[Verse 1] In your skull there's a billion neurons firing away Each one's got a story, but not what scientists used to say No grandmother cell for grandma's face alone It's populations dancing, codes they've always known Quiroga found the truth in twenty-oh-five Jennifer Aniston neurons, sparse but still alive Not one cell screaming "That's the star I see!" But clusters whispering in distributed harmony [Chorus] Neural codes, neural codes, how does information flow? Rate and time and spike patterns, there's so much we need to know Sparse or dense, the tradeoffs dance, capacity meets the cost In the manifold geometry, no signal should be lost Neural codes, neural codes, mixing high dimensionally Population doctrine rising, that's the brain's reality [Verse 2] Rate codes count the spikes per second, slow but reliable Temporal codes use precise timing, fast and quite pliable Spike-timing rides the millisecond waves of neural chatter Each format carries different loads, and bandwidth's what matters Sparse codes save on energy, few neurons active at once Dense codes pack more information, but metabolism confronts The tradeoff between efficiency and what the brain can hold Decodability versus cost, the story that unfolds [Chorus] Neural codes, neural codes, how does information flow? Rate and time and spike patterns, there's so much we need to know Sparse or dense, the tradeoffs dance, capacity meets the cost In the manifold geometry, no signal should be lost Neural codes, neural codes, mixing high dimensionally Population doctrine rising, that's the brain's reality [Bridge] Mixed selectivity's the secret sauce that Rigotti revealed Prefrontal cortex neurons mix variables unrepealed Nonlinear combinations in the high-dimensional space Give flexibility for reasoning, cognitive interface Why neurons mix, Fusi explained the theory behind Dimensional expansion lets the cortex redesign [Verse 3] Representational similarity maps the neural terrain Kriegeskorte showed us how to measure what the patterns contain Activity flows on manifolds, geometry defines How concepts sit in neural space, mathematical designs Chung and Lee proved capacity lives in the manifold's shape Saxena synthesized the doctrine, population landscape From single cells to群体codes, the paradigm has shifted Neural space holds all the answers, dimensionally gifted [Chorus] Neural codes, neural codes, how does information flow? Rate and time and spike patterns, there's so much we need to know Sparse or dense, the tradeoffs dance, capacity meets the cost In the manifold geometry, no signal should be lost Neural codes, neural codes, mixing high dimensionally Population doctrine rising, that's the brain's reality [Outro] In the format of representation, populations reign supreme Mixed selectivity and manifolds fulfill the neural dream
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