[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