[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