Padjective Tag Hierarchy

Dataset coverage

Training data spans 3,241 products across 209 taxonomies. Of 18,154 total tags in the dataset, 6,551 tags were used (tags appearing fewer than 5 times were filtered out). 2,544 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)

0.8713 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

0.3352 Avg p-adic loss

402 Avg non-zero coefficients

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Unconstrained Logistic Regression

L1-regularized model using ALL tags

0.2152 Avg p-adic loss

1,545 Non-zero params

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Decision Tree

Unconstrained tree using ALL tags

0.1724 Avg p-adic loss

11,396 Effective params

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Unconstrained Neural Network

L1-regularized NN with weight pruning

0.1812 Avg p-adic loss

60,800 Non-zero params

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Parameter Constrained Neural Network

Neural network predicting taxonomy from tags

0.5697 Avg p-adic loss

864 Avg input weights

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Parameter Constrained Logistic Regression

Logistic regression model predicting Shopify taxonomy from tags

0.6226 Avg p-adic loss

6,669 Avg parameters

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ELO-Inspired Rankings

Battle-tested tag hierarchy from product title positions

1,452 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	7.7%
gid://shopify/TaxonomyCategory/aa-1-13-8	Apparel & Accessories > Clothing > Clothing Tops > T-Shirts	1.1.13.8	161	5.0%
gid://shopify/TaxonomyCategory/ae-2-1	Arts & Entertainment > Hobbies & Creative Arts > Arts & Crafts	3.2.1	117	3.6%
gid://shopify/TaxonomyCategory/aa-1-4	Apparel & Accessories > Clothing > Dresses	1.1.4	89	2.7%
gid://shopify/TaxonomyCategory/ha-6-2-5	Hardware > Hardware Accessories > Cabinet Hardware > Cabinet Knobs & Handles	12.6.2.5	87	2.7%
gid://shopify/TaxonomyCategory/ae-2-2	Arts & Entertainment > Hobbies & Creative Arts > Collectibles	3.2.2	79	2.4%
gid://shopify/TaxonomyCategory/lb	Luggage & Bags	15	78	2.4%
gid://shopify/TaxonomyCategory/vp-1-3	Vehicles & Parts > Vehicle Parts & Accessories > Motor Vehicle Electronics	26.1.3	69	2.1%
gid://shopify/TaxonomyCategory/aa-6-6	Apparel & Accessories > Jewelry > Earrings	1.6.6	63	1.9%
gid://shopify/TaxonomyCategory/aa-6-8	Apparel & Accessories > Jewelry > Necklaces	1.6.8	50	1.5%

Tags with strongest signal

Tag	Top taxonomy	Weight	Max \|weight\|
WHISKEY/WHISKY	9.1.1.5.9	6.2361	6.2361
GIFT	14.11.10	5.2538	5.2538
SHOP	2.2.1.6.2	5.2201	5.2201
HOME DECOR	14.3.57	5.0823	5.0823
ACCESSORIES	15.3.3	5.0134	5.0134
MEN	1.5.5.7	4.8928	4.8928
DRESSES	1.1.4	4.6258	4.6258
VEGAN	13.3.10.13.3	4.5306	4.5306
SUMMER	1.1.10.6	4.2220	4.2220
FRAMED ARTWORK	3.2.2	4.1683	4.1683

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	0.000006	0.3124	0.0106	0.5493
PCLR	0.000050	0.3259	0.2221	0.0037
PCNN	0.000073	0.2465	0.5126	9.14e-07
ULR	0.000117	-0.1728	0.7613	0.0104
Dummy Baseline	0.000013	0.8253	0.3487	0.0048

Model performance vs number of distinct tags

Model	Slope (per tag)	Intercept	R²	p-value
Importance-Optimised p-adic LR	0.000019	0.2108	0.0458	0.2099
PCLR	0.000072	0.0096	0.1925	0.0074
PCNN	0.000110	-0.2454	0.4922	1.87e-06
ULR	0.000162	-0.8547	0.6778	0.0229
Dummy Baseline	0.000028	0.6856	0.4552	7.95e-04

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	-0.1230	0.8213	0.5448	0.0939	No	6
Without Dummy	-0.0646	0.6088	0.0757	0.6542	No	5

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
-0.1550	-0.0877	0.9469	0.0053	Yes	5