[Verse 1]
In Whittington and Bogacz's maze of thought
Where prediction errors dance and weave
When those errors shrink to whispers caught
The network learns what minds achieve
Predictive coding holds the key
To gradients that backprop would decree
But using only local rules
Hebbian magic breaks the schools
[Chorus]
Small errors linearize the game
Forward backward weights the same
Transport problem haunts the frame
But feedback alignment stakes its claim
Predictive coding shows the way
Gaussian assumptions hold the sway
Free energy guides the neural play
In cortical columns day by day
[Verse 2]
The weight transport demon rears its head
Symmetric pathways must align
Forward flowing backward fed
Perfect balance by design
But approximations find their place
Feedback alignment saves the race
Random matrices suffice
When biology pays the price
[Chorus]
Small errors linearize the game
Forward backward weights the same
Transport problem haunts the frame
But feedback alignment stakes its claim
Predictive coding shows the way
Gaussian assumptions hold the sway
Free energy guides the neural play
In cortical columns day by day
[Bridge]
Variational inference underneath
Gaussian bells ring crystal clear
Free energy principles beneath
Make cortical computation near
What silicon dreams could never reach
Through biological mystique
[Verse 3]
When prediction errors fade to dust
Linearization takes command
Gradients emerge through neural thrust
Identical to what we planned
Backpropagation's ghost appears
In Hebbian updates crystal clear
Local learning global smart
Biology's computational art
[Verse 4]
Layered hierarchies unfold
Top-down priors shape the scene
Bottom-up the story's told
Prediction meets what eyes have seen
Error signals propagate
Through cortical laminar gates
Interneurons modulate
As learning and perception mate
[Chorus]
Small errors linearize the game
Forward backward weights the same
Transport problem haunts the frame
But feedback alignment stakes its claim
Predictive coding shows the way
Gaussian assumptions hold the sway
Free energy guides the neural play
In cortical columns day by day
[Outro]
Distributed units compute and learn
Through predictive coding's gentle burn
Mathematics wrapped in flesh and bone
Where artificial meets our own