[Verse 1]
Scellier and Bengio found a bridge to cross
Between energy landscapes and backprop's force
When networks settle into equilibrium states
The gradient flows through computational gates
Two phases dancing, free and clamped in time
Teaching without error signals climbing up the line
[Chorus]
Equilibrium propagation, let the energy flow
Settle down then nudge the system, watch the gradients grow
No need for separate backward passes through the maze
Just perturb the steady state and let the learning blaze
Energy minimization shows the path ahead
Local updates match the global signal being fed
[Verse 2]
Ernoult took the concept to recurrent terrain
Showed that static inputs make the math crystal plain
Through time the updates mirror backprop's careful dance
When sequences freeze in place, gradients advance
RNN dynamics prove the theory holds its ground
Mathematical beauty in convergence can be found
[Chorus]
Equilibrium propagation, let the energy flow
Settle down then nudge the system, watch the gradients grow
No need for separate backward passes through the maze
Just perturb the steady state and let the learning blaze
Energy minimization shows the path ahead
Local updates match the global signal being fed
[Verse 3]
Laborieux scaled the vision to convolutional heights
Deep networks learning through equilibrium's insights
Kernels and feature maps in steady-state arrays
Biological plausibility through computational ways
Each layer settles while the whole system learns to see
Cortical inspiration sets the parameters free
[Verse 4]
What makes this method so elegant and pure?
No credit assignment problems to endure
Each neuron knows its role without looking back
Through energy landscapes, staying on the track
Physics meets computation in this graceful way
Where settling dynamics guide what networks learn to say
[Bridge]
From energy functions to neural computation
Bridging gaps between theory and implementation
Two-phase learning cycles mirror how brains might work
Local rules emerging where global patterns lurk
[Chorus]
Equilibrium propagation, let the energy flow
Settle down then nudge the system, watch the gradients grow
No need for separate backward passes through the maze
Just perturb the steady state and let the learning blaze
Energy minimization shows the path ahead
Local updates match the global signal being fed
[Outro]
Three papers weaving equilibrium's tale
From foundational theory to practical scale
Energy and gradients dancing hand in hand
Teaching us how cortical columns understand