[Verse 1] In ninety-six Monderer and Shapley wrote the page Potential games where players seek their stage Every Nash equilibrium has a special trait Global optimization that we can calculate Cortical columns learn through feedback loops Game theory models how the neural groups Align their gradients without central command Distributed units working hand in hand [Chorus] Potential functions guide the way Players converge where gradients stay Feedback alignment breaks the chain Backward passes need not strain Column dynamics, game theory's dance Differential mechanics advance Learning rules that nature knows How intelligence truly grows [Verse 2] Balduzzi came in twenty-eighteen strong N-player games where differentials belong Mechanics of the gradient descent flow Saddle points and eigenvalues show When cortical networks face the learning task Multiple objectives behind the mask Each column plays against the rest Cooperative competition at its best [Chorus] Potential functions guide the way Players converge where gradients stay Feedback alignment breaks the chain Backward passes need not strain Column dynamics, game theory's dance Differential mechanics advance Learning rules that nature knows How intelligence truly grows [Bridge] Lillicrap showed us feedback doesn't need Precise transpose weights to succeed Random connections still align the flow Biological plausibility starts to show Cortical columns as computational games Each one learning different aims Yet somehow coordination emerges clean From this distributed learning machine [Verse 3] Potential games have special symmetry What helps one player helps the harmony No conflicting gradients tear apart The system's unified learning heart Cortical columns mirror this design Independent yet their goals align Nature's algorithm runs so deep Game theoretic promises to keep [Verse 4] Continuous-time dynamics show the path Where neural computation does its math Local updates serve the global good Self-organizing as evolution would Each minicolumn seeks its payoff high While system-wide improvements multiply No central planner guides the way Just local rules in neural play [Chorus] Potential functions guide the way Players converge where gradients stay Feedback alignment breaks the chain Backward passes need not strain Column dynamics, game theory's dance Differential mechanics advance Learning rules that nature knows How intelligence truly grows [Outro] From Monderer's potential to feedback's grace Mathematics finds biology's trace Columns computing in concert sublime Game theory's rhythm keeps perfect time
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