[Verse 1]
Deep in neural networks, patterns start to form
Representations clustering through each hidden storm
Huh and Cheung discovered something quite profound
Platonic shapes emerging where convergence can be found
Different architectures, trained on separate tasks
Still develop similar maps when we remove their masks
Like ancient geometric forms that Plato once described
Universal structures in the code we've inscribed
[Chorus]
CKA measures how these networks align
Centered Kernel Analysis draws the line
Between what's truly shared and what's unique
Platonic representations that we seek
UMAP reveals the manifold's true face
Geometric structures hiding in high-dimensional space
Reading representations like a language we can speak
[Verse 2]
Kornblith showed us metrics that could bridge the gap
Between different neural networks and their feature map
Linear CKA strips away the noise and scale
While RV coefficients tell a different tale
Similarity matrices become our guide
To understand what networks learn deep inside
When training converges on the same solution
We see the platonic representation evolution
[Chorus]
CKA measures how these networks align
Centered Kernel Analysis draws the line
Between what's truly shared and what's unique
Platonic representations that we seek
UMAP reveals the manifold's true face
Geometric structures hiding in high-dimensional space
Reading representations like a language we can speak
[Bridge]
McInnes gave us UMAP for dimension reduction
Preserving local neighborhoods through careful construction
Topological data analysis shows the way
To visualize what high dimensions want to say
Cross-dataset generalization starts to make sense
When universal patterns break down the defense
[Verse 3]
Cortical columns process information in streams
These computational units fulfill biological dreams
Distributed processing mirrors what we've learned
About representation spaces where knowledge is earned
The mathematics tells us there's a deeper truth
That brains and artificial networks share the proof
[Verse 4]
From vision models learning edge and texture maps
To language models bridging semantic gaps
The same abstractions rise from different seeds
As if geometry dictates what learning needs
Perhaps intelligence itself has certain laws
That guide how meaning from raw data draws
[Chorus]
CKA measures how these networks align
Centered Kernel Analysis draws the line
Between what's truly shared and what's unique
Platonic representations that we seek
UMAP reveals the manifold's true face
Geometric structures hiding in high-dimensional space
Reading representations like a language we can speak