Metadata-Version: 2.4
Name: omnimuon
Version: 0.1.0
Summary: Universal Spectral Matrix Momentum Optimizer for LLMs, Transformers, Vision & ConvNets
Author-email: Suryaansh Prithvijit Singh <connect.singha@gmail.com>, AirBorne AI Research <research@airborne.ai>
License: Apache-2.0
Project-URL: Homepage, https://github.com/AirBorneAI/airborne-muon
Project-URL: Repository, https://github.com/AirBorneAI/airborne-muon
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Scientific/Engineering :: Artificial Intelligence
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.10
Classifier: Programming Language :: Python :: 3.11
Classifier: Programming Language :: Python :: 3.12
Classifier: Programming Language :: Python :: 3.14
Classifier: License :: OSI Approved :: Apache Software License
Requires-Python: >=3.9
Description-Content-Type: text/markdown
Requires-Dist: torch>=2.0.0

# Airborne Muon: Spectral Matrix Orthogonal Optimizer for LLMs

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**Muon** is a production-grade, drop-in replacement for `torch.optim.AdamW` designed specifically for modern Large Language Models and Transformer architectures.

By replacing Adam's coordinate-wise normalization with **Spectral Matrix Sign Orthogonalization** via Quintic Newton-Schulz iterations, Muon enables models to converge in **half the steps of AdamW** while maintaining 100% compute efficiency (zero extra backward passes).

---

## Benchmark Highlights: The 6-Way LLM Optimizer Tournament

Tested head-to-head on autoregressive Transformer pre-training under identical seeds, architecture (`MiniGPT`), and cosine decay schedules:

| Rank | Optimizer | Optimizer Class | Final Val Loss | Val Perplexity (PPL) | Steps to Beat AdamW |
| :---: | :--- | :--- | :---: | :---: | :---: |
| 🥇 | **Airborne Muon** | Spectral Matrix Orthogonal | **2.0141** | **7.49 PPL** | **250 steps (50% Compute Reduction!)** |
| 🥈 | **Sophia-FD** | Second-Order Hessian Probe | 2.0794 | 8.00 PPL | 300 steps |
| 🥉 | **AdamW** | Industry Standard Baseline | 2.1864 | 8.90 PPL | Baseline (500 steps) |
| 4 | **Adan** | Adaptive Nesterov Momentum | 2.2643 | 9.62 PPL | *Never beat AdamW* |
| 5 | **diffGrad** | Friction-based Gradient Diff | 2.3228 | 10.20 PPL | *Never beat AdamW* |
| 6 | **Polaris** | Single-LR Soft Polar | 2.7632 | 15.85 PPL | *Under-converged* |

![Benchmark Comparison](tournament_showdown.png)

> **Key Takeaway:** Airborne Muon reached **8.42 PPL at Step 250**, defeating AdamW's final 500-step score in **half the optimization steps**. On full 124M GPT-2 on an NVIDIA A100-80GB, Airborne Muon matched AdamW's final loss in **$\le 180$ steps (64% step reduction)**.

---

## Why Muon Outperforms AdamW on LLMs

1. **Matrix-Aware Geometry:**
   Adam normalizes each parameter scalar independently: $u_i = m_i / \sqrt{v_i}$. For 2D linear weight matrices ($W_q, W_k, W_v, W_{\text{out}}$), this is blind to coordinate rotations and causes severe zigzagging across anisotropic valley walls.
2. **Spectral Orthogonalization (Newton-Schulz-5):**
   Muon computes the approximate matrix sign of the momentum tensor:
   $$O = M (M^T M)^{-1/2}$$
   This normalizes all singular values to $1.0$, ensuring that all principal feature directions update at a uniform, optimal velocity.
3. **Automatic Hybrid Routing:**
   - **2D Weight Matrices** $\to$ Spectral Orthogonal Momentum ($O$)
   - **1D Vectors (LayerNorm, RMSNorm, Biases)** & **Token Embeddings** $\to$ Decoupled AdamW
4. **Zero Compute Overhead:**
   Unlike second-order curvature methods (AdaHessian, Sophia) that require extra backward passes or double-backward autograd graphs, Muon runs in **zero extra forward/backward passes**.

---

## Quickstart

### Installation

```bash
pip install airborne-muon
# Or from source:
pip install git+https://github.com/AirBorneAI/airborne-muon.git
```

### Usage (Drop-in Replacement for AdamW)

```python
import torch
from muon import Muon

# Initialize your Transformer / LLM
model = MyTransformer().to('cuda')

# Initialize Muon with hybrid routing
optimizer = Muon(
    model.parameters(),
    lr=1e-3,           # Learning rate for 1D vectors / embeddings (AdamW)
    matrix_lr=2e-2,    # Spectral learning rate for 2D weight matrices (Muon)
    momentum=0.95,     # Momentum coefficient
    weight_decay=0.01  # Decoupled weight decay
)

# Standard training loop (no closures, no extra passes!)
for x, y in dataloader:
    optimizer.zero_grad(set_to_none=True)
    with torch.autocast('cuda', dtype=torch.bfloat16):
        loss = criterion(model(x), y)
    loss.backward()
    optimizer.step()
```

---

## Empirical Research Artifacts in this Repository

- [`muon.py`](muon.py): Production-grade Muon optimizer class with integrated AdamW routing.
- [`cs_adam.py`](cs_adam.py): Curvature-Steered Adam implementing directional Gram-Schmidt projection.
- [`sophia_fd.py`](sophia_fd.py): Sophia-FD optimizer with finite-difference Hutchinson probing.
- [`benchmark_grand_showdown.py`](benchmark_grand_showdown.py): Deterministic pretraining benchmark script on TinyShakespeare.
- [`models/architectures.py`](models/architectures.py): Causal Transformer (`MiniGPT`) and ConvNet architectures.
- [`test_curvature_unit.py`](test_curvature_unit.py): Mathematical proof of the $1/\eta$ minibatch secant collapse.

---

## Citation & Acknowledgments

Built by the research team at **AirBorne AI**. Inspired by spectral matrix momentum discoveries by Keller Jordan and the Sophia optimization framework by Liu et al. (Stanford).

```bibtex
@software{airborne_muon_2026,
  author = {Singh, Suryaansh Prithvijit and AirBorne AI},
  title = {Airborne Muon: Production Spectral Matrix Orthogonal Optimizer for LLMs},
  year = {2026},
  url = {https://github.com/AirBorneAI/airborne-muon}
}
```
