Learning about Language with Normalizing Flows
Graham Neubig Language Technologies Institute, Carnegie Mellon University
Junxian He Chunting Zhou
Di Wang, Daniel Spokoyny, Xian Li, Taylor Berg-Kirkpatrick, Eduard Hovy
Xuezhe Ma
Learning about Language with Normalizing Flows Graham Neubig - - PowerPoint PPT Presentation
Learning about Language with Normalizing Flows Graham Neubig Language Technologies Institute, Carnegie Mellon University Chunting Zhou Junxian He Xuezhe Ma Di Wang, Daniel Spokoyny, Xian Li, Taylor Berg-Kirkpatrick, Eduard Hovy Learning
Graham Neubig Language Technologies Institute, Carnegie Mellon University
Junxian He Chunting Zhou
Di Wang, Daniel Spokoyny, Xian Li, Taylor Berg-Kirkpatrick, Eduard Hovy
Xuezhe Ma
2
Dependency:
DT NN VBD IN DT JJ NN
Parts-of-speech:
The cat sat on a green wall
the cat sat a green wall
の は 上 壁 猫 緑 座った
3
X Y
Supervised Learning
θ
4
X Y
Supervised Learning
θ
5
6
X
(e.g. word2vec, skipthought, BERT)
continuous features?
X Y
Unsupervised
θ
7
X Y
Unsupervised
θ
8
Chunting Zhou, Xuezhe Ma, Di Wang, Graham Neubig
(NAACL 2019)
9
10
apple pear dog cat canine school professor piazza basketball planet earth
⽝ 猫 りんご 梨 教授 学校 ピアッツ 星 地球 バスケット
languages into a single vector space
distance between distributions of discrete vector sets:
"typical" unsupervised generative model
12
dog cat canine
bird
Japanese Space English Space
12
flow
13
X ∼ P(X)
<latexit sha1_base64="x6E2kl/41zLzrUTZRP09f040wUY=">AB8nicbVBNS8NAEJ3Ur1q/qh69LBahXkpSBT0WvXisYGsgDWz3bRLd7NhdyOU0J/hxYMiXv013vw3btsctPXBwO9GWbmRSln2rjut1NaW9/Y3CpvV3Z29/YPqodHXS0zRWiHSC6VH2FNOUtoxzDqZ8qikXE6WM0vp35j09UaSaTBzNJaSjwMGExI9hYKfBRTzOB2nX/vF+tuQ13DrRKvILUoEC7X/3qDSTJBE0M4VjrwHNTE+ZYGUY4nVZ6maYpJmM8pIGlCRZUh/n85Ck6s8oAxVLZSgyaq78nciy0nojIdgpsRnrZm4n/eUFm4uswZ0maGZqQxaI48hINPsfDZixPCJZgoZm9FZIQVJsamVLEheMsvr5Jus+FdNJr3l7XWTRFHGU7gFOrgwRW04A7a0AECEp7hFd4c47w4787HorXkFDPH8AfO5w+SX5Ai</latexit>Z ∼ N(0, I)
<latexit sha1_base64="Z/gR+uIC+bj4zXnm516ybItP9Q=">AB9XicbVBNSwMxEJ31s9avqkcvwSJUkLJbBT0WvehFKtgPbNeSTdM2NMkuSVYpS/+HFw+KePW/ePfmLZ70NYHA4/3ZpiZF0ScaeO6387C4tLympmLbu+sbm1ndvZrekwVoRWSchD1QiwpxJWjXMcNqIFMUi4LQeDC7Hfv2RKs1CeWeGEfUF7knWZQbKz3co5ZmAt0U3GN0fdTO5d2iOwGaJ15K8pCi0s59tTohiQWVhnCsdNzI+MnWBlGOB1lW7GmESYD3KNSyUWVPvJ5OoROrRKB3VDZUsaNF/TyRYaD0Uge0U2PT1rDcW/Oaseme+wmTUWyoJNF3ZgjE6JxBKjDFCWGDy3BRDF7KyJ9rDAxNqisDcGbfXme1EpF76RYuj3Nly/SODKwDwdQA/OoAxXUIEqEFDwDK/w5jw5L8678zFtXDSmT34A+fzB7AykK0=</latexit>Z = fθ(X)
<latexit sha1_base64="IDq8cdH7NY313/u9S3rZypQ+wFI=">AB+nicbVBNS8NAEN3Ur1q/Uj16WSxCvZSkCnoRil48VrAf2Iay2W7apZtN2J0oJfanePGgiFd/iTf/jds2B219MPB4b4aZeX4suAbH+bZyK6tr6xv5zcLW9s7unl3cb+oUZQ1aCQi1faJZoJL1gAOgrVjxUjoC9byR9dTv/XAlOaRvINxzLyQDCQPOCVgpJ5dvMeXOilXRgyIJNy+6Rnl5yKMwNeJm5GSihDvWd/dfsRTUImgQqidcd1YvBSoBTwSaFbqJZTOiIDFjHUElCpr10dvoEHxulj4NImZKAZ+rviZSEWo9D3SGBIZ60ZuK/3mdBIL+UyToBJOl8UJAJDhKc54D5XjIYG0Ko4uZWTIdEQomrYIJwV18eZk0qxX3tFK9PSvVrI48ugQHaEyctE5qEbVEcNRNEjekav6M16sl6sd+tj3pqzspkD9AfW5w/CxZMI</latexit>X = f −1
θ
(Z)
<latexit sha1_base64="/fc4xHZsNC/YMH6XAT25PjHrcA=">AB/3icbVDLSgNBEJyNrxhfq4IXL4NBiAfDbhT0IgS9eIxgHpisYXYymwyZfTDTK4R1D/6KFw+KePU3vPk3TpI9aGJBQ1HVTXeXGwmuwLK+jdzC4tLySn61sLa+sblbu80VBhLyuo0FKFsuUQxwQNWBw6CtSLJiO8K1nSHV2O/+cCk4mFwC6OIOT7pB9zjlICWuZeC19g7z45tNu0oEBA5KW7o6ZtEqWxPgeWJnpIgy1LrmV6cX0thnAVBlGrbVgROQiRwKlha6MSKRYQOSZ+1NQ2Iz5STO5P8aFWetgLpa4A8ET9PZEQX6mR7+pOn8BAzXpj8T+vHYN37iQ8iGJgAZ0u8mKBIcTjMHCPS0ZBjDQhVHJ9K6YDIgkFHVlBh2DPvjxPGpWyfVKu3JwWq5dZHm0jw5QCdnoDFXRNaqhOqLoET2jV/RmPBkvxrvxMW3NGdnMLvoD4/MHL4GU7g=</latexit>pθ(x) = pZ(fθ(x))
∂x )
Change of variable formula: Normalizing Flow: A series of such invertible transformations f
<latexit sha1_base64="aj1VrWgqSrqkgqJ/bLgtsTmRK/w=">AB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm/GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlZtgvV9yqOwdZJV5OKpCj0S9/9QYxSyOUhgmqdzE+NnVBnOBE5LvVRjQtmYDrFrqaQRaj+bHzolZ1YZkDBWtqQhc/X3REYjrSdRYDsjakZ62ZuJ/3nd1ITXfsZlkhqUbLEoTAUxMZl9TQZcITNiYglitbCRtRZmx2ZRsCN7y6ukXat6F9Va87JSv8njKMIJnMI5eHAFdbiDBrSAcIzvMKb8+i8O/Ox6K14OQzx/AHzucPzD+M7g=</latexit>Intuitively, prevents degenerative mapping of everything to zero vector
14
dog cat canine
bird
Japanese Space English Space
Notations:
x ∈ Rd y ∈ Rd
,
: denote vectors in the src and tgt embedding space
fxy, fyx
: denote src->tgt, and tgt-src mapping functions : denote an actual word in src and tgt vocabularies
xi, yj
space: Gaussian mixture model
15
⽝ 猫 ⿃
16
xi ∼ π(xi) x ∼ ˜ p(x|xi)
vector in the target space.
fxy
fxy(·) = Wxy·
⽝ 猫 ⿃
dog cat canine bird
that the transformation is close to orthogonal
advantage of the fact that identical strings are usually the same word in both languages
similarity local scaling (CSLS)
17
(Conneau el al., 2017)
pl, tr
18
19
70 73.75 77.5 81.25 85 en-de de-en en-es es-en
Procrustes(R) MUSE (U+R) SL-unsup-ID DeMa-BWE
20
16.25 32.5 48.75 65 en-et et-en en-el el-en en-ja ja-en
Procrustes(R) MUSE (U+R) DeMa-BWE
Junxian He, Graham Neubig, Taylor Berg-Kirkpatrick
(EMNLP 2018)
21
z1
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x2
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z1
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[Lin et al. 2015]
x2
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z1
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<latexit sha1_base64="8oxgnabmEamXCM6ELWdhWTrt8c=">ACHicZVA9SwNBEJ3z2/gVFSubwyhECOFio3ZBG0sFzwgmhL3NnlncvT1254Rw3G8RW+2tbazEVvBnWNi7d0lh4sAyb9+8Wd6+IBbcoOd9OVPTM7Nz8wuLpaXldW18vrGlVGJpsynSih9HRDBI+YjxwFu41IzIQrBXcnebz1j3ThqvoEgcx60hyG/GQU4KW6pa3wm7aDmTajvs8y6o5ZNl+t1zx6l5R7n/QGIFKc/fn5RUAzrvl73ZP0USyCKkgxtw0vBg7KdHIqWBZqZ0YFhN6R27ZjYURkcx0sJ+5u5ZpueGStsToVuwfzdSIo0k2LfKvJmxWc6gUsLUrAr7Mm/5M8XdDGRQC2QtF2kTmgkjGB51Uh7FCbKIDn2EiXBRuXlUbo9rRlEMLCBUc/sVl/aJhRtoCWbUWMykf/AP6gf170Lm9UJDGsBtmEHqtCAQ2jCGZyDxRSeIQneHYenDfn3fkYSqec0c4mjJXz+QtiKWs</latexit><latexit sha1_base64="JbCPJ2fHAGZa8Ebw6DTj/vFjWE=">ACHicZVDLSgMxFM34rK2PqrhyM1iFCqXMuF3RTcuK1hbaEvJpJk2NJkMyZ1CGeZbxK3u/QFxJW4FP8OFrs20Xdj2Qrgn54bTo4XcqbBcb6speWV1bX1zEY2t7m1vZPf3bvXMlKE1ojkUjU8rClnAa0BA04boaJYeJzWvcF1Oq8PqdJMBncwCmlb4F7AfEYwGKqTP/A7csTcSvsyQpAmp518wSk747IXgTsFhcrxz8vrMPdb7eS/W1JIkEDIBxr3XSdENoxVsAIp0m2FWkaYjLAPdo0MC6nY8tp/YJ4bp2r5U5gRgj9n/GzEWmDoG2Xa9MwsZUBKrktGBX2RtvSZ8V2PhFfyRCkVKe3rOSPgX7RjFoQR0IBMfPgRt0HaVR2lylKgI8MwEQx8xWb9LHCBEygWZORO5/IqidlS/Lzq3J6gpNKoMO0REqIhedowq6QVUQwTF6BE9oWfrwXqz3q2PiXTJmu7so5myPv8Ah3SnJg=</latexit><latexit sha1_base64="JbCPJ2fHAGZa8Ebw6DTj/vFjWE=">ACHicZVDLSgMxFM34rK2PqrhyM1iFCqXMuF3RTcuK1hbaEvJpJk2NJkMyZ1CGeZbxK3u/QFxJW4FP8OFrs20Xdj2Qrgn54bTo4XcqbBcb6speWV1bX1zEY2t7m1vZPf3bvXMlKE1ojkUjU8rClnAa0BA04boaJYeJzWvcF1Oq8PqdJMBncwCmlb4F7AfEYwGKqTP/A7csTcSvsyQpAmp518wSk747IXgTsFhcrxz8vrMPdb7eS/W1JIkEDIBxr3XSdENoxVsAIp0m2FWkaYjLAPdo0MC6nY8tp/YJ4bp2r5U5gRgj9n/GzEWmDoG2Xa9MwsZUBKrktGBX2RtvSZ8V2PhFfyRCkVKe3rOSPgX7RjFoQR0IBMfPgRt0HaVR2lylKgI8MwEQx8xWb9LHCBEygWZORO5/IqidlS/Lzq3J6gpNKoMO0REqIhedowq6QVUQwTF6BE9oWfrwXqz3q2PiXTJmu7so5myPv8Ah3SnJg=</latexit>ei ∼ N(µzi, Σzi)
<latexit sha1_base64="8CLMr+o0dZvNiJKf8rFwAP/jQ=">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</latexit><latexit sha1_base64="N3CijJIqFBowULdbrh+WNrhPgX8=">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</latexit><latexit sha1_base64="N3CijJIqFBowULdbrh+WNrhPgX8=">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</latexit>zi ∼
<latexit sha1_base64="A0vAn9BPw9kDXHS9rkuB7rpTAE=">ACDnicZVDLTgIxFO3gC/GFunTSExcEDJjTNQd0Y1LTEQwMCGd0oGdjp75jghI8wbvU7XBm3/oKf4R/YgVkI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKWtSJZRuB8QwSPWBA6CtWPNiAwEawWjm2zemLacBXdwzhmviSDiIecErDU43OP467hEvfKFbfmTgsvAy8HFZRXo1f+7fYVTSLgApiTMdzY/BToFTwSalbmJYTOiIDFjHwohIZvx0aniCTyzTx6HS9kSAp+z/jZRIwkMrTJrZm6WMaCUMFWrgqHMWvbM9G7GMqgGspqJtAnNghEIL/2UR3ECLKIzH2EiMCichYP7XDMKYmwBoZrbr2A6JpQsBGWbEbeYiLoHlWu6q5d+eV+nUeVhEdoWN0ijx0geroFjVQE1Ek0St6Q+/Oi/PhfDpfM2nByXcO0Vw539MaJ0J</latexit><latexit sha1_base64="A0vAn9BPw9kDXHS9rkuB7rpTAE=">ACDnicZVDLTgIxFO3gC/GFunTSExcEDJjTNQd0Y1LTEQwMCGd0oGdjp75jghI8wbvU7XBm3/oKf4R/YgVkI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKWtSJZRuB8QwSPWBA6CtWPNiAwEawWjm2zemLacBXdwzhmviSDiIecErDU43OP467hEvfKFbfmTgsvAy8HFZRXo1f+7fYVTSLgApiTMdzY/BToFTwSalbmJYTOiIDFjHwohIZvx0aniCTyzTx6HS9kSAp+z/jZRIwkMrTJrZm6WMaCUMFWrgqHMWvbM9G7GMqgGspqJtAnNghEIL/2UR3ECLKIzH2EiMCichYP7XDMKYmwBoZrbr2A6JpQsBGWbEbeYiLoHlWu6q5d+eV+nUeVhEdoWN0ijx0geroFjVQE1Ek0St6Q+/Oi/PhfDpfM2nByXcO0Vw539MaJ0J</latexit><latexit sha1_base64="A0vAn9BPw9kDXHS9rkuB7rpTAE=">ACDnicZVDLTgIxFO3gC/GFunTSExcEDJjTNQd0Y1LTEQwMCGd0oGdjp75jghI8wbvU7XBm3/oKf4R/YgVkI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKWtSJZRuB8QwSPWBA6CtWPNiAwEawWjm2zemLacBXdwzhmviSDiIecErDU43OP467hEvfKFbfmTgsvAy8HFZRXo1f+7fYVTSLgApiTMdzY/BToFTwSalbmJYTOiIDFjHwohIZvx0aniCTyzTx6HS9kSAp+z/jZRIwkMrTJrZm6WMaCUMFWrgqHMWvbM9G7GMqgGspqJtAnNghEIL/2UR3ECLKIzH2EiMCichYP7XDMKYmwBoZrbr2A6JpQsBGWbEbeYiLoHlWu6q5d+eV+nUeVhEdoWN0ijx0geroFjVQE1Ek0St6Q+/Oi/PhfDpfM2nByXcO0Vw539MaJ0J</latexit>Markov Structure
xi ∼
<latexit sha1_base64="4XmkafD4EWeU6wrjePkY8qE6No=">ACE3icZVDLTgIxFO3gC/GFunTSExcEDIYE3VHdOMSE0dIGCSd0oGdjp7xjJhN8wbvU7XBm3foCf4R/YGVgI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKfOoEkq3A2KY4BHzgINg7VgzIgPBWsHoJpu3npg2XEX3MI5ZV5JBxENOCVjq0Q9k+jzpcewbLnGvXHFrbl54GdRnoIJm1eyVf/2+olkEVBjOnU3Ri6KdHAqWCTkp8YFhM6IgPWsTAikplumrue4BPL9HGotD0R4Jz9v5ESaSBoVmzczNMgaUEqZqVTCUWcueye9mLINqIKuZSJvQLBiB8LKb8ihOgEV06iNMBAaFs4Rwn2tGQYwtIFRz+xVMh0QTCjbHks2ovpjIMvDOalc19+680riehVER+gYnaI6ukANdIuayEMUafSK3tC78+J8OJ/O1RacGY7h2iunO8/lwWfXA=</latexit><latexit sha1_base64="4XmkafD4EWeU6wrjePkY8qE6No=">ACE3icZVDLTgIxFO3gC/GFunTSExcEDIYE3VHdOMSE0dIGCSd0oGdjp7xjJhN8wbvU7XBm3foCf4R/YGVgI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKfOoEkq3A2KY4BHzgINg7VgzIgPBWsHoJpu3npg2XEX3MI5ZV5JBxENOCVjq0Q9k+jzpcewbLnGvXHFrbl54GdRnoIJm1eyVf/2+olkEVBjOnU3Ri6KdHAqWCTkp8YFhM6IgPWsTAikplumrue4BPL9HGotD0R4Jz9v5ESaSBoVmzczNMgaUEqZqVTCUWcueye9mLINqIKuZSJvQLBiB8LKb8ihOgEV06iNMBAaFs4Rwn2tGQYwtIFRz+xVMh0QTCjbHks2ovpjIMvDOalc19+680riehVER+gYnaI6ukANdIuayEMUafSK3tC78+J8OJ/O1RacGY7h2iunO8/lwWfXA=</latexit><latexit sha1_base64="4XmkafD4EWeU6wrjePkY8qE6No=">ACE3icZVDLTgIxFO3gC/GFunTSExcEDIYE3VHdOMSE0dIGCSd0oGdjp7xjJhN8wbvU7XBm3foCf4R/YGVgI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKfOoEkq3A2KY4BHzgINg7VgzIgPBWsHoJpu3npg2XEX3MI5ZV5JBxENOCVjq0Q9k+jzpcewbLnGvXHFrbl54GdRnoIJm1eyVf/2+olkEVBjOnU3Ri6KdHAqWCTkp8YFhM6IgPWsTAikplumrue4BPL9HGotD0R4Jz9v5ESaSBoVmzczNMgaUEqZqVTCUWcueye9mLINqIKuZSJvQLBiB8LKb8ihOgEV06iNMBAaFs4Rwn2tGQYwtIFRz+xVMh0QTCjbHks2ovpjIMvDOalc19+680riehVER+gYnaI6ukANdIuayEMUafSK3tC78+J8OJ/O1RacGY7h2iunO8/lwWfXA=</latexit>fφ(ei)
<latexit sha1_base64="ISFMuiBWVv5rfvJnq9uM8Osfvo=">ACHnicZVBNS8NAEN34WetX1YMHL8EiVCglEUG9Fb14rGBsoS1hs920S3ezYXcilJAfI171d3gSr/oz/Adu0h5sO7DM2zdvhpkXxJxpcJwfa2V1bX1js7RV3t7Z3duvHBw+aZkoQj0iuVSdAGvKWUQ9YMBpJ1YUi4DTdjC+y+vtZ6o0k9EjTGLaF3gYsZARDIbyK8ehn/YCkfbiEcuyWg5p5rNzv1J1Gk4R9jJwZ6CKZtHyK7+9gSJoBEQjrXuk4M/RQrYITrNxLNI0xGeMh7RoYUF1Py0OyOwzwzsUCrzIrAL9n9HioUWGEZGmSc9V8sZkJLrulHBSOQpH1P89UQE9UDUc5HSoV5YBMLrfsqiOAEakekeYcJtkHZulj1gihLgEwMwUcycYpMRVpiAsbRsPHIXHVkG3kXjpuE8XFabtzOzSugEnaIactEVaqJ71EIeIihDr+gNvVsv1of1aX1NpSvWrOcIzYX1/QfnyqO9</latexit><latexit sha1_base64="ISFMuiBWVv5rfvJnq9uM8Osfvo=">ACHnicZVBNS8NAEN34WetX1YMHL8EiVCglEUG9Fb14rGBsoS1hs920S3ezYXcilJAfI171d3gSr/oz/Adu0h5sO7DM2zdvhpkXxJxpcJwfa2V1bX1js7RV3t7Z3duvHBw+aZkoQj0iuVSdAGvKWUQ9YMBpJ1YUi4DTdjC+y+vtZ6o0k9EjTGLaF3gYsZARDIbyK8ehn/YCkfbiEcuyWg5p5rNzv1J1Gk4R9jJwZ6CKZtHyK7+9gSJoBEQjrXuk4M/RQrYITrNxLNI0xGeMh7RoYUF1Py0OyOwzwzsUCrzIrAL9n9HioUWGEZGmSc9V8sZkJLrulHBSOQpH1P89UQE9UDUc5HSoV5YBMLrfsqiOAEakekeYcJtkHZulj1gihLgEwMwUcycYpMRVpiAsbRsPHIXHVkG3kXjpuE8XFabtzOzSugEnaIactEVaqJ71EIeIihDr+gNvVsv1of1aX1NpSvWrOcIzYX1/QfnyqO9</latexit><latexit sha1_base64="ISFMuiBWVv5rfvJnq9uM8Osfvo=">ACHnicZVBNS8NAEN34WetX1YMHL8EiVCglEUG9Fb14rGBsoS1hs920S3ezYXcilJAfI171d3gSr/oz/Adu0h5sO7DM2zdvhpkXxJxpcJwfa2V1bX1js7RV3t7Z3duvHBw+aZkoQj0iuVSdAGvKWUQ9YMBpJ1YUi4DTdjC+y+vtZ6o0k9EjTGLaF3gYsZARDIbyK8ehn/YCkfbiEcuyWg5p5rNzv1J1Gk4R9jJwZ6CKZtHyK7+9gSJoBEQjrXuk4M/RQrYITrNxLNI0xGeMh7RoYUF1Py0OyOwzwzsUCrzIrAL9n9HioUWGEZGmSc9V8sZkJLrulHBSOQpH1P89UQE9UDUc5HSoV5YBMLrfsqiOAEakekeYcJtkHZulj1gihLgEwMwUcycYpMRVpiAsbRsPHIXHVkG3kXjpuE8XFabtzOzSugEnaIactEVaqJ71EIeIihDr+gNvVsv1of1aX1NpSvWrOcIzYX1/QfnyqO9</latexit>Point mass at
xi = fφ(ei)
<latexit sha1_base64="270VJLD7gt0vH7AtNf4cVJpk6VA=">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</latexit><latexit sha1_base64="PuNspGjpc2SeVmkDWfr5ab2W0=">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</latexit><latexit sha1_base64="PuNspGjpc2SeVmkDWfr5ab2W0=">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</latexit>Neural Projector
x
f −1(e; φ)
<latexit sha1_base64="0TvUX8MzRC5izm1cmvW9PX4J8iQ=">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</latexit><latexit sha1_base64="0TvUX8MzRC5izm1cmvW9PX4J8iQ=">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</latexit><latexit sha1_base64="0TvUX8MzRC5izm1cmvW9PX4J8iQ=">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</latexit>24
[Klein and Manning 2004]
NN
cat
VBD
stopped
NN
dog
IN
in
DT DT NN
The a Paris
25
[Klein and Manning 2004]
NN
VBD
NN IN DT DT NN
26
Dependency Parse Induction from POS
NN
VBD
NN IN DT DT NN
27
z1
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x3
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<latexit sha1_base64="OUe9NQ3ny9IilmHPU3ONQ4TtfRo=">ACDXicZVDLSgMxFM3UV62vqks3g0VwUcpMEdRd0Y3LCo4tEPJpJk2NJkMyR2xDP0Hcavf4Urc+g1+hn9gZjoL214I9+Tc8PJCWLONDjOj1VaW9/Y3CpvV3Z29/YPqodHj1omilCPSC5VN8CachZRDxhw2o0VxSLgtBNMbrN54kqzWT0ANOY+gKPIhYygsFQ3X4g0ufZoDmo1pyGk5e9CtwC1FBR7UH1tz+UJBE0AsKx1j3XicFPsQJGOJ1V+omMSYTPKI9AyMsqPbT3O/MPjPM0A6lMicCO2f/b6RYaIFhbJRZ0wuzjAEpua4bFYxF1rJn8rueiqAeiHomUjrUS0YgvPJTFsUJ0IjMfYQJt0HaWTb2kClKgE8NwEQx8xWbjLHCBEyCFZORu5zIKvCajeuGc39Ra90UYZXRCTpF58hFl6iF7lAbeYgjl7RG3q3XqwP69P6mktLVrFzjBbK+v4DLZmdBA=</latexit><latexit sha1_base64="OUe9NQ3ny9IilmHPU3ONQ4TtfRo=">ACDXicZVDLSgMxFM3UV62vqks3g0VwUcpMEdRd0Y3LCo4tEPJpJk2NJkMyR2xDP0Hcavf4Urc+g1+hn9gZjoL214I9+Tc8PJCWLONDjOj1VaW9/Y3CpvV3Z29/YPqodHj1omilCPSC5VN8CachZRDxhw2o0VxSLgtBNMbrN54kqzWT0ANOY+gKPIhYygsFQ3X4g0ufZoDmo1pyGk5e9CtwC1FBR7UH1tz+UJBE0AsKx1j3XicFPsQJGOJ1V+omMSYTPKI9AyMsqPbT3O/MPjPM0A6lMicCO2f/b6RYaIFhbJRZ0wuzjAEpua4bFYxF1rJn8rueiqAeiHomUjrUS0YgvPJTFsUJ0IjMfYQJt0HaWTb2kClKgE8NwEQx8xWbjLHCBEyCFZORu5zIKvCajeuGc39Ra90UYZXRCTpF58hFl6iF7lAbeYgjl7RG3q3XqwP69P6mktLVrFzjBbK+v4DLZmdBA=</latexit><latexit sha1_base64="OUe9NQ3ny9IilmHPU3ONQ4TtfRo=">ACDXicZVDLSgMxFM3UV62vqks3g0VwUcpMEdRd0Y3LCo4tEPJpJk2NJkMyR2xDP0Hcavf4Urc+g1+hn9gZjoL214I9+Tc8PJCWLONDjOj1VaW9/Y3CpvV3Z29/YPqodHj1omilCPSC5VN8CachZRDxhw2o0VxSLgtBNMbrN54kqzWT0ANOY+gKPIhYygsFQ3X4g0ufZoDmo1pyGk5e9CtwC1FBR7UH1tz+UJBE0AsKx1j3XicFPsQJGOJ1V+omMSYTPKI9AyMsqPbT3O/MPjPM0A6lMicCO2f/b6RYaIFhbJRZ0wuzjAEpua4bFYxF1rJn8rueiqAeiHomUjrUS0YgvPJTFsUJ0IjMfYQJt0HaWTb2kClKgE8NwEQx8xWbjLHCBEyCFZORu5zIKvCajeuGc39Ra90UYZXRCTpF58hFl6iF7lAbeYgjl7RG3q3XqwP69P6mktLVrFzjBbK+v4DLZmdBA=</latexit>29
ei ∼ N(µzi, Σzi)
<latexit sha1_base64="8CLMr+o0dZvNiJKf8rFwAP/jQ=">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</latexit><latexit sha1_base64="N3CijJIqFBowULdbrh+WNrhPgX8=">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</latexit><latexit sha1_base64="N3CijJIqFBowULdbrh+WNrhPgX8=">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</latexit>xi = fφ(ei)
<latexit sha1_base64="270VJLD7gt0vH7AtNf4cVJpk6VA=">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</latexit><latexit sha1_base64="PuNspGjpc2SeVmkDWfr5ab2W0=">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</latexit><latexit sha1_base64="PuNspGjpc2SeVmkDWfr5ab2W0=">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</latexit>zi ∼
<latexit sha1_base64="A0vAn9BPw9kDXHS9rkuB7rpTAE=">ACDnicZVDLTgIxFO3gC/GFunTSExcEDJjTNQd0Y1LTEQwMCGd0oGdjp75jghI8wbvU7XBm3/oKf4R/YgVkI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKWtSJZRuB8QwSPWBA6CtWPNiAwEawWjm2zemLacBXdwzhmviSDiIecErDU43OP467hEvfKFbfmTgsvAy8HFZRXo1f+7fYVTSLgApiTMdzY/BToFTwSalbmJYTOiIDFjHwohIZvx0aniCTyzTx6HS9kSAp+z/jZRIwkMrTJrZm6WMaCUMFWrgqHMWvbM9G7GMqgGspqJtAnNghEIL/2UR3ECLKIzH2EiMCichYP7XDMKYmwBoZrbr2A6JpQsBGWbEbeYiLoHlWu6q5d+eV+nUeVhEdoWN0ijx0geroFjVQE1Ek0St6Q+/Oi/PhfDpfM2nByXcO0Vw539MaJ0J</latexit><latexit sha1_base64="A0vAn9BPw9kDXHS9rkuB7rpTAE=">ACDnicZVDLTgIxFO3gC/GFunTSExcEDJjTNQd0Y1LTEQwMCGd0oGdjp75jghI8wbvU7XBm3/oKf4R/YgVkI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKWtSJZRuB8QwSPWBA6CtWPNiAwEawWjm2zemLacBXdwzhmviSDiIecErDU43OP467hEvfKFbfmTgsvAy8HFZRXo1f+7fYVTSLgApiTMdzY/BToFTwSalbmJYTOiIDFjHwohIZvx0aniCTyzTx6HS9kSAp+z/jZRIwkMrTJrZm6WMaCUMFWrgqHMWvbM9G7GMqgGspqJtAnNghEIL/2UR3ECLKIzH2EiMCichYP7XDMKYmwBoZrbr2A6JpQsBGWbEbeYiLoHlWu6q5d+eV+nUeVhEdoWN0ijx0geroFjVQE1Ek0St6Q+/Oi/PhfDpfM2nByXcO0Vw539MaJ0J</latexit><latexit sha1_base64="A0vAn9BPw9kDXHS9rkuB7rpTAE=">ACDnicZVDLTgIxFO3gC/GFunTSExcEDJjTNQd0Y1LTEQwMCGd0oGdjp75jghI8wbvU7XBm3/oKf4R/YgVkI3KS5p+e25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evH/wYFSiKWtSJZRuB8QwSPWBA6CtWPNiAwEawWjm2zemLacBXdwzhmviSDiIecErDU43OP467hEvfKFbfmTgsvAy8HFZRXo1f+7fYVTSLgApiTMdzY/BToFTwSalbmJYTOiIDFjHwohIZvx0aniCTyzTx6HS9kSAp+z/jZRIwkMrTJrZm6WMaCUMFWrgqHMWvbM9G7GMqgGspqJtAnNghEIL/2UR3ECLKIzH2EiMCichYP7XDMKYmwBoZrbr2A6JpQsBGWbEbeYiLoHlWu6q5d+eV+nUeVhEdoWN0ijx0geroFjVQE1Ek0St6Q+/Oi/PhfDpfM2nByXcO0Vw539MaJ0J</latexit>Syntax Model
xi ∼
<latexit sha1_base64="4XmkaafD4EWeU6wrjePkY8qE6No=">AAACE3icZVDLTgIxFO3gC/GFunTTSExcEDIYE3VHdOMSE0dIGCSd0oGGdjpp7xjJhN8wbvU7XBm3foCf4R/YGVgI3KS5p+ee25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evvH/wYFSiKfOoEkq3A2KY4BHzgINg7VgzIgPBWsHoJpu3npg2XEX3MI5ZV5JBxENOCVjq0Q9k+jzpcewbLnGvXHFrbl54GdRnoIJm1eyVf/2+oolkEVBBjOnU3Ri6KdHAqWCTkp8YFhM6IgPWsTAikplumrue4BPL9HGotD0R4Jz9v5ESaSSBoVVmzczNMgaUEqZqVTCUWcueye9mLINqIKuZSJvQLBiB8LKb8ihOgEV06iNMBAaFs4Rwn2tGQYwtIFRz+xVMh0QTCjbHks2ovpjIMvDOalc19+680riehVVER+gYnaI6ukANdIuayEMUafSK3tC78+J8OJ/O11RacGY7h2iunO8/lwWfXA==</latexit> <latexit sha1_base64="4XmkaafD4EWeU6wrjePkY8qE6No=">AAACE3icZVDLTgIxFO3gC/GFunTTSExcEDIYE3VHdOMSE0dIGCSd0oGGdjpp7xjJhN8wbvU7XBm3foCf4R/YGVgI3KS5p+ee25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evvH/wYFSiKfOoEkq3A2KY4BHzgINg7VgzIgPBWsHoJpu3npg2XEX3MI5ZV5JBxENOCVjq0Q9k+jzpcewbLnGvXHFrbl54GdRnoIJm1eyVf/2+oolkEVBBjOnU3Ri6KdHAqWCTkp8YFhM6IgPWsTAikplumrue4BPL9HGotD0R4Jz9v5ESaSSBoVVmzczNMgaUEqZqVTCUWcueye9mLINqIKuZSJvQLBiB8LKb8ihOgEV06iNMBAaFs4Rwn2tGQYwtIFRz+xVMh0QTCjbHks2ovpjIMvDOalc19+680riehVVER+gYnaI6ukANdIuayEMUafSK3tC78+J8OJ/O11RacGY7h2iunO8/lwWfXA==</latexit> <latexit sha1_base64="4XmkaafD4EWeU6wrjePkY8qE6No=">AAACE3icZVDLTgIxFO3gC/GFunTTSExcEDIYE3VHdOMSE0dIGCSd0oGGdjpp7xjJhN8wbvU7XBm3foCf4R/YGVgI3KS5p+ee25yeIBbcgOv+OIWV1bX1jeJmaWt7Z3evvH/wYFSiKfOoEkq3A2KY4BHzgINg7VgzIgPBWsHoJpu3npg2XEX3MI5ZV5JBxENOCVjq0Q9k+jzpcewbLnGvXHFrbl54GdRnoIJm1eyVf/2+oolkEVBBjOnU3Ri6KdHAqWCTkp8YFhM6IgPWsTAikplumrue4BPL9HGotD0R4Jz9v5ESaSSBoVVmzczNMgaUEqZqVTCUWcueye9mLINqIKuZSJvQLBiB8LKb8ihOgEV06iNMBAaFs4Rwn2tGQYwtIFRz+xVMh0QTCjbHks2ovpjIMvDOalc19+680riehVVER+gYnaI6ukANdIuayEMUafSK3tC78+J8OJ/O11RacGY7h2iunO8/lwWfXA==</latexit>fφ(ei)
<latexit sha1_base64="ISFMuiBWVv5rfvJnq9uM8Osfvo=">ACHnicZVBNS8NAEN34WetX1YMHL8EiVCglEUG9Fb14rGBsoS1hs920S3ezYXcilJAfI171d3gSr/oz/Adu0h5sO7DM2zdvhpkXxJxpcJwfa2V1bX1js7RV3t7Z3duvHBw+aZkoQj0iuVSdAGvKWUQ9YMBpJ1YUi4DTdjC+y+vtZ6o0k9EjTGLaF3gYsZARDIbyK8ehn/YCkfbiEcuyWg5p5rNzv1J1Gk4R9jJwZ6CKZtHyK7+9gSJoBEQjrXuk4M/RQrYITrNxLNI0xGeMh7RoYUF1Py0OyOwzwzsUCrzIrAL9n9HioUWGEZGmSc9V8sZkJLrulHBSOQpH1P89UQE9UDUc5HSoV5YBMLrfsqiOAEakekeYcJtkHZulj1gihLgEwMwUcycYpMRVpiAsbRsPHIXHVkG3kXjpuE8XFabtzOzSugEnaIactEVaqJ71EIeIihDr+gNvVsv1of1aX1NpSvWrOcIzYX1/QfnyqO9</latexit><latexit sha1_base64="ISFMuiBWVv5rfvJnq9uM8Osfvo=">ACHnicZVBNS8NAEN34WetX1YMHL8EiVCglEUG9Fb14rGBsoS1hs920S3ezYXcilJAfI171d3gSr/oz/Adu0h5sO7DM2zdvhpkXxJxpcJwfa2V1bX1js7RV3t7Z3duvHBw+aZkoQj0iuVSdAGvKWUQ9YMBpJ1YUi4DTdjC+y+vtZ6o0k9EjTGLaF3gYsZARDIbyK8ehn/YCkfbiEcuyWg5p5rNzv1J1Gk4R9jJwZ6CKZtHyK7+9gSJoBEQjrXuk4M/RQrYITrNxLNI0xGeMh7RoYUF1Py0OyOwzwzsUCrzIrAL9n9HioUWGEZGmSc9V8sZkJLrulHBSOQpH1P89UQE9UDUc5HSoV5YBMLrfsqiOAEakekeYcJtkHZulj1gihLgEwMwUcycYpMRVpiAsbRsPHIXHVkG3kXjpuE8XFabtzOzSugEnaIactEVaqJ71EIeIihDr+gNvVsv1of1aX1NpSvWrOcIzYX1/QfnyqO9</latexit><latexit sha1_base64="ISFMuiBWVv5rfvJnq9uM8Osfvo=">ACHnicZVBNS8NAEN34WetX1YMHL8EiVCglEUG9Fb14rGBsoS1hs920S3ezYXcilJAfI171d3gSr/oz/Adu0h5sO7DM2zdvhpkXxJxpcJwfa2V1bX1js7RV3t7Z3duvHBw+aZkoQj0iuVSdAGvKWUQ9YMBpJ1YUi4DTdjC+y+vtZ6o0k9EjTGLaF3gYsZARDIbyK8ehn/YCkfbiEcuyWg5p5rNzv1J1Gk4R9jJwZ6CKZtHyK7+9gSJoBEQjrXuk4M/RQrYITrNxLNI0xGeMh7RoYUF1Py0OyOwzwzsUCrzIrAL9n9HioUWGEZGmSc9V8sZkJLrulHBSOQpH1P89UQE9UDUc5HSoV5YBMLrfsqiOAEakekeYcJtkHZulj1gihLgEwMwUcycYpMRVpiAsbRsPHIXHVkG3kXjpuE8XFabtzOzSugEnaIactEVaqJ71EIeIihDr+gNvVsv1of1aX1NpSvWrOcIzYX1/QfnyqO9</latexit>Point mass at Neural Projector
x3
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x
f(e; φ)
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x
f(e; φ)
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η
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x
f(e; φ)
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η
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x
zi
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φ (xi)|zi; η)
∂xi
dim(x) = dim(e) and is invertible
f
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φ (xi)|zi; η)
∂xi
dim(x) = dim(e) and is invertible
f
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35
x
zi
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φ (xi)|zi; η)
∂xi
dim(x) = dim(e) and is invertible
f
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<latexit sha1_base64="0TvUX8MzRC5izm1cmvW9PX4J8iQ=">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</latexit><latexit sha1_base64="0TvUX8MzRC5izm1cmvW9PX4J8iQ=">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</latexit><latexit sha1_base64="0TvUX8MzRC5izm1cmvW9PX4J8iQ=">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</latexit>Gaussian distribution Determinant of Jacobian matrix
36
z1
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φ (xi)|zi; η)
∂xi
+ X log
∂f −1
φ
∂xi
x
f −1(e; φ)
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−∞
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log p(x) = log pGHMM(f −1
φ (x))
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sha1_base64="jBAzhNAJ26J1i9dTzZ4SO1PLZqY=">ACOXicZVHLTsMwEHTKq4Ty6JlLBELiUFVpL8ANiQtHkAhUIhVynA216kdkb6BVlB/gylfxCXwFJ8QVp+2BlpWsHc/uWuPZJBfcYh+eo219Y3Nrea2v9Pyd/f2D1r3VheGQcS0GaQUAuCK4iQo4BboDKRMBDMr6q6w8vYCzX6g6nOQwlfVY84yio26eDo7DbjiL4D/oLcAxWcRT2+vHqWaFBIVMUGsfe2GOw5Ia5ExA5ceFhZyMX2GRwcVlWCH5UxnFZw4Jg0ybdxRGMzYvxMlVZSHLnOtmlWs2g1sJ2XBeOZJ3qZ2Z3O5VJ5GdusnYzK4Iwex8WHKVFwiKzXVkhQhQB7UnQcoNMBRTBygz3H0lYCNqKEPn3JKIRFa+Hyt4ZVpKqtIynlRlnMhyUlXLPMx5cLwzubdq6X8Q9bsX3fA2JE1ySI7IKemRM3JrskNiQgjKXkj796H9+V9z3fR8BZLaZOl8H5+AY4YsXk=</latexit><latexit 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f
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φ (xi)
<latexit sha1_base64="T5O2W5fdBe9YVbRkg7tBseU/cmg=">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</latexit><latexit sha1_base64="fjhIxws58GsuvPWxj5BWS9qhG8=">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</latexit><latexit sha1_base64="fjhIxws58GsuvPWxj5BWS9qhG8=">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</latexit>Inverse
ei
<latexit sha1_base64="REkAECskl6vTPQb6KrE5yd3HUvc=">ACDXicZVDLSgMxFM3UV62vqks3wSK4KGUqgrorunFZwbGFdiZNOGJpMhuSOUof8gbvU7XIlbv8HP8A/MTGdh2wvhnpx7bjg5QSy4Adf9cUpr6xubW+Xtys7u3v5B9fDoyahEU+ZRJZTuBsQwSPmAQfBurFmRAaCdYLJXTbvPDNtuIoeYRozX5JRxENOCViq2w9kymYDPqjW3IabF14FzQLUFHtQfW3P1Q0kSwCKogxvaYbg58SDZwKNqv0E8NiQidkxHoWRkQy46e53xk+s8wQh0rbEwHO2f8bKZFGEhbZdbMwixjQClh6lYFY5m17Jn8bqYyqAeynom0Cc2SEQiv/ZRHcQIsonMfYSIwKJxlg4dcMwpiagGhmtuvYDomlCwCVZsRs3lRFaBd9G4abgPl7XWbRFWGZ2gU3SOmugKtdA9aiMPUSTQK3pD786L8+F8Ol9zackpdo7RQjnf2gonSg=</latexit><latexit sha1_base64="REkAECskl6vTPQb6KrE5yd3HUvc=">ACDXicZVDLSgMxFM3UV62vqks3wSK4KGUqgrorunFZwbGFdiZNOGJpMhuSOUof8gbvU7XIlbv8HP8A/MTGdh2wvhnpx7bjg5QSy4Adf9cUpr6xubW+Xtys7u3v5B9fDoyahEU+ZRJZTuBsQwSPmAQfBurFmRAaCdYLJXTbvPDNtuIoeYRozX5JRxENOCViq2w9kymYDPqjW3IabF14FzQLUFHtQfW3P1Q0kSwCKogxvaYbg58SDZwKNqv0E8NiQidkxHoWRkQy46e53xk+s8wQh0rbEwHO2f8bKZFGEhbZdbMwixjQClh6lYFY5m17Jn8bqYyqAeynom0Cc2SEQiv/ZRHcQIsonMfYSIwKJxlg4dcMwpiagGhmtuvYDomlCwCVZsRs3lRFaBd9G4abgPl7XWbRFWGZ2gU3SOmugKtdA9aiMPUSTQK3pD786L8+F8Ol9zackpdo7RQjnf2gonSg=</latexit><latexit sha1_base64="REkAECskl6vTPQb6KrE5yd3HUvc=">ACDXicZVDLSgMxFM3UV62vqks3wSK4KGUqgrorunFZwbGFdiZNOGJpMhuSOUof8gbvU7XIlbv8HP8A/MTGdh2wvhnpx7bjg5QSy4Adf9cUpr6xubW+Xtys7u3v5B9fDoyahEU+ZRJZTuBsQwSPmAQfBurFmRAaCdYLJXTbvPDNtuIoeYRozX5JRxENOCViq2w9kymYDPqjW3IabF14FzQLUFHtQfW3P1Q0kSwCKogxvaYbg58SDZwKNqv0E8NiQidkxHoWRkQy46e53xk+s8wQh0rbEwHO2f8bKZFGEhbZdbMwixjQClh6lYFY5m17Jn8bqYyqAeynom0Cc2SEQiv/ZRHcQIsonMfYSIwKJxlg4dcMwpiagGhmtuvYDomlCwCVZsRs3lRFaBd9G4abgPl7XWbRFWGZ2gU3SOmugKtdA9aiMPUSTQK3pD786L8+F8Ol9zackpdo7RQjnf2gonSg=</latexit>xi
<latexit sha1_base64="YThJcjf7ThL3C1arIc7iYN4iXU=">ACDXicZVDLSgMxFM34rPVdekmWAQXpUxFUHdFNy4rOLbQDiWTZtrQZDIkd8Qy9B/ErX6HK3HrN/gZ/oGZ6SxseyHck3PDScniAU34Lo/zsrq2vrGZmrvL2zu7dfOTh8NCrRlHlUCaU7ATFM8Ih5wEGwTqwZkYFg7WB8m83bT0wbrqIHmMTMl2QY8ZBTApbq9AKZPk/7vF+punU3L7wMGgWoqJa/cpvb6BoIlkEVBjug03Bj8lGjgVbFruJYbFhI7JkHUtjIhkxk9zv1N8apkBDpW2JwKcs/83UiKNJDCyqyZuVnGgFLC1KwKRjJr2TP53UxkUAtkLRNpE5oFIxBe+SmP4gRYRGc+wkRgUDjLBg+4ZhTExAJCNbdfwXRENKFgEyzbjBqLiSwD7x+XfvL6rNmyKsEjpGJ+gMNdAlaqI71EIeokigV/SG3p0X58P5dL5m0hWn2DlCc+V8/wGHZ507</latexit><latexit sha1_base64="YThJcjf7ThL3C1arIc7iYN4iXU=">ACDXicZVDLSgMxFM34rPVdekmWAQXpUxFUHdFNy4rOLbQDiWTZtrQZDIkd8Qy9B/ErX6HK3HrN/gZ/oGZ6SxseyHck3PDScniAU34Lo/zsrq2vrGZmrvL2zu7dfOTh8NCrRlHlUCaU7ATFM8Ih5wEGwTqwZkYFg7WB8m83bT0wbrqIHmMTMl2QY8ZBTApbq9AKZPk/7vF+punU3L7wMGgWoqJa/cpvb6BoIlkEVBjug03Bj8lGjgVbFruJYbFhI7JkHUtjIhkxk9zv1N8apkBDpW2JwKcs/83UiKNJDCyqyZuVnGgFLC1KwKRjJr2TP53UxkUAtkLRNpE5oFIxBe+SmP4gRYRGc+wkRgUDjLBg+4ZhTExAJCNbdfwXRENKFgEyzbjBqLiSwD7x+XfvL6rNmyKsEjpGJ+gMNdAlaqI71EIeokigV/SG3p0X58P5dL5m0hWn2DlCc+V8/wGHZ507</latexit><latexit sha1_base64="YThJcjf7ThL3C1arIc7iYN4iXU=">ACDXicZVDLSgMxFM34rPVdekmWAQXpUxFUHdFNy4rOLbQDiWTZtrQZDIkd8Qy9B/ErX6HK3HrN/gZ/oGZ6SxseyHck3PDScniAU34Lo/zsrq2vrGZmrvL2zu7dfOTh8NCrRlHlUCaU7ATFM8Ih5wEGwTqwZkYFg7WB8m83bT0wbrqIHmMTMl2QY8ZBTApbq9AKZPk/7vF+punU3L7wMGgWoqJa/cpvb6BoIlkEVBjug03Bj8lGjgVbFruJYbFhI7JkHUtjIhkxk9zv1N8apkBDpW2JwKcs/83UiKNJDCyqyZuVnGgFLC1KwKRjJr2TP53UxkUAtkLRNpE5oFIxBe+SmP4gRYRGc+wkRgUDjLBg+4ZhTExAJCNbdfwXRENKFgEyzbjBqLiSwD7x+XfvL6rNmyKsEjpGJ+gMNdAlaqI71EIeokigV/SG3p0X58P5dL5m0hWn2DlCc+V8/wGHZ507</latexit>38
[Dinh et al. 2014]
f
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φ (xi)
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g
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sha1_base64="BSeNPzIye1eC45VcyN+Ot1HADN0=">ACGnicZVDLSgMxFM3UV62vapdugkWoUMqMCOqu6MZlBWsLbS2ZNOGJpMhuSOUYT5F3Op3uBK3bvwM/8BM24VtL4R7cu654eT4keAGXPfHya2tb2xu5bcLO7t7+wfFw6NHo2JNWZMqoXTbJ4YJHrImcBCsHWlGpC9Yyx/fZvPWM9OGq/ABJhHrSTIMecApAUv1i6WuL5NR2k94FYv0Kal4Z2m/WHZr7rTwKvDmoIzm1egXf7sDRWPJQqCGNPx3Ah6CdHAqWBpoRsbFhE6JkPWsTAkpleMjWf4lPLDHCgtD0h4Cn7fyMh0kgCI6vMmlmYZQwoJUzVqmAks5Y9M72bifSrvqxmIm0Cs2QEgqtewsMoBhbSmY8gFhgUzoLCA64ZBTGxgFDN7VcwHRFNKNg4CzYjbzmRVdA8r13X3PuLcv1mHlYeHaMTVEeukR1dIcaqIkomqBX9IbenRfnw/l0vmbSnDPfKaGFcr7/AHw0oVI=</latexit><latexit sha1_base64="BSeNPzIye1eC45VcyN+Ot1HADN0=">ACGnicZVDLSgMxFM3UV62vapdugkWoUMqMCOqu6MZlBWsLbS2ZNOGJpMhuSOUYT5F3Op3uBK3bvwM/8BM24VtL4R7cu654eT4keAGXPfHya2tb2xu5bcLO7t7+wfFw6NHo2JNWZMqoXTbJ4YJHrImcBCsHWlGpC9Yyx/fZvPWM9OGq/ABJhHrSTIMecApAUv1i6WuL5NR2k94FYv0Kal4Z2m/WHZr7rTwKvDmoIzm1egXf7sDRWPJQqCGNPx3Ah6CdHAqWBpoRsbFhE6JkPWsTAkpleMjWf4lPLDHCgtD0h4Cn7fyMh0kgCI6vMmlmYZQwoJUzVqmAks5Y9M72bifSrvqxmIm0Cs2QEgqtewsMoBhbSmY8gFhgUzoLCA64ZBTGxgFDN7VcwHRFNKNg4CzYjbzmRVdA8r13X3PuLcv1mHlYeHaMTVEeukR1dIcaqIkomqBX9IbenRfnw/l0vmbSnDPfKaGFcr7/AHw0oVI=</latexit><latexit sha1_base64="BSeNPzIye1eC45VcyN+Ot1HADN0=">ACGnicZVDLSgMxFM3UV62vapdugkWoUMqMCOqu6MZlBWsLbS2ZNOGJpMhuSOUYT5F3Op3uBK3bvwM/8BM24VtL4R7cu654eT4keAGXPfHya2tb2xu5bcLO7t7+wfFw6NHo2JNWZMqoXTbJ4YJHrImcBCsHWlGpC9Yyx/fZvPWM9OGq/ABJhHrSTIMecApAUv1i6WuL5NR2k94FYv0Kal4Z2m/WHZr7rTwKvDmoIzm1egXf7sDRWPJQqCGNPx3Ah6CdHAqWBpoRsbFhE6JkPWsTAkpleMjWf4lPLDHCgtD0h4Cn7fyMh0kgCI6vMmlmYZQwoJUzVqmAks5Y9M72bifSrvqxmIm0Cs2QEgqtewsMoBhbSmY8gFhgUzoLCA64ZBTGxgFDN7VcwHRFNKNg4CzYjbzmRVdA8r13X3PuLcv1mHlYeHaMTVEeukR1dIcaqIkomqBX9IbenRfnw/l0vmbSnDPfKaGFcr7/AHw0oVI=</latexit><latexit sha1_base64="BSeNPzIye1eC45VcyN+Ot1HADN0=">ACGnicZVDLSgMxFM3UV62vapdugkWoUMqMCOqu6MZlBWsLbS2ZNOGJpMhuSOUYT5F3Op3uBK3bvwM/8BM24VtL4R7cu654eT4keAGXPfHya2tb2xu5bcLO7t7+wfFw6NHo2JNWZMqoXTbJ4YJHrImcBCsHWlGpC9Yyx/fZvPWM9OGq/ABJhHrSTIMecApAUv1i6WuL5NR2k94FYv0Kal4Z2m/WHZr7rTwKvDmoIzm1egXf7sDRWPJQqCGNPx3Ah6CdHAqWBpoRsbFhE6JkPWsTAkpleMjWf4lPLDHCgtD0h4Cn7fyMh0kgCI6vMmlmYZQwoJUzVqmAks5Y9M72bifSrvqxmIm0Cs2QEgqtewsMoBhbSmY8gFhgUzoLCA64ZBTGxgFDN7VcwHRFNKNg4CzYjbzmRVdA8r13X3PuLcv1mHlYeHaMTVEeukR1dIcaqIkomqBX9IbenRfnw/l0vmbSnDPfKaGFcr7/AHw0oVI=</latexit><latexit sha1_base64="BSeNPzIye1eC45VcyN+Ot1HADN0=">ACGnicZVDLSgMxFM3UV62vapdugkWoUMqMCOqu6MZlBWsLbS2ZNOGJpMhuSOUYT5F3Op3uBK3bvwM/8BM24VtL4R7cu654eT4keAGXPfHya2tb2xu5bcLO7t7+wfFw6NHo2JNWZMqoXTbJ4YJHrImcBCsHWlGpC9Yyx/fZvPWM9OGq/ABJhHrSTIMecApAUv1i6WuL5NR2k94FYv0Kal4Z2m/WHZr7rTwKvDmoIzm1egXf7sDRWPJQqCGNPx3Ah6CdHAqWBpoRsbFhE6JkPWsTAkpleMjWf4lPLDHCgtD0h4Cn7fyMh0kgCI6vMmlmYZQwoJUzVqmAks5Y9M72bifSrvqxmIm0Cs2QEgqtewsMoBhbSmY8gFhgUzoLCA64ZBTGxgFDN7VcwHRFNKNg4CzYjbzmRVdA8r13X3PuLcv1mHlYeHaMTVEeukR1dIcaqIkomqBX9IbenRfnw/l0vmbSnDPfKaGFcr7/AHw0oVI=</latexit>h(1)
i,r
<latexit sha1_base64="M6AXFmCURF5oagaj1n7FJbNekI=">ACGnicZVDLSgMxFM3UV62vapdugkWoUMqMCOqu6MZlBWsLbS2ZNOGJpMhuSOUYT5F3Op3uBK3bvwM/8BM24VtL4R7cu654eT4keAGXPfHya2tb2xu5bcLO7t7+wfFw6NHo2JNWZMqoXTbJ4YJHrImcBCsHWlGpC9Yyx/fZvPWM9OGq/ABJhHrSTIMecApAUv1i6WuL5NR2k94Fev0Kal4Z2m/WHZr7rTwKvDmoIzm1egXf7sDRWPJQqCGNPx3Ah6CdHAqWBpoRsbFhE6JkPWsTAkpleMjWf4lPLDHCgtD0h4Cn7fyMh0kgCI6vMmlmYZQwoJUzVqmAks5Y9M72bifSrvqxmIm0Cs2QEgqtewsMoBhbSmY8gFhgUzoLCA64ZBTGxgFDN7VcwHRFNKNg4CzYjbzmRVdA8r13X3PuLcv1mHlYeHaMTVEeukR1dIcaqIkomqBX9IbenRfnw/l0vmbSnDPfKaGFcr7/AIYqoVg=</latexit><latexit sha1_base64="M6AXFmCURF5oagaj1n7FJbNekI=">ACGnicZVDLSgMxFM3UV62vapdugkWoUMqMCOqu6MZlBWsLbS2ZNOGJpMhuSOUYT5F3Op3uBK3bvwM/8BM24VtL4R7cu654eT4keAGXPfHya2tb2xu5bcLO7t7+wfFw6NHo2JNWZMqoXTbJ4YJHrImcBCsHWlGpC9Yyx/fZvPWM9OGq/ABJhHrSTIMecApAUv1i6WuL5NR2k94Fev0Kal4Z2m/WHZr7rTwKvDmoIzm1egXf7sDRWPJQqCGNPx3Ah6CdHAqWBpoRsbFhE6JkPWsTAkpleMjWf4lPLDHCgtD0h4Cn7fyMh0kgCI6vMmlmYZQwoJUzVqmAks5Y9M72bifSrvqxmIm0Cs2QEgqtewsMoBhbSmY8gFhgUzoLCA64ZBTGxgFDN7VcwHRFNKNg4CzYjbzmRVdA8r13X3PuLcv1mHlYeHaMTVEeukR1dIcaqIkomqBX9IbenRfnw/l0vmbSnDPfKaGFcr7/AIYqoVg=</latexit><latexit sha1_base64="M6AXFmCURF5oagaj1n7FJbNekI=">ACGnicZVDLSgMxFM3UV62vapdugkWoUMqMCOqu6MZlBWsLbS2ZNOGJpMhuSOUYT5F3Op3uBK3bvwM/8BM24VtL4R7cu654eT4keAGXPfHya2tb2xu5bcLO7t7+wfFw6NHo2JNWZMqoXTbJ4YJHrImcBCsHWlGpC9Yyx/fZvPWM9OGq/ABJhHrSTIMecApAUv1i6WuL5NR2k94Fev0Kal4Z2m/WHZr7rTwKvDmoIzm1egXf7sDRWPJQqCGNPx3Ah6CdHAqWBpoRsbFhE6JkPWsTAkpleMjWf4lPLDHCgtD0h4Cn7fyMh0kgCI6vMmlmYZQwoJUzVqmAks5Y9M72bifSrvqxmIm0Cs2QEgqtewsMoBhbSmY8gFhgUzoLCA64ZBTGxgFDN7VcwHRFNKNg4CzYjbzmRVdA8r13X3PuLcv1mHlYeHaMTVEeukR1dIcaqIkomqBX9IbenRfnw/l0vmbSnDPfKaGFcr7/AIYqoVg=</latexit>h(1)
i,l = xi,l
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i,r = xi,r + g(xi,l)
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1 1 1 1 1 1
39
[Dinh et al. 2014]
f
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φ (xi)
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i,l = xi,l
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i,r = xi,r + g(xi,l)
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1 1 1 1 1 1
40
Trained on sentences of length <= 10 in section 2-21 Tested on sentences in section 23
41
50 75 100 80.8 75.4 62.7
HM Gaussia Neural
Many-to-1 %
50 75 100 74.1 68.5 53.8
VM
Feature-based 72.1 Feature-based 80.2
HM Gaussia Neural
42
Outperform feature-based SOTA
DM
Directed % on len <= 10
Oracle POS
25 50 75 60.2 55.4 49.6
Gaussi Neural
≤
DM
Directed % on all
Oracle POS
25 50 75 47.9 43.1 35.8
Gaussi Neural
≤
43
noun proper verb base cardinal number verb gerund adjective noun singular noun plural adverb verb past tense verb past participle verb 3rd singular
44
x
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noun proper verb base cardinal number verb gerund adjective noun singular noun plural adverb verb past tense verb past participle verb 3rd singular
46
noun proper verb base cardinal number verb gerund adjective noun singular noun plural adverb verb past tense verb past participle verb 3rd singular
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noun proper verb base cardinal number verb gerund adjective noun singular noun plural adverb verb past tense verb past participle verb 3rd singular
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FlowSeq: Non-Autoregressive Conditional Sequence Generation with Generative
Xuezhe Ma*, Chunting Zhou*, Xian Li, Graham Neubig, Eduard Hovy
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decoder)
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– Transform a simple distribution into a complex one through a chain
– Change of variable formula: – Generative Flow:
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lower bound (ELBO)
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– Standard Transformer encoder
– The latent variables z are represented as a sequence of continuous random variables with the same length as the target sequence y: –
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[dz x dz])
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pre-trained auto-regressive model.
candidates by importance samples.
56
– IWSLT 2014 EN-DE – WMT14 EN-DE, DE-EN – WMT16 EN-RO, RO-EN
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Z = fθ(X)
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θ
(Z)
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https://github.com/violet-zct/DeMa-BWE https://github.com/jxhe/struct-learning-with-flow
The cat sat on a green wall
https://github.com/XuezheMax/flowseq