[Verse 1] When cortical columns compute in parallel space Each unit holds a piece of the computational race Decomposable losses split the gradient clean Local SGD and centralized meet at the same scene Prove convergence when the math breaks apart Each column learns its designated part [Chorus] Alignment is the key, alignment sets us free When local meets global, that's the harmony Gradient directions pointing true Distributed learning, synchronized view Alignment is the key, computational spree [Verse 2] But misalignment breeds catastrophic drift Local objectives start to create a rift Construct examples where the goals diverge Watch the network learning curve submerge Individual columns chase their private dreams While global performance tears apart at the seams [Chorus] Alignment is the key, alignment sets us free When local meets global, that's the harmony Gradient directions pointing true Distributed learning, synchronized view Alignment is the key, computational spree [Bridge] Measure the angles between gradient flows Feedback alignment, see how it grows Empirical traces through training epochs long Watch misaligned vectors slowly grow strong Cosine similarity climbing from the noise Each iteration finds its balanced poise [Verse 3] Start with random weights, chaotic and wild Gradients scattered like an untrained child But iteration by iteration the magic unfolds Alignment emerges as the story retold Local updates synchronize their dance Giving distributed computation its chance [Verse 4] Theoretical bounds on the convergence rate Show how aligned gradients accelerate Communication rounds reduce the noise Synchronized workers make the optimal choice Variance decreases with each passing step As local and global objectives are kept [Chorus] Alignment is the key, alignment sets us free When local meets global, that's the harmony Gradient directions pointing true Distributed learning, synchronized view Alignment is the key, computational spree [Outro] From cortical columns to SGD's embrace Mathematical proof finds its rightful place When local and global objectives unite Distributed learning reaches its height [Final Chorus] Alignment is the key, alignment sets us free When local meets global, that's the harmony Gradient directions pointing true Distributed learning, synchronized view Alignment is the key, computational spree
← Gradients Dancing Without Central Command | Cortical Harmony's Grand Design →