arXiv:2512.18471v2 Announce Type: replace Abstract: Continual learning systems face a fundamental geometric obstacle: as experience accumulates on a fixed-capacity manifold, covering numbers grow linearly with time, eventually forcing representational overlap and catastrophic interference. Prevailing approaches attack this problem by \emph{expansion} - projecting into higher-dimensional spaces via kernels, overparameterization, or replay. We argue the solution is the opposite: \emph{contraction}. We formalize abstraction as the \textbf{Urysohn Ladder}, a hierarchy of quotient maps that recursi
The paper addresses a fundamental limitation in continual learning (catastrophic interference), which becomes increasingly critical as AI systems are deployed in dynamic, real-world environments requiring continuous adaptation without retraining.
This research proposes a novel theoretical framework to overcome a core challenge for AI scalability and robustness, potentially enabling more efficient and adaptable AI systems crucial for advanced applications.
The proposed 'Urysohn Ladder' concept offers a new paradigm for continual learning, shifting from high-dimensional expansion to metric contraction, suggesting a different architectural approach for future AI designs.
- · AI researchers (continual learning)
- · Developers of embodied AI
- · Robotics sector
- · Edge AI providers
- · AI architectures reliant solely on expansion
- · Systems requiring frequent full model retraining
More robust and efficient AI models capable of learning continuously without forgetting past knowledge.
Accelerated development of AI agents that can adapt to long-term, dynamic environments with limited resources.
Reduced computational and energy footprint for maintaining and updating complex AI systems over their operational lifespan.
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