[Verse 1] Three algorithms walking different roads Recurrent Backprop with its gradient loads Equilibrium Prop finds the steady state Predictive Coding predicts what we anticipate But underneath these separate schemes Lives a unified mathematical dream One framework binding all three tight Same equations, different light [Chorus] Energy functions, gradients flow Different assumptions, same math below Recurrent loops or equilibrium's call Prediction errors connecting it all One framework rules them, special cases three The cortical column's grand unity [Verse 2] Start with energy landscapes wide Where neural states and targets collide Add temporal dynamics to the mix Watch how each algorithm picks Its favorite path through parameter space Recurrent Backprop shows its face When time unfolds in sequence clean Forward pass, then backward scene [Chorus] Energy functions, gradients flow Different assumptions, same math below Recurrent loops or equilibrium's call Prediction errors connecting it all One framework rules them, special cases three The cortical column's grand unity [Verse 3] Equilibrium Prop takes a different stance Finds the fixed point, skips the dance No time unrolling, just converge Let positive and negative phases merge The energy minimum calls the shots Connect the computational dots Same gradients, different derivation Steady-state optimization [Bridge] Predictive Coding breaks the mold Hierarchical stories to be told Error signals propagate up high Predictions flowing from the sky Top-down meets bottom-up collision In this computational vision Three faces of one deeper truth Mathematical fountain of youth [Verse 4] The magic lies in what we assume Time dynamics, equilibrium Forward models, error correction Each choice shapes our algorithm's direction But strip away these surface layers Find the common mathematical players Energy gradients rule supreme In cortical column's unified scheme [Verse 5] From artificial to biological This bridge spans the neurological Machine learning meets the brain's design Where silicon and neurons align Cortical circuits compute and learn Through energy landscapes they discern The patterns hidden in the data flow Three algorithms help us know [Chorus] Energy functions, gradients flow Different assumptions, same math below Recurrent loops or equilibrium's call Prediction errors connecting it all One framework rules them, special cases three The cortical column's grand unity [Outro] Many small models become one large This composability takes charge Distributed computation's art Each column plays its vital part
← Blurry Gradients Tell the Story | Climbing Up The Ladder →