[Verse 1] Building neural architectures with gates that learn to choose Mixture of Experts dancing, each module finds its groove Training with constraints explicit, force the specialization Measure how each expert clusters, functional separation [Chorus] Modular minds, distributed design Cortical columns keeping knowledge aligned Test the damage, watch the curves decline Quantify structure, modularity's sign Networks that fragment, networks that bind Mathematical measures help us define [Verse 2] Take your scalpel to the circuits, damage units one by one Localist networks crumble fast when critical nodes are done But distributed computation shows a graceful degradation Plot the performance falling slow, resilient information [Chorus] Modular minds, distributed design Cortical columns keeping knowledge aligned Test the damage, watch the curves decline Quantify structure, modularity's sign Networks that fragment, networks that bind Mathematical measures help us define [Bridge] Newman's metric cuts through layers Q-modularity reveals the players Clustering coefficient shows the way How connections group and stay Small networks, large networks, patterns emerge Scale-free topology on the verge [Verse 3] Graph theory meets neuroscience in the silicon substrate Adjacency matrices tell us how the modules congregate Community detection algorithms slice through hidden structure Betweenness centrality maps the computational juncture [Verse 4] Hierarchical organization builds from simple to complex Visual cortex processing shows how features interconnect V1 detects the edges, V4 builds the shapes complete Higher levels integrate the whole, making vision concrete [Chorus] Modular minds, distributed design Cortical columns keeping knowledge aligned Test the damage, watch the curves decline Quantify structure, modularity's sign Networks that fragment, networks that bind Mathematical measures help us define [Bridge 2] Hebbian learning carves the pathways Cells that fire together always Strengthen bonds while others fade Functional modules slowly made [Chorus] Modular minds, distributed design Cortical columns keeping knowledge aligned Test the damage, watch the curves decline Quantify structure, modularity's sign Networks that fragment, networks that bind Mathematical measures help us define [Outro] From cortex inspiration to the digital domain Exercises teach us how intelligence can reign Through modular computation, robust and refined The mathematics of thinking, finally defined
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