🤖 AI Summary
This work proposes a novel computational paradigm for artificial general intelligence grounded in set theory and hyperdimensional computing, addressing the limitations of conventional neural networks that rely on continuous weights and matrix operations and struggle to efficiently emulate biological neural coding. By employing sparse binary representations and subset-based pattern matching, the framework unifies associative memory and symbolic processing without scalar weight adjustments. Instead, it leverages topological plasticity within combinatorially expanded hidden layers, enabling memory capabilities to emerge naturally and seamlessly bridging perceptual and symbolic representations. The resulting system supports constant-time information retrieval and maps directly onto in-memory computing hardware, offering a highly energy-efficient pathway toward artificial general intelligence.
📝 Abstract
This work introduces a new computational theory of mind grounded in set theory and hyperdimensional computing. Whereas traditional neural networks rely on continuous weights and matrix multiplication, this framework works with sparse binary data. It represents information as discrete sets, directly modeling biological neural population codes. I demonstrate that associative memory emerges naturally from network topologies featuring a combinatorially expanded hidden layer. Learning is driven by topological plasticity rather than scalar weight adjustments. This architecture unifies auto-associative and hetero-associative learning under a single core algorithm: information retrieval via subset pattern matching and exact nearest-neighbor search. Operating with constant-time complexity, these mechanisms bridge perceptual data (sparse distributed representations) and symbols (sparse holographic representations) without continuous bottlenecks. Mapping this framework to neuroanatomy, I propose that both the cerebellum and the neocortex implement variants of this algorithm, making subset pattern matching the fundamental engine of cognition. Because it relies on discrete logic rather than matrix arithmetic, this algorithm translates directly into in-memory hardware. This opens a new route toward synthetic intelligence with human-level energy efficiency.