Datasets:

luoojason
/

muddle-eval-bundle-md

Wenhu Chen, Hongmin Wang, Jianshu Chen, Yunkai Zhang, Hong Wang, Shiyang Li, Xiyou Zhou, William Yang Wang University of California, Santa Barbara, CA, USA Tencent AI Lab, Bellevue, WA, USA {wenhuchen,hongmin wang,yunkai zhang,hongwang600,william}@ucsb.edu {shiyangli,xiyou}@cs.ucsb.edu jianshuchen@tencent.com

ABSTRACT

The problem of verifying whether a textual hypothesis holds based on the given evidence, also known as fact veriﬁcation, plays an important role in the study of natural language understanding and semantic representation. However, existing studies are mainly restricted to dealing with unstructured evidence (e.g., natu- ral language sentences and documents, news, etc), while veriﬁcation under struc- tured evidence, such as tables, graphs, and databases, remains under-explored. This paper speciﬁcally aims to study the fact veriﬁcation given semi-structured data as evidence. To this end, we construct a large-scale dataset called TabFact with 16k Wikipedia tables as the evidence for 118k human-annotated natural lan- guage statements, which are labeled as either ENTAILED or REFUTED. TabFact is challenging since it involves both soft linguistic reasoning and hard symbolic reasoning. To address these reasoning challenges, we design two different mod- els: Table-BERT and Latent Program Algorithm (LPA). Table-BERT leverages the state-of-the-art pre-trained language model to encode the linearized tables and statements into continuous vectors for veriﬁcation. LPA parses statements into programs and executes them against the tables to obtain the returned binary value for veriﬁcation. Both methods achieve similar accuracy but still lag far be- hind human performance. We also perform a comprehensive analysis to demon- strate great future opportunities. The data and code of the dataset are provided in https://github.com/wenhuchen/Table-Fact-Checking.

INTRODUCTION

Verifying whether a textual hypothesis is entailed or refuted by the given evidence is a fundamental problem in natural language understanding (Katz & Fodor, 1963; Van Benthem et al., 2008). It can beneﬁt many downstream applications like misinformation detection, fake news detection, etc. Recently, the ﬁrst-ever end-to-end fact-checking system has been designed and proposed in Hassan et al. (2017). The veriﬁcation problem has been extensively studied under different natural language tasks such as recognizing textual entailment (RTE) (Dagan et al., 2005), natural language inference (NLI) (Bowman et al., 2015), claim veriﬁcation (Popat et al., 2017; Hanselowski et al., 2018; Thorne et al., 2018) and multimodal language reasoning (NLVR/NLVR2) (Suhr et al., 2017; 2019). RTE and NLI view a premise sentence as the evidence, claim veriﬁcation views passage collection like Wikipedia1 as the evidence, NLVR/NLVR2 views images as the evidence. These problems have been previously addressed using a variety of techniques including logic rules, knowledge bases, and neural networks. Recently large-scale pre-trained language models (Devlin et al., 2019; Peters et al., 2018; Yang et al., 2019; Liu et al., 2019) have surged to dominate the other algorithms to approach human performance on several textual entailment tasks (Wang et al., 2018; 2019).

However, existing studies are restricted to dealing with unstructured text as the evidence, which would not generalize to the cases where the evidence has a highly structured format. Since such structured evidence (graphs, tables, or databases) are also ubiquitous in real-world applications like

1https://www.wikipedia.org/

Published as a conference paper at ICLR 2020

Figure 1: Examples from the TABFACT dataset. The top table contains the semi-structured knowl- edge facts with caption ”United...”. The left and right boxes below provide several entailed and refuted statements. The error parts are highlighted with red font.

database systems, dialog systems, commercial management systems, social networks, etc, we argue that the fact veriﬁcation under structured evidence forms is an equivalently important yet under- explored problem. Therefore, in this paper, we are speciﬁcally interested in studying fact veriﬁcation with semi-structured Wikipedia tables (Bhagavatula et al., 2013)2 as evidence owing to its structured and ubiquitous nature (Jauhar et al., 2016; Zhong et al., 2017; Pasupat & Liang, 2015). To this end, we introduce a large-scale dataset called TABFACT, which consists of 118K manually annotated statements with regard to 16K Wikipedia tables, their relations are classiﬁed as ENTAILED and REFUTED3. The entailed and refuted statements are both annotated by human workers. With some examples in Figure 1, we can clearly observe that unlike the previous veriﬁcation related problems, TABFACT combines two different forms of reasoning in the statements, (i) Linguistic Reasoning: the veriﬁcation requires semantic-level understanding. For example, “John J. Mcfall failed to be re-elected though being unopposed.” requires understanding over the phrase “lost renomination ...” in the table to correctly classify the entailment relation. Unlike the existing QA datasets (Zhong et al., 2017; Pasupat & Liang, 2015), where the linguistic reasoning is dominated by paraphrasing, TABFACT requires more linguistic inference or common sense. (ii) Symbolic Reasoning: the veriﬁ- cation requires symbolic execution on the table structure. For example, the phrase “There are three Democrats incumbents” requires both condition operation (where condition) and arithmetic oper- ation (count). Unlike question answering, a statement could contain compound facts, all of these facts need to be veriﬁed to predict the verdict. For example, the ”There are ...” in Figure 1 requires verifying three QA pairs (total count=5, democratic count=2, republic count=3). The two forms of reasoning are interleaved across the statements making it challenging for existing models.

In this paper, we particularly propose two approaches to deal with such mixed-reasoning challenge: (i) Table-BERT, this model views the veriﬁcation task completely as an NLI problem by linearizing a table as a premise sentence p, and applies state-of-the-art language understanding pre-trained model to encode both the table and statements h into distributed representation for classiﬁcation. This model excels at linguistic reasoning like paraphrasing and inference but lacks symbolic reasoning skills. (ii) Latent Program Algorithm, this model applies lexical matching to ﬁnd linked entities and triggers to ﬁlter pre-deﬁned APIs (e.g. argmax, argmin, count, etc). We adopt bread-ﬁrst-search with memorization to construct the potential program candidates, a discriminator is further utilized to select the most “consistent” latent programs. This model excels at the symbolic reasoning aspects by executing database queries, which also provides better interpretability by laying out the decision rationale. We perform extensive experiments to investigate their performances: the best-achieved accuracy of both models are reasonable, but far below human performance. Thus, we believe that the proposed table-based fact veriﬁcation task can serve as an important new benchmark towards the goal of building powerful AI that can reason over both soft linguistic form and hard symbolic forms. To facilitate future research, we released all the data, code with the intermediate results.

2In contrast to the database tables, where each column has strong type constraint, the cell records in our

semi-structured tables can be string/data/integer/ﬂoating/phrase/sentences.

3we leave out NEUTRAL due to its low inter-worker agreement, which is easily confused with REFUTED.

DistrictIncumbentPartyResultCandidatesCalifornia 3John E. Mossdemocraticre-electedJohn E. Moss (d) 69.9% John Rakus(r) 30.1%California 5Phillip Burtondemocraticre-electedPhillip Burton (d) 81.8% EdloE. Powell (r) 18.2%California 8George Paul Millerdemocraticlost renominationdemocratic holdPeteStark(d) 52.9% Lew M. Warden, Jr. (r) 47.1%California 14Jerome R. Waldierepublicanre-electedJeromeR. Waldie(d) 77.6% FloydE. Sims(r) 22.4%California 15John J. Mcfallrepublicanre-electedJohn J. Mcfall(d) unopposed1.John E. Moss and Phillip Burton are both re-elected in the house of representative election.2.John J. Mcfallis unopposed during the re-election.3.There are three different incumbents from democratic.1.John E. Moss and George Paul Miller are both re-electedin the house of representative election.2.John J. Mcfallfailed to be re-elected though being unopposed.3.There are five candidates in total, two of them are democrats and three of them are republicans.United States House of Representatives Elections, 1972Entailed StatementRefuted StatementPublished as a conference paper at ICLR 2020

2 TABLE FACT VERIFICATION DATASET

First, we follow the previous Table-based Q&A datasets (Pasupat & Liang, 2015; Zhong et al., 2017) to extract web tables (Bhagavatula et al., 2013) with captions from WikiTables4. Here we ﬁlter out overly complicated and huge tables (e.g. multirows, multicolumns, latex symbol) and obtain 18K relatively clean tables with less than 50 rows and 10 columns.

For crowd-sourcing jobs, we follow the human subject research protocols5 to pay Amazon Mechani- cal Turk6 workers from the native English-speaking countries “US, GB, NZ, CA, AU” with approval rates higher than 95% and more than 500 accepted HITs. Following WikiTableQuestion (Pasupat & Liang, 2015), we provide the annotators with the corresponding table captions to help them better understand the background. To ensure the annotation quality, we develop a pipeline of “positive two-channel annotation” → “negative statement rewriting” → “veriﬁcation”, as described below.

2.1 POSITIVE TWO-CHANNEL COLLECTION & NEGATIVE REWRITING STRATEGY

To harvest statements of different difﬁculty levels, we design a two-channel collection process: Low-Reward Simple Channel: the workers are paid 0.45 USD for annotating one Human Intel- ligent Task (HIT) that requires writing ﬁve statements. The workers are encouraged to produce plain statements meeting the requirements: (i) corresponding to a single row/record in the table with unary fact without involving compound logical inference. (ii) mention the cell values without dra- matic modiﬁcation or paraphrasing. The average annotation time of a HIT is 4.2 min. High-Reward Complex Channel: the workers are paid 0.75 USD for annotating a HIT (ﬁve state- ments). They are guided to produce more sophisticated statements to meet the requirements: (i) involving multiple rows in the tables with higher-order semantics like argmax, argmin, count, differ- ence, average, summarize, etc. (ii) rephrase the table records to involve more semantic understand- ing. The average annotation time of a HIT is 6.8 min. The data obtained from the complex channel are harder in terms of both linguistic and symbolic reasoning, the goal of the two-channel split is to help us understand the proposed models can reach under different levels of difﬁculty.

As suggested in (Zellers et al., 2018), there might be annotation artifacts and conditional stylistic patterns such as length and word-preference biases, which can allow shallow models (e.g. bag-of- words) to obtain artiﬁcially high performance. Therefore, we design a negative rewriting strategy to minimize such linguistic cues or patterns. Instead of letting the annotators write negative statements from scratch, we let them rewrite the collected entailed statements. During the annotation, the workers are explicitly guided to modify the words, phrases or sentence structures but retain the sentence style/length to prevent artiﬁcial cues. We disallow naive negations by adding “not, never, etc” to revert the statement polarity in case of obvious linguistic patterns.

2.2 QUALITY CONTROL

To control the quality of the annotation process, we review a randomly sampled statement from each HIT to decide whether the whole annotation job should be rejected during the annotation process. Speciﬁcally, a HIT must satisfy the following criteria to be accepted: (i) the statements should contain neither typos nor grammatical errors. (ii) the statements do not contain vague claims like might, few, etc. (iii) the claims should be explicitly supported or contradicted by the table without requiring the additional knowledge, no middle ground is permitted. After the data collection, we re-distribute all the annotated samples to further ﬁlter erroneous statements, the workers are paid 0.05 USD per statement to decide whether the statement should be rejected. The criteria we apply are similar: no ambiguity, no typos, explicitly supported or contradictory. Through the post-ﬁltering process, roughly 18% entailed and 27% refuted instances are further abandoned due to poor quality.

4http://websail-fe.cs.northwestern.edu/wikiTables/about/ 5https://en.wikipedia.org/wiki/Minimum_wage_in_the_United_States 6https://www.mturk.com/

Published as a conference paper at ICLR 2020

Figure 2: Proportion of different higher-order operations from the simple/complex channels.

Channel

#Sentence

#Table

Len(Ent)

Len(Ref)

Split

#Sentence

Table

Row Col

Simple Complex Total

50,244 68,031 118,275

9,189 7,392 16,573

13.2 14.2 13.8

13.1 14.2 13.8

Train Val Test

92,283 12,792 12,779

13,182 1,696 1,695

14.1 14.0 14.2

5.5 5.4 5.4

Table 1: Basic statistics of the data collected from the simple/complex channel and the division of Train/Val/Test Split in the dataset, where “Len” denotes the averaged sentence length.

2.3 DATASET STATISTICS

Inter-Annotator Agreement: After the data collection pipeline, we merged the instances from two different channels to obtain a diverse yet clean dataset for table-based fact veriﬁcation. We sample 1000 annotated (table, statement) pairs and re-distribute each to 5 individual workers to re-label them as either ENTAILED or REFUTED. We follow the previous works (Thorne et al., 2018; Bowman et al., 2015) to adopt the Fleiss Kappa (Fleiss, 1971) as an indicator, where Fleiss κ = ¯pc− ¯pe is 1− ¯pe computed from from the observed agreement ¯pc and the agreement by chance ¯pe. We obtain a Fleiss κ = 0.75, which indicates strong inter-annotator agreement and good-quality.

Dataset Statistics: As shown in Table 1, the amount of data harvested via the complex channel slightly outnumbers the simple channel, the averaged length of both the positive and negative sam- ples are indistinguishable. More speciﬁcally, to analyze to which extent the higher-order operations are included in two channels, we group the common higher-order operations into 8 different cate- gories. As shown in Figure 2, we sample 200 sentences from two different channels to visualize their distribution. We can see that the complex channel overwhelms the simple channel in terms of the higher-order logic, among which, count and superlatives are the most frequent. We split the whole data roughly with 8:1:1 into train, validation7, and test splits and shows their statistics in Table 1. Each table with an average of 14 rows and 5-6 columns corresponds to 2-20 different statements, while each cell has an average of 2.1 words. In the training split, the positive instances slightly outnumber the negative instances, while the validation and test split both have rather bal- anced distributions over positive and negative instances.

3 MODELS

With the collected dataset, we now formally deﬁne the table-based fact veriﬁcation task: the dataset is comprised of triple instances (T, S, L) consisting of a table T, a natural language statement S = s1, · · · , sn and a veriﬁcation label L ∈ {0, 1}. The table T = {Ti,j|i ≤ RT , j ≤ CT } has RT rows and CT columns with the Tij being the content in the (i, j)-th cell. Tij could be a word, a number, a phrase, or even a natural language sentence. The statement S describes a fact to be veriﬁed against the content in the table T. If it is entailed by T, then L = 1, otherwise the label L = 0. Figure 1 shows some entailed and refuted examples. During training, the model and the learning algorithm are presented with K instances like (T, S, L)K k=1 from the training split. In the testing stage, the model is presented with (T, S)K(cid:48) k=1 and supposed to predict the label as ˆL. We I( ˆLk = Lk) on the test set. measure the performance by the prediction accuracy Acc = 1 K(cid:48) Before building the model, we ﬁrst perform entity linking to detect all the entities in the statements. Brieﬂy, we ﬁrst lemmatize the words and search for the longest sub-string matching pairs between statements and table cells/captions, where the matched phrases are denoted as the linked entities. To focus on statement veriﬁcation against the table, we do not feed the caption to the model and simply

(cid:80)K(cid:48) 1

7We ﬁlter roughly 400 sentences from abnormal tables including hyperlinks, math symbols, etc

02040AGGREGATIONNEGATESUPERLATIVECOUNTCOMPATIVEORDINALUNIQUEALLPercentProportion of different Higher-order OperationsSimpleComplexOverallPublished as a conference paper at ICLR 2020

mask the phrases in the statements which link to the caption with placeholders. The details of the entity linker are listed in the Appendix. We describe our two proposed models as follows.

3.1 LATENT PROGRAM ALGORITHM (LPA)

In this approach, we formulate the table fact veriﬁcation as a program synthesis problem, where the latent program algorithm is not given in TABFACT. Thus, it can be seen as a weakly supervised learning problem as discussed in Liang et al. (2017); Lao et al. (2011). Under such a setting, we propose to break down the veriﬁcation into two stages: (i) latent program search, (ii) discriminator ranking. In the ﬁrst program synthesis step, we aim to parse the statement into programs to represent its semantics. We deﬁne the plausible API set to include roughly 50 different functions like min, max, count, average, ﬁlter, and and realize their interpreter with Python-Pandas. Each API is deﬁned to take arguments of speciﬁc types (number, string, bool, and view (e.g sub-table)) to output speciﬁc- type variables. During the program execution, we store the generated intermediate variables to different-typed caches N , R, B, V (Num, Str, Bool, View). At each execution step, the program can fetch the intermediate variable from the caches to achieve semantic compositionality. In order to shrink the search space, we follow NSM (Liang et al., 2017) to use trigger words to prune the API set and accelerate the search speed. The deﬁnitions of all API, trigger words can be found in the Appendix. The comprehensive the latent program search procedure is summarized in Algorithm 1,

while (P, N , R, B, V) = Q.pop() do:

while loop over function set f ∈ F do:

if arguments of f are in the caches then

Pop out the required arguments arg1, arg2, · · · , argn for different cachess. Execute A = f (arg1, · · · , argn) and concatenate the program trace P . if Type(A)=Bool then

Algorithm 1 Latent Program Search with Comments 1: Initialize Number Cache N , String Cache R, Bool Cache B, View Cache V → ∅ 2: Push linked numbers, strings from the given statement S into N , R, and push T into V 3: Initialize the result collector P → ∅ and an empty program trace P = ∅ 4: Initialize the Queue Q = [(P, N , R, B, V)], we use Q to store the intermediate states 5: Use trigger words to ﬁnd plausible function set F, for example, more will trigger Greater function. 6: while loop over time t = 1 → MAXSTEP do: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: Return the triple (T, S, P) # Return (Table, Statement, Program Set)

P.push((P, A)) # The program P is valid since it consumes all the variables. P = ∅ # Collect the valid program P into set P and reset P

B.push(A) # The intermediate boolean value is added to the bool cache Q.push((P, N , R, B, V)) # Add the refreshed state to the queue again

push A into N or S or V # Add the refreshed state to the queue for further search Q.push((P, N , R, B, V))

P = ∅;break # The program ends without consuming the cache, throw it.

if Type(A) ∈ {Num, Str, View} then

if N = S = B = ∅ then

else

and the searching procedure is illustrated in Figure 3.

After we collected all the potential program candidates P = {(P1, A1), · · · , (Pn, An)} for a given statement S (where (Pi, Ai) refers to i-th candidate), we need to learn a discriminator to iden- tify the “appropriate” traces from the set from many erroneous and spurious traces. Since we do not have the ground truth label about such discriminator, we use a weakly supervised training al- gorithm by viewing all the label-consistent programs as positive instances {Pi|(Pi, Ai); Ai = L} and the label-inconsistent program as negative instances {Pi|(Pi, Ai); Ai (cid:54)= L} to minimize the cross-entropy of discriminator pθ(S, P ) with the weakly supervised label. Speciﬁcally, we build our discriminator with a Transformer-based two-way encoder (Vaswani et al., 2017), where the statement encoder encodes the input statement S as a vector EncS(S) ∈ Rn×D with dimen- sion D, while the program encoder encodes the program P = p1, · · · , pm as another vector EncP (P ) ∈ Rm×D, we concatenate these two vectors and feed it into a linear projection layer

Published as a conference paper at ICLR 2020

Figure 3: The program synthesis procedure for the table in Figure 1. We link the entity (e.g. demo- cratic, republican), and then composite functions on the ﬂy to return the values from the table.

Figure 4: The diagram of Table-BERT with horizontal scan, two different linearizations are depicted.

to compute pθ(S, P ) = σ(vT p [EncS(S); EncP (P )]) as the relevance between S and P with weight vp ∈ RD. At test time, we use the discriminator pθ to assign conﬁdence pθ(S, P ) to each candidate P ∈ P, and then either aggregate the prediction from all hypothesis with the conﬁdence weights or rank the highest-conﬁdent hypothesis and use their outputs as the prediction.

3.2 TABLE-BERT

In this approach, we view the table veriﬁcation problem as a two-sequence binary classiﬁcation problem like NLI or MPRC (Wang et al., 2018) by linearizing a table T into a sequence and treating the statement as another sequence. Since the linearized table can be extremely long surpassing the limit of sequence models like LSTM, Transformers, etc. We propose to shrink the sequence by only retaining the columns containing entities linked to the statement to alleviate such a memory issue. In order to encode such sub-table as a sequence, we propose two different linearization methods, as is depicted in Figure 4. (i) Concatenation: we simply concatenate the table cells with [SEP] tokens in between and restart position counter at the cell boundaries; the column name is fed as another type embedding to the input layer. Such design retains the table information in its machine format. (ii) Template: we adopt simple natural language templates to transform a table into a “somewhat natural” sentence. Taking the horizontal scan as an example, we linearize a table as “row one’s game is 51; the date is February; ..., the score is 3.4 (ot). row 2 is ...”. The isolated cells are connected with punctuations and copula verbs in a language-like format. After obtaining the linearized sub-table ˜T, we concatenate it with the natural language state- ment S and preﬁx a [CLS] token to the sentence to obtain the sequence-level representation H = fBERT ([ ˜T, S]), with H ∈ R768 from pre-trained BERT (Devlin et al., 2019). The rep- resentation is further fed into multi-layer perceptron fM LP to obtain the entailment probability pθ( ˜T, S) = σ(fM LP (H)), where σ is the sigmoid function. We ﬁnetune the model θ (including the parameters of BERT and MLP) to minimize the binary cross entropy L(pθ( ˜T, S), L) on the training set. At test time, we use the trained BERT model to compute the matching probability between the (table, statement) pair, and classify it as ENTAILED statement when pθ( ˜T, S) is greater than 0.5.

There are more democratsthan republicansin the election.incumbentdemocraticincumbentrepublicanV1=Filter(T, incumbent==democratic))Feature-based Entity LinkingV2=Filter(T, incumbent==republican))StringincumbentrepublicanSubV1SubV2SubV1Viewpop3=Count(V1)popCount3SubV1SubV2ViewNum2=Count(V2)Count2Count3NumGreater(3, 2)BoolTrueBoolpopTableLISP EngineEntailedSearchGameDateOpponentScore51February 3 , 2009Florida3-4 52February 4 , 2009Buffalo0-5 53February 7 , 2010Montreal5-2 TypePositionWordFebruary3,2009[SEP][CLS]51[SEP]10123400gameTOKdatedatedatedateTOKTOKTOK0[SEP]Floridaisplaying123SSS12-Layer BERT-Base Modelonegameis51;date[CLS]isFebruary32019;[SEP]123456708910111220PositionWordrowLabelFlorida13ConcatTemplatePublished as a conference paper at ICLR 2020

4 EXPERIMENTS

In this section, we aim to evaluate the proposed methods on TABFACT. Besides the standard valida- tion and test sets, we also split the test set into a simple and a complex partition based on the channel from which they were collected. This facilitates analyzing how well the model performs under dif- ferent levels of difﬁculty. Additionally, we also hold out a small test set with 2K samples for human evaluation, where we distribute each (table, statement) pair to 5 different workers to approximate human judgments based on their majority voting, the results are reported in Table 2.

Model

BERT classiﬁer w/o Table

Table-BERT-Horizontal-F+T-Concatenate Table-BERT-Vertical-F+T-Template Table-BERT-Vertical-T+F-Template Table-BERT-Horizontal-F+T-Template Table-BERT-Horizontal-T+F-Template

NSM w/ RL (Binary Reward) NSM w/ LPA-guided ML + RL LPA-Voting w/o Discriminator LPA-Weighted-Voting LPA-Ranking w/ Discriminator LPA-Ranking w/ Discriminator (Caption)

Human Performance

Val

50.9

50.7 56.7 56.7 66.0 66.1

54.1 63.2 57.7 62.5 65.2 65.1

Test

50.5

50.4 56.2 57.0 65.1 65.1

54.1 63.5 58.2 63.1 65.0 65.3

Test (simple)

Test (complex)

Small Test

51.0

50.8 59.8 60.6 79.0 79.1

55.4 77.4 68.5 74.6 78.4 78.7

50.1

50.0 55.0 54.3 58.1 58.2

53.1 56.1 53.2 57.3 58.5 58.5

50.4

50.3 56.2 55.5 67.9 68.1

55.8 66.9 61.5 66.8 68.6 68.9

92.1

Table 2: The results of different models, the numbers are in percentage. T+F means table followed by fact, while F+T means fact followed by table. NSM is modiﬁed from Liang et al. (2017).

NSM We follow Liang et al. (2017) to modify their approach to ﬁt the setting of TABFACT. Specif- ically, we adopt an LSTM as an encoder and another LSTM with copy mechanism as a decoder to synthesize the program. However, without any ground truth annotation for the intermediate programs, directly training with reinforcement learning is difﬁcult as the binary reward is under- speciﬁed, which is listed in Table 2 as ”NSM w/ RL”. Further, we use LPA as a teacher to search the top programs for the NSM to bootstrap and then use reinforcement learning to ﬁnetune the model, which achieves reasonable performance on our dataset listed as ”NSM w/ ML + RL”. Table-BERT We build Table-BERT based on the open-source implementation of BERT8 using the pre-trained model with 12-layer, 768-hidden, 12-heads, and 110M parameters trained in 104 lan- guages. We use the standard BERT tokenizer to break the words in both statements and tables into subwords and join the two sequences with a [SEP] token in between. The representation correspond- ing to [CLS] is fed into an MLP layer to predict the veriﬁcation label. We ﬁnetune the model on a single TITAN X GPU with a mini-batch size of 6. The best performance is reached after about 3 hours of training (around 10K steps). We implement and compare the following variants of the Table-BERT model including (i) Concatenation vs. Template: whether to use natural language tem- plates during linearization. (ii) Horizontal vs. Vertical: scan direction in linearization. LPA We run the latent program search in a distributed fashion on three 64-core machines to gener- ate the latent programs. The search terminates once the buffer has more than 50 traces or the path length is larger than 7. The average search time for each statement is about 2.5s. For the discrimina- tor model, we design two transformer-based encoders (3 layers, 128-dimension hidden embedding, and 4 heads at each layer) to encode the programs and statements, respectively. The variants of LPA models considered include (i) Voting: assign each program with equal weight and vote without the learned discriminator. (ii) Weighted-Voting: compute a weighted-sum to aggregate the predictions of all latent programs with the discriminator conﬁdence as the weights. (iii) Ranking: rank all the hypotheses by the discriminator conﬁdence and use the top-rated hypothesis as the output. (Caption) means feeding the caption as a sequence of words to the discriminator during ranking. Preliminary Evaluation In order to test whether our negative rewriting strategy eliminates the ar- tifacts or shallow cues, we also ﬁne-tune a pre-trained BERT (Devlin et al., 2019) to classify the statement S without feeding in table information. The result is reported as “BERT classiﬁer w/o

8https://github.com/huggingface/pytorch-pretrained-BERT

Published as a conference paper at ICLR 2020

Table” in Table 2, which is approximately the majority guess and reﬂects the effectiveness of the rewriting strategy. Before presenting the experiment results, we ﬁrst perform a preliminary study to evaluate how well the entity linking system, program search, and the statement-program discrimi- nator perform. Since we do not have the ground truth labels for these models, we randomly sample 100 samples from the dev set to perform the human study. For the entity linking, we evaluate its accuracy as the number of correctly linked sentences / total sentences. For the latent program search, we evaluate whether the “true” programs are included in the candidate set P as recall score.

Results We report the performance of different methods as well as human performance in Table 2. First of all, we observe that the naive serialized model fails to learn anything effective (same as the Majority Guess). It reveals the importance of template when using the pre-trained BERT (Devlin et al., 2019) model: the “natural” connection words between individual cells is able to unleash the power of the large pre-trained language model and enable it to perform reasoning on the structured table form. Such behavior is understandable given the fact that BERT is pre-trained on purely natural language corpora. In addition, we also observe that the horizontal scan excels in the vertical scan because it better captures the convention of human expression. Among different LPA methods, we found that LPA-Ranking performs the best since it can better suppress the spurious programs than the voting-based algorithm. Overall, the LPA model is on par with Table-BERT on both simple and test split without any pre-training on external corpus, which reﬂects the effectiveness of LPA to leverage symbolic operations in the veriﬁcation process.

Through our human evaluation, we found that only 58% of sentences have been correctly linked without missing-link or over-link, while the systematic search has a recall of 51% under the cases where the sentence is correctly linked. With that being said, the chance for LPA method to cover the correct program (rationale) is roughly under 30%. After the discriminator’s re-ranking step, the probability of selecting these particular oracle program is even much lower. However, we still observe a ﬁnal overall accuracy of 65%, which indicates that the spurious problem is quite severe in LPA, where the correct label is predicted based on the wrong reason.

Through our human evaluation, we also observe that Table-BERT exhibits poor consistency as it can misclassify simple cases but correctly-classify hard cases. These two major weaknesses are yet to be solved in future studies. In contrast, LPA behaves much more consistently and provides a clear latent rationale for its decision. But, such a pipeline system requires laborious handcrafting of API operations and is also very sensitive to the entity linking accuracy. Both methods have pros and cons; how to combine them still remains an open question.

Program Annotation To further promote the development of different models in our dataset, we collect roughly 1400 human-annotated programs paired with the original statements. These state- ments include the most popular logical operations like superlative, counting, comparison, unique, etc. We provide these annotations in Github9, which can either be used to bootstrap the semantic parsers or provide the rationale for NLI models.

5 RELATED WORK

Natural Language Inference & Reasoning: Modeling reasoning and inference in human language is a fundamental and challenging problem towards true natural language understanding. There has been extensive research on RTE in the early years (Dagan et al., 2005) and more recently shifted to NLI (Bowman et al., 2015; Williams et al., 2017). NLI seeks to determine whether a natural language hypothesis h can be inferred from a natural language premise p. With the surge of deep learning, there have been many powerful algorithms like the Decomposed Model (Parikh et al., 2016), Enhanced-LSTM (Chen et al., 2017) and BERT (Devlin et al., 2019). Besides the textual ev- idence, NLVR (Suhr et al., 2017) and NLVR2 (Suhr et al., 2019) have been proposed to use images as the evidence for statement veriﬁcation on multi-modal setting. Our proposed fact veriﬁcation task is closely related to these inference tasks, where our semi-structured table can be seen as a collection of “premises” exhibited in a semi-structured format. Our proposed problem hence could be viewed as the generalization of NLI under the semi-structured domain. Table Question Answering: Another line of research closely related to our task is the table-based

9https://github.com/wenhuchen/Table-Fact-Checking/tree/master/bootstrap

Published as a conference paper at ICLR 2020

Figure 5: The two uniqueness of Table-based fact veriﬁcation against standard QA problems.

question answering, such as MCQ (Jauhar et al., 2016), WikiTableQuestion (Pasupat & Liang, 2015), Spider (Yu et al., 2018), Sequential Q&A (Iyyer et al., 2017), and WikiSQL (Zhong et al., 2017), for which approaches have been extended to handle large-scale tables from Wikipedia (Bha- gavatula et al., 2013). However, in these Q&A tasks, the question types typically provide strong signals needed for identifying the type of answers, while TABFACT does not provide such speci- ﬁcity. The uniqueness of TABFACT lies in two folds: 1) a given fact is regarded as a false claim as long as any part of the statement contains misinformation. Due to the conjunctive nature of veriﬁca- tion, a fact needs to be broken down into several sub-clauses or (Q, A) pairs to separate evaluate their correctness. Such a compositional nature of the veriﬁcation problem makes it more challenging than a standard QA setting. On one hand, the model needs to recognize the multiple QA pairs and their relationship. On the other hand, the multiple sub-clauses make the semantic form longer and logic inference harder than the standard QA setting. 2) some facts cannot even be handled using semantic forms, as they are driven by linguistic inference or common sense. In order to verify these state- ments, more inference techniques have to be leveraged to enable robust veriﬁcation. We visualize the above two characteristics of TABFACT in Figure 5.

Program Synthesis & Semantic Parsing: There have also been great interests in using program synthesis or logic forms to solve different natural language processing problems like question answering (Liang et al., 2013; Berant et al., 2013; Berant & Liang, 2014), visual navigation (Artzi et al., 2014; Artzi & Zettlemoyer, 2013), code generation (Yin & Neubig, 2017; Dong & Lapata, 2016), SQL synthesis (Yu et al., 2018), etc. The traditional semantic parsing papers (Artzi et al., 2014; Artzi & Zettlemoyer, 2013; Zettlemoyer & Collins, 2005; Liang et al., 2013; Berant et al., 2013) greatly rely on rules, lexicon to parse natural language sentences into different forms like lambda calculus, DCS, etc. More recently, researchers strive to propose neural models to directly perform end-to-end formal reasoning like Theory Prover (Riedel et al., 2017; Rockt¨aschel & Riedel, 2017), Neural Turing Machine (Graves et al., 2014), Neural Programmer (Neelakantan et al., 2016; 2017) and Neural-Symbolic Machines (Liang et al., 2017; 2018; Agarwal et al., 2019). The proposed TABFACT serves as a great benchmark to evaluate the reasoning ability of different neural reasoning models. Speciﬁcally, TABFACT poses the following challenges: 1) spurious programs (i.e., wrong programs with the true returned answers): since the program output is only a binary label, which can cause serious spurious problems and misguide the reinforcement learning with the under-speciﬁed binary rewards. 2) decomposition: the model needs to decompose the statement into sub-clauses and verify the sub-clauses one by one, which normally requires the longer logic in- ference chains to infer the statement verdict. 3) linguistic reasoning like inference and paraphrasing.

Fact Checking The problem of verifying claims and hypotheses on the web has drawn signiﬁcant at- tention recently due to its high social inﬂuence. Different fact-checking pioneering studies have been

DistrictIncumbentPartyResultCandidatesCalifornia 3John E. Mossdemocraticre-electedJohn E. Moss (d) 69.9% John Rakus(r) 30.1%California 5Phillip Burtondemocraticre-electedPhillip Burton (d) 81.8% EdloE. Powell (r) 18.2%California 8George Paul Millerdemocraticlost renominationdemocratic holdPeteStark(d) 52.9% Lew M. Warden, Jr. (r) 47.1%California 14Jerome R. Waldierepublicanre-electedJeromeR. Waldie(d) 77.6% FloydE. Sims(r) 22.4%California 15John J. Mcfallrepublicanre-electedJohn J. Mcfall(d) unopposedUnited States House of Representatives Elections, 1972There are five candidates in total, two of them are democrats and three of them are republicans.Question: How many of candidates in total?Answer: 5Question: How many democrats are there?Answer: 2Question: How many republicans are there?Answer: 3∧∧ConjunctiveEq(Count(T), 5)=TEq(Count(Filter(T, party=‘dem..’)), 2)=FEq(Count(Filter(T, party=‘rep..’)), 3)=F∧∧outcomedatetournamentsurfacepartneropponents in the finalscore in the finalrunner -up1985bologna , italyclayalberto touspaolocanèsimonecolombo5 -7 , 4 -6winner1986bordeaux , franceclaydavid de miguelronald agénor mansour bahrami7 -5 , 6 -4winner1989prague , czechoslovakiaclayhorst skoffpetr korda tomáš šmíd6 -4 , 6 -4Jordi Arreseachieves better score in 1986 than in 1985.Jordi ArreseJordi Arresewon both of the final games in 1986.1986: Winner1986: Runner-upLinguistic Inference7 -5 , 6 -4Mathematic Inference(2)(1)Published as a conference paper at ICLR 2020

performed including LIAR (Wang, 2017), PolitiFact (Vlachos & Riedel, 2014), FEVER (Thorne et al., 2018) and AggChecker (Jo et al., 2019), etc. The former three studies are mainly based on textual evidence on social media or Wikipedia, while AggChecker is closest to ours in using re- lational databases as the evidence. Compared to AggChecker, our paper proposes a much larger dataset to benchmark the progress in this direction.

6 CONCLUSION

This paper investigates a very important yet previously under-explored research problem: semi- structured fact veriﬁcation. We construct a large-scale dataset and proposed two methods, Table- BERT and LPA, based on the state-of-the-art pre-trained natural language inference model and pro- gram synthesis. In the future, we plan to push forward this research direction by inspiring more sophisticated architectures that can perform both linguistic and symbolic reasoning.

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A APPENDIX

A.1 FUNCTION DESCRIPTION

We list the detailed function description in Figure 6. We also visualize the functionality of the most

Figure 6: The function deﬁnition used in TabFact.

typical functions and their input/output examples in Figure 7.

Figure 7: The visualization of different functions.

NameArgumentsOutputCommentCountViewNumberReturnthe number of rows in the ViewWithinView, Header String, Cell String/NumberBoolReturn whetherthe cell string/number exists under the Header Column of the given viewWithoutView, Header String, Cell String/NumberBoolReturn whetherthe cell string/number does not exist under the Header Column of the given viewNoneStringBoolWhether the string representsNone, like “None”, “No”, “-”, “No information provided”Before/AfterRow, RowRowReturnswhether row1 is before/after row2First/Second/Third/FourthView, RowBoolReturns whether the rowis in the first/second/third position of the viewAverage/Sum/Max/MinView, HeaderStringNumberReturns theaverage/summation/max/min value under the Header Column of the given viewArgmin/ArgmaxView, Header StringRowReturns the row with the maximum/minimum value under the Header Column of thegiven viewHopRow,Header StringNumber/StringReturns thecell value under the Header Column of the given rowDiff/AddNumber, NumberNumberPerform arithmetic operations on twonumbersGreater/LessNumber, NumberBoolReturns whetherthe first number is greater/less than the second numberEqual/UnequalString, String/Number,NumberBoolComparetwo numbers or strings to see whether they are the sameFilter_eq/Filter_greater/Filter_less/Filter_greater_or_equal/Filter_less_or_equalView, HeaderString, NumberViewReturnsthe subviewof the given with the cell values under the Header column greater/less/eq/…against the given numberAll_eq/All_greater/All_less/All_greater_or_equal/All_less_or_equalView, HeaderString, NumberBoolReturnsthe whether all of the cell values under the Header column are greater/less/eq/…against the given numberAnd/OrBool, BoolBoolReturns the Booleanoperation results of two inputsCountNameAge()=2within(, Name, A)=𝑇𝑟𝑢𝑒NameAgeABwithout(, Name, A)=𝐹𝑎𝑙𝑠𝑒NameAgeABNone() =𝑇𝑟𝑢𝑒-/Not Given/NABeforeNameAgeA()=𝑇𝑟𝑢𝑒NameAgeBFirstNameAgeA() =𝑇𝑟𝑢𝑒Avg(, Age)=3NameAgeA2B4Argmin(, Age)=NameAgeA2B4NameAgeA2Filter_eq(, Age, 2)=NameAgeA2B4NameAgeA2All_eq(, Age, 2)=TrueNameAgeA2B2HopNameAgeA(, Name)=𝐴Diff(2, 1)=1Greater(2, 1)=𝑇𝑟𝑢𝑒Equal(2, 2)=𝑇𝑟𝑢𝑒, Published as a conference paper at ICLR 2020

We list all the trigger words for different functions in Figure 8

Figure 8: The trigger words used to shrink the search space.

B HIGHER-ORDER OPERATIONS

Aggregation: the aggregation operation refers to sentences like “the averaged age of all

....”, “the total amount of scores obtained in ...”, etc.

Negation: the negation operation refers to sentences like “xxx did not get the best score”,

“xxx has never obtained a score higher than 5”.

Superlative: the superlative operation refers to sentences like “xxx achieves the highest

score in”, “xxx is the lowest player in the team”.

Comparative: the comparative operation refers to sentences like “xxx has a higher score

than yyy”.

Ordinal: the ordinal operation refers to sentences like “the ﬁrst country to achieve xxx is

xxx”, “xxx is the second oldest person in the country”.

Unique: the unique operation refers to sentences like “there are 5 different nations in the

tournament, ”, “there are no two different players from U.S”

All:

the for all operation refers to sentences like “all of the trains are departing in the

morning”, “none of the people are older than 25.”

None: the sentences which do not involve higher-order operations like “xxx achieves 2

points in xxx game”, “xxx player is from xxx country”.

C ERROR ANALYSIS

Before we quantitatively demonstrate the error analysis of the two methods, we ﬁrst theoretically analyze the bottlenecks of the two methods as follows:

Symbolic We ﬁrst provide a case in which the symbolic execution can not deal with theoretically in Figure 9. The failure cases of symbolic are either due to the entity link problem or function coverage problem. For example, in the given statement below, there is no explicit mention of ”7-5, 6-4” cell. Therefore, the entity linking model fails to link to this cell content. Furthermore, even

TriggerFunction'average'average'difference', 'gap', 'than', 'separate'diff'sum', 'summation', 'combine', 'combined', 'total', 'add', 'all', 'there are'ddd, sum'not', 'no', 'never', "didn't", "won't", "wasn't", "isn't,"haven't", "weren't", "won't", 'neither', 'none', 'unable,'fail', 'different', 'outside', 'unable', 'fail'not_eq, not_within,Filter_not_eq,none'not', 'no', 'none'none'first', 'top', 'latest', 'most'first'last', 'bottom', 'latest', 'most'last'RBR', 'JJR', 'more', 'than', 'above', 'after'filter_greater,greater'RBR', 'JJR', 'less', 'than', 'below', 'under'filter_less, less'all', 'every', 'each'all_eq, all_less, all_greater, ['all', 'every', 'each'], ['not', 'no', 'never', "didn't", "won't", "wasn't"]all_not_eq'at most', 'than'all_less_eq, all_greater_eq'RBR', 'RBS', 'JJR', 'JJS'max, min'JJR', 'JJS', 'RBR', 'RBS', 'top', 'first'argmax, argmin'within', 'one', 'of', 'among'within'follow', 'following', 'followed', 'after', 'before', 'above', 'precede'before'follow', 'following', 'followed', 'after', 'before', 'above', 'precede'after’most’most_freqordinalFirst, second,third, fourthPublished as a conference paper at ICLR 2020

though we can successfully link to this string, there is no deﬁned function to parse ”7-5, 6-5” as ”won two games” because it requires linguistic/mathematical inference to understand the implication from the string. Such cases are the weakness of symbolic reasoning models.

Figure 9: The error case of symbolic reasoning model

BERT In contrast, Table-BERT model seems to have no coverage problem as long as it can feed the whole table content. However, due to the template linearization, the table is unfolded into a long sequence as depicted in Figure 10. The useful information, ”clay” are separated in a very long span of unrelated words. How to grasp such a long dependency and memorize the history information poses a great challenge to the Table-BERT model.

Figure 10: The error case of BERT NLI model

Statistics Here we pick 200 samples from the validation set which only involve single semantic and divide them into different categories. We denote the above-mentioned cases as ”linguistic in- ference”, and the sentences which only describe information from one row as ”Trivial”, the rest are based on their logic operation like Aggregation, Superlative, Count, etc. We visualize the accuracy of LPA and Table-BERT in Figure 11. From which we can observe that the statements with linguis- tic inference are much better handled with the BERT model, while LPA achieves an accuracy barely higher than a random guess. The BERT model can deal with trivial cases well as it uses a horizontal scan order. In contrast, the LPA model outperforms BERT on higher-order logic cases, especially when the statement involves operations like Count and Superlative.

outcomedatetournamentsurfacepartneropponents in the finalscore in the finalrunner -up1985Bologna , ItalyclayAlberto TousPaolo CanèSimone Colombo5 -7 , 4 -6winner1986Bordeaux , FranceclayDavid De MiguelRonald AgénorMansour Bahrami7 -5 , 6 -4winner1989Prague , CzechoslovakiaclayHorst SkoffPetr KordaTomáššmíd6 -4 , 6 -4Jordi Arreseachieves better score in 1986 than in 1985.Jordi ArreseJordi Arresewon both of the final games in 1986.1986: Winner1986: Runner-upLinguistic Inference7 -5 , 6 -4Mathematic Inferenceoutcomedatetournamentsurfacepartneropponents in the finalscore in the finalrunner -up1985Bologna , ItalyclayAlberto TousPaolo CanèSimone Colombo5 -7 , 4 -6winner1986Bordeaux , FranceclayDavid De MiguelRonald AgénorMansour Bahrami7 -5 , 6 -4winner1989Prague , CzechoslovakiaclayHorst SkoffPetr KordaTomáššmíd6 -4 , 6 -4Jordi ArreseJordi Arreseplayed all of his games on clay surface.Given the table titled “Jordi Arrese”, in row one, the outcome is runner-up, the date is 1985, … , the surface is clay…. …… , In row two, the outcome is … , the surface is clay. In row three, the outcome is …, … the surface is clay.TemplateLong DependencyThe three “Clay” are separated by more over 20 wordsPublished as a conference paper at ICLR 2020

Figure 11: The error analysis of two different models

D REASONING DEPTH

Given that our LPA has the breadth to cover a large semantic space. Here we also show the reasoning depth in terms of how many logic inference steps are required to tackle verify the given claims. We visualize the histogram in Figure 12 and observe that the reasoning steps are concentrated between 4 to 7. Such statistics indicate the difﬁculty of fact veriﬁcation in our TABFACT dataset.

Figure 12: The histogram of reasoning steps required to verify the claims

E WHETHER TO KEEP WIKIPEDIA CONTEXT

Before crowd-sourcing the annotation for the tables, we observed that the previous WikiTableQues- tion Pasupat & Liang (2015) provides context (Wikipedia title) during annotation while the Wik- iSQL Zhong et al. (2017) does not. Therefore, we particularly design ablation annotation tasks to compare the annotation quality between w/ and w/o Wikipedia title as context. We demonstrate a typical example in Figure 13, where a Wiki table10 aims to describe the achievements of a tennis player named Dennis, but itself does not provide any explicit hint about “Tennis Player Dennis”. Unsurprisingly, the sentence ﬂuency and coherence signiﬁcantly drop without such information. Actually, a great portion of these Wikipedia tables requires background knowledge (like sports, celebrity, music, etc) to understand. We perform a small user study to measure the ﬂuency of an- notated statements. Speciﬁcally, we collected 50 sentences from both annotation w/ and w/o title context and randomly shufﬂe them as pairs, which are distributed to the 8 experts without telling them their source to compare the language ﬂuency. It turns out that the experts ubiquitously agree that the statements with Wikipedia titles are more human-readable. Therefore, we argue that such a context is necessary for annotators to understand the background knowledge to write more ﬂu- ent sentences. On the other end, we also hope to minimize the inﬂuence of the textual context in the table-based veriﬁcation task, therefore, we design an annotation criterion: the Wikipedia title

10https://en.wikipedia.org/wiki/Dennis_Ralston

4550556065707580LinguisticTrivialAggregationSuperlativeCountCompareNegationError Analysis of LPA/Table-BERTTable-BERTLPA050000100000150000200000250000300000350000400000450000Reasoning Depth Statistics in LPA1234567Published as a conference paper at ICLR 2020

is provided to the workers during the annotation, but they are explicitly banned from bringing any unrelated background information other than the title into the annotation. As illustrated in Figure 13, the title only acts as a placeholder in the statements to make it sound more natural.

Figure 13: Comparison of worker annotation w/ and w/o Wikipedia title as context

F ENTITY LINKING

Here we propose to use the longest string match to ﬁnd all the candidate entities in the table, when multiple candidates coexist, we select the one with the minimum edit distances. The visualization is demonstrated in Figure 14.

Figure 14: Entity Linking System.

G THE PROGRAM CANDIDATES

Here we demonstrate some program candidates in Figure 15, and show how our proposed discrimi- nator is designed to compute the matching probability between the statement and program. Specif- ically, we employ two transformer-based encoder Vaswani et al. (2017), the left one is aimed to encode the program sequence and the right one is aimed to encode the statement sequence. Their output from [CLS] position is concatenated and fed into an MLP to classify the veriﬁcation label.

H HIT INTERFACE

We provide the human intelligent task interface on AMT in the following. Very detailed instructions on what are trivial statements and what are non-trivial statements. Comprehensive examples have been given to guide the Turkers to write well-formed while logically plausible statements. In order to harvest fake statements without statistical cues, we also provide detailed instructions on how to re-write the ”fake” statements. During the annotation, we hire 8 experts to perform sanity checks on each of the HIT to make sure that the annotated dataset is clean and meets our requirements.

Context(Title)Richard Dennis Ralston(born July 27, 1942, an American formertennisplayerNo Informationis providedAnnotateFrom 1960 to 1969, Ralston won five major double championships.Winner is on the grass surface.Rafael Osuna is partner in the Wimbeldonoutcomeyearchampionshipsurfacepartnerwinner1960Wimbledon championshipsgrassRafael Osunawinner1961US ChampionshipsgrassChuck Mckinleyrunner -up1962US ChampionshipsgrassChuck Mckinleywinner1963US Championships (2)grassChuck MckinleyDistrictIncumbentPartyResultCandidatesCalifornia 3John E. Mossdemocraticre-electedJohn E. Moss (d) 69.9% John Rakus(r) 30.1%California 5Phillip Burtondemocraticre-electedPhillip Burton (d) 81.8% EdloE. Powell (r) 18.2%california8George Paul Millerdemocraticlost renomination democratic holdPeteStark(d) 52.9% Lew M. Warden, Jr. (r) 47.1%California 14Jerome R. Waldierepublicanre-electedJeromeR. Waldie(d) 77.6% FloydE. Sims(r) 22.4%California 15John J. Mcfallrepublicanre-electedJohn J. Mcfall(d) unopposedStatement: John E. Mossis a democratic who is from California 3 districtJohnJohn E. Moss (d) 69.9% johnrakus(r) 30.1%John E. MossJohn J. McfallJohnE. MossJohn E. Moss (d) 69.9% johnrakus(r) 30.1%John E. MossisPublished as a conference paper at ICLR 2020

Figure 15: We demonstrate the top program candidates and use the discriminator to rank them.

Statement: There are more democraticthan republicanin the election. Less(Count(Filter(incumbent==democratic)), Count(Filter(incumbent==republican)))=FalseLess(Count(Filter(incumbent==republican)), Count(Filter(incumbent==democratic)))=TrueGreater(Count(Filter(incumbent==republican)), Count(Filter(incumbent==democratic)))=FalseGreater(Count(Filter(incumbent==democratic)),Count(Filter(incumbent==republican)))=TrueWithin((Filter(incumbent==democratic), incumbent, republican)=FalseWithin((Filter(incumbent==republican), incumbent, democratic)=FalseAnd(Same(all_rows, incumbent, democratic), Same(all_rows, incumbent, republican))=TrueOr(Same(all_rows, incumbent, democratic), Same(all_rows, incumbent, republican))=TrueEq(Count(Filter(incumbent==republican)), Count(Filter(incumbent==democratic)))=FalseProgram EncoderStatement EncoderLabel11/8/2019HIThttps://s3.amazonaws.com/mturk_bulk/hits/370501562/uNGk1Dz1zM48BZI6mALfxA.html1/4Survey Instructions (Click to expand)You are given a table with its wikipedia source, your job is to compose non-trivial statements supportedby the table.- "Trivial": the sentence can be easily generated by looking only a certain row without understanding thetable.- "Non-trivial": the sentence requires reading multiple rows of the table and understanding of the tablecontent. For example, the sentences which include summarization, comparative, negation, relational,inclusion, superlative, aggregational, rephrase or combinations of them are non-trivial. But non-trvial is notlimited to these types, any statement involving understanding and reasoning is accepted. We list two examples below to help you understand, you are encouraged to open the table wikipedia link tounderstand the context of the table. (Everything in the table is lower-cased, you are free to use lower or uppercase in your sentence):Table Wikipedia Link: Road_Rules_Challenge:_The_Island(https://en.wikipedia.org/wiki/Real_World/Road_Rules_Challenge:_The_Island)playeroriginal seasongendereliminatedplacingderrick kosinskirr : x - trememalewinnerwinnerevelyn smithfresh meatfemalewinnerwinnerjohnny devenanziorw : key westmalewinnerwinnerkenny santuccifresh meatmalewinnerwinnerjenn grijalvarw : denverfemaleepisode 8runner - uppaula meronekrw : key westfemaleepisode 8runner - uprobin hibbardrw : san diegofemaleepisode 8runner - upryan kehoefresh meatmaleepisode 8runner - updunbar merrillrw : sydneymaleepisode 89th placejohanna bottarw : austinfemaleepisode 810th placekellyanne juddrw : sydneyfemaleepisode 811th placedan walshrr : viewers' revengemaleepisode 812th placecolie edisonrw : denverfemaleepisode 713th placecohutta grindstaffrw : sydneymaleepisode 614th placetyrie ballardrw : denvermaleepisode 515th placeashli robsonrw : sydneyfemaleepisode 416th placerachel robinsonrr : campus crawlfemaleepisode 317th placeabram boiserr : south pacificmaleepisode 218th placedave malinoskyrw : hollywoodmaleepisode 2 (quit)19th placeRejected ("Trivial") examples:1. In the TV series "The Island", Derrick Kosinski is a male character. (Easy! You can simply look into ﬁrstrow to produce this sentence.)2. Derrick Kosinski has the placing of winner in the TV series.3. Kenny Santucci is from original season of "Fresh Meat".11/8/2019HIThttps://s3.amazonaws.com/mturk_bulk/hits/370501562/uNGk1Dz1zM48BZI6mALfxA.html2/4Table Wikipedia Link: AFC_Champions_League (https://en.wikipedia.org/wiki/AFC_Champions_League) Tips1: We set minimum length to 9, and sentences with more complicated grammar structures arepreferred. Tips2: Do not limited to only one type of description like superlative or relative. Tips3: Copying the records from the table is encouraged, which can help avoid typos and mis-spelling asmuch as possible, . Tips4: Do not vague words like "maybe", "perhaps", "good", "excellent", "most", etc. 4. Jenn Grijalva is Runner-Up of the challenge.Accepted ("Non-Trivial") examples: (Superlative): In the TV series "The Island", Evelyn Smith is the highest ranked female. (Comparitive): In the TV series "The Island", Jenn Grijalva appears later than Colie Edison in the series.(Relational): Ashli Robson appears one episode later than Rachel Robinson in the TV series.(Summarization): there are three male winners in the challenge.(Rephrase): Evelyn Smith never eliminated in any episode in the TV series.(Combination): Derrick Kosinski is the winner and Jenn Grijalva is Runner-Up of the challenge.(Negation): jenn grijalva is not the female winning the challenge. (Inclusion): Evelyn smith is one of the four winner for the challenge.rankmember associationpointsgroup stageplay - offafc cup1saudi arabia860.54002qatar838.24003iran813.53104uae750.22205uzbekistan680.81006india106.40027jordan128.7002Rejected ("Trivial") examples:1. In the rank, it has 0 play - oﬀ.2. ratar is in rank 2.3. When member association is india, the points is 106.4.Accepted ("Non-Trivial") examples: (Negation): iran is one of the two countries getting into the 4th stage. (Average): uae and qatar have anaverage of 1 play - oﬀ during the champion league. (Algorithmic): saudi arabia achieves 22.3 more points than qatar. (Comparison): india got lower points than jordan in the league. (Summarization): there are two team which have won the afc cup twice.(Superlative): In the Champions League, saudi arabia achieves the highest points. (Combination): saudi arabia is the group stage 4 while iran is in group stage 3.11/8/2019HIThttps://s3.amazonaws.com/mturk_bulk/hits/370501562/uNGk1Dz1zM48BZI6mALfxA.html3/4First Read the following table, then write ﬁve diverse non-trivial facts for this given table:Table Source: athletics at the 1952 summer olympics - men 's pole vault(https://en.wikipedia.org/wiki/Athletics_at_the_1952_Summer_Olympics_%E2%80%93_Men%27s_pole_vault)athletenationality3.603.803.95resultbob richardsunited states--o4.55 ordon lazunited states--o4.50ragnar lundbergsweden--o4.40petro denysenkosoviet union--o4.40valto oleniusfinland---4.30bunkichi sawadajapan-oxxo4.20volodymyr brazhnyksoviet union-oo4.20viktor knyazevsoviet union-oo4.20george mattosunited states--o4.20erkki katajafinland--o4.10tamás homonnaysweden-oo4.10lennart lindhungary-oo4.10milan milakovyugoslavia-oxo4.10rigas efstathiadisgreece-oo3.95torfy bryngeirssoniceland-oo3.95erling kaasnorway-oxxx3.80theodosios balafasgreeceooxxx3.80jukka piironenfinland-xoxx3.80zeno dragomirromania-xoxx3.80Please write a non-trivial statement, minimum 9 wordsPlease write a non-trivial statement, minimum 9 wordsPlease write a non-trivial statement, minimum 9 wordsPlease write a non-trivial statement, minimum 9 wordsPlease write a non-trivial statement, minimum 9 words11/8/2019HIThttps://s3.amazonaws.com/mturk_bulk/hits/391922557/v_5b2TrRmw9TnD5hSI_CnA.html1/3Survey Instructions (Click to expand)Please ﬁrst read a table to understand its content, an example is shown below, which contains theleaderboard of a competition.PlayerOriginal SeasonGenderEliminatedPlacingDerrick KosinskiRR: X-TremeMaleWinnerWinnerEvelyn SmithFresh MeatFemaleWinnerWinnerJohnny DevenanzioRW: Key WestMaleWinnerWinnerKenny SantucciFresh MeatMaleWinnerWinnerJenn GrijalvaRW: DenverFemaleEpisode 8Runner-UpPaula MeronekRW: Key WestFemaleEpisode 8Runner-UpRobin HibbardRW: San DiegoFemaleEpisode 8Runner-UpRyan KehoeFresh MeatMaleEpisode 8Runner-UpDunbar MerrillRW: SydneyMaleEpisode 89th PlaceJohanna BottaRW: AustinFemaleEpisode 810th PlaceKellyAnne JuddRW: SydneyFemaleEpisode 811th PlaceDan WalshRR: Viewers' RevengeMaleEpisode 812th PlaceColie EdisonRW: DenverFemaleEpisode 713th PlaceCohutta GrindstaffRW: SydneyMaleEpisode 614th PlaceTyrie BallardRW: DenverMaleEpisode 515th PlaceAshli RobsonRW: SydneyFemaleEpisode 416th PlaceRachel RobinsonRR: Campus CrawlFemaleEpisode 317th PlaceAbram BoiseRR: South PacificMaleEpisode 218th PlaceDave MalinoskyRW: HollywoodMaleEpisode 2 (quit)19th PlaceTonya CooleyRW: ChicagoFemaleEpisode 120th PlaceYou are given a sentence to describe a fact in the table, please follow the following two cases to ﬁnish thejob:* If the given sentence is ﬂuent and consistent with the table, then please re-write it to make it"fake" based on the following criteria:1. Contradictory: it should still be a ﬂuent and coherent, but it needs be explicitly contrdictory to thefacts in the table.2. Do not simply add NOT to revert the sentence meaning.3. Do not write neutral or non-veriﬁable sentences, you need to conﬁrm it in the table.3. The fake statement needs to be clear, explicit and natural, do not use vague or ambiguous words like"bad", "good", "many", etc.4. try to use diverse fake types during annotatoin.Example 1. Given statement: Ashli Robson was eliminated in episode 4.Good Faking: Ashli Robson survives through episode 1 to episode 5.Good Faking: Ashli Robson is not the only one eliminated in episode 4.Bad Faking (Simply add not): Ashli Robson was not eliminated on episode 4.11/8/2019HIThttps://s3.amazonaws.com/mturk_bulk/hits/391922557/v_5b2TrRmw9TnD5hSI_CnA.html2/3Bad Faking (Ambiguous, who is Ashli?): Ashli was not eliminated on episode 4.Bad Faking (Irrelevant): Ashli was born in Mexico.Bad Faking (Too subjective, what do you mean by "early"): AshlDerrick Kosinski lost the game very early.Bad Faking (Not veriﬁable): AshlDerrick Kosinski was the most popular player.Example 2. Given statement: Tonya Cooley is in the 20th place.Good Faking: Tonya Cooley is not the last in placing.Good Faking: Tonya Cooley is eliminated in episode 1 but not the last in placing.Bad Faking: (There is nothing larger than 20th) Tonya Cooley is after the 20th place.Bad Faking: (Half Wrong/half Right) When the gneder is female, the player is Tonya Colley.Bad Faking (Introduce values outside the table): Tonya Cooley is in the 43th place. Bad Faking (Typo): Tonya Cooler is in the 20th palace. * If the given statement is erroneous (see following), please type in N/A in the input box.1. critical grammar error like missing verbs, nouns, etc. Do not count small errors like tense,singular/plural, case errors.2. serious typo, misspelling.3. the described fact is contradictory to the table.You can use the highlight button to help you ﬁnd the mentions in the table, you can use eitherupper or lower case, not important11/8/2019HIThttps://s3.amazonaws.com/mturk_bulk/hits/391922557/v_5b2TrRmw9TnD5hSI_CnA.html3/3SubmitFirst Read the given tables, then rewrite the statements to make them fake:Table Source: 2003 - 04 isu junior grand prix(https://en.wikipedia.org/wiki/2003%E2%80%9304_ISU_Junior_Grand_Prix)ranknationgoldsilverbronzetotal1russia10148322united states967223canada4210164japan454135hungary40266czech republic21146ukraine13046italy01347sweden12038israel11029finland00119france0101Hightlight Mentions, Click Me!Given Statement: russia won the most silver medals in the grand prixPlease rewrite a sentence which is contradictory to the tableHightlight Mentions, Click Me!Given Statement: france and ﬁnland won the least medals in the grand prixPlease rewrite a sentence which is contradictory to the tableHightlight Mentions, Click Me!Given Statement: hungary and ﬁnland were the only countries that idd not win any silver medalsPlease rewrite a sentence which is contradictory to the tableHightlight Mentions, Click Me!Given Statement: the united states won more gold medals than canadaPlease rewrite a sentence which is contradictory to the tableHightlight Mentions, Click Me!Given Statement: canada won the most bronze medals in the grand prixPlease rewrite a sentence which is contradictory to the table