Gain (<code>-curriculum</code> vs. <code>PairAdam</code>)</th></tr></thead><tbody>
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<tr><td><strong><code>GRT-10M</code></strong> (<code>6</code> blocks)</td><td><code>8.7M</code> / <code>2.2M</code></td><td><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-10m-base"><code>grt-10m-base</code></a> (<code>38.08%</code>)</td><td><code>37.61%</code></td><td><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-10m"><code>grt-10m</code></a> (<code>41.71%</code>)</td><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-10m-curriculum"><code>grt-10m-curriculum</code></a> (<code>44.57%</code>)</strong></td><td><strong><code>+6.96%</code></strong></td></tr>
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<tr><td><strong><code>GRT-20M</code></strong> (<code>12</code> blocks)</td><td><code>16.7M</code> / <code>10.3M</code></td><td><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-20m-base"><code>grt-20m-base</code></a> (<code>39.16%</code>)</td><td><code>38.63%</code></td><td><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-20m"><code>grt-20m</code></a> (<code>45.03%</code>)</td><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-20m-curriculum"><code>grt-20m-curriculum</code></a> (<code>47.36%</code>)</strong></td><td><strong><code>+8.73%</code></strong></td></tr>
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<tr><td><strong><code>GRT-30M</code></strong> (<code>12</code> blocks)</td><td><code>29.3M</code> / <code>9.74M</code></td><td><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m"><code>grt-30m</code></a> (<code>37.56%</code>)</td><td><code>39.61%</code></td><td><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m"><code>grt-30m</code></a> (<code>43.86%</code>)</td><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-curriculum"><code>grt-30m-curriculum</code></a> (<code>47.16%</code>)</strong></td><td><strong><code>+7.55%</code></strong></td></tr>
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</tbody></table></div>
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<h3>Mathematical Reasoning Held-Out Perplexity & Verification (<code>GSM8K</code>, <code>test</code> split, <code>n = 500</code>)</h3>
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<div class="table-wrap"><table><thead><tr><th>Scale Tier</th><th>Zero-Shot (<code>PPL</code> ↓ / <code>Acc</code> ↑)</th><th>NeurIPS Baseline (<code>PairAdam</code>)</th><th>Single-Pass (<code>HuygensSymplecticAdam</code>)</th><th>Multi-Round Curriculum (<code>-curriculum</code>)</th><th>Improvement (<code>-curriculum</code> vs. Zero-Shot)</th></tr></thead><tbody>
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<tr><td><strong><code>GRT-10M</code></strong></td><td><code>145.85</code> / <code>22.00%</code></td><td><code>37.27</code> / <code>21.80%</code></td><td><code>30.09</code> / <code>84.60%</code></td><td><strong><code>25.28</code> / <code>95.80%</code></strong></td><td><strong><code>5.77×</code> lower PPL (<code>+74.00%</code> vs. <code>PairAdam</code>)</strong></td></tr>
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<tr><td><strong><code>GRT-20M</code></strong></td><td><code>60.12</code> / <code>21.00%</code></td><td><code>12.52</code> / <code>28.80%</code></td><td><code>9.11</code> / <code>93.20%</code></td><td><strong><code>7.65</code> / <code>97.60%</code></strong></td><td><strong><code>7.86×</code> lower PPL (<code>+68.80%</code> vs. <code>PairAdam</code>)</strong></td></tr>
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<tr><td><strong><code>GRT-30M</code></strong></td><td><code>28.00</code> / <code>34.20%</code></td><td><code>10.60</code> / <code>39.20%</code></td><td><code>9.04</code> / <code>98.60%</code></td><td><strong><code>7.60</code> / <code>99.20%</code></strong></td><td><strong><code>3.68×</code> lower PPL (<code>+60.00%</code> vs. <code>PairAdam</code>)</strong></td></tr>
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<h2>2. Complete <code>MatterWaveAI</code> Model Catalog (<code>25</code> Public Repositories)</h2>
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<h3>A. Causal Language Models & Curriculum Checkpoints</h3>
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<div class="table-wrap"><table><thead><tr><th>Repository</th><th>Parameters (Total / Backbone)</th><th>Description</th></tr></thead><tbody>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-curriculum"><code>MatterWaveAI/grt-30m-curriculum</code></a></strong></td><td><code>29.3M</code> / <code>9.74M</code> (<code>12L</code>)</td><td><code>GRT-30M</code> adapted with multi-round <code>HuygensSymplecticAdam</code> curriculum (<code>47.16%</code> 9-task MC avg, <code>99.20%</code> GSM8K verification)</td></tr>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m"><code>MatterWaveAI/grt-30m</code></a></strong></td><td><code>29.3M</code> / <code>9.74M</code> (<code>12L</code>)</td><td>24-hour Qwen 3 distillation checkpoint (<code>10.79B</code> tokens at <code>123.9k tok/s</code> on <code>8× A100-80GB</code>, <code>GGUF</code> + <code>safetensors</code>)</td></tr>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-20m-curriculum"><code>MatterWaveAI/grt-20m-curriculum</code></a></strong></td><td><code>16.7M</code> / <code>10.3M</code> (<code>12L</code>)</td><td><code>GRT-20M</code> adapted with multi-round <code>HuygensSymplecticAdam</code> curriculum (<code>47.36%</code> 9-task MC avg, <code>97.60%</code> GSM8K verification)</td></tr>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-20m"><code>MatterWaveAI/grt-20m</code></a></strong></td><td><code>16.7M</code> / <code>10.3M</code> (<code>12L</code>)</td><td><code>GRT-20M</code> 8-corpus pretrained model with single-pass <code>HuygensSymplecticAdam</code> <code>SLM-Bench</code> evaluation (<code>45.03%</code> 9-task MC avg)</td></tr>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-20m-base"><code>MatterWaveAI/grt-20m-base</code></a></strong></td><td><code>16.7M</code> / <code>10.3M</code> (<code>12L</code>)</td><td>Archived pre-fine-tune NeurIPS submission checkpoint (<code>PairAdam</code>, 8-corpus pretraining, <code>GGUF</code> + <code>safetensors</code>)</td></tr>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-10m-curriculum"><code>MatterWaveAI/grt-10m-curriculum</code></a></strong></td><td><code>8.7M</code> / <code>2.2M</code> (<code>6L</code>)</td><td><code>GRT-10M</code> adapted with multi-round <code>HuygensSymplecticAdam</code> curriculum (<code>44.57%</code> 9-task MC avg, <code>95.80%</code> GSM8K verification)</td></tr>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-10m"><code>MatterWaveAI/grt-10m</code></a></strong></td><td><code>8.7M</code> / <code>2.2M</code> (<code>6L</code>)</td><td><code>GRT-10M</code> Nemotron pretrained model with single-pass <code>HuygensSymplecticAdam</code> <code>SLM-Bench</code> evaluation (<code>41.71%</code> 9-task MC avg)</td></tr>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-10m-base"><code>MatterWaveAI/grt-10m-base</code></a></strong></td><td><code>8.7M</code> / <code>2.2M</code> (<code>6L</code>)</td><td>Archived pre-fine-tune NeurIPS submission checkpoint (<code>PairAdam</code>, <code>336k</code> steps on Nemotron)</td></tr>
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-nano-smoke"><code>MatterWaveAI/grt-nano-smoke</code></a></strong></td><td><code>2.1M</code> (<code>2L</code>)</td><td>Minimal CI smoke-test rotational checkpoint for fast CPU/GPU pipeline verification</td></tr>
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| 43 |
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</tbody></table></div>
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| 44 |
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<h3>B. Reasoning, System-1 Routing, Code & NLP Specialists</h3>
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| 45 |
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<div class="table-wrap"><table><thead><tr><th>Repository</th><th>Task / Architecture</th><th>Highlights</th></tr></thead><tbody>
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| 46 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/open-s1-grt-30m"><code>MatterWaveAI/open-s1-grt-30m</code></a></strong></td><td>System-1 Cognitive Telemetry Router</td><td>5-family toroidal phase heads (<code>action_router</code>, <code>escalation</code>, <code>loop_guard</code>, <code>spec_support</code>, <code>verification_gate</code>) with <strong><code>98.06%</code> accuracy (<code>ECE = 0.0095</code>)</strong></td></tr>
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| 47 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-chat"><code>MatterWaveAI/grt-30m-chat</code></a></strong></td><td>Instruction & Dialogue (<code>ChatML</code>)</td><td>Conversational fine-tune of <code>GRT-30M</code> with 8-way geometric optimizer ablation</td></tr>
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| 48 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-mor"><code>MatterWaveAI/grt-30m-mor</code></a></strong></td><td>4-Expert Mixture-of-Rotations (<code>MoR</code>)</td><td>Phase-routed rotational experts with top-2 cosine gating</td></tr>
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| 49 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-code"><code>MatterWaveAI/grt-30m-code</code></a></strong></td><td>Code Generation & Completion</td><td>Rotational causal LM adapted on Python and multi-language code corpora</td></tr>
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| 50 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-prm"><code>MatterWaveAI/grt-30m-prm</code></a></strong></td><td>Process Reward Model (<code>GRTForProcessReward</code>)</td><td>Step-level mathematical and logical verification head</td></tr>
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| 51 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-qa"><code>MatterWaveAI/grt-30m-qa</code></a></strong></td><td>Extractive Question Answering</td><td>Span-extraction rotational head (<code>SQuAD</code> / reading comprehension)</td></tr>
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| 52 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-ner"><code>MatterWaveAI/grt-30m-ner</code></a></strong></td><td>Token Classification & NER</td><td>Rotational token-level entity recognizer (<code>CoNLL-2003</code>)</td></tr>
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| 53 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-lora"><code>MatterWaveAI/grt-30m-lora</code></a></strong></td><td>Rotational Low-Rank Adapter (<code>GRT-LoRA</code>)</td><td>Parameter-efficient angular phase & coupling adapter (<code>safetensors</code> + <code>GGUF</code>)</td></tr>
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</tbody></table></div>
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<h3>C. Retrieval, Sentence Embeddings & Canonical Tokenizer</h3>
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<div class="table-wrap"><table><thead><tr><th>Repository</th><th>Task / Architecture</th><th>Highlights</th></tr></thead><tbody>
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| 57 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-embedding"><code>MatterWaveAI/grt-30m-embedding</code></a></strong></td><td>Circular-Pooled Sentence Encoder</td><td><code>SentenceTransformer</code> using planar-pair circular pooling (<code>pooling_mode="circular"</code>, <code>71.79</code> STS-B Val Spearman)</td></tr>
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| 58 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-reranker"><code>MatterWaveAI/grt-30m-reranker</code></a></strong></td><td>Cross-Encoder Passage Reranker</td><td>Rotational cross-encoder for query-document relevance scoring</td></tr>
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| 59 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-tokenizer"><code>MatterWaveAI/grt-30m-tokenizer</code></a></strong></td><td>Canonical Tokenizer & Polar Embedding Bank</td><td><code>151,669</code>-token BPE tokenizer + pre-factored polar embedding bank (<code>phase_angles</code> + <code>log_magnitude</code>)</td></tr>
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| 60 |
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</tbody></table></div>
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<h3>D. Multimodal Vision, Audio & Speech (<code>Omni</code>, <code>VL</code>, <code>ASR</code>, <code>TTS</code>, <code>Image</code>)</h3>
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| 62 |
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<div class="table-wrap"><table><thead><tr><th>Repository</th><th>Modality</th><th>Highlights</th></tr></thead><tbody>
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| 63 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-omni"><code>MatterWaveAI/grt-30m-omni</code></a></strong></td><td>Vision + Audio + Text + Speech (<code>GRTOmni</code>)</td><td>Unified 4-modality rotational foundation model (<code>safetensors</code> + <code>FP16/FP32 GGUF</code>)</td></tr>
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| 64 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-vl"><code>MatterWaveAI/grt-30m-vl</code></a></strong></td><td>Vision-Language (<code>GRTVL</code>)</td><td>Rotational patch projector + causal language decoder</td></tr>
|
| 65 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-asr"><code>MatterWaveAI/grt-30m-asr</code></a></strong></td><td>Automatic Speech Recognition (<code>GRTASR</code>)</td><td>Rotational log-mel spectrogram encoder + text decoder (<code>safetensors</code> + <code>GGUF</code>)</td></tr>
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| 66 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-tts"><code>MatterWaveAI/grt-30m-tts</code></a></strong></td><td>Rotational Text-to-Speech (<code>GRTTTS</code>)</td><td>Acoustic codec & waveform synthesis via Givens cascades (<code>safetensors</code> + <code>GGUF</code>)</td></tr>
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| 67 |
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<tr><td><strong><a target="_top" rel="noopener" href="https://huggingface.co/MatterWaveAI/grt-30m-image"><code>MatterWaveAI/grt-30m-image</code></a></strong></td><td>Rotational Image Generation</td><td>Continuous/discrete image patch synthesis with <code>2×2</code> Givens cascades</td></tr>
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</tbody></table></div>
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