phanerozoic / cofiber-detection

Cofiber Detection

Object detection heads built on cofiber decomposition of frozen EUPE-ViT-B features. The cofiber decomposition produces multi-scale representations with zero learned parameters, replacing the 11M-parameter FPN typically used in FCOS-style detectors. Heads range from 70-parameter analytical constructions to 3.85M-parameter trained networks, evaluated on COCO val2017.

The Cofiber Decomposition

Given spatial backbone features f : [768, H, W] , the cofiber decomposition produces n scale bands via iterated subtraction of downsampled-then-upsampled content:

residual = f
for k = 0 to n-2:
    omega_k = avgpool(residual, 2)
    sigma_omega_k = upsample_bilinear(omega_k, size=residual.shape)
    cofiber_k = residual - sigma_omega_k
    residual = omega_k
cofiber_{n-1} = residual

Each cofiber_k captures frequency content at a distinct scale with no cross-scale interference. The decomposition is a fixed two-line operation, yet it provides the same multi-scale structure that an FPN synthesizes with 11M trained parameters.

The construction is machine-checked in Rocq/HoTT ( CofiberDecomposition.v ). The proof frames average pooling and bilinear upsampling as an adjoint pair whose counit gives a short exact sequence in a semi-additive category; the cofiber bands are the kernels of the projections, and the sum is exact by construction.

Best Results (COCO val2017)

The best split_tower head reaches 20.7 mAP with 4.02M parameters — 50.5% of the FCOS baseline's 41.0 mAP at 24.9% of its parameters. The architecture has separate classification and regression towers, each consisting of 5 standard 3×3 convolutions followed by 4 depthwise residual blocks at 192 hidden channels, operating on cofiber-decomposed features with a stride-8 P3 level and top-down lateral connections. An earlier variant at 224 hidden channels with 3 standard + 6 depthwise layers reached 20.3 mAP at 3.85M parameters; narrowing the channels while adding more cross-channel-mixing standard convolutions gave the +0.4 mAP improvement.

Repository Structure

`analytical/`

`trained/`

`circuit/`

`scripts/`

`CofiberDecomposition.v`

Rocq/HoTT machine-checked proof that the cofiber decomposition is exact in a semi-additive category: every input decomposes uniquely as a sum of scale bands with zero cross-term residual.

Scaling Curve

The relationship between head parameters and mAP is approximately logarithmic across four orders of magnitude:

      105 params → 1.3 mAP  (evolved circuit, person only)
       70K params → 1.6 mAP  (analytical closed-form)
       92K params → 8.2 mAP  (depthwise conv on regression)
      182K params → 10.6 mAP (evolved dim selection + 10-layer MLP)
      912K params → 17.2 mAP (depthwise conv stack)
     3.97M params → 19.7 mAP (with stride-8 P3)
     3.85M params → 20.3 mAP (split cls/reg towers, 3 std + 6 dw at 224 hidden)
     4.02M params → 20.7 mAP (split cls/reg towers, 5 std + 4 dw at 192 hidden)
    16.14M params → 41.0 mAP (FCOS baseline with FPN)

Broader Detection Work

Non-cofiber detection heads (FCOS baseline, untrained architectural variants, alternative formulations) are hosted in phanerozoic/detection-heads , which also includes the top-performing cofiber head (split_tower) for reference. This repository is the canonical host for cofiber-based detection research.

License

Fair Research License. See LICENSE .