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)

Variant	Params	mAP	mAP@0.50	mAP@0.75	Category
split_tower_192h_5std_4dw	4,016,441	20.7	28.5	22.8	trained
split_tower_224h_3std_6dw	3,849,657	20.3	28.1	22.3	trained
conv_deep_p3_lateral	4,269,785	19.9	28.4	22.0	trained
conv_deep_p3	3,972,569	19.7	28.3	21.6	trained
conv_deep_3.38M	3,381,592	18.8	27.4	20.9	trained
conv_deep_912k	911,960	17.2	25.6	19.2	trained
evolved_deep	182,580	10.6	18.9	10.8	trained
spatialreg_92k	91,960	8.2	25.7	2.8	trained
box32_92k	91,640	5.9	21.4	1.3	trained
box32 pruned R2	~62,000 nz	5.9	20.4	1.5	trained
dim20	22,076	3.9	14.8	0.9	trained
analytical_70k	69,976	1.6	6.0	0.4	analytical
evolved K=100 person	105	1.3	5.8	0.1	circuit
Baseline FCOS (non-cofiber)	16,138,074	41.0	64.8	43.2	reference

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/`

Path	Description
analytical_70k/	Closed-form least-squares head. 70K params, 1.6 mAP, zero training
analytical_h1/	Sheaf cohomology (H^1) features. Experimental
variants/	Exotic feature experiments (quadratic, RFF, Fourier, fractal) with result JSONs
scripts/	analytical_greedy_gpu.py, analytical_exotic_gpu.py, analytical_empbayes.py, etc.

`trained/`

Path	Params	mAP	Description
split_tower/	4.02M	20.7	Split cls/reg towers with standard + depthwise hybrid. Current best
conv_deep/	912K-4.27M	17.2-19.9	Depthwise residual stack variants (scaled, P3, lateral)
evolved_deep/	182K	10.6	10-layer MLP on 92 evolutionarily-selected dims
spatialreg_92k/	92K	8.2	3x3 depthwise conv on regression output
linear_70k/	70K	5.2	Trained linear classifier
box32_92k/	92K	5.9	INT8 threshold logic circuit + pruned variants (46K-76K)
box32_distilled/	92K	—	Self-distillation of box32
dim_sweeps/	9K-80K	0.3-?	SVD-initialized fixed-dim heads (5, 10, 15, 20, 30, 80)
sloe/	—	0.0	Spectral Laplacian object emergence (failed experiment)
person_specialist/	9K	—	Person-only detector
waldo_specialist/	5K	—	Waldo-finding detector
experimental_scaffolds/	—	—	Untrained architectural scaffolds (5scale, adaptive, centernet, linear)

`circuit/`

File	Description
person_analytical.pth	Person classifier at 93 parameters, 99.8% recall
person_detector.sv, cofiber_detector.sv	Verilog implementations
rom/*.hex	INT8 weight ROMs
evolved_K100_person_eval.json	Evolutionary search result, 105 params, 1.3 mAP
tb_person.sv	Testbench

`scripts/`

Script	Target
train_split_tower.py	Split tower (best)
train_conv_deep.py	Conv deep family (912K-4.27M)
train_evolved_deep.py	Evolved deep on 92 dims
eval_conv_deep_step.py	Eval any conv_deep checkpoint
eval_evolved_deep.py	Eval evolved_deep checkpoint
eval_coco_map.py	Generic COCO mAP eval

`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.