369 lines
13 KiB
TeX
369 lines
13 KiB
TeX
%% SCRAP: papers/FINAL_REPORT/appendix_glossary
|
|
%% SOURCE: docs/working/papers/FINAL_REPORT/appendix_glossary.adoc
|
|
%% STATUS: CURRENT
|
|
%% FITS: ssrn/app-glossary, vol3-research/app-glossary
|
|
%% EDITORIAL: lifted — AsciiDoc syntax translated to LaTeX; adoc stem[] → $...$,
|
|
%% |=== tables → tabular with booktabs, [glossary] → description env
|
|
|
|
\chapter*{Glossary of Terms}
|
|
\addcontentsline{toc}{chapter}{Glossary of Terms}
|
|
\label{app:glossary}
|
|
|
|
Precise definitions for all terminology used throughout this work.
|
|
Terms are organized alphabetically within three groups: core concepts,
|
|
feedback loop taxonomy, and deprecated terminology. A mathematical
|
|
notation table follows.
|
|
|
|
\section*{Core Concepts}
|
|
|
|
\begin{description}
|
|
|
|
\item[Adaptive Heartbeat]
|
|
Time-driven coordination mechanism that orchestrates feedback loop execution
|
|
at dynamically-adjusted intervals. The heartbeat thread executes
|
|
\texttt{vm\_tick()} at frequency $f_{\text{tick}}$, where
|
|
$f_{\text{tick}} \in [f_{\min}, f_{\max}]$ adapts based on system stability
|
|
metrics.
|
|
|
|
\textit{Measurement}: tick period in nanoseconds, configurable via
|
|
\texttt{HEARTBEAT\_TICK\_NS}.
|
|
|
|
\textit{Implementation}: background pthread executing
|
|
\texttt{heartbeat\_thread\_main()}.
|
|
|
|
\item[Attractor]
|
|
Stable equilibrium point or region in phase space toward which execution
|
|
trajectories converge. Formally, a fixed point $\mathbf{x}^*$ where
|
|
$F(\mathbf{x}^*) = \mathbf{x}^*$ for dynamical system
|
|
$\mathbf{x}_{t+1} = F(\mathbf{x}_t)$.
|
|
|
|
\textit{Measurement}: coordinates in $(w, \lambda, \sigma^2)$ phase space.
|
|
|
|
\textit{Empirical observation}: StarForth exhibits a stable fixed-point
|
|
attractor across 90 experimental runs.
|
|
|
|
\item[Coefficient of Variation (CV)]
|
|
Normalized measure of dispersion, defined as the ratio of standard deviation
|
|
to mean:
|
|
\begin{equation*}
|
|
\mathrm{CV} = \frac{\sigma}{\mu}
|
|
\end{equation*}
|
|
|
|
\textit{Convergence criterion}: $\mathrm{CV} \to 0$ indicates deterministic
|
|
convergence.
|
|
|
|
\textit{Application}: quantifies variance reduction in steady-state metrics.
|
|
|
|
\item[Decay Coefficient ($\lambda$)]
|
|
Rate parameter controlling exponential reduction in execution frequency over
|
|
time; units $[1/\text{time}]$.
|
|
\begin{equation*}
|
|
f(t) = f_0 \cdot e^{-\lambda t}
|
|
\end{equation*}
|
|
|
|
\textit{Measurement}: derived via exponential regression on rolling window
|
|
data; stored as \Qtype\ fixed-point.
|
|
|
|
\textit{Typical range}: $\lambda \in [10^{-6}, 10^{-3}]$ per microsecond.
|
|
|
|
\item[Deterministic Convergence]
|
|
Property whereby repeated executions of identical workloads produce
|
|
statistically indistinguishable steady-state metrics. Formally:
|
|
\begin{equation*}
|
|
\forall\, i, j\colon \frac{|\text{metric}_i - \text{metric}_j|}{\sigma} < \varepsilon
|
|
\end{equation*}
|
|
where $\varepsilon \to 0$ as $t \to \infty$.
|
|
|
|
\textit{Empirical result}: 0\% algorithmic variance across 90 runs
|
|
($\mathrm{CV} < 0.001\%$).
|
|
|
|
\textit{Significance}: enables reproducible performance characterization.
|
|
|
|
\item[Execution Frequency]
|
|
Count of times a dictionary entry has been executed since VM initialization,
|
|
optionally adjusted by temporal decay. This is the \emph{primary measurable
|
|
quantity} in the adaptive runtime.
|
|
\begin{equation*}
|
|
f = \sum \text{executions} - \int \text{decay}(t)\,dt
|
|
\end{equation*}
|
|
|
|
\textit{Implementation}: unsigned 64-bit integer (\texttt{uint64\_t
|
|
execution\_heat}).
|
|
|
|
\textit{Note}: ``heat'' is a metaphorical naming convention; the actual
|
|
quantity is an execution count.
|
|
|
|
\item[Exponential Decay]
|
|
Mathematical function modeling reduction in execution frequency proportional
|
|
to current value:
|
|
\begin{equation*}
|
|
f(t) = f_0 \cdot e^{-\lambda t}
|
|
\end{equation*}
|
|
where $f_0$ is the initial frequency.
|
|
|
|
\textit{Metaphorical parallel}: mathematically similar to radioactive decay
|
|
or thermal dissipation (conceptual metaphor only; no physical process implied).
|
|
|
|
\textit{Application}: applied periodically by the heartbeat system to reduce
|
|
the weight of stale frequency counts.
|
|
|
|
\item[Feedback Loop]
|
|
Self-referential process in which system output influences future input.
|
|
Classified as:
|
|
\begin{itemize}
|
|
\item \emph{Positive} (amplifying): output reinforces input
|
|
\item \emph{Negative} (stabilizing): output opposes input
|
|
\item \emph{Neutral} (monitoring): no direct influence
|
|
\end{itemize}
|
|
|
|
\textit{Example}: Loop~1 (Execution Heat Tracking) is positive feedback:
|
|
\begin{center}
|
|
Execution $\to$ Frequency$\uparrow$ $\to$ Cache Rank$\uparrow$
|
|
$\to$ Lookup Speed$\uparrow$ $\to$ More Execution
|
|
\end{center}
|
|
|
|
\item[Hot-Words Cache]
|
|
Fixed-size array storing pointers to the $K$ most frequently executed
|
|
dictionary entries, enabling O(1) lookup acceleration.
|
|
|
|
\textit{Selection criterion}:
|
|
\begin{equation*}
|
|
e \in \text{Cache} \iff \text{rank}(e) \leq K
|
|
\end{equation*}
|
|
where $\text{rank}(e) = |\{e' \in \text{Dictionary} : f(e') > f(e)\}| + 1$.
|
|
|
|
\textit{Performance impact}: reduces average lookup time by 70--95\%
|
|
(workload-dependent).
|
|
|
|
\item[Levene's Test]
|
|
Non-parametric statistical test for homogeneity of variance across groups.
|
|
Tests $H_0\colon \sigma_1^2 = \sigma_2^2 = \cdots = \sigma_k^2$ (equal
|
|
variances).
|
|
|
|
\textit{Test statistic}: F-statistic with associated $p$-value.
|
|
|
|
\textit{Application}: used in window width inference (Loop~5) to detect
|
|
variance changes when adjusting window size.
|
|
|
|
\textit{Decision threshold}: typically $\alpha = 0.05$ (5\% significance
|
|
level).
|
|
|
|
\item[Phase Space]
|
|
Multi-dimensional coordinate system where each axis represents a system state
|
|
variable. For StarForth:
|
|
\begin{equation*}
|
|
\mathcal{S} = \{(w, \lambda, \sigma^2) \mid w \in \mathbb{N},\;
|
|
\lambda \in \mathbb{R}^+,\; \sigma^2 \in \mathbb{R}^+\}
|
|
\end{equation*}
|
|
|
|
\textit{Dimensions}: $w$ (window size, execution events retained);
|
|
$\lambda$ (decay slope, frequency reduction rate);
|
|
$\sigma^2$ (variance, metric dispersion).
|
|
|
|
\textit{Analysis technique}: execution trajectories in phase space reveal
|
|
attractor basins.
|
|
|
|
\item[Rolling Window of Truth]
|
|
Circular buffer recording recent execution history for deterministic metric
|
|
seeding. Guarantees identical initial conditions across runs.
|
|
|
|
\textit{Data structure}: ring buffer $B[i] = \text{word\_id}$ at execution
|
|
event $i \bmod |B|$.
|
|
|
|
\textit{Buffer size}: configurable (default: \texttt{ROLLING\_WINDOW\_SIZE =
|
|
4096}).
|
|
|
|
\textit{Purpose}: enables reproducible variance calculations by providing
|
|
consistent historical context.
|
|
|
|
\item[Steady-State Equilibrium]
|
|
Condition where adaptive system metrics stabilize within bounded oscillation.
|
|
Formally:
|
|
\begin{equation*}
|
|
\exists\, t_0\colon \forall\, t > t_0,\; |x(t) - x^*| < \delta
|
|
\end{equation*}
|
|
for small $\delta$.
|
|
|
|
\textit{Empirical criterion}: variance $\mathrm{CV} < 0.1\%$ over a
|
|
1{,}000-tick window.
|
|
|
|
\textit{Physical analogy}: similar to thermodynamic equilibrium in that
|
|
macroscopic properties cease changing (conceptual metaphor only).
|
|
|
|
\item[Thermodynamic Metaphor]
|
|
Conceptual mapping between thermodynamic quantities and execution metrics.
|
|
This is a \emph{metaphorical framework}, not literal physics.
|
|
|
|
\textit{Mappings}:
|
|
\begin{itemize}
|
|
\item Heat $\leftrightarrow$ Execution Frequency
|
|
\item Temperature $\leftrightarrow$ Normalized Rank
|
|
\item Cooling $\leftrightarrow$ Exponential Decay
|
|
\item Equilibrium $\leftrightarrow$ Steady State
|
|
\end{itemize}
|
|
|
|
\textit{Academic usage}: must be qualified as metaphor in formal writing.
|
|
|
|
\item[Transition Probability]
|
|
Conditional probability that word $B$ is executed immediately after word $A$.
|
|
Maximum likelihood estimate:
|
|
\begin{equation*}
|
|
P(B \mid A) = \frac{\text{count}(A \to B)}{\text{count}(A)}
|
|
\end{equation*}
|
|
|
|
\textit{Implementation}: stored as \Qtype\ fixed-point in the
|
|
\texttt{transition\_metrics} structure.
|
|
|
|
\textit{Application}: used for speculative execution (prefetching the
|
|
likely-next word).
|
|
|
|
\item[Variance Inflection Point]
|
|
Window size $w^*$ where variance begins to increase when window shrinks below
|
|
$w^*$. Represents the optimal trade-off between sample size and temporal
|
|
locality.
|
|
\begin{equation*}
|
|
w^* = \arg\min_{w \in [w_{\min},\, w_{\text{current}}]} \mathrm{Var}(w)
|
|
\end{equation*}
|
|
|
|
\textit{Search method}: binary search with Levene's test validation.
|
|
|
|
\textit{Purpose}: adaptive window size tuning (Loop~5).
|
|
|
|
\end{description}
|
|
|
|
\section*{Feedback Loop Taxonomy}
|
|
|
|
\begin{description}
|
|
|
|
\item[Loop 1: Execution Heat Tracking]
|
|
\textit{Type}: positive feedback (amplifying).
|
|
\textit{Mechanism}: increment frequency counter on each word execution.
|
|
\textit{Effect}: more executions $\to$ higher rank $\to$ more cache hits
|
|
$\to$ more executions.
|
|
\textit{Implementation}: \texttt{physics\_execution\_heat\_increment()} in
|
|
\texttt{vm.c}.
|
|
|
|
\item[Loop 2: Rolling Window History]
|
|
\textit{Type}: neutral (monitoring).
|
|
\textit{Mechanism}: record execution events in circular buffer.
|
|
\textit{Effect}: provides historical context for inference.
|
|
\textit{Implementation}: \texttt{rolling\_window\_record\_execution()} in
|
|
\texttt{rolling\_window\_of\_truth.c}.
|
|
|
|
\item[Loop 3: Linear Decay]
|
|
\textit{Type}: negative feedback (stabilizing).
|
|
\textit{Mechanism}: reduce frequency proportional to current value.
|
|
\textit{Effect}: high frequency $\to$ faster decay $\to$ lower frequency
|
|
$\to$ slower decay.
|
|
\textit{Implementation}: \texttt{vm\_tick\_slope\_validator()} applies linear
|
|
decay.
|
|
|
|
\item[Loop 4: Pipelining Metrics]
|
|
\textit{Type}: positive feedback (amplifying).
|
|
\textit{Mechanism}: track word-to-word transitions, predict next word.
|
|
\textit{Effect}: more transitions $\to$ better prediction $\to$ more
|
|
prefetch hits.
|
|
\textit{Implementation}: \texttt{transition\_metrics\_record()} in
|
|
\texttt{physics\_pipelining\_metrics.c}.
|
|
|
|
\item[Loop 5: Window Width Inference]
|
|
\textit{Type}: negative feedback (stabilizing).
|
|
\textit{Mechanism}: shrink window if variance increases (Levene's test).
|
|
\textit{Effect}: high variance $\to$ smaller window $\to$ lower variance.
|
|
\textit{Implementation}: \texttt{find\_variance\_inflection()} in
|
|
\texttt{inference\_engine.c}.
|
|
|
|
\item[Loop 6: Decay Slope Inference]
|
|
\textit{Type}: negative feedback (stabilizing).
|
|
\textit{Mechanism}: increase decay rate if metrics are unstable (exponential
|
|
regression).
|
|
\textit{Effect}: unstable metrics $\to$ steeper decay $\to$ faster
|
|
stabilization.
|
|
\textit{Implementation}: \texttt{infer\_decay\_slope\_from\_trajectory()} in
|
|
\texttt{inference\_engine.c}.
|
|
|
|
\item[Loop 7: Adaptive Heartbeat]
|
|
\textit{Type}: meta-loop (coordination).
|
|
\textit{Mechanism}: adjust tick rate based on system stability.
|
|
\textit{Effect}: stable system $\to$ slower ticks $\to$ reduced overhead.
|
|
\textit{Implementation}: \texttt{heartbeat\_thread\_main()} in \texttt{vm.c}.
|
|
|
|
\end{description}
|
|
|
|
\section*{Deprecated Terminology}
|
|
|
|
The following terms should be avoided in formal academic writing.
|
|
|
|
\begin{description}
|
|
|
|
\item[``Physics-based optimization'']
|
|
\textit{Use instead}: ``thermodynamically-inspired metaphor for frequency
|
|
decay.''
|
|
\textit{Reason}: implies literal physics; the implementation uses integer
|
|
counters and exponential functions only.
|
|
|
|
\item[``Execution heat'' (formal context)]
|
|
\textit{Use instead}: ``execution frequency with temporal decay.''
|
|
\textit{Reason}: ``heat'' is a metaphorical label; the precise term avoids
|
|
confusion in academic writing.
|
|
|
|
\item[``AI-driven'' or ``ML-based'']
|
|
\textit{Use instead}: ``statistically-inferred'' or ``adaptive via Levene's
|
|
test.''
|
|
\textit{Reason}: no neural networks or machine learning are involved.
|
|
|
|
\item[``Learning'']
|
|
\textit{Use instead}: ``adaptive inference'' or ``parameter convergence.''
|
|
\textit{Reason}: not supervised or unsupervised learning; this is statistical
|
|
convergence.
|
|
|
|
\item[``Quantum-inspired'']
|
|
\textit{Use instead}: N/A.
|
|
\textit{Reason}: no quantum mechanics or superposition is involved.
|
|
|
|
\end{description}
|
|
|
|
\section*{Mathematical Notation}
|
|
|
|
\begin{table}[h]
|
|
\centering
|
|
\caption{Mathematical symbols used throughout this work.}
|
|
\label{tab:notation}
|
|
\begin{tabular}{ll}
|
|
\toprule
|
|
\textbf{Symbol} & \textbf{Definition} \\
|
|
\midrule
|
|
$f$ & Execution frequency (count with decay) \\
|
|
$\lambda$ & Decay coefficient $[1/\text{time}]$ \\
|
|
$w$ & Window size (number of events) \\
|
|
$K$ & Cache size (constant) \\
|
|
$\sigma$ & Standard deviation \\
|
|
$\mu$ & Mean value \\
|
|
$\mathrm{CV}$ & Coefficient of variation $= \sigma / \mu$ \\
|
|
$P(B \mid A)$ & Transition probability (word $B$ after word $A$) \\
|
|
$w^*$ & Variance inflection point \\
|
|
$\mathcal{S}$ & State space $= \{(w, \lambda, \sigma^2)\}$ \\
|
|
$\mathbf{x}^*$ & Attractor (fixed point) \\
|
|
$F$ & State transition function \\
|
|
$f_0$ & Initial frequency \\
|
|
$t$ & Time (ticks or microseconds) \\
|
|
$r(t)$ & Execution rate $[\text{executions}/\text{second}]$ \\
|
|
\bottomrule
|
|
\end{tabular}
|
|
\end{table}
|
|
|
|
\section*{References}
|
|
|
|
\begin{itemize}
|
|
\item Strogatz, S. (2015). \emph{Nonlinear Dynamics and Chaos}. Westview
|
|
Press.
|
|
\item \r{A}str\"{o}m, K. \& Murray, R. (2008). \emph{Feedback Systems}.
|
|
Princeton University Press.
|
|
\item Casella, G. \& Berger, R. (2002). \emph{Statistical Inference}.
|
|
Duxbury Press.
|
|
\item Bolz, C.\ et al.\ (2009). ``Tracing the Meta-Level: PyPy's Tracing
|
|
JIT Compiler.'' \emph{ICOOOLPS}.
|
|
\item Ertl, M.A.\ (1996). ``Stack Caching for Interpreters.''
|
|
\emph{SIGPLAN Notices}.
|
|
\end{itemize}
|