RomanAILabs — White Hole Steering (Logit/Temperature Control)

Given a context signal x and reference signal y, define:

  f(i) = (i+1)^(-α)
  K(i) = (i+1)^(-β)
  σ(u) = 1 / (1 + e^(−u))                 (sigmoid)
  φ(z) = sign(z) · ln(1 + |z|)            (log-compress with sign)
  H(z) = tanh(z)                          (bounded squashing)

Let T(·,·) be a transform, and let N be the steering depth.

Compute the normalized White Hole sum:

               N
  S(x,y) =  ( Σ  a₁ · f(i) · σ( f(i)·K(i)·T(x,i)·T(y,0)·e^(−i·T(x,i)·T(y,0)) ) )
              i=1
            -------------------------------------------------------------------
                              N
                              Σ  f(i)
                             i=1

Then the steering scalar is:

  s = F(x,y) = H( φ( S(x,y) ) )
            = tanh( sign(S)·ln(1+|S|) )

Dynamic temperature mapping (example):

  τ(s) = clamp( 1.1 + 0.4·s , 0.7, 1.5 )

And you can apply s either to:
- logits:  logits' = logits − λ·s·softmax(logits)   (small probability reshaping)
- temperature: use τ(s) per token (or per step-window) to modulate creativity.