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Why do models often attend to salient words, and how does this evolve throughout training? We approximate model training as a two stage process: early on in training when the attention weights are uniform, the model learns to translate individual input word i to o if they cooccur frequently. Later, the model learns to attend to i while the correct output is o because it knows i translates to o. To formalize, we define a model property, Knowledge to Translate Individual Words (KTIW) (e.g. knowing that i translates to o), and claim that it drives the learning of the attention. This claim is supported by the fact that before the attention mechanism is learned, KTIW can be learned from word co-occurrence statistics, but not the other way around. Particularly, we can construct a training distribution that makes KTIW hard to learn, the learning of the attention fails, and the model cannot even learn the simple task of copying the input words to the output. Our approximation explains why models sometimes attend to salient words, and inspires a toy example where a multi-head attention model can overcome the above hard training distribution by improving learning dynamics rather than expressiveness.

We introduce APEL, a new framework that enables non-programmers to indirectly annotate natural language utterances with executable meaning representations, such as SQL programs. Based on a natural language utterance, we first run a seed semantic parser to generate a prior over a list of candidate programs. To obtain information about which candidate is correct, we synthesize an input on which the more likely programs tend to produce different outputs, and ask an annotator which output is appropriate for the utterance. Hence, the annotator does not have to directly inspect the programs. To further reduce effort required from annotators, we aim to synthesize simple input databases that nonetheless have high information gain. With human annotators and Bayesian inference to handle annotation errors, we outperform Codex's top-1 performance (59%) and achieve the same accuracy as the original expert annotators (75%), by soliciting answers for each utterance on only 2 databases with an average of 9 records each. In contrast, it would be impractical to solicit outputs on the original 30K-record databases provided by SPIDER.

How do two distributions of text differ? Humans are slow at answering this, since discovering patterns might require tediously reading through hundreds of samples. We propose to automatically summarize the differences by "learning a natural language hypothesis": given two distributions D 0 and D 1 , we search for a description that is more often true for D 1 , e.g., "is military-related." To tackle this problem, we fine-tune GPT-3 to propose descriptions with the prompt: "[samples of D 0 ] + [samples of D 1 ] + the difference between them is ". We then re-rank the descriptions by checking how often they hold on a larger set of samples with a learned verifier. On a benchmark of 54 real-world binary classification tasks, while GPT-3 Curie (13B) only generates a description similar to human annotation 7% of the time, the performance reaches 61% with fine-tuning and reranking, and our best system using GPT-3 Davinci (175B) reaches 76%. We apply our system to describe distribution shifts, debug dataset shortcuts, summarize unknown tasks, and label text clusters, and present analyses based on automatically generated descriptions. 1