[Verse 1] In the brain's cathedral, neurons fire and learn But backprop's got a secret that makes biologists concerned It sends the signal backward through symmetric pathways clean But cortex doesn't mirror what our algorithms have seen The weight transport's too perfect, like a highway built both ways When biology uses shortcuts through its tangled neural maze [Chorus] Gradients flow like rivers, but the question's how they move Forward pass or backward pass, which direction do we choose Same equation, different dance, the math will find its way Biological plausibility starts with gradients today Same destination, different roads, the cortex knows the score There's always more than one way to unlock the gradient door [Verse 2] The separate backward phases need their own distinct command But living tissue can't divide its processes so planned No teacher signal traveling down the exact reverse of tracks The brain computes its learning while the forward signal acts Simultaneous processing in the cortical domain Not waiting for the echo to come traveling back again [Chorus] Gradients flow like rivers, but the question's how they move Forward pass or backward pass, which direction do we choose Same equation, different dance, the math will find its way Biological plausibility starts with gradients today Same destination, different roads, the cortex knows the score There's always more than one way to unlock the gradient door [Bridge] Equilibrium propagation finds the balance in the flow Predictive coding whispers what the next layer needs to know Contrastive learning teaches through the difference and compare While feedback alignment shows the gradients were always there [Verse 3] The columns hold their secrets in distributed arrays Each unit solving pieces of the optimization maze No central backward sweeping through the network's rigid spine Just local computation making global patterns shine The mathematics promise what biology can achieve When gradients find new pathways we're ready to believe [Chorus] Gradients flow like rivers, but the question's how they move Forward pass or backward pass, which direction do we choose Same equation, different dance, the math will find its way Biological plausibility starts with gradients today Same destination, different roads, the cortex knows the score There's always more than one way to unlock the gradient door [Outro] The foundation's in the knowing that the gradient's just math Not married to the method or the computational path
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