[Verse 1] Deep in cortical layers where neurons convene Distributed units process what we've never seen Forward dynamics flowing like electric streams But here's the twist that changes computational dreams When gradients need flowing in reverse direction There's a biological trick for error correction [Chorus] J transpose, J transpose Symmetric weights the brain proposes Forward pass can substitute For backward flow, that's the route J transpose, J transpose Nature's hack that science knows Same result, different way Forward dynamics saves the day [Verse 2] Traditional backprop sends signals upstream Against the natural cortical scheme But running forward with transposed connections Mimics backward error corrections The Jacobian matrix holds the secret key Its transpose unlocks biological mystery [Chorus] J transpose, J transpose Symmetric weights the brain proposes Forward pass can substitute For backward flow, that's the route J transpose, J transpose Nature's hack that science knows Same result, different way Forward dynamics saves the day [Bridge] Columns compute in parallel arrays Each unit learns through forward-flowing maze Symmetric transport breaks the training rule Makes biological networks learning tools Weight matrices mirror their reflection Perfect mathematical connection [Verse 3] Module seven waits to solve the puzzle piece How symmetric transport finds its sweet release But for now we glimpse the elegant design Where forward substitutes for backward line Cortical columns dancing in formation Through distributed computational creation [Verse 4] Synaptic weights align in perfect symmetry Creating pathways through neural geometry Error signals transform through matrix magic Making backward flow less problematic Dendrites and axons share the learning load Following the transpose computational code [Chorus] J transpose, J transpose Symmetric weights the brain proposes Forward pass can substitute For backward flow, that's the route J transpose, J transpose Nature's hack that science knows Same result, different way Forward dynamics saves the day [Outro] In neural circuits where the mysteries hide Forward and backward learning coincide Through transpose magic, nature found the code For distributed learning on the cortical road
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