Red Discouragement

Let $p$ be the next-token distribution at a decoding step, obtained by soft-maxing the model logits $z$. Let $R$ be the set of token IDs we want to discourage.

We modulate the discouragement using the model’s uncertainty at the decoding step, to preserve fluency. When the model is certain about what should be produced next, we intervene softly, when it is uncertain, we apply the maximum intervention strength.

We use Shannon entropy $H(p)$:

$$H(p)=-\sum _i{p}_i\log p_i$$

and we use it to define a smooth gating coefficient $\varphi \in [0,1]$:

$$\varphi =\sigma (\frac{H(p)-\tau }{s})$$

where
$\tau$ is the threshold, $s$ is a softness parameter, $\sigma (\cdot )$ is the logistic function.
To discourage, we intervene in logit space. i.e.:

$${\mathbf{z}}^{\prime }=\mathbf{z}-\lambda \mathbf{r}$$

where the penalty term $\lambda \ge 0$ is controlled by $g$, $\lambda =\varphi {\lambda }_{max}$ and $r$ is a vector that shapes where the penalty lands over the vocabulary.

Building $r$
Uniform

$$\mathbf{r}=\{\begin{array}{ll}\frac{1}{|R|}& \text{if }i\in R\\ 0& \text{otherwise}\end{array}$$

Unnormalized uniform

$$\mathbf{r}=\{\begin{array}{ll}1& \text{if }i\in R\\ 0& \text{otherwise}\end{array}$$

topk red

$$\mathbf{r}=\{\begin{array}{ll}\frac{1}{K}& \text{if }r\in \text{TopK}(R)\\ 0& \text{otherwise}\end{array}$$

unnorm topk

$$\mathbf{r}=\{\begin{array}{ll}1& \text{if }r\in \text{TopK}(R)\\ 0& \text{otherwise}\end{array}$$

p_renorm

$$\mathbf{r}=\{\begin{array}{ll}\frac{p_i}{{\sum }_{j\in R}{p}_j}& \text{if }in\in R\\ 0& \text{otherwise}\end{array}$$

the effeect is that the total penalty $\lambda$ is conserved over $R$ and allocated more towards those red tokens that the model currently prefers.

In all normalized modes (uniform, top-KKK, ppp-renormalized), ∑iri=1\sum_i r_i = 1∑i​ri​=1 over the selected subset, ensuring that λ\lambdaλ is interpreted as the total penalty magnitude.
In contrast, the unnormalized top-KKK variant applies the full penalty independently to each selected token, yielding stronger targeted suppression.