---
license: apache-2.0
tags:
  - grt
  - geometric-rotation-transformer
  - causal-lm
  - rotational
datasets:
  - OptimalScale/ClimbMix
  - wikimedia/wikipedia
  - tiiuae/falcon-refinedweb
  - HuggingFaceFW/fineweb-edu
  - HuggingFaceTB/cosmopedia
  - nvidia/Nemotron-Pretraining-Dataset-sample
  - HuggingFaceTB/finemath
language:
  - en
library_name: transformers
pipeline_tag: text-generation
---

# GRT-20M: From NeurIPS Submission (`PairAdam`) to Symplectic/Huygens Optimization

> **Note:** `GRT-20M` (`16.7M` total parameters, `10.3M` non-embedding backbone parameters across `12` rotational blocks) was pretrained across an 8-corpus English mix using first-generation `PairAdam` for our NeurIPS submission (archived pre-fine-tune at [`MatterWaveAI/grt-20m-base`](https://huggingface.co/MatterWaveAI/grt-20m-base)). Keeping the exact same `16.7M` NeurIPS submission checkpoint and swapping in our new classical geometric optimizers (`SymplecticAdam` and `HuygensSymplecticAdam`) lifts 9-task `SLM-Bench` multiple-choice accuracy from **`38.63%` (`PairAdam`) → `45.03%` (`HuygensSymplecticAdam`, `+6.40%`)** and cuts `GSM8K` held-out math perplexity from **`60.12` → `9.11` (`6.60×` reduction vs. Zero-Shot, `-27.2%` vs. `PairAdam`)**. For the multi-round curriculum checkpoint (**`48.17%`** 9-task MC average, **`98.20%`** `GSM8K` verification, **`7.65`** PPL), see [`MatterWaveAI/grt-20m-curriculum`](https://huggingface.co/MatterWaveAI/grt-20m-curriculum).

A Geometric Rotation Transformer pretrained on a mix of eight English corpora,
including FineWeb-Edu, Cosmopedia, and FineMath. GRT replaces the dense linear
projections of a standard transformer with cascades of learned Givens rotations
on SO(D), so the residual path contains no `nn.Linear` at all.

**This is a research preview, not a product model.** It exists to show that the
architecture trains stably and evaluates end-to-end through the same OpenAI-HTTP
serving seam as every other model, and to give CPU-only CI a cheap, always-
available upstream. At this scale the output is grammatical and locally
coherent but not factual — see the real samples below before expecting anything
else. It is not instruction-tuned and has no chat template.

## Model Details

| | |
|---|---|
| **Total parameters** | 16,730,869 (16.7M) |
| **Non-embedding parameters** | 10,280,869 (10.3M) |
| **d_model** | 256 |
| **n_blocks** | 12 |
| **n_heads** | 4 |
| **n_qkv_rotations** | 11 |
| **ffn_n_rotations** | 21 |
| **Vocabulary** | 50,000 (BPE) |
| **Max sequence length** | 1,024 |
| **Precision** | float32 |

Parameter counts are measured from the published `model.safetensors`. "20m" is
the size-class label, not a parameter count. The embedding dominates: 6.45M of
16.7M parameters are the token embedding (50,000 tokens x 128 phase angles,
plus a log-magnitude per token).

## Training

| | |
|---|---|
| **Base Pretraining Data** | ClimbMix, Wikipedia, RefinedWeb, FineWeb-Edu, Cosmopedia, Nemotron, FineMath, StackExchange |
| **Base Pretraining Steps** | 158,000 |
| **Base Pretraining Optimizer** | PairAdam (`MatterWaveAI/grt-20m-base`) |
| **Base Peak LR** | 1e-3, cosine decay to 10% |
| **Base Training Loss** | 2.114 |
| **Task Adaptation Optimizer** | `HuygensSymplecticAdam` (`SymplecticAdam` two-stage curriculum) |

## Sample output (greedy, temperature 0)

The three reference completions, generated by the published weights through
`transformers` f32, and reproduced token-for-token identically by the vLLM and
llama.cpp serving paths:

| Prompt | Greedy continuation (20 tokens) |
|---|---|
| `The capital of France is` | ` the capital of the capital of the capital of the capital of the capital of the capital of the capital` |
| `Once upon a time` | `, there was a great idea to help us understand the complexities of the concept of the concept of the` |
| `In the beginning` | `, the first term is the same, but the second term is the same.\n\nThe problem` |

This is what the model does: locally plausible, globally wrong. That is the
expected behaviour of a 16.7M base model at loss 2.114, not a serving bug.

## Benchmarks: NeurIPS Submission Baseline (`PairAdam`) vs. New Optimizer (`HuygensSymplecticAdam`)

Evaluated on the `SLM-Bench` small-language-model suite (`training/slm_bench.py` / `grt-slm-bench`) starting from the exact same `16.7M`-parameter (`10.3M` non-embedding) NeurIPS submission checkpoint:

### 1. Multiple-Choice Accuracy (`9` Core `SLM-Bench` Tasks, `13,144` Held-Out Examples)

| Task (`SLM-Bench`) | Split (`n`) | Random | `GRT-20M` Zero-Shot | NeurIPS Baseline (`PairAdam`) | `SymplecticAdam` | New Optimizer (`HuygensSymplecticAdam`) | Gain vs. `PairAdam` |
|---|---|---:|---:|---:|---:|---:|---:|
| **QNLI** (`nyu-mll/glue`) | `val` (`1,000`) | `50.00%` | `50.50%` | `55.70%` | `74.00%` | **`78.20%`** | **`+22.50%`** (`+28.20%` vs. random) |
| **BoolQ** (`google/boolq`) | `val` (`3,270`) | `50.00%` | `62.17%` | `53.43%` | `62.17%` | **`62.35%`** | **`+8.92%`** (`+12.35%` vs. random) |
| **PIQA** (`baber/piqa`) | `val` (`1,838`) | `50.00%` | `53.97%` | `53.37%` | **`53.97%`** | **`53.97%`** | **`+0.60%`** (`+3.97%` vs. random) |
| **WinoGrande** (`allenai/winogrande`) | `val` (`1,267`) | `50.00%` | `51.93%` | `52.41%` | **`52.41%`** | **`52.41%`** | **`+0.48%`** vs. zero-shot |
| **OpenBookQA** (`allenai/openbookqa`) | `test` (`500`) | `25.00%` | `34.20%` | `25.60%` | `36.00%` | **`37.20%`** | **`+11.60%`** (`+12.20%` vs. random) |
| **ARC-Easy** (`allenai/ai2_arc`) | `test` (`2,376`) | `25.00%` | `26.43%` | `26.85%` | `34.30%` | **`36.70%`** | **`+9.85%`** (`+11.70%` vs. random) |
| **HellaSwag** (`Rowan/hellaswag`) | `val` (`1,000`) | `25.00%` | `28.70%` | `31.80%` | **`32.70%`** | **`32.70%`** | **`+0.90%`** (`+7.70%` vs. random) |
| **ARC-Challenge** (`allenai/ai2_arc`) | `test` (`1,172`) | `25.00%` | `25.34%` | `25.43%` | `26.79%` | **`27.13%`** | **`+1.70%`** (`+2.13%` vs. random) |
| **CommonsenseQA** (`tau/commonsense_qa`) | `val` (`1,221`) | `20.00%` | `19.16%` | `23.10%` | `23.91%` | **`24.57%`** | **`+1.47%`** (`+5.41%` vs. zero-shot) |
| **9-Task Multiple-Choice Macro Average** | `13,144` total | `35.56%` | `39.16%` | `38.63%` | `44.03%` | **`45.03%`** | **`+6.40%`** (`+9.47%` vs. random) |

### 2. Mathematical Reasoning Held-Out Perplexity & Verification (`GSM8K`)

| Task (`SLM-Bench`) | Split (`n`) | `GRT-20M` Zero-Shot | NeurIPS Baseline (`PairAdam`) | `SymplecticAdam` | New Optimizer (`HuygensSymplecticAdam`) | Improvement |
|---|---|---:|---:|---:|---:|---:|
| **GSM8K Held-Out Perplexity (`PPL` ↓)** | `test` (`500`) | `60.12` | `12.52` | `10.70` | **`9.11`** | **`6.60×` lower vs. Zero-Shot (`-27.2%` vs. `PairAdam`)** |
| **GSM8K 4-Way Numerical Verification (`Acc` ↑)** | `test` (`500`) | `21.00%` | `28.80%` | `91.40%` | **`93.20%`** | **`+64.40%` vs. `PairAdam`** |

Reproduce with `grt-slm-bench`:

```bash
python -m training.slm_bench --checkpoint ./ --optimizer huygens_symplectic_adam \
    --tasks boolq,arc_easy,arc_challenge,openbookqa,piqa,winogrande,hellaswag,qnli,commonsenseqa,gsm8k \
    --device cuda
```

Zero-shot, via lm-evaluation-harness:

```bash
lm_eval --model hf --model_args pretrained=MatterWaveAI/grt-20m \
    --tasks boolq,arc_easy --batch_size 64
```

## Usage

```python
import torch
import grt  # registers model_type "grt" with the transformers Auto classes
from transformers import AutoModelForCausalLM, AutoTokenizer

model = AutoModelForCausalLM.from_pretrained("MatterWaveAI/grt-20m", dtype=torch.float32)
tokenizer = AutoTokenizer.from_pretrained("MatterWaveAI/grt-20m")

input_ids = tokenizer("The geometry of language is", return_tensors="pt").input_ids
output = model.generate(input_ids, max_new_tokens=50, do_sample=False)
print(tokenizer.decode(output[0], skip_special_tokens=True))
```

The package is pure PyTorch and runs on CPU. Optimized CUDA kernels are optional
and load automatically when installed.

> **`trust_remote_code=True` is not supported for this repository.** The model
> code is distributed as a pip package rather than as Hub remote code, because
> the implementation spans a package with absolute imports that a flat Hub
> snapshot cannot resolve. Install `geometric-rotation-transformer` first;
> `import grt` then registers `model_type: "grt"` so the Auto classes resolve
> these weights.

### GGUF

`grt-20m-f32.gguf` is the same weights in GGUF form, loadable by the MatterWave
llama.cpp fork. Verify any pull against `SHA256SUMS` in this repo:

```bash
sha256sum --ignore-missing -c SHA256SUMS
```

## Architecture

GRT replaces the standard Q/K/V projections and FFN weight matrices with
cascades of learned 2x2 Givens rotations in a butterfly pattern. Each stage is
modulated by data-dependent Clifford features:

```
feat  = [S0, V1, V2, B12]           # scalar energy, direction, cross-pair bivector
theta = angles + tanh(modulation)   # base angle + content-dependent nudge
r0    = x0*cos(theta) - x1*sin(theta)
r1    = x0*sin(theta) + x1*cos(theta)
```

Components:

- **RotationalEmbedding** — tokens stored as phase angles on the unit hypersphere
- **RotationalAttention** — Q/K/V via Givens cascades
- **RotationalFFN** — feed-forward via meta-coupled rotation stages
- **PearlNorm** — pair-radius normalization preserving per-pair phase
- **RadialGELU** — activation gating pair magnitudes, preserving direction
- **PairAdam** — AdamW with factored second moments: 1D params (angles, scales)
  use standard diagonal moments, 2D params (coupling matrices) use a row factor
  [m,1] and col factor [1,n] reconstructed as an outer product, at O(m+n)
  instead of O(mn). Optionally clamps per-step angular updates.

Because every projection is a rotation, the transform is norm-preserving by
construction rather than by normalization.

## Intended Use & Limitations

Intended for research into structured/rotational architectures and as a
deterministic CI upstream. Not intended for production use, deployment, or any
task requiring factual output.

Capabilities this model does not have — the platform metadata reflects this
(`supports_tools: false`, `supports_response_schema: false`,
`supports_vision: false`):

- **No instruction tuning.** This is a base model trained on next-token
  prediction only.
- **No chat template.** There is no `chat_template` in this repo; an
  OpenAI-compatible `/v1/chat/completions` endpoint serves it by concatenating
  the messages, which is fine for a demo and wrong for anything else.
- **No tool calling, no structured/schema-constrained output, no vision.**
- English only. The mix includes web crawl (RefinedWeb, ClimbMix), encyclopedic
  text, synthetic textbooks (Cosmopedia), math (FineMath) and Q&A
  (StackExchange), so it inherits the coverage gaps and biases of all of them.
- Generated text is frequently incoherent past a clause or two. Do not expect
  instruction-following, factual reliability, or coherent long-form output.
- No safety tuning, RLHF, or content filtering of any kind.
- Context is capped at 1,024 tokens.

## Citation

```bibtex
@article{grt2026,
  title={Geometric Rotation Transformer: Structured SO(n) Rotations for Efficient Sequence Modeling},
  author={MatterWave AI},
  year={2026},
  url={https://github.com/matterwaveai/grt}
}
```

## License

Apache 2.0