[Verse 1] In backpropagation's elegant dance Each layer needs the transpose to advance But biology's wiring tells a different tale No weight sharing pathways, the standard methods fail Forward signals travel through synaptic gates While backward gradients must calculate The brain can't flip matrices on command So how does learning truly understand [Chorus] Weight transport problem blocks the neural way Biology can't share what forward pathways say Feedback alignment breaks the rigid chain Random matrices keep the learning train Direct or sign-symmetric, find your route When transpose isn't an option, substitute [Verse 2] Feedback alignment throws convention out Replace transpose with random matrices throughout Fixed matrix B becomes your backward guide Though it's not the transpose, gradients still slide The magic happens in the learning flow Approximate updates help the knowledge grow No biological implausibility here Just clever workarounds crystal clear [Chorus] Weight transport problem blocks the neural way Biology can't share what forward pathways say Feedback alignment breaks the rigid chain Random matrices keep the learning train Direct or sign-symmetric, find your route When transpose isn't an option, substitute [Verse 3] Direct feedback takes a bolder leap Bypass hidden layers, connections deep Straight from output error to each weight Skip the intermediate calculation fate Cortical columns work in distributed style Each unit processing all the while No need for perfect mathematical flow Just signals that help the network grow [Bridge] Sign-symmetric strikes a middle ground Matching signs where patterns can be found Not fully random, not transpose complete A compromise that makes the system neat Biology inspires computational art Each solution plays a vital part [Verse 4] Plasticity rules in neural substrate Where fixed connections can still innovate Local computations rule the day While global gradients show the way Evolution carved pathways through the night No designer needed, natural insight The brain solves puzzles we barely perceive Teaching silicon what to believe [Chorus] Weight transport problem blocks the neural way Biology can't share what forward pathways say Feedback alignment breaks the rigid chain Random matrices keep the learning train Direct or sign-symmetric, find your route When transpose isn't an option, substitute [Outro] From rigid math to flexible design Nature's wisdom helps the neurons shine No transpose needed, learning finds a way Through feedback paths that guide us every day
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