AbstractPhil/math_collective_v1

V2 first epoch ready

Looking much stronger.

V1 BAD END - V2 using qwen 2.5 math 1.5b

Will the Qwen 2.5 1.5b model cut through the noise?

======================================================================
GALAXY BRAIN COLLECTIVE - GSM8K FINAL RESULTS
======================================================================

Streams:
  FUZZY:        MathBERT (symbolic), T5 (linguistic)
  DETERMINISTIC: Eigenspectrum, Cayley-Menger, Symbolic Calc, Fractal

| Epoch | Collective | MathBERT | T5 | Eigen | Cayley | Symbolic | Fractal | ρ |
|-------|------------|----------|-----|-------|--------|----------|---------|-------|
| 1 | 8.9% | 10.4% | 13.0% | 5.4% | 5.4% | 5.7% | 6.7% | 0.686 |
| 2 | 9.6% | 8.9% | 13.0% | 6.5% | 6.5% | 4.6% | 6.1% | 0.738 |
| 3 | 9.9% | 9.6% | 13.6% | 5.8% | 5.8% | 4.5% | 5.8% | 0.728 |
| 4 | 8.3% | 10.1% | 13.3% | 6.1% | 4.5% | 4.8% | 4.5% | 0.619 |
| 5 | 9.0% | 11.1% | 14.6% | 4.5% | 4.6% | 5.0% | 5.9% | 0.620 |

✓ Best epoch: 3 with collective accuracy 9.9%
✓ All checkpoints available at: https://huggingface.co/AbstractPhil/math_collective

Math Collective - Galaxy Brain Router

6-stream collective intelligence system for mathematical reasoning.

Architecture

┌─────────────────────────────────────────────────────────────┐
│                    GALAXY BRAIN COLLECTIVE                   │
├─────────────────────────────────────────────────────────────┤
│  FUZZY STREAMS (learned representations)                    │
│  ├── MathBERT (frozen) → Head A → "symbolic understanding"  │
│  └── T5-base (frozen)  → Head B → "linguistic reasoning"    │
│                                                             │
│  DETERMINISTIC STREAMS (pure computation)                   │
│  ├── Eigenspectrum    → Head C → "covariance geometry"      │
│  ├── Cayley-Menger    → Head D → "distance geometry"        │
│  ├── Symbolic Calc    → Head E → "actual arithmetic"        │
│  └── Fractal Dim      → Head F → "complexity measure"       │
│                                                             │
│  All 6 streams → Fusion → Classifier                        │
└─────────────────────────────────────────────────────────────┘

Key Innovation

Fuzzy + Deterministic Routing

The router learns WHEN to trust each stream:

• Simple arithmetic? Trust the Symbolic Calculator (deterministic)
• Complex word problem? Trust MathBERT/T5 (semantic)
• Ambiguous? Triangulate across all 6 perspectives

Streams

Stream	Type	Source	Purpose
MathBERT	Fuzzy	tbs17/MathBERT (frozen)	Mathematical notation understanding
T5-base	Fuzzy	t5-base (frozen)	General language reasoning
Eigenspectrum	Deterministic	Covariance eigenvalues	Geometric structure of embeddings
Cayley-Menger	Deterministic	Distance matrix geometry	Simplex volume features
Symbolic	Deterministic	Regex + arithmetic	Actual number extraction & computation
Fractal	Deterministic	Correlation dimension	Problem complexity measure

Training

• Dataset: GSM8K (Grade School Math 8K)
• Task: Answer magnitude bucket prediction (20 buckets)
• Frozen params: ~330M (MathBERT + T5)
• Trainable params: ~15M (routing heads, fusion, projections)

Emergence Metric (ρ)

ρ = collective_accuracy / max(individual_accuracies)

ρ > 1.0 = emergence (collective outperforms best individual)

Usage

from huggingface_hub import hf_hub_download
import torch

# Download checkpoint
checkpoint_path = hf_hub_download(
    repo_id="AbstractPhil/math_collective",
    filename="checkpoints/checkpoint_epoch_5.pt"
)

# Load and use (see geofractal-router for full implementation)
checkpoint = torch.load(checkpoint_path)
print(f"Epoch: {checkpoint['epoch']}")
print(f"Metrics: {checkpoint['metrics']}")

Related

• Framework: AbstractPhil/geofractal_router
• Paper: Coming soon
• Code: GitHub - geofractal

Citation

@misc{abstractphil2025mathcollective,
  title={Math Collective: Galaxy Brain Routing for Mathematical Reasoning},
  author={AbstractPhil},
  year={2025},
  publisher={Hugging Face},
  url={https://huggingface.co/AbstractPhil/math_collective}
}

License

Apache 2.0