[Verse 1] When data flows through cortical lanes Monoids hold the computational reins Associative law breaks the sequential chain Log n depth where linear once remained Group the operations, bracket as you please Same result emerges with mathematical ease Parallel processors dancing in sync Faster than the old sequential link [Chorus] Monoids make the magic, associative and clean Commutative freedom, reorder the machine Weighted sums and attention, it's the same old game Mathematical structures underneath the neural frame Log time not linear, parallel we go Monoid operations, let the data flow [Verse 2] Commutative monoids shuffle left and right Order independence, permutation's delight DeepSets architecture, invariant by design Transformers use attention, monoid operations align Set the elements dancing, any sequence works Mathematical symmetry where the power lurks Addition multiplication, maximum or minimum too Commutative monoids carry neural networks through [Chorus] Monoids make the magic, associative and clean Commutative freedom, reorder the machine Weighted sums and attention, it's the same old game Mathematical structures underneath the neural frame Log time not linear, parallel we go Monoid operations, let the data flow [Bridge] Attention mechanism, weighted sum at heart Scalar multiplication, monoid counterpart Query key and value, aggregate the score Commutative monoid patterns we explore Distributed columns, cortical arrays Monoid mathematics guides the neural ways [Verse 3] Aggregation schemes reduce to this one truth Monoid operations, algebraic proof Parallel reduction trees, logarithmic height Computational efficiency, mathematical might From cortical columns to transformer heads Monoid principles guide where the data spreads Associate commute, the laws that never bend Mathematical beauty, on which we all depend [Verse 4] Identity elements anchor every set Zero for addition, the baseline that's met One for multiplication, the neutral ground Empty set for unions, where nothing is found These fundamental anchors hold the structure tight Monoid axioms burning mathematical bright From silicon circuits to biological fire The same elegant patterns lift intelligence higher [Chorus] Monoids make the magic, associative and clean Commutative freedom, reorder the machine Weighted sums and attention, it's the same old game Mathematical structures underneath the neural frame Log time not linear, parallel we go Monoid operations, let the data flow [Outro] When the columns fire and the networks learn Monoid mathematics, watch the patterns turn Associative commutative, the foundation stays Mathematical monoids light computational ways
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