Iteration T: 3.0 0

Add a momentum term to smooth the aggressive step:

v = momentum*v + (1-momentum)*grad
x = x - λ*v + β

In real-time control loops, one might log: iteration t 3.0 0

iteration <time> <setpoint> <output>

Then "iteration t 3.0 0" means:

Example from a PID log:

iteration t 3.0 0   # t=10 → setpoint=3.0, measured output=0

Execute a single iteration (one forward pass/decoding cycle) and return the raw model output plus metadata.