arXiv AI By Tiansi Dong, Mateja Jamnik, Pietro Li\`o

Non-Zero Radius: The Missing Component of Neural Networks

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The paper proposes Sphere Neural Networks (SphNNs), which replace the conventional zero‑radius vector representation with spheres of non‑zero radius to better capture biological cognition and enable symbolic reasoning. By relaxing the zero‑radius constraint, the authors argue that concepts can be represented as spatial regions, allowing reasoning through model construction and inspection. SphNNs employ a transition map that achieves Aristotelian syllogistic reasoning without training data, aiming to address the black‑box nature and symbolic reasoning limitations of current neural networks.

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arXiv Machine Learning
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