---
tags:
- vision
- image-classification
- fractal-positional-encoding
- geometric-deep-learning
- devil-staircase
- simplex-geometry
license: mit
---

# ViT-Beatrix: Fractal PE + Geometric Simplex Vision Transformer

This repository contains Vision Transformers integrating Devil's Staircase positional encoding 
with geometric simplex features for vision tasks.

## Key Features

- **Fractal Positional Encoding**: Devil's Staircase multi-scale position embeddings
- **Geometric Simplex Features**: k-simplex vertex computations from Cantor measure
- **SimplexFactory Initialization**: Pre-initialized simplices with geometrically meaningful shapes (regular/random/uniform)
- **Adaptive Augmentation**: Progressive augmentation escalation to prevent overfitting
- **Beatrix Formula Suite**: Flow alignment, hierarchical coherence, and multi-scale consistency losses

### Simplex Initialization

Instead of random initialization, the model uses **SimplexFactory** to create geometrically sound starting configurations:

- **Regular** (default): All edges equal length, perfectly balanced symmetric structure
- **Random**: QR decomposition ensuring affine independence
- **Uniform**: Hypercube sampling with perturbations

Regular simplices provide the most stable and mathematically meaningful initialization, giving the model a better starting point for learning geometric features.

### Adaptive Augmentation System

The trainer includes an intelligent augmentation system that monitors train/validation accuracy gap and progressively enables more augmentation:

1. **Baseline**: RandomCrop + RandomHorizontalFlip
2. **Stage 1**: + ColorJitter
3. **Stage 2**: + RandomRotation  
4. **Stage 3**: + RandomAffine
5. **Stage 4**: + RandomErasing
6. **Stage 5**: + AutoAugment (CIFAR policy)
7. **Stage 6**: Enable Mixup (α=0.2)
8. **Stage 7**: Enable CutMix (α=1.0) - Final stage

When train accuracy exceeds validation accuracy by 2% or more, the system automatically escalates to the next augmentation stage.

## Available Models (Best Checkpoints Only)

| Model Name | Training Session | Accuracy | Epoch | Weights Path | Logs Path |
|------------|------------------|----------|-------|--------------|----------|
| beatrix-cifar100 | 20251007_182851 | 0.5819 | 42 | `weights/beatrix-cifar100/20251007_182851` | `N/A` |
| beatrix-simplex4-patch4-512d-flow | 20251008_115206 | 0.5674 | 87 | `weights/beatrix-simplex4-patch4-512d-flow/20251008_115206` | `logs/beatrix-simplex4-patch4-512d-flow/20251008_115206` |
| beatrix-simplex7-patch4-256d-ce | 20251008_034231 | 0.5372 | 77 | `weights/beatrix-simplex7-patch4-256d-ce/20251008_034231` | `logs/beatrix-simplex7-patch4-256d-ce/20251008_034231` |
| beatrix-simplex7-patch4-256d | 20251008_020048 | 0.5291 | 89 | `weights/beatrix-simplex7-patch4-256d/20251008_020048` | `logs/beatrix-simplex7-patch4-256d/20251008_020048` |
| beatrix-cifar100 | 20251007_215344 | 0.5161 | 41 | `weights/beatrix-cifar100/20251007_215344` | `logs/beatrix-cifar100/20251007_215344` |
| beatrix-cifar100 | 20251007_195812 | 0.4701 | 42 | `weights/beatrix-cifar100/20251007_195812` | `logs/beatrix-cifar100/20251007_195812` |
| beatrix-cifar100 | 20251008_002950 | 0.4363 | 49 | `weights/beatrix-cifar100/20251008_002950` | `logs/beatrix-cifar100/20251008_002950` |
| beatrix-cifar100 | 20251007_203741 | 0.4324 | 40 | `weights/beatrix-cifar100/20251007_203741` | `logs/beatrix-cifar100/20251007_203741` |
| beatrix-simplex7-patch4-45d | 20251008_010524 | 0.2917 | 95 | `weights/beatrix-simplex7-patch4-45d/20251008_010524` | `logs/beatrix-simplex7-patch4-45d/20251008_010524` |
| beatrix-4simplex-45d | 20251007_231008 | 0.2916 | 85 | `weights/beatrix-4simplex-45d/20251007_231008` | `logs/beatrix-4simplex-45d/20251007_231008` |
| beatrix-cifar100 | 20251007_193112 | 0.2802 | 10 | `weights/beatrix-cifar100/20251007_193112` | `N/A` |
| beatrix-4simplex-45d | 20251008_001147 | 0.1382 | 10 | `weights/beatrix-4simplex-45d/20251008_001147` | `logs/beatrix-4simplex-45d/20251008_001147` |


## Latest Updated Model: beatrix-simplex4-patch4-512d-flow (Session: 20251008_115206)

### Model Details

- **Architecture**: Vision Transformer with fractal positional encoding
- **Dataset**: CIFAR-100 (100 classes)
- **Embedding Dimension**: 512
- **Depth**: 8 layers
- **Patch Size**: 4x4
- **PE Levels**: 12
- **Simplex Dimension**: 4-simplex
- **Simplex Initialization**: regular (scale=1.0)

### Training Details

- **Training Session**: 20251008_115206
- **Best Accuracy**: 0.5674
- **Epochs Trained**: 87
- **Batch Size**: 512
- **Learning Rate**: 0.0001
- **Adaptive Augmentation**: Enabled

### Loss Configuration

- Task Loss Weight: 0.5
- Flow Alignment Weight: 1.0
- Coherence Weight: 0.3
- Multi-Scale Weight: 0.2

### TensorBoard Logs

Training logs are available in the repository at:
```
logs/beatrix-simplex4-patch4-512d-flow/20251008_115206
```

To view them locally:
```bash
# Clone the repo
git clone https://huggingface.co/AbstractPhil/vit-beatrix

# View logs in TensorBoard
tensorboard --logdir vit-beatrix/logs/beatrix-simplex4-patch4-512d-flow/20251008_115206
```

## Usage

### Installation

For Google Colab:
```python
# Install for Colab
try:
  !pip uninstall -qy geometricvocab
except:
  pass

!pip install -q git+https://github.com/AbstractEyes/lattice_vocabulary.git
```

For local environments:
```bash
# install the repo into your environment
pip install -q git+https://github.com/AbstractEyes/lattice_vocabulary.git
```

### Loading Models

```python
from geovocab2.train.model.core.vit_beatrix import SimplifiedGeometricClassifier
from safetensors.torch import load_file
from huggingface_hub import hf_hub_download
import json

# Download and view manifest to see all available models
manifest_path = hf_hub_download(
    repo_id="AbstractPhil/vit-beatrix",
    filename="manifest.json"
)

with open(manifest_path, 'r') as f:
    manifest = json.load(f)
    
# List all available models sorted by accuracy
for key, info in sorted(manifest.items(), key=lambda x: x[1]['accuracy'], reverse=True):
    print(f"{info['model_name']} ({info['timestamp']}): {info['accuracy']:.4f}")

# Download weights for the latest training session of beatrix-simplex4-patch4-512d-flow
weights_path = hf_hub_download(
    repo_id="AbstractPhil/vit-beatrix",
    filename="weights/beatrix-simplex4-patch4-512d-flow/20251008_115206/model.safetensors"
)

# Load model
model = SimplifiedGeometricClassifier(
    num_classes=100,
    img_size=32,
    embed_dim=512,
    depth=8
)

# Load weights
state_dict = load_file(weights_path)
model.load_state_dict(state_dict)
model.eval()

# Inference
output = model(images)
```

## Citation

```bibtex
@misc{vit-beatrix,
  author = {AbstractPhil},
  title = {ViT-Beatrix: Fractal Positional Encoding with Geometric Simplices},
  year = {2025},
  url = {https://github.com/AbstractEyes/lattice_vocabulary}
}
```

## License

MIT License