Quantum MoE — Matrix Lab

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\title{QUANTUM MoE Matrix Lab: An Evidence-Aware Architecture, Prototype Evaluation, and Integration Roadmap}
\author{\IEEEauthorblockN{Aaron Singh}
\IEEEauthorblockA{\textit{Department of Electrical and Computer Engineering} \\
\textit{San Francisco State University}}}
\maketitle

\begin{abstract}
This paper presents QUANTUM MoE Matrix Lab, a project in a twenty-project AI infrastructure portfolio. The current repository is an active prototype with implemented behavior, automated correctness tests, and explicit boundaries around unverified hardware or production claims. We describe the system model, current implementation, goals, and evaluation method, then propose five integrations that advance the project toward reproducible system-level validation. A local audit on August 14, 2026 executed 3 project tests successfully. No accelerator, deployment, or performance conclusion is inferred unless a corresponding committed benchmark or profiler artifact exists.
\end{abstract}

\begin{IEEEkeywords}
QUANTUM, AI infrastructure, reproducibility, prototype validation, systems evaluation, hardware--software co-design
\end{IEEEkeywords}

\section{Introduction}
QUANTUM MoE Matrix Lab (P04) addresses a bounded problem within the portfolio's track-01-gpu-kernels track. Its declared status is \emph{Active Prototype} \cite{metadata}. The project validates its central mechanism before adding device-specific acceleration, production orchestration, or real-world hardware. This ordering matters because optimization without a trusted reference can make incorrect behavior appear successful.

The project goals are to establish deterministic behavior, encode correctness as tests, create machine-readable evidence, identify limiting resources through measurement, and integrate results with adjacent portfolio systems without losing provenance. The repository contains one paper named exactly after its singular folder: \texttt{P04-quantum-moe-matrix-lab.tex}.

\section{Technical Context}
GPU kernel development requires a correct numerical reference before optimization. Reference equivalence, workload shape, warm-up policy, and profiler evidence are therefore first-class design concerns. The portfolio benchmark standard requires environment, workload, method, metric, artifact, reproduction, and limitation fields; unknown values remain explicitly unmeasured \cite{benchmark}.

\section{System Model and Architecture}
The prototype is organized around the following domain model:
\begin{equation}
e_i=\operatorname{TopK}(g(x_i)),\quad C=\left\lceil c\frac{Nk}{E}\right\rceil
\end{equation}
The equation is a design and test abstraction rather than a claimed empirical law. It supports invariants and expected-value checks while later implementations replace synthetic inputs with representative workloads or devices.

The software architecture contains an input/configuration layer, a deterministic core, validation and evidence output, and a local visualization. The principal inspected source artifacts are \texttt{python/moe\_router.py}. Unsupported real-world conditions are surfaced as limitations rather than silently simulated.

\section{Detailed Script Operation and Rationale}
The router receives token-to-expert scores, selects top experts deterministically, enforces per-expert capacity, and accounts for dropped assignments. It tests routing policy correctness separately from expert computation and grouped matrix multiplication.

The execution path is:
\begin{enumerate}
    \item Validate scores, top-k, and capacity parameters.
    \item Rank experts for every token with deterministic tie behavior.
    \item Accept assignments while each expert remains below capacity.
    \item Count dropped assignments instead of silently overfilling experts.
    \item Return routing state for tests and later grouped-GEMM integration.
\end{enumerate}

\begin{table*}[t]
\caption{Implementation artifacts and why they exist}
\label{tab:p04-implementation}
\centering
\small
\begin{tabularx}{\textwidth}{p{0.24\textwidth}YY}
\toprule
\textbf{Artifact} & \textbf{Observed responsibility} & \textbf{Engineering rationale} \\
\midrule
python/moe\_router.py & route, main & Implements the inspectable, unit-tested project core. \\
scripts/reproduce.sh & Fixed test and demonstration entry point & Gives another developer one command for local reproduction. \\
PROJECT.yaml and ANALYSIS.md & Status, completed work, planned work, and claim boundaries & Separates declared intent from evidence-backed implementation. \\
streamlit\_app.py & Local evidence and status visualization & Makes outputs inspectable without upgrading simulation into a hardware claim. \\
\bottomrule
\end{tabularx}
\end{table*}

\section{Implemented Prototype}
The metadata and source audit found these completed features \cite{analysis}:
\begin{itemize}
    \item Deterministic top-k expert routing
    \item Capacity limits and dropped-assignment accounting
    \item Unit tests
\end{itemize}

On August 14, 2026, \texttt{python3 -m unittest discover -s tests -p 'test\_*.py'} completed successfully with 3 tests. The inspected test artifacts are \texttt{tests/test\_router.py}. This is evidence of local correctness for encoded cases, not production scale or hardware performance.

\section{Testing Methodology and Observed Results}
Testing uses Python's standard \texttt{unittest} discovery and exercises the public behavior of the reference implementation. The audit reran the suite from the project folder with \texttt{python3 -m unittest discover -s tests -p 'test\_*.py'}. All 3 discovered tests passed. The result establishes correctness only for the encoded local cases; it does not establish accelerator correctness, real-device behavior, production reliability, or benchmark completion.

\begin{table*}[t]
\caption{Audited test matrix}
\label{tab:p04-tests}
\centering
\scriptsize
\begin{tabularx}{\textwidth}{p{0.37\textwidth}Yp{0.21\textwidth}}
\toprule
\textbf{Test artifact and case} & \textbf{Behavior being checked} & \textbf{Observed result} \\
\midrule
tests/test\_router.py:test\_top & Top. & Pass (local, 2026-08-14) \\
tests/test\_router.py:test\_capacity & Capacity. & Pass (local, 2026-08-14) \\
tests/test\_router.py:test\_invalid & Invalid. & Pass (local, 2026-08-14) \\
\bottomrule
\end{tabularx}
\end{table*}

No numerical performance result is promoted by this test run. Where scripts emit JSON or JSONL, those outputs remain raw or simulation-specific until a reviewed summary includes hardware, software, workload, warm-up, repetition, correctness threshold, Git revision, and limitations.

\begin{table*}[t]
\caption{Declared status versus audited evidence}
\label{tab:p04-audit}
\centering
\small
\begin{tabularx}{\textwidth}{p{0.20\textwidth}Yp{0.25\textwidth}}
\toprule
\textbf{Audit field} & \textbf{Finding} & \textbf{Evidence source} \\
\midrule
Declared status & Active Prototype & PROJECT.yaml \\
Evidence-backed status & Active local prototype; 3 tests passed & Source plus local unittest run \\
Accepted measured results & None recorded in measured\_results & PROJECT.yaml \\
Mismatch / claim boundary & No grouped GEMM or accelerator result & PROJECT.yaml and ANALYSIS.md \\
Next proof required & Expert computations; Grouped GEMM & Planned features \\
\bottomrule
\end{tabularx}
\end{table*}

\section{Claim Boundaries and Risks}
The project records these unverified or excluded claims:
\begin{itemize}
    \item No grouped GEMM or accelerator result
\end{itemize}
The main risk is confusing synthetic or modeled behavior with deployed-system behavior. Other risks include incomplete workloads, platform-dependent timing, missing failure injection, and interfaces not yet exercised across device boundaries. Performance claims require a reviewed record meeting the portfolio standard.

\section{Evaluation Plan}
Evaluation proceeds through correctness tests, deterministic reproduction with Git and environment metadata, repeated benchmarks reporting latency/throughput/memory/error metrics, and a named profiler capture tied to exact hardware and source revision. Success requires reference equivalence within a documented tolerance, preservation of safety and resource invariants, clear failures, and evidence reproducible from a clean environment.

\section{Goals, Milestones, and Success Criteria}
The project goals are staged so that correctness precedes performance and integration. A goal is complete only when its proof artifact is committed or otherwise reviewable; prose or a simulated number alone is insufficient.

\begin{table*}[t]
\caption{Project goals and required proof}
\label{tab:p04-goals}
\centering
\small
\begin{tabularx}{\textwidth}{p{0.06\textwidth}YY}
\toprule
\textbf{ID} & \textbf{Goal} & \textbf{Completion evidence} \\
\midrule
G1 & Expert computations & Passing tests and a reviewed source artifact \\
G2 & Grouped GEMM & Machine-readable result with reproduction metadata \\
G3 & SYCL profiler evidence & Reference-equivalence or domain-correctness report \\
G4 & Add expert computation and grouped GEMM & Named profiler, deployment, or integration artifact \\
G5 & Measure routing balance and dropped-token behavior & Dashboard/report link preserving provenance and limitations \\
\bottomrule
\end{tabularx}
\end{table*}

\section{Future Work and Integrations}
The five project-specific next steps are:
\begin{enumerate}
    \item Expert computations
    \item Grouped GEMM
    \item SYCL profiler evidence
    \item Add load-balancing sweeps and expert-parallel communication costs.
    \item Connect routing to P10 placement and P12 reliability telemetry.
\end{enumerate}
The early items complete declared evidence; the later items connect downstream portfolio consumers. Each integration should add tests and a reviewable artifact such as JSONL evidence, a report, profiler capture, deployment manifest, trace, or labeled data set.

\section{Conclusion}
QUANTUM MoE Matrix Lab is an evidence-aware active prototype: its implemented behavior and tests are real, while unbuilt hardware, deployment, and performance goals remain labeled. Completing the five integrations in dependency order will advance it from a learning artifact toward a credible portfolio component.

\begin{thebibliography}{00}
\bibitem{metadata} Aaron Singh, ``QUANTUM MoE Matrix Lab PROJECT.yaml,'' local portfolio repository, updated 2026-08-13.
\bibitem{analysis} Aaron Singh, ``QUANTUM MoE Matrix Lab: README, ANALYSIS, source, and test artifacts,'' local portfolio repository, accessed Aug. 14, 2026.
\bibitem{benchmark} Aaron Singh, ``AI Infrastructure Portfolio Benchmark Standard,'' local portfolio repository, accessed Aug. 14, 2026.
\end{thebibliography}
\end{document}