---
language:
- en
tags:
- biology
- genomics
- codon-optimization
- p-adic-math
- hyperbolic-geometry
- ddg-prediction
license: other
metrics:
- spearmanr
---

# Ternary Codon Encoder: P-adic Hyperbolic Embeddings

The Ternary Codon Encoder is a neural embedding model that maps the 64 genetic codons into a 16-dimensional hyperbolic space. It is the first model to explicitly use **3-adic valuation** as a mathematical prior to organize the genetic code's hierarchical structure.

## Model Description

- **Architecture:** MLP-based encoder (12-dim one-hot input $
ightarrow$ 16-dim hyperbolic output).
- **Mathematical Foundation:** Leverages 3-adic mathematics to represent the discrete hierarchy of the codon table.
- **Latent Space:** Poincaré ball where radial distance encodes 3-adic valuation (conservation/variability).

## Key Discoveries

- **Physics Dimension:** Latent dimension 13 correlates strongly ($
ho = -0.70$) with molecular mass, volume, and force constants ($k$).
- **Linear Stability Manifold:** Provides high-quality feature vectors for sequence-only protein stability ($\Delta\Delta G$) prediction.
- **Synonymous Cohesion:** Synonymous codons cluster together in hyperbolic space while maintaining clear boundaries between amino acid groups.

## Performance

- **DDG Spearman $
ho$:** 0.614 (Sequence-only benchmarking on diverse datasets).
- **Improvement:** +105% over baseline p-adic embedding models.

## Usage

```python
import torch
from trainable_codon_encoder import TrainableCodonEncoder

# Load model
encoder = TrainableCodonEncoder(latent_dim=16, hidden_dim=64)
checkpoint = torch.load("pytorch_model.bin", map_location="cpu")
encoder.load_state_dict(checkpoint["model_state_dict"])
encoder.eval()

# Get embedding for a codon (e.g., ATG index 14)
codon_idx = torch.tensor([14])
with torch.no_grad():
    z_hyp = encoder(codon_idx)

print(f"Hyperbolic Embedding: {z_hyp}")
```

## Citation

```bibtex
@software{ternary_codon_2026,
  author = {AI Whisperers},
  title = {Ternary Codon Encoder: P-adic Hyperbolic Embeddings},
  year = {2026},
  url = {https://huggingface.co/ai-whisperers/ternary-codon-encoder}
}
```