[Verse 1] In the cortex where neurons fire and dance Credit assignment needs a fighting chance The Jacobian matrix holds the key Parameters need structure we can see Rank and sparsity must align For learning signals to clearly shine Without this order chaos reigns No pathway back through neural chains [Chorus] Identifiability, the theorem we need Mixture experts competing, each with different creed Distributed codes spread wisdom around But credit gets lost when signals aren't found Structure the gradient, make the path clear Mathematical truth is what we hold dear [Verse 2] Mixture of Experts divides the load Each specialist walks their chosen road The gating network decides who speaks When input data has what it seeks Modular minds beat dense arrays When assumptions hold in provable ways Efficiency blooms through separation Smart division beats brute computation [Chorus] Identifiability, the theorem we need Mixture experts competing, each with different creed Distributed codes spread wisdom around But credit gets lost when signals aren't found Structure the gradient, make the path clear Mathematical truth is what we hold dear [Bridge] Hinton saw the parallel dream Processing spread across the team Robust to damage, hard to break But attribution's hard to make Which unit caused the magic spark When representations blur and arc The tradeoff haunts our neural quest Robustness versus credit's test [Verse 3] Cortical columns stand in rows Each one computing what it knows The brain's own mixture, gates unknown Distributed wisdom, locally grown From theorem to biology's dance Mathematics guides our neural glance Credit flows where structure permits The gradient speaks in precise bits [Verse 4] Back-propagation needs its map To close the learning feedback gap Each layer's contribution clear When gradients flow without the fear Of vanishing into the void When proper structure is deployed The chain rule walks the neural tree Assigning blame mathematically [Chorus] Identifiability, the theorem we need Mixture experts competing, each with different creed Distributed codes spread wisdom around But credit gets lost when signals aren't found Structure the gradient, make the path clear Mathematical truth is what we hold dear [Outro] In cortical mathematics we trust Jacobians clean away the dust From chaos comes computational grace When structure finds its rightful place
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