papers/hanzo-consensus-ai/sections/04-gpu-cluster-consensus.tex

\section{GPU Cluster Consensus}

\label{sec:cluster}
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Distributed training and tensor-parallel inference require consensus among GPU
nodes on intermediate computation results. Unlike blockchain consensus (agreeing
on transaction order), GPU cluster consensus must agree on tensor values---high-dimensional floating-point data.

\subsection{Tensor-Parallel Consensus}

In tensor-parallel inference~\cite{megatron}, model layers are sharded across
$P$ GPUs. Each GPU computes a partial result, and an all-reduce operation
aggregates them:
\begin{equation}
\mathbf{h}^{(l)} = \sum_{p=1}^{P} \mathbf{h}_p^{(l)},
\end{equation}
where $\mathbf{h}_p^{(l)}$ is the partial activation from GPU $p$ at layer $l$.

In a trusted cluster, all-reduce is a simple communication primitive. In an
untrusted ACI network, a Byzantine GPU could submit incorrect partial results
to corrupt the final output.

\begin{definition}[Byzantine All-Reduce]
A Byzantine-tolerant all-reduce protocol guarantees that the aggregated result
equals the sum of honest contributions, even if up to $f < P/3$ participants
submit arbitrary values.
\end{definition}

\begin{algorithm}
\caption{Byzantine All-Reduce with Commitment}
\label{alg:allreduce}
\begin{algorithmic}[1]
\Require Partial results $\{\mathbf{h}_p\}_{p=1}^{P}$, threshold $f < P/3$
\Ensure Verified aggregate $\mathbf{h} = \sum_p \mathbf{h}_p$ (for honest $p$)
\For{each GPU $p$}
    \State Compute commitment: $c_p = \texttt{Hash}(\mathbf{h}_p)$
    \State Broadcast $c_p$ to all peers
\EndFor
\For{each GPU $p$}
    \State After receiving all commitments, broadcast $\mathbf{h}_p$
    \State Verify: $\texttt{Hash}(\mathbf{h}_p) \stackrel{?}{=} c_p$ for all $p$
    \State Discard contributions with invalid commitments
\EndFor
\State $\mathbf{h} = \sum_{p \in \text{valid}} \mathbf{h}_p$
\end{algorithmic}
\end{algorithm}

\subsection{Redundant Computation}

For high-value inference (e.g., financial decisions, medical diagnoses), ACI
supports redundant computation:
\begin{itemize}[leftmargin=1.1em]
    \item The request is sent to $k$ independent workers.
    \item Results are compared using the verification distance metric
    (\S\ref{sec:poai}).
    \item The majority result (or median for continuous outputs) is returned.
    \item Outlier workers are flagged for investigation.
\end{itemize}

\begin{proposition}[Redundancy Security]
With $k = 2f + 1$ independent workers and at most $f$ Byzantine workers, the
majority vote produces the correct output with probability 1 (assuming
deterministic execution with fixed seeds).
\end{proposition}

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