From 6ae0f24af37c2d0714180d762ffdd0beb57a5b8d Mon Sep 17 00:00:00 2001
From: DaZuo0122 <1085701449@qq.com>
Date: Wed, 4 Feb 2026 13:07:59 +0800
Subject: [PATCH] Add: first 3 paragraphs to methodology section

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 arxiv-style/main.tex | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/arxiv-style/main.tex b/arxiv-style/main.tex
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@@ -91,7 +91,11 @@ From the perspective of high-level synthesis, the temporal structure is equally
 % 3. Methodology
 \section{Methodology}
 \label{sec:method}
-Here we describe our proposed method in detail.
+Industrial control system (ICS) telemetry is intrinsically mixed-type and mechanistically heterogeneous: continuous process trajectories (e.g., sensor and actuator signals) coexist with discrete supervisory states (e.g., modes, alarms, interlocks), and the underlying generating mechanisms range from physical inertia to program-driven step logic. This heterogeneity is not cosmetic—it directly affects what “realistic” synthesis means, because a generator must jointly satisfy (i) temporal coherence, (ii) distributional fidelity, and (iii) discrete semantic validity (i.e., every discrete output must belong to its legal vocabulary by construction). These properties are emphasized broadly in operational-technology security guidance and ICS engineering practice, where state logic and physical dynamics are tightly coupled \citep{nist2023sp80082}.
+
+We formalize each training instance as a fixed-length window of length We model each training instance as a fixed-length window of length $L$, comprising continuous channels $\bm{X} \in \mathbb{R}^{L \times d_c}$ and discrete channels $\bm{Y} = \{y^{(j)}_{1:L}\}_{j=1}^{d_d}$, where each discrete variable satisfies $y^{(j)}_t \in \mathcal{V}_j$ for a finite vocabulary $\mathcal{V}_j$. Our objective is to learn a generator that produces synthetic $(\hat{\bm{X}}, \hat{\bm{Y}})$ that are simultaneously coherent and distributionally faithful, while also ensuring $\hat{y}^{(j)}_t\in\mathcal{V}_j$ for all $j$, $t$ by construction (rather than via post-hoc rounding or thresholding).
+
+A key empirical and methodological tension in ICS synthesis is that temporal realism and marginal/distributional realism can compete when optimized monolithically: sequence models trained primarily for regression often over-smooth heavy tails and intermittent bursts, while purely distribution-matching objectives can erode long-range structure. Diffusion models provide a principled route to rich distribution modeling through iterative denoising, but they do not, by themselves, resolve (i) the need for a stable low-frequency temporal scaffold, nor (ii) the discrete legality constraints for supervisory variables \citep{ho2020denoising,song2021score}. Recent time-series diffusion work further suggests that separating coarse structure from stochastic refinement can be an effective inductive bias for long-horizon realism \citep{kollovieh2023tsdiff,sikder2023transfusion}.
 
 % 4. Benchmark
 \section{Benchmark}