francoishernandez
commented
3 years ago but I cann't see 'Gold Score' when I trainslate image to text and
You need to pass the reference target to -tgt for the gold score to be computed. Not sure how it'll go with the image2text task but worth a try.
the accuracy of results(predicted text) is poor
You may look for other issues on the topic, or posts on the forum. I don't have much experience with this task myself.
StephenKyung
da03
Hello, I am following 'Image to Text' example(https://opennmt.net/OpenNMT-py/legacy/im2text.html)
and using provided trained model(http://lstm.seas.harvard.edu/latex/py-model.pt)
but I cann't see 'Gold Score' when I trainslate image to text and the accuracy of results(predicted text) is poor
I calculated edit distance accuracy by using(https://github.com/harvardnlp/im2markup/blob/master/scripts/evaluation/evaluate_text_edit_distance.py)
my command :
CUDA_VISIBLE_DEVICES=7 python ./onmt/bin/translate.py -data_type img -model /data/math/im2latex-100k/model/pre-trained.pt -src_dir /data/math/OpenNMT-py/data/im2text/images -src /data/math/OpenNMT-py/data/im2text/src-test.txt -output /data/math/OpenNMT-py/output/pred.txt -max_length 150 -beam_size 5 -gpu 0 -verbose
results :
[2021-05-06 15:13:05,650 INFO] Translating shard 0. [2021-05-06 15:13:15,737 INFO] SENT 1: None PRED 1: \alpha { 1 } ^ { r } \gamma { 1 } + \ldots + \alpha { N } ^ { r } \gamma { N } = 0 \quad ( r = 1 , . . . , R ) \; , PRED SCORE: -1.0136
[2021-05-06 15:13:15,738 INFO] SENT 2: None PRED 2: \eta = - \frac { 1 } { 2 } \operatorname { l n } \left( \frac { \operatorname { c o s h } \left( \sqrt { 2 } b _ { \infty } \sqrt { 1 + \alpha ^ { 2 } } } { \sqrt { 1 + \alpha ^ { 2 } } } \right) PRED SCORE: -1.6110
[2021-05-06 15:13:15,739 INFO] SENT 3: None PRED 3: P _ { ( 2 ) } ^ { - } = \int \beta d \beta d ^ { 9 } p d ^ { 8 } \lambda \Phi ( - p , - \lambda ) \left( - \frac { p ^ { I } p ^ { I } } { 2 \beta } \right) \Phi ( p , \lambda ) \, . PRED SCORE: -0.2545
[2021-05-06 15:13:15,740 INFO] SENT 4: None PRED 4: \Gamma ( z + 1 ) = \int _ { 0 } ^ { \infty } \ d x \ e ^ { - x } x ^ { z } . PRED SCORE: -0.8213
[2021-05-06 15:13:15,741 INFO] SENT 5: None PRED 5: \frac { d } { d s } { \bf C } { i } = \frac { 1 } { 2 } \epsilon { i j k } { \bf C } { j } \times { \bf C } { k } \, . PRED SCORE: -1.4827
[2021-05-06 15:13:15,741 INFO] SENT 6: None PRED 6: Z = \sum { s p i n s } \prod { c b e s } W ( a | e , f , g | b , c , d | h ) , PRED SCORE: -2.8351
[2021-05-06 15:13:15,742 INFO] SENT 7: None PRED 7: \left{ Q ^ { i } , Q ^ { j } \right} = c ^ { i j } \Gamma ^ { M } C P _ { M } + C c ^ { i j } Z , PRED SCORE: -0.1228
[2021-05-06 15:13:15,743 INFO] SENT 8: None PRED 8: \vec { c } { n , \nu } = \sum { m = n } ^ { 2 n } \frac { \Gamma \left( \nu + m - \frac { D - 1 } { 2 } \right) } { 2 } \, \, \dot { a } _ { 2 ( m - n ) , m } \quad . PRED SCORE: -4.4491
[2021-05-06 15:13:15,744 INFO] SENT 9: None PRED 9: R ( g ) = - f \left[ 3 \left[ ( \operatorname { l n } f ) ^ { 2 } \right] ^ { 2 } + \frac { \Lambda ( x ^ { 5 } ) } { M ^ { 3 } } \right] \, , PRED SCORE: -2.6601
[2021-05-06 15:13:15,745 INFO] SENT 10: None PRED 10: \frac { d } { d s } \frac { 1 } { \Gamma ( - s ) } \right\vert _ { s = 0 } = - 1 , PRED SCORE: -2.0433
[2021-05-06 15:13:15,746 INFO] SENT 11: None PRED 11: \dot { z } { 1 } = - N ^ { z } ( z { 1 } ) = - g ( z { 1 } ) = - \frac { z { 1 } } { P { z } ( z { 2 } - z { 1 } ) } ; \quad \dot { z } { 2 } = - \frac { z { 2 } } { P { z } ( z { 2 } - z { 1 } ) } ; \quad \dot { z } { 2 } = - \frac { z { 2 } } { P { z } ( z { 2 } - z { 1 } ) } ; \quad \dot { z } { PRED SCORE: -1.4384
[2021-05-06 15:13:15,747 INFO] SENT 12: None PRED 12: c { \alpha } = \sum { \beta \in \Lambda _ { R } } \epsilon ( \alpha , \beta ) | \beta + \bar { p } > < \beta + \bar { p } | PRED SCORE: -0.3520
[2021-05-06 15:13:15,748 INFO] SENT 13: None PRED 13: { \cal L } = - \frac { 1 } { 4 } F { \mu \nu } F ^ { \mu \nu } + \bar { \psi } ( i \gamma ^ { \mu } D { \mu } - m ) \psi \, , PRED SCORE: -0.6102
[2021-05-06 15:13:15,808 INFO] SENT 14: None PRED 14: e ^ { i \mathbf { k } \cdot r } = e ^ { i k r \operatorname { c o s } ( \theta - \Theta ) } = \sum { l = - \infty } ^ { \infty } i ^ { l } J { l } ( k r ) \, e ^ { i l ( \theta - \Theta ) } \, , PRED SCORE: -2.3008
[2021-05-06 15:13:15,809 INFO] SENT 15: None PRED 15: i \sqrt { 2 } \partial { - } \chi - g [ \phi , \psi ] = 0 , \quad \partial { - } ^ { 2 } \bar { A } _ { + } - g ^ { 2 } J ^ { + } = 0 . PRED SCORE: -0.3988
[2021-05-06 15:13:15,810 INFO] SENT 16: None PRED 16: \Omega { k } ^ { ( l ) } = \sum { s = 0 } \int d ^ { 3 } y \left( ( - 1 ) ^ { s + 1 } \frac { d ^ { s } } { d t ^ { s } } \phi { k } ^ { [ s ] } ( x , y ) L { i } ^ { ( 0 ) } ( y ) \right) . PRED SCORE: -1.0611
[2021-05-06 15:13:15,811 INFO] SENT 17: None PRED 17: L { g } ^ { ' } ( v ( h ) ) = v ( L { g } h ) = v ( g h ) \, , \; \; \forall g , h \in G , PRED SCORE: -1.8916
[2021-05-06 15:13:15,811 INFO] SENT 18: None PRED 18: \xi ^ { 2 } = \left( \frac { \varepsilon { 1 } - \varepsilon { 2 } } { \varepsilon { 1 } + \varepsilon { 2 } } \right) ^ { 2 } = \left( \frac { \mu { 1 } - \mu { 2 } } { \mu { 1 } + \mu { 2 } } \right) ^ { 2 } , PRED SCORE: -0.1803
[2021-05-06 15:13:15,812 INFO] SENT 19: None PRED 19: R ( e { 1 } ) = \epsilon ^ { - J { 6 } + J { 3 9 } } , \quad R ( e { 2 } ) = \epsilon ^ { J { 2 } - J { 8 9 } } . PRED SCORE: -2.0980
[2021-05-06 15:13:15,813 INFO] SENT 20: None PRED 20: \tilde { \cal E } { m < 0 } = { \cal E } { m < 0 } ( B ) - { \cal E } ( 0 ) = \frac { B ^ { 2 } } { 2 \pi } + \frac { ( e B ) ^ { \frac { 3 } { 2 } } } { m ^ { 2 } } g \left( \frac { e B } { m ^ { 2 } } \right) \; , PRED SCORE: -3.2907
[2021-05-06 15:13:15,814 INFO] SENT 21: None PRED 21: \hat { O } { 2 } ^ { r } \mid 1 > { ( 0 ) } = O { 2 } ^ { r } \mid 0 > { ( 0 ) } \; . PRED SCORE: -0.7837
[2021-05-06 15:13:15,815 INFO] SENT 22: None PRED 22: I ^ { c } = \mp \frac { \pi b \sqrt { 1 - \Lambda a ^ { 2 } } } { 2 G } \ \ , PRED SCORE: -1.2772
[2021-05-06 15:13:15,816 INFO] SENT 23: None PRED 23: g { n } ^ { > } ( r , r ^ { \prime } ) = E { n } K _ { | n , \alpha | } ( \beta r ) , \quad \mathrm { f o r } \; r > r ^ { ' } . PRED SCORE: -2.9471
[2021-05-06 15:13:15,817 INFO] SENT 24: None PRED 24: R ^ { \frac { 1 } { 2 } } ( \theta ) | { a { k } \cdots \frac { 1 } { 2 } , b { 1 } ; \frac { 1 } { 2 } } | n { k } . . . , m { 1 , n { 1 } } \rangle = R { a { 1 } b { 1 } } ^ { \frac 1 2 } ( \theta ) \prod { i = 1 } ^ { k - 1 } ( \theta ) \prod { i = 1 } ^ { k - 1 } ( \theta ) \prod { i = 1 } ^ { k - 1 } ( \theta ) \prod _ { i = 1 } ^ { k - PRED SCORE: -9.5341
[2021-05-06 15:13:15,817 INFO] SENT 25: None PRED 25: Q { 1 } ^ { a b } ( x , y ) \equiv Q { 1 } ^ { a b } + x \, J { 1 } ^ { a b } + y \, K { 1 } ^ { a b } , PRED SCORE: -0.2009
[2021-05-06 15:13:15,818 INFO] SENT 26: None PRED 26: \left( \begin{array} { c c } { \partial _ { \tau } R + \vec { \nabla } \cdot \left( \vec { \nabla } \Theta } { R ^ { 2 } + a ^ { 2 } } \right) ^ { 2 } \right) = 0 , PRED SCORE: -4.0745
[2021-05-06 15:13:15,819 INFO] SENT 27: None PRED 27: \Delta ^ { ( N , 0 ) } ( s ) = - PRED SCORE: -3.6537
[2021-05-06 15:13:15,820 INFO] SENT 28: None PRED 28: { \Psi \circ \mu , f } = ( \overline { { X } } _ { i } f ) \left( Y ^ { i } \Psi \right) \circ \mu \, , PRED SCORE: -0.5954
[2021-05-06 15:13:15,821 INFO] SENT 29: None PRED 29: F { n } ^ { \cal S | \mu { 1 } \ldots \mu { n } } ( \theta { 1 } + \lambda , \ldots , \theta { n } + \lambda ) = e ^ { s \lambda } F { n } ^ { S | \mu { 1 } \ldots \mu { n } } ( \theta { 1 } , \ldots , \theta { n } ) F { n } ^ { S | \mu { 1 } \ldots \mu { n } } ( \theta { 1 } , \ldots , \theta { n } ) F { n } ^ { S | \mu { 1 } \ldots \mu { n } } ( \theta _ { 1 } , \ldots , PRED SCORE: -10.1701
[2021-05-06 15:13:15,822 INFO] SENT 30: None PRED 30: S = S { P h y { s } } ( \Phi ^ { a } , \Phi ^ { a } ) + S _ { T } ( \vartheta ^ { b } , \vartheta ^ { b } , c ^ { \alpha } ) PRED SCORE: -0.7177
[2021-05-06 15:13:17,768 INFO] SENT 31: None PRED 31: { \cal A } \equiv \operatorname { e x p } \left[ \int _ { 0 } ^ { \lambda } d \tilde { \lambda } \, \theta ( \tilde { \lambda } ) \right] \, . PRED SCORE: -0.7727
[2021-05-06 15:13:17,773 INFO] SENT 32: None PRED 32: F { - \frac { 1 } { 2 } } ( x ) = \bar { \epsilon } { 0 } S ( x ) e ^ { - 1 / 2 \phi ( x ) } \; , \qquad F { \frac 1 2 } ( x ) = \bar { \epsilon } { 0 } \gamma _ { \mu } S ( x ) \partial X ^ { \mu } ( x ) e ^ { 1 / 2 \phi ( x ) } , PRED SCORE: -1.2610
[2021-05-06 15:13:17,774 INFO] SENT 33: None PRED 33: \rho ^ { 0 } = \left( \begin{array} { c c } { 0 } & { - i } \ { i } & { 0 } \ \end{array} \right) \; \mathrm { a n d } \; \; \rho ^ { 1 } = \left( \begin{array} { c c } { 0 } & { i } \ { i } & { 0 } \ \end{array} \right) . PRED SCORE: -1.7859
[2021-05-06 15:13:17,775 INFO] SENT 34: None PRED 34: \psi = \sum { i = 0 } ^ { 3 } ( \psi { i } ^ { A } + ( \psi _ { i } ^ { A } ) ^ { c } ) T ^ { A } PRED SCORE: -0.1553
[2021-05-06 15:13:17,776 INFO] SENT 35: None PRED 35: G = e ^ { i \tau L { - 1 } } e ^ { i U ^ { ( 1 ) } L { 1 } } e ^ { i U ^ { ( 2 ) } L { 2 } } e ^ { i U ^ { ( 3 ) } L { 3 } } \ldots e ^ { i U ^ { ( 0 ) } L _ { 0 } } , PRED SCORE: -3.1609
[2021-05-06 15:13:17,777 INFO] SENT 36: None PRED 36: V ( z , \bar { z } ) = e ^ { - q \Phi ( z ) } e ^ { i \alpha \cdot H } e ^ { i ( P { R } X { R } - P { L } . X { L } ) } \ , PRED SCORE: -2.5423
[2021-05-06 15:13:17,778 INFO] SENT 37: None PRED 37: \epsilon { i } = \tau { i } + \rho { i } + \rho { i - 1 } , \quad ( \tau { 3 } = 0 , \, \rho { 0 } = \rho _ { 4 } ) PRED SCORE: -0.8785
[2021-05-06 15:13:17,779 INFO] SENT 38: None PRED 38: s { \infty } ( k ^ { 2 } ) - s { J { a k x } } ( k ^ { 2 } ) \sim O ( J { \mathrm { m a x } } ^ { - 2 } ) . PRED SCORE: -2.4233
[2021-05-06 15:13:17,780 INFO] SENT 39: None PRED 39: A ( u ) \ = \ \mathrm { R e s } | _ { v = u } \left( \frac { 1 } { v - u } \, R ( u , v ) \cdot L ( v ) \right) + \, \frac { 1 } { 2 } \, \zeta ( 2 u ) \, L ( u ) PRED SCORE: -2.2349
[2021-05-06 15:13:17,781 INFO] SENT 40: None PRED 40: \partial { a } ^ { m } \Gamma { i } = \frac { \Gamma ^ { n } } { \lambda { i } } { \delta { n m } \psi { a } ^ { i } - \phi { b } ^ { n } \phi { c } ^ { m } \psi { b } ^ { i } \psi { c } ^ { i } \frac { \psi { c } ^ { i } } { \lambda { i } ^ { 2 } - \lambda { j } ^ { 2 } } \right) PRED SCORE: -4.0750
[2021-05-06 15:13:17,782 INFO] SENT 41: None PRED 41: \int \mathrm { d } ^ { 4 } x { 1 } \; \; \cdots \; \mathrm { d } ^ { 4 } x { n } \; P { 4 } ( x { 1 } , \cdots , x { n } ) \; \Gamma { x { 1 } \cdots x { n } 0 } = 0 PRED SCORE: -2.0407
[2021-05-06 15:13:17,783 INFO] SENT 42: None PRED 42: L = \frac { \dot { x } _ { \mu } ^ { 2 } } { 2 e } + \frac { \lambda } { l } ( e - M ^ { - 1 } \dot { x } ^ { 0 } ) , PRED SCORE: -0.3601
[2021-05-06 15:13:17,783 INFO] SENT 43: None PRED 43: J _ { 2 } ( z ) \times X ^ { + } ( w ) \rightarrow 0 . PRED SCORE: -0.4424
[2021-05-06 15:13:17,784 INFO] SENT 44: None PRED 44: F ( z { 1 2 } ^ { \prime } ) = \bar { K } ( z { 2 } ; g ) F ( z { 1 2 } ) K ( z { 1 } ; g ) PRED SCORE: -0.0415
[2021-05-06 15:13:17,785 INFO] SENT 45: None PRED 45: \xi { i } ^ { * } , p { i } ^ { * } , \quad i = 2 , \ldots , l + 1 PRED SCORE: -0.8730
[2021-05-06 15:13:17,786 INFO] SENT 46: None PRED 46: \varrho { L } - { \cal L } { E } = [ 2 \dot { \Phi } ^ { 2 } ] \ K ^ { \prime } [ \dot { \Phi } ^ { 2 } , \Phi ) - K ( \dot { \Phi } ^ { 2 } , \Phi ) + K ( - \dot { \Phi } ^ { 2 } , \Phi ) . PRED SCORE: -1.2599
[2021-05-06 15:13:17,787 INFO] SENT 47: None PRED 47: K ^ { \prime } = \sqrt { c - 2 f } \ , \quad K ^ { \prime \prime } = - \frac { 1 } { \sqrt { c - 2 f } } \ , PRED SCORE: -1.1396
[2021-05-06 15:13:17,788 INFO] SENT 48: None PRED 48: \kappa { \omega } = \frac { 2 \Gamma ( \Delta { \omega } ) } { \pi \Gamma ( 1 - \Delta { \omega } ) } \left( \frac { \sqrt \pi \Gamma \left( \frac { 1 } { 2 \Gamma } \Delta { \omega } \right) } \right) PRED SCORE: -4.3694
[2021-05-06 15:13:17,788 INFO] SENT 49: None PRED 49: < \frac { 1 } { 2 } , m { s } | \psi { - } ^ { ( \frac { 1 } { 2 } ) } ( g ) > \equiv D { m { s } - \frac { 1 } { 2 } } ^ { ( \frac 1 2 ) } ( g ) = < g , l + \frac { 1 } { 2 } | T { m { s } } ^ { \frac { 1 } { 2 } } | g , l > . PRED SCORE: -3.2746
[2021-05-06 15:13:17,789 INFO] SENT 50: None PRED 50: \sum { l , n } \frac { \mu { p - 1 } \lambda ^ { k + n + l } i ^ { k } p { l } ^ { l } } { k ! n ! ! ( p - l ) ! } \partial { x ^ { i } 1 } \ldots \partial { x ^ { i } n } C { i { 1 } } ^ { 0 } \ldots \partial { a { i } } \phi ^ { i { 1 } } \ldots \partial { x ^ { i } n } C { i _ { 1 } } ^ { 0 } . . . PRED SCORE: -12.3821
[2021-05-06 15:13:17,790 INFO] SENT 51: None PRED 51: D ^ { \mu } \frac { \delta f ( A { \nu } ) } { \delta A { \mu } } = D { \mu } \partial ^ { \mu } ( \partial { \nu } A ^ { \nu } ) PRED SCORE: -0.0920
[2021-05-06 15:13:17,791 INFO] SENT 52: None PRED 52: \delta \chi { \mu \nu } = i b { \mu \nu } , \qquad \delta b _ { \mu \nu } = 0 . PRED SCORE: -0.1502
[2021-05-06 15:13:17,792 INFO] SENT 53: None PRED 53: V { a b } ^ { k } \; \; \; m n = \frac { 1 } { g } \; E { a } ^ { r } \; E { b } ^ { s } \epsilon { r s ( m \; } \delta _ { n ) } ^ { i } . PRED SCORE: -3.8972
[2021-05-06 15:13:17,793 INFO] SENT 54: None PRED 54: f ( r ) = \left( 1 - \frac { m } { 2 r ^ { n - 1 } } \right) ^ { 2 } + \frac { r ^ { 2 } } { l ^ { 2 } } . PRED SCORE: -0.2880
[2021-05-06 15:13:17,794 INFO] SENT 55: None PRED 55: E { 1 2 } \; \; \Phi = 2 \sqrt { ( m + \frac { 1 } { 2 } b r ) ^ { 2 } + p { r } ^ { 2 } + \frac { \ell ( \ell + 1 ) } { r ^ { 2 } } } \; \; \; \Phi , PRED SCORE: -2.0364
[2021-05-06 15:13:17,795 INFO] SENT 56: None PRED 56: T { G } ( - t { , } - t ^ { - 1 } ) = T _ { G ^ { * } } ( - t ^ { - 1 } , - t ) PRED SCORE: -1.0182
[2021-05-06 15:13:17,795 INFO] SENT 57: None PRED 57: d s { 1 1 } ^ { 2 } = d x ^ { + } d x ^ { - } + l { p } ^ { 9 } \frac { p { - } } { r ^ { 7 } } \delta ( x ^ { - } ) d x ^ { - } d x ^ { - } + d x { 1 } ^ { 2 } + ~ \cdots ~ + ~ d x _ { 9 } ^ { 2 } PRED SCORE: -2.2141
[2021-05-06 15:13:17,796 INFO] SENT 58: None PRED 58: F { a b } = \frac { 1 } { 2 } \epsilon { a b c d } F ^ { c d } PRED SCORE: -0.5117
[2021-05-06 15:13:17,797 INFO] SENT 59: None PRED 59: 2 f ^ { 2 } - 4 f ^ { 2 } - g ^ { 2 } ( 1 - \Gamma ) \, , PRED SCORE: -0.0385
[2021-05-06 15:13:17,798 INFO] SENT 60: None PRED 60: ( a ^ { \dagger } L { m n } a ) = a { k } ^ { \dagger } ( L { m n } ) { k l } a { l } = i a { [ m } ^ { \dagger } a { n ] } , \; \; \; \; \; \; ( L { m n } ) { k l } = i ( \delta { m k } \delta { n l } - \delta { n k } \delta _ { m l } ) PRED SCORE: -2.6739
[2021-05-06 15:13:19,334 INFO] SENT 61: None PRED 61: \int d t d ^ { 3 } x \bar { \lambda } \partial ^ { \mu } \gamma _ { \mu } \lambda , PRED SCORE: -0.4218
[2021-05-06 15:13:19,342 INFO] SENT 62: None PRED 62: h = \frac { s \lambda } { 1 + 2 n + s N + | N | } , PRED SCORE: -0.3337
[2021-05-06 15:13:19,344 INFO] SENT 63: None PRED 63: Q = c \sum { i } f { i } ^ { \prime } p ^ { i } + \sum { k } c { k } p ^ { k } f _ { k } + i n f i n i t e \; m o r e . PRED SCORE: -0.8055
[2021-05-06 15:13:19,345 INFO] SENT 64: None PRED 64: \mathrm { T r } \; \operatorname { l o g } ( 1 - \sum { i = 0 } ^ { N } A { i } ) \; = \; \mathrm { T r } \; \operatorname { l o g } ( 1 - \phi ) \; . PRED SCORE: -1.6545
[2021-05-06 15:13:19,346 INFO] SENT 65: None PRED 65: H { i j } ^ { a } = F { i j } ^ { a } - g f { \; \; b c } ^ { a } A { i } ^ { b } A _ { j } ^ { c } , PRED SCORE: -0.9688
[2021-05-06 15:13:19,347 INFO] SENT 66: None PRED 66: \tilde { \rho } { \mathrm { q } } = \sum { \bf k } [ \Lambda { \bf k } ( { \bf q } ) a { \bf k } ( - { \bf q } ) + \Lambda { \bf k } ( - { \bf q } ) a { \bf k } ^ { \dagger } ( { \bf q } ) ] PRED SCORE: -2.7138
[2021-05-06 15:13:19,348 INFO] SENT 67: None PRED 67: { \bf N } ( { \bf p } , { \bf s } ) : = i p { 0 } \nabla { \bf p } - { \frac { 8 \times \bf p } { p { 0 } + m } } , \quad { \bf J } ( { \bf p } , s ) : = - i { \bf p } \times \nabla { \bf p } + { \bf s } : = { \bf L } ( { \bf p } ) + { \bf s } , PRED SCORE: -3.6193
[2021-05-06 15:13:19,349 INFO] SENT 68: None PRED 68: A { \mu } \; = \; \partial { \mu } \varphi + \epsilon { \mu \nu } \, \partial { \nu } \sigma \; . PRED SCORE: -0.8633
[2021-05-06 15:13:19,350 INFO] SENT 69: None PRED 69: C { J } ( \nu { 1 } , \nu { 2 } ) = ( 2 J + \nu { 1 } + \nu { 2 } + 1 ) \frac { \Gamma ( J + 1 ) I ( J + \nu { 1 } + \nu { 2 } + 1 ) } { \Gamma ( J + \nu { 1 } + 1 ) T ( J + \nu _ { 2 } + 1 ) } \, . PRED SCORE: -3.1626
[2021-05-06 15:13:19,351 INFO] SENT 70: None PRED 70: ( \psi \otimes { \zeta , z } \chi ) \mapsto ( e ^ { - u L { - 1 } } \psi \otimes { \zeta + u , z + v } e ^ { - v L { - 1 } } \chi ) , PRED SCORE: -1.3228
[2021-05-06 15:13:19,352 INFO] SENT 71: None PRED 71: u { 0 } ( k , r ) = \sqrt { \frac { \pi } { 2 } } \, i \sqrt { r } \, J { 0 } ( k r ) - \sqrt { \frac { \pi } { 2 } } \, A ( k ) \sqrt { k r } \, H _ { 0 } ^ { ( 1 ) } ( k r ) . PRED SCORE: -0.3653
[2021-05-06 15:13:19,353 INFO] SENT 72: None PRED 72: J { k } = \oint p { k } d q _ { k } , \; \; k = r , \; \theta , \; \phi , PRED SCORE: -0.9435
[2021-05-06 15:13:19,354 INFO] SENT 73: None PRED 73: \delta { \perp } \kappa { 1 } = \kappa { 3 } \kappa { 2 } \Psi { 3 } + 2 \kappa { 2 } \Psi { 2 } { } ^ { \prime } + \kappa { 2 } ^ { \prime } \Psi { 2 } + \Psi { 1 } ^ { \prime \prime } - \left( \kappa { 1 } ^ { 2 } + \kappa { 2 } ^ { ~ 2 } \right) \Psi _ { 1 } \, . PRED SCORE: -2.8010
[2021-05-06 15:13:19,355 INFO] SENT 74: None PRED 74: ( \gamma { \mu } \partial { \mu } + m ) \, \psi ^ { ( b ) } ( x ) = 0 , \hspace { 1 c m } b = 1 , 2 , 3 , 4 PRED SCORE: -1.1217
[2021-05-06 15:13:19,355 INFO] SENT 75: None PRED 75: f _ { \alpha } ( x ) = \left( 4 \operatorname { s i n } ^ { 2 } \frac { x } { 2 } \right) ^ { \alpha } . PRED SCORE: -0.4402
[2021-05-06 15:13:19,356 INFO] SENT 76: None PRED 76: r _ { h } ^ { 2 } = \frac { l ^ { 2 } } { 2 } ( \sqrt { K ^ { 2 } + 4 l ^ { - 2 } \mu } - K ) . PRED SCORE: -0.8208
[2021-05-06 15:13:19,357 INFO] SENT 77: None PRED 77: \mu ^ { \prime \prime } + \left[ n ^ { 2 } - \frac { a ^ { \prime \prime } } { a } \right] \mu = 0 . PRED SCORE: -0.9794
[2021-05-06 15:13:19,358 INFO] SENT 78: None PRED 78: x { \vec { m } } = \frac { 1 } { 2 } ( x { m } + x _ { m + 1 } ) , PRED SCORE: -1.0249
[2021-05-06 15:13:19,359 INFO] SENT 79: None PRED 79: S { i j } \left( \theta \right) = \prod { x , y } \left[ x , y \right] _ { \theta } PRED SCORE: -0.4235
[2021-05-06 15:13:19,360 INFO] SENT 80: None PRED 80: A { d } ( p ^ { 2 } + \omega { n } ^ { 2 } ) ^ { \frac { 1 } { 2 } d - 2 } \left[ \left( 1 + v ^ { 2 } \right) ^ { \frac { 1 } { 2 } d - \frac { 1 } { 2 } } + \frac { \Gamma ( \frac { 1 } { 2 } d - \frac { d } { 2 } ) } { 1 + v ^ { 2 } } \right) ^ { \frac { 1 } { 2 } d - \frac { 1 } { 2 } } + \frac { \Gamma ( \frac { 1 } { 2 } d - \frac { d } { 2 } ) } { 1 + v ^ { 2 } } { } PRED SCORE: -7.1486
[2021-05-06 15:13:19,361 INFO] SENT 81: None PRED 81: \psi _ { c } ( x ) = \gamma ^ { 1 } \psi ^ { * } ( x ) \ , PRED SCORE: -0.7356
[2021-05-06 15:13:19,362 INFO] SENT 82: None PRED 82: L = L ^ { \Lambda } { \bf T } { \Lambda } = d Z ^ { M } L { M } ^ { \Lambda } { \bf T } _ { \Lambda } \, . PRED SCORE: -2.0648
[2021-05-06 15:13:19,363 INFO] SENT 83: None PRED 83: z { t , 0 } ^ { ' ( r ) } \quad = \quad z { t , 0 } ^ { ' ( r ) } \quad = \quad 0 PRED SCORE: -2.2678
[2021-05-06 15:13:19,364 INFO] SENT 84: None PRED 84: d T ( x ) = \left( \begin{array} { c c } { \delta ( x ) 1 { N - k } } & { 0 } \ { 0 } & { - \delta ( x ) 1 { k } } \ \end{array} \right) d x PRED SCORE: -0.8363
[2021-05-06 15:13:19,365 INFO] SENT 85: None PRED 85: 1 - \frac { 2 G M } { \rho } = ( \nabla \rho ) ^ { 2 } \equiv f PRED SCORE: -0.3811
[2021-05-06 15:13:19,366 INFO] SENT 86: None PRED 86: M { g } = M { c { 1 } } M { c { 2 } } M { c { 3 } } M { c { 1 } } M { c { 5 } } M { r = \infty } = 1 PRED SCORE: -0.8456
[2021-05-06 15:13:19,367 INFO] SENT 87: None PRED 87: \delta F \left( \operatorname { s i n } \theta \, d x ^ { 0 } d x ^ { 1 } , 0 , 0 , \epsilon \, d x ^ { 0 } \cdots d x ^ { 3 } \right) . PRED SCORE: -0.7219
[2021-05-06 15:13:19,368 INFO] SENT 88: None PRED 88: S { \mathrm { p a r t , b } } ^ { ( \mathrm { N ) } } = \int d t \sum { \alpha = 1 } ^ { N } \left( \xi { \alpha } ^ { a } \left( E { j , \alpha } ^ { a } \right) ^ { j } + E { 0 , \alpha } ^ { a } \right) - \frac { 1 } { 2 } \xi { \alpha } ^ { a } \xi _ { \alpha } ^ { a } \right) \, . PRED SCORE: -4.5846
[2021-05-06 15:13:19,369 INFO] SENT 89: None PRED 89: \xi = v { 1 } \left( u { 1 } - \kappa v { 2 } \right) + v { 2 } \left( u { 2 } - \kappa v { 1 } \right) . PRED SCORE: -0.1510
[2021-05-06 15:13:19,370 INFO] SENT 90: None PRED 90: U ( r ) = U ( r { 0 } ) + 4 \pi ^ { 2 } K A ( d , \sigma ) \int { r _ { 0 } } ^ { r } d s \frac { s ^ { \sigma - d - 1 } } { \varepsilon ( s ) } . PRED SCORE: -0.1737
[2021-05-06 15:13:21,615 INFO] SENT 91: None PRED 91: | 0 \rangle \rightarrow | 0 \rangle { \beta } = ( 1 + \mathrm { e } ^ { - \beta \epsilon } ) ^ { - 1 / 2 } { | 0 \rangle { a } \otimes b ^ { \dagger } \tilde { b } | 0 \rangle _ { b } } . PRED SCORE: -1.8395
[2021-05-06 15:13:21,616 INFO] SENT 92: None PRED 92: S { E } = \int { 0 } ^ { \tau } d \tau \left( \frac { 1 } { 2 } x { \tau } ^ { 2 } + \frac { 1 } { 2 } W ^ { 2 } ( x ) - \psi ^ { * } [ \partial { \tau } - W ^ { \prime } ( x ) ] \psi \right) PRED SCORE: -0.8081
[2021-05-06 15:13:21,617 INFO] SENT 93: None PRED 93: R { \mu \nu } { } ^ { a } = \partial { \mu } \omega { \nu } ^ { a } - \partial { \nu } \omega { \mu } ^ { a } + \omega { \mu } ^ { a } \, c ^ { } \omega { \nu } ^ { c } - \omega { \nu } ^ { a } . \omega _ { \mu } ^ { c } \, PRED SCORE: -6.8046
[2021-05-06 15:13:21,618 INFO] SENT 94: None PRED 94: M = \int { r \rightarrow \infty } d ^ { p } x r ^ { p / 2 } f ^ { - 1 / 2 } T { t t } = \frac { p m V { p } } { 1 6 \pi G { p + 2 } } . PRED SCORE: -0.3161
[2021-05-06 15:13:21,619 INFO] SENT 95: None PRED 95: j { H W } ( x ) = W { i } ( x ) T ^ { i } \; , \; T ^ { i } \in k e r ( A d ( M _ { - } ) ) PRED SCORE: -0.5463
[2021-05-06 15:13:21,620 INFO] SENT 96: None PRED 96: k { 0 } \sim \omega \sqrt { \frac { g \phi { 0 } } { 2 M ^ { 2 } } } \ll \omega PRED SCORE: -0.1046
[2021-05-06 15:13:21,621 INFO] SENT 97: None PRED 97: Y ( T , U ) = \int { \cal F } \frac { d ^ { 2 } \tau } { \Im \tau } \Gamma { 2 , 2 } ( T , U ) \left( - 6 \left[ \overline { { \Omega } } _ { 2 } - \frac { 1 } { 8 \pi \Im \tau } \right] \frac { \overline { { y } } } { \eta ^ { 2 4 } } - \frac { \overline { { y } } } { 8 } + 1 2 6 \right) ~ , PRED SCORE: -5.9557
[2021-05-06 15:13:21,621 INFO] SENT 98: None PRED 98: P { 0 } S ^ { * } P { 0 } S P { 0 } = P { 0 } = P { 0 0 } { } ^ { - 1 } \quad \mathrm { o n } \quad { \cal H } { \mathrm { p h y s } } . PRED SCORE: -2.9351
[2021-05-06 15:13:21,622 INFO] SENT 99: None PRED 99: \langle \psi { F a } ^ { 1 - a } \mid \phi { F a ^ { \prime } } ^ { 1 - a ^ { \prime } } \rangle _ { t } = \frac { 1 } { 2 } \delta ( a - a ^ { \prime } ) \theta ( t - 1 + a ) \theta ( t - 1 + a ^ { \prime } ) PRED SCORE: -0.6380
[2021-05-06 15:13:21,623 INFO] SENT 100: None PRED 100: L ( z , u { a } , D ) \equiv \int { 0 } ^ { \infty } d \hat { T } \, J ( z , u { a } , \hat { T } , D ) = L { 0 2 } ( z , u _ { B a } ) ^ { 2 - \frac { D } { 2 } } ) PRED SCORE: -3.8088
[2021-05-06 15:13:21,623 INFO] PRED AVG SCORE: -0.0324, PRED PPL: 1.0329