In multi-dimensional classification (MDC), there are multiple class variables in the output space with each of them corresponding to one heterogeneous class space. Due to the heterogeneity of class spaces, it is quite challenging to consider the dependencies among class variables when learning from MDC examples. In this paper, we propose a novel MDC approach named SLEM which learns the predictive model in an encoded label space instead of the original heterogeneous one. Specifically, SLEM works in an encoding-training-decoding framework. In the encoding phase, each class vector is mapped into a real-valued one via three cascaded operations including pairwise grouping, one-hot conversion and sparse linear encoding. In the training phase, a multi-output regression model is learned within the encoded label space. In the decoding phase, the predicted class vector is obtained by adapting orthogonal matching pursuit over outputs of the learned multi-output regression model. Experimental results clearly validate the superiority of SLEM against state-of-the-art MDC approaches.

A key problem in program synthesis is searching over the large space of possible programs. Human programmers might decide the high-level structure of the desired program before thinking about the details; motivated by this intuition, we consider two-level search for program synthesis, in which the synthesizer first generates a plan, a sequence of symbols that describes the desired program at a high level, before generating the program. We propose to learn representations of programs that can act as plans to organize such a two-level search. Discrete latent codes are appealing for this purpose, and can be learned by applying recent work on discrete autoencoders. Based on these insights, we introduce the Latent Programmer (LP), a program synthesis method that first predicts a discrete latent code from input/output examples, and then generates the program in the target language. We evaluate the LP on two domains, demonstrating that it yields an improvement in accuracy, especially on longer programs for which search is most difficult.

Answering complex natural language questions on knowledge graphs (KGQA) is a challenging task. It requires reasoning with the input natural language questions as well as a massive, incomplete heterogeneous KG. Prior methods obtain an abstract structured query graph/tree from the input question and traverse the KG for answers following the query tree. However, they inherently cannot deal with missing links in the KG. Here we present LEGO, a Latent Execution-Guided reasOning framework to handle this challenge in KGQA. LEGO works in an iterative way, which alternates between (1) a Query Synthesizer, which synthesizes a reasoning action and grows the query tree step-by-step, and (2) a Latent Space Executor that executes the reasoning action in the latent embedding space to combat against the missing information in KG. To learn the synthesizer without step-wise supervision, we design a generic latent execution guided bottom-up search procedure to find good execution traces efficiently in the vast query space. Experimental results on several KGQA benchmarks demonstrate the effectiveness of our framework compared with previous state of the art.

Spreadsheet formula prediction has been an important program synthesis problem with many real-world applications. Previous works typically utilize input-output examples as the specification for spreadsheet formula synthesis, where each input-output pair simulates a separate row in the spreadsheet. However, this formulation does not fully capture the rich context in real-world spreadsheets. First, spreadsheet data entries are organized as tables, thus rows and columns are not necessarily independent from each other. In addition, many spreadsheet tables include headers, which provide high-level descriptions of the cell data. However, previous synthesis approaches do not consider headers as part of the specification. In this work, we present the first approach for synthesizing spreadsheet formulas from tabular context, which includes both headers and semi-structured tabular data. In particular, we propose SpreadsheetCoder, a BERT-based model architecture to represent the tabular context in both row-based and column-based formats. We train our model on a large dataset of spreadsheets, and demonstrate that SpreadsheetCoder achieves top-1 prediction accuracy of 42.51%, which is a considerable improvement over baselines that do not employ rich tabular context. Compared to the rule-based system, SpreadsheetCoder assists 82% more users in composing formulas on Google Sheets.