[Verse 1]
In the cortex where the columns dance and sway
Local learning finds its mathematical way
When objectives break apart piece by piece
Global gradients and local ones find peace
Decomposable functions split the load
Each column walks its own descent road
But somehow magic happens in the sum
All pathways lead where optimization comes
[Chorus]
Three keys unlock the learning maze
Decompose, align, and play the games
When locals talk to globals right
Convergence blooms in neural night
Break it down, correlate, potential flows
That's how distributed wisdom grows
Three keys, three ways, the cortex knows
[Verse 2]
Feedback alignment whispers soft and low
Perfect gradients? We don't need to know
Just positive correlation in the dance
Gives slower learning still a fighting chance
The updates point in roughly the right direction
Like compass needles seeking true connection
Regularity conditions pave the street
Where imperfect signals still compete
[Chorus]
Three keys unlock the learning maze
Decompose, align, and play the games
When locals talk to globals right
Convergence blooms in neural night
Break it down, correlate, potential flows
That's how distributed wisdom grows
Three keys, three ways, the cortex knows
[Bridge]
Multi-agent minds in potential games
Each player optimizing, none to blame
But hidden underneath their selfish quest
A global function puts them to the test
Best-response dynamics find their groove
When local objectives smoothly move
Toward equilibrium's sweet embrace
Where every agent finds their place
[Verse 3]
Provable descent when terms add clean
Mathematical beauty rarely seen
Convergence rates may shift and bend
But learning finds its destined end
Whether fast decomposition leads
Or correlation plants the seeds
Or potential games align the crew
Distributed minds will see it through
[Verse 4]
Nature's wisdom coded in the brain
Each neuron learns through pleasure and through pain
No backprop signals traveling upstream
Yet somehow global patterns fulfill the dream
Biological networks find their way
Through local rules that guide the neural play
Evolution's gift to learning minds
The distributed truth that each cell finds
[Chorus]
Three keys unlock the learning maze
Decompose, align, and play the games
When locals talk to globals right
Convergence blooms in neural night
Break it down, correlate, potential flows
That's how distributed wisdom grows
Three keys, three ways, the cortex knows
[Outro]
From columns small to networks grand
The mathematics help us understand
How local actions serve the whole
In learning's distributed soul