---
language: en
license: mit
tags:
  - propagation-logic
  - mechanism-first
  - abstract-reasoning
  - derivation-traces
  - boundary-conditions
datasets:
  - ApplePiesFromScratch/dta-benchmark
metrics:
  - dta
---

# MechanismBase — P / G → Q

A 10M parameter transformer trained on derivation traces, not natural language.

## What this is

Standard language models learn statistical patterns over text.
This model was trained on the **procedure** P / G → Q — explicit derivation
traces showing closure analysis, fixed point detection, cycle structure
identification, and forced boundary condition derivation.

**The claim:** given any carrier V and gradient family Γ, the model can derive
forced boundary conditions — what logic system the carrier implies, what
fixed points exist, what cycle structure is forced.

## Theory

Propagation Logic v13 — SSRN Abstract ID: 6439258 (James Pugmire)

The single primitive operator: `P / G → Q`

A loaded pattern P propagates through gradient field G in context C to
produce updated pattern Q. All of classical logic, fuzzy logic, arithmetic,
calculus, and grammar fall out of different (V, Γ) choices.

## Model

- Architecture: Transformer decoder (custom, mechanism-aligned)
- Parameters: 10.5M
- Training tokens: ~1M (derivation traces)
- Training epochs: 5

## Benchmark: DTA (Derivation Trace Accuracy)

The correct benchmark for this model is not BLiMP or MMLU.
It is DTA — how accurately does the model predict forced boundary conditions
on novel carriers?

See: `ApplePiesFromScratch/dta-benchmark`
| Model | DTA-Overall | DTA-Closure | DTA-FixedPts | DTA-Involution | DTA-Cycle |
|-------|-------------|-------------|--------------|----------------|-----------|
| MechanismBase (10M) | 77.5% | 80.0% | 90.0% | 100.0% | 40.0% |
| GPT-3.5-turbo (175B)| 55.0% | 70.0% | 10.0% |  50.0% | 90.0% |
| GPT-4 (1.8T)        | 87.5% |100.0% | 70.0% |  90.0% | 90.0% |
| Random baseline     | 25.0% | 50.0% | 25.0% |  50.0% | 25.0% |
| Engine (oracle)     |100.0% |100.0% |100.0% | 100.0% |100.0% |


## Usage

```python
# The model requires the pl/ library and engine.py from the repo
# Clone: github.com/ApplePiesFromScratch/propagation-logic

from model import MechanismBase, SmallConfig
from tokenizers import Tokenizer
import torch

config = SmallConfig()
model = MechanismBase(config)
# Load weights from Hub (see full usage in repo)

tokenizer = Tokenizer.from_file("mechanism_tokenizer/tokenizer.json")

# Give the model a partial derivation trace
partial = """DOMAIN: color_domain
CARRIER: ['red', 'green', 'blue']
GRADIENTS: ['complement', 'id']
THETA: 1.0
---
"""

ids = torch.tensor(tokenizer.encode(partial).ids).unsqueeze(0)
output = model.generate(ids, max_new_tokens=200, temperature=0.3)
print(tokenizer.decode(output[0].tolist()))
```

## Training

```
python generate_data.py    # generates derivation trace corpus
python tokenizer_train.py  # BPE tokenizer on corpus
python train.py            # SmallConfig, ~30 min on RTX 4060 Ti
```

## Repository

GitHub: [ApplePiesFromScratch/propagation-logic](https://github.com/ApplePiesFromScratch/propagation-logic)