Cognitive Computing Lab (CCL), Baidu Research, USA Emails...

Cognitive Computing Lab (CCL), Baidu Research, USAEmails: {huangxiao518, pingli98}@gmail.com, {lidingcheng, zhangjingyuan03}@baidu.com

WSDM 2019, Melbourne, USA

Knowledge Graph

Ø A fact: head entity ⟶ predicate ⟶ tail entity

2

Question Answering Over Knowledge Graph is Crucial

Ø Large-scale knowledge graphs are available.• Difficult for regular users to find particular facts.

Ø Question answering over knowledge graph aims toautomatically identify facts in KG to answer natural languagequestions.• It provides a way for AI systems to incorporate KG as a key

ingredient to answer human questions.• Applications: search engine design & conversational agent

building.3

Challenges

Ø A predicate often has various expressions.• person.nationality: what is …’s nationality, which country

is … from, where is … from, etc.

Ø Ambiguity of entity names and partial names make it hard tofind correct entities.• Many entities share the same name.• Partial names: how old is Obama?

Ø Domains of end users’ questions are often unbounded.• Any KG is far from complete.• New questions might involve predicates that are different

from training ones. 4

Existing Methods

Ø Semantic parsing based methods:• It converts natural language questions into logical expressions.

Ø Embedding based methods:• It projects questions and candidate facts into a unified low-

dimensional space based on training questions.• It measure their matching scores by the similarities between

their low-dimensional representations.• A typical way is to define a margin-based ranking criterion

and train together with negative samples, i.e., wrong answers.

5

Opportunity: Knowledge Graph Embedding

Ø The idea is to learn a low-dimensional vector representationfor each predicate/entity in a KG to preserve original relations.

Ø Learn vector representations benefit downstream tasks.• KG completion.• Recommender systems.• Relation extraction. 6

Knowledge Graph G

𝒆#𝒆$𝒆%𝒆&𝒆'⋮𝒆)

Preserve

𝒑#𝒑$⋮𝒑+

Entities:

Predicates:

• KG Completion• Recommendation• Relation Extraction• Question Answering?

Knowledge Graph Embedding

Ø Represent each predicate/entity in a KG as a low-dimensional vector, such that original relations are preserved.

7

Barack Obama 𝒆,

Honolulu 𝒆-

Birthplace 𝒑.

Birthplace 𝒑.

Michelle Obama

Chicago

Ø Typical Solution• TransE

• TransH

• TransRminimize

XkehM` + p` � etM`k22

<latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">AAACN3icbVDLShxBFL3t2/GRidtsCkUQxKF7NroMuMkmYMDxwfTYVNfcdgqrqpuq2yGTtr/NjV+QnR/gxkVCyA+kph3B14GCc885l6o6aaGkozC8C2Zm5+YXFpeWWyura+sf2h9XT1xeWoE9kavcnqXcoZIGeyRJ4VlhketU4Wl6dTjxT7+jdTI3xzQucKD5pZGZFJy8lLTPY8IfVGlppJY/sY5dqePrKk4zhnUyasjXOqliVKrebcbiadx7itHLWHyddC+6SXsr7IQN2FsSTckWTHGUtH/Fw1yUGg0JxZ3rR2FBg4pbkkJh3YpLhwUXV/wS+54artENqqaCmm17Zciy3PpjiDXq842Ka+fGOvVJzWnkXnsT8T2vX1J2MKikKUpCIx4vykrFKGeTPtlQWhSkxp5wYaV/KxMjbrkg33rLlxC9/vJbctLtRGEn+hbCEnyCTdiBCPbhM3yBI+iBgBu4h9/wJ7gNHoK/j3XNBNPeNuAFgn//AacJsTc=</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">AAACN3icbVDLShxBFL3t2/GRidtsCkUQxKF7NroMuMkmYMDxwfTYVNfcdgqrqpuq2yGTtr/NjV+QnR/gxkVCyA+kph3B14GCc885l6o6aaGkozC8C2Zm5+YXFpeWWyura+sf2h9XT1xeWoE9kavcnqXcoZIGeyRJ4VlhketU4Wl6dTjxT7+jdTI3xzQucKD5pZGZFJy8lLTPY8IfVGlppJY/sY5dqePrKk4zhnUyasjXOqliVKrebcbiadx7itHLWHyddC+6SXsr7IQN2FsSTckWTHGUtH/Fw1yUGg0JxZ3rR2FBg4pbkkJh3YpLhwUXV/wS+54artENqqaCmm17Zciy3PpjiDXq842Ka+fGOvVJzWnkXnsT8T2vX1J2MKikKUpCIx4vykrFKGeTPtlQWhSkxp5wYaV/KxMjbrkg33rLlxC9/vJbctLtRGEn+hbCEnyCTdiBCPbhM3yBI+iBgBu4h9/wJ7gNHoK/j3XNBNPeNuAFgn//AacJsTc=</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">AAACQnicbVBNaxsxFNQ6aeO4X056zEXEFAqlZtcU2mNoLrkEUohjB6+7aOW3sbCkXaS3oc56f1su+QW59Qf00kNDyLWHymsb8tEBwbyZeUiaOJPCou//9Gpr68+eb9Q3Gy9evnr9prm1fWLT3HDo8lSmph8zC1Jo6KJACf3MAFOxhF482Z/7vXMwVqT6GKcZDBU70yIRnKGTouZpiPADCyW0UOICytDmKpwVYZxQKKNxRQ7LqAhByvJDNWar8eMqhg9j4SzqfO9EzZbf9ivQpyRYkhZZ4ihqXoejlOcKNHLJrB0EfobDghkUXELZCHMLGeMTdgYDRzVTYIdFVUFJ3zllRJPUuKORVur9jYIpa6cqdknFcGwfe3Pxf94gx+TLsBA6yxE0X1yU5JJiSud90pEwwFFOHWHcCPdWysfMMI6u9YYrIXj85afkpNMO/Hbw7VNr7+uyjjrZIbvkPQnIZ7JHDsgR6RJOLskv8ofceFfeb+/Wu1tEa95y5y15AO/vP0yZsuQ=</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">AAACN3icbVDLShxBFL3t2/GRidtsCkUQxKF7NroMuMkmYMDxwfTYVNfcdgqrqpuq2yGTtr/NjV+QnR/gxkVCyA+kph3B14GCc885l6o6aaGkozC8C2Zm5+YXFpeWWyura+sf2h9XT1xeWoE9kavcnqXcoZIGeyRJ4VlhketU4Wl6dTjxT7+jdTI3xzQucKD5pZGZFJy8lLTPY8IfVGlppJY/sY5dqePrKk4zhnUyasjXOqliVKrebcbiadx7itHLWHyddC+6SXsr7IQN2FsSTckWTHGUtH/Fw1yUGg0JxZ3rR2FBg4pbkkJh3YpLhwUXV/wS+54artENqqaCmm17Zciy3PpjiDXq842Ka+fGOvVJzWnkXnsT8T2vX1J2MKikKUpCIx4vykrFKGeTPtlQWhSkxp5wYaV/KxMjbrkg33rLlxC9/vJbctLtRGEn+hbCEnyCTdiBCPbhM3yBI+iBgBu4h9/wJ7gNHoK/j3XNBNPeNuAFgn//AacJsTc=</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">AAACQnicbVBNaxsxFNQ6aeO4X056zEXEFAqlZtcU2mNoLrkEUohjB6+7aOW3sbCkXaS3oc56f1su+QW59Qf00kNDyLWHymsb8tEBwbyZeUiaOJPCou//9Gpr68+eb9Q3Gy9evnr9prm1fWLT3HDo8lSmph8zC1Jo6KJACf3MAFOxhF482Z/7vXMwVqT6GKcZDBU70yIRnKGTouZpiPADCyW0UOICytDmKpwVYZxQKKNxRQ7LqAhByvJDNWar8eMqhg9j4SzqfO9EzZbf9ivQpyRYkhZZ4ihqXoejlOcKNHLJrB0EfobDghkUXELZCHMLGeMTdgYDRzVTYIdFVUFJ3zllRJPUuKORVur9jYIpa6cqdknFcGwfe3Pxf94gx+TLsBA6yxE0X1yU5JJiSud90pEwwFFOHWHcCPdWysfMMI6u9YYrIXj85afkpNMO/Hbw7VNr7+uyjjrZIbvkPQnIZ7JHDsgR6RJOLskv8ofceFfeb+/Wu1tEa95y5y15AO/vP0yZsuQ=</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">AAACQnicbVBNaxsxFNQ6aeO4X056zEXEFAqlZtcU2mNoLrkEUohjB6+7aOW3sbCkXaS3oc56f1su+QW59Qf00kNDyLWHymsb8tEBwbyZeUiaOJPCou//9Gpr68+eb9Q3Gy9evnr9prm1fWLT3HDo8lSmph8zC1Jo6KJACf3MAFOxhF482Z/7vXMwVqT6GKcZDBU70yIRnKGTouZpiPADCyW0UOICytDmKpwVYZxQKKNxRQ7LqAhByvJDNWar8eMqhg9j4SzqfO9EzZbf9ivQpyRYkhZZ4ihqXoejlOcKNHLJrB0EfobDghkUXELZCHMLGeMTdgYDRzVTYIdFVUFJ3zllRJPUuKORVur9jYIpa6cqdknFcGwfe3Pxf94gx+TLsBA6yxE0X1yU5JJiSud90pEwwFFOHWHcCPdWysfMMI6u9YYrIXj85afkpNMO/Hbw7VNr7+uyjjrZIbvkPQnIZ7JHDsgR6RJOLskv8ofceFfeb+/Wu1tEa95y5y15AO/vP0yZsuQ=</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="WZ17Nrd9LtHjCgtTzuN5RIGuw7s=">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</latexit><latexit sha1_base64="bD5KUU2uflq86yt2NSe0hmkynlM=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">AAACQnicbVBNaxsxFNQ6aeO4X056zEXEFAqlZtcU2mNoLrkEUohjB6+7aOW3sbCkXaS3oc56f1su+QW59Qf00kNDyLWHymsb8tEBwbyZeUiaOJPCou//9Gpr68+eb9Q3Gy9evnr9prm1fWLT3HDo8lSmph8zC1Jo6KJACf3MAFOxhF482Z/7vXMwVqT6GKcZDBU70yIRnKGTouZpiPADCyW0UOICytDmKpwVYZxQKKNxRQ7LqAhByvJDNWar8eMqhg9j4SzqfO9EzZbf9ivQpyRYkhZZ4ihqXoejlOcKNHLJrB0EfobDghkUXELZCHMLGeMTdgYDRzVTYIdFVUFJ3zllRJPUuKORVur9jYIpa6cqdknFcGwfe3Pxf94gx+TLsBA6yxE0X1yU5JJiSud90pEwwFFOHWHcCPdWysfMMI6u9YYrIXj85afkpNMO/Hbw7VNr7+uyjjrZIbvkPQnIZ7JHDsgR6RJOLskv8ofceFfeb+/Wu1tEa95y5y15AO/vP0yZsuQ=</latexit><latexit sha1_base64="4NJRiJtAGOtmEU1gZ74/OsIZTps=">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</latexit>

minimizeX

keh + p` � etk22<latexit sha1_base64="m3wRRUnZQmo2xfzX6+FByQ+PxpE=">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</latexit><latexit sha1_base64="m3wRRUnZQmo2xfzX6+FByQ+PxpE=">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</latexit><latexit sha1_base64="m3wRRUnZQmo2xfzX6+FByQ+PxpE=">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</latexit><latexit sha1_base64="m3wRRUnZQmo2xfzX6+FByQ+PxpE=">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</latexit>

minimizeX

ke?h + p` � e?t k22,

where e?t = et �m>` etm`

<latexit sha1_base64="cEDOc0xno9fQu/7OvIyh4Z/e6Ss=">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</latexit><latexit sha1_base64="cEDOc0xno9fQu/7OvIyh4Z/e6Ss=">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</latexit><latexit sha1_base64="cEDOc0xno9fQu/7OvIyh4Z/e6Ss=">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</latexit><latexit sha1_base64="cEDOc0xno9fQu/7OvIyh4Z/e6Ss=">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</latexit>

Problem Statement

8

Ø Input: a KG, predicates’ and entities’ names & embeddingrepresentations, training questions with answers.

Ø Output: a trained end-to-end framework that takes a newsimple question as input and returns its head entity & predicate.

KG Embedding

HumanQuestion

Head Entity& Predicate

!"!#!$!%!&⋮!(

)")#⋮)*

Entities: Predicates:

Questionswith

Answers

Names of PartialEntities

�

End-to-end Framework

Learn

Knowledge Embedding based Question Answering

Ø Each fact (ℎ, 𝑙, 𝑡) can be represented as (𝒆,, 𝒑., 𝒆-).

Ø Given a question, we aim to jointly predict 𝒆,, 𝒑., and 𝒆-.

Ø Three components:• Predicate learning model & head entity learning model.• Head entity detection model.• Joint search on embedding spaces. 9

Knowledge Graph G

!"!#!$!%!&⋮!(

Embed

)")#⋮)*

Question:Which Olympics was in Australia?

PredicateLearning

Head EntityLearning+!,

Predicted Fact:(+!,, -)., +!/)

Answer:Find ClosestFact in G

Tail Entity:+!/ = f(+!,, -).)

Entities:

Predicates: -).

Predicate Embedding Space

Entity Embedding Space

Predicate & Head Entity Learning Model

Ø Each fact (ℎ, 𝑙, 𝑡) can be represented as (𝒆,, 𝒑., 𝒆-).• For a question can be answered by KG, its predicates’ vector

representation lies in the predicate embedding space.

Ø Design a model.• Input: a question.• Output: a vector 𝒑3. that is as close as possible to the 𝒑.. 10

Knowledge Graph G

𝒆#𝒆$𝒆%𝒆&𝒆'⋮𝒆)

Embed

𝒑#𝒑$⋮𝒑+

𝒆45

Entities:

Predicates: 𝒑3.



11


Ø Train on all training questions and use their 𝒑. as the labels.

Ø Pseudocode:

that HEDentity might be only part of the correct head entity name.Thus, all entities that are the same as or contain HEDentity would beincluded as the candidate head entities, which might still be largesince many entities would share the same names in a large KG.

3.4 Joint Search on Embedding SpacesFor each new simple question, we have predicted its predicate andhead entity representations p` and eh , as well as its candidate headentities. Our goal is to �nd a fact in G that matches these learnedrepresentations and candidates the most.

3.4.1 Joint Distance Metric. If a fact’s head entity belongs to thecandidate head entities, we name it as a candidate fact. Let C bea set that collects all the candidate facts. To measure the distancebetween a candidate fact (h, `, t ) and the predicted representations(eh , p` ), an intuitive solution is to represent (h, `, t ) as (eh , p` ) andde�ne the distance metric as the sum of the distance between ehand eh and distance between p` and p` . This solution, however,does not take the meaningful relation information preserved in theKG embedding representations into consideration.

We propose a joint distance metric by taking advantage of therelation information et ⇡ f (eh , p` ). Mathematically, the proposedjoint distance metric is de�ned as,

minimize(h,`,t )2C

kp` � p` k2 + �1keh � eh k2 + �2k f (eh , p` ) � et k2

� �3sim[n(h),HEDentity] � �4sim[n(`),HEDnon], (9)

where et = f (eh , p` ). Function n(·) returns the name of the entityor predicate. HEDentity and HEDnon denote the tokens that areclassi�ed as entity name and non entity name by the HED model.Function sim[·, ·] measures the similarity of two strings. �1, �2, �3,and �4 are prede�ned weights to balance the contribution of eachterm. In this paper, we use `2 norm to measure the distance, and itis straightforward to extend to other vector distance measures.

The �rst three terms in Eq. (9) measure the distance between afact (h, `, t ) and our prediction in the KG embedding spaces. We usef (eh , p` ) to represent the tail entity’s embedding vector, insteadof et . It is because in a KG, there might be several facts that havethe same head entity and predicate, but di�erent tail entities. Thus,a single tail entity et might not be able to answer the question.Meanwhile, f (eh , p` ) matches the predicted tail entity et since itis also inferred based on f (·). We tend to select a fact with headentity name exactly the same as HEDentity, and with predicatename mentioned by the question. We achieve these two goals viathe fourth and �fth terms in Eq. (9) respectively. The fact (h⇤, `⇤, t⇤)that minimizes the objective function is returned.

3.4.2 Knowledge Embedding based �estion Answering. The entireprocesses of KEQA is summarized in Algorithm 1. Given a KGG and a question set Q with corresponding answers, we train apredicate learning model, a head entity learning model, and a HEDmodel, as shown from line 1 to line 9. Then, for any new simplequestion Q , we input it into the trained predicate learning model,head entity learning model, and HED model to learn its predictedpredicate representation p` , head entity representation eh , entityname tokens HEDentity, and non entity name tokens HEDnon. Basedon the learned entity name/names in HEDentity, we search the entireG to �nd the candidate fact set C. For all facts in C, we compute

Algorithm 1: The proposed KEQA frameworkInput: G, predicates’ and entities’ names, P, E, Q, a new

simple question Q .Output: head entity h⇤ and predicate `⇤./* Training the predicate learning model: */

1 for Qi in Q do2 Take the L tokens of Qi as the input and its predicate ` as

the label to train, as shown in Figure 2;3 Update weight matrices {W}, w, {b}, and bq to minimize

the objective function kp` � 1LPLj=1 r

>j k2;

/* Training the head entity learning model: */

4 for Qi in Q do5 Take the L tokens of Qi as the input and its head entity h

as the label to train, as shown in Figure 2;6 Update weight matrices and bias terms to minimize the

objective function keh � 1LPLj=1 r

>j k2;

/* Training the HED model: */

7 for Qi in Q do8 Take the L tokens of Qi as the input and its head entity

name positions as the label to train;9 Update weight matrices and bias as shown in Figure 3;/* Question answering processes: */

10 Input Q into the predicate learning model to learn p` ;11 Input Q into the head entity learning model to learn eh ;12 Input Q into the HED model to learn HEDentity and HEDnon;13 Find the candidate fact set C from G, based on HEDentity;14 For all facts in C, calculate the fact (h⇤, `⇤, t⇤) that minimizes

the objective function in Eq. (9).

their joint distance to the predicted representations (eh , p` , et )based on the objective function in Eq. (9). The fact (h⇤, `⇤, t⇤) withthe minimum distance is selected. Finally, we return the head entityh⇤ and predicate `⇤ as the answer of Q .

In summary, the proposed framework KEQA enjoys several niceproperties. First, by performing question answering based on theKG embedding, KEQA is able to handle questions with predicatesand entities that are di�erent from all the ones in the trainingdata. Second, by taking advantage of the structure and relationinformation preserved in the KG embedding representations, KEQAcould perform the head entity, predicate, and tail entity predictionsjointly. The three subtasks would mutually complement each other.Third, KEQA is generalizable to di�erent KG embedding algorithms.Thus, the performance of KEQAmight be further improved by moresophisticated KG embedding algorithms.

4 EXPERIMENTSWe evaluate the e�ectiveness and generalizability of the proposedframework KEQA on a large QA-KG benchmark. In this section,we aim to study the following three research questions:

• Q1. How e�ective is KEQA compared with the state-of-the-art QA-KG methods w.r.t. di�erent freebase subsets?

!" = [ ]

Word Embeddingof Tokens $"

Bidirectional LSTM

Weighted !"Concatenation

Attention Weights

Target Vectors ofTokens %"

Predicate/Head EntityRepresentation &'( / )*+

“which” “Olympics” “Australia”

. . .

. . .

. . .

. . .

. . .

. . .

. . .

!,

!,!-

!-!.

!.

. . .

!"!";

!" = [ ]

Word Embeddingof Tokens $"

Bidirectional LSTM

Weighted !"Concatenation

Attention Weights

Target Vectors ofTokens %"

Predicate/Head EntityRepresentation &'( / )*+


. . .

. . .

. . .

. . .

. . .

. . .

. . .

!,

!,!-

!-!.

!.

. . .

!"!";


12

Head Entity Detection Model (HED)

Ø Select successive tokens as the name of head entity.

Ø Reduce the search space from entire entities to a number ofentities with the same or similar names.

Ø Head entity name position is used as the label.

Ø is used to handle the ambiguity. 13eh<latexit sha1_base64="6e1nk5Ofjq6+2JhYHwz0+oqAEyM=">AAAB+nicbVBNS8NAEJ3Ur1q/Uj16WSyCp5KIoMeiF48V7Ae0IWy2m2bpZhN2N0qJ+SlePCji1V/izX/jts1BWx8MPN6bYWZekHKmtON8W5W19Y3Nrep2bWd3b//Arh92VZJJQjsk4YnsB1hRzgTtaKY57aeS4jjgtBdMbmZ+74FKxRJxr6cp9WI8FixkBGsj+XY9H0ZY58MgRLQo/DwqfLvhNJ050CpxS9KAEm3f/hqOEpLFVGjCsVID10m1l2OpGeG0qA0zRVNMJnhMB4YKHFPl5fPTC3RqlBEKE2lKaDRXf0/kOFZqGgemM8Y6UsveTPzPG2Q6vPJyJtJMU0EWi8KMI52gWQ5oxCQlmk8NwUQycysiEZaYaJNWzYTgLr+8SrrnTddpuncXjdZ1GUcVjuEEzsCFS2jBLbShAwQe4Rle4c16sl6sd+tj0Vqxypkj+APr8we0RZRG</latexit><latexit sha1_base64="6e1nk5Ofjq6+2JhYHwz0+oqAEyM=">AAAB+nicbVBNS8NAEJ3Ur1q/Uj16WSyCp5KIoMeiF48V7Ae0IWy2m2bpZhN2N0qJ+SlePCji1V/izX/jts1BWx8MPN6bYWZekHKmtON8W5W19Y3Nrep2bWd3b//Arh92VZJJQjsk4YnsB1hRzgTtaKY57aeS4jjgtBdMbmZ+74FKxRJxr6cp9WI8FixkBGsj+XY9H0ZY58MgRLQo/DwqfLvhNJ050CpxS9KAEm3f/hqOEpLFVGjCsVID10m1l2OpGeG0qA0zRVNMJnhMB4YKHFPl5fPTC3RqlBEKE2lKaDRXf0/kOFZqGgemM8Y6UsveTPzPG2Q6vPJyJtJMU0EWi8KMI52gWQ5oxCQlmk8NwUQycysiEZaYaJNWzYTgLr+8SrrnTddpuncXjdZ1GUcVjuEEzsCFS2jBLbShAwQe4Rle4c16sl6sd+tj0Vqxypkj+APr8we0RZRG</latexit><latexit sha1_base64="6e1nk5Ofjq6+2JhYHwz0+oqAEyM=">AAAB+nicbVBNS8NAEJ3Ur1q/Uj16WSyCp5KIoMeiF48V7Ae0IWy2m2bpZhN2N0qJ+SlePCji1V/izX/jts1BWx8MPN6bYWZekHKmtON8W5W19Y3Nrep2bWd3b//Arh92VZJJQjsk4YnsB1hRzgTtaKY57aeS4jjgtBdMbmZ+74FKxRJxr6cp9WI8FixkBGsj+XY9H0ZY58MgRLQo/DwqfLvhNJ050CpxS9KAEm3f/hqOEpLFVGjCsVID10m1l2OpGeG0qA0zRVNMJnhMB4YKHFPl5fPTC3RqlBEKE2lKaDRXf0/kOFZqGgemM8Y6UsveTPzPG2Q6vPJyJtJMU0EWi8KMI52gWQ5oxCQlmk8NwUQycysiEZaYaJNWzYTgLr+8SrrnTddpuncXjdZ1GUcVjuEEzsCFS2jBLbShAwQe4Rle4c16sl6sd+tj0Vqxypkj+APr8we0RZRG</latexit><latexit sha1_base64="6e1nk5Ofjq6+2JhYHwz0+oqAEyM=">AAAB+nicbVBNS8NAEJ3Ur1q/Uj16WSyCp5KIoMeiF48V7Ae0IWy2m2bpZhN2N0qJ+SlePCji1V/izX/jts1BWx8MPN6bYWZekHKmtON8W5W19Y3Nrep2bWd3b//Arh92VZJJQjsk4YnsB1hRzgTtaKY57aeS4jjgtBdMbmZ+74FKxRJxr6cp9WI8FixkBGsj+XY9H0ZY58MgRLQo/DwqfLvhNJ050CpxS9KAEm3f/hqOEpLFVGjCsVID10m1l2OpGeG0qA0zRVNMJnhMB4YKHFPl5fPTC3RqlBEKE2lKaDRXf0/kOFZqGgemM8Y6UsveTPzPG2Q6vPJyJtJMU0EWi8KMI52gWQ5oxCQlmk8NwUQycysiEZaYaJNWzYTgLr+8SrrnTddpuncXjdZ1GUcVjuEEzsCFS2jBLbShAwQe4Rle4c16sl6sd+tj0Vqxypkj+APr8we0RZRG</latexit>

Word Embeddingof Tokens !"

Bidirectional LSTM

Fully ConnectedLayer


. . .

. . .

. . .

. . .

. . .

#$

#$#%

#%#&

#&

. . .

#" = [ ]#"#";

Target Vectors ofTokens ("

Softmax Function

Entity Name Token Non Entity Name Token

Head Entity Detection Model (HED)

14Word Embeddingof Tokens !"

Bidirectional LSTM

Fully ConnectedLayer


. . .

. . .

. . .

. . .

. . .

#$

#$#%

#%#&

#&

. . .

#" = [ ]#"#";

Target Vectors ofTokens ("

Softmax Function

Entity Name Token Non Entity Name Token

Joint Search on Embedding Spaces

Ø

Ø .

Ø Function returns the name of the entity or predicate.

Ø HEDentity and HEDnon denote the tokens that are classified asentity name and non entity name by the HED model.

Ø sim measures the similarity of two strings.

15

et = f(eh, p`)<latexit sha1_base64="cmtBntFeP+p2ozyEqGicdm2iEvA=">AAACJ3icbZDJSgNBEIZ7XGPcoh69NAYhgoQZEfSiBL14jGAWyITQ06lJmvQsdNcIYZi38eKreBFURI++iZ0F1MQfGn6+qqK6fi+WQqNtf1oLi0vLK6u5tfz6xubWdmFnt66jRHGo8UhGqukxDVKEUEOBEpqxAhZ4Ehre4HpUb9yD0iIK73AYQztgvVD4gjM0qFO4TN0+w9T1fApZ1kkxoxfUL83QfnZMf1A8Qi5ImR11CkW7bI9F540zNUUyVbVTeHG7EU8CCJFLpnXLsWNsp0yh4BKyvJtoiBkfsB60jA1ZALqdju/M6KEhXepHyrwQ6Zj+nkhZoPUw8ExnwLCvZ2sj+F+tlaB/3k5FGCcIIZ8s8hNJMaKj0GhXKOAoh8YwroT5K+V9phhHE23ehODMnjxv6idlxy47t6fFytU0jhzZJwekRBxyRirkhlRJjXDyQJ7IK3mzHq1n6936mLQuWNOZPfJH1tc3Hrmmsg==</latexit><latexit sha1_base64="cmtBntFeP+p2ozyEqGicdm2iEvA=">AAACJ3icbZDJSgNBEIZ7XGPcoh69NAYhgoQZEfSiBL14jGAWyITQ06lJmvQsdNcIYZi38eKreBFURI++iZ0F1MQfGn6+qqK6fi+WQqNtf1oLi0vLK6u5tfz6xubWdmFnt66jRHGo8UhGqukxDVKEUEOBEpqxAhZ4Ehre4HpUb9yD0iIK73AYQztgvVD4gjM0qFO4TN0+w9T1fApZ1kkxoxfUL83QfnZMf1A8Qi5ImR11CkW7bI9F540zNUUyVbVTeHG7EU8CCJFLpnXLsWNsp0yh4BKyvJtoiBkfsB60jA1ZALqdju/M6KEhXepHyrwQ6Zj+nkhZoPUw8ExnwLCvZ2sj+F+tlaB/3k5FGCcIIZ8s8hNJMaKj0GhXKOAoh8YwroT5K+V9phhHE23ehODMnjxv6idlxy47t6fFytU0jhzZJwekRBxyRirkhlRJjXDyQJ7IK3mzHq1n6936mLQuWNOZPfJH1tc3Hrmmsg==</latexit><latexit sha1_base64="cmtBntFeP+p2ozyEqGicdm2iEvA=">AAACJ3icbZDJSgNBEIZ7XGPcoh69NAYhgoQZEfSiBL14jGAWyITQ06lJmvQsdNcIYZi38eKreBFURI++iZ0F1MQfGn6+qqK6fi+WQqNtf1oLi0vLK6u5tfz6xubWdmFnt66jRHGo8UhGqukxDVKEUEOBEpqxAhZ4Ehre4HpUb9yD0iIK73AYQztgvVD4gjM0qFO4TN0+w9T1fApZ1kkxoxfUL83QfnZMf1A8Qi5ImR11CkW7bI9F540zNUUyVbVTeHG7EU8CCJFLpnXLsWNsp0yh4BKyvJtoiBkfsB60jA1ZALqdju/M6KEhXepHyrwQ6Zj+nkhZoPUw8ExnwLCvZ2sj+F+tlaB/3k5FGCcIIZ8s8hNJMaKj0GhXKOAoh8YwroT5K+V9phhHE23ehODMnjxv6idlxy47t6fFytU0jhzZJwekRBxyRirkhlRJjXDyQJ7IK3mzHq1n6936mLQuWNOZPfJH1tc3Hrmmsg==</latexit><latexit sha1_base64="cmtBntFeP+p2ozyEqGicdm2iEvA=">AAACJ3icbZDJSgNBEIZ7XGPcoh69NAYhgoQZEfSiBL14jGAWyITQ06lJmvQsdNcIYZi38eKreBFURI++iZ0F1MQfGn6+qqK6fi+WQqNtf1oLi0vLK6u5tfz6xubWdmFnt66jRHGo8UhGqukxDVKEUEOBEpqxAhZ4Ehre4HpUb9yD0iIK73AYQztgvVD4gjM0qFO4TN0+w9T1fApZ1kkxoxfUL83QfnZMf1A8Qi5ImR11CkW7bI9F540zNUUyVbVTeHG7EU8CCJFLpnXLsWNsp0yh4BKyvJtoiBkfsB60jA1ZALqdju/M6KEhXepHyrwQ6Zj+nkhZoPUw8ExnwLCvZ2sj+F+tlaB/3k5FGCcIIZ8s8hNJMaKj0GhXKOAoh8YwroT5K+V9phhHE23ehODMnjxv6idlxy47t6fFytU0jhzZJwekRBxyRirkhlRJjXDyQJ7IK3mzHq1n6936mLQuWNOZPfJH1tc3Hrmmsg==</latexit>

minimize(h,`,t)2C

kp` � p`k2 + �1keh � ehk2 + �2kf(eh,p`)� etk2

� �3sim[n(h),HEDentity]� �4sim[n(`),HEDnon].<latexit sha1_base64="0Z76p473I2YItneGuwVF1W5FZMA=">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</latexit><latexit sha1_base64="0Z76p473I2YItneGuwVF1W5FZMA=">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</latexit><latexit sha1_base64="0Z76p473I2YItneGuwVF1W5FZMA=">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</latexit><latexit sha1_base64="0Z76p473I2YItneGuwVF1W5FZMA=">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</latexit>

n(·)<latexit sha1_base64="T5IeV7Ajtt/K2YvqJ0LyROIx1EQ=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBahXkoigh6LXjxWsB/QhrLZbNqlm03cnQil9E948aCIV/+ON/+N2zYHbX0w8Hhvhpl5QSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoZZJMM95kiUx0J6CGS6F4EwVK3kk1p3EgeTsY3c789hPXRiTqAccp92M6UCISjKKVOqraY2GC5/1yxa25c5BV4uWkAjka/fJXL0xYFnOFTFJjup6boj+hGgWTfFrqZYanlI3ogHctVTTmxp/M752SM6uEJEq0LYVkrv6emNDYmHEc2M6Y4tAsezPxP6+bYXTtT4RKM+SKLRZFmSSYkNnzJBSaM5RjSyjTwt5K2JBqytBGVLIheMsvr5LWRc1za979ZaV+k8dRhBM4hSp4cAV1uIMGNIGBhGd4hTfn0Xlx3p2PRWvByWeO4Q+czx9vZo+P</latexit><latexit sha1_base64="T5IeV7Ajtt/K2YvqJ0LyROIx1EQ=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBahXkoigh6LXjxWsB/QhrLZbNqlm03cnQil9E948aCIV/+ON/+N2zYHbX0w8Hhvhpl5QSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoZZJMM95kiUx0J6CGS6F4EwVK3kk1p3EgeTsY3c789hPXRiTqAccp92M6UCISjKKVOqraY2GC5/1yxa25c5BV4uWkAjka/fJXL0xYFnOFTFJjup6boj+hGgWTfFrqZYanlI3ogHctVTTmxp/M752SM6uEJEq0LYVkrv6emNDYmHEc2M6Y4tAsezPxP6+bYXTtT4RKM+SKLRZFmSSYkNnzJBSaM5RjSyjTwt5K2JBqytBGVLIheMsvr5LWRc1za979ZaV+k8dRhBM4hSp4cAV1uIMGNIGBhGd4hTfn0Xlx3p2PRWvByWeO4Q+czx9vZo+P</latexit><latexit sha1_base64="T5IeV7Ajtt/K2YvqJ0LyROIx1EQ=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBahXkoigh6LXjxWsB/QhrLZbNqlm03cnQil9E948aCIV/+ON/+N2zYHbX0w8Hhvhpl5QSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoZZJMM95kiUx0J6CGS6F4EwVK3kk1p3EgeTsY3c789hPXRiTqAccp92M6UCISjKKVOqraY2GC5/1yxa25c5BV4uWkAjka/fJXL0xYFnOFTFJjup6boj+hGgWTfFrqZYanlI3ogHctVTTmxp/M752SM6uEJEq0LYVkrv6emNDYmHEc2M6Y4tAsezPxP6+bYXTtT4RKM+SKLRZFmSSYkNnzJBSaM5RjSyjTwt5K2JBqytBGVLIheMsvr5LWRc1za979ZaV+k8dRhBM4hSp4cAV1uIMGNIGBhGd4hTfn0Xlx3p2PRWvByWeO4Q+czx9vZo+P</latexit><latexit sha1_base64="T5IeV7Ajtt/K2YvqJ0LyROIx1EQ=">AAAB73icbVBNS8NAEJ3Ur1q/qh69LBahXkoigh6LXjxWsB/QhrLZbNqlm03cnQil9E948aCIV/+ON/+N2zYHbX0w8Hhvhpl5QSqFQdf9dgpr6xubW8Xt0s7u3v5B+fCoZZJMM95kiUx0J6CGS6F4EwVK3kk1p3EgeTsY3c789hPXRiTqAccp92M6UCISjKKVOqraY2GC5/1yxa25c5BV4uWkAjka/fJXL0xYFnOFTFJjup6boj+hGgWTfFrqZYanlI3ogHctVTTmxp/M752SM6uEJEq0LYVkrv6emNDYmHEc2M6Y4tAsezPxP6+bYXTtT4RKM+SKLRZFmSSYkNnzJBSaM5RjSyjTwt5K2JBqytBGVLIheMsvr5LWRc1za979ZaV+k8dRhBM4hSp4cAV1uIMGNIGBhGd4hTfn0Xlx3p2PRWvByWeO4Q+czx9vZo+P</latexit>

[·, ·]<latexit sha1_base64="7jAn/bF7ng1rhRCEIt5yeOomWL4=">AAAB9HicbVDLSgMxFM3UV62vqks3wSK4kDIjgi6LblxWsA9oh5LJZNrQTDImdwpl6He4caGIWz/GnX9jOp2Fth64l8M595KbEySCG3Ddb6e0tr6xuVXeruzs7u0fVA+P2kalmrIWVULpbkAME1yyFnAQrJtoRuJAsE4wvpv7nQnThiv5CNOE+TEZSh5xSsBKfq9PQwUXefcH1Zpbd3PgVeIVpIYKNAfVr36oaBozCVQQY3qem4CfEQ2cCjar9FPDEkLHZMh6lkoSM+Nn+dEzfGaVEEdK25KAc/X3RkZiY6ZxYCdjAiOz7M3F/7xeCtGNn3GZpMAkXTwUpQKDwvMEcMg1oyCmlhCqub0V0xHRhILNqWJD8Ja/vEral3XPrXsPV7XGbRFHGZ2gU3SOPHSNGugeNVELUfSEntErenMmzovz7nwsRktOsXOM/sD5/AGE8JHs</latexit><latexit sha1_base64="7jAn/bF7ng1rhRCEIt5yeOomWL4=">AAAB9HicbVDLSgMxFM3UV62vqks3wSK4kDIjgi6LblxWsA9oh5LJZNrQTDImdwpl6He4caGIWz/GnX9jOp2Fth64l8M595KbEySCG3Ddb6e0tr6xuVXeruzs7u0fVA+P2kalmrIWVULpbkAME1yyFnAQrJtoRuJAsE4wvpv7nQnThiv5CNOE+TEZSh5xSsBKfq9PQwUXefcH1Zpbd3PgVeIVpIYKNAfVr36oaBozCVQQY3qem4CfEQ2cCjar9FPDEkLHZMh6lkoSM+Nn+dEzfGaVEEdK25KAc/X3RkZiY6ZxYCdjAiOz7M3F/7xeCtGNn3GZpMAkXTwUpQKDwvMEcMg1oyCmlhCqub0V0xHRhILNqWJD8Ja/vEral3XPrXsPV7XGbRFHGZ2gU3SOPHSNGugeNVELUfSEntErenMmzovz7nwsRktOsXOM/sD5/AGE8JHs</latexit><latexit sha1_base64="7jAn/bF7ng1rhRCEIt5yeOomWL4=">AAAB9HicbVDLSgMxFM3UV62vqks3wSK4kDIjgi6LblxWsA9oh5LJZNrQTDImdwpl6He4caGIWz/GnX9jOp2Fth64l8M595KbEySCG3Ddb6e0tr6xuVXeruzs7u0fVA+P2kalmrIWVULpbkAME1yyFnAQrJtoRuJAsE4wvpv7nQnThiv5CNOE+TEZSh5xSsBKfq9PQwUXefcH1Zpbd3PgVeIVpIYKNAfVr36oaBozCVQQY3qem4CfEQ2cCjar9FPDEkLHZMh6lkoSM+Nn+dEzfGaVEEdK25KAc/X3RkZiY6ZxYCdjAiOz7M3F/7xeCtGNn3GZpMAkXTwUpQKDwvMEcMg1oyCmlhCqub0V0xHRhILNqWJD8Ja/vEral3XPrXsPV7XGbRFHGZ2gU3SOPHSNGugeNVELUfSEntErenMmzovz7nwsRktOsXOM/sD5/AGE8JHs</latexit><latexit sha1_base64="7jAn/bF7ng1rhRCEIt5yeOomWL4=">AAAB9HicbVDLSgMxFM3UV62vqks3wSK4kDIjgi6LblxWsA9oh5LJZNrQTDImdwpl6He4caGIWz/GnX9jOp2Fth64l8M595KbEySCG3Ddb6e0tr6xuVXeruzs7u0fVA+P2kalmrIWVULpbkAME1yyFnAQrJtoRuJAsE4wvpv7nQnThiv5CNOE+TEZSh5xSsBKfq9PQwUXefcH1Zpbd3PgVeIVpIYKNAfVr36oaBozCVQQY3qem4CfEQ2cCjar9FPDEkLHZMh6lkoSM+Nn+dEzfGaVEEdK25KAc/X3RkZiY6ZxYCdjAiOz7M3F/7xeCtGNn3GZpMAkXTwUpQKDwvMEcMg1oyCmlhCqub0V0xHRhILNqWJD8Ja/vEral3XPrXsPV7XGbRFHGZ2gU3SOPHSNGugeNVELUfSEntErenMmzovz7nwsRktOsXOM/sD5/AGE8JHs</latexit>

Advantages of Proposed Framework

Ø KEQA could handle questions with predicates and entitiesthat not exist in training data.

Ø KG embedding enables KEQA to perform head entity,predicate, and tail entity predictions jointly.

Ø KEQA is general to all KG embedding algorithms. It mightbe further improved by more effective embedding algorithms.

16

Knowledge Graph G

!"!#!$!%!&⋮!(

Embed

)")#⋮)*

Question:Which Olympics was in Australia?

PredicateLearning

Head EntityLearning+!,

Predicted Fact:(+!,, -)., +!/)

Answer:Find ClosestFact in G

Tail Entity:+!/ = f(+!,, -).)

Entities:

Predicates: -).



Datasets

Ø SimpleQuestions: Benchmark for most recent methods.

Ø FB2M & FB5M: subsets of Freebase knowledge graph.

17

Table 2: The statistics of the question answering datasets.

FB2M FB5M SimpleQuestions

# Training 14,174,246 17,872,174 75,910# Validation N.A. N.A. 10,845

# Test N.A. N.A. 21,687# Predicates (M ) 6,701 7,523 1,837# Entities (N ) 1,963,130 3,988,105 131,681

# Words 733,278 1,213,205 61,336

QA_KG methods w.r.t. di�erent freebase subsets?Q2. How does the performance of KEQA vary when di�erent KGembedding algorithms are employed?Q3. The objective function of KEQA consists of �ve terms as shownin Eq. (9). How much does each term contribute?

4.1 DatasetsWe �rst introduce the knowledge graph subsets and question an-swering dataset used in the experiments. They all are publiclyavailable. Their statistics are presented in Table 2.

FB2M and FB5M [17]: Freebase is a highly reliable KG sinceit is collected and trimmed mainly by the community members.Two large subsets of freebase are employed in this paper, i.e., FB2Mand FB5M. Their predicate numberM and entity number N are listin Table 2. The repeated facts have been deleted. The applicationprogramming interface (API) of freebase is no long available. Thus,we use an entity name collection3 to build the mapping betweenentities and their names.

SimpleQuestions [6]: It contains more than ten thousand sim-ple questions associated with corresponding facts. All these factsbelong to FB2M. All questions are phrased by English speakersbased on the facts and their context. It has been used as the bench-mark for most of the recent QA_KG methods [6, 16, 26].

4.2 Experimental SettingsTo evaluate the performance of the QA_KG methods, we follow thetraditional settings [10, 24, 43] and use the same training, validation,and test splits that are originally provided in SimpleQuestions [6].Either FB2M or FB5M is employed as the KG G. Then a KG embed-ding algorithm such as TransE [7] and TransR [22] is applied to Gto learn the P and E. It should be noted that P and E are not extrainformation sources. Finally, a QA_KG method is applied to predictthe head entity and predicate of each question in the test split. Itsperformance is measured by the accuracy of predicting both headentity and predicate correctly.

As claimed in our formal problem de�nition, the evaluationcriterion is de�ned as the accuracy of predicting a new question’both head entity and predicate correctly. The dimension of the KGembedding representations d is set to be 250. A pre-trained wordembedding based on GloVe [28] is used. To measure the similarityof two string, i.e., to build the function sim[·, ·], we use the imple-mentation Fuzzy4. If it is not speci�c, the KG embedding algorithmTransE [7] would be employed.

3https://github.com/zihangdai/CFO4https://pypi.org/project/Fuzzy/

Table 3: The performance of di�erent methods on Simple-Questions with di�erent freebase subsets.

FB2M (Accuracy) FB5M

Bordes et al. (2015) [6] 0.627 0.639Dai et al.3 (2016) [10] N.A. 0.626Yin et al. (2016) [43] 0.683 (+8.9%) 0.672

Golub and He (2016) [16] 0.709 (+13.1%) 0.703Bao et al. (2016) [2] 0.728 (+16.1%) Entire Freebase

Lukovnikov et al. (2017) [24] 0.712 (+13.6%) N.A.Mohammed et al.5(2018) [26] 0.732 (+16.7%) N.A.

KEQA 0.754 (+20.3%) 0.749

4.3 E�ectiveness of KEQAWe now answer the �rst research question asked at the beginningof this section, i.e., how e�ective is KEQA. We include seven state-of-the-art QA_KG algorithms as the baselines, and introduce themin the order of the publication years as follows.• Bordes et al. [6]: It learns latent representations for words,predicates, and entities, based on the training questions, suchthat a new question and candidate facts could be projectedinto the same space and compared.• Dai et al. [10]: It employs a bidirectional gated recurrentunits based neural network to rank the candidate predicates.Suggestions from the freebase API are used.• Yin et al. [43]: It employs a character-level convolutionalneural network to match the questions and predicates.• Golub and He [16]: It designs a character-level and attention-based LSTM to encode and decode questions.• Bao et al. [2]: It manually de�nes several types of constraintsand performs constraint learning to handle complex ques-tions, in which each question is related to several facts. Extratraining questions and freebase API are used.• Lukovnikov et al. [24]: It utilizes a character-level gated re-current units neural network to project questions and predi-cates/entities into the same space.• Mohammed et al. [26]: It treats the predicate prediction as aclassi�cation problem and uses di�erent neural networks tosolve it. It performs entity linking based on Fuzzy.4

As shown in the introduction above, all the baselines have takenadvantage of deep learning models to advance their methods. Weuse their results reported in the corresponding papers or the au-thors’ implementations. The performance of di�erent methods onSimpleQuestions w.r.t. FB2M and FB5M is listed in Table 3. Theresults in Table 3 demonstrate that the proposed framework KEQAoutperforms all the baselines. KEQA achieves 20.3% improvementcomparing to the accuracy when SimpleQuestions was released [6].The performance of KEQA decreases 0.7%when applied to FB5M. Itis because all the ground truth facts belong to FB2M [6], and FB5Mhas 26.1% more facts than FB2M.

As mentioned by several other work [24, 26], there are few algo-rithms [10, 43] achieve high accuracy, but they either used extrainformation sources or have no available implementations [32, 44].The extra training data includes freebase API suggestions, freebase5https://github.com/castorini/BuboQA/tree/master/evidence_integration

Effectiveness of KEQA

Ø KEQA outperforms all baselines.

Ø KEQA achieves 3.1% higher accuracy than KEQA_noEmbed.

Ø KEQA decreases 0.7% when applied to FB5M. 18

• Q2. How does the performance of KEQA vary when di�erentKG embedding algorithms are employed?• Q3. The objective function of KEQA consists of �ve termsas shown in Eq. (9). How much does each term contribute?

4.1 DatasetsWe �rst introduce the knowledge graph subsets and question an-swering dataset used in the experiments. All the data are publiclyavailable. Their statistics are shown in Table 2.

Table 2: The statistics of the question answering datasets.

FB2M FB5M SimpleQuestions

# Training 14,174,246 17,872,174 75,910# Validation N.A. N.A. 10,845

# Test N.A. N.A. 21,687# Predicates (M ) 6,701 7,523 1,837# Entities (N ) 1,963,130 3,988,105 131,681Vocabulary Size 733,278 1,213,205 61,336

FB2M and FB5M [19]: Freebase is often regarded as a reliableKG since it is collected and trimmed mainly by the communitymembers. Two large subsets of freebase are employed in this paper,i.e., FB2M and FB5M. Their predicate numberM and entity numberN are list in Table 2. The repeated facts have been deleted. Theapplication programming interface (API) of freebase is no longavailable. Thus, we use an entity name collection3 to build themapping between entities and their names.

SimpleQuestions [6]: It contains more than ten thousand sim-ple questions associated with corresponding facts. All these factsbelong to FB2M. All questions are phrased by English speakersbased on the facts and their context. It has been used as the bench-mark for the recent QA-KG methods [6, 18, 29].

4.2 Experimental SettingsTo evaluate the performance of the QA-KG methods, we follow thetraditional settings [10, 27, 46] and use the same training, validation,and test splits that are originally provided in SimpleQuestions [6].Either FB2M or FB5M is employed as the KG G. Then a KG embed-ding algorithm such as TransE [7] and TransR [25] is applied to Gto learn the P and E. It should be noted that P and E are not extrainformation sources. Then, a QA-KG method is applied to predictthe head entity and predicate of each question in the test split. Itsperformance is measured by the accuracy of predicting both headentity and predicate correctly.

As claimed in our formal problem de�nition, the evaluationcriterion is de�ned as the accuracy of predicting a new question’both head entity and predicate correctly. The dimension of the KGembedding representations d is set to be 250. A pre-trained wordembedding based on GloVe [31] is used. To measure the similar-ity of two string, i.e., to build the function sim[·, ·], we use theimplementation Fuzzy4. If it is not speci�c, the KG embedding al-gorithm TransE [7] would be employed to learn the embeddingrepresentations of all predicates P and entities E.3https://github.com/zihangdai/CFO4https://pypi.org/project/Fuzzy/

4.3 E�ectiveness of KEQAWe now answer the �rst research question asked at the beginningof this section, i.e., how e�ective is KEQA.We include 7 state-of-the-art QA-KG algorithms and one variation of KEQA as the baselines:• Bordes et al. [6]: It learns latent representations for words,predicates, and entities, based on the training questions, suchthat a new question and candidate facts could be projectedinto the same space and compared.• Dai et al. [10]: It employs a bidirectional gated recurrentunits based neural network to rank the candidate predicates.Suggestions from the freebase API are used.• Yin et al. [46]: It employs a character-level convolutionalneural network to match the questions and predicates.• Golub and He [18]: It designs a character-level and attention-based LSTM to encode and decode questions.• Bao et al. [2]: It manually de�nes several types of constraintsand performs constraint learning to handle complex ques-tions, in which each question is related to several facts. Extratraining questions and freebase API are used.• Lukovnikov et al. [27]: It utilizes a character-level gated re-current units neural network to project questions and predi-cates/entities into the same space.• Mohammed et al. [29]: It treats the predicate prediction as aclassi�cation problem and uses di�erent neural networks tosolve it. It performs entity linking based on Fuzzy4.• KEQA_noEmbed: No KG embedding algorithm is used. In-stead, it generates the predicate and entity embedding rep-resentations P and E randomly.

As shown in the introduction above, all the baselines have takenadvantage of deep learning models to advance their methods. Weuse their results reported in the corresponding papers or the au-thors’ implementations. The performance of di�erent methods onSimpleQuestions w.r.t. FB2M and FB5M is listed in Table 3.

Table 3: Performance of all methods on SimpleQuestions.

FB2M (Accuracy) FB5M

Bordes et al. (2015) [6] 0.627 0.639Dai et al.3 (2016) [10] N.A. 0.626Yin et al. (2016) [46] 0.683 (+8.9%) 0.672

Golub and He (2016) [18] 0.709 (+13.1%) 0.703Bao et al. (2016) [2] 0.728 (+16.1%) Entire Freebase

Lukovnikov et al. (2017) [27] 0.712 (+13.6%) N.A.Mohammed et al.5(2018) [29] 0.732 (+16.7%) N.A.

KEQA_noEmbed 0.731 (+16.6%) 0.726KEQA 0.754 (+20.3%) 0.749

Asmentioned by several otherwork [27, 29], a few algorithms [10,46] achieve high accuracy, but they either used extra informationsources or have no available implementations [35, 47]. The extratraining data freebase API suggestions, freebase entity linking re-sults, and trained segmentation models. These rely on the freebaseAPI, which is no longer available. Instead, our framework KEQAuses an entity name collection3, which is incomplete. Thus, for Dai

5https://github.com/castorini/BuboQA/tree/master/evidence_integration

Experimental Results

Ø Apply different KG embedding algorithms to learn thepredicate and entity embedding representations.

Ø SimpleQ_Missing: All predicates in test have never beenmentioned in the training and validation.

Ø KEQA is general and robust.

19

Table 4: Performance of KEQA with di�erent knowledgegraph embedding algorithm on FB2M.

SimpleQuestions SimpleQ_Missing

KEQA_noEmbed 0.731 0.386KEQA_TransE 0.754 (+3.1%) 0.418 (+8.3%)KEQA_TransH 0.749 (+2.5%) 0.411 (+6.5%)KEQA_TransR 0.753 (+3.0%) 0.417 (+8.0%)

entity linking results, and trained segmentation models. They relyon the freebase API, which is no longer available. Instead, our frame-work KEQA uses an entity name collection3, which is incomplete.Thus, for Dai et al. [10] and Yin et al. [43], we report their resultswhen no extra training data is used. There are two work [32, 44]claimed much higher accuracy, but without publicly available im-plementations. We are not able to replicate them, which has alsobeen pointed out by other work [26].

By jointly predicting the question’s predicate and head entity,KEQA achieves an accuracy of 0.754. In the predicate predictionsubtask, KEQA achieves an accuracy of 0.815 on the validation split,which is worse than the most recent one 0.828 achieved by Mo-hammed et al. [26]. This gap implies that our framework might befurther improved by a more sophisticated model. However, KEQAoutperforms Mohammed et al. [26] in the simple question answer-ing problem, which demonstrates the e�ectiveness of our proposedjointly learning framework. Through the jointly learning, KEQAachieves an accuracy of 0.816 in predicting the head entity, 0.754 inpredicting both head entity and predicate, and 0.680 in predictingthe entire fact, on the test split and FB2M. It implies that some ofthe ground truth facts do not exist in FB2M.

4.4 Generalizability and Robustness Evaluation4.4.1 Generalizability of KEQA. To study the second research ques-tion, i.e., how general is KEQA when di�erent KG embedding algo-rithms are used, we include three scalable KG embedding methodsin the comparison. Detailed introductions are listed as follows.• KEQA_noEmbed: No KG embedding algorithm is used. In-stead, it generates the predicate and entity embedding rep-resentations P and E randomly.• KEQA_TransE: TransE [7] is used to perform the KG embed-ding. TransE is a typical translation-based method. It de�nesthe relation function as et ⇡ f (eh , p` ) = eh + p` , and thenperforms the margin-based ranking to make all the factsapproach to satisfy the relation function.• KEQA_TransH: TransH [36] is used to perform the KG em-bedding. TransH is similar to TransE, and de�nes the relationfunction as e?t ⇡ e?h +p` , where e

?t = et �m>` etm` andm`

is the hyperplane of predicate `.• KEQA_TransR: TransR [22] is similar to TransE, and de�nesthe relation function as etM` ⇡ ehM` + p` , whereM` is atransform matrix of `.

The performance of KEQA when using di�erent KG embeddingalgorithms is shown in Table 4. From the results, we have threemajor observations as follows. First, the KG embedding algorithmshave enhanced the performance of KEQA. For example, KEQA

Table 5: The performance of KEQA with di�erent objectivefunctions on FB2M.

Only_Keep Remove Accumulate

kp` � p` k2 0.728 0.701 0.728keh � eh k2 0.195 0.751 0.745

k f (eh , p` ) � et k2 0.730 0.753 0.745sim[n(h),HEDentity] 0.173 0.754 0.746sim[n(`),HEDnon] 0.435 0.746 0.754

achieves 3.1% improvement when it is based on TransE, compar-ing to KEQA_noEmbed. Second, KEQA has similar performancewhen using di�erent KG embedding algorithms. It demonstratesthe generalizability of KEQA. Third, even though no KG embeddingalgorithm is used, KEQA could still achieve comparable perfor-mance to the state-of-the-art QA_KG methods as shown in Table 3.It validates the robustness of KEQA. The reason that randomly-generated P and E could achieve comparable performance is that ittends to make all {p` } uniformly distributed and far away from eachother. This would convert the representation prediction problem toa one that is similar to the classi�cation problem.

4.4.2 Robustness of KEQA. To further validate the robustness ofKEQA, we reshu�e all the 108,442 questions in SimpleQuestionsand get a new dataset named SimpleQ_Missing. To perform thereshu�e, we randomly split all the types of predicates into threegroups, and assign questions to these groups based on the predi-cates. Thus, in SimpleQ_Missing, all the corresponding predicatesof the questions in the test split have never been mentioned in thetraining and validation splits. In the end, we get 75,474 questions inthe training split, 11,017 questions in the validation split, and 21,951questions in the test split, which are roughly the same ratios as theones in SimpleQuestions. The performance of KEQA with di�erentKG embedding algorithms on SimpleQ_Missing is shown in Table 4.From the results, we observe that KEQA could still achieve an ac-curacy of 0.418 with the help of TransE. The global relation andstructure information preserved in the KG embedding representa-tions P and E enables KEQA to perform 8.3% better than Random.These observations demonstrate the robustness of KEQA.

4.5 Parameter AnalysisWenow investigate the third research question, i.e., howmuch couldeach term in the objective function of KEQA contribute. There are�ve terms in the objective function of KEQA as shown in Eq. (9).We valid the performance of KEQA w.r.t. three groups of di�erentobjective functions. To study the contribution of every single termin Eq. (9), in the �rst group, i.e., Only_Keep, we only keep one ofthe �ve terms as the new objective function. To study the impactof missing one of the �ve terms in Eq. (9), in the second group, i.e.,Remove, we remove one of the �ve terms. To study the accumulatedcontributions, in the third group, i.e., Accumulate, we add terms asthe new objective function one by one.

The performance of KEQA w.r.t. di�erent objective functions onFB2M is summarized in Table 5. From the results, we have threemajor observations. First, the predicted predicate representationp` has the most signi�cant contribution in our framework. The

Conclusions

Ø We formally define knowledge graph embedding based question answering problem.

Ø KEQA could answer a natural language question by jointly recovering its head entity, predicate, and tail entity representations in the KG embedding spaces.

Ø We design a joint distance metric that takes the structures and relations preserved in the KG embedding representations into consideration.

Ø We empirically demonstrate that the separate task KG embedding indeed could help the question answering task.

20

21

Acknowledgement

Ø Cognitive Computing Lab

Ø

Ø Everyone attending the talk

WSDM 2019, Melbourne, USA

Cognitive Computing Lab (CCL), Baidu Research, USA Emails...

Documents

Transcript of Cognitive Computing Lab (CCL), Baidu Research, USA Emails...