This repository hosts a trained Manifold model that demonstrates rule learning and extreme length generalization on the XOR/Parity task. Unlike transformers that scale quadratically with sequence length, Manifold uses continuous-time Hamiltonian dynamics to achieve O(1) memory complexity.

For the full framework, see the GitHub repository.

What This Model Demonstrates

✅ Learns parity as a rule, not via memorization
✅ Generalizes to sequence lengths >2000× training length (trained on L=20, tested up to L=100,000)
✅ Maintains constant memory usage (O(1) via symplectic integration)
✅ Uses continuous-time dynamics instead of attention mechanisms

Benchmarks: Manifold vs Transformer

Metric	Manifold GFN (1.4 MB)	MicroGPT Transformer
Model Size	1.4 MB	~2 MB
Training Length	20 tokens	20 tokens
Test Accuracy @ L=20	100%	90%
Test Accuracy @ L=100	100%	50%
Test Accuracy @ L=1,000	100%	52%
Test Accuracy @ L=10,000	100%	OOM (Out of Memory)
Test Accuracy @ L=100,000	100%	OOM (Out of Memory)
VRAM @ L=100	30 MB	85 MB
VRAM @ L=10,000	60 MB	>8 GB (quadratic)
Memory Complexity	O(1)	O(N²)

Benchmarks run on NVIDIA GTX 1650 (4gb vram). Transformer fails at L>5000 due to attention matrix explosion.

Architecture

Manifold is a next-generation neural architecture based on Riemannian Geometry and Hamiltonian Dynamics.

This particular model uses:

Type: Manifold v2.6.2 (Symplectic Neural ODE)
Dimensions: 128 (Latent), 16 (Coordinate)
Depth: 6 Layers (Continuous Time)
Heads: 4 (Isomeric Geodesic Flows)
Integrator: Leapfrog (Symplectic)
Physics:
- Active Inference: Enabled (Plasticity 0.1)
- Singularities: Enabled (Strength 5.0)
- Fractal Manifolds: Enabled

Task

The model solves the Cumulative Parity (XOR) problem:

Input: Binary sequence (e.g., 1 0 1 1 ...)
Output: Cumulative sum modulo 2

Usage

1. Install the Manifold library:

pip install gfn

2. Download the model files:

bash

# Clone this repository
git clone https://huggingface.co/Manifold-Labs/manifold-gfn-xor-128d
cd manifold-gfn-xor-128d

3. Run inference:

bash

# Test on sequences of length 100 (5 samples)
python inference.py --length 100 --samples 5

# Test on longer sequences (e.g., 1000 tokens)
python inference.py --length 1000 --samples 3

Expected Output:

[*] Testing Parity/XOR (Length: 100)
------------------------------------------------------------
Seq 1: ✅ PASS
  Input:  00110000000101110110...
  Target: 00100000000110100100...
  Pred:   00100000000110100100...
------------------------------------------------------------
Total Success: 5/5

Performance

Accuracy: 100% on test set
Length-Invariant Generalization: Verified up to 100,000 tokens
Stability: Energy conserved via Hamiltonian constraint

Manifold-Labs/manifold-gfn-xor-128d

Manifold GFN: 100% Accuracy on 100k Token Parity with O(1) Memory