| Human: | | i am looking for abbey pool and astroturf pitch can you help me ? |
| Turn 1 | Gold Dialog State: | (attraction-name,abbey pool and astroturf pitch) |
| Predicted Dialog State: | (attraction-name,abbey pool and astroturf pitch) |
| | yes,abbey pool and astroturf pitch is a swimmingpool east of town .their number is O1223902088, |
| System: | and address is pool way,whitehill road,off newmarket road . postcode cb58nt . |
| Turn 2 | Human: | thank you very much for the information .that is alli needed help with . have a nice day. |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool) |
| Predicted Dialog State: | (attraction-area, east),(attraction-name,abbey pool and astroturf pitch) |
| System: | you are welcome .let me know if i can do anything else for you . |
| Human: | i actually do need to find a train going to ely. |
| Turn 3 | Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), |
| | (train-destination-ely) |
| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-destination-ely) |
| System: | is that leaving from cambridge ?and if so,what time would you like to arrive in ely ? |
| Turn 4 | Human: | yes,i willbe leaving cambridge and going toely,i would like it toarrive by 11:30. (atraction-area,east),(attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-departure,cambridge),(train-destination, ely) |
| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| | (train-departure,cambridge),(train-destination, ely) what day would yoube traveling ?there are 2,828 trains on that route.there isa train that departs friday at |
| Turn 5 | System: | 9:50 and will arrive in ely at 10:07 . |
| Human: | Oops !i guess forgot to mention it s thursday that i need to travel . |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination, ely) |
| Predicted Dialog State: | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| System: | (train-day, thursday),(train-departure,cambridge),(train-destination, ely) there are 3 trains that would fit,leaving at O5:50,O7:50,or 09:50. |
| Turn 6 | Human: | can i get info for the O9:5O the price and the trains id please ? |
| | (attraction-area,east),(attraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge), (train-destination, ely), (train-leaveat, 09:50) |
| | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat, 09:50) |
| System: | certainly .the train s id is tr1923,and the price for a ticket is 4.40 pounds . |
| Turn 7 | Human: | great,thank you ! that will be allineed for now. |
| Gold Dialog State: | (atraction-area,east), (attraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat,09:50) |
| System: | are you certain you do not need further assistance ? |
| Turn 8 | Human: | 9:50 departure,4.40 pounds,trl923 .i got it,thank you ！ (atraction-area,east), (attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O), (train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) |
| Predicted Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
+
+
+Figure 5: Visualization of all attention heads in the last attention step $T _ { s t a t e }$ in the state decoder. The DST prediction is done for the $6 ^ { t h }$ turn in dialogue ID MUL0536 in MultiWOZ2.1.
+
+Table 11: Full set of predicted dialogue states for dialogue ID PMUL3759 in MultiWOZ2.1.
+
+ | Human: | what s your favorite college to visit in cambridge ? |
| Turn 1 | Gold Dialog State: | (attraction-type,college) |
| Predicted Dialog State: | (attraction-type,college) |
| | ilike christ scollege in the center of town,but there are many others throughout the city.what part of |
| System: | |
| | the city did you want to visit ? |
| Turn 2 Human: | | i think i would like to visit that location,it seems nice .could i get the phone number and the area ? |
| Gold Dialog State: | (attraction-name,christ college),(attraction-type,college) |
| Predicted Dialog State: | (attraction-area,centre),(attraction-name,christ college),(attraction-type,college) |
| System: | the area is centre and the phone number is O122333490o.is there anything else ican help you with ? actually,iam hungry .can you find me arestaurant that serves north american food ? something not |
| Turn 3Human: | super expensive,maybe in a moderate price range ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-food,modern american), (restaurant-pricerange, moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college),(restaurant-food, north american), |
| System: | (restaurant-pricerange,moderate) iam sorry,there s no restaurant serving specifically north american or american food in my database, |
| Turn 4Human: | | is there another type of food you would consider ? how about modern european food ? |
| | (attraction-name,christ college),(atraction-type,collge),(restaurant-food,modern european), |
| Gold Dialog State: | (restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-food, modern european), (restaurant-pricerange, moderate) |
| System: | there are 3 modern european restaurant -s 2 in the center and1 in the south .do you have a preference ? |
| Turn 5 | Human: | i would prefer the 1 on the centre,could i have the phone number and postcode please ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | (restaurant-food, modern european),(restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-area,centre), (restaurant-food, modern european),(restaurant-pricerange, moderate) |
| System: | de luca cucina and bar s phone number is O1223356666. postcode is cb2law. |
| Turn 6 | Human: | could you help me get a taxi to get from the college to the restaurant ? |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate),(taxi-departure,christcolge), (taxi-destination,de luca cucina and bar) |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ colge), (taxi-destination,de luca cucina and bar) |
| System: | what time would you like to leave thecollege?icanbook youataxi to take you to the restaurant if you |
| Turn 7 | | would like. |
| Human: | i would like to leave by 13:00. (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christcolge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,13:00) |
| System: | ihave booked youataxi leaving at12:45.the car will beared toyotaand contact number is O7350032543 .anything else today ? |
| Turn 8Human: | | that s it .thank you very much . |
| | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ college), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| System: | will you need anymore information concerning your stay ? |
| | that is all,thanks for the help. |
| Turn 9 | Human: | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate), (taxi-departure,christ college), |
| | |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | |
| | |
| | |
| | |
| | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| Predicted Dialog State: | | |
+
+
+Figure 6: Visualization of all attention heads in the last attention step $T _ { s } t a t e$ in the state decoder. The DST prediction is done for the $6 ^ { t h }$ turn in dialogue ID PMUL3759 in MultiWOZ2.1.
\ No newline at end of file
diff --git a/parse/train/H1e_cC4twS/H1e_cC4twS_content_list.json b/parse/train/H1e_cC4twS/H1e_cC4twS_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..2adf1d54456598abe8f03cb657531dc125573259
--- /dev/null
+++ b/parse/train/H1e_cC4twS/H1e_cC4twS_content_list.json
@@ -0,0 +1,1890 @@
+[
+ {
+ "type": "text",
+ "text": "NON-AUTOREGRESSIVE DIALOG STATE TRACKING ",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Hung Le‡∗, Richard Socher†, Steven C.H. Hoi† † Salesforce Research {rsocher,shoi}@salesforce.com $\\ddagger$ Singapore Management University hungle.2018@phdcs.smu.edu.sg ",
+ "bbox": [
+ 184,
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "",
+ "bbox": [
+ 184,
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "ABSTRACT ",
+ "text_level": 1,
+ "bbox": [
+ 454,
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Recent efforts in Dialogue State Tracking (DST) for task-oriented dialogues have progressed toward open-vocabulary or generation-based approaches where the models can generate slot value candidates from the dialogue history itself. These approaches have shown good performance gain, especially in complicated dialogue domains with dynamic slot values. However, they fall short in two aspects: (1) they do not allow models to explicitly learn signals across domains and slots to detect potential dependencies among (domain, slot) pairs; and (2) existing models follow auto-regressive approaches which incur high time cost when the dialogue evolves over multiple domains and multiple turns. In this paper, we propose a novel framework of Non-Autoregressive Dialog State Tracking (NADST) which can factor in potential dependencies among domains and slots to optimize the models towards better prediction of dialogue states as a complete set rather than separate slots. In particular, the non-autoregressive nature of our method not only enables decoding in parallel to significantly reduce the latency of DST for realtime dialogue response generation, but also detect dependencies among slots at token level in addition to slot and domain level. Our empirical results show that our model achieves the state-of-the-art joint accuracy across all domains on the MultiWOZ 2.1 corpus, and the latency of our model is an order of magnitude lower than the previous state of the art as the dialogue history extends over time. ",
+ "bbox": [
+ 233,
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "1 INTRODUCTION ",
+ "text_level": 1,
+ "bbox": [
+ 176,
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+ 336,
+ 582
+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "In task-oriented dialogues, a dialogue agent is required to assist humans for one or many tasks such as finding a restaurant and booking a hotel. As a sample dialogue shown in Table 1, each user utterance typically contains important information identified as slots related to a dialogue domain such as attraction-area and train-day. A crucial part of a task-oriented dialogue system is Dialogue State Tracking (DST), which aims to identify user goals expressed during a conversation in the form of dialogue states. A dialogue state consists of a set of (slot, value) pairs e.g. (attraction-area, centre) and (train-day, tuesday). Existing DST models can be categorized into two types: fixed- and open-vocabulary. Fixed vocabulary models assume known slot ontology and generate a score for each candidate of (slot,value) (Ramadan et al., 2018; Lee et al., 2019). Recent approaches propose open-vocabulary models that can generate the candidates, especially for slots such as entity names and time, from the dialogue history (Lei et al., 2018; Wu et al., 2019). ",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Most open-vocabulary DST models rely on autoregressive encoders and decoders, which encode dialogue history sequentially and generate token $t _ { i }$ of individual slot value one by one conditioned on all previously generated tokens $t _ { [ 1 : i - 1 ] }$ . For downstream tasks of DST that emphasize on low latency (e.g. generating real-time dialogue responses), auto-regressive approaches incur expensive time cost as the ongoing dialogues become more complex. The time cost is caused by two major components: length of dialogue history i.e. number of turns, and length of slot values. For complex dialogues extended over many turns and multiple domains, the time cost will increase significantly in both encoding and decoding phases. ",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Similar problems can be seen in the field of Neural Machine Translation (NMT) research where a long piece of text is translated from one language to another. Recent work has tried to improve the latency in NMT by using neural network architectures such as convolution (Krizhevsky et al., 2012) and attention (Luong et al., 2015). Several non- and semi-autoregressive approaches aim to generate tokens of the target language independently (Gu et al., 2018; Lee et al., 2018; Kaiser et al., 2018). Motivated by this line of research, we thus propose a non-autoregressive approach to minimize the time cost of DST models without a negative impact on the model performance. ",
+ "bbox": [
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+ {
+ "type": "table",
+ "img_path": "images/f9dd915fe95aef8e42354382ae062260c57489b113f4d5376d274712cc98775e.jpg",
+ "table_caption": [
+ "Table 1: A sample task-oriented dialogue with annotated dialogue states after each user turn. The dialogue states in red and blue denote slots from the attraction domain and train domain respectively. Slot values are expressed in user and system utterances (highlighted by underlined text). "
+ ],
+ "table_footnote": [],
+ "table_body": "| Human: | | i am looking for abbey pool and astroturf pitch can you help me ? |
| Turn 1 | Gold Dialog State: | (attraction-name,abbey pool and astroturf pitch) |
| Predicted Dialog State: | (attraction-name,abbey pool and astroturf pitch) |
| | yes,abbey pool and astroturf pitch is a swimmingpool east of town .their number is O1223902088, |
| System: | and address is pool way,whitehill road,off newmarket road . postcode cb58nt . |
| Turn 2 | Human: | thank you very much for the information .that is alli needed help with . have a nice day. |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool) |
| Predicted Dialog State: | (attraction-area, east),(attraction-name,abbey pool and astroturf pitch) |
| System: | you are welcome .let me know if i can do anything else for you . |
| Human: | i actually do need to find a train going to ely. |
| Turn 3 | Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), |
| | (train-destination-ely) |
| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-destination-ely) |
| System: | is that leaving from cambridge ?and if so,what time would you like to arrive in ely ? |
| Turn 4 | Human: | yes,i willbe leaving cambridge and going toely,i would like it toarrive by 11:30. (atraction-area,east),(attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-departure,cambridge),(train-destination, ely) |
| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| | (train-departure,cambridge),(train-destination, ely) what day would yoube traveling ?there are 2,828 trains on that route.there isa train that departs friday at |
| Turn 5 | System: | 9:50 and will arrive in ely at 10:07 . |
| Human: | Oops !i guess forgot to mention it s thursday that i need to travel . |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination, ely) |
| Predicted Dialog State: | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| System: | (train-day, thursday),(train-departure,cambridge),(train-destination, ely) there are 3 trains that would fit,leaving at O5:50,O7:50,or 09:50. |
| Turn 6 | Human: | can i get info for the O9:5O the price and the trains id please ? |
| | (attraction-area,east),(attraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge), (train-destination, ely), (train-leaveat, 09:50) |
| | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat, 09:50) |
| System: | certainly .the train s id is tr1923,and the price for a ticket is 4.40 pounds . |
| Turn 7 | Human: | great,thank you ! that will be allineed for now. |
| Gold Dialog State: | (atraction-area,east), (attraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat,09:50) |
| System: | are you certain you do not need further assistance ? |
| Turn 8 | Human: | 9:50 departure,4.40 pounds,trl923 .i got it,thank you ！ (atraction-area,east), (attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O), (train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) |
| Predicted Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
",
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+ "page_idx": 17
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+ {
+ "type": "image",
+ "img_path": "images/1f28e20e859a4b30dd11d58f27bcd11faf036c53f9734e61292e6231b7416ec6.jpg",
+ "image_caption": [
+ "Figure 5: Visualization of all attention heads in the last attention step $T _ { s t a t e }$ in the state decoder. The DST prediction is done for the $6 ^ { t h }$ turn in dialogue ID MUL0536 in MultiWOZ2.1. "
+ ],
+ "image_footnote": [],
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+ "page_idx": 18
+ },
+ {
+ "type": "table",
+ "img_path": "images/f5de6ca3b516ac04cdf94f8ad0bbda7298658e1e2f790593d11ceaad4797aa4e.jpg",
+ "table_caption": [
+ "Table 11: Full set of predicted dialogue states for dialogue ID PMUL3759 in MultiWOZ2.1. "
+ ],
+ "table_footnote": [],
+ "table_body": " | Human: | what s your favorite college to visit in cambridge ? |
| Turn 1 | Gold Dialog State: | (attraction-type,college) |
| Predicted Dialog State: | (attraction-type,college) |
| | ilike christ scollege in the center of town,but there are many others throughout the city.what part of |
| System: | |
| | the city did you want to visit ? |
| Turn 2 Human: | | i think i would like to visit that location,it seems nice .could i get the phone number and the area ? |
| Gold Dialog State: | (attraction-name,christ college),(attraction-type,college) |
| Predicted Dialog State: | (attraction-area,centre),(attraction-name,christ college),(attraction-type,college) |
| System: | the area is centre and the phone number is O122333490o.is there anything else ican help you with ? actually,iam hungry .can you find me arestaurant that serves north american food ? something not |
| Turn 3Human: | super expensive,maybe in a moderate price range ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-food,modern american), (restaurant-pricerange, moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college),(restaurant-food, north american), |
| System: | (restaurant-pricerange,moderate) iam sorry,there s no restaurant serving specifically north american or american food in my database, |
| Turn 4Human: | | is there another type of food you would consider ? how about modern european food ? |
| | (attraction-name,christ college),(atraction-type,collge),(restaurant-food,modern european), |
| Gold Dialog State: | (restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-food, modern european), (restaurant-pricerange, moderate) |
| System: | there are 3 modern european restaurant -s 2 in the center and1 in the south .do you have a preference ? |
| Turn 5 | Human: | i would prefer the 1 on the centre,could i have the phone number and postcode please ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | (restaurant-food, modern european),(restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-area,centre), (restaurant-food, modern european),(restaurant-pricerange, moderate) |
| System: | de luca cucina and bar s phone number is O1223356666. postcode is cb2law. |
| Turn 6 | Human: | could you help me get a taxi to get from the college to the restaurant ? |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate),(taxi-departure,christcolge), (taxi-destination,de luca cucina and bar) |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ colge), (taxi-destination,de luca cucina and bar) |
| System: | what time would you like to leave thecollege?icanbook youataxi to take you to the restaurant if you |
| Turn 7 | | would like. |
| Human: | i would like to leave by 13:00. (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christcolge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,13:00) |
| System: | ihave booked youataxi leaving at12:45.the car will beared toyotaand contact number is O7350032543 .anything else today ? |
| Turn 8Human: | | that s it .thank you very much . |
| | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ college), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| System: | will you need anymore information concerning your stay ? |
| | that is all,thanks for the help. |
| Turn 9 | Human: | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate), (taxi-departure,christ college), |
| | |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | |
| | |
| | |
| | |
| | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| Predicted Dialog State: | | |
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| Turn 1 | Gold Dialog State: | (attraction-name,abbey pool and astroturf pitch) |
| Predicted Dialog State: | (attraction-name,abbey pool and astroturf pitch) |
| | yes,abbey pool and astroturf pitch is a swimmingpool east of town .their number is O1223902088, |
| System: | and address is pool way,whitehill road,off newmarket road . postcode cb58nt . |
| Turn 2 | Human: | thank you very much for the information .that is alli needed help with . have a nice day. |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool) |
| Predicted Dialog State: | (attraction-area, east),(attraction-name,abbey pool and astroturf pitch) |
| System: | you are welcome .let me know if i can do anything else for you . |
| Human: | i actually do need to find a train going to ely. |
| Turn 3 | Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), |
| | (train-destination-ely) |
| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-destination-ely) |
| System: | is that leaving from cambridge ?and if so,what time would you like to arrive in ely ? |
| Turn 4 | Human: | yes,i willbe leaving cambridge and going toely,i would like it toarrive by 11:30. (atraction-area,east),(attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-departure,cambridge),(train-destination, ely) |
| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| | (train-departure,cambridge),(train-destination, ely) what day would yoube traveling ?there are 2,828 trains on that route.there isa train that departs friday at |
| Turn 5 | System: | 9:50 and will arrive in ely at 10:07 . |
| Human: | Oops !i guess forgot to mention it s thursday that i need to travel . |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination, ely) |
| Predicted Dialog State: | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| System: | (train-day, thursday),(train-departure,cambridge),(train-destination, ely) there are 3 trains that would fit,leaving at O5:50,O7:50,or 09:50. |
| Turn 6 | Human: | can i get info for the O9:5O the price and the trains id please ? |
| | (attraction-area,east),(attraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge), (train-destination, ely), (train-leaveat, 09:50) |
| | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat, 09:50) |
| System: | certainly .the train s id is tr1923,and the price for a ticket is 4.40 pounds . |
| Turn 7 | Human: | great,thank you ! that will be allineed for now. |
| Gold Dialog State: | (atraction-area,east), (attraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat,09:50) |
| System: | are you certain you do not need further assistance ? |
| Turn 8 | Human: | 9:50 departure,4.40 pounds,trl923 .i got it,thank you ！ (atraction-area,east), (attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O), (train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) |
| Predicted Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
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| | yes,abbey pool and astroturf pitch is a swimmingpool east of town .their number is O1223902088, |
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| Turn 2 | Human: | thank you very much for the information .that is alli needed help with . have a nice day. |
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| System: | you are welcome .let me know if i can do anything else for you . |
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| Turn 3 | Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), |
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| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-destination-ely) |
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| Turn 4 | Human: | yes,i willbe leaving cambridge and going toely,i would like it toarrive by 11:30. (atraction-area,east),(attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-departure,cambridge),(train-destination, ely) |
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| | (train-departure,cambridge),(train-destination, ely) what day would yoube traveling ?there are 2,828 trains on that route.there isa train that departs friday at |
| Turn 5 | System: | 9:50 and will arrive in ely at 10:07 . |
| Human: | Oops !i guess forgot to mention it s thursday that i need to travel . |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination, ely) |
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| System: | (train-day, thursday),(train-departure,cambridge),(train-destination, ely) there are 3 trains that would fit,leaving at O5:50,O7:50,or 09:50. |
| Turn 6 | Human: | can i get info for the O9:5O the price and the trains id please ? |
| | (attraction-area,east),(attraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge), (train-destination, ely), (train-leaveat, 09:50) |
| | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat, 09:50) |
| System: | certainly .the train s id is tr1923,and the price for a ticket is 4.40 pounds . |
| Turn 7 | Human: | great,thank you ! that will be allineed for now. |
| Gold Dialog State: | (atraction-area,east), (attraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat,09:50) |
| System: | are you certain you do not need further assistance ? |
| Turn 8 | Human: | 9:50 departure,4.40 pounds,trl923 .i got it,thank you ！ (atraction-area,east), (attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O), (train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) |
| Predicted Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
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+ "html": " | Human: | what s your favorite college to visit in cambridge ? |
| Turn 1 | Gold Dialog State: | (attraction-type,college) |
| Predicted Dialog State: | (attraction-type,college) |
| | ilike christ scollege in the center of town,but there are many others throughout the city.what part of |
| System: | |
| | the city did you want to visit ? |
| Turn 2 Human: | | i think i would like to visit that location,it seems nice .could i get the phone number and the area ? |
| Gold Dialog State: | (attraction-name,christ college),(attraction-type,college) |
| Predicted Dialog State: | (attraction-area,centre),(attraction-name,christ college),(attraction-type,college) |
| System: | the area is centre and the phone number is O122333490o.is there anything else ican help you with ? actually,iam hungry .can you find me arestaurant that serves north american food ? something not |
| Turn 3Human: | super expensive,maybe in a moderate price range ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-food,modern american), (restaurant-pricerange, moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college),(restaurant-food, north american), |
| System: | (restaurant-pricerange,moderate) iam sorry,there s no restaurant serving specifically north american or american food in my database, |
| Turn 4Human: | | is there another type of food you would consider ? how about modern european food ? |
| | (attraction-name,christ college),(atraction-type,collge),(restaurant-food,modern european), |
| Gold Dialog State: | (restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-food, modern european), (restaurant-pricerange, moderate) |
| System: | there are 3 modern european restaurant -s 2 in the center and1 in the south .do you have a preference ? |
| Turn 5 | Human: | i would prefer the 1 on the centre,could i have the phone number and postcode please ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | (restaurant-food, modern european),(restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-area,centre), (restaurant-food, modern european),(restaurant-pricerange, moderate) |
| System: | de luca cucina and bar s phone number is O1223356666. postcode is cb2law. |
| Turn 6 | Human: | could you help me get a taxi to get from the college to the restaurant ? |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate),(taxi-departure,christcolge), (taxi-destination,de luca cucina and bar) |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ colge), (taxi-destination,de luca cucina and bar) |
| System: | what time would you like to leave thecollege?icanbook youataxi to take you to the restaurant if you |
| Turn 7 | | would like. |
| Human: | i would like to leave by 13:00. (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christcolge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,13:00) |
| System: | ihave booked youataxi leaving at12:45.the car will beared toyotaand contact number is O7350032543 .anything else today ? |
| Turn 8Human: | | that s it .thank you very much . |
| | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ college), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| System: | will you need anymore information concerning your stay ? |
| | that is all,thanks for the help. |
| Turn 9 | Human: | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate), (taxi-departure,christ college), |
| | |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | |
| | |
| | |
| | |
| | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| Predicted Dialog State: | | |
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| Turn 1 | Gold Dialog State: | (attraction-type,college) |
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| | ilike christ scollege in the center of town,but there are many others throughout the city.what part of |
| System: | |
| | the city did you want to visit ? |
| Turn 2 Human: | | i think i would like to visit that location,it seems nice .could i get the phone number and the area ? |
| Gold Dialog State: | (attraction-name,christ college),(attraction-type,college) |
| Predicted Dialog State: | (attraction-area,centre),(attraction-name,christ college),(attraction-type,college) |
| System: | the area is centre and the phone number is O122333490o.is there anything else ican help you with ? actually,iam hungry .can you find me arestaurant that serves north american food ? something not |
| Turn 3Human: | super expensive,maybe in a moderate price range ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-food,modern american), (restaurant-pricerange, moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college),(restaurant-food, north american), |
| System: | (restaurant-pricerange,moderate) iam sorry,there s no restaurant serving specifically north american or american food in my database, |
| Turn 4Human: | | is there another type of food you would consider ? how about modern european food ? |
| | (attraction-name,christ college),(atraction-type,collge),(restaurant-food,modern european), |
| Gold Dialog State: | (restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-food, modern european), (restaurant-pricerange, moderate) |
| System: | there are 3 modern european restaurant -s 2 in the center and1 in the south .do you have a preference ? |
| Turn 5 | Human: | i would prefer the 1 on the centre,could i have the phone number and postcode please ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | (restaurant-food, modern european),(restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-area,centre), (restaurant-food, modern european),(restaurant-pricerange, moderate) |
| System: | de luca cucina and bar s phone number is O1223356666. postcode is cb2law. |
| Turn 6 | Human: | could you help me get a taxi to get from the college to the restaurant ? |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate),(taxi-departure,christcolge), (taxi-destination,de luca cucina and bar) |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ colge), (taxi-destination,de luca cucina and bar) |
| System: | what time would you like to leave thecollege?icanbook youataxi to take you to the restaurant if you |
| Turn 7 | | would like. |
| Human: | i would like to leave by 13:00. (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christcolge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,13:00) |
| System: | ihave booked youataxi leaving at12:45.the car will beared toyotaand contact number is O7350032543 .anything else today ? |
| Turn 8Human: | | that s it .thank you very much . |
| | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ college), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| System: | will you need anymore information concerning your stay ? |
| | that is all,thanks for the help. |
| Turn 9 | Human: | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate), (taxi-departure,christ college), |
| | |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | |
| | |
| | |
| | |
| | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| Predicted Dialog State: | | |
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+ "html": "| Human: | | i am looking for abbey pool and astroturf pitch can you help me ? |
| Turn 1 | Gold Dialog State: | (attraction-name,abbey pool and astroturf pitch) |
| Predicted Dialog State: | (attraction-name,abbey pool and astroturf pitch) |
| | yes,abbey pool and astroturf pitch is a swimmingpool east of town .their number is O1223902088, |
| System: | and address is pool way,whitehill road,off newmarket road . postcode cb58nt . |
| Turn 2 | Human: | thank you very much for the information .that is alli needed help with . have a nice day. |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool) |
| Predicted Dialog State: | (attraction-area, east),(attraction-name,abbey pool and astroturf pitch) |
| System: | you are welcome .let me know if i can do anything else for you . |
| Human: | i actually do need to find a train going to ely. |
| Turn 3 | Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), |
| | (train-destination-ely) |
| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-destination-ely) |
| System: | is that leaving from cambridge ?and if so,what time would you like to arrive in ely ? |
| Turn 4 | Human: | yes,i willbe leaving cambridge and going toely,i would like it toarrive by 11:30. (atraction-area,east),(attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-departure,cambridge),(train-destination, ely) |
| Predicted Dialog State: | (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| | (train-departure,cambridge),(train-destination, ely) what day would yoube traveling ?there are 2,828 trains on that route.there isa train that departs friday at |
| Turn 5 | System: | 9:50 and will arrive in ely at 10:07 . |
| Human: | Oops !i guess forgot to mention it s thursday that i need to travel . |
| Gold Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination, ely) |
| Predicted Dialog State: | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| System: | (train-day, thursday),(train-departure,cambridge),(train-destination, ely) there are 3 trains that would fit,leaving at O5:50,O7:50,or 09:50. |
| Turn 6 | Human: | can i get info for the O9:5O the price and the trains id please ? |
| | (attraction-area,east),(attraction-name,abbey pool and astroturf pitch),(atraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge), (train-destination, ely), (train-leaveat, 09:50) |
| | (attraction-area, east), (atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat, 09:50) |
| System: | certainly .the train s id is tr1923,and the price for a ticket is 4.40 pounds . |
| Turn 7 | Human: | great,thank you ! that will be allineed for now. |
| Gold Dialog State: | (atraction-area,east), (attraction-name,abbey pool and astroturf pitch),(attraction-type,swimming pool), (train-arriveby,11:3O),(train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) (attraction-area, east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
| Predicted Dialog State: | (train-day,thursday),(train-departure,cambridge),(train-destination,ely),(train-leaveat,09:50) |
| System: | are you certain you do not need further assistance ? |
| Turn 8 | Human: | 9:50 departure,4.40 pounds,trl923 .i got it,thank you ！ (atraction-area,east), (attraction-name,abbey pooland astroturf pitch),(attraction-type,swimming pool), |
| Gold Dialog State: | (train-arriveby,11:3O), (train-day,thursday),(train-departure,cambridge),(train-destination,ely), |
| | (train-leaveat, 09:50) |
| Predicted Dialog State: | (attraction-area,east),(atraction-name,abbey pool and astroturf pitch),(train-arriveby,11:30), |
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+ "html": " | Human: | what s your favorite college to visit in cambridge ? |
| Turn 1 | Gold Dialog State: | (attraction-type,college) |
| Predicted Dialog State: | (attraction-type,college) |
| | ilike christ scollege in the center of town,but there are many others throughout the city.what part of |
| System: | |
| | the city did you want to visit ? |
| Turn 2 Human: | | i think i would like to visit that location,it seems nice .could i get the phone number and the area ? |
| Gold Dialog State: | (attraction-name,christ college),(attraction-type,college) |
| Predicted Dialog State: | (attraction-area,centre),(attraction-name,christ college),(attraction-type,college) |
| System: | the area is centre and the phone number is O122333490o.is there anything else ican help you with ? actually,iam hungry .can you find me arestaurant that serves north american food ? something not |
| Turn 3Human: | super expensive,maybe in a moderate price range ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-food,modern american), (restaurant-pricerange, moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college),(restaurant-food, north american), |
| System: | (restaurant-pricerange,moderate) iam sorry,there s no restaurant serving specifically north american or american food in my database, |
| Turn 4Human: | | is there another type of food you would consider ? how about modern european food ? |
| | (attraction-name,christ college),(atraction-type,collge),(restaurant-food,modern european), |
| Gold Dialog State: | (restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-food, modern european), (restaurant-pricerange, moderate) |
| System: | there are 3 modern european restaurant -s 2 in the center and1 in the south .do you have a preference ? |
| Turn 5 | Human: | i would prefer the 1 on the centre,could i have the phone number and postcode please ? |
| Gold Dialog State: | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | (restaurant-food, modern european),(restaurant-pricerange,moderate) |
| Predicted Dialog State: | (attraction-name,christ college),(atraction-type,college),(restaurant-area,centre), (restaurant-food, modern european),(restaurant-pricerange, moderate) |
| System: | de luca cucina and bar s phone number is O1223356666. postcode is cb2law. |
| Turn 6 | Human: | could you help me get a taxi to get from the college to the restaurant ? |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate),(taxi-departure,christcolge), (taxi-destination,de luca cucina and bar) |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ colge), (taxi-destination,de luca cucina and bar) |
| System: | what time would you like to leave thecollege?icanbook youataxi to take you to the restaurant if you |
| Turn 7 | | would like. |
| Human: | i would like to leave by 13:00. (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| Predicted Dialog State: | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christcolge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,13:00) |
| System: | ihave booked youataxi leaving at12:45.the car will beared toyotaand contact number is O7350032543 .anything else today ? |
| Turn 8Human: | | that s it .thank you very much . |
| | (attraction-name,christ college),(attraction-type,college), (restaurant-area,centre), |
| Gold Dialog State: | (restaurant-food, modern european),(restaurant-pricerange,moderate), (taxi-departure,christ collge), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | (araction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| Predicted Dialog State: | (restaurant-food, modern european), (restaurant-pricerange,moderate),(taxi-departure,christ college), |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| System: | will you need anymore information concerning your stay ? |
| | that is all,thanks for the help. |
| Turn 9 | Human: | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| Gold Dialog State: | (restaurant-food,modern european),(restaurant-pricerange,moderate), (taxi-departure,christ college), |
| | |
| | (taxi-destination,de luca cucina and bar),(taxi-leaveat,12:45) |
| | |
| | |
| | |
| | |
| | |
| | (attraction-name,christ college),(attraction-type,college),(restaurant-area,centre), |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| | |
| Predicted Dialog State: | | |
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+# DATA AUGMENTATION INSTEAD OFEXPLICIT REGULARIZATION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Modern deep artificial neural networks have achieved impressive results through models with orders of magnitude more parameters than training examples which control overfitting with the help of regularization. Regularization can be implicit, as is the case of stochastic gradient descent and parameter sharing in convolutional layers, or explicit. Explicit regularization techniques, most common forms are weight decay and dropout, have proven successful in terms of improved generalization, but they introduce sensitive hyper-parameters and, incongruously, often require deeper and wider architectures to compensate for the reduced capacity. In contrast, data augmentation techniques exploit domain knowledge to increase the number of training examples and improve generalization without reducing the representational capacity and without introducing model-dependent parameters, since it is applied on the training data. In this paper we systematically contrast data augmentation and explicit regularization on three popular architectures and three image object classification data sets. Our results demonstrate that data augmentation alone can achieve the same performance or higher as regularized models and exhibits much higher adaptability to changes in the architecture and the amount of training data.
+
+# 1 INTRODUCTION
+
+One of the central issues in machine learning research and application is finding ways of improving generalization. Regularization, loosely defined as any modification applied to a learning algorithm that helps prevent overfitting, plays therefore a key role in machine learning (Girosi et al., 1995; Müller, 2012). In the case of deep learning, where neural networks tend to have several orders of magnitude more parameters than training examples, statistical learning theory (Vapnik & Chervonenkis, 1971) indicates that regularization becomes even more crucial. Accordingly, a myriad of techniques have been proposed as regularizers: weight decay (Hanson & Pratt, 1989) and other $L ^ { p }$ penalties; dropout (Srivastava et al., 2014) and stochastic depth (Huang et al., 2016), to name a few examples. Moreover, whereas in simpler machine learning algorithms the regularizers can be easily identified as explicit terms in the objective function, in modern deep neural networks the sources of regularization are not only explicit, but implicit (Neyshabur et al., 2014). In this regard, many techniques have been studied for their regularization effect, despite not being explicitly intended as such. That is the case of unsupervised pre-training (Erhan et al., 2010), multi-task learning (Caruana, 1998), convolutional layers (LeCun et al., 1990), batch normalization (Ioffe & Szegedy, 2015) or adversarial training (Szegedy et al., 2013). In sum, there are multiple elements in deep learning that contribute to reduce overfitting and thus improve generalization.
+
+Driven by the success of such techniques and the efficient use of GPUs, considerable research effort has been devoted to finding ways of training deeper and wider networks with larger capacity (Simonyan & Zisserman, 2014; He et al., 2016; Zagoruyko & Komodakis, 2016). Ironically, the increased representational capacity is eventually reduced in practice by the use of explicit regularization, most commonly weight decay and dropout. It is known, for instance, that the gain in generalization provided by dropout comes at the cost of using larger models and training for longer (Goodfellow et al., 2016). Hence, it seems that with these standard regularization methods deep networks are wasting capacity (Dauphin & Bengio, 2013).
+
+Unlike explicit regularization, data augmentation improves generalization without reducing the capacity of the model. Data augmentation, that is synthetically expanding a data set by applying transformations on the available examples, has been long used in machine learning (Simard et al., 1992) and identified as a critical component of many recent successful models, like AlexNet (Krizhevsky et al., 2012), All-CNN (Springenberg et al., 2014) or ResNet (He et al., 2016), among others. Although it is most popular in computer vision, data augmentation has also proven effective in speech recognition (Jaitly & Hinton, 2013), music source separation (Uhlich et al., 2017) or text categorization (Lu et al., 2006). Today, data augmentation is an almost ubiquitous technique in deep learning, which can also be regarded as an implicit regularizer for it improves generalization.
+
+Recently, the deep learning community has become more aware of the importance of data augmentation (Hernández-García & König, 2018b) and new techniques, such as cutout (DeVries & Taylor, 2017a) or augmentation in the feature space (DeVries & Taylor, 2017b), have been proposed. Very interestingly, a promising avenue for future research has been set by recently proposed models that automatically learn the data transformations (Hauberg et al., 2016; Lemley et al., 2017; Ratner et al., 2017; Antoniou et al., 2017). Nonetheless, another study by Perez & Wang (2017) analyzed the performance of different techniques for object recognition and concluded that one of the most successful techniques so far is still the traditional data augmentation carried out in most studies.
+
+However, despite its popularity, the literature lacks, to our knowledge, a systematic analysis of the impact of data augmentation on convolutional neural networks compared to explicit regularization. It is a common practice to train the models with both explicit regularization, typically weight decay and dropout, and data augmentation, assuming they all complement each other. Zhang et al. (2017) included data augmentation in their analysis of generalization of deep networks, but it was questionably considered an explicit regularizer similar to weight decay and dropout. To our knowledge, the first time data augmentation and explicit regularization were systematically contrasted was the preliminary study by Hernández-García & König (2018b). The present work aims at largely extending that work both with more empirical results and a theoretical discussion.
+
+Our specific contributions are the following:
+
+• Propose definitions of explicit and implicit regularization that aim at solving the ambiguity in the literature (Section 2).
+• A theoretical discussion based on statistical learning theory about the differences between explicit regularization and data augmentation, highlighting the advantages of the latter (Section 3).
+• An empirical analysis of the performance of models trained with and without explicit regularization, and different levels of data augmentation on several benchmarks (Sections 4 and 5). Further, we study their adaptability to learning from fewer examples (Section 5.2) and to changes in the architecture (Section 5.3).
+• A discussion on why encouraging data augmentation instead of explicit regularization can benefit both theory and practice in deep learning (Section 6).
+
+# 2 EXPLICIT AND IMPLICIT REGULARIZATION
+
+Zhang et al. (2017) raised the thought-provoking idea that “explicit regularization may improve generalization performance, but is neither necessary nor by itself sufficient for controlling generalization error.” The authors came to this conclusion from the observation that turning off the explicit regularizers of a model does not prevent the model from generalizing reasonably well. This contrasts with traditional machine learning involving convex optimization, where regularization is necessary to avoid overfitting and generalize (Vapnik & Chervonenkis, 1971). Such observation led the authors to suggest the need for “rethinking generalization” in order to understand deep learning.
+
+We argue it is not necessary to rethink generalization if we instead rethink regularization and, in particular, data augmentation. Despite their thorough analysis and relevant conclusions, Zhang et al. (2017) arguably underestimated the role of implicit regularization and considered data augmentation an explicit form of regularization much like weight decay and dropout. This illustrates that the terms explicit and implicit regularization have been used subjectively and inconsistently in the literature before. In order to avoid the ambiguity and facilitate the discussion, we propose the following definitions of explicit and implicit regularization1:
+
+• Explicit regularization techniques are those which reduce the representational capacity of the model they are applied on. That is, given a model class $\mathcal { H } _ { 0 }$ , for instance a neural network architecture, the introduction of explicit regularization will span a new hypothesis set $\mathcal { H } _ { 1 }$ , which is a proper subset of the original set, i.e. $\mathcal { H } _ { 1 } \subsetneq \mathcal { H } _ { 0 }$ .
+
+• Implicit regularization is the reduction of the generalization error or overfitting provided by means other than explicit regularization techniques. Elements that provide implicit regularization do not reduce the representational capacity, but may affect the effective capacity of the model, that is the achievable set of hypotheses given the model, the optimization algorithm, hyperparameters, etc.
+
+One of the most common explicit regularization techniques in machine learning is $L ^ { p }$ -norm regularization, of which weight decay is a particular case, widely used in deep learning. Weight decay sets a penalty on the $L ^ { 2 }$ norm of the learnable parameters, thus constraining the representational capacity of the model. Dropout is another common example of explicit regularization, where the hypothesis set is reduced by stochastically deactivating a number of neurons during training. Similar to dropout, stochastic depth, which drops whole layers instead of neurons, is also an explicit regularization technique.
+
+There are multiple elements in deep neural networks that implicitly regularize the models. Note, in this regard, that the above definition, contrary to explicit regularization, does not refer to techniques, but to a regularization effect, as it can be provided by elements of very different nature. For instance, stochastic gradient descent (SGD) is known to have an implicit regularization effect without constraining the representational capacity. Batch normalization does not either reduce the capacity, but it improves generalization by smoothing the optimization landscape Santurkar et al. (2018). Of quite a different nature, but still implicit, is the regularization effect provided by early stopping, which does not reduce the representational, but the effective capacity.
+
+By analyzing the literature, we identified some previous pieces of work which, lacking a definition of explicit and implicit regularization, made a distinction apparently based on the mere intention of the practitioner. Under such notion, data augmentation has been considered in some cases an explicit regularization technique, as in Zhang et al. (2017). Here, we have provided definitions for explicit and implicit regularization based on their effect on the representational capacity and argue that data augmentation is not explicit, but implicit regularization, since it does not affect the representational capacity of the model.
+
+# 3 THEORETICAL INSIGHTS
+
+The generalization of a model class $\mathcal { H }$ can be analyzed through complexity measures such as the VC-dimension or, more generally, the Rademacher complexity $\mathcal { \bar { R } } _ { n } ( \mathcal { H } ) = \mathbb { E } _ { S \sim D ^ { n } } \left[ \hat { \mathcal { R } } _ { S } ( \mathcal { H } ) \right]$ , where:
+
+$$
+\hat { \mathcal { R } } _ { S } ( \mathcal { H } ) = \mathbb { E } _ { \sigma } \left[ \operatorname* { s u p } _ { h \in \mathcal { H } } \left| \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \sigma _ { i } h ( x _ { i } ) \right| \right]
+$$
+
+is the empirical Rademacher complexity, defined with respect to a set of data samples $S = ( x _ { i } , . . . , x _ { n } )$ . Then, in the case of binary classification and the class of linear separators, the generalization error of a hypothesis, $\hat { \epsilon } _ { S } ( h )$ , can be bounded using the Rademacher complexity:
+
+$$
+\hat { \epsilon } _ { S } ( h ) \leq \mathcal { R } _ { n } ( \mathcal { H } ) + \mathcal { O } \left( \sqrt { \frac { \ln ^ { 1 } / \delta } { n } } \right)
+$$
+
+with probability $1 - \delta$ . Tighter bounds for some model classes, such as fully connected neural networks, can be obtained (Bartlett $\&$ Mendelson, 2002), but it is not trivial to formally analyze the influence on generalization of specific architectures or techniques.
+
+Nonetheless, we can use these theoretical insights to discuss the differences between explicit regularization—particularly weight decay and dropout—and implicit regularization—particularly data augmentation. A straightforward yet very relevant conclusion from the analysis of any generalization bound is the strong dependence on the number of training examples $n$ . Increasing $n$ drastically improves the generalization guarantees, as reflected by the second term in RHS of Equation 1 and the dependence of the Rademacher complexity (LHS) on the sample size as well. Data augmentation exploits prior knowledge of the data domain $D$ to create new examples and its impact on generalization is related to an increment in $n$ , since stochastic data augmentation can generate virtually infinite different samples. Admittedly, the augmented samples are not independent and identically distributed and thus, the effective increment of samples does not strictly correspond to the increment in $n$ . This is why formally analyzing the impact of data augmentation on generalization is complex and out of the scope of this paper. Recently, some studies have taken steps in this direction by analyzing the effect of simplified data transformations on generalization from a theoretical point of view Chen et al. (2019); Rajput et al. (2019).
+
+In contrast, explicit regularization methods aim, in general, at improving the generalization error by constraining the hypothesis class $\mathcal { H }$ , which hopefully should reduce its complexity, $\textstyle { \mathcal { R } } _ { n } ( { \mathcal { H } } )$ , and, in turn, the generalization error $\hat { \epsilon } _ { S } ( h )$ . Crucially, while data augmentation exploits domain knowledge, most explicit regularization methods only naively constrain the hypothesis class. For instance, weight decay constrains the learnable models $\mathcal { H }$ by setting a penalty on the weights norm. However, Bartlett et al. (2017) have recently shown that weight decay has little impact on the generalization bounds and confidence margins.
+
+Dropout has been extensively used and studied as a regularization method for neural networks (Wager et al., 2013), but the exact way in which dropout may improve generalization is still an open question and it has been concluded that the effects of dropout on neural networks are somewhat mysterious, complicated and its penalty highly non-convex (Helmbold & Long, 2017). Recently, Mou et al. (2018) have established new generalization bounds on the variance induced by a particular type of dropout on feedforward neural network. Nevertheless, dropout can also be analyzed as a random form of data augmentation without domain knowledge Bouthillier et al. (2015), that is data-dependent regularization. Therefore, any generalization bound derived for dropout can be regarded as a pessimistic bound for domain-specific, standard data augmentation.
+
+A similar argument applies for weight decay, which, as first shown by Bishop (1995), is equivalent to training with noisy examples if the noise amplitude is small and the objective is the sum-of-squares error function. In sum, many forms of explicit regularization are at least approximately equivalent to adding random noise to the training examples, which is the simplest form of data augmentation2. Thus, it is reasonable to argue that more sophisticated data augmentation can overshadow the benefits provided by explicit regularization.
+
+In general, we argue that the reason why explicit regularization may not be necessary is that neural networks are already implicitly regularized by many elements—stochastic gradient descent (SGD), convolutional layers, normalization and data augmentation, to name a few—that provide a more successful inductive bias (Neyshabur et al., 2014). For instance, it has been shown that linear models optimized with SGD converge to solutions with small norm, without any explicit regularization (Zhang et al., 2017). In the remainder of the paper, we present a set of experiments that shed more light on the advantages of data augmentation over weight decay and dropout.
+
+# 4 METHODS
+
+This section describes the experimental setup for systematically analyzing the role of data augmentation in deep neural networks compared to weight decay and dropout and builds upon the methods used in preliminary studies (Hernández-García & König, 2018a;b; Zhang et al., 2017).
+
+# 4.1 NETWORK ARCHITECTURES
+
+We perform our experiments on three distinct, popular architectures that have achieved successful results in object recognition tasks: the all convolutional network, All-CNN (Springenberg et al.,
+
+2014); the wide residual network, WRN (Zagoruyko & Komodakis, 2016); and the densely connected network, DenseNet (Huang et al., 2017). Importantly, we keep the same training hyper-parameters (learning rate, training epochs, batch size, optimizer, etc.) as in the original papers in the cases they are reported. Below we present the main features of each network and more details can be found in the supplementary material.
+
+• All-CNN: it consists only of convolutional layers with ReLU activation (Glorot et al., 2011), it is relatively shallow and has few parameters. For ImageNet, the network has 16 layers and 9.4 million parameters; for CIFAR, it has 12 layers and 1.3 million parameters. In our experiments to compare the adaptability of data augmentation and explicit regularization to changes in the architecture, we also test a shallower version, with 9 layers and 374,000 parameters, and a deeper version, with 15 layers and 2.4 million parameters.
+WRN: a residual network, ResNet (He et al., 2016), that achieves better performance with fewer layers, but more units per layer. Here, we choose for our experiments the WRN-28-10 version (28 layers and about $3 6 . 5 \mathrm { ~ M ~ }$ parameters), which is reported to achieve the best results on CIFAR.
+DenseNet: a network architecture arranged in blocks whose layers are connected to all previous layers, allowing for very deep architectures with few parameters. Specifically, for our experiments we use a DenseNet-BC with growth rate $k = 1 2$ and 16 layers in each block, which has a total of 0.8 million parameters.
+
+# 4.2 DATA
+
+We perform the experiments on the highly benchmarked data sets ImageNet (Russakovsky et al., 2015) ILSVRC 2012, CIFAR-10 and CIFAR-100 (Krizhevsky & Hinton, 2009). We resize the $1 . 3 { \bf M }$ images from ImageNet into $1 5 0 \times 2 0 0$ pixels, as a compromise between keeping a high resolution and speeding up the training. Both on ImageNet and on CIFAR, the pixel values are in the range [0, 1] and have 32 bits floating precision.
+
+So as to analyze the role of data augmentation, we train every network architecture with two different augmentation schemes as well as with no data augmentation at all:
+
+• Light augmentation: This scheme is common in the literature, for example (Goodfellow et al., 2013; Springenberg et al., 2014), and performs only horizontal flips and horizontal and vertical translations of $10 \%$ of the image size. • Heavier augmentation: This scheme performs a larger range of affine transformations such as scaling, rotations and shear mappings, as well as contrast and brightness adjustment. On ImageNet we additionally perform a random crop of $1 2 8 \times 1 2 8$ pixels. The choice of the allowed transformations is arbitrary and the only criterion was that the objects are still recognizable in general. We deliberately avoid designing a particularly successful scheme. The details of the heavier scheme can be consulted in the supplementary material.
+
+# 4.3 TRAIN AND TEST
+
+Every architecture is trained on each data set both with explicit regularization—weight decay and dropout as specified in the original papers—and with no explicit regularization. Furthermore, we train each model with the three data augmentation schemes. The performance of the models is computed on the held out test tests. As in previous works (Krizhevsky et al., 2012; Simonyan & Zisserman, 2014), we average the softmax posteriors over 10 random light augmentations, since slightly better results are obtained.
+
+All the experiments are performed on Keras (Chollet et al., 2015) on top of TensorFlow (Abadi et al., 2015) and on a single GPU NVIDIA GeForce GTX 1080 Ti.
+
+# 5 RESULTS
+
+This section presents the most relevant results of the experiments comparing the roles of data augmentation and explicit regularization on convolutional neural networks. First, we present the experiments with the original architectures in section 5.1. Then, Sections 5.2 and 5.3 show the results of training the models with fewer training examples and with shallower and deeper versions of the All-CNN architecture.
+
+The figures aim at facilitating the comparison between the models trained with and without explicit regularization, as well as between the different levels of data augmentation. The purple bars (top of each pair) correspond to the models trained without explicit regularization—weight decay and dropout—and the red bars (bottom) to the models trained with it. The different color shades correspond to the three augmentation schemes. The figures show the relative performance of each model with respect to a particular baseline in order to highlight the relevant comparisons. A detailed and complete report of all the results can be found in the supplementary material. The results on CIFAR refer to the top-1 test accuracy while on ImageNet we report the top-5.
+
+
+5.1 AN ALTERNATIVE TO EXPLICIT REGULARIZATION
+Figure 1: Relative improvement of adding data augmentation and explicit regularization to the baseline models, $( a c c u r a c y - b a s e l i n e ) / a c c u r a c y * 1 0 0$ . The baseline accuracy is shown on the left. The results suggest that data augmentation alone (purple bars) can achieve even better performance than the models trained with both weight decay and dropout (red bars).
+
+First, we contrast the regularization effect of data augmentation and weight decay and dropout on the original networks trained with the complete data sets. For that purpose, in Figure 1 we show the relative improvement in test performance achieved by adding each technique or combination of techniques to the baseline model, that is the model trained with neither explicit regularization nor data augmentation (see the left of the bars). Table 1 shows the mean and standard deviation of each combination.3
+
+Table 1: Average accuracy improvement over the baseline model of each combination of data augmentation level and presence of weight decay and dropout.
+
+| Model (batch size = 1, beam size = 1) | Param | BLEU | Sent/sec | Tok/sec |
| NAT (+ FT) (Gu et al., 2018) | | 17.7 | 25.6 | = |
| NAT (+ FT + NPD=10) (Gu et al., 2018) | | 18.7 | 12.7 | = |
| NAT (+ FT + NPD=10O) (Gu et al., 2018) | | 19.2 | 3.9 | |
| LT, Improved Semhash (Kaiser et al.,2018) | | 19.8 | 9.5 | 1 |
| IRidec 二 :1 (Lee et al., 2018) | | 13.9 | 1 | 511.4 |
| IR idec 二 :2 (Lee et al., 2018) | | 17.0 | = | 393.6 |
| IR idec 二 : 5 (Lee et al., 2018) | | 20.3 | = | 139.7 |
| IR idec 二 :10 (Lee et al., 2018) | | 21.6 | | 90.4 |
| IR Adaptive ( (Lee et al., 2018) | | 21.5 | 1 | 107.2 |
| NART w/hints (Li et al., 2019) | | 21.1 | 38.5 | |
| NART w/ hints (B = 4, 9 candidates) (Li et al., 2019) | | 25.2 | 22.7 | = |
| ENAT Embedding l gMapping (Guo et al.,2019) ENAT Embedding Mapping (rescoring 9 candidates) | | 20.7 | 41.7 | |
| (Guo et al., 2019) | | 24.3 | 20.4 | |
| Autoregressive (Gu et al., 2018) | | 22.7 | 2.5 | |
| Autoregressive (Lee et al., 2018) | | 23.8 | 1 | = 54.0 |
| Transformer (Li et al., 2019) | | 27.3 | 1.3 | |
| Transformer (Guo et al., 2019) | - | 27.4 | 1.6 | 1 1 |
| DynamicConv (1-decoder layer (k=31)) | 124M | 26.1 | 15.2 | |
| DynamicConv (3-decoder layers (k=3,7,15)) | 153M | 27.7 | 7.2 | 423.0 202.3 |
| DynamicConv (6-decoder layers (k=3,7,15,31,31,31)) | 200M | 28.5 | 3.9 | 110.9 |
+
+Table 7: Inference speed of non-autoregressive models and small decoder versions of DynamicConv on WMT English-German newstest2014. For some models, the decoding speed (sent/sec) is derived by taking the inverse of the sentence generation latency in the literature.
\ No newline at end of file
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new file mode 100644
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| NAT (+ FT) (Gu et al., 2018) | | 17.7 | 25.6 | = |
| NAT (+ FT + NPD=10) (Gu et al., 2018) | | 18.7 | 12.7 | = |
| NAT (+ FT + NPD=10O) (Gu et al., 2018) | | 19.2 | 3.9 | |
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| IRidec 二 :1 (Lee et al., 2018) | | 13.9 | 1 | 511.4 |
| IR idec 二 :2 (Lee et al., 2018) | | 17.0 | = | 393.6 |
| IR idec 二 : 5 (Lee et al., 2018) | | 20.3 | = | 139.7 |
| IR idec 二 :10 (Lee et al., 2018) | | 21.6 | | 90.4 |
| IR Adaptive ( (Lee et al., 2018) | | 21.5 | 1 | 107.2 |
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| NART w/ hints (B = 4, 9 candidates) (Li et al., 2019) | | 25.2 | 22.7 | = |
| ENAT Embedding l gMapping (Guo et al.,2019) ENAT Embedding Mapping (rescoring 9 candidates) | | 20.7 | 41.7 | |
| (Guo et al., 2019) | | 24.3 | 20.4 | |
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| DynamicConv (6-decoder layers (k=3,7,15,31,31,31)) | 200M | 28.5 | 3.9 | 110.9 |
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+# COMPUTATION-EFFICIENT QUANTIZATION METHODFOR DEEP NEURAL NETWORKS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Deep Neural Networks, being memory and computation intensive, are a challenge to deploy in smaller devices. Numerous quantization techniques have been proposed to reduce the inference latency/memory consumption. However, these techniques impose a large overhead on the training procedure or need to change the training process. We present a non-intrusive quantization technique based on re-training the full precision model, followed by directly optimizing the corresponding binary model. The quantization training process takes no longer than the original training process. We also propose a new loss function to regularize the weights, resulting in reduced quantization error. Combining both help us achieve full precision accuracy on CIFAR dataset using binary quantization. We also achieve full precision accuracy on WikiText-2 using 2 bit quantization. Comparable results are also shown for ImageNet. We also present a 1.5 bits hybrid model exceeding the performance of TWN LSTM model for WikiText-2.
+
+# 1 INTRODUCTION
+
+Different variants of Deep Neural Networks have achieved state-of-the-art results in various domains from computer vision to language processing (Krizhevsky et al., 2012; Ren et al., 2015; Vaswani et al., 2017; Cho et al., 2014). However, newer models are becoming more memory and computation intensive to achieve performance improvements. For example, winner of ILSVRC 2015 ResNet (He et al., 2016) increased the number of layers by over $4 \mathbf { x }$ to gain less than $2 \%$ Top-1 accuracy improvement on ImageNet (Russakovsky et al., 2015). Compression techniques, such as knowledge distillation, pruning, low rank approximation and quantization, have been proposed to reduce the model size (Vapnik & Izmailov, 2015; Han et al., 2015; Sainath et al., 2013; Courbariaux et al., 2015). These compression techniques are evolving the field of model compression towards the goal of deploying DNN models on mobile-phone and other embedded devices.
+
+Courbariaux et al. (2015) proposed the widely used technique for training quantized neural networks, where binary weights are used during forward and backward propagation, while full precision weights are preserved for accumulating gradients. Binary weights are approximated from full precision weights every iteration. (Zhou et al., 2018; 2017a) have proposed incremental quantization training procedure where the range for the weights is incrementally reduced. Choi et al. (2017) use Hessian weighted $\mathbf { k }$ -means clustering for quantization. Lee & Kim (2018) used iterative procedure of quantizing, de-quantizing and complete retraining of the full precision model, performed multiple times. All the techniques aimed to reduce the quantization error (error between full precision model and corresponding quantized model). However, most of these quantization techniques either adds extra set of hyper-parameters or modifies/lengthens the original training procedure.
+
+Designing a neural network model consists of two main steps - choose a proper architecture/model given the characteristics of the task, and optimize the hyper-parameters for convergence and accuracy. Hyper-parameter search varies from number of layers in a model (Zoph et al., 2018) to learning rate (lr), batch-size (bs) combo (compare ResNet (He et al., 2016) and Inception (Szegedy et al., 2016) networks with altogether different hyper-parameter set). Courbariaux et al. (2015) requires updating the back-propagation procedure to train quantized networks. (Zhou et al., 2018; Lee & Kim, 2018) require very long training time because of multiple iterations of training and extra introduced hyper-parameters. Over time, focus on reducing the model size and the corresponding inference latency has led to either lengthening or major modifications to training procedure. Our Proposed quantization technique addresses these issues resulting in easy adoption of our technique.
+
+Our contributions include but are not limited to
+
+• A simple quantization training method based on re-training without requiring major modifications to the original training procedure. Training consists of two phases: phase1 trains the full precision model (with quantization) and phase2 trains the binary model constructed by phase1.
+• Reduce the overhead of expensive quantization techniques as quantization is performed only every few steps (specifically once every 500 iterations for the experiments).
+Maintained the total number of iterations and time required to train the quantized network compared to the full precision network.
+• Achieve full precision accuracy for WikiText-2 and CIFAR dataset with 2-bit and 1-bit quantization respectively. Present a hybrid 1.5 bits LSTM models for WikiText-2 outperforming TWN LSTM model. Achieve performance comparable to existing works for ImageNet.
+
+# 2 RELATED WORK
+
+Quantization. Courbariaux et al. (2015) proposed the idea of training binary neural networks with quantized weights. Rastegari et al. (2016) introduced shared scaling factors to allow more range for binary values. (Hubara et al., 2016; Zhou et al., 2016; Lin et al., 2017; McDonnell, 2018; Hubara et al., 2018) built upon the training methodology along with introduction of binary activation units. Lee & Kim (2018) performs full precision retraining multiple times to train a quantized network. Ternary quantization was proposed (Zhu et al., 2017; Li et al., 2016; Wang et al., 2018) to mitigate the gap between full precision and quantized weight networks. Let $\mathbf { W } ~ \in ~ \mathbb { R } ^ { k \times c \times f \times f }$ represent a weight of a convolution layer $l$ with total n elements where $k , c , f$ represents output channels, input channels and size of the filter respectively. Rastegari et al. (2016) splits $\boldsymbol { \mathsf { W } }$ into binary weight $\mathsf { B } ^ { \mathsf { ^ { * } } } \in \{ - 1 , + 1 \} ^ { k \times c \times f \times f }$ and scaling factor $\pmb { \alpha } \in \mathbb { R } ^ { + k }$ shared per output, where
+
+$$
+\begin{array} { r } { \mathbf { B } = \mathrm { s i g n } ( \mathbf { W } ) \qquad \mathbf { \alpha } \mathbf { \alpha } = \langle \mathbf { B } , \mathbf { W } \rangle / n } \end{array}
+$$
+
+obtained by minimizing $\| \boldsymbol { \mathsf { W } } - \alpha \boldsymbol { \mathsf { B } } \| ^ { 2 }$ . Binary quantization is extended to ternary where ${ \textbf { \textsf { B } } } \in$ $\{ - 1 , 0 , + 1 \} ^ { n \times c \times k \times k }$ . Ternary quantization introduces a threshold factor $\triangle _ { l }$ to assign the ternary value to a weight. (Li et al., 2016; Zhu et al., 2017; Wang et al., 2018) have proposed various methodologies to evaluate the threshold. Lee & Kim (2018) performed ternary quantization by combining pruning and binary quantization.
+
+Binary quantization was extended to multi-bit quantization using a greedy methodology by Guo et al. (2017). For k-bit quantization, minimizing $\| \hat { \pmb { \mathsf { W } } } _ { i } - \pmb { \alpha } _ { i } \pmb { \mathsf { B } } _ { i } \|$ for $\mathrm { i ^ { \mathrm { t h } } }$ bit quantization resulted in,
+
+$$
+\mathbf { B } _ { i } = \mathrm { s i g n } ( \hat { \mathsf { W } } _ { i } ) \qquad \quad \alpha _ { i } = \langle \bar { \mathbf { B } } _ { i } , \hat { \mathsf { W } } _ { i } \rangle / n \qquad \mathrm { w h e r e } \ \hat { \mathsf { W } } _ { i } = \mathsf { W } - \sum _ { j = 1 } ^ { i - 1 } \alpha _ { j } \mathsf { B } _ { j }
+$$
+
+referred as the greedy approach. Greedy approach was improved by refined method, where $\alpha _ { i }$ is computed by using $( ( \bar { \mathbf { B } } _ { i } ^ { \bar { T } } \bar { \mathbf { B } } _ { i } ) ^ { - 1 } \mathbf { B } _ { i } ^ { T } \mathbf { W } ) ^ { T }$ . Xu et al. (2018) improved refined method by performing a binary search on the given refined $\alpha$ set and alternately evaluating $_ { \pmb { \alpha } }$ and $\mathsf { B }$ . Low precision networks have also been proposed to reduce the gap with quantized activation units (Zhuang et al. (2018)). Quantization has also been applied to RNNs and Long Short Term Memory (LSTM) models as well (Hou et al. (2017); Guo et al. (2017); Zhou et al. (2017b); Xu et al. (2018); Lee & Kim (2018)). We use greedy quantization in this work due to its simple operations (although alternating yields the better results at the cost of higher computation overhead). Next section describes our quantization training procedure in detail.
+
+# 3 ITERATIVE QUANTIZATION
+
+Choromanska et al. (2015) shows that minima of high quality (measured by test accuracy) for largesize networks occur in a well-defined band. Choromanska et al. (2015) also conjectured that training using methods like stochastic gradient descent, simulated annealing converges to a minimum in the band. Minima in the band can have varying flatness, where flat minima have smaller error introduced to the accuracy upon adding distortion to the weight (Hochreiter & Schmidhuber (1995)). However, exploring through multiple minima has been a challenging task. Simulated annealing1 (Kirkpatrick et al., 1983) explores through various minima, but does not aim to find wider minima. Motivated from simulated annealing, we propose a training technique to enable exploration of wider minimum among multiple minima. The technique allows escaping from relatively sharper minima and aims to find wider minima in the band. Our training procedure consists of two phases. Phase1 trains the full precision network with quantization. Phase2 fine-tunes the binary network obtained from phase1.
+
+
+Figure 1: (a) Quantization Training algorithm (b) Convergence of accuracy using step training (Phase1) for ResNet32 on CIFAR-10 dataset.
+
+
+
+# 3.1 PHASE1: STEP TRAINING
+
+The goal of phase1 is to produce a full precision model with optimized B and reduced quantization error (error between full precision and quantized model). Phase1 does not modify the original training procedure. Instead, in addition to the original training, phase1 just adds an extra distortion step using quantization (referred as quantized-distortion step), performed once every few iterations. Applying quantized-distortion to the weights consists of 3 parts - quantize the weights of each layer (quantization), convert the quantized weights back to full precision format (de-quantization), and update the full precision model with the de-quantized weights. Quantized-distortion is performed once every Quantized Step Size (QSS) iterations. Original training procedure combined with quantization-distortion is referred as Step Training (Figure 1a). Step training is performed in phase1 until the convergence of training (in principle).
+
+Full precision training of the network for QSS iterations explores the curvature of the local convex surface of the current local minimum. Applying quantized-distortion post-training moves the model to the quantized lattice point on the training contour. Suppose that the quantized lattice point exist outside the curvature around a sharp minimum. Then, the network escapes such sharper minima in phase1. In contrast to existing quantization training methods, step training does not store quantized weights. Instead, step training updates and replaces full precision weights with their quantized version every few iterations.
+
+Quantization Step Size. QSS determines the amount of retraining to be done between two quantized-distortion steps. QSS needs to be big enough to compensate for the error added by the distortion and let the network explore the current local curvature. However, QSS should not be too large to diverge the weights far away from a nearby quantized lattice point. Comparing big vs small QSS - big QSS allows the weights to explore farther allowing the binary representation of the weights to change (weights need large amount of updates to change their sign). On the other hand, small QSS allows the training to exploit the current local curvature and fine-tune $_ { \pmb { \alpha } }$ .
+
+
+Figure 2: (left) Histogram of bit flips for all the weights of ResNet32 for CIFAR-10. (right) weights flipping their signs over the course of step training. Weight is randomly chosen from layer 30 of ResNet32 for CIFAR-10. Larger learning rate allows for more exploration and flipping of weights while small learning rate allows for fine-tuning and final convergence.
+
+We observe that for a training procedure with fixed learning rate, starting with a big QSS and reducing QSS over the training period results in better convergence. However, the same behavior can be approximated with a fixed QSS and a varying learning rate. Figure 1b shows the movement of accuracy using step training with step-wise reducing learning rate and fixed QSS for ResNet32 on CIFAR-10. Larger learning rate enables larger amount of updates (and hence more curvature exploration) given the same gradient from the back propagation (fluctuations in the accuracy). On the other hand, smaller learning rate helps exploit (fine-tune the parameters inside the current minimum) as shown by a smoother rise in accuracy. Hence, we use fixed QSS (500 iterations) in the rest of the manuscript, although one can use varying QSS for further fine-tuning.
+
+Convergence of B. We observe that B converges earlier compared to $_ { \pmb { \alpha } }$ during step training. Such an observation is demonstrated in our experiment with step training for CIFAR-10 with ResNet32. Figure 2 shows the movement of weight with step training2. Initially, the sign bits of the weight flip frequently (with higher learning rate). However, with smaller learning rate (after 80K iterations for CIFAR-10), B do not change and only $_ { \pmb { \alpha } }$ is optimized.
+
+Convergence of $_ { \pmb { \alpha } }$ . Let $\pmb { \mathsf { W } }$ be a tensor of full precision weights with n elements. $\boldsymbol { \mathsf { W } }$ is quantized into $\mathsf { B }$ (binary tensor) and $_ { \pmb { \alpha } }$ (shared scaling factors). Step training updates $\boldsymbol { \mathsf { W } }$ every iteration. On the other hand, $( \boldsymbol { \mathsf { B } } , \alpha )$ are calculated every QSS iterations. Let $\triangle \boldsymbol { \mathsf { W } }$ denote the total update accumulated for $\boldsymbol { \mathsf { W } }$ since the last distortion step. Let $\triangle \alpha$ denote the change between the new $_ { \pmb { \alpha } }$ and the $_ \alpha$ calculated at previous distortion step. For binary quantization, the updated $_ \alpha$ is given by
+
+$$
+\pmb { \alpha } + \triangle \pmb { \alpha } = \frac { 1 } { n } \sum \vert \pmb { W } + \triangle \pmb { W } \vert
+$$
+
+where $| . |$ is the absolute function. Starting from a common absolute quantized value $( \alpha )$ , the weights sharing the same $\alpha$ update independently $( \forall i , j w _ { i } , w _ { j } \in \mathbf { W }$ , $\partial w _ { i } / \bar { \partial } w _ { j } = 0 ,$ ). With large QSS, as the weights diverge from $\alpha$ , the update for $\alpha$ becomes inefficient and noisy. Although phase1 results in optimized $\mathbf { B }$ , phase1 does not completely optimize $_ { \pmb { \alpha } }$ (within the limited number of iterations). Need for improved convergence of $_ { \pmb { \alpha } }$ forms the motivation for phase2.
+
+# 3.2 PHASE2: $_ { \pmb { \alpha } }$ TRAINING
+
+Phase2 starts by converting the full precision trained model from phase1 to the corresponding binary model. The full precision weights $\boldsymbol { \mathsf { W } }$ in phase1 are replaced with the corresponding binary version, $_ \alpha$ and $\mathsf { B }$ in the model. $\mathbf { B }$ is fixed and only $_ { \pmb { \alpha } }$ is trained. Phase2 only constructs the binary model and does not construct the full precision model. Phase2 is faster compared to phase1 due to fewer training parameters, use of binary weights, and no quantized-distortion step. Phase2 is performed with a smaller learning rate after the bit-flips do not occur anymore in phase1. Similar to phase1, phase2 also uses the original training procedure but with fewer number of trainable parameters.
+
+In the complete training procedure, we first perform phase1 followed by phase2. The trained binary model at the end of phase2 represents the output of the complete training procedure. This complete training procedure uses the same number of iterations as that in the original training procedure. As a result, the total training time combining phase1 and phase2 is equivalent to the original full precision training time.
+
+# 3.3 SPECIAL CARE FOR CNNS
+
+This section compares different ways to apply quantization on a 4D tensor kernel. Quantization for a 2D weight matrix $W$ with n elements outputs a binary 2D matrix $B \in \{ - 1 , + 1 \} ^ { n }$ and shared scaling factor $_ \alpha$ per row of $W$ . All the weights in a row share the same $\alpha$ , where $\alpha \in \alpha$ . Further, a row in the matrix can be split into $t$ sub-rows (referred as tables), where each table has a different $\alpha$ . For quantizing a 4D tensor kernel $\pmb { \mathsf { W } } \in \mathbb { R } ^ { k \times \overset { \cdot } { c } \times f \times f }$ in a convolution layer, $\boldsymbol { \mathsf { W } }$ is reshaped to 2D matrix $\dot { W } \in \mathbb { R } ^ { k \times c f f }$ (Rastegari et al., 2016) $k$ is the number of output features, $c$ is the number of inputs features and $f$ is the filter size). There are total $k \alpha$ , each shared by $c \times f \times f$ number of weights. Each output feature in the convolution layer has $c \times f \times f$ weights. Thus, there is only 1 $\alpha$ shared by all the weights for an output feature. As the quantized weights can only take the value of $\left\{ + \alpha , - \alpha \right\}$ , all the inputs for an output feature can only be weighted by the same absolute factor $\alpha$ . Hence, the representative power of the quantized network is limited.
+
+To alleviate this problem, we convert the 4D tensor $\boldsymbol { \mathsf { W } }$ to 2D matrix differently. $\pmb { \mathsf { W } }$ is transposed to $f \times k \times c \times f$ and then reshaped to 2D matrix $\mathbb { R } ^ { f \times k c f }$ (referred as skewed matrix). Next, each row of size $k \times c \times f$ is split into $k / f$ sub-rows. Each sub-row has a different $\alpha$ . Total number of $\alpha$ remains the same as above $( k )$ . Furthermore, the inputs for an output feature can now be weighted by $f$ number of unique $\alpha$ . Note that some $\alpha$ will be shared among different output features as well. In our experiments, skewed matrix shows better results. Section 5.1 shows the benefit in accuracy using the skewed matrix for quantization.
+
+# 4 K-MEANS LOSS AND SHUFFLING
+
+This section aims to limit the divergence of weights from each other during training to get more accurate estimation of $\alpha$ . $L _ { 2 }$ regularization (in the form of $L _ { 2 }$ loss) is frequently used in training of neural networks. $L _ { 2 }$ loss prevents the weights from exploding and suppresses the magnitude of the weights. However, $L _ { 2 }$ loss does apply any restriction on the variance of the weights. As $_ \alpha$ is obtained using Equation 1, higher variance in weights results in higher quantization error. We aim to reduce quantization error by introducing $L _ { K M }$ loss function to reduce the variance of the weights. Let $\boldsymbol { \mathsf { W } } _ { i }$ represent all the weights in a layer $i$ . Let $\mathbf { \pmb { w } } \in \mathbb { W } _ { i }$ be a subset of weights sharing common $\alpha$ ( $\pmb { w }$ are referred as clusters from now). The new loss is represented as:
+
+$$
+L _ { K M } = \frac { c } { \| \mathbf { W } \| ^ { 0 } } \sum _ { \forall \pmb { w } \in \mathbb { W } } \| \pmb { w } - \mathrm { a v g } ( | \pmb { w } | ) \| ^ { 2 }
+$$
+
+where c is a constant, $\mathrm { a v g ( . ) }$ computes the average of the inputs. $L _ { K M }$ divides the weights $\boldsymbol { \mathsf { W } }$ into different clusters $\pmb { w }$ with common $\alpha$ and limits the divergence of weights from the cluster average of its absolute values $_ { \pmb { \alpha } }$ . $L _ { K M }$ restricts the independent movement of weights. Similar with $L _ { 2 }$ loss, a diverged weight increases the $L _ { K M }$ . In addition, a diverged weight also shifts the cluster average, increasing the $L _ { K M }$ loss further. Thus $L _ { K M }$ encourages a lower variance in the weights with common $\alpha$ and improve quantization as a result. The constant factor $c$ is set to be the same as weight decay rate (the constant for $L _ { 2 }$ loss is reduced to mitigate the effect of $L _ { 2 }$ ).
+
+Shuffling. $L _ { K M }$ can be extended for multiple tables, where a row of a quantized matrix has multiple shared $_ { \pmb { \alpha } }$ . With multiple tables, let $\textbf { \em w }$ correspond to a subset of row, where the subset shares the common $\alpha$ . $L _ { K M }$ helps in better approximation for $_ \alpha$ by forcing a predetermined group of weights to exhibit low variance. We could also achieve a better approximation for $_ { \pmb { \alpha } }$ by re-arranging the weights so that similar values are grouped together. Note that rearranging is applicable for DNNs with multiple tables only.
+
+Let the weight matrix between two fully connected layers $l ^ { i }$ and $l ^ { i - 1 }$ be represented by $W ^ { i , i - 1 }$ . Two nodes in a layer $l ^ { i }$ given as $l _ { j } ^ { i }$ and $l _ { k } ^ { i }$ can be swapped by switching the rows $j , k$ of weight matrix $W ^ { i , i - 1 }$ and the columns $j , k$ of $W ^ { i + 1 , i }$ . The layout of the weight matrix can be set to cluster the desired weights without impacting the output of the network. Swapping the nodes in layer $l ^ { i }$ , $l ^ { i - 1 }$ swaps the rows and columns of $\breve { W } ^ { i , i - 1 }$ respectively. Thus, nodes in each layer can be swapped independently. K-means clustering is used to find an optimized configuration of weights in terms of grouping similar values together first. And then the nodes in the layer are swapped to enforce such configuration, reducing the quantization error. The methodology of finding and applying the optimal swapping configuration is termed as shuffling of nodes.
+
+Because applying shuffling of nodes to the current layer requires a layer before and after the current layer, we introduce a shuffle layer in the start and end of the network to allow shuffling in first and last layer of the network. The shuffle layer stores the shuffle configuration and behaves as a mapping layer. The overhead of the shuffle layer is less than $1 \%$ of the model size (same as the size of bias in a layer). Shuffling is applied in the weight distortion step in phase1, when quantizing the weights.
+
+# 5 EXPERIMENTS
+
+Experiments are performed with CNNs and RNNs to show the effectiveness of the proposed method. All the experiments are performed using Tensorflow (Abadi et al., 2016) using 2 Titan X GPUs. Full precision models for CNNs are obtained from tensorflow models repository3, while RNN models are obtained from Verwimp et al. $( 2 0 1 7 ) ^ { 4 }$ . We quantize all the layers of the network unless specified otherwise. Iterative quantization training is performed on pre-trained full precision models. Greedy quantization using Equation 1 is used for all the experiments. Quantization Step Size is set to 500 constant throughout all the experiments.
+
+# 5.1 CIFAR
+
+ResNet32 is trained on CIFAR-10 (Krizhevsky, 2009) for $9 0 \mathrm { k }$ iterations, where the first $6 0 \mathrm { k }$ iterations are performed using step training and remaining 30k iterations are performed with $_ \alpha$ training. $60 \%$ pruning rate is set for ternary quantization. Training ResNet32 using our proposed quantization training method does not incur any increase in training time.
+
+Table 1 shows the improvement by combining the techniques discussed in previous sections in an incremental manner for ResNet32. We use the $k \alpha$ for quantization following Rastegari et al. (2016) as default quantization mode $k$ is the number of output features for a convolution layer). Different QSS schedules were tried where QSS starts with a high value and is reduced over the training procedure. QSS schedule produces better accuracy compared to fixed QSS for step training. Note that, however, $_ \alpha$ training eliminates the need to fine-tune over the QSS and achieves the same accuracy. Number of tables for skewed mode have been set to have the same model size as default mode (resulting in the same number of $\alpha$ ).
+
+Table 2 provides our final accuracy for CIFAR dataset with all the techniques combined using ResNet32 and WideResNet 28-10 models $7 0 \mathrm { x }$ bigger model size compared to ResNet32). Our model provides similar performance compared to TTQ (Zhu et al., 2017) using ResNet32. Our method achieves full precision accuracy for WideResNet 28-10 on both CIFAR-10 and CIFAR-100, compared to the results by McDonnell (2018) without changing the training procedure. We believe that WideResNet demonstrates smaller quantization error than ResNet32 because Li et al. (2018) reported that wider networks facilitates flatter minima.
+
+# 5.2 WIKITEXT-2
+
+LSTM model with 1 layer consisting of 512 nodes is used for WikiText-2 (Merity et al., 2017) dataset, with same hyper-parameter settings as followed by Xu et al. (2018). Performance is measured with Perplexity Per Word metric (PPW). Full precision PPW is 100.2. Activation quantization requires quantization to be performed every iteration for inference, wiping out the speed up obtained with quantized weights for inference. Activation quantization slows down training as well. Thus, we use 32bit activations while 3bit activations used by $\mathrm { X u }$ et al. (2018). Our 2-bit alternating quantization (greedy quantization replaced with alternating quantization in our proposed method) reaches full precision PPW (Table 3).
+
+Table 1: Accuracy improvement by each method incrementally for ResNet32 on CIFAR-10.
+
+