This paper explores potential architectural directions for addressing key limitations of current Large Language Models (LLMs) based on the Transformer architecture. We focus on approaches that could enable continuous learning, unlimited memory access, and enhanced reasoning capabilities. Rather than proposing a definitive new architecture, we survey promising research directions and discuss how components from different approaches might be integrated to create a system capable of learning, remembering, and selfimproving without context window limitations. We provide mathematical foundations for these components and discuss implementation considerations. This work aims to serve as a roadmap for researchers exploring next-generation language model architectures.
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