Padjective Tag Hierarchy

Dataset coverage

Training data spans 3,423 products across 219 taxonomies. Of 18,672 total tags in the dataset, 6,784 tags were used (tags appearing fewer than 5 times were filtered out). 2,752 products were discarded due to missing or sparse taxonomy labels. Explore the full dataset → | View defective taxonomy labels →

Dummy Baseline

Always predicts most common taxonomy (baseline for comparison)

0.8781 Avg p-adic loss

1 Parameter

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Importance-Optimised p-adic Linear Regression

P-adic coefficients assigned to tags to predict taxonomy

0.3405 Avg p-adic loss

425 Avg non-zero coefficients

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Zubarev Polynomial Regression

Stochastic p-adic optimization with Mahler basis (arXiv:2503.23488)

0.3735 Avg p-adic loss

1,443 Non-zero coefficients

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Unconstrained Logistic Regression

L1-regularized model using ALL tags

0.2187 Avg p-adic loss

1,630 Non-zero params

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Decision Tree

Unconstrained tree using ALL tags

0.1650 Avg p-adic loss

12,083 Effective params

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Unconstrained Neural Network

L1-regularized NN with weight pruning

0.1510 Avg p-adic loss

40,779 Non-zero params

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Parameter Constrained Neural Network

Neural network predicting taxonomy from tags

0.5783 Avg p-adic loss

864 Avg input weights

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Parameter Constrained Logistic Regression

Logistic regression model predicting Shopify taxonomy from tags

0.5646 Avg p-adic loss

6,976 Avg parameters

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ELO-Inspired Rankings

Battle-tested tag hierarchy from product title positions

1,548 Tag battles

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Taxonomy distribution

Taxonomy class distribution — Distribution of products across the most common taxonomy classes

Top 10 taxonomy classes

Taxonomy ID	Name	Path	Samples	Share
gid://shopify/TaxonomyCategory/fb-2-3-2	Food, Beverages & Tobacco > Food Items > Candy & Chocolate > Chocolate	9.2.3.2	249	7.3%
gid://shopify/TaxonomyCategory/aa-1-13-8	Apparel & Accessories > Clothing > Clothing Tops > T-Shirts	1.1.13.8	200	5.8%
gid://shopify/TaxonomyCategory/ae-2-1	Arts & Entertainment > Hobbies & Creative Arts > Arts & Crafts	3.2.1	117	3.4%
gid://shopify/TaxonomyCategory/aa-1-4	Apparel & Accessories > Clothing > Dresses	1.1.4	95	2.8%
gid://shopify/TaxonomyCategory/ha-6-2-5	Hardware > Hardware Accessories > Cabinet Hardware > Cabinet Knobs & Handles	12.6.2.5	87	2.5%
gid://shopify/TaxonomyCategory/ae-2-2	Arts & Entertainment > Hobbies & Creative Arts > Collectibles	3.2.2	79	2.3%
gid://shopify/TaxonomyCategory/lb	Luggage & Bags	15	78	2.3%
gid://shopify/TaxonomyCategory/vp-1-3	Vehicles & Parts > Vehicle Parts & Accessories > Motor Vehicle Electronics	26.1.3	69	2.0%
gid://shopify/TaxonomyCategory/aa-6-6	Apparel & Accessories > Jewelry > Earrings	1.6.6	64	1.9%
gid://shopify/TaxonomyCategory/aa-6-8	Apparel & Accessories > Jewelry > Necklaces	1.6.8	51	1.5%

Tags with strongest signal

Tag	Top taxonomy	Weight	Max \|weight\|
WHISKEY/WHISKY	9.1.1.5.9	6.2974	6.2974
SHOP	2.2.1.6.3	5.2791	5.2791
HOME DECOR	14.3.56	4.9866	4.9866
GIFT	14.11.10	4.9590	4.9590
MEN	1.5.5.7	4.9505	4.9505
ACCESSORIES	15.3.3	4.9484	4.9484
DRESSES	1.1.4	4.7396	4.7396
VEGAN	13.3.10.13.3	4.5494	4.5494
SUMMER	1.1.10.6	4.2894	4.2894
FRAMED ARTWORK	3.2.2	4.2008	4.2008

Historical Performance Trends

Tracking model performance and dataset growth over time. Lower p-adic loss indicates better predictions.

Model	Slope (per product)	Intercept	R²	p-value
Importance-Optimised p-adic LR	0.000007	0.3104	0.0193	0.3928
PCLR	0.000076	0.2787	0.3868	1.83e-05
PCNN	0.000090	0.2144	0.6335	8.30e-10
ULR	0.000069	-0.0277	0.5175	0.0126
UNN	0.000059	-0.0339	0.2078	0.2175
Decision Tree	0.000025	0.0744	0.1136	0.4142
Dummy Baseline	0.000016	0.8185	0.5259	4.11e-05

Model performance vs number of distinct tags

Model	Slope (per tag)	Intercept	R²	p-value
Importance-Optimised p-adic LR	0.000018	0.2178	0.0548	0.1460
PCLR	0.000113	-0.2235	0.3712	3.01e-05
PCNN	0.000137	-0.3962	0.6300	9.96e-10
ULR	0.000066	-0.2365	0.3720	0.0463
UNN	0.000032	-0.0538	0.0602	0.5246
Decision Tree	0.000014	0.0661	0.0366	0.6499
Dummy Baseline	0.000029	0.6815	0.6287	2.29e-06

Model complexity vs performance (parameter count vs p-adic loss) — Parameter count (log scale) vs p-adic loss. Sparse models use fewer non-zero parameters.

Regression: p-adic loss = slope × log₁₀(params) + intercept

Line	Slope	Intercept	R²	p-value	Significant?	n
With Dummy	-0.1454	0.8536	0.6548	0.0150	Yes	8
Without Dummy	-0.1166	0.7491	0.2127	0.2976	No	7

Unconstrained models: complexity vs performance (log-log scale) — Unconstrained models only (no PCLR/PCNN). Both axes on log scale.

Regression: log₁₀(loss) = slope × log₁₀(params) + intercept

Slope	Intercept	R²	p-value	Significant?	n
-0.1697	-0.0356	0.9241	0.0022	Yes	6