phanerozoic / threshold-cofiber-detection

Cofiber Detection Circuit

A depth-3 threshold gate network for multi-scale object detection on frozen vision transformer features. 61,520 INT8 learned parameters. 2,184,000 gates. The multi-scale decomposition is analytic (zero parameters); only the classification layer is learned.

Circuit

Input: feature grid [768, 40, 40] from frozen ViT at stride 16

Layer 0 — Pool (fixed, 0 learned params)
  pool(x)_{i,j} = 0.25 * (x_{2i,2j} + x_{2i+1,2j} + x_{2i,2j+1} + x_{2i+1,2j+1})

Layer 1 — Cofiber (fixed, 0 learned params)
  cofib(x)_{i,j} = x_{i,j} - upsample(pool(x))_{i,j}

Layer 2 — Classify (61,520 INT8 params)
  detect(i,j,c) = H( Σ_d w_{c,d} · cofib(x)_{i,j,d} + b_c )

Output: per-location, per-class binary detection decisions

The cofiber x - upsample(pool(x)) isolates information present at a given spatial scale but absent from the next coarser scale. Applied iteratively, it decomposes the feature grid into three scale bands (strides 16, 32, 64) with zero learned parameters. The classification layer operates on each band independently.

Equations

The decomposition satisfies three properties, proven in CofiberDecomposition.v :

1. Block diagonal : The low-frequency block of any morphism between decomposed features equals the functorial low-frequency component. Classification on cofibers is equivalent to multi-scale classification on the original features.

2. Cross-term vanishing (high→low) : Low-frequency input produces zero high-frequency output. A large object detected at stride 32 creates no signal in the stride-16 cofiber.

3. Cross-term vanishing (low→high) : High-frequency input produces zero low-frequency output. Scale bands do not interfere.

These properties are consequences of the adjoint pair (bilinear upsample ⊣ average pool) forming a counit in a semi-additive category. The cofiber of the counit decomposes objects along an exact sequence, guaranteeing lossless scale separation.

Parameters

Gates

All layer 0–1 gates use integer weights from {-1, 0, 1}. Layer 2 gates use INT8 quantized weights. INT8 quantization produces 99.7% detection agreement with FP32.

Usage

from model import CofiberDetector

detector = CofiberDetector.from_safetensors("model.safetensors")

# features: [768, 40, 40] numpy array from any frozen ViT at stride 16
detections = detector.detect(features, score_thresh=0.3)

for d in detections:
    print(f"class {d['label']} at {d['box']} score {d['score']:.3f} scale {d['scale']}")

Proof

CofiberDecomposition.v contains a machine-checked proof (Coq/HoTT) of the three cross-term vanishing theorems. The proof establishes that the block structure of the decomposition is exact in any semi-additive category with a suspension-loop adjunction. The concrete instantiation (average pool, bilinear upsample, float32 tensors) satisfies the hypotheses up to machine precision (reconstruction error < 3e-7).

Files

threshold-cofiber-detection/
├── model.safetensors      # 241 KB circuit weights
├── model.py               # standalone inference
├── config.json            # architecture metadata
├── CofiberDecomposition.v # machine-checked proof
└── README.md

License

Apache 2.0