[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