Radial Suppression Accelerates Algorithmic Generalization: A Geometric Analysis of Delayed Generalization
arXiv:2606.32000v1 Announce Type: new Abstract: Why do neural networks memorize algorithmic training data long before they generalize? We present a geometric case study demonstrating that, on tasks where generalization requires discovering structured low-dimensional circuits, the memorization-generalization delay is driven by radial inflation of hidden representations under cross-entropy optimization. We formalize a radial-angular decomposition of activation-space dynamics and derive three testable propositions: (i) that penalizing radial inflation induces anisotropic, data-dependent weight re
This research provides a theoretical advancement in understanding a core machine learning challenge, published as the field's fundamental issues are increasingly under scrutiny for practical application.
Improving neural network generalization is critical for developing more reliable and efficient AI systems, impacting their widespread deployment and economic utility.
A clearer path emerges for designing neural networks that generalize faster and more efficiently, potentially reducing the computational resources and data required for training.
- · AI researchers
- · AI development platforms
- · Deep learning hardware providers
- · AI models that rely on pure brute-force memorization
- · Companies with inefficient training pipelines
More efficient and generalizable AI models become possible, reducing training costs and increasing performance.
This could accelerate the development of complex AI applications, fostering broader adoption across various industries.
Reduced compute requirements for generalization might lower barriers to entry for AI development, diversifying the landscape of AI innovators.
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Read at arXiv cs.LG