• No results found

A Stack Propagation Framework with Token Level Intent Detection for Spoken Language Understanding

N/A
N/A
Protected

Academic year: 2020

Share "A Stack Propagation Framework with Token Level Intent Detection for Spoken Language Understanding"

Copied!
10
0
0

Loading.... (view fulltext now)

Full text

(1)

Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing

2078

A Stack-Propagation Framework with Token-Level Intent Detection for

Spoken Language Understanding

Libo Qin, Wanxiang Che∗, Yangming Li, Haoyang Wen, Ting Liu

Research Center for Social Computing and Information Retrieval Harbin Institute of Technology, China

{lbqin,car,yangmingli,hywen,tliu}@ir.hit.edu.cn

Abstract

Intent detection and slot filling are two main tasks for building a spoken language

under-standing (SLU) system. The two tasks are

closely tied and the slots often highly

de-pend on the intent. In this paper, we

pro-pose a novel framework for SLU to better in-corporate the intent information, which

fur-ther guides the slot filling. In our

frame-work, we adopt a joint model with Stack-Propagation which can directly use the intent information as input for slot filling, thus to

capture the intent semantic knowledge. In

addition, to further alleviate the error propa-gation, we perform the token-level intent de-tection for the Stack-Propagation framework. Experiments on two publicly datasets show that our model achieves the state-of-the-art performance and outperforms other previous methods by a large margin. Finally, we use the Bidirectional Encoder Representation from Transformer (BERT) model in our framework, which further boost our performance in SLU task.

1 Introduction

Spoken language understanding (SLU) is a criti-cal component in task-oriented dialogue systems. It usually consists of intent detection to identify users’ intents and slot filling task to extract se-mantic constituents from the natural language

ut-terances (Tur and De Mori, 2011). As shown in

Table 1, given a movie-related utterance “watch

action movie”, there are different slot labels for each token and an intent for the whole utterance.

Usually, intent detection and slot filling are

implemented separately. But intuitively, these

two tasks are not independent and the slots of-ten highly depend on the inof-tent (Goo et al., 2018). For example, if the intent of a utterance is

* Email corresponding.

Sentence watch action movie

Gold Slots O B-movie name I-movie name

Gold Intent WatchMovie

Table 1: An example with intent and slot annotation (BIO format), which indicates the slot of movie name

from an utterance with an intentWatchMovie.

WatchMovie, it is more likely to contain the slot

movie namerather than the slotmusic name.

Hence, it is promising to incorporate the intent in-formation to guide the slot filling.

Considering this strong correlation between the two tasks, some joint models are proposed based on the multi-task learning framework (Zhang and

Wang, 2016; Hakkani-T¨ur et al., 2016; Liu and

Lane,2016) and all these models outperform the

pipeline models via mutual enhancement between

two tasks. However, their work just modeled

the relationship between intent and slots by shar-ing parameters. Recently, some work begins to model the intent information for slot filling

ex-plicitly in joint model. Goo et al. (2018) and Li

et al.(2018) proposed the gate mechanism to

ex-plore incorporating the intent information for slot filling. Though achieving the promising perfor-mance, their models still suffer from two issues including: (1) They all adopt the gate vector to incorporate the intent information. In the paper, we argue that it is risky to simply rely on the gate function to summarize or memorize the intent in-formation. Besides, the interpretability of how the intent information guides slot filling procedure is still weak due to the interaction with hidden vector between the two tasks. (2) The utterance-level in-tent information they use for slot filling may mis-lead the prediction for all slots in an utterance if the predicted utterance-level intent is incorrect.

(2)

Encoder

Task B Task A

Encoder Task B

Task A differentiable link

[image:2.595.74.292.64.153.2]

(a) Multi-task framework (b) Stack-propagation

Figure 1: Multi-task framework vs. Stack-Propagation.

proposed by Zhang and Weiss(2016) to leverage

the POS tagging features for parsing and achieved good performance, we propose a joint model with Stack-Propagation for SLU tasks. Our framework directly use the output of the intent detection as the input for slot filling to better guide the slot

prediction process. In addition, the framework

make it easy to design oracle intent experiment to intuitively show how intent information enhances slot filling task. For the second issue, we perform a token-level intent prediction in our framework, which can provide the token-level intent informa-tion for slot filling. If some token-level intents in the utterance are predicted incorrectly, other cor-rect token-level intents will still be useful for the corresponding slot prediction. In practice, we use a self-attentive encoder for intent detection to cap-ture the contextual information at each token and hence predict an intent label at each token. The intent of an utterance is computed by voting from predictions at each token of the utterance. This token-level prediction, like ensemble neural

net-works (Lee et al., 2016), reduces the predicted

variance to improve the performance of intent de-tection. And it fits better in our Stack-Propagation framework, where intent detection can provide token-level intent features and retain more useful intent information for slot filling.

We conduct experiments on two benchmarks

SNIPS (Coucke et al.,2018) and ATIS (Goo et al.,

2018) datasets. The results of both experiments show the effectiveness of our framework by out-performing the current state-of-the-art methods by

a large margin. Finally, Bidirectional Encoder

Representation from Transformer (Devlin et al., 2018, BERT), as the pre-trained model, is used to further boost the performance of our model.

To summarize, the contributions of this work are as follows:

• We propose a Stack-Propagation framework

in SLU task, which can better incorporate the

intent semantic knowledge to guide the slot filling and make our joint model more inter-pretable.

• We perform the token-level intent detection

for Stack-Propagation framework, which im-proves the intent detection performance and further alleviate the error propagation.

• We present extensive experiments

demon-strating the benefit of our proposed frame-work. Our experiments on two publicly avail-able datasets show substantial improvement and our framework achieve the state-of-the-art performance.

• We explore and analyze the effect of

incorpo-rating BERT in SLU tasks.

For reproducibility, our code for this paper is

publicly available at https://github.com/

LeePleased/StackPropagation-SLU.

2 Background

In this section, we will describe the formulation definition for intent detection and slot filling, and then we give a brief description of the multi-task framework and the joint model with Stack-Propagation framework.

2.1 Intent Detection and Slot Filling

Intent detection can be seen as a classification

problem to decide the intent label oI of an

utter-ance. Slot filling is a sequence labeling task that

maps an input word sequencex=(x1, . . . , xT)to

slots sequenceoS =(oS

1, . . . , oST).

2.2 Multi-task Framework vs.

Stack-Propagation

For two correlative tasksTask AandTask B,

multi-task framework which is shown in Figure 1 (a)

can learn the correlations between these two tasks by the shared encoder. However, the basic multi-task framework cannot provide features from up-stream task to down-up-stream task explicitly. The joint model with Stack-Propagation framework

which is shown in Figure 1 (b) can mitigate the

shortcoming. In this figure, Task B can leverage

features ofTask A without breaking the

(3)

Token-level Intent Detection decoder !"#$%&' Self-Attentive Encoder Slot Filling decoder

watch action movie

ListenMusic WatchMovie WatchMovie

O B-movie_name I-movie_name

Slot Filling Input layer

e1

<latexit sha1_base64="UOJMj9uT+rMuVRiicAlHNm5A4CY=">AAACyHicjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFl0I64qmLZQS0mm0zo0TcJkopTSjT/gVr9M/AP9C++MKahFdEKSM+fec2buvUESilQ5zmvBWlhcWl4prpbW1jc2t8rbO400ziTjHovDWLYCP+WhiLinhAp5K5HcHwUhbwbDcx1v3nGZiji6VuOEd0b+IBJ9wXxFlMe7E3faLVecqmOWPQ/cHFSQr3pcfsENeojBkGEEjgiKcAgfKT1tuHCQENfBhDhJSJg4xxQl0maUxSnDJ3ZI3wHt2jkb0V57pkbN6JSQXklKGwekiSlPEtan2SaeGWfN/uY9MZ76bmP6B7nXiFiFW2L/0s0y/6vTtSj0cWpqEFRTYhhdHctdMtMVfXP7S1WKHBLiNO5RXBJmRjnrs200qald99Y38TeTqVm9Z3luhnd9Sxqw+3Oc86BxVHWdqnt1XKmd5aMuYg/7OKR5nqCGC9ThkbfAI57wbF1aiXVvjT9TrUKu2cW3ZT18AHwckRo=</latexit><latexit sha1_base64="UOJMj9uT+rMuVRiicAlHNm5A4CY=">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</latexit><latexit sha1_base64="UOJMj9uT+rMuVRiicAlHNm5A4CY=">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</latexit><latexit sha1_base64="UOJMj9uT+rMuVRiicAlHNm5A4CY=">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</latexit> e2<latexit sha1_base64="F3mSGmP2ncMwlvmE/DRl8ixSd+o=">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</latexit><latexit sha1_base64="F3mSGmP2ncMwlvmE/DRl8ixSd+o=">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</latexit><latexit sha1_base64="F3mSGmP2ncMwlvmE/DRl8ixSd+o=">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</latexit><latexit sha1_base64="F3mSGmP2ncMwlvmE/DRl8ixSd+o=">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</latexit> e3<latexit sha1_base64="eb4TJOGLUZm66tydoux6u5LjkOo=">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</latexit><latexit sha1_base64="eb4TJOGLUZm66tydoux6u5LjkOo=">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</latexit><latexit sha1_base64="eb4TJOGLUZm66tydoux6u5LjkOo=">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</latexit><latexit sha1_base64="eb4TJOGLUZm66tydoux6u5LjkOo=">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</latexit>

hI

1

<latexit sha1_base64="DT+3KsZZtd7aVK4fLuT/2gohxms=">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</latexit><latexit sha1_base64="DT+3KsZZtd7aVK4fLuT/2gohxms=">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</latexit><latexit sha1_base64="DT+3KsZZtd7aVK4fLuT/2gohxms=">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</latexit><latexit sha1_base64="DT+3KsZZtd7aVK4fLuT/2gohxms=">AAACzHicjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFl0oxupYB+itSTTaRuaF8lEKKFbf8Ctfpf4B/oX3hmnoBbRCUnOnHvPmbn3urHvpcKyXgvG3PzC4lJxubSyura+Ud7caqZRljDeYJEfJW3XSbnvhbwhPOHzdpxwJ3B93nJHpzLeuudJ6kXhlRjHvBM4g9Dre8wRRF0Pu7k9ucvPJ91yxapaapmzwNagAr3qUfkFt+ghAkOGABwhBGEfDlJ6bmDDQkxcBzlxCSFPxTkmKJE2oyxOGQ6xI/oOaHej2ZD20jNVakan+PQmpDSxR5qI8hLC8jRTxTPlLNnfvHPlKe82pr+rvQJiBYbE/qWbZv5XJ2sR6ONY1eBRTbFiZHVMu2SqK/Lm5peqBDnExEnco3hCmCnltM+m0qSqdtlbR8XfVKZk5Z7p3Azv8pY0YPvnOGdB86BqW1X78rBSO9GjLmIHu9ineR6hhjPU0SDvAI94wrNxYQgjNyafqUZBa7bxbRkPH/5pkuQ=</latexit> h I 2

<latexit sha1_base64="HeowE0H4h5VL5Eukv4XZhEZLcw4=">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</latexit><latexit sha1_base64="HeowE0H4h5VL5Eukv4XZhEZLcw4=">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</latexit><latexit sha1_base64="HeowE0H4h5VL5Eukv4XZhEZLcw4=">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</latexit><latexit sha1_base64="HeowE0H4h5VL5Eukv4XZhEZLcw4=">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</latexit>

hI

3

<latexit sha1_base64="Lhjjb5BqmKlvyQ2nXCZJSds+ox4=">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</latexit><latexit sha1_base64="Lhjjb5BqmKlvyQ2nXCZJSds+ox4=">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</latexit><latexit sha1_base64="Lhjjb5BqmKlvyQ2nXCZJSds+ox4=">AAACzHicjVHLSsNAFD2Nr1pfVZdugkVwVRIVdFl0oxupYB9Sa0mm0zY0L5KJUEK2/oBb/S7xD/QvvDOmoBbRCUnOnHvPmbn32qHrxMIwXgva3PzC4lJxubSyura+Ud7casZBEjHeYIEbRG3birnr+LwhHOHydhhxy7Nd3rLHZzLeuudR7AT+tZiEvOtZQ98ZOMwSRN2MeulhdpdeZL1yxagaaumzwMxBBfmqB+UX3KKPAAwJPHD4EIRdWIjp6cCEgZC4LlLiIkKOinNkKJE2oSxOGRaxY/oOadfJWZ/20jNWakanuPRGpNSxR5qA8iLC8jRdxRPlLNnfvFPlKe82ob+de3nECoyI/Us3zfyvTtYiMMCJqsGhmkLFyOpY7pKorsib61+qEuQQEidxn+IRYaaU0z7rShOr2mVvLRV/U5mSlXuW5yZ4l7ekAZs/xzkLmgdV06iaV0eV2mk+6iJ2sIt9mucxajhHHQ3y9vCIJzxrl5rQUi37TNUKuWYb35b28AEDQpLm</latexit><latexit sha1_base64="Lhjjb5BqmKlvyQ2nXCZJSds+ox4=">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</latexit>

yI

1

<latexit sha1_base64="aXffR0+U7zD6WDCXHpfQVh2mHEs=">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</latexit><latexit sha1_base64="aXffR0+U7zD6WDCXHpfQVh2mHEs=">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</latexit><latexit sha1_base64="aXffR0+U7zD6WDCXHpfQVh2mHEs=">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</latexit><latexit sha1_base64="aXffR0+U7zD6WDCXHpfQVh2mHEs=">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</latexit> y I 2

<latexit sha1_base64="lCQF+ce0PZhNE9W3CXyq0bRUSS4=">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</latexit><latexit sha1_base64="lCQF+ce0PZhNE9W3CXyq0bRUSS4=">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</latexit><latexit sha1_base64="lCQF+ce0PZhNE9W3CXyq0bRUSS4=">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</latexit><latexit sha1_base64="lCQF+ce0PZhNE9W3CXyq0bRUSS4=">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</latexit> y I 3

<latexit sha1_base64="9uFL3tkFHzoasuUxqza6+iqxvSI=">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</latexit><latexit sha1_base64="9uFL3tkFHzoasuUxqza6+iqxvSI=">AAACzHicjVHLSsNAFD2Nr1pfVZdugkVwVRIVdFl0oxupYB9Sa0mm0zqYF8lEKKFbf8Ctfpf4B/oX3hlTUIvohCRnzr3nzNx73cgTibSs14IxMzs3v1BcLC0tr6yuldc3mkmYxow3WOiFcdt1Eu6JgDekkB5vRzF3fNfjLffuRMVb9zxORBhcylHEu74zDMRAMEcSdTXqZfvjm+xs3CtXrKqllzkN7BxUkK96WH7BNfoIwZDCB0cASdiDg4SeDmxYiIjrIiMuJiR0nGOMEmlTyuKU4RB7R98h7To5G9BeeSZazegUj96YlCZ2SBNSXkxYnWbqeKqdFfubd6Y91d1G9HdzL59YiVti/9JNMv+rU7VIDHCkaxBUU6QZVR3LXVLdFXVz80tVkhwi4hTuUzwmzLRy0mdTaxJdu+qto+NvOlOxas/y3BTv6pY0YPvnOKdBc69qW1X74qBSO85HXcQWtrFL8zxEDaeoo0HePh7xhGfj3JBGZow/U41CrtnEt2U8fAAsKpL3</latexit><latexit sha1_base64="9uFL3tkFHzoasuUxqza6+iqxvSI=">AAACzHicjVHLSsNAFD2Nr1pfVZdugkVwVRIVdFl0oxupYB9Sa0mm0zqYF8lEKKFbf8Ctfpf4B/oX3hlTUIvohCRnzr3nzNx73cgTibSs14IxMzs3v1BcLC0tr6yuldc3mkmYxow3WOiFcdt1Eu6JgDekkB5vRzF3fNfjLffuRMVb9zxORBhcylHEu74zDMRAMEcSdTXqZfvjm+xs3CtXrKqllzkN7BxUkK96WH7BNfoIwZDCB0cASdiDg4SeDmxYiIjrIiMuJiR0nGOMEmlTyuKU4RB7R98h7To5G9BeeSZazegUj96YlCZ2SBNSXkxYnWbqeKqdFfubd6Y91d1G9HdzL59YiVti/9JNMv+rU7VIDHCkaxBUU6QZVR3LXVLdFXVz80tVkhwi4hTuUzwmzLRy0mdTaxJdu+qto+NvOlOxas/y3BTv6pY0YPvnOKdBc69qW1X74qBSO85HXcQWtrFL8zxEDaeoo0HePh7xhGfj3JBGZow/U41CrtnEt2U8fAAsKpL3</latexit><latexit sha1_base64="9uFL3tkFHzoasuUxqza6+iqxvSI=">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</latexit>

e1

<latexit sha1_base64="UOJMj9uT+rMuVRiicAlHNm5A4CY=">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</latexit><latexit sha1_base64="UOJMj9uT+rMuVRiicAlHNm5A4CY=">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</latexit><latexit sha1_base64="UOJMj9uT+rMuVRiicAlHNm5A4CY=">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</latexit><latexit sha1_base64="UOJMj9uT+rMuVRiicAlHNm5A4CY=">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</latexit> e2<latexit sha1_base64="F3mSGmP2ncMwlvmE/DRl8ixSd+o=">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</latexit><latexit sha1_base64="F3mSGmP2ncMwlvmE/DRl8ixSd+o=">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</latexit><latexit sha1_base64="F3mSGmP2ncMwlvmE/DRl8ixSd+o=">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</latexit><latexit sha1_base64="F3mSGmP2ncMwlvmE/DRl8ixSd+o=">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</latexit> e3<latexit sha1_base64="eb4TJOGLUZm66tydoux6u5LjkOo=">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</latexit><latexit sha1_base64="eb4TJOGLUZm66tydoux6u5LjkOo=">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</latexit><latexit sha1_base64="eb4TJOGLUZm66tydoux6u5LjkOo=">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</latexit><latexit sha1_base64="eb4TJOGLUZm66tydoux6u5LjkOo=">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</latexit>

yS

1

<latexit sha1_base64="7KQn+jiaa+WDI5N+WNipX54diVg=">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</latexit><latexit sha1_base64="7KQn+jiaa+WDI5N+WNipX54diVg=">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</latexit><latexit sha1_base64="7KQn+jiaa+WDI5N+WNipX54diVg=">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</latexit>

<latexit sha1_base64="7KQn+jiaa+WDI5N+WNipX54diVg=">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</latexit> y

S 2 <latexit sha1_base64="n1sH4BzpnCpJUU+cZTcSZN5qnqM=">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</latexit> <latexit sha1_base64="n1sH4BzpnCpJUU+cZTcSZN5qnqM=">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</latexit> <latexit sha1_base64="n1sH4BzpnCpJUU+cZTcSZN5qnqM=">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</latexit> <latexit sha1_base64="n1sH4BzpnCpJUU+cZTcSZN5qnqM=">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</latexit> yS 3 <latexit sha1_base64="YBzyFPDCtdngi/81pQ8hwLv1T6k=">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</latexit> <latexit sha1_base64="YBzyFPDCtdngi/81pQ8hwLv1T6k=">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</latexit> <latexit sha1_base64="YBzyFPDCtdngi/81pQ8hwLv1T6k=">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</latexit> <latexit sha1_base64="YBzyFPDCtdngi/81pQ8hwLv1T6k=">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</latexit> hS 1 <latexit sha1_base64="koGtsOnLJ5gNktNbiWo158+rn34=">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</latexit> <latexit sha1_base64="koGtsOnLJ5gNktNbiWo158+rn34=">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</latexit> <latexit sha1_base64="koGtsOnLJ5gNktNbiWo158+rn34=">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</latexit> <latexit sha1_base64="koGtsOnLJ5gNktNbiWo158+rn34=">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</latexit> hS 2 <latexit sha1_base64="3ALZUvutjwDg3w01ckmR7hv6LO0=">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</latexit> <latexit sha1_base64="3ALZUvutjwDg3w01ckmR7hv6LO0=">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</latexit> <latexit sha1_base64="3ALZUvutjwDg3w01ckmR7hv6LO0=">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</latexit> <latexit sha1_base64="3ALZUvutjwDg3w01ckmR7hv6LO0=">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</latexit> hS 3 <latexit sha1_base64="WDHlYMnkm+sSstpAtExanW9AleI=">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</latexit> <latexit sha1_base64="WDHlYMnkm+sSstpAtExanW9AleI=">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</latexit> <latexit sha1_base64="WDHlYMnkm+sSstpAtExanW9AleI=">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</latexit> <latexit sha1_base64="WDHlYMnkm+sSstpAtExanW9AleI=">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</latexit> oS 1 <latexit sha1_base64="8bMqy/XTwZZ49li6ATaPll+NUlo=">AAACzHicjVHLSsNAFD2Nr1pfVZdugkVwVRIRdFl040oq2ofUWpJ0WkOTTEgmQgnd+gNu9bvEP9C/8M44BbWITkhy5tx7zsy9140DPxWW9Vow5uYXFpeKy6WV1bX1jfLmVjPlWeKxhscDnrRdJ2WBH7GG8EXA2nHCnNANWMsdncp4654lqc+jKzGOWTd0hpE/8D1HEHXNe7k9uc0vJ71yxapaapmzwNagAr3qvPyCG/TB4SFDCIYIgnAAByk9HdiwEBPXRU5cQshXcYYJSqTNKItRhkPsiL5D2nU0G9FeeqZK7dEpAb0JKU3skYZTXkJYnmaqeKacJfubd6485d3G9He1V0iswB2xf+mmmf/VyVoEBjhWNfhUU6wYWZ2nXTLVFXlz80tVghxi4iTuUzwh7CnltM+m0qSqdtlbR8XfVKZk5d7TuRne5S1pwPbPcc6C5kHVtqr2xWGldqJHXcQOdrFP8zxCDWeoo0HeIR7xhGfj3BBGbkw+U42C1mzj2zIePgAnGpL1</latexit> <latexit sha1_base64="8bMqy/XTwZZ49li6ATaPll+NUlo=">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</latexit> <latexit sha1_base64="8bMqy/XTwZZ49li6ATaPll+NUlo=">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</latexit>

<latexit sha1_base64="8bMqy/XTwZZ49li6ATaPll+NUlo=">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</latexit> o

S 2

<latexit sha1_base64="yza2LYCy4pl1iLmGZ9rXHT3DCMQ=">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</latexit><latexit sha1_base64="yza2LYCy4pl1iLmGZ9rXHT3DCMQ=">AAACzHicjVHLSsNAFD2Nr1pfVZdugkVwVZIi6LLoxpVUtA/RWpLptIbmRTIRSujWH3Cr3yX+gf6Fd8YpqEV0QpIz595zZu69bux7qbCs14IxN7+wuFRcLq2srq1vlDe3WmmUJYw3WeRHScd1Uu57IW8KT/i8EyfcCVyft93RiYy373mSelF4KcYx7wbOMPQGHnMEUVdRL69NbvOLSa9csaqWWuYssDWoQK9GVH7BDfqIwJAhAEcIQdiHg5Sea9iwEBPXRU5cQshTcY4JSqTNKItThkPsiL5D2l1rNqS99EyVmtEpPr0JKU3skSaivISwPM1U8Uw5S/Y371x5yruN6e9qr4BYgTti/9JNM/+rk7UIDHCkavCoplgxsjqmXTLVFXlz80tVghxi4iTuUzwhzJRy2mdTaVJVu+yto+JvKlOycs90boZ3eUsasP1znLOgVavaVtU+P6jUj/Woi9jBLvZpnoeo4xQNNMk7wCOe8GycGcLIjclnqlHQmm18W8bDByl/kvY=</latexit>

<latexit sha1_base64="yza2LYCy4pl1iLmGZ9rXHT3DCMQ=">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</latexit>

<latexit sha1_base64="yza2LYCy4pl1iLmGZ9rXHT3DCMQ=">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</latexit> o

[image:3.595.74.281.60.264.2]

S 3 <latexit sha1_base64="05BLDbvFUmjoMdr8QHxP2FEZZGc=">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</latexit> <latexit sha1_base64="05BLDbvFUmjoMdr8QHxP2FEZZGc=">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</latexit> <latexit sha1_base64="05BLDbvFUmjoMdr8QHxP2FEZZGc=">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</latexit> <latexit sha1_base64="05BLDbvFUmjoMdr8QHxP2FEZZGc=">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</latexit>

Figure 2: Illustration of our Stack-Propagation frame-work for joint intent detection and slot filling. It con-sists of one shared self-attentive encoder and two de-coders. The output distribution of intent detection net-work and the representations from encoder are concate-nated as the input for slot filling.

3 Approach

In this section, we will describe our

Stack-Propagation framework for SLU task. The

ar-chitecture of our framework is demonstrated in

Figure 2, which consists of an encoder and two

decoders. First, the encoder module uses one

shared self-attentive encoder to represent an utter-ance, which can grasp the shared knowledge be-tween two tasks. Then, the intent-detection de-coder performs a token-level intent detection. Fi-nally, our Stack-Propagation framework leverages the explicit token-level intent information for slot filling by concatenating the output of intent detec-tion decoder and the representadetec-tions from encoder as the input for slot filling decoder. Both intent detection and slot filling are optimized simultane-ously via a joint learning scheme.

3.1 Self-Attentive Encoder

In our Stack-Propagation framework, intent detec-tion task and slot filling task share one encoder, In the self-attentive encoder, we use BiLSTM with self-attention mechanism to leverage both advan-tages of temporal features and contextual informa-tion, which are useful for sequence labeling tasks

(Zhong et al.,2018;Yin et al.,2018).

The BiLSTM (Hochreiter and Schmidhuber,

1997) reads input utterance X = (x1,x2, ..,xT)

(T is the number of tokens in the input utterance)

forwardly and backwardly to produce

context-sensitive hidden states H = (h1,h2, ...,hT)

by repeatedly applying the recurrence hi =

BiLSTM φemb(x

i),hi−1

.

Self-attention is a very effective method of leveraging context-aware features over variable-length sequences for natural language processing

tasks (Tan et al.,2018;Zhong et al.,2018). In our

case, we use self-attention mechanism to capture the contextual information for each token. In this

paper, we adoptVaswani et al. (2017), where we

first map the matrix of input vectorsX∈RT×d(d

represents the mapped dimension) to queries (Q), keys (K) and values (V) matrices by using differ-ent linear projections and the self-attdiffer-ention output

C∈RT×dis a weighted sum of values:

C= softmax

QK> √ dk V. (1)

After obtaining the output of self-attention and BiLSTM. We concatenate these two representa-tions as the final encoding representation:

E=H⊕C, (2)

whereE∈RT×2d and⊕is concatenation

opera-tion.

3.2 Token-Level Intent Detection Decoder

In our framework, we perform a token-level tent detection, which can provide token-level in-tent features for slot filling, different from regard-ing the intent detection task as the sentence-level

classification problem (Liu and Lane,2016). The

token-level intent detection method can be formal-ized as a sequence labeling problem that maps a

input word sequencex=(x1, ..., xT)to sequence

of intent labeloI = (oI

1, ..., oIT). In training time,

we set the sentence’s intent label as every token’s gold intent label. The final intent of an utterance is computed by voting from predictions at each token of the utterance.

The self-attentive encoder generates a sequence

of contextual representationsE= (e1, ...,eT)and

each token can grasp the whole contextual infor-mation by self-attention mechanism. We use a uni-directional LSTM as the intent detection network.

At each decoding step i, the decoder state hI

i is

calculated by previous decoder statehIi1, the

pre-vious emitted intent label distributionyIi1and the

aligned encoder hidden stateei:

hIi =f hIi1,yiI1,ei

(4)

Then the decoder statehIi is utilized for intent de-tection:

yIi = softmax WIhhIi

, (4)

oIi = argmax(yIi), (5)

where yiI is the intent output distribution of the

ith token in the utterance;oI

i represents the intent

lable ofith token andWIhare trainable parameters

of the model.

The final utterance resultoIis generated by

vot-ing from all token intent results:

oI = argmax

m

X

i=1

nI

X

j=1

αj1[oIi =j], (6)

where m is the length of utterance andnI is the

number of intent labels;αj denotes a 0-1 vectorα

∈RnI of which thejth unit is one and the others

are zero;argmaxindicates the operation returning

the indices of the maximum values inα.

By performing the token-level intent detection, there are mainly two advantages:

1. Performing the token-level intent detection can provide features at each token to slot filling in our Stack-Propagation framework, which can ease the error propagation and retain more useful infor-mation for slot filling. Compared with

sentence-level intent detection (Li et al., 2018), if the

in-tent of the whole sentence is predicted wrongly, the wrong intent would possibly apply a negative impact on all slots. However, in token-level intent detection, if some tokens in the utterance predicted wrongly, other correct token-level intent informa-tion will still be useful for the corresponding slot filling.

2. Since each token can grasp the whole ut-terance contextual information by using the self-attentive encoder, we can consider predictions at each token in an utterance as individual predic-tion to the intent of this utterance. And there-fore, like ensemble neural networks, this approach will reduce the predicted variance and improve the performance of intent detection. The experiments section empirically demonstrate the effectiveness of the token-level intent detection.

3.3 Stack-propagation for Slot Filling

In this paper, one of the advantages of our Stack-Propagation framework is directly leveraging the explicit intent information to constrain the slots into a specific intent and alleviate the burden of

slot filling decoder. In our framework, we com-pose the input units for slot filling decoder by

con-catenating the intent output distributionyIi and the

aligned encoder hidden stateei.

For the slot-filling decoder, we similarly use an-other unidirectional LSTM as the slot-filling

de-coder. At the decoding stepi, the decoder statehSi

can be formalized as:

hSi =f hSi−1,ySi−1,yIi ⊕ei

, (7)

wherehS

i−1 is the previous decoder state;ySi−1 is

the previous emitted slot label distribution.

Similarily, the decoder state hIi is utilized for

slot filling:

yiS = softmax WhShSi

, (8)

oSi = argmax(ySi), (9)

where oS

i is the slot label of the ith word in the

utterance.

3.4 Joint Training

Another major difference between existing joint

work (Zhang and Wang, 2016;Goo et al., 2018)

and our framework is the training method for in-tent detection, where we convert the sentence-level classification task into token-sentence-level prediction to directly leverage token-level intent information for slot filling. And the intent detection objection is formulated as:

L1,

m

X

j=1

nI

X

i=1 ˆ

yi,Ij logyji,I. (10)

Similarly, the slot filling task objection is defined as:

L2 ,−

m

X

j=1

nS

X

i=1 ˆ

yi,Sj logyi,Sj , (11)

whereyˆji,I andyˆi,Sj are the gold intent label and

gold slot label separately;nSis the number of slot

labels.

To obtain both slot filling and intent detection jointly, the final joint objective is formulated as

Lθ =L1+L2. (12)

Through the joint loss function, the shared rep-resentations learned by the shared self-attentive encoder can consider two tasks jointly and further ease the error propagation compared with pipeline

(5)

4 Experiments

4.1 Experimental Settings

To evaluate the efficiency of our proposed model, we conduct experiments on two bench-mark datasets. One is the publicly ATIS dataset

(Hemphill et al., 1990) containing audio

record-ings of flight reservations, and the other is the custom-intent-engines collected by Snips (SNIPS

dataset) (Coucke et al., 2018). 1 Both datasets

used in our paper follows the same format and

par-tition as inGoo et al.(2018). The dimensionalities

of the word embedding is 256 for ATIS dataset and 512 for SNIPS dataset. The self-attentive encoder hidden units are set as 256. L2 regularization is

used on our model is 1 ×10−6 and dropout

ra-tio is adopted is 0.4 for reducing overfit. We use

Adam (Kingma and Ba,2014) to optimize the

pa-rameters in our model and adopted the suggested hyper-parameters for optimization. For all the ex-periments, we select the model which works the best on the dev set, and then evaluate it on the test set.

4.2 Baselines

We compare our model with the existing baselines including:

• Joint Seq. Hakkani-T¨ur et al. (2016)

pro-posed a multi-task modeling approach for jointly modeling domain detection, intent de-tection, and slot filling in a single recurrent neural network (RNN) architecture.

• Attention BiRNN. Liu and Lane (2016)

leveraged the attention mechanism to allow the network to learn the relationship between slot and intent.

• Slot-Gated Atten. Goo et al. (2018)

pro-posed the slot-gated joint model to explore the correlation of slot filling and intent detec-tion better.

• Self-Attentive Model. Li et al. (2018)

pro-posed a novel self-attentive model with the intent augmented gate mechanism to utilize the semantic correlation between slot and in-tent.

1https://github.com/snipsco/

nlu-benchmark/tree/master/ 2017-06-custom-intent-engines

• Bi-Model. Wang et al. (2018) proposed the

Bi-model to consider the intent and slot fill-ing cross-impact to each other.

• CAPSULE-NLU. Zhang et al. (2019)

proposed a capsule-based neural network model with a dynamic routing-by-agreement schema to accomplish slot filling and intent detection.

• SF-ID Network. (E et al.,2019) introduced

an SF-ID network to establish direct connec-tions for the slot filling and intent detection to help them promote each other mutually.

For the Joint Seq, Attention BiRNN, Slot-gated

Atten, CAPSULE-NLU and SF-ID Network, we

adopt the reported results fromGoo et al.(2018);

Zhang et al.(2019);E et al.(2019). For the

Self-Attentive Model, Bi-Model, we re-implemented

the models and obtained the results on the same

datasets.2

4.3 Overall Results

FollowingGoo et al.(2018), we evaluate the SLU

performance of slot filling using F1 score and the performance of intent prediction using accuracy, and sentence-level semantic frame parsing using

overall accuracy. Table2shows the experiment

re-sults of the proposed models on SNIPS and ATIS datasets.

From the table, we can see that our model sig-nificantly outperforms all the baselines by a large margin and achieves the state-of-the-art perfor-mance. In the SNIPS dataset, compared with the

best prior joint workBi-Model, we achieve 0.7%

improvement on Slot (F1) score, 0.8% improve-ment on Intent (Acc) and 3.1% improveimprove-ment on Overall (Acc). In the ATIS dataset, we achieve 0.4% improvement on Slot (F1) score, 0.5% im-provement on Intent (Acc) and 0.8% imim-provement

on Overall (Acc). This indicates the

effective-ness of our Stack-Propagation framework. Espe-cially, our framework gains the largest improve-ments on sentence-level semantic frame accuracy,

2

(6)

Model SNIPS ATIS

Slot (F1) Intent (Acc) Overall (Acc) Slot (F1) Intent (Acc) Overall (Acc) Joint Seq (Hakkani-T¨ur et al.,2016) 87.3 96.9 73.2 94.3 92.6 80.7 Attention BiRNN (Liu and Lane,2016) 87.8 96.7 74.1 94.2 91.1 78.9 Slot-Gated Full Atten (Goo et al.,2018) 88.8 97.0 75.5 94.8 93.6 82.2 Slot-Gated Intent Atten (Goo et al.,2018) 88.3 96.8 74.6 95.2 94.1 82.6 Self-Attentive Model (Li et al.,2018) 90.0 97.5 81.0 95.1 96.8 82.2 Bi-Model (Wang et al.,2018) 93.5 97.2 83.8 95.5 96.4 85.7 CAPSULE-NLU (Zhang et al.,2019) 91.8 97.3 80.9 95.2 95.0 83.4 SF-ID Network (E et al.,2019) 90.5 97.0 78.4 95.6 96.6 86.0

Our model 94.2* 98.0* 86.9* 95.9* 96.9* 86.5*

Oracle (Intent) 96.1 - - 96.0 -

-Table 2: Slot filling and intent detection results on two datasets. The numbers with * indicate that the improvement

of our model over all baselines is statistically significant withp <0.05under t-test.

we attribute this to the fact that our framework di-rectly take the explicit intent information into con-sideration can better help grasp the relationship between the intent and slots and improve the SLU performance.

To see the role of intent information for SLU tasks intuitively, we also present the result when

using the gold intent information.3 The result is

shown in theoraclerow of Table2. From the

re-sult, we can see that further leveraging better in-tent information will lead to better slot filling per-formance. The result also verifies our assumptions that intent information can be used for guiding the slots prediction.

4.4 Analysis

In Section 4.3, significant improvements among all three metrics have been witnessed on both two publicly datasets. However, we would like

to know the reason for the improvement. In

this section, we first explore the effect of Stack-Propagation framework. Next, we study the ef-fect of our proposed token-level intent detection mechanism. Finally, we study the effect of self-attention mechanism in our framework.

4.4.1 Effect of Stack-Propagation

Framework

To verify the effectiveness of the

Stack-Propagation framework. we conduct experiments with the following ablations:

3

During the inference time, we concatenate the gold in-tent label distribution (one-hot vector) and the aligned en-coder hidden stateei as the composed input for slot filling

decoder. To keep the train and test procedure as the same, we replace our intent distribution as one-hot intent information for slot filling when train our model in our oracle experiments setting.

1) We conduct experiments to incorporate in-tent information by using gate-mechanism which

is similar to Goo et al.(2018), providing the

in-tent information by interacting with the slot filling

decoder by gate function.4 We refer it as

gate-mechanism.

2) We conduct experiments on the pipelined model where the intent detection and slot fill-ing has their own self-attentive encoder separately. The other model components keep the same as our

framework. We name it aspipelined model.

Table 3 gives the result of the comparison

ex-periment. From the result ofgate-mechanismrow,

we can observe that without the Stack-Propagation learning and simply using the gate-mechanism to incorporate the intent information, the slot fill-ing (F1) performance drops significantly, which demonstrates that directly leverage the intent in-formation with Stack-Propagation can improve the slot filling performance effectively than using the gate mechanism. Besides, we can see that the in-tent detection (Acc) and overall accuracy (Acc) decrease a lot. We attribute it to the fact that the bad slot filling performance harms the intent de-tection and the whole sentence semantic perfor-mance due to the joint learning scheme.

Besides, from the pipeline model row of

Ta-ble 3, we can see that without shared encoder,

the performance on all metrics declines signifi-cantly. This shows that Stack-Propagation model can learn the correlation knowledge which may promote each other and ease the error propagation effectively.

[image:6.595.72.522.61.193.2]

Figure

Figure 1: Multi-task framework vs. Stack-Propagation.
Figure 2: Illustration of our Stack-Propagation frame-work for joint intent detection and slot filling
Table 2: Slot filling and intent detection results on two datasets. The numbers with * indicate that the improvementof our model over all baselines is statistically significant with p < 0.05 under t-test.
Table 3: The SLU performance on baseline models compared with our Stack-Propagation model on two datasets.
+2

References

Related documents