[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
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