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table2_full_results.tex
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table2_full_results.tex
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\begin{table*}
\caption{MRR results on ICEWS14. The group $\text{avg}_{x}$ wraps to two rows. \textbf{AVG} denotes average performance under all query types.}
\label{table:MRR_results_ICEWS14}
\centering
\resizebox{\textwidth}{!}{
\begin{tabular}{lrrrrrrrrrrrrrrrrrrrrrrrrrrrrr }
\toprule
\textbf{Model} & $\text{avg}_e$ & \textbf{Pe} & \textbf{Pe2} & \textbf{Pe3} & \textbf{e2i} & \textbf{e3i} \\
\midrule
Query2box & 25.06 & 25.81 & 17.29 & 12.97 & 16.00 & 53.25 \\
BetaE & 37.19 & 39.52 & 23.77 & 17.50 & 23.77 & 81.38 \\
ConE & 41.94 & 42.55 & 30.90 & 24.78 & 26.52 & 84.93 \\
ConE(temporal) & 42.23& 41.21& 31.83& 24.99& 28.98& 84.17\\
FLEX & 43.67 & 45.25 & 33.07 & 27.22 & 27.62 & 85.18 \\
TFLEX & 56.79 & 48.21 & 37.27 & 33.53 & 69.24 & 95.70 \\
X(ConE) & 40.93 & 40.58 & 28.84 & 24.31 & 30.93 & 79.98 \\
X-1F & 56.89 & 48.61 & 37.51 & 32.61 & 71.25 & 94.47 \\
X-logic & 56.64 & 48.00 & 37.42 & 31.23 & 73.11 & 93.45 \\
\midrule
\midrule
& $\text{avg}_t$ & \textbf{Pt} & \textbf{aPt} & \textbf{bPt} & \textbf{Pe\_Pt} & \textbf{Pt\_sPe\_Pt} & \textbf{Pt\_oPe\_Pt} & \textbf{t2i} & \textbf{t3i} \\
\midrule
TFLEX & 17.56 & 20.87 & 3.00 & 2.96 & 14.27 & 9.57 & 9.46 & 27.49 & 52.84 \\
X(ConE) & 16.41 & 19.45 & 3.06 & 3.01 & 13.96 & 8.79 & 8.67 & 25.01 & 49.36 \\
X-1F & 18.77 & 21.94 & 3.04 & 2.99 & 16.69 & 10.73 & 10.44 & 29.66 & 54.71 \\
X-logic & 18.03 & 21.33 & 3.10 & 3.05 & 15.76 & 9.85 & 9.94 & 28.57 & 52.63 \\
\midrule
\midrule
& $\text{avg}_{e, \mathcal{C}_e}$ & \textbf{e2i\_N} & \textbf{e3i\_N} & \textbf{Pe\_e2i\_N} & \textbf{e2i\_PeN} & \textbf{e2i\_NPe} \\
\midrule
BetaE & 36.69 & 30.44 & 87.93 & 19.94 & 22.80 & 22.36 \\
ConE & 44.88 & 40.98 & 99.12 & 29.22 & 29.84 & 25.22 \\
ConE(temporal) & 44.94& 41.45& 98.99& 29.48& 30.71&24.09\\
FLEX & 44.41 & 38.30 & 99.22 & 31.18 & 30.49 & 22.84 \\
TFLEX & 50.82 & 45.55 & 99.56 & 34.74 & 35.63 & 38.61 \\
X(ConE) & 42.15 & 39.10 & 96.25 & 26.92 & 27.59 & 20.89 \\
X-1F & 49.78 & 42.31 & 99.31 & 34.89 & 34.77 & 37.61 \\
X-logic & 51.17 & 44.65 & 99.25 & 35.30 & 36.31 & 40.33 \\
\midrule
\midrule
& $\text{avg}_{t, \mathcal{C}_t}$ & t2i\_N & t3i\_N & Pe\_t2i\_N & t2i\_PtN & t2i\_NPt \\
\midrule
TFLEX & 36.37 & 25.38 & 98.91 & 34.05 & 11.42 & 12.07 \\
X(ConE) & 35.24 & 26.90 & 98.82 & 30.30 & 9.44 & 10.75 \\
X-1F & 37.73 & 26.40 & 98.82 & 37.85 & 12.38 & 13.23 \\
X-logic & 36.39 & 25.68 & 98.69 & 33.30 & 11.34 & 12.93 \\
\midrule
\midrule
& $\text{avg}_{\{\mathcal{U}_e\}}$ & \textbf{e2u} & \textbf{Pe\_e2u} \\
\midrule
BetaE & 19.95 & 18.61 & 21.28 \\
ConE & 26.47 & 21.84 & 31.11 \\
ConE(temporal) & 27.63& 23.01& 32.26\\
FLEX & 29.25 & 24.05 & 34.46 \\
TFLEX & 35.74 & 29.20 & 42.28 \\
X(ConE) & 25.46 & 20.26 & 30.67 \\
X-1F & 34.48 & 30.04 & 38.93 \\
X-logic & 34.68 & 29.44 & 39.92 \\
\midrule
\midrule
& $\text{avg}_{\{\mathcal{U}_t\}}$ & \textbf{t2u} & \textbf{Pe\_t2u} \\
\midrule
TFLEX & 26.24 & 30.73 & 21.74 \\
X(ConE) & 24.07 & 27.63 & 20.51 \\
X-1F & 28.04 & 33.91 & 22.16 \\
X-logic & 26.36 & 31.21 & 21.52 \\
\midrule
\midrule
& $\text{avg}_{x}$ & \textbf{e2i\_Pe} & \textbf{Pe\_e2i} & \textbf{Pe\_aPt} & \textbf{Pe\_bPt} & \textbf{Pe\_at2i} & \textbf{Pe\_bt2i} \\
TFLEX & 28.03 & 98.86 & 36.77 & 8.66 & 9.74 & 7.90 & 7.78 \\
X(ConE) & 26.65 & 87.31 & 28.72 & 11.01 & 10.40 & 11.21 & 11.27 \\
X-1F & 29.31 & 98.87 & 36.00 & 10.04 & 10.21 & 8.30 & 8.06 \\
X-logic & 28.61 & 97.64 & 36.96 & 10.09 & 10.27 & 8.76 & 8.93 \\
\cmidrule(lr){3-10}
& \textbf{AVG} & \textbf{t2i\_Pe} & \textbf{Pe\_t2i} & \textbf{Pt\_sPe} & \textbf{Pt\_oPe} & \textbf{Pt\_se2i} & \textbf{Pt\_oe2i} & \textbf{between} \\
TFLEX & 35.93 & 96.62 & 64.50 & 4.32 & 10.58 & 8.20 & 7.95 & 2.57 \\
X(ConE) & 30.13 & 95.40 & 63.04 & 3.77 & 8.82 & 6.44 & 5.76 & 3.32 \\
X-1F & 36.43 & 97.24 & 70.32 & 4.88 & 10.73 & 12.24 & 11.55 & 2.55 \\
X-logic & 35.98 & 96.35 & 64.31 & 4.97 & 10.35 & 10.59 & 10.35 & 2.34 \\
\bottomrule
\end{tabular}
}
\end{table*}
\begin{table*}
\caption{MRR results on ICEWS05-15. The group $\text{avg}_{x}$ wraps to two rows. \textbf{AVG} denotes average performance under all query types.}
\label{table:MRR_results_ICEWS05-15}
\centering
\resizebox{\textwidth}{!}{
\begin{tabular}{lrrrrrrrrrrrrrrrrrrrrrrrrrrrrr }
\toprule
\textbf{Model} & $\text{avg}_e$ & \textbf{Pe} & \textbf{Pe2} & \textbf{Pe3} & \textbf{e2i} & \textbf{e3i} \\
\midrule
Query2box & 24.00 & 25.94 & 16.62 & 14.22 & 17.68 & 45.52 \\
BetaE & 31.33 & 35.78 & 21.47 & 18.18 & 18.10 & 63.11 \\
ConE & 40.93 & 42.67 & 29.39 & 24.79 & 26.15 & 81.64 \\
ConE(temporal) & 40.74& 42.64& 29.30& 24.76& 25.35& 81.65\\
FLEX & 38.96 & 41.60 & 29.80 & 24.58 & 24.37 & 74.46 \\
TFLEX & 48.99 & 43.04 & 36.28 & 33.89 & 41.17 & 90.60 \\
X(ConE) & 36.29 & 39.90 & 26.62 & 22.85 & 22.52 & 69.56 \\
X-1F & 49.90 & 43.07 & 36.87 & 34.96 & 40.85 & 93.76 \\
X-logic & 44.80 & 40.57 & 31.47 & 30.67 & 35.80 & 85.47 \\
\midrule
\midrule
& $\text{avg}_t$ & \textbf{Pt} & \textbf{aPt} & \textbf{bPt} & \textbf{Pe\_Pt} & \textbf{Pt\_sPe\_Pt} & \textbf{Pt\_oPe\_Pt} & \textbf{t2i} & \textbf{t3i} \\
\midrule
TFLEX & 4.39 & 10.62 & 0.38 & 0.38 & 7.29 & 2.63 & 1.83 & 3.85 & 8.15 \\
X(ConE) & 4.41 & 10.98 & 0.38 & 0.38 & 6.75 & 2.16 & 1.63 & 4.22 & 8.81 \\
X-1F & 4.43 & 10.71 & 0.38 & 0.38 & 7.40 & 2.73 & 1.86 & 3.80 & 8.16 \\
X-logic & 3.29 & 8.57 & 0.38 & 0.39 & 6.37 & 1.69 & 1.41 & 2.49 & 5.06 \\
\midrule
\midrule
& $\text{avg}_{e, \mathcal{C}_e}$ & \textbf{e2i\_N} & \textbf{e3i\_N} & \textbf{Pe\_e2i\_N} & \textbf{e2i\_PeN} & \textbf{e2i\_NPe} \\
\midrule
BetaE & 29.70 & 21.68 & 71.08 & 20.31 & 21.11 & 14.30 \\
ConE & 43.52 & 43.04 & 96.08 & 28.41 & 28.75 & 21.30 \\
ConE(temporal) & 43.34& 42.85& 96.08& 28.33&28.62& 20.83 \\
FLEX & 42.10 & 36.22 & 97.47 & 27.93 & 27.23 & 21.64 \\
TFLEX & 46.17 & 41.34 & 96.69 & 34.29 & 34.63 & 23.88 \\
X(ConE) & 38.12 & 33.70 & 88.83 & 24.80 & 25.60 & 17.64 \\
X-1F & 46.11 & 38.06 & 96.82 & 35.76 & 36.20 & 23.73 \\
X-logic & 41.92 & 36.57 & 91.16 & 30.37 & 31.42 & 20.07 \\
\midrule
\midrule
& $\text{avg}_{t, \mathcal{C}_t}$ & \textbf{t2i\_N} & \textbf{t3i\_N} & \textbf{Pe\_t2i\_N} & \textbf{t2i\_PtN} & \textbf{t2i\_NPt} \\
\midrule
TFLEX & 30.16 & 16.09 & 98.40 & 31.39 & 3.35 & 1.58 \\
X(ConE) & 29.49 & 16.55 & 98.46 & 28.23 & 2.53 & 1.69 \\
X-1F & 30.26 & 16.05 & 98.37 & 32.07 & 3.27 & 1.56 \\
X-logic & 28.34 & 12.94 & 96.03 & 29.47 & 2.18 & 1.07 \\
\midrule
\midrule
& $\text{avg}_{\{\mathcal{U}_e\}}$ & \textbf{e2u} & \textbf{Pe\_e2u} \\
\midrule
BetaE & 21.54 & 20.95 & 22.13 \\
ConE & 43.02 & 37.21 & 48.83 \\
ConE(temporal) & 43.14& 37.05& 49.24\\
FLEX & 44.38 & 35.72 & 53.04 \\
TFLEX & 54.37 & 52.99 & 55.75 \\
X(ConE) & 36.37 & 29.89 & 42.86 \\
X-1F & 54.05 & 52.47 & 55.64 \\
X-logic & 45.36 & 43.84 & 46.88 \\
\midrule
\midrule
& $\text{avg}_{\{\mathcal{U}_t\}}$ & \textbf{t2u} & \textbf{Pe\_t2u} \\
\midrule
TFLEX & 28.69 & 44.99 & 12.39 \\
X(ConE) & 26.40 & 40.35 & 12.46 \\
X-1F & 27.70 & 43.38 & 12.02 \\
X-logic & 23.39 & 37.07 & 9.71 \\
\midrule
\midrule
& $\text{avg}_{x}$ & \textbf{e2i\_Pe} & \textbf{Pe\_e2i} & \textbf{Pe\_aPt} & \textbf{Pe\_bPt} & \textbf{Pe\_at2i} & \textbf{Pe\_bt2i} \\
TFLEX & 24.26 & 94.23 & 57.16 & 5.07 & 4.56 & 4.38 & 3.93 \\
X(ConE) & 21.69 & 81.36 & 38.20 & 5.63 & 5.03 & 5.80 & 5.36 \\
X-1F & 24.41 & 94.26 & 55.97 & 5.14 & 4.79 & 4.37 & 3.95 \\
X-logic & 21.95 & 87.48 & 50.11 & 4.28 & 3.95 & 3.96 & 3.55 \\
\cmidrule(lr){3-10}
& \textbf{AVG} & \textbf{t2i\_Pe} & \textbf{Pe\_t2i} & \textbf{Pt\_sPe} & \textbf{Pt\_oPe} & \textbf{Pt\_se2i} & \textbf{Pt\_oe2i} & \textbf{between} \\
TFLEX & 33.72 & 92.25 & 48.35 & 0.46 & 2.82 & 0.98 & 1.02 & 0.22 \\
X(ConE) & 27.54 & 91.92 & 43.83 & 0.58 & 2.18 & 0.95 & 1.02 & 0.14 \\
X-1F & 33.98 & 92.21 & 50.77 & 0.46 & 2.89 & 1.13 & 1.23 & 0.17 \\
X-logic & 29.86 & 86.17 & 40.78 & 0.62 & 1.98 & 1.10 & 1.21 & 0.16 \\
\bottomrule
\end{tabular}
}
\end{table*}
\begin{table*}
\caption{MRR results on GDELT-500. The group $\text{avg}_{x}$ wraps to two rows. \textbf{AVG} denotes average performance under all query types.}
\label{table:MRR_results_GDELT-500}
\centering
\resizebox{\textwidth}{!}{
\begin{tabular}{lrrrrrrrrrrrrrrrrrrrrrrrrrrrrr }
\toprule
\textbf{Model} & $\text{avg}_e$ & \textbf{Pe} & \textbf{Pe2} & \textbf{Pe3} & \textbf{e2i} & \textbf{e3i} \\
\midrule
Query2box & 9.67 & 10.70 & 4.73 & 3.41 & 12.28 & 17.22 \\
BetaE & 14.75 & 14.02 & 5.76 & 4.71 & 18.61 & 30.67 \\
ConE & 18.44 & 16.65 & 6.18 & 4.70 & 23.11 & 41.55 \\
ConE(temporal) & 18.51& 17.61& 5.62& 4.57& 24.52& 40.22\\
FLEX & 19.07 & 17.72 & 5.78 & 4.67 & 24.30 & 42.85 \\
TFLEX & 19.60 & 18.50 & 5.76 & 4.68 & 25.94 & 43.14 \\
X(ConE) & 17.83 & 17.05 & 5.76 & 4.66 & 24.02 & 37.66 \\
X-1F & 17.92 & 16.18 & 6.35 & 4.84 & 22.41 & 39.80 \\
X-logic & 17.36 & 15.80 & 6.22 & 4.85 & 22.45 & 37.47 \\
\midrule
\midrule
& $\text{avg}_t$ & \textbf{Pt} & \textbf{aPt} & \textbf{bPt} & \textbf{Pe\_Pt} & \textbf{Pt\_sPe\_Pt} & \textbf{Pt\_oPe\_Pt} & \textbf{t2i} & \textbf{t3i} \\
\midrule
TFLEX & 5.38 & 6.49 & 3.25 & 3.27 & 6.16 & 3.06 & 2.88 & 6.78 & 11.17 \\
X(ConE) & 3.16 & 2.15 & 3.39 & 3.33 & 6.96 & 2.29 & 2.31 & 2.34 & 2.49 \\
X-1F & 5.49 & 6.62 & 3.30 & 3.30 & 5.84 & 3.07 & 3.05 & 7.08 & 11.66 \\
X-logic & 5.75 & 7.15 & 3.34 & 3.31 & 5.95 & 3.14 & 3.06 & 7.52 & 12.54 \\
\midrule
\midrule
& $\text{avg}_{e, \mathcal{C}_e}$ & \textbf{e2i\_N} & \textbf{e3i\_N} & \textbf{Pe\_e2i\_N} & \textbf{e2i\_PeN} & \textbf{e2i\_NPe} \\
\midrule
BetaE & 11.15 & 11.22 & 24.17 & 5.53 & 5.46 & 9.39 \\
ConE & 12.67 & 12.69 & 29.09 & 5.47 & 5.42 & 10.66 \\
ConE(temporal) & 12.67& 13.42 & 27.98& 5.31& 5.00& 11.63\\
FLEX & 13.35 & 13.57 & 30.25 & 5.47 & 5.47 & 11.99 \\
TFLEX & 13.52 & 14.46 & 30.09 & 5.51 & 5.19 & 12.36 \\
X(ConE) & 12.34 & 13.42 & 26.28 & 5.54 & 5.35 & 11.14 \\
X-1F & 12.13 & 11.77 & 27.63 & 5.70 & 5.40 & 10.14 \\
X-logic & 12.11 & 12.32 & 27.00 & 5.70 & 5.55 & 10.01 \\
\midrule
\midrule
& $\text{avg}_{t, \mathcal{C}_t}$ & \textbf{t2i\_N} & \textbf{t3i\_N} & \textbf{Pe\_t2i\_N} & \textbf{t2i\_PtN} & \textbf{t2i\_NPt} \\
\midrule
TFLEX & 6.31 & 5.92 & 9.01 & 9.30 & 2.76 & 4.56 \\
X(ConE) & 3.93 & 2.24 & 2.43 & 10.00 & 2.26 & 2.74 \\
X-1F & 6.50 & 5.90 & 9.70 & 9.15 & 2.85 & 4.90 \\
X-logic & 6.86 & 6.51 & 10.94 & 8.78 & 2.94 & 5.14 \\
\midrule
\midrule
& $\text{avg}_{\{\mathcal{U}_e\}}$ & \textbf{e2u} & \textbf{Pe\_e2u} \\
\midrule
BetaE & 6.20 & 4.64 & 7.75 \\
ConE & 6.96 & 4.68 & 9.25 \\
ConE(temporal) & 7.30& 4.50& 10.09\\
FLEX & 7.44 & 4.47 & 10.42 \\
TFLEX & 7.58 & 4.62 & 10.55 \\
X(ConE) & 7.41 & 4.64 & 10.19 \\
X-1F & 6.92 & 4.80 & 9.04 \\
X-logic & 6.91 & 4.74 & 9.09 \\
\midrule
\midrule
& $\text{avg}_{\{\mathcal{U}_t\}}$ & \textbf{t2u} & \textbf{Pe\_t2u} \\
\midrule
TFLEX & 6.71 & 9.03 & 4.38 \\
X(ConE) & 6.35 & 10.39 & 2.31 \\
X-1F & 6.59 & 8.60 & 4.58 \\
X-logic & 6.80 & 8.85 & 4.76 \\
\midrule
\midrule
& $\text{avg}_{x}$ & \textbf{e2i\_Pe} & \textbf{Pe\_e2i} & \textbf{Pe\_aPt} & \textbf{Pe\_bPt} & \textbf{Pe\_at2i} & \textbf{Pe\_bt2i} \\
TFLEX & 6.17 & 17.53 & 6.38 & 4.73 & 4.58 & 4.47 & 4.58 \\
X(ConE) & 6.17 & 17.53 & 6.44 & 6.45 & 6.18 & 6.02 & 5.97 \\
X-1F & 6.47 & 18.13 & 6.82 & 5.48 & 5.35 & 5.19 & 5.31 \\
X-logic & 6.64 & 17.45 & 6.79 & 5.56 & 5.44 & 5.35 & 5.37 \\
\cmidrule(lr){3-10}
& \textbf{AVG} & \textbf{t2i\_Pe} & \textbf{Pe\_t2i} & \textbf{Pt\_sPe} & \textbf{Pt\_oPe} & \textbf{Pt\_se2i} & \textbf{Pt\_oe2i} & \textbf{between} \\
TFLEX & 9.32 & 8.36 & 15.83 & 3.11 & 2.81 & 2.93 & 3.07 & 1.85 \\
X(ConE) & 8.17 & 2.45 & 17.97 & 2.70 & 2.24 & 2.20 & 2.29 & 1.76 \\
X-1F & 8.86 & 8.80 & 15.13 & 2.92 & 2.72 & 3.11 & 3.29 & 1.87 \\
X-logic & 8.92 & 10.28 & 15.28 & 3.27 & 3.11 & 3.23 & 3.36 & 1.79 \\
\bottomrule
\end{tabular}
}
\end{table*}
% bib
@inproceedings{Query2box,
title={Query2box: Reasoning Over Knowledge Graphs In Vector Space Using Box Embeddings},
author={Ren, H and Hu, W and Leskovec, J},
booktitle={International Conference on Learning Representations (ICLR)},
year={2020}
}
@article{BetaE,
title={Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs},
author={Ren, Hongyu and Leskovec, Jure},
journal={Neural Information Processing Systems (NeurIPS)},
year={2020}
}
@article{ConE,
title={ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs},
author={Zhang, Zhanqiu and Wang, Jie and Chen, Jiajun and Ji, Shuiwang and Wu, Feng},
journal={Advances in Neural Information Processing Systems},
volume={34},
year={2021}
}
% TFLEX
@inproceedings{xueyuan2023tflex,
title={{TFLEX}: Temporal Feature-Logic Embedding Framework for Complex Reasoning over Temporal Knowledge Graph},
author={Lin Xueyuan and Haihong E and Chengjin Xu and Gengxian Zhou and Haoran Luo and Tianyi Hu and Fenglong Su and Ningyuan Li and Mingzhi Sun},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=oaGdsgB18L}
}