diff --git a/arxiv-style/main.tex b/arxiv-style/main.tex index c62f14c..8c7098a 100644 --- a/arxiv-style/main.tex +++ b/arxiv-style/main.tex @@ -10,6 +10,7 @@ \usepackage{amsfonts} % blackboard math symbols \usepackage{nicefrac} % compact symbols for 1/2, etc. \usepackage{microtype} % microtypography +\usepackage{amsmath} % cleveref must be loaded after amsmath! \usepackage{cleveref} % smart cross-referencing \usepackage{lipsum} % Can be removed after putting your text content \usepackage{graphicx} @@ -181,10 +182,10 @@ Discrete ICS variables must remain categorical, making Gaussian diffusion inappr We therefore adopt masked (absorbing) diffusion for discrete channels, where corruption replaces tokens with a special $\texttt{[MASK]}$ symbol according to a schedule \citep{shi2024simplified}. For each variable $j$, define a masking schedule $\{m_k\}_{k=1}^K$ (with $m_k\in[0,1]$) increasing in $k$. The forward corruption process is: \begin{equation} -q(y^{(j)}_k \mid y^{(j)}_0)= +q(y^{(j)}_k \mid y^{(j)}_0) = \begin{cases} -y^{(j)}, & \text{with probability } 1-m_k,\\ -\texttt{[MASK]}, & \text{with probability } m_k, +y^{(j)}_0, & \text{with probability } 1 - m_k, \\ +\texttt{[MASK]}, & \text{with probability } m_k, \end{cases} \label{eq:masking_process} \end{equation}