task
stringclasses 3
values | gt_id
int64 0
655
⌀ | gt_latex
stringlengths 21
649
⌀ | similarity
float64 -1
0.98
| strict_similarity
float64 -1
0.97
| semantic_similarity
float64 -1
0.98
| structural_similarity
float64 -1
1
| element_overlap
float64 -1
1
| page
stringclasses 70
values | bbox
listlengths 4
4
| raw_ocr
stringlengths 0
1.67k
| paper_id
stringclasses 170
values |
|---|---|---|---|---|---|---|---|---|---|---|---|
repair_no_gt
| null | null | 0.481416
| 0.412698
| 0.489796
| 0.522727
| 0.571429
|
page_4
|
[
1088.1143798828125,
1185.2830810546875,
1488.9521484375,
1314.9154052734375
] |
\mathrm{SMMA}_{n}=\frac{1}{n}\sum_{i=1}^{n}\mathrm{GloSe}_{i}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.452715
| 0.384615
| 0.410959
| 0.42029
| 0.888889
|
page_4
|
[
829.18310546875,
1519.0767822265625,
1753.3846435546875,
1616.2474365234375
] |
\mathrm{{EMA}}_{n}=\mathrm{{EMA}}_{n-1}+{\frac{2}{n+1}}\times(\mathrm{{Close}}_{n}-\mathrm{{EMA}}_{n-1})
|
2511.16657v1
|
repair_no_gt
| null | null | 0.244533
| 0.199288
| 0.189526
| 0.244681
| 0.6
|
page_4
|
[
732.8687133789062,
1869.9207763671875,
1859.419677734375,
2286.003173828125
] |
\begin{array}{l}{{\mathrm{Lorwer~band:~BBL}_{n,k}=\mathrm{SMA}_{n}(\mathrm{Close})-k\times\mathrm{StdDev}_{n}(\mathrm{Close})}}\\ {{\mathrm{Middute~band:~BBM}_{n,k}=\mathrm{SMA}_{n}(\mathrm{Close})}}\\ {{\mathrm{Band~width}:~\mathrm{BBD}_{n,k}=\mathrm{BBW}_{n,k}=\mathrm{BB}\mathrm{BBT}_{n,k}}}\\ {{\mathrm{BBT}_{n,k}=\mathrm{\frac{\mathrm{BBU}_{n,k}-B B L}{B B E n}_{n,k}}}}\end{array}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.364871
| 0.353982
| 0.352941
| 0.4
| 0.375
|
page_5
|
[
1088.5531005859375,
700.5897216796875,
1490.662109375,
805.6161499023438
] |
\mathrm{RSI}_{n}=100-{\frac{100}{1+\mathrm{RS}}}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.334582
| 0.302158
| 0.32
| 0.32967
| 0.5
|
page_5
|
[
1084.2340087890625,
861.3573608398438,
1486.7899169921875,
972.755859375
] |
\mathrm{RS}=\frac{\mathrm{Average\;Gain}_{n}}{\mathrm{Average\;Loss}_{n}}.
|
2511.16657v1
|
repair_no_gt
| null | null | 0.268256
| 0.208251
| 0.228228
| 0.294671
| 0.555556
|
page_5
|
[
844.1702880859375,
1187.4500732421875,
1736.75634765625,
1375.390869140625
] |
\begin{array}{l}{{\mathrm{MACD}_{n,m}=\mathrm{EM}\mathrm{A}_{n}(\mathrm{Close})-\mathrm{EM}\mathrm{A}_{m}(\mathrm{Close})}}\\ {{\mathrm{MACD}\mathrm{B}_{n,m,p}=\mathrm{MAC}\mathrm{D}_{n,m}-\mathrm{EM}\mathrm{A}_{p}(\mathrm{MACD}_{n,m})}}\\ {{\mathrm{MACD}\mathrm{S}_{n,m,m}=\mathrm{EM}\mathrm{A}_{p}(\mathrm{MACD}_{n,m})}}\end{array}
|
2511.16657v1
|
with_gt
| 4
|
\[ \text{ADX}_{t} = \frac{\text{ADX}_{t-1} \times (n-1) + \text{DX}_{t}}{n} \]
| 0.573224
| 0.517073
| 0.608696
| 0.606452
| 0.533333
|
page_5
|
[
970.0152587890625,
1753.7607421875,
1608.4010009765625,
1859.8529052734375
] |
\mathrm{\bfAD}{\bf X}_{t}\,=\,\frac{\mathrm{\bfAD}{\bf X}_{t-1}\,\times\,\bigl(\eta-1\bigr)\,+\,\mathrm{\bfD}{\bf X}_{t}}{\eta}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.507322
| 0.530466
| 0.471698
| 0.497512
| 0.6
|
page_5
|
[
1095.8880615234375,
1965.560791015625,
1474.804931640625,
2093.052734375
] |
\mathrm{DX}_{t}={\frac{\left|{\bf D_{t}^{\ +}}-{\bf D_{t}^{\lbrack-\rbrack}}\right|}{\left|{\bf D}\rbrack_{t}^{+}+{\bf D}\rbrack_{t}^{-}\right|}}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.253234
| 0.24186
| 0.254958
| 0.282353
| 0.222222
|
page_5
|
[
1071.2098388671875,
2162.99267578125,
1503.3956298828125,
2299.131591796875
] |
\begin{array}{l}{{\displaystyle{\int}\Pi_{t}^{+}\implies\Pi\mathrm{i}_{\Theta}\mathrm{l}_{t}\dots\Pi\mathrm{i}_{\Theta}\mathrm{l}_{t-1}}}\\ {{\mathrm{I})\Omega_{t}^{-}\begin{array}{l}{{\displaystyle{\int}\Omega_{t-1}}}\\ {{\displaystyle{\int}\Omega_{t}^{-}\implies\mathrm{I}.\Psi_{t}}}\end{array}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.406974
| 0.480769
| 0.366812
| 0.38009
| 0.4
|
page_5
|
[
918.3305053710938,
2509.54736328125,
1663.6865234375,
2623.80517578125
] |
\mathrm{Williams~}\zeta_{0}\mathrm{R}_{n}=\frac{\mathrm{High}_{n}-\mathrm{Close}}{\mathrm{High}_{n}-\mathrm{Iow}_{n}}\times100\gamma_{0}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.403242
| 0.373089
| 0.425703
| 0.451327
| 0.307692
|
page_5
|
[
633.5162963867188,
2902.94091796875,
1950.931640625,
3034.577880859375
] |
\mathrm{ATR}_{n}=\frac{1}{n}\sum_{i=1}^{n}\operatorname*{max}(\mathrm{High}_{i}-\mathrm{Low}_{i},|\mathrm{High}_{i}-\mathrm{Close}_{i-1}|,|\mathrm{Low}_{i}-\mathrm{Close}_{i-1}|)
|
2511.16657v1
|
repair_no_gt
| null | null | 0.19783
| 0.17033
| 0.198813
| 0.216981
| 0.238095
|
page_6
|
[
939.6572265625,
430.7757263183594,
1641.141845703125,
666.8075561523438
] |
\begin{array}{l}{{\nabla_{0}\mathrm{K}=\frac{\displaystyle{\nabla}\!{\mathrm{lose}}-{\mathrm{Min~Low}_{n}}}_{n}}}\\ {{\mathrm{~}\!\!\!\nabla_{\mathrm{dC}}\mathrm{In}\mathrm{s}\,\mathrm{High}_{n}-{\mathrm{Min~Low}_{n}}}}\\ {{\mathrm{~}\!\!\mathrm{~}\!\!\mathrm{~}\!\!\mathrm{~}\!\!\mathrm{~}\!\!\vphantom{~}\!\!\mathrm{~}\!\!\vphantom{~}\!\!\mathrm{~}\!\!\sim\mathrm{~}\!\!\mathrm{~}\!{\displaystyle\bar{~}\!\!\times\!\!\widetilde{~}\!\!\sqrt{}_{0}\mathrm{~}\!\!\times\!\!\vphantom{~}\!\!\times\!\!\displaystyle\langle\!\!\mathrm{D}\!\!\mathrm{s}\!\!\overbrace{~}\!\!\mathrm{~}\!\mathrm{~}\!\!\ H}_{n}}}\\ {{\mathrm{}\!\!\mathrm{}\!\!\mathrm{~}\!\!\mathrm{~}\!\!\mathrm{~}\!\!\displaystyle\sim3\!\forall\widetilde{\displaystyle\forall}\!{\forall}_{0}\!\!\!\forall}\!\!\displaystyle\displaystyle\displaystyle\right.}}}\mathrm{}}\mathrm{{\Psi}_{{\l}\!{{\l}\!\l}\!\mathrm{{{{\l}\!\l}\!0}\!\!\displaystyle{\forall}}}}}}}}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.393814
| 0.433735
| 0.370044
| 0.378378
| 0.4
|
page_6
|
[
878.1707153320312,
1010.1703491210938,
1698.8084716796875,
1125.40283203125
] |
\mathrm{SQZ}_{n,m,p,q}=\frac{\mathrm{SM}\mathrm{IA}(\mathrm{Close}_{n})-\mathrm{SM}\mathrm{A}(\mathrm{Close}_{m})}{\mathrm{SMA}(\mathrm{Close}_{p})\times q}
|
2511.16657v1
|
with_gt
| 8
|
\[
w_i = \{ P_t \mid t \in [20(i-1)+1, 20i] \}.
\]
| 0.808059
| 0.598291
| 0.875
| 0.892857
| 1
|
page_6
|
[
973.2694091796875,
1943.4090576171875,
1604.5711669921875,
2005.1082763671875
] |
w_{i}\,=\,\{P_{t}\,\mid\,t\,\in\,[20(i\,-\,1)\,+\,1,20i]\}.
|
2511.16657v1
|
with_gt
| 9
|
\[
M_i = \{ \max(\text{High}_{w_i}), \max(\text{Close}_{w_i}) \}, \quad
m_i = \{ \min(\text{Low}_{w_i}), \min(\text{Close}_{w_i}) \}.
\]
| 0.718748
| 0.662461
| 0.769912
| 0.77451
| 0.571429
|
page_6
|
[
613.574462890625,
2168.63916015625,
1964.8392333984375,
2227.96435546875
] |
M_{i}=\{\mathrm{max}(\mathrm{High}_{w},),\mathrm{max}(\mathrm{Close}_{w_{i}})\},\quad m_{i}=\{\mathrm{min}(\mathrm{Low}_{w_{i}}),\mathrm{min}(\mathrm{Close}_{w_{i}})\}.
|
2511.16657v1
|
with_gt
| 10
|
\[
L = \text{sort}\left( \bigcup_{i=1}^{10} (M_i \cup m_i) \right).
\]
| 0.800568
| 0.748299
| 0.823529
| 0.844444
| 0.777778
|
page_6
|
[
1045.0712890625,
2332.823974609375,
1531.0760498046875,
2474.712890625
] |
L\simeq\mathrm{sort}\left(\bigcup_{i=1}^{10}(M_{i}\cup m_{i})\right).
|
2511.16657v1
|
repair_no_gt
| null | null | 0.258387
| 0.261538
| 0.228571
| 0.306122
| 0.272727
|
page_6
|
[
1046.169921875,
2332.8408203125,
1531.345703125,
2474.806640625
] |
L\simeq\mathrm{sort}\left(\bigcup_{i=1}^{10}(M_{i}\cup m_{i})\right).
|
2511.16657v1
|
repair_no_gt
| null | null | 0.511082
| 0.424242
| 0.542857
| 0.5
| 0.666667
|
page_6
|
[
1152.0052490234375,
2707.5146484375,
1432.9051513671875,
2760.5859375
] |
\left|{\mathcal D}_{i+1}-{\mathcal A}_{i}\right|\,<\,\delta,
|
2511.16657v1
|
with_gt
| 12
|
\[
\mathcal{G} = \{ G_1, G_2, \dots, G_k \},
\]
| 0.576128
| 0.438095
| 0.666667
| 0.590164
| 0.6
|
page_6
|
[
1079.7393798828125,
2960.88525390625,
1495.3179931640625,
3024.648681640625
] |
\displaystyle{\cal G}=\{G_{1},G_{2},\dots,G_{k}\},
|
2511.16657v1
|
with_gt
| 14
|
\[
\bar{x}_j = \frac{1}{|G_j|} \sum_{x_i \in G_j} x_i.
\]
| 0.810917
| 0.666667
| 0.841121
| 0.87234
| 1
|
page_7
|
[
1114.11181640625,
431.8594665527344,
1461.8114013671875,
559.9429931640625
] |
\bar{x}_{j}=\left.\frac{1}{\left|G_{j}\right|}\sum_{x_{i}\in G_{j}}x_{i}.
|
2511.16657v1
|
repair_no_gt
| null | null | 0.488773
| 0.472222
| 0.544
| 0.504673
| 0.285714
|
page_7
|
[
1102.4364013671875,
681.8671875,
1477.4854736328125,
741.0512084960938
] |
S\,=\,\{\overline{{{x}}}_{1},\overline{{{x}}}_{2},\ast\cdot,\overline{{{x}}}_{k}\}
|
2511.16657v1
|
with_gt
| 16
|
\[
\text{Support}_1 = \max\{ \bar{x}_j \in S \mid \bar{x}_j < P_t \}, \quad
\text{Support}_2 = \max\{ \bar{x}_j \in S \mid \bar{x}_j < \text{Support}_1 \},
\]
| 0.605672
| 0.603261
| 0.649007
| 0.625455
| 0.4
|
page_7
|
[
549.1729736328125,
976.7181396484375,
2025.124755859375,
1038.21826171875
] |
{\mathrm{Support}}_{1}=\operatorname*{max}\{{\vec{x}}_{j}\in S\mid{\vec{x}}_{j}<P_{t}\},\quad{\mathrm{Support}}_{2}=\operatorname*{max}\{{\vec{x}}_{j}\in S\mid{\vec{x}}_{j}<{\mathrm{Support}}_{1}\},
|
2511.16657v1
|
with_gt
| 17
|
\[
\text{Resistance}_1 = \min\{ \bar{x}_j \in S \mid \bar{x}_j > P_t \}, \quad
\text{Resistance}_2 = \min\{ \bar{x}_j \in S \mid \bar{x}_j > \text{Resistance}_1 \}.
\]
| 0.602043
| 0.601036
| 0.64375
| 0.62116
| 0.4
|
page_7
|
[
505.9270935058594,
1158.494873046875,
2085.3837890625,
1218.644287109375
] |
{\mathrm{Resistance}}_{1}=\operatorname*{min}\{{\vec{x}}_{i}\in S\mid{\vec{x}}_{i}>P_{t}\},\quad{\mathrm{Resistance}}_{2}=\operatorname*{min}\{{\vec{x}}_{i}\in S\mid{\vec{x}}_{i}>{\mathrm{Resistance}}_{1}\}.
|
2511.16657v1
|
repair_no_gt
| null | null | 0.515867
| 0.109091
| 0.72
| 0.70903
| 0.533333
|
page_8
|
[
408.7941589355469,
2300.36181640625,
2075.035400390625,
2417.005859375
] |
D(n,h)=\frac{1}{2}\left(\operatorname*{max}_{i\in\left[n+1,n+h\right]}P(i)-P(n)\right)+\frac{1}{2}\left(\operatorname*{min}_{i\in\left[n+1,n+h\right]}P(i)-P(n)\right)+\frac{1}{2}\left(P(n+h)-P(n)\right)
|
2511.16657v1
|
repair_no_gt
| null | null | 0.175327
| 0.210526
| 0.185185
| 0.190476
| 0
|
page_8
|
[
2012.922119140625,
2411.056884765625,
2066.2041015625,
2456.4501953125
] |
({\mathbf{1}})
|
2511.16657v1
|
repair_no_gt
| null | null | 0.466182
| 0.392453
| 0.484018
| 0.44086
| 0.666667
|
page_8
|
[
987.9466552734375,
2922.436279296875,
1496.0771484375,
3054.287109375
] |
Y(n)=\left\{\begin{array}{l l}{{1}}&{{\mathrm{if~}D(n,h)>0}}\\ {{0}}&{{\mathrm{if~}D(n,h)\leq0}}\end{array}\right.
|
2511.16657v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_8
|
[
2012.2508544921875,
2964.544189453125,
2066.090576171875,
3012.71435546875
] |
(2)
|
2511.16657v1
|
repair_no_gt
| null | null | 0.37635
| 0.305195
| 0.295964
| 0.474886
| 0.714286
|
page_9
|
[
929.9833374023438,
1214.66259765625,
1550.6265869140625,
1269.40185546875
] |
\begin{array}{l l l}{{\mathrm{AUC}_{\mathrm{diff}}}}&{{=}}&{{\mathrm{AUC}_{\mathrm{train}}-\mathrm{AUC}_{\mathrm{test}}}}\end{array}
|
2511.16657v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_9
|
[
2012.806396484375,
1216.6064453125,
2065.69140625,
1266.7677001953125
] |
(3)
|
2511.16657v1
|
repair_no_gt
| null | null | 0.270217
| 0.336683
| 0.25
| 0.312727
| 0.066667
|
page_9
|
[
930.9403686523438,
1279.346923828125,
1549.3377685546875,
1334.0821533203125
] |
\Delta(\mathrm{\boldmath{~x~}})_{\mathrm{diff}}\;\;\;\;\longrightarrow\;\;\;\;\Delta(\mathrm{\boldmath{~x~}}_{\mathrm{train}}\;\longrightarrow\;\Lambda\mathrm{\<_{y}~}_{\mathrm{\boldmath{~x~}}\to}^{\mathrm{\boldmath{~v~}}}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.204973
| 0.181818
| 0.222222
| 0.307692
| 0
|
page_9
|
[
2012.901611328125,
1283.531982421875,
2065.595458984375,
1331.931640625
] |
\mathbf{\tau}(4)
|
2511.16657v1
|
repair_no_gt
| null | null | 0.26114
| 0.338624
| 0.3
| 0.16835
| 0.058824
|
page_10
|
[
912.7753295898438,
780.35986328125,
1567.1976318359375,
837.3226928710938
] |
\Delta\lbrack\mathrm{{{\cal{O}_{m i n}}}}\implies\mathrm{{\cal{I}_{\ell}}}\Lambda\S\Lambda\lbrack\mathrm{{\cal{C}_{t r a i n}}},\Lambda\rbrack\Lambda\lbrack\ast\rbrack\mathrm{{\cal{C}_{t e s t}}}\rbrace
|
2511.16657v1
|
repair_no_gt
| null | null | 0.196581
| 0.179487
| 0.222222
| 0.269231
| 0
|
page_10
|
[
2012.973876953125,
784.6788940429688,
2066.295166015625,
834.5150146484375
] |
({\mathfrak{I}})
|
2511.16657v1
|
with_gt
| 3
|
\begin{equation}
\mathrm{Prob}_{\text{weighted}} = \frac{{\mathrm{Prob} - \mathrm{Prob}_{\text{min}}}}{{\mathrm{Prob}_{\text{max}} - \mathrm{Prob}_{\text{min}}}}
\end{equation}
| 0.728253
| 0.763636
| 0.734513
| 0.741071
| 0.571429
|
page_11
|
[
918.5040283203125,
2561.101318359375,
1559.192626953125,
2672.685791015625
] |
{\mathrm{Prob}}_{\mathrm{weighted}}={\frac{{\mathrm{Prob}}-{\mathrm{Prob}}_{\mathrm{min}}}{{\mathrm{Prob}}_{\mathrm{max}}-{\mathrm{Prob}}_{\mathrm{min}}}}
|
2511.16657v1
|
repair_no_gt
| null | null | 0.204973
| 0.181818
| 0.222222
| 0.307692
| 0
|
page_11
|
[
2013.0509033203125,
2594.22216796875,
2065.526611328125,
2642.97607421875
] |
\mathbf{\tau}(6)
|
2511.16657v1
|
with_gt
| 0
|
\begin{equation} \label{eq:acousitcHelm}
-\Delta p - \omega^{2}\kappa^2\left(1-\frac{\gamma}{\omega}\im\right)p = q
\end{equation}
| 0.658771
| 0.682692
| 0.662921
| 0.662722
| 0.5625
|
page_1
|
[
813.31591796875,
1499.24658203125,
1327.2105712890625,
1589.7100830078125
] |
-\Delta p-\omega^{2}\kappa^{2}\left(1-\frac{\gamma}{\omega}\nu\right)p\equiv q
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_1
|
[
299.4112854003906,
1516.3756103515625,
387.2133483886719,
1568.0081787109375
] |
(1.1)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.219903
| 0.181818
| 0.19708
| 0.182628
| 0.5
|
page_3
|
[
536.5584716796875,
1373.981201171875,
1595.64892578125,
1579.3143310546875
] |
H=\frac{1}{h^{2}}\left[-\frac{\frac{1}{6}}{-\frac{2}{3}}\begin{array}{c c c}{{-\frac{2}{3}}}&{{-\frac{1}{6}}}\\ {{-\frac{2}{3}}}&{{\frac{10}{3}}}&{{-\frac{2}{3}}}\\ {{-\frac{1}{6}}}&{{-\frac{2}{3}}}&{{-\frac{1}{6}}}\end{array}\right]\left[\frac{1}{12}\begin{array}{c c c}{{\frac{1}{2}}}&{{\frac{1}{12}}}&{{\frac{1}{12}}}\\ {{\frac{1}{12}}}&{{\frac{1}{3}}}&{{\frac{1}{12}}}\\ {{\frac{1}{12}}}&{{\frac{1}{12}}}&{{-\frac{1}{6}}}\end{array}\right]
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_3
|
[
298.25201416015625,
1450.20263671875,
387.6949462890625,
1502.51318359375
] |
(2.1)
|
2511.16808v1
|
with_gt
| 2
|
\begin{equation}\label{eq:disc4thCompact3D}
H = L - \kappa^2 \omega^2 \left(1-\frac{\gamma}{\omega} \im\right) M
\end{equation}
| 0.597358
| 0.60733
| 0.583851
| 0.586667
| 0.642857
|
page_3
|
[
816.974853515625,
1732.7340087890625,
1317.5357666015625,
1824.945556640625
] |
H=L-\kappa^{2}\omega^{2}\left(1-\frac{\gamma}{\omega}\nu\right)M
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_3
|
[
298.2362976074219,
1751.7244873046875,
389.2129821777344,
1803.2335205078125
] |
(2.2)
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_3
|
[
298.2623596191406,
1751.7745361328125,
388.74200439453125,
1803.038818359375
] |
(2.2)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.313792
| 0.277778
| 0.321429
| 0.309434
| 0.4
|
page_3
|
[
603.4992065429688,
1914.2413330078125,
1528.12109375,
2092.0830078125
] |
{\cal L}=-\frac{1}{6h^{2}}\left[\left[1\begin{array}{c c c}{{1}}&{{1}}&{{\mp}}\\ {{1}}&{{2}}&{{1}}\\ {{1}}&{{1}}&{{1}}\end{array}\right]\left[1\begin{array}{c c c}{{\ 2}}&{{1}}\\ {{\ 2}}&{{2}}&{{1}}\\ {{1}}&{{1}}&{{\mp}}\end{array}\right]\right]
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_3
|
[
298.0514221191406,
1976.43994140625,
388.0951843261719,
2027.9371337890625
] |
(2.4)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.315175
| 0.28496
| 0.294479
| 0.273764
| 0.571429
|
page_3
|
[
681.6275634765625,
2175.45849609375,
1451.159912109375,
2353.080078125
] |
M={\frac{1}{12}}\left[\left[\begin{array}{c c c}{{}}&{{1}}&{{\mp}}\\ {{}}&{{1}}&{{}}\\ {{}}&{{}}&{{}}\\ {{}}&{{}}&{{1}}\end{array}\right]\left[\begin{array}{c c}{{}}&{{1}}\\ {{}}&{{}}\\ {{}}&{{}}\\ {{}}&{{}}\end{array}\right]\ .
|
2511.16808v1
|
repair_no_gt
| null | null | 0.079237
| 0.075758
| 0.074766
| 0.042105
| 0.181818
|
page_3
|
[
298.379638671875,
2237.184814453125,
388.18109130859375,
2288.757568359375
] |
(\ 2.4)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.2078
| 0.188976
| 0.212389
| 0.247423
| 0.166667
|
page_4
|
[
298.87158203125,
488.48919677734375,
387.8479919433594,
540.3455810546875
] |
(2.{\mathfrak{f}})
|
2511.16808v1
|
repair_no_gt
| null | null | 0.230563
| 0.22695
| 0.240741
| 0.24
| 0.181818
|
page_4
|
[
985.8971557617188,
490.5947265625,
1156.6787109375,
542.512451171875
] |
\mathbf{\}A_{h}\mathbf{u}=\mathbf{\partial}\mathbf{q}
|
2511.16808v1
|
repair_no_gt
| null | null | 0.255768
| 0.263804
| 0.28
| 0.29682
| 0.052632
|
page_4
|
[
793.3056640625,
915.827392578125,
1346.1561279296875,
977.95361328125
] |
\mathcal{A}_{H}\otimes_{H}\longrightarrow\mathrm{\small{~\tilde{~}~\tilde{~}~\longrightarrow~}}_{H}\longrightarrow\sum_{\Delta_{\Delta_{\Delta_{\Delta}}}}^{\Delta_{\Delta_{\Delta}}}\Pi
|
2511.16808v1
|
repair_no_gt
| null | null | 0.252297
| 0.25
| 0.243243
| 0.257143
| 0.285714
|
page_4
|
[
975.4103393554688,
1155.9127197265625,
1156.8306884765625,
1207.51806640625
] |
\mathbf{e}=P\mathbf{e}_{H}.
|
2511.16808v1
|
repair_no_gt
| null | null | 0.297777
| 0.279279
| 0.295567
| 0.322581
| 0.3125
|
page_4
|
[
792.0021362304688,
1367.6326904296875,
1335.7452392578125,
1429.9700927734375
] |
T\mathrm{G}_{4}=\mathbb{\varepsilon}^{2}-\delta^{2}\hat{\varepsilon}^{2}+\mu_{3}\alpha\hat{\nu}^{2}+\mu_{3}\hat{\nu}^{2}\hat{\nu}_{4},
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_4
|
[
298.8861083984375,
1373.046630859375,
387.4305725097656,
1424.289794921875
] |
(2.6)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.456971
| 0.448276
| 0.45045
| 0.461538
| 0.5
|
page_5
|
[
896.820556640625,
692.0440063476562,
1241.6939697265625,
750.093505859375
] |
H_{s}={\cal H}-\imath\alpha\omega^{2}M,
|
2511.16808v1
|
repair_no_gt
| null | null | 0.079237
| 0.075758
| 0.074766
| 0.042105
| 0.181818
|
page_5
|
[
298.23944091796875,
696.4129028320312,
388.26068115234375,
747.8347778320312
] |
(\ 2.7)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.45258
| 0.413043
| 0.454545
| 0.452991
| 0.5625
|
page_5
|
[
856.5474853515625,
2069.58935546875,
1275.406982421875,
2164.490478515625
] |
\mathcal{H}_{l o c}:\underline{{{\mp\Gamma}}}\begin{array}{l}{{\mathrm{SUp}}}\\ {{\theta\in T^{h}i\,g h}}\end{array}\mathcal{P}(\widetilde{S}(\theta)).
|
2511.16808v1
|
repair_no_gt
| null | null | 0.478046
| 0.458333
| 0.509259
| 0.526316
| 0.315789
|
page_5
|
[
849.0430297851562,
2611.3037109375,
1286.042236328125,
2709.246337890625
] |
\rho_{l o c}:=\mathrm{~{\frac{\mathrm{Sup}}{\theta{\in}T^{l o w}}}}\,\rho(\overline{{{T{G}}}}\langle\theta)\rangle.
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_5
|
[
298.47930908203125,
2622.34130859375,
389.1498107910156,
2674.7158203125
] |
(2.8)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.364838
| 0.402985
| 0.343612
| 0.378641
| 0.307692
|
page_6
|
[
829.4612426757812,
689.34375,
1308.8636474609375,
748.22216796875
] |
E(\theta)=\,s p a n\left\{\theta,\theta^{\prime},\theta^{\prime\prime},\theta^{\prime\prime\prime}\right\}
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_6
|
[
298.1045837402344,
692.5729370117188,
390.1686706542969,
744.2731323242188
] |
(2.9)
|
2511.16808v1
|
with_gt
| 9
|
\begin{equation} \label{eq:symbolTG}
\widetilde{TG}(\theta) = \widetilde{\mathbf{S}}(\theta)^{\nu_2} (I-\widetilde{P}(\theta) \widetilde{H}_c^{-1}(\theta) \widetilde{R}(\theta) \widetilde{H}(\theta)) \widetilde{\mathbf{S}}(\theta)^{\nu_1}.
\end{equation}
| 0.732504
| 0.635135
| 0.797136
| 0.794118
| 0.642857
|
page_6
|
[
603.7705688476562,
895.3079833984375,
1526.1475830078125,
963.6588134765625
] |
\widehat{T G}(\theta)=\widetilde{\bf S}(\theta)^{\nu_{2}}(I-\widetilde{P}(\theta)\widetilde{H}_{c}^{-1}(\theta)\widetilde{R}(\theta)\widetilde{H}(\theta))\widetilde{\bf S}(\theta)^{\nu_{1}}.
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_6
|
[
298.8012390136719,
906.548828125,
409.5874328613281,
958.564697265625
] |
(2.10)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.454184
| 0.390244
| 0.444444
| 0.38
| 0.833333
|
page_6
|
[
854.8790283203125,
2398.7392578125,
1276.21533203125,
2565.802001953125
] |
R_{b i l i n}={\frac{1}{16}}\left[{\frac{1}{2}}\begin{array}{l l l}{{2}}&{{1}}\\ {{4}}&{{4}}&{{2}}\\ {{1}}&{{2}}&{{1}}\end{array}\right]
|
2511.16808v1
|
repair_no_gt
| null | null | 0.120084
| 0.21875
| 0.063158
| 0.045977
| 0.2
|
page_6
|
[
298.3182678222656,
2455.099609375,
388.06085205078125,
2507.182861328125
] |
\left(3.1\right)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.408943
| 0.153132
| 0.524862
| 0.348624
| 0.833333
|
page_6
|
[
738.1574096679688,
2647.4990234375,
1393.344482421875,
2913.9072265625
] |
R_{b i c u b}={\frac{1}{256}}\left[{\frac{1}{4}}{\begin{array}{l l l l l}{4}&{4}&{6}&{4}&{1}\\ {4}&{16}&{24}&{16}&{4}\\ {6}&{24}&{36}&{24}&{6}\\ {4}&{16}&{24}&{16}&{4}\\ {4}&{4}&{6}&{4}\end{array}}\right].
|
2511.16808v1
|
repair_no_gt
| null | null | 0.106975
| 0.203125
| 0.042105
| 0.045977
| 0.2
|
page_6
|
[
297.64764404296875,
2751.278564453125,
387.93426513671875,
2804.0029296875
] |
\left(3.2\right)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.196096
| 0.205556
| 0.234234
| 0.170347
| 0.066667
|
page_7
|
[
775.3008422851562,
591.9102172851562,
1362.3583984375,
650.7713012695312
] |
P_{\Omega1\longrightarrow2}\stackrel{\longrightarrow}{\longrightarrow}\Phi_{\b\o{i c u b}},\qquad P_{2\longrightarrow1}\stackrel{\textstyle}{\longrightarrow}\stackrel{\textstyle{\cal P}_{3}}{\longrightarrow}\stackrel{\textstyle{\cal P}_{3}}{\i c v u b}
|
2511.16808v1
|
repair_no_gt
| null | null | 0.295217
| 0.348837
| 0.336207
| 0.230415
| 0.1
|
page_7
|
[
775.5849609375,
591.9531860351562,
1363.17138671875,
650.74462890625
] |
P_{\Omega1\longrightarrow2}\implies{P_{b i c u b},\qquad P_{2}}_{\longrightarrow1}\underline{{{P_{2}}}}_{\longrightarrow}\underline{{{P_{b i c a u}}}}
|
2511.16808v1
|
repair_no_gt
| null | null | 0.290884
| 0.367347
| 0.262295
| 0.301887
| 0.153846
|
page_7
|
[
297.9279479980469,
593.5247802734375,
388.21026611328125,
643.9705200195312
] |
\left({{\bar{3}}\cdot{\bar{3}}}\right)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.13818
| 0.230769
| 0.082474
| 0.088889
| 0.181818
|
page_7
|
[
298.44964599609375,
771.7753295898438,
389.7696838378906,
824.5966796875
] |
\left(\Im.4\right)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.332434
| 0.360656
| 0.3379
| 0.320388
| 0.25
|
page_7
|
[
724.8262329101562,
772.0444946289062,
1411.286376953125,
831.51708984375
] |
R_{k\to k+1}\underline{{{1}}}{}_{\mu}i\i n,\quad\Pi_{k+1\to k}\underline{{{-}}}\underline{{{-}}}\underline{{{P}}}_{b i c u b}.
|
2511.16808v1
|
repair_no_gt
| null | null | 0.373364
| 0.168889
| 0.432584
| 0.498316
| 0.5
|
page_7
|
[
629.4073486328125,
1643.93115234375,
1509.006591796875,
1737.4566650390625
] |
R_{t r i l i n}=\frac{1}{4^{3}}\left[1\mathrm{\boldmath~\nabla~}\ 2\mathrm{\boldmath~\1~}\otimes\left[1\mathrm{\boldmath~\nabla~}\ 2\mathrm{\boldmath~\1~}\right]\otimes\left[1\mathrm{\boldmath~\nabla~}\ 2\mathrm{\boldmath~\nabla~}\right]
|
2511.16808v1
|
repair_no_gt
| null | null | 0.196853
| 0.335664
| 0.115385
| 0.159091
| 0.181818
|
page_7
|
[
298.65643310546875,
1665.5244140625,
387.38824462890625,
1717.176513671875
] |
\left(\mathbf{3},\mathbf{f}\right)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.284432
| 0.1133
| 0.291971
| 0.355769
| 0.625
|
page_7
|
[
461.9779357910156,
1844.194580078125,
1758.4383544921875,
1938.627197265625
] |
R_{t r i c u b}=\frac{1}{16^{3}}\left[1\quad4\quad6\quad4\quad1\right]\otimes\left[1\quad4\quad6\quad4\quad1\right]\otimes\left[1\quad4\quad6\quad4\quad4\quad1\right].
|
2511.16808v1
|
repair_no_gt
| null | null | 0.106975
| 0.203125
| 0.042105
| 0.045977
| 0.2
|
page_7
|
[
299.0321350097656,
1865.6292724609375,
387.00775146484375,
1917.57177734375
] |
\left(3.6\right)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.454631
| 0.45098
| 0.442105
| 0.443243
| 0.538462
|
page_7
|
[
921.6295166015625,
2599.343994140625,
1215.4503173828125,
2715.015869140625
] |
\frac{\sum_{H=1}^{m}(\mathrm{nn}z\bigl(H_{c}^{l}\bigr)\bigr)}{\mathrm{nn}z\bigl(H\bigr)}
|
2511.16808v1
|
repair_no_gt
| null | null | 0.207967
| 0.26087
| 0.211765
| 0.225
| 0
|
page_7
|
[
299.10028076171875,
2634.27880859375,
388.83538818359375,
2686.967529296875
] |
({\mathbf{3}}.{\overline{{T}}})
|
2511.16808v1
|
repair_no_gt
| null | null | 0.194264
| 0.158273
| 0.188034
| 0.27451
| 0.166667
|
page_7
|
[
298.7181701660156,
2634.4287109375,
388.0821533203125,
2686.340576171875
] |
({\mathfrak{I}}.{\mathcal{T}})
|
2511.16808v1
|
repair_no_gt
| null | null | 0.417136
| 0.394366
| 0.393939
| 0.40625
| 0.6
|
page_8
|
[
944.3551025390625,
2421.3935546875,
1191.3470458984375,
2484.16796875
] |
H_{i}=V_{i}H V_{i}^{T}
|
2511.16808v1
|
repair_no_gt
| null | null | 0.247107
| 0.331126
| 0.174603
| 0.306306
| 0.166667
|
page_8
|
[
299.1658630371094,
2428.761962890625,
387.6405334472656,
2479.709228515625
] |
\left({\mathfrak{I}}.{\mathfrak{G}}\right)
|
2511.16808v1
|
with_gt
| 18
|
\begin{equation}
H_i\bfe_i = V_i\left(\bfq - H\bfu^{(k)}\right)
\qquad \text{and} \qquad
\bfu^{(k+1)} = \bfu^{(k)} + W_i \bfe_i
\end{equation}
| 0.69061
| 0.671533
| 0.683417
| 0.694301
| 0.769231
|
page_8
|
[
541.8753662109375,
2686.0087890625,
1595.8973388671875,
2769.727783203125
] |
H_{i}{\bf e}_{i}=V_{i}\left({\bf q-}\,H\,{\bf u}^{(k)}\right)\qquad\mathrm{and}\qquad{\bf u}^{(k+1)}={\bf u}^{(k)}+W_{i}{\bf e}_{i}
|
2511.16808v1
|
repair_no_gt
| null | null | 0.106975
| 0.203125
| 0.042105
| 0.045977
| 0.2
|
page_8
|
[
298.85552978515625,
2702.697998046875,
387.8091735839844,
2755.641357421875
] |
\left(3.9\right)
|
2511.16808v1
|
with_gt
| 19
|
\begin{equation}\label{eq:smoother}
S = I - w \left(\sum_{i=1}^m V_i^T W_i H_i^{-1} V_i \right) H
\end{equation}
| 0.574138
| 0.574713
| 0.553191
| 0.552239
| 0.7
|
page_9
|
[
760.9052734375,
1658.055908203125,
1376.0931396484375,
1797.980224609375
] |
S=I-w\left(\sum_{i=1}^{m}V_{i}^{T}W_{i}H_{i}^{-1}V_{i}\right)H
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_9
|
[
298.4886169433594,
1701.3280029296875,
409.6883239746094,
1753.0306396484375
] |
(3.10)
|
2511.16808v1
|
with_gt
| 20
|
\begin{equation}\label{eq:smoother_symbol}
\widetilde{S}(\theta) = 1 - w \left( V^T W \Phi(\theta)^H H_i^{-1} \Phi(\theta) V \right) \widetilde{H}(\theta)
\end{equation}
| 0.638363
| 0.623377
| 0.634686
| 0.641221
| 0.692308
|
page_11
|
[
661.575927734375,
743.0997314453125,
1473.51611328125,
809.8226928710938
] |
\widetilde{S}(\theta)=1-w\left(V^{T}W^{\ }\Phi(\theta)^{H}H_{i}^{-1}\Phi(\theta)^{H}+\widetilde{H}(\theta)^{\ }\right)\widetilde{H}(\theta)
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_11
|
[
298.33837890625,
751.8760375976562,
390.20965576171875,
805.988525390625
] |
(4.1)
|
2511.16808v1
|
with_gt
| 21
|
\begin{equation}\label{eq:Hsymbol}
\widetilde{H} = a + 2b \cos(\theta_1) + 2b \cos(\theta_2) + 4c \cos(\theta_1)\cos(\theta_2).
\end{equation}
| 0.689175
| 0.678414
| 0.712963
| 0.71066
| 0.583333
|
page_11
|
[
599.437744140625,
1270.3809814453125,
1533.3297119140625,
1329.8128662109375
] |
\tilde{H}=a+2b\cos(\theta_{1})+2b\cos(\theta_{2})+4c\cos(\theta_{1})\cos(\theta_{2}).
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_11
|
[
298.2567443847656,
1274.5023193359375,
389.525634765625,
1326.878173828125
] |
(4.2)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.369157
| 0.244576
| 0.318408
| 0.508772
| 0.666667
|
page_11
|
[
506.1001892089844,
1424.236572265625,
1624.8677978515625,
1640.19482421875
] |
\Phi=d i a g\left[1,e^{\l_{\L}\theta_{1}},e^{\l_{\L}\theta_{2}},e^{\l(\theta_{1}+\theta_{2})}\right]\quad\mathrm{and}\quad H_{\L\L}=\left[\begin{array}{l l l}{{a}}&{{b}}&{{b}}&{{c}}\\ {{b}}&{{a}}&{{b}}\\ {{c}}&{{b}}&{{b}}&{{a}}\end{array}\right].
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_11
|
[
298.1316833496094,
1506.1661376953125,
389.0720520019531,
1559.3939208984375
] |
(4.4)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.402082
| 0.344398
| 0.402948
| 0.402204
| 0.571429
|
page_11
|
[
495.0959167480469,
1730.8486328125,
1720.5435791015625,
1997.518310546875
] |
\Phi=d i a g\left[e^{-u\theta_{2}},e^{-\imath\theta_{1}},1,e^{\imath\theta_{1}},e^{\imath\theta_{2}}\right]\quad\mathrm{and}\quad H_{i}=\left[\begin{array}{l l l l}{{e}}&{{c}}&{{b}}&{{c}}\\ {{c}}&{{a}}&{{b}}&{{b}}\\ {{b}}&{{b}}&{{a}}&{{c}}\\ {{c}}&{{b}}&{{c}}&{{a}}\end{array}\right]\ ,
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_11
|
[
297.3470458984375,
1836.695556640625,
389.5015563964844,
1889.4110107421875
] |
(4.4)
|
2511.16808v1
|
with_gt
| 24
|
\begin{equation}\label{eq:skew5lfa}
\Phi = diag\left[e^{-\im(\theta_1 + \theta_2)}, e^{-\im(\theta_2-\theta_1)},1, e^{\im(\theta_2 - \theta_1)}, e^{\im(\theta_1 + \theta_2)} \right]
\end{equation}
| 0.736925
| 0.738889
| 0.755418
| 0.744027
| 0.642857
|
page_11
|
[
588.853515625,
2087.76318359375,
1544.5477294921875,
2176.0859375
] |
\Phi=d i a g\left[e^{-\imath(\theta_{1}+\theta_{2})},e^{-\imath(\theta_{2}-\theta_{1})},1,e^{\imath(\theta_{2}-\theta_{1})},e^{\imath(\theta_{1}+\theta_{2})}\right]
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_11
|
[
298.1009216308594,
2106.619140625,
388.1571350097656,
2159.448486328125
] |
(4.5)
|
2511.16808v1
|
repair_no_gt
| null | null | 0.355471
| 0.252011
| 0.347541
| 0.204255
| 1
|
page_11
|
[
835.7207641601562,
2258.0673828125,
1298.61962890625,
2523.219970703125
] |
H_{i}=\left[\begin{array}{c c c c}{{a}}&{{c}}&{{}}&{{}}\\ {{}}&{{a}}&{{c}}&{{}}\\ {{c}}&{{c}}&{{a}}&{{c}}&{{}}\\ {{}}&{{c}}&{{a}}&{{}}\\ {{}}&{{c}}&{{}}&{{a}}&{{}}\\ {{}}&{{c}}&{{}}&{{}}&{{a}}\end{array}\right].
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_11
|
[
297.73065185546875,
2364.612548828125,
387.8220520019531,
2416.55517578125
] |
(4.6)
|
2511.16808v1
|
with_gt
| 26
|
\begin{equation}
\widetilde{R}(\theta) = \frac{1}{4}\left(1+\cos(\theta_1)\right)\left(1+\cos(\theta_2)\right)
\end{equation}
| 0.597854
| 0.638783
| 0.59
| 0.601093
| 0.5
|
page_12
|
[
739.6994018554688,
695.3617553710938,
1397.4256591796875,
790.9442749023438
] |
\widetilde{\cal{M}}(\theta)\ --\frac{1}{4}\left(1\ +\mathrm{{\bf{COS}}}(\theta_{1})\right)\left(1\ +\mathrm{{\bf{COS}}}(\theta_{2})\right)
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_12
|
[
298.10455322265625,
716.8741455078125,
389.753173828125,
770.8369140625
] |
(4.7)
|
2511.16808v1
|
with_gt
| 27
|
\begin{equation}
\widetilde{R}(\theta) = \frac{1}{64}\left(3+4\cos(\theta_1)+\cos(2\theta_1)\right)\left(3+4\cos(\theta_2)+\cos(2\theta_2)\right).
\end{equation}
| 0.802066
| 0.819444
| 0.821138
| 0.805556
| 0.666667
|
page_12
|
[
501.1246337890625,
913.8964233398438,
1636.0086669921875,
1006.865478515625
] |
\tilde{R}(\theta)=\frac{1}{64}\left(3+4\cos(\theta_{1})+\cos(2\theta_{1})\right)(3+4\cos(\theta_{2})+\cos(2\theta_{2})\right).
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_12
|
[
298.75860595703125,
934.0109252929688,
388.9785461425781,
988.0309448242188
] |
(4.8)
|
2511.16808v1
|
noise
| null | null | -1
| -1
| -1
| -1
| -1
|
page_12
|
[
298.3057861328125,
934.2164306640625,
388.3071594238281,
988.0075073242188
] |
(4.8)
|
2511.16808v1
|
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