[Verse 1]
Random storage locations scattered through the space
High-dimensional vectors finding their place
SDM remembers what you give it to hold
But as patterns increase, will the memories fold?
Start with just a few, recall stays crystal clear
Add a hundred more, watch accuracy veer
The saturation point creeps in like dawn
Some patterns survive while others are gone
[Chorus]
Bind and bundle, that's the VSA way
Circular convolution makes structures stay
Unbind with inverses, decode what you made
In hyperdimensional realms where memories fade
Count the dimensions, find the magic threshold
Where random vectors break orthogonal
Near-perpendicular angels dancing in flight
When n gets massive, everything's right
[Verse 2]
Binding operation takes two vectors strong
Twists them together like a neural song
Bundling adds them up, creates a sum
Multiple concepts rolled into one
Want to extract? Use the inverse key
Unbind the structure, set the data free
Like opening boxes within nested halls
VSA magic through cortical walls
[Chorus]
Bind and bundle, that's the VSA way
Circular convolution makes structures stay
Unbind with inverses, decode what you made
In hyperdimensional realms where memories fade
Count the dimensions, find the magic threshold
Where random vectors break orthogonal
Near-perpendicular angels dancing in flight
When n gets massive, everything's right
[Bridge]
Ten dimensions? Vectors cluster tight
Fifty dimensions? Still not quite right
Push to hundreds, watch the miracle bloom
Random patterns find orthogonal room
Johnson-Lindenstrauss whispers the truth
High-dimensional spaces fountain of youth
Each new vector stands almost alone
In this vast mathematical zone
[Verse 3]
Code the SDM with storage array
Measure how recall accuracy plays
Plot the curves as pattern count grows
See where interference overflow shows
Implement binding with convolution's dance
Give structured data its fighting chance
Test dimensionality's climbing stair
Find where orthogonal properties flare
[Chorus]
Bind and bundle, that's the VSA way
Circular convolution makes structures stay
Unbind with inverses, decode what you made
In hyperdimensional realms where memories fade
Count the dimensions, find the magic threshold
Where random vectors break orthogonal
Near-perpendicular angels dancing in flight
When n gets massive, everything's right
[Outro]
Cortical columns compute and store
In dimensions numbering thousand or more
Exercise these concepts, make them your own
In hyperdimensional zones unknown