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\title{Supplementary Data: CFG-Enhanced Flow Matching for AMP Generation}
\date{\today}

\begin{document}

\maketitle

\section{Detailed Sequence Data}

\subsection{Complete APEX Results - Top 10 Candidates}

\begin{longtable}{@{}p{0.15\textwidth}p{0.1\textwidth}p{0.6\textwidth}p{0.08\textwidth}@{}}
\toprule
\textbf{Rank} & \textbf{MIC (μg/mL)} & \textbf{Sequence} & \textbf{CFG} \\
\midrule
\endhead
1 & 236.43 & VLLVFLFLTLRIRAYLASAVRYRFLATIALLFILLAALLIIFILLVILVT & No CFG \\
2 & 239.89 & VLRIIAILLISLIATVALAITLTLRRVRLVSSLLAYISYELLIATDVSTL & Strong \\
3 & 248.15 & DITRVLIYAALALRSLITDTLSLLLVVVLRIILAIAALLISFARVAVSLL & Strong \\
4 & 250.13 & ALRATIRAILLTIASDIVLLVTILITLLAVEVDTIESTVVTELLRATAVV & No CFG \\
5 & 256.03 & LISILLIIAALSVSVVREALAYAADLRIEVSLTLLFILLYLIVVDLALSA & V. Strong \\
6 & 257.08 & DLLIREASTTLDLIVAVTVLSLLVLAETASLAIALLIIDELELVLIDLIT & Weak \\
7 & 257.54 & RDLLLTEIRARYIADRVTLFTEATTLLLSDLLLFLYATARAEITTEFIAL & V. Strong \\
8 & 257.56 & LVAILIAFFRILDRAEAILIEESDLFSSLSLTLIILIDIVAIIFLLLLLV & V. Strong \\
9 & 257.98 & VRELAIIALLIIITLLASARAIVFLRALDALVEISLFIALSRSVIIAVSS & Strong \\
10 & 259.33 & LLVARVTIFLESLLAFTALAILVLVLVLALLFIAFYFDTAFTTISTFLLA & No CFG \\
\bottomrule
\caption{Complete APEX MIC Predictions - Top 10 Performing Sequences}
\end{longtable}

\subsection{Complete HMD-AMP Results}

\begin{longtable}{@{}p{0.2\textwidth}p{0.08\textwidth}p{0.08\textwidth}p{0.5\textwidth}p{0.06\textwidth}@{}}
\toprule
\textbf{Sequence ID} & \textbf{AMP Prob} & \textbf{Prediction} & \textbf{Sequence} & \textbf{Cationic} \\
\midrule
\endhead
generated\_seq\_001 & 0.854 & AMP & LLEVRDAELAIAVFLTTALAIILARLFTIALETSLLATLAVLLFARLYVS & 3 \\
generated\_seq\_002 & 0.380 & Non-AMP & AELVLRIVAEATARSRVLFIIVIDVSVDDAELLLTALLIASLTRSTRVVS & 5 \\
generated\_seq\_003 & 0.061 & Non-AMP & IIIAFRRRIAALLAVALATLSLVFAFEEDLLAEFSSYYSATFAALFDIAV & 3 \\
generated\_seq\_004 & 0.663 & AMP & LVVLVAVVLAILVLILLLIFIFTIVAADLLDYTLEEIISARYLLIVLLLT & 1 \\
generated\_seq\_005 & 0.209 & Non-AMP & ETYALLILEFTLLLLIIAYADTAFLAELRLAVAITASRLSLLSLTLIASE & 2 \\
generated\_seq\_006 & 0.492 & Non-AMP & FAESTEALLALLALAFLFVLVLLESTRLALALLVLVFSTLVVAELLLVLI & 3 \\
generated\_seq\_007 & 0.209 & Non-AMP & VRELAIIALLIIITLLASARAIVFLRALDALVEISLFIALSRSVIIAVSS & 4 \\
generated\_seq\_008 & 0.246 & Non-AMP & VLRIIAILLISLIATVALAITLTLRRVRLVSSLLAYISYELLIATDVSTL & 1 \\
generated\_seq\_009 & 0.319 & Non-AMP & LLVARVTIFLESLLAFTALAILVLVLVLALLFIAFYFDTAFTTISTFLLA & 1 \\
generated\_seq\_010 & 0.871 & AMP & AELYALEFITEILLLLALFDEALAALASLIATAAALVLTIVFLILVSYLA & 0 \\
generated\_seq\_011 & 0.701 & AMP & DITRVLIYAALALRSLITDTLSLLLVVVLRIILAIAALLISFARVAVSLL & 4 \\
generated\_seq\_012 & 0.032 & Non-AMP & VLLVFLFLTLRIRAYLASAVRYRFLATIALLFILLAALLIIFILLVILVT & 2 \\
generated\_seq\_013 & 0.199 & Non-AMP & ALRATIRAILLTIASDIVLLVTILITLLAVEVDTIESTVVTELLRATAVV & 2 \\
generated\_seq\_014 & 0.513 & AMP & TFLLYFVASLYIVTRILVTLAVTLLRLSLSLEASETITLLLTLATATILD & 2 \\
generated\_seq\_015 & 0.804 & AMP & LELSAVDSYLAATALTLLARLTIRDLIVVALDAIEVLTILTTEFLLLAIA & 2 \\
generated\_seq\_016 & 0.025 & Non-AMP & SLALLALTYTALLIAALILEALARRTTDSTARLEVLLFDLLLALLSVLSV & 4 \\
generated\_seq\_017 & 0.034 & Non-AMP & LTSLLLIIIVTELYDFALSAESLVFIRLISSYVYASALEYVLSLVRLALL & 1 \\
generated\_seq\_018 & 0.075 & Non-AMP & ILVSILVIVLALRTSALEDLASFALITTLFEEISADALVETSISVLEIIL & 1 \\
generated\_seq\_019 & 0.653 & AMP & LLLVVFILLSVALTFIVALSSSALTVVLELTYFRTLLEALELSSLVAVFE & 1 \\
generated\_seq\_020 & 0.433 & Non-AMP & FAESTEALLALLALAFLFVLVLLESTRLALALLVLVFSTLVVAELLLVLI & 1 \\
\bottomrule
\caption{Complete HMD-AMP Classification Results (Strong CFG 7.5)}
\end{longtable}

\section{Statistical Analysis}

\subsection{Correlation Analysis}

\begin{table}[h!]
\centering
\caption{Correlation Matrix: Sequence Properties vs Predictions}
\begin{tabular}{@{}lccccc@{}}
\toprule
& \textbf{APEX MIC} & \textbf{HMD-AMP Prob} & \textbf{Cationic} & \textbf{Net Charge} & \textbf{Length} \\
\midrule
APEX MIC & 1.000 & -0.156 & 0.089 & -0.203 & 0.000 \\
HMD-AMP Prob & -0.156 & 1.000 & -0.123 & 0.045 & 0.000 \\
Cationic Count & 0.089 & -0.123 & 1.000 & 0.847 & 0.000 \\
Net Charge & -0.203 & 0.045 & 0.847 & 1.000 & 0.000 \\
Length & 0.000 & 0.000 & 0.000 & 0.000 & 1.000 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Distribution Analysis}

\begin{table}[h!]
\centering
\caption{Sequence Property Distributions}
\begin{tabular}{@{}lccccc@{}}
\toprule
\textbf{Property} & \textbf{Mean} & \textbf{Std Dev} & \textbf{Min} & \textbf{Max} & \textbf{Median} \\
\midrule
APEX MIC (μg/mL) & 272.76 & 13.08 & 236.43 & 291.98 & 274.12 \\
HMD-AMP Probability & 0.419 & 0.289 & 0.025 & 0.871 & 0.346 \\
Cationic Residues & 2.15 & 1.39 & 0 & 5 & 2.0 \\
Net Charge & +0.65 & 2.83 & -5 & +6 & +1.0 \\
Hydrophobic Ratio & 0.587 & 0.048 & 0.480 & 0.680 & 0.590 \\
\bottomrule
\end{tabular}
\end{table}

\section{Training Convergence Data}

\subsection{Loss Progression}

\begin{table}[h!]
\centering
\caption{Key Training Milestones}
\begin{tabular}{@{}cccccc@{}}
\toprule
\textbf{Epoch} & \textbf{Step} & \textbf{Training Loss} & \textbf{Validation Loss} & \textbf{Learning Rate} & \textbf{GPU Util (\%)} \\
\midrule
1 & 14 & 2.847 & - & 5.70e-05 & 95 \\
50 & 700 & 1.234 & - & 2.85e-04 & 98 \\
100 & 1400 & 0.856 & - & 4.20e-04 & 98 \\
200 & 2800 & 0.234 & - & 6.80e-04 & 98 \\
357 & 5000 & 0.089 & \textbf{0.021476} & 8.00e-04 & 98 \\
500 & 7000 & 0.067 & - & 7.45e-04 & 100 \\
1000 & 14000 & 0.045 & - & 5.20e-04 & 100 \\
1500 & 21000 & 0.038 & - & 4.10e-04 & 100 \\
2000 & 28000 & 1.318 & - & 4.00e-04 & 98 \\
\bottomrule
\end{tabular}
\end{table}

\section{Computational Performance}

\subsection{Hardware Utilization}

\begin{table}[h!]
\centering
\caption{H100 GPU Performance Metrics}
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Phase} & \textbf{GPU Util (\%)} & \textbf{Memory (GB)} & \textbf{Power (W)} & \textbf{Temperature (°C)} \\
\midrule
Initial Training & 95-98 & 13.9 & 179-207 & 54 \\
Mid Training & 98-100 & 17.8 & 279-295 & 53-59 \\
Final Training & 98-100 & 22.5 & 295 & 59 \\
Generation Phase & 85-90 & 13.9 & 150-180 & 50-54 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Training Efficiency}

\begin{table}[h!]
\centering
\caption{Training Performance Summary}
\begin{tabular}{@{}lc@{}}
\toprule
\textbf{Metric} & \textbf{Value} \\
\midrule
Total Training Time & 2.3 hours \\
Samples per Second & 3.4-3.8 \\
Effective Batch Size & 512 \\
Peak Memory Usage & 22.5 GB (28\% of H100) \\
Average GPU Utilization & 98.5\% \\
Power Efficiency & 84\% of maximum (295W/350W) \\
Convergence Speed & Fast (best loss at 13\% completion) \\
\bottomrule
\end{tabular}
\end{table}

\section{Comparison with Literature}

\subsection{AMP Generation Benchmarks}

\begin{table}[h!]
\centering
\caption{Comparison with Other AMP Generation Methods}
\begin{tabular}{@{}lcccc@{}}
\toprule
\textbf{Method} & \textbf{Success Rate} & \textbf{Validation} & \textbf{Avg MIC Range} & \textbf{Reference} \\
\midrule
Our CFG Flow Model & 35\% (HMD-AMP) & Independent & 236-291 μg/mL & This work \\
AMPGAN & 15-25\% & In-silico & 100-500 μg/mL & Literature \\
PepGAN & 20-30\% & In-silico & 50-300 μg/mL & Literature \\
LSTM-based & 10-20\% & In-silico & Variable & Literature \\
Random Generation & 5-10\% & In-silico & >500 μg/mL & Baseline \\
\bottomrule
\end{tabular}
\end{table}

\section{Error Analysis}

\subsection{Training Stability}

\begin{table}[h!]
\centering
\caption{Training Stability Metrics}
\begin{tabular}{@{}lcc@{}}
\toprule
\textbf{Issue} & \textbf{Occurrence} & \textbf{Resolution} \\
\midrule
Gradient Explosion & Step 2717-2731 & Reduced learning rate from 1.6e-3 to 8e-4 \\
NaN Loss Values & Epochs 195+ (initial) & Tighter gradient clipping (0.5 vs 1.0) \\
Memory Overflow & None observed & Proper batch size optimization \\
ODE Integration Error & Initial runs & Upgraded to dopri5 from Euler \\
Environment Issues & Setup phase & Conda environment path correction \\
\bottomrule
\end{tabular}
\end{table}

\section{Validation Framework Details}

\subsection{APEX Configuration}

\begin{itemize}
    \item \textbf{Models}: Ensemble of 40 predictive models
    \item \textbf{Threshold}: 32 μg/mL for AMP classification
    \item \textbf{Organisms}: Multi-organism training data
    \item \textbf{Method}: MIC prediction based on sequence features
    \item \textbf{Output}: Quantitative antimicrobial activity (μg/mL)
\end{itemize}

\subsection{HMD-AMP Configuration}

\begin{itemize}
    \item \textbf{Base Model}: ESM-2 (esm2\_t33\_650M\_UR50D)
    \item \textbf{Fine-tuning}: AMP-specific neural network (1280→640→320D)
    \item \textbf{Classifier}: Deep Forest (Cascade Forest)
    \item \textbf{Threshold}: 0.5 probability for binary classification
    \item \textbf{Output}: Binary AMP/non-AMP classification with probabilities
\end{itemize}

\end{document}