Recently, deep learning models have made great progress in MWP solving on answer accuracy. However, they are uninterpretable since they mainly rely on shallow heuristics to achieve high performance without understanding and reasoning the grounded math logic. To address this issue and make a step towards interpretable MWP solving, we first construct a high-quality MWP dataset named InterMWP which consists of 11,495 MWPs and annotates interpretable logical formulas based on algebraic knowledge as the grounded linguistic logic of each solution equation. Different from existing MWP datasets, our InterMWP benchmark asks for a solver to not only output the solution expressions but also predict the corresponding logical formulas. We further propose a novel approach with logical prompt and interpretation generation, called LogicSolver. For each MWP, our LogicSolver first retrieves some highly-correlated algebraic knowledge and then passes them to the backbone model as prompts to improve the semantic representations of MWPs. With these improved semantic representations, our LogicSolver generates corresponding solution expressions and interpretable knowledge formulas in accord with the generated solution expressions, simultaneously. Experimental results show that our LogicSolver has stronger logical formula-based interpretability than baselines while achieving higher answer accuracy with the help of logical prompts, simultaneously.
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The goal of inductive logic programming (ILP) is to search for a hypothesis that generalises training examples and background knowledge (BK). To improve performance, we introduce an approach that, before searching for a hypothesis, first discovers where not to search. We use given BK to discover constraints on hypotheses, such as that a number cannot be both even and odd. We use the constraints to bootstrap a constraint-driven ILP system. Our experiments on multiple domains (including program synthesis and game playing) show that our approach can (i) substantially reduce learning times by up to 97%, and (ii) scale to domains with millions of facts.
Multi-hop Question Answering over Knowledge Graph~(KGQA) aims to find the answer entities that are multiple hops away from the topic entities mentioned in a natural language question on a large-scale Knowledge Graph (KG). To cope with the vast search space, existing work usually adopts a two-stage approach: it firstly retrieves a relatively small subgraph related to the question and then performs the reasoning on the subgraph to accurately find the answer entities. Although these two stages are highly related, previous work employs very different technical solutions for developing the retrieval and reasoning models, neglecting their relatedness in task essence. In this paper, we propose UniKGQA, a novel approach for multi-hop KGQA task, by unifying retrieval and reasoning in both model architecture and parameter learning. For model architecture, UniKGQA consists of a semantic matching module based on a pre-trained language model~(PLM) for question-relation semantic matching, and a matching information propagation module to propagate the matching information along the edges on KGs. For parameter learning, we design a shared pre-training task based on question-relation matching for both retrieval and reasoning models, and then propose retrieval- and reasoning-oriented fine-tuning strategies. Compared with previous studies, our approach is more unified, tightly relating the retrieval and reasoning stages. Extensive experiments on three benchmark datasets have demonstrated the effectiveness of our method on the multi-hop KGQA task. Our codes and data are publicly available at //github.com/RUCAIBox/UniKGQA.
Math word problem (MWP) solving is an important task in question answering which requires human-like reasoning ability. Analogical reasoning has long been used in mathematical education, as it enables students to apply common relational structures of mathematical situations to solve new problems. In this paper, we propose to build a novel MWP solver by leveraging analogical MWPs, which advance the solver's generalization ability across different kinds of MWPs. The key idea, named analogy identification, is to associate the analogical MWP pairs in a latent space, i.e., encoding an MWP close to another analogical MWP, while moving away from the non-analogical ones. Moreover, a solution discriminator is integrated into the MWP solver to enhance the association between the representations of MWPs and their true solutions. The evaluation results verify that our proposed analogical learning strategy promotes the performance of MWP-BERT on Math23k over the state-of-the-art model Generate2Rank, with 5 times fewer parameters in the encoder. We also find that our model has a stronger generalization ability in solving difficult MWPs due to the analogical learning from easy MWPs.
We apply classical statistical methods in conjunction with the state-of-the-art machine learning techniques to develop a hybrid interpretable model to analyse 454,897 online customers' behavior for a particular product category at the largest online retailer in China, that is JD. While most mere machine learning methods are plagued by the lack of interpretability in practice, our novel hybrid approach will address this practical issue by generating explainable output. This analysis involves identifying what features and characteristics have the most significant impact on customers' purchase behavior, thereby enabling us to predict future sales with a high level of accuracy, and identify the most impactful variables. Our results reveal that customers' product choice is insensitive to the promised delivery time, but this factor significantly impacts customers' order quantity. We also show that the effectiveness of various discounting methods depends on the specific product and the discount size. We identify product classes for which certain discounting approaches are more effective and provide recommendations on better use of different discounting tools. Customers' choice behavior across different product classes is mostly driven by price, and to a lesser extent, by customer demographics. The former finding asks for exercising care in deciding when and how much discount should be offered, whereas the latter identifies opportunities for personalized ads and targeted marketing. Further, to curb customers' batch ordering behavior and avoid the undesirable Bullwhip effect, JD should improve its logistics to ensure faster delivery of orders.
Current math word problem (MWP) solvers are usually Seq2Seq models trained by the (one-problem; one-solution) pairs, each of which is made of a problem description and a solution showing reasoning flow to get the correct answer. However, one MWP problem naturally has multiple solution equations. The training of an MWP solver with (one-problem; one-solution) pairs excludes other correct solutions, and thus limits the generalizability of the MWP solver. One feasible solution to this limitation is to augment multiple solutions to a given problem. However, it is difficult to collect diverse and accurate augment solutions through human efforts. In this paper, we design a new training framework for an MWP solver by introducing a solution buffer and a solution discriminator. The buffer includes solutions generated by an MWP solver to encourage the training data diversity. The discriminator controls the quality of buffered solutions to participate in training. Our framework is flexibly applicable to a wide setting of fully, semi-weakly and weakly supervised training for all Seq2Seq MWP solvers. We conduct extensive experiments on a benchmark dataset Math23k and a new dataset named Weak12k, and show that our framework improves the performance of various MWP solvers under different settings by generating correct and diverse solutions.
Data in Knowledge Graphs often represents part of the current state of the real world. Thus, to stay up-to-date the graph data needs to be updated frequently. To utilize information from Knowledge Graphs, many state-of-the-art machine learning approaches use embedding techniques. These techniques typically compute an embedding, i.e., vector representations of the nodes as input for the main machine learning algorithm. If a graph update occurs later on -- specifically when nodes are added or removed -- the training has to be done all over again. This is undesirable, because of the time it takes and also because downstream models which were trained with these embeddings have to be retrained if they change significantly. In this paper, we investigate embedding updates that do not require full retraining and evaluate them in combination with various embedding models on real dynamic Knowledge Graphs covering multiple use cases. We study approaches that place newly appearing nodes optimally according to local information, but notice that this does not work well. However, we find that if we continue the training of the old embedding, interleaved with epochs during which we only optimize for the added and removed parts, we obtain good results in terms of typical metrics used in link prediction. This performance is obtained much faster than with a complete retraining and hence makes it possible to maintain embeddings for dynamic Knowledge Graphs.
Neural network models usually suffer from the challenge of incorporating commonsense knowledge into the open-domain dialogue systems. In this paper, we propose a novel knowledge-aware dialogue generation model (called TransDG), which transfers question representation and knowledge matching abilities from knowledge base question answering (KBQA) task to facilitate the utterance understanding and factual knowledge selection for dialogue generation. In addition, we propose a response guiding attention and a multi-step decoding strategy to steer our model to focus on relevant features for response generation. Experiments on two benchmark datasets demonstrate that our model has robust superiority over compared methods in generating informative and fluent dialogues. Our code is available at //github.com/siat-nlp/TransDG.
The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.
Providing model-generated explanations in recommender systems is important to user experience. State-of-the-art recommendation algorithms -- especially the collaborative filtering (CF) based approaches with shallow or deep models -- usually work with various unstructured information sources for recommendation, such as textual reviews, visual images, and various implicit or explicit feedbacks. Though structured knowledge bases were considered in content-based approaches, they have been largely ignored recently due to the availability of vast amount of data and the learning power of many complex models. However, structured knowledge bases exhibit unique advantages in personalized recommendation systems. When the explicit knowledge about users and items is considered for recommendation, the system could provide highly customized recommendations based on users' historical behaviors and the knowledge is helpful for providing informed explanations regarding the recommended items. In this work, we propose to reason over knowledge base embeddings for explainable recommendation. Specifically, we propose a knowledge base representation learning framework to embed heterogeneous entities for recommendation, and based on the embedded knowledge base, a soft matching algorithm is proposed to generate personalized explanations for the recommended items. Experimental results on real-world e-commerce datasets verified the superior recommendation performance and the explainability power of our approach compared with state-of-the-art baselines.
State-of-the-art recommendation algorithms -- especially the collaborative filtering (CF) based approaches with shallow or deep models -- usually work with various unstructured information sources for recommendation, such as textual reviews, visual images, and various implicit or explicit feedbacks. Though structured knowledge bases were considered in content-based approaches, they have been largely neglected recently due to the availability of vast amount of data, and the learning power of many complex models. However, structured knowledge bases exhibit unique advantages in personalized recommendation systems. When the explicit knowledge about users and items is considered for recommendation, the system could provide highly customized recommendations based on users' historical behaviors. A great challenge for using knowledge bases for recommendation is how to integrated large-scale structured and unstructured data, while taking advantage of collaborative filtering for highly accurate performance. Recent achievements on knowledge base embedding sheds light on this problem, which makes it possible to learn user and item representations while preserving the structure of their relationship with external knowledge. In this work, we propose to reason over knowledge base embeddings for personalized recommendation. Specifically, we propose a knowledge base representation learning approach to embed heterogeneous entities for recommendation. Experimental results on real-world dataset verified the superior performance of our approach compared with state-of-the-art baselines.
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