papers/zoo-dex/sections/05-inference-credit-swaps.tex

\section{Inference Credit Swaps}

\label{sec:credits}

\subsection{Credit Denominations}

The Zoo ecosystem uses two inference credit tokens:

\begin{itemize}
    \item \textbf{ZINF} (Zoo Inference Credits): Used on Zoo L2. 1 ZINF = 1 GPU-second of A100 inference.
    \item \textbf{BINF} (Beluga Inference Credits): Used on Beluga L3. 1 BINF = 1 GPU-second of A100 inference on Beluga's model marketplace.
\end{itemize}

\subsection{Swap Mechanism}

ZINF/BINF swaps use a constant-product AMM pool with a dynamic fee that adjusts based on the cross-chain inference utilization ratio:

\begin{equation}
\text{fee} = \text{baseFee} \cdot \left(1 + \delta \cdot \left|\frac{U_{\text{zoo}}}{U_{\text{beluga}}} - 1\right|\right)
\end{equation}

where $U_{\text{zoo}}$ and $U_{\text{beluga}}$ are inference utilization rates on each chain. When utilization is balanced, the fee is minimal; when one chain is overloaded, the fee increases to incentivize rebalancing.

\subsection{Atomic Cross-Chain Conversion}

For ZOO $\to$ BINF conversions, the DEX performs an atomic two-step:

\begin{algorithm}[t]
\caption{Atomic Inference Credit Conversion}
\label{alg:credits}
\begin{algorithmic}[1]
\STATE \textbf{Input}: $x$ ZOO on Zoo L2, destination: Beluga L3
\STATE Swap $x$ ZOO $\to$ $y$ ZINF on Zoo DEX (LP-9012)
\STATE Bridge $y$ ZINF $\to$ Beluga via Warp message
\STATE On Beluga: convert $y$ ZINF $\to$ $z$ BINF at bridge rate
\STATE Total: $x$ ZOO $\to$ $z$ BINF in $\sim$2.5s
\end{algorithmic}
\end{algorithm}