[Verse 1] In the cortex where the neurons dance and fire Only fragments wake while millions stay quiet Sparse activation holds the secret key Few cells lighting up in vast circuitry This selective pattern isn't random chance It's the foundation of computational dance When stimuli arrive at neural gates Just a whisper of cells participates [Chorus] Sparse codes, sparse codes, scattered like the stars High dimensions where the orthogonal magic sparks Few awake, most asleep, that's the cortical way Superimpose and retrieve what the networks say Sparse codes, sparse codes, nearly perpendicular Content-addressable broadcast spectacular [Verse 2] Picture vectors stretching through dimensional space When they're sparse and wide, they barely touch or trace Orthogonal means perpendicular and clean Separate signals in the mathematical scene Like whispers in a crowded concert hall Each voice distinct though others may call The mathematics proves what neurons know Sparse representations steal the show [Chorus] Sparse codes, sparse codes, scattered like the stars High dimensions where the orthogonal magic sparks Few awake, most asleep, that's the cortical way Superimpose and retrieve what the networks say Sparse codes, sparse codes, nearly perpendicular Content-addressable broadcast spectacular [Bridge] Superposition layers meaning upon meaning While orthogonality keeps signals from careening The brain discovered what the math predicts Sparse high-dimensional coding does the tricks Content-addressable memory comes alive When only scattered neural clusters thrive [Verse 3] Broadcast systems need this special property Sparse codes enable neural democracy Messages can layer without interference Mathematical beauty in neural adherence Part three will show how this principle grows Into networks where information flows But first grasp how the cortical design Makes sparse activation so divine [Verse 4] Evolution found this elegant solution To pack more data without convolution Each pattern carved from silence and from sound Where absent signals are as profound As those that fire in their destined place Negative space gives meaning its embrace [Chorus] Sparse codes, sparse codes, scattered like the stars High dimensions where the orthogonal magic sparks Few awake, most asleep, that's the cortical way Superimpose and retrieve what the networks say Sparse codes, sparse codes, nearly perpendicular Content-addressable broadcast spectacular [Outro] In the silence between the firing cells Lives the wisdom that neuroscience tells Sparse is powerful, sparse is smart Mathematical cortical art
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