[Verse 1] In eighty-two, Hopfield showed the way Neural networks storing memories each day Symmetric weights and energy landscapes deep Where patterns settle down and memories keep Like magnets finding their ground state low Collective computation starts to grow Each neuron talks to every other one Until the system finds what can't be undone [Chorus] Energy flows down, patterns emerge strong Hopfield nets remember what belongs Boltzmann heat shakes up the stable scene Free energy principle keeps the brain machine clean Cortical columns computing as one tribe Distributed units where thoughts come alive [Verse 2] Hinton and Sejnowski turned up the heat Boltzmann machines make learning complete Hidden units dance with thermal noise Stochastic updates give the network voice Temperature cooling like annealing steel Optimal inference becomes surreal Visible and hidden layers communicate Until the perfect representation takes the bait [Chorus] Energy flows down, patterns emerge strong Hopfield nets remember what belongs Boltzmann heat shakes up the stable scene Free energy principle keeps the brain machine clean Cortical columns computing as one tribe Distributed units where thoughts come alive [Bridge] Then Friston came with his grand design Free energy principle, the unifying line Prediction errors cascade through the cortex maze Hierarchical inference sets the brain ablaze Surprise minimization drives each neural choir Bayesian updates never seem to tire [Verse 3] Cortical columns standing like cathedral spires Six layers deep with processing fires Minicolumns clustered in organized arrays Distributed computation through neural pathways From primary sensory to association zones Each column speaks in electrical tones The mathematics binding Hopfield's dream With Boltzmann's heat and Friston's scheme [Verse 4] Attractor basins pull the wandering mind Stable states that memories can find Local minima trap the flowing thought Global optimization that can't be bought While variance and precision dance their part In predictive coding's neural art Expectation flows down, errors climb up Consciousness emerges from this neural cup [Chorus] Energy flows down, patterns emerge strong Hopfield nets remember what belongs Boltzmann heat shakes up the stable scene Free energy principle keeps the brain machine clean Cortical columns computing as one tribe Distributed units where thoughts come alive [Outro] Three papers bridging decades of thought Neural computation finally caught In mathematical frameworks crystal clear The brain's deep mysteries drawing near
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