[Verse 1]
In the cortex where neurons dance and weave
Same pattern copied endlessly
Columns standing like soldiers in formation
Each one holds the computation
Tiled across the brain's vast territory
Circuit motifs tell the same story
From visual fields to motor command
Identical blueprints across the land
[Chorus]
Permutation invariant, that's the key
Swap the columns, same functionality
Sum and max, the operations we need
Dendritic trees make the magic proceed
Tileability, tileability
Cortical columns work in harmony
[Verse 2]
Winner-take-all dynamics firing strong
Max-like functions where signals belong
Dendritic integration adds them up
Sum operations fill the neural cup
Each column speaks its local truth
Aggregated wisdom, that's the proof
Algebraic structure guides the way
How distributed units have their say
[Chorus]
Permutation invariant, that's the key
Swap the columns, same functionality
Sum and max, the operations we need
Dendritic trees make the magic proceed
Tileability, tileability
Cortical columns work in harmony
[Bridge]
From somatosensory to auditory streams
Visual cortex processing all our dreams
The same computational architecture flows
Through every region where cognition grows
Biological constraints shape what we can do
Sum and max emerge from neural circuitry true
Not multiplication or complex transforms
Simple operations keep the brain's norms
[Verse 3]
Distributed processing across the sheet
Where cortical columns gather and meet
Each tile contributing its unique voice
Aggregation methods give us choice
Summation pools the collective thought
Maximum selection finds what's sought
Mathematical beauty in biological form
Cortical columns weather every storm
[Verse 4]
Layer by layer, the signals cascade
Through minicolumns where connections are made
Six-layered architecture holds the design
Pyramidal neurons in perfect line
Inhibitory circuits keep balance tight
While excitatory paths spread the light
Modular processing, scalable and clean
The most elegant network we've ever seen
[Chorus]
Permutation invariant, that's the key
Swap the columns, same functionality
Sum and max, the operations we need
Dendritic trees make the magic proceed
Tileability, tileability
Cortical columns work in harmony
[Outro]
Tiled and ready, the cortex computes
Through permutation-invariant routes
Sum and max in neural concert
Making minds that can assert
[Final Chorus]
Permutation invariant, that's the key
Swap the columns, same functionality
Sum and max, the operations we need
Dendritic trees make the magic proceed
Tileability, tileability
Cortical columns work in harmony