Informational Frustration in Neural Manifolds: Shannon Bottlenecks and the Limits of Learnability
arXiv:2606.30512v1 Announce Type: new Abstract: Why overparameterised deep networks generalise so remarkably well remains one of the most stubborn open questions in machine learning theory. Classical frameworks like VC dimension and Rademacher complexity predict catastrophic overfitting in modern models, leaving a massive theoretical gap between theory and reality. In this paper, we bridge this divide by introducing a unified framework that links information theory, topology, and statistical mechanics to map the hard limits of deep learning. Central to our approach is the Entropic Learnability
This research is published as the theoretical understanding of deep learning struggles to keep pace with its empirical success, creating a significant gap for foundational work.
A unified framework linking information theory, topology, and statistical mechanics could unlock a deeper understanding of deep learning's fundamental limits and capabilities, guiding future AI development.
The theoretical landscape for machine learning shifts to incorporate information-theoretic and topological constraints, potentially revealing new bottlenecks and optimal architectures.
- · AI theoreticians
- · Deep learning researchers
- · AI hardware designers
- · Optimized AI model developers
- · Developers relying solely on brute-force overparameterisation
- · Traditional statistical learning theorists
- · AI projects with inefficient architectures
The paper provides a new theoretical lens to explain the generalization power of overparameterized deep networks.
This understanding could lead to the development of more efficient and robust AI models, reducing computational resource requirements.
These theoretical insights might inform new AI safety and alignment strategies by defining inherent boundaries of what deep learning can learn.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG