[Verse 1]
In Mac Lane's world where arrows compose
Monoids gather, operation flows
Identity waits while multiplication chains
Categories map where structure remains
From objects linked by morphisms bright
Functors preserve the mapping sight
Composition rules like clockwork turn
Mathematical bridges help us learn
[Chorus]
Deep sets and categories, neurons align
Permutation invariant, order declined
Graph networks weaving cortical dreams
Relational bias in learning schemes
Sum them up, the elements dance
Equivariant transformations advance
Column by column, the patterns unfold
Mathematical stories in neural code told
[Verse 2]
Zaheer showed us sets can think
No matter how elements rearrange or link
Phi transforms each piece alone
Rho combines what phi has grown
Symmetric functions hold the key
Order independence sets us free
Like cortical columns processing sight
Each neuron fires without sequence fright
[Chorus]
Deep sets and categories, neurons align
Permutation invariant, order declined
Graph networks weaving cortical dreams
Relational bias in learning schemes
Sum them up, the elements dance
Equivariant transformations advance
Column by column, the patterns unfold
Mathematical stories in neural code told
[Verse 3]
Battaglia's graphs connect the dots
Nodes and edges, neural thoughts
Entity networks, relation space
Message passing finds its place
Update functions learn to grow
Aggregation lets patterns flow
Inductive bias guides the way
Structure teaches night and day
[Verse 4]
Group actions twist through hidden layers
Symmetry breaks, the model slayers
Equivariant maps preserve the form
Through transformations, features transform
CNN filters slide with translation
Pooling layers find correlation
Invariance built in every stride
Mathematical principles as our guide
[Bridge]
From category theory's abstract height
To neural columns processing light
Distributed units compute as one
Mathematical harmony has just begun
Monoid structure meets the brain
Deep learning breaks the pattern chain
[Chorus]
Deep sets and categories, neurons align
Permutation invariant, order declined
Graph networks weaving cortical dreams
Relational bias in learning schemes
Sum them up, the elements dance
Equivariant transformations advance
Column by column, the patterns unfold
Mathematical stories in neural code told
[Outro]
Cortical columns, distributed and wise
Mathematical frameworks help them rise
Categories, sets, and graphs combine
In neural architectures by design