[Verse 1] In the cortex where the columns dance and sway Local learning finds its mathematical way When objectives break apart piece by piece Global gradients and local ones find peace Decomposable functions split the load Each column walks its own descent road But somehow magic happens in the sum All pathways lead where optimization comes [Chorus] Three keys unlock the learning maze Decompose, align, and play the games When locals talk to globals right Convergence blooms in neural night Break it down, correlate, potential flows That's how distributed wisdom grows Three keys, three ways, the cortex knows [Verse 2] Feedback alignment whispers soft and low Perfect gradients? We don't need to know Just positive correlation in the dance Gives slower learning still a fighting chance The updates point in roughly the right direction Like compass needles seeking true connection Regularity conditions pave the street Where imperfect signals still compete [Chorus] Three keys unlock the learning maze Decompose, align, and play the games When locals talk to globals right Convergence blooms in neural night Break it down, correlate, potential flows That's how distributed wisdom grows Three keys, three ways, the cortex knows [Bridge] Multi-agent minds in potential games Each player optimizing, none to blame But hidden underneath their selfish quest A global function puts them to the test Best-response dynamics find their groove When local objectives smoothly move Toward equilibrium's sweet embrace Where every agent finds their place [Verse 3] Provable descent when terms add clean Mathematical beauty rarely seen Convergence rates may shift and bend But learning finds its destined end Whether fast decomposition leads Or correlation plants the seeds Or potential games align the crew Distributed minds will see it through [Verse 4] Nature's wisdom coded in the brain Each neuron learns through pleasure and through pain No backprop signals traveling upstream Yet somehow global patterns fulfill the dream Biological networks find their way Through local rules that guide the neural play Evolution's gift to learning minds The distributed truth that each cell finds [Chorus] Three keys unlock the learning maze Decompose, align, and play the games When locals talk to globals right Convergence blooms in neural night Break it down, correlate, potential flows That's how distributed wisdom grows Three keys, three ways, the cortex knows [Outro] From columns small to networks grand The mathematics help us understand How local actions serve the whole In learning's distributed soul
← Gradient Whispers in the Neural Maze | Gradients Dancing Without Central Command →