120 lines
6.2 KiB
TeX
120 lines
6.2 KiB
TeX
%% SCRAP: architecture/03-architecture/adaptive-systems/multivariate-dynamics
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%% SOURCE: docs/working/architecture/03-architecture/adaptive-systems/multivariate-dynamics.md
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%% STATUS: WORKING
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%% FITS: dev-guide/ch-physics
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%% EDITORIAL: lifted — prose rewritten to press voice
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\section{Multivariate Coupled Dynamics: Golden-Configuration Discovery}
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This section describes the experimental framework, dated 2025-11-20 and in
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design at the time of writing, for discovering a golden runtime configuration by
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stability fingerprinting. It is deliberately not a factorial design of
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experiments. The premise is that the adaptive runtime is a coupled dynamical
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system in which every metric is at once a measurable signal, a feedback variable
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that shapes future state, and a coordinate in a high-dimensional attractor
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landscape. The analysis therefore measures the shape of each configuration's
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trajectory through metric space rather than isolated main effects.
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The dynamical-systems vocabulary --- attractors, basins, eigenmodes, coupling
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--- is modeling language for the runtime's tick-by-tick behavior, applied to the
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domain of configuration selection; it is not a claim of literal physics.
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\subsection{The Coupling Web}
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Within a single tick the metrics form a feedback web. Cache and bucket hit rates
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feed bucket load, which feeds heat, which feeds decay, which feeds window width,
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which feeds prediction accuracy; prediction accuracy and load feed back into the
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next tick's cache behavior and into the adaptive heartbeat interval. Load
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intensity shapes the word-access pattern, which shapes the heat distribution,
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which governs decay effectiveness and the jitter envelope. Each configuration
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traces a distinct path through this web.
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\subsection{Three Levels of Measurement}
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The framework records state at three nested scopes. \emph{Per tick}, at roughly
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one-millisecond cadence, it captures a snapshot of the coupled system: a temporal
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anchor, the cache and bucket wave functions $\psi_{\text{cache}}(t)$ and
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$\psi_{\text{bucket}}(t)$, the feedback signals (hot-word count, mean heat,
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inferred decay, window width), the load response (executions, prediction
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attempts, prefetch hits), and the stability measures (tick jitter and a composite
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smoothness index). \emph{Per run}, over roughly a hundred thousand ticks, it
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distills a stability fingerprint: convergence time and coefficients of variation,
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steady-state means, dynamics (rise time, settling time, overshoot), coupling
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strengths including a full cross-correlation matrix, spectral properties
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(dominant frequency, spectral entropy, dominant eigenvalue), and an overall
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stability score. \emph{Per configuration}, over 150 or more runs, it aggregates
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those fingerprints into between-run statistics: the mean and spread of the
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stability score, convergence reliability, coupling stability, an attractor-basin
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depth estimate, the jitter envelope and its whiteness, and noise-propagation
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measures.
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\begin{equation}
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\textit{overall\_stability\_score} =
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\tfrac{1}{3}\,\textit{jitter\_score}
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+ \tfrac{1}{3}\,\textit{convergence\_score}
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+ \tfrac{1}{3}\,\textit{coupling\_score}
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\end{equation}
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\subsection{Experimental Design}
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The design holds five elite configurations carried forward from an earlier stage,
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runs each 150 to 200 times for statistical power, and runs each for roughly a
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hundred thousand ticks to capture both convergence and steady state --- on the
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order of seventy-five million ticks in total, some six to eight hours of
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wall-clock time. Run order is randomized and configurations are interleaved to
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avoid temporal and thermal confounds, background tasks are minimized, and every
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tick is captured without subsampling to preserve time-series fidelity.
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\subsection{Analysis Pipeline}
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Analysis proceeds in three phases. Per-run fingerprinting detects convergence
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(when the cache hit-rate coefficient of variation falls below five percent),
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computes steady-state statistics, extracts the transient dynamics, measures
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coupling with lag search and a full correlation matrix, performs spectral
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analysis to find dominant modes, and reduces all of it to a stability index.
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Per-configuration fingerprinting aggregates the run fingerprints into robustness,
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convergence reliability, coupling strength, basin depth, and noise
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characteristics. Golden-configuration selection then scores the five candidates
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on weighted dimensions and takes the argmax.
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\begin{table}[h]
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\centering
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\begin{tabular}{lll}
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\toprule
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Dimension & Weight & Ideal behavior \\
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\midrule
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Stability score & 30\% & highest mean, lowest spread \\
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Convergence reliability & 25\% & full convergence, low variability \\
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Coupling strength & 20\% & strong ($0.8+$), stable load-to-heartbeat \\
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Attractor basin depth & 15\% & fast eigenmode decay, noise-resilient \\
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Jitter smoothness & 10\% & low variation, white noise \\
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\bottomrule
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\end{tabular}
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\caption{Weighted dimensions for golden-configuration selection.}
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\end{table}
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\subsection{Interpretation}
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A strong configuration fingerprint shows a high mean stability score with low
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spread (reproducibility), full convergence across runs, tight load-to-heartbeat
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coupling, a low jitter coefficient of variation, and a large dominant eigenvalue
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indicating a deep attractor basin. A weak fingerprint inverts each of these: a low
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and widely scattered stability score, incomplete convergence, loose and noisy
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coupling, high jitter variation, and a shallow, noise-prone basin.
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\subsection{Implementation Roadmap}
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The build sequence instruments the heartbeat loop with a per-tick circular
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buffer, implements per-run fingerprinting (convergence detection, coefficients of
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variation, correlations, eigenvalues, spectral properties), aggregates run
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fingerprints into per-configuration fingerprints, scores and selects the golden
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configuration, and finally produces the visual reporting suite --- time-series
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plots, correlation heatmaps, a principal-component projection of runs, and
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stability-score distributions.
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%% PATENT: stability fingerprinting and golden-configuration selection over the
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%% coupled adaptive runtime are patent-adjacent; no claims drafted here.
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%% TODO(bob): confirm whether the harness was built and whether a golden
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%% configuration was selected, for a results subsection.
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