Current commonsense reasoning research focuses on developing models that use commonsense knowledge to answer multiple-choice questions. However, systems designed to answer multiple-choice questions may not be useful in applications that do not provide a small list of candidate answers to choose from. As a step towards making commonsense reasoning research more realistic and useful, we propose to study open-ended commonsense reasoning (OpenCSR)  the task of answering a commonsense question without any pre-defined choices  using as a resource only a knowledge corpus of commonsense facts written in natural language. OpenCSR is challenging due to a large decision space, and because many questions require implicit multi-hop reasoning. As an approach to OpenCSR, we propose DRFACT , an efficient D ifferentiable model for multi-hop Reasoning over knowledge Facts. To evaluate OpenCSR methods, we adapt three popular multiple-choice datasets, and collect multiple new answers to each test question via crowd-sourcing. Experiments show that DRFACT outperforms strong baseline methods by a large margin. 1 1 Introduction The conventional task setting for most current commonsense reasoning research is multiple-choice question answering (QA)  i.e., given a question and a small set of pre-defined answer choices, models are required to determine which of the candidate choices best answers the question. Existing commonsense reasoning models usually work by scoring a question-candidate pair (Lin et al., 2019; Lv et al., 2020; Feng et al., 2020). Hence, even an accurate multiple-choice  The work was mainly done during Bill Yuchen Lin's internship at Google Research. 1 Our code and data are available at the project website  https://open-csr.github.io/ . QA model cannot be directly applied in practical applications where answer candidates are not provided (e.g., answering a question asked on a search engine, or during conversation with a chat-bot). Because we seek to advance commonsense reasoning towards practical applications, we propose to study open-ended commonsense reasoning (OpenCSR), where answers are generated efficiently, rather than selected from a small list of candidates (see Figure 1). As a step toward this, here we explore a setting where the model produces a ranked list of answers from a large question-independent set of candidate concepts that are extracted offline from a corpus of common-sense facts written in natural language. The OpenCSR task is inherently challenging. One problem is that for many questions, find-ing an answer requires reasoning over two or more natural-language facts from a corpus. In the multiple-choice QA setting, as the set of candidates is small, we can pair a question with an answer, and use the combination to retrieve relevant facts and then reason with them. In the open-ended setting, this is impractical: instead one needs to retrieve facts from the corpus using the question alone. In this respect, OpenCSR is similar to multi-hop factoid QA about named entities, e.g. as done for HotpotQA (Yang et al., 2018). However, the underlying reasoning chains of most multi-hop factoid QA datasets are relatively clear and context-independent , and are thus easier to infer. Commonsense questions, in contrast, exhibit more variable types of reasoning, and the relationship between a question and the reasoning to answer the question is often unclear. (For example, a factoid question like  who starred in a movie directed by Bradley Cooper?  clearly suggests following a directed-by relationship and then a starred-in relationship, while the underlying reasoning chains of a question like what can help alleviate global warming? is relatively implicit from the question.) Furthermore, annotations are not available to identify which facts are needed in the latent reasoning chains that lead to an answer  the only supervision is a set of questions and their answers. We discuss the formulation of OpenCSR and its challenges further in Section 3. As shown in Fig. 1, another challenge is that many commonsense questions require reasoning about facts that link several concepts together. E.g., the fact trees remove carbon dioxide from the atmosphere through photosynthesis cannot be easily decomposed into pairwise relationships between trees, carbon dioxide, the atmosphere, and photosynthesis, which makes it more difficult to store in a knowledge graph (KG). However, such facts have been collected as sentences in common-sense corpora, e.g., GenericsKB (Bhakthavatsalam et al., 2020). This motivates the question: how can we conduct multi-hop reasoning over such a knowledge corpus, similar to the way multi-hop reasoning methods traverse a KG? Moreover, can we achieve this in a differentiable way, to support end-to-end learning? To address this question, we extend work by Seo et al. (2019) and Dhingra et al. (2020), and propose an efficient, differentiable multi-hop reasoning method for OpenCSR, named DRFACT (for Differentiable Reasoning over Facts). Specifically, we formulate multi-hop reasoning over a corpus as an iterative process of differentiable fact-following operations over a hypergraph. We first encode all fact sentences within the corpus as dense vectors to form a neural fact index, such that a fast retrieval can be done via maximum inner product search (MIPS). This dense representation is supplemented by a sparse fact-to-fact matrix to store symbolic links between facts (i.e., a pair of facts are linked if they share common concepts). DRFACT thus merges both neural and symbolic aspects of the relationships between facts to model reasoning in an end-to-end differentiable framework (Section 4). To evaluate OpenCSR methods, we construct new OpenCSR datasets by adapting three existing multiple-choice QA datasets: QASC (Khot et al., 2020), OBQA (Mihaylov et al., 2018), and ARC (Clark et al., 2018). Note that unlike factoid questions that usually have a single correct answer, open-ended commonsense questions can have multiple correct answers. Thus, we collect a collection of new answers for each test question by crowd-sourcing human annotations. We compare with several strong baseline methods and show that our proposed DRFACT outperforms them by a large margin. Overall DRFACT gives an 4.6% absolute improvement in Hit@100 accuracy over DPR (Karpukhin et al., 2020), a state-of-the-art text retriever for QA, and 3.2% over DrKIT (Dhin-gra et al., 2020), a strong baseline for entity-centric multi-hop reasoning. With a relatively more expensive re-ranking module, the gap between DRFACT and others is even larger. (Sec. 5) 2 Related Work Commonsense Reasoning. Many recent commonsense-reasoning (CSR) methods focus on multiple-choice QA. For example, KagNet (Lin et al., 2019) and MHGRN (Feng et al., 2020) use an external commonsense knowledge graph as structural priors to individually score each choice. These methods, though powerful in determining the best choice for a multi-choice question, are less realistic for practical applications where answer candidates are typically not available. UnifiedQA (Khashabi et al., 2020) and other closed-book QA models (Roberts et al., 2020) generate answers to questions by fine-tuning a text-to-text transformer such as BART (Lewis et al., 2020a) or T5 (Raffel et al., 2020), but a disadvantage of closed-book QA models is that they do not provide intermediate explanations for their answers, i.e., the supporting facts, which makes them less trustworthy in downstream applications. Although closed-book models exist that are augmented with an additional retrieval module (Lewis et al., 2020b), these models mainly work for single-hop reasoning. QA over KGs or Text. A conventional source of commonsense knowledge is triple-based symbolic commonsense knowledge graphs (CSKGs) such as ConceptNet (Speer et al., 2017). However, the binary relations in CSKGs greatly limit the types of the knowledge that can be encoded. Here, instead of a KB, we use a corpus of generic sentences about commonsense facts, in particular GenericsKB (Bhakthavatsalam et al., 2020). The advantage of this approach is that text can represent more complex commonsense knowledge, including facts that relate three or more concepts. Formalized in this way, OpenCSR is a question answering task requiring (possibly) iterative retrieval, similar to other open-domain QA tasks (Chen et al., 2017) such as HotpotQA (Yang et al., 2018) and Natural Questions (Kwiatkowski et al., 2019). As noted above, however, the surface of commonsense questions in OpenCSR have fewer hints about kinds of multi-hop reasoning required to answer them than the factoid questions in open-domain QA, resulting in a particularly challenging reasoning problem (see Sec. 3). Multi-Hop Reasoning. Many recent models for open-domain QA tackle multi-hop reasoning through iterative retrieval, e.g., GRAFT-Net (Sun et al., 2018), MUPPET (Feldman and El-Yaniv, 2019), PullNet (Sun et al., 2019), and GoldEn (Qi et al., 2019). These models, however, are not end-to-end differentiable and thus tend to have slower inference speed, which is a limitation shared by many other works using reading comprehension for multi-step QA (Das et al., 2019; Lee et al., 2019). As another approach, Neural Query Language (Cohen et al., 2020) designs differentiable multi-hop entity-following templates for reasoning over a compactly stored symbolic KG, but this KG is limited to binary relations between entities from an explicitly enumerated set. DrKIT (Dhingra et al., 2020) is the most similar work to our DRFACT , as it also supports multi-hop reasoning over a corpus. Unlike DRFACT , DrKIT is designed for entity-centric reasoning. DrKIT begins with an entity-linked corpus, and computes both sparse and dense indices of entity mentions (i.e., linked named-entity spans). DrKIT's fundamental reasoning operation is to hop from one weighted set of X entities to another, by 1) find-ing mentions of new entities x (cid:48) that are related to some entity in X , guided by the indices, and then 2) aggregating these mentions to produce a new weighted set of entities. DrKIT's operations are differentiable, and by learning to construct appropriate queries to the indices, it can be trained to answer multi-hop entity-related questions. Prior to our work DrKIT been applied only on factoid questions about named entities. In CSR, the concepts that drive reasoning are generally less precise than entities, harder to disambiguate in context, and are also much more densely connected, so it is unclear to what extent DrKIT would be effective. We present here novel results using DrKIT on OpenCSR tasks, and show experimentally that our new approach, DRFACT , improves over DrKIT. DRFACT mainly differs from DrKIT in that its reasoning process learns to hop from one fact to another, rather than from one entity to another, thus effectively using the full information from a fact for multi-hop reasoning. Task Formulation. We denote a corpus of knowledge facts as F , and use V to denote a vocabulary of concepts ; both are sets consisting of unique elements. A fact f i  F is a sentence that describes generic commonsense knowledge, such as  trees remove carbon dioxide from the atmosphere through photosynthesis . A concept c j  V is a noun or base noun phrase mentioned frequently in these facts (e.g., tree' and carbon dioxide'). Concepts are considered identical if their surface forms are the same (after lemma-tization). Given only a question q (e.g.,  what can help alleviate global warming? ), an open-ended commonsense reasoner is supposed to answer it by returning a weighted set of concepts, such as { ( a 1 = renewable energy' , w 1 ), ( a 2 = tree' , w 2 ), . . . } , where w i  R is the weight of the predicted concept a i  V . To learn interpretable, trustworthy reasoning models, it is expected that models can output intermediate results that justify the reasoning process  i.e., the supporting facts from F . E.g., an explanation for tree' to be an answer to the ques= carbon dioxide is the major greenhouse gas contributing to global warming . Implicit Multi-Hop Structures. Commonsense questions (i.e., questions that need commonsense knowledge to reason) contrast with better-studied multi-hop factoid QA datasets, e.g., HotpotQA (Yang et al., 2018), which primarily focus on querying about evident relations between named entities . For example, an example multihop factoid question can be which team does the player named 2015 Diamond Head Classic's MVP play for? Its query structure is relatively clear and self-evident from the question itself: in this case the reasoning process can be decomposed into q 1 = the player named 2015 DHC's MVP and q 2 = which team does q 1 . answer play for. The reasoning required to answer commonsense questions is usually more implicit and relatively unclear. Consider the previous example in Fig. 1, q = what can help alleviate global warm-ing?' can be decomposed by q 1 = what contributes to global warming and q 2 = what removes q 1 . answer from the atmosphere  but many other decompositions are also plausible. In addition, unlike HotpotQA, we assume that we have no ground-truth justifications for training, which makes OpenCSR even more challenging. In this section we present DRFACT , a model for multi-hop reasoning over facts. More implementation details are in Appendix B. 4.1 Overview In DRFACT , we propose to model reasoning as traversing a hypergraph , where each hyperedge corresponds to a fact in F , and connects the concepts in V that are mentioned in that fact. This is shown in Figure 2. Notice that a fact, as a hyperedge, connects multiple concepts that are mentioned, while the textual form of the fact maintains the contextual information of the original natural language statement, and hence we do not assume a fixed set of relations. Given such a hypergraph, our open-ended reasoning model will traverse the hypergraph starting from the question (concepts) and finally arrive at a set of concept nodes by following multiple hyperedges (facts). A probabilistic view of this process over T hops is: P ( c | q ) = P ( c | q, FT ) (cid:81) Tt =1 P ( F t | q, F t  1 ) P ( F 0 | q ) Intuitively, we want to model the distribution of a concept c  V being an answer to a question q as P ( c | q ) . This answering process can be seen as a process of multiple iterations of fact-following, or moving from one fact to another based on shared concepts, and finally moving from facts to concepts. We use F t to represent a weighted set of retrieved facts at the hop t , and F 0 for the initial facts below. Then, given the question and the current retrieved facts, we iteratively retrieve the facts for the next hop. Finally, we score a concept using retrieved facts. We encode the hypergraph (Fig. 2) with a concept-to-fact sparse matrix E and a fact-to-fact sparse matrix S . The dense fact index D is pre-computed with a pre-trained bi-encoder. A weighed set of facts is represented as a sparse vector F . The workflow (left) of DRFACT starts mapping a question to a set of initial facts that have common concepts with it. Then, it recursively performs Fact-Follow operations (right) for computing F t and A t . Finally, it uses learnable hop-weights  t to aggregate the answers. 2019), which learns to maximize the score of facts that contain correct answers to a given question, following the steps of Karpukhin et al. (2020) (i.e., dense passage retrieval), so that we can use MIPS to do dense retrieval over the facts. After pre-training, we embed each fact in F with a dense vector (using the [CLS] token representa-tion). Hence D is a |F|  d dense matrix. Sparse Fact-to-Fact Index S . We pre-compute the sparse links between facts by a set of connection rules, such as f i  f j when f i and f j have at least one common concept and f j introduces at least two more new concepts that are not in f i (see Appendix B (2) for more). Hence S is a binary sparse tensor with the dense shape |F|  |F| . Sparse Index of Concept-to-Fact Links E . As shown in Figure 2, a concept can appear in multiple facts and a fact also usually mentions multiple concepts. We encode these co-occurrences between each fact and its mentioned concepts into a sparse matrix with the dense shape |V|  |F|  i.e., the concept-to-fact index . The most important part in our framework is how to model the fact-following step in our formulation, i.e., P ( F t | F t  1 , q ) . For modeling the translation from a fact to another fact under the context of a question q , we propose an efficient approach with a differentiable operation that uses both neural embeddings of the facts and their symbolic connections in the hypergraph. S , which in our model is efficiently implemented with the tf.RaggedTensor construct of TensorFlow (Dhingra et al., 2020). S stores a precomputed dependency between pairs of facts, S ij . Intuitively, if we can traverse from f i to f j these facts should mention some common concepts, and also the facts' semantics are related, so our S ij will reflect this intuition. The fact embeddings computed by a pre-trained bi-encoder are in the dense index of fact vectors D , which contains rich semantic information about each fact, and helps measure the plausibility of a fact in the context of a given question. The proposed fact-follow operation has two parallel sub-steps: 1) sparse retrieval and 2) dense retrieval. The sparse retrieval uses a fact-to-fact sparse matrix to obtain possible next-hop facts. We can compute F st = F t  1 S efficiently thanks to the ragged representation of sparse matrices. For the neural dense retrieval, we use a maximum inner product search (MIPS) (Johnson et al., 2019; Guo et al., 2020) over the dense fact embedding index D : z t  1 = F t  1 D h t  1 = g ( z t  1 , q t ) F dt = MIPSK ( h t  1 , D ) We first aggregate the dense vectors of the facts in F t  1 into the dense vector z t  1 , which is fed into a neural layer with the query embedding at the current step, q t (encoded by BERT), to create a query vector h t  1 . Here g (  ) is an MLP that maps the concatenation of the two input vectors to a dense output with the same dimensionality as the fact vectors, which we named to be fact-translating function. Finally, we retrieve the next-hop top-K facts F dt with the MIPSK operator. To get the best of both symbolic and neural world, we use element-wise multiplication to combine the sparse and dense retrieved results: F t = F st (cid:12) F dt . We summarize the fact-following operation with these differentiable steps: F t = Fact-Follow( F t  1 , q ) (1) = F t  1 S (cid:12) MIPSK ( g ( F t  1 D, q t ) , D ) After each hop, we multiply F t with a precomputed fact-to-concept matrix E , thus generating A t , a set of concept predictions. To aggregate the concept scores, we take the maximum score among the facts that mention a concept c . Finally we take the weighted sum of the concept predictions at all hops as the final weighted concept sets A = (cid:80) Tt =1  t A t , where  t is a learnable parameter. Please read Appendix B for more details. Equation 1 defines a random-walk process on the hypergraph associated with the corpus. We found that performance was improved by making this a lazy random walkin particular by augmenting F t with the facts in F t  1 which have a weight higher than a threshold  : F t = Fact-Follow( F t  1 , q ) + Filter( F t  1 ,  ) . We call this as self-following , which means that F t contains highly-relevant facts for all distances t (cid:48) < t , and thus improve models when there are variable numbers of hops for different questions. Initial Facts. Note that the set of initial facts F 0 is computed differently, as they are produced using the input question q , instead of a previous-hop F t  1 . We first use our pre-trained bi-encoder and the associated index D via MIPS query to finds facts related to q , and then select from the retrieved set those facts that contain question concepts (i.e., concepts that are matched in the question text), using the concept-to-fact index E . Intermediate evidence, i.e., supporting facts, is significant for guiding multi-hop reasoning models during training. In a weakly supervised setting, however, we usually do not have ground-truth annotations as they are expensive to obtain. based on the training questions. Specifically, we concatenate the question and the best candidate answer to build a query to our pre-trained index D , and then we divide the results into four groups depending on whether they contain question/answer concepts: 1) question-answer facts, 2) question-only facts, 3) answer-only facts, and 4) none-facts. Then, to get a 2-hop evidence chain, we first check if a question-only fact can be linked to an answer-only fact through the sparse fact-to-fact matrix S . Similarly, we can also get 3-hop distant evidence. In this manner, we can collect the set of supporting facts at each hop position, denoted as { F  1 , F  2 , . . . , F  T } . The final learning objective is thus to optimize the sum of the cross-entropy loss l between the final weighed set of concepts A and the answer set A  , as well as the auxiliary loss from distant evidence  i.e., the mean of the hop-wise loss between the predicted facts F t and the distant supporting facts at that hop F  t , defined as follows: L = l ( A, A  ) + 1 TT (cid:88) t =1 l ( F t , F  t ) 5 Experiments 5.1 Experimental Setup Fact corpus and concept vocabulary We use the GenericsKB-Best corpus as the main knowledge source 2 . In total, we have 1,025,413 unique facts as our F . We use the spaCy toolkit to prepossess all sentences in the corpus and then extract frequent noun chunks within them as our concepts. The vocabulary V has 80,524 concepts, and every concept is mentioned at least 3 times. To facilitate the research on open-ended commonsense reasoning (OpenCSR), we reformatted three existing multi-choice question answering datasets to allow evaluating OpenCSR methods. We choose three datasets: QASC, OBQA, and ARC, as their questions require commonsense knowledge about science and everyday objects and are presented in natural language. By applying a set of filters and rephrasing rules, we selected those open-ended commonsense questions that query concepts in our vocabulary V . As we know that there can be multiple correct answers for a question in OpenCSR, we employed crowd-workers to collect more answers for each test question based on a carefully designed annotation protocol. In total, we collect 15,691 answers for 2,138 rephrased questions for evaluation, which results in 7.5 answers per question on average. Please find more details about crowd-sourcing and analysis in Appendix A. We show some statistics of the OpenCSR datasets and our new annotations in Table 1. To understand the multi-hop nature and the difficulty of each dataset, we use a heuristic to estimate the percentage of single-hop questions, for which we can find a fact (from top-1k facts retrieved by BM25) containing both a question concept and an answer concept. The ARC dataset has about 67% one-hop questions and thus is the easiest, while OBQA has only 50%. Recall that, given a question q , the final output of every method is a weighted set of concepts A = { ( a 1 , w 1 ) , . . . } . We denote the set of true answer concepts , as defined above, as A  = { a  1 , a  2 , . . . } . We define Hit@K accuracy to be the fraction of questions for which we can find at least one correct answer concept a  i  A  in the topK concepts of A (sorted in descending order of weight). As questions have multiple correct answers, recall is also an important aspect for evaluating OpenCSR, so we also use Rec@K to evaluate the average recall of the top-K proposed answers. We present baseline methods and an optional reranker component for boosting the performance on OpenCSR. Table 3 shows a summary of the comparisions of the three methods and our DrFact. retrieve relevant facts, and then use the concepts mentioned in the top-ranked facts as answer predictions. BM25 is one of the most popular unsupervised method for retrieval, while the Dense Passage Retrieval (DPR) model is a state-of-the-art trainable, neural retriever (Karpukhin et al., 2020). Following prior work with DPR, we used BM25-retrieved facts to create positive and (hard-)negative examples as supervision. For both methods, we score a concept by the max 3 of the relevance scores of retrieved facts that mention it. DrKIT. Following Dhingra et al. (2020), we use DrKIT for OpenCSR, treating concepts as entities. DrKIT is also an efficient multi-hop reasoning model that reasons over a pre-computed indexed corpus, which, as noted above (Sec. 2), differs from our work in that DrKIT traverses a graph of entities and entity mentions, while DRFACT traverses a hypergraph of facts. Multiple-choice style re-ranking (MCQA). A conventional approach to multiple-choice QA (MCQA) is to fine-tune a pre-trained language model such as BERT, by combining a question and a particular concept as a single input sequence in the form of  [CLS] question [SEP] choice and using [CLS] vectors for learning to score choices. We follow this schema and train 4 such a multiple-choice QA model on top of BERT-Large, and use this to re-rank the topK concept predictions. Main results. For a comprehensive understanding, we report the Hit@K and Rec@K of all methods, at K=50 and K=100, in Table 2. The overall results are the average over the three datasets. 3 We also tried mean and sum , but max performs the best. 4 Specifically, we fine-tune BERT-Large to score truth answers over 9 sampled distractors, and use it to rank the top-500 concepts produced by each above retrieval method. We can see that DRFACT outperforms all baseline methods for all datasets and metrics. Comparing with the state-of-the-art text retriever DPR, DRFACT improves by about 4.1% absolute points in Hit@50 accuracy overall. With the expensive yet powerful MCQA reranker module DRFACT gives an even large gap (  8% gain in H@50 acc). The performance gains on the QASC and OBQA datasets are larger than the one on ARC. This observation correlates the statistics that the former two have more multi-hop questions and thus DRFACT has more advantages. As shown in Figure 4, we can see that DRFACT consistently outperforms other retrieval methods at different K by a considerable margin. Interestingly, we find that with the MCQA reranker, DrKIT does not yield a large improvement over DPR, and it usually has a lower than other methods. We conjecture this is because that entity-centric reasoning schema produces too many possible concepts and thus is more likely to take more irrelevant concepts at the top positions. The results on Rec@K in bottom section of Table 2 show that even our DRFACT +MCQA model only recalls about 50% of the correct answers in top-100 results on average. This suggests that OpenCSR is still a very challenging problem and 10 20 30 40 50 60 70 80 90 100 K 0.3 0.4 0.5 0.6 0.7 0.8 0.9 H i t @ KA cc u r a c y ( % ) BM25 DPR DrKIT DrFact BM25+MCQA DPR+MCQA DrKIT+MCQA DrFact+MCQA Figure 4: The curve of Hit@K accuracy in overall . Run-time efficiency analysis. We use Table 4 to summarize the online inference speed of each OpenCSR method. At inference time, DPR will make one call to BERT-base for encoding a question and do one MIPS search. Similarly, DrKIT and DRFACT with T hops will make one call to BERT-base for query encoding and do TMIPS searches. However, since the entity-to-mention Methods Major Computations Speed (sec/q) BM25 Sparse Retrieval 0.14 DPR BERT-base + MIPS 0.08 DrKIT BERT-base + T *(MIPS+ sp e 2 m ) 0.47 DRFACT BERT-base + T *(MIPS+ sp f 2 f ) 0.23 X+ MCQA X + K * BERT-Large + 14.12 Table 4: The major competitions of each method and their online (batch-size=1) inference speed in sec/q . matrix ( sp e 2 m ) of DrKIT is much larger than the fact-to-fact matrix ( sp f 2 f ) of DRFACT , DrKIT is about twice as slow as DRFACT . The MCQA is much more computationally expensive, as it makes K calls to BERT-Large for each combination of question and choice. Note that in these experiments we use T =2 for DrKIT, T =3 for DRFACT and K =500 for the MCQA re-rankers. 5 Ablation study. Varying the maximum hops (T= { 1,2,3 } )  i.e., the number of calls to Fact-Follow  indicates that overall performance is the best when T=3 as shown in Table 5. The performance with T=2 drops 0.7% point on OBQA. We conjecture this is due to nature of the datasets, in particular the percentage of hard questions. We also test the model (with T=3) without the auxiliary learning loss (Sec. 4.4) or the self-following trick. Both are seen to be important to DRFACT . Self-following is especially helpful for QASC and OBQA, where there are more multihop questions. It also makes learning and inference more faster than an alternative approach of ensembling multiple models with different maximum hops as done in some prior works. Qualitative analysis. We show a concrete example in Fig. 5 to compare the behaviour of DPR and DRFACT in reasoning. DPR uses purely dense retrieval without any regularization, yielding irrelevant facts. The fact f 2 matches the phrase sepa-5 We note the MCQA-reranker could be speed up by scoring more choices in parallel. All run-time tests were performed on NVIDIA V100 (16GB), but MCQA with batch-size of 1 requires only  5GB. This suggests more parallel inference on a V100 could obtain 4.5 sec/q for MCQA. Q: What will separate iron filings from sand?  magnets attract magnetic metals through magnetism (in F2) iron filings show the magnetic fields . rating...from sand, but does not help reason about the question. The f 3 shows here for the semantic relatedness of steel and iron while fill-ing here is not related to question concepts. Our DRFACT , however, can faithfully reason about the question via fact-following over the hypergraph, and use neural fact embeddings to cumulatively reason about a concept, e.g., magnet . By backtracking with our hypergraph, we can use retrieved facts as explanations for a particular prediction. We introduce and study a new task  open-ended commonsense reasoning (OpenCSR)  which is both realistic and challenging. We construct three OpenCSR versions of widely used datasets targeting commonsense reasoning with a novel crowdsourced collection of multiple answers, and evaluate a number of baseline methods for this task. We also present a novel method, DRFACT . DRFACT is a scalable multi-hop reasoning method that traverses a corpus (as a hypergraph) via a differentiable fact-following reasoning process, employing both a neural dense index of facts and sparse tensors of symbolic links between facts, using a combination of MIPS and sparse-matrix computation. DRFACT outperforms several strong baseline methods on our data, making a significant step towards adapting commonsense reasoning approaches to more practical applications. Base on the multi-hop reasoning framework of DRFACT , we hope the work can benefit future research on neural-symbolic commonsense reasoning. Xiang Ren is supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via Contract No. 2019-19051600007, the DARPA MCS program under Contract No. N660011924033 with the United States Office Of Naval Research, the Defense Advanced Research Projects Agency with award W911NF-19-20271, and NSF SMA 18-29268. We thank all reviewers for their constructive feedback and comments. Crowd-workers. This work presents three datasets for addressing a new problem, open common-sense reasoning. The datasets are all derived from existing multiple-choice CSR datasets, and were produced by filtering questions and using crowd-workers to annotate common-sense questions by suggesting additional answers. Most of the questions are about elementary science and common knowledge about our physical world. None of the questions involve sensitive personal opinions or involve personally identifiable information. We study posted tasks to be completed by crowd-workers instead of crowd-workers themselves, and we do not retrieve any identifiable private information about a human subject. Data bias. Like most crowdsourced data, and in particular most common-sense data, these crowdsourced answers are inherently subject to bias: for example, a question like what do people usually do at work might be answered very differently by people from different backgrounds and cultures. The prior multiple-choice CSR datasets which our datasets are built on are arguably more strongly biased culturally, as they include a single correct answer and a small number of distractor answers, while our new datasets include many answers considered correct by several annotators. However, this potential bias (or reduction in bias) has not been systematically measured in this work. Sustainability. For most of the experiments, we use the virtual compute engines on Google Cloud Platform, which is committed to purchasing enough renewable energy to match consumption for all of their operations globally. 6 With such virtual machine instances, we are able to use the resources only when we have jobs to run, instead of holding them all the time like using physical machines, thus avoiding unnecessary waste. Application. The work also evaluates a few proposed baselines for OpenCSR, and introduced a new model which outperforms them. This raises the question of whether harm might arise from applications of OpenCSRor more generally, since 6 https://cloud.google.com/ sustainability OpenCSR is intended as a step toward making multiple-choice CSR more applicable, whether harm might arise more generally from CSR methods. Among the risks that need to be considered in any deployment of NLP technology are that responses may be wrong, or biased, in ways that would lead to improperly justified decisions. Although in our view the current technology is still relatively immature, and unlikely to be fielded in applications that would cause harm of this sort, it is desirable that CSR methods provide audit trails, and recourse so that their predictions can be explained to and critiqued by affected parties. Our focus on methods that provide chains of evidence is largely a reflection of this perceived need.
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