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_5scale_192h_5std_4dw	4,068,954	24.6	37.1	27.0	trained
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 24.6 mAP on COCO val2017 with 4.07 million parameters. This corresponds to approximately 60 percent of the mAP of the FCOS baseline (41.0 mAP at 16.14 million parameters) while using roughly one quarter of the parameter budget. The architecture consists of separate classification and regression convolutional towers, each built from five standard 3×3 convolutions followed by four depthwise residual blocks at a hidden dimension of 192 channels. Its input is a cofiber decomposition of the backbone patch features into four frequency-separated bands (corresponding to spatial strides of 16, 32, 64, and 128 pixels), with an additional finer-resolution level (stride 8) synthesized by a single transposed convolution from the stride-16 band. Top-down lateral connections pass information from coarser bands into finer ones before the towers run. The five resulting prediction levels — strides 8, 16, 32, 64, and 128 — match the scale coverage of the FCOS simple feature pyramid while obtaining their multi-scale structure from a zero-parameter decomposition rather than from a learned feature pyramid network.

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_5scale/	4.07M	24.6	Five-scale split-tower head (P3-P7). Current best
split_tower/	4.02M	20.7	Four-scale split-tower head (predecessor)
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 scales)
     4.02M params → 20.7 mAP (split cls/reg towers, 5 std + 4 dw at 192 hidden, 4 scales)
     4.07M params → 24.6 mAP (same tower, 5 scales / P3-P7 coverage)
    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.