Abstract:Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that learns through subdirect decomposition of algebraic structure rather than numerical optimization, against standard baselines on image and tabular classification across varying training-set sizes. We find that AML trained only on training data without using validation or cross-validation outperforms a family of cross-validated baseline methods including CNNs on small to medium image datasets (50--2000 training examples). On tabular datasets in the same size range, XGBoost is overall the best performing method, but AML is nonetheless comparable to methods incorporating task-specific biases such as LightGBM and random forests. AML achieves this competitive performance across two very different types of datasets using a generic algebraic inductive bias, rather than the modality-specific biases built into standard baselines like CNNs for images or XGBoost for tabular data, and requires no cross validation because it has no task-dependent hyperparameters to tune.
| Comments: | 9 pages, 4 figures |
| Subjects: | Machine Learning (cs.LG) |
| ACM classes: | I.2.6 |
| Cite as: | arXiv:2605.22155 [cs.LG] |
| (or arXiv:2605.22155v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22155 arXiv-issued DOI via DataCite (pending registration) |
From: Gonzalo G. De Polavieja [view email]
[v1]
Thu, 21 May 2026 08:25:22 UTC (262 KB)
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