papers/lux-fraud-proofs/sections/16-ai-computation-fraud-proofs.tex

\section{AI Computation Fraud Proofs}


Lux introduces specialized fraud proofs for AI workloads, addressing the unique challenges of verifying machine learning computations.

\subsection{Neural Network Layer Verification}

Verifying neural network inference layer by layer:

\begin{algorithm}
\caption{Layer-wise Neural Network Verification}
\begin{algorithmic}[1]
\State \textbf{Input:} Input $X$, Weights $W$, Output $Y$, Activations $A$
\State \textbf{Output:} Valid $\in \{\text{true}, \text{false}\}$
\State $X_{\text{current}} \gets X$
\For{each layer $l$ in network}
    \State $Z_l \gets W_l \times X_{\text{current}} + b_l$
    \State $A_l \gets \text{activation}(Z_l)$
    \State \textbf{if} $A_l \neq$ provided activation \textbf{then return} false
    \State $X_{\text{current}} \gets A_l$
\EndFor
\State \textbf{return} $(X_{\text{current}} = Y)$
\end{algorithmic}
\end{algorithm}

\subsection{Matrix Operation Verification}

Efficient verification of matrix multiplication using sumcheck protocol:

\begin{theorem}[Sumcheck-based MatMul Verification]
For matrices $A \in \mathbb{R}^{m \times k}$ and $B \in \mathbb{R}^{k \times n}$, the product $C = A \times B$ can be verified with:
\begin{itemize}
    \item Prover complexity: $O(mnk)$
    \item Verifier complexity: $O(m + n + k + \log(mnk))$
    \item Communication: $O(\log(mnk))$
\end{itemize}
\end{theorem}

\subsection{Gradient Computation Validation}

Verifying backpropagation through numerical gradient checking:

\begin{equation}
\text{GradientCheck}(f, x, \epsilon) = \left|\nabla f(x) - \frac{f(x+\epsilon) - f(x-\epsilon)}{2\epsilon}\right| < \delta
\end{equation}

For small samples, this provides efficient verification of gradient computations.

\subsection{Quantized Model Verification}

For quantized models, verification becomes more efficient:

\begin{equation}
\text{Error}_{\text{quantization}} = ||Y_{\text{float32}} - Y_{\text{int8}}||_2 < \tau
\end{equation}

This allows verification using integer arithmetic, reducing on-chain costs.