aiqbench analysis
The paper builds a two-hidden-layer network with step activations directly from geometric separation of the training data, using leaf nodes of an oblique decision tree as neurons, and reports perfect training-set accuracy on MNIST. The abstract sets aside regularization and reports no test-set generalization, so the practical value is unclear. The interpretability and scalability claims are plausible but unquantified, so readers should treat this as a constructive, training-free idea to evaluate, not a replacement for gradient-based training.
A Geometrical Approach to Constructing Neural Networks for Perfect Training-set Classification
arXiv:2610.17312v1 Announce Type: new Abstract: This paper proposes a method for constructing a neural network that achieves perfect classification of all samples in a given training set, without taking regularization into account. The network is constructed on-demand, with its layer sizes and neuron parameters determined through a geometrical analysis of the input data, in which separating hyperplanes are created and mapped to neurons with step activation functions. The proposed architecture consists of two hidden layers with distinct roles: inter-class separation and transformation of the data into a linearly separable representation. Inter-class separation requires every bi-chromatic pair of samples belonging to different classes to be separated by at least one hyperplane. We show that when this separation is achieved through a hierarchical partitioning of the data, the leaf nodes of the oblique decision tree, obtained as a byproduct, directly define the neurons of the linear separability layer, whose size is only one neuron greater than that of the inter-class separation layer. Experiments on the MNIST dataset demonstrate that the proposed method achieves perfect training-set classification, and compact models. The direct correspondence between the decision tree and network neurons enhances interpretability and explainability, while the construction procedure offers opportunities for parallel implementation and improved scalability.
Abstract:This paper proposes a method for constructing a neural network that achieves perfect classification of all samples in a given training set, without taking regularization into account. The network is constructed on-demand, with its layer sizes and neuron parameters determined through a geometrical analysis of the input data, in which separating hyperplanes are created and mapped to neurons with step activation functions. The proposed architecture consists of two hidden layers with distinct roles: inter-class separation and transformation of the data into a linearly separable representation. Inter-class separation requires every bi-chromatic pair of samples belonging to different classes to be separated by at least one hyperplane. We show that when this separation is achieved through a hierarchical partitioning of the data, the leaf nodes of the oblique decision tree, obtained as a byproduct, directly define the neurons of the linear separability layer, whose size is only one neuron greater than that of the inter-class separation layer. Experiments on the MNIST dataset demonstrate that the proposed method achieves perfect training-set classification, and compact models. The direct correspondence between the decision tree and network neurons enhances interpretability and explainability, while the construction procedure offers opportunities for parallel implementation and improved scalability.
Machine Learning (cs.LG)
arXiv:2610.17312 [cs.LG]
(or arXiv:2610.17312v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.17312 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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