Autoregressive Reasoning over Chains of Facts with Transformers (2020)

Abstract: This paper proposes an iterative inference algorithm for multi-hop explanation regeneration, that retrieves relevant factual evidence in the form of text snippets, given a natural language question and its answer. Combining multiple sources of evidence or facts for multi-hop reasoning becomes increasingly hard when the number of sources needed to make an inference grows. Our algorithm copes with this by decomposing the selection of facts from a corpus autoregressively, conditioning the next iteration on previously selected facts. This allows us to use a pairwise learning-to-rank loss. We validate our method on datasets of the TextGraphs 2019 and 2020 Shared Tasks for explanation regeneration. Existing work on this task either evaluates facts in isolation or artificially limits the possible chains of facts, thus limiting multi-hop inference. We demonstrate that our algorithm, when used with a pre-trained transformer model, outperforms the previous state-of-the-art in terms of precision, training time and inference efficiency.

## introduction the task of multi-hop explanation generation has recently received interest as it could be a stepping-stone towards general multi-hop inference over language. multi-hop reasoning requires algorithms to combine multiple sources of evidence. this becomes increasingly hard when the number of required facts for an inference grows, because of the exploding number of combinations and phenomena such as semantic drift @xcite . the worldtree dataset was designed specifically for (>2)-fact inference @xcite : it consists of elementary science exam questions that can be explained by an average of 6 facts from a complementary dataset of textual facts. the explanation regeneration task as in the textgraphs shared tasks @xcite asks participants to retrieve and rank relevant facts (given one of these natural language questions and its answer as input 1 ) such that the top-ranked facts explain the answer to the question. an example is shown in the upper left part of fig. 1 (and more in appendix a). as each question-answer pair potentially has many supporting facts, evaluating all combinations of facts is computationally prohibitive. previous work remedies this by computing scores for facts in isolation, or by severely limiting the number of combinations of facts @xcite @xcite . the latter is done by considering combinations of few facts only and/or by reranking combinations of only the top retrieved facts by a simpler method. both approaches limit multi-hop reasoning as facts are not combined or too many facts are ignored by the simple first-stage retriever. in this paper we propose a method to retrieve facts that does build long chains of facts, while being efficient. during training, a pre-trained neural language model encodes the question-answer pair as well as a randomly selected combination of ground-truth facts, before evaluating candidate facts. for efficiency, only a set of neighborhood facts (which we call 'visible' facts) is considered. this set is obtained by selecting the nearest facts by tf-idf distance to the question, answer and set of ground truth facts. during inference, facts are ranked iteratively: in each iteration, the highest scoring fact is selected and encoded together with previously selected facts and the question-answer pair, so the next ranking is always conditioned on the current set of chosen facts. at each inference step, the set of visible facts consists of the nearest facts to the already selected facts and question-answer pair. this autoregressive formulation and the definition of neighborhoods together enable the use of losses that incorporate interactions between different facts, like the pairwise ranknet loss from the learning-to-rank literature @xcite . most methods in earlier work use some form of rank-rerank set-up, but none dynamically expand the set of reranked facts, and the reranked set is usually too small @xcite @xcite . @xcite and @xcite use iterative schemes, but the former only reconsiders the top 15 initially retrieved facts and the latter uses a term frequency based approach. @xcite consider chains of facts during training and inference, but only up to length 2, because of the explosive number of combinations. all of the above systems use pointwise losses only. while components of our method are inspired by previous work, we are the first to put them together in a principled way, so that they enable each other. our neighborhoods enable both our iterative inference procedure to efficiently build chains of up to 10 facts, and the use of more informative losses. our training is designed to support iterative inference and to close the gap between training and inference as much as possible. contributions. ## related work explanation regeneration was promoted as a textgraphs 2019 shared task @xcite . we briefly summarize systems proposed in 2019. most methods finetuned a pre-trained transformer like bert @xcite in a learning-to-rank set-up, as reranker with the question and answer as query and facts as documents, like @xcite . @xcite use bert to classify chains of 2 facts, drawn from initially retrieved facts by a tf-idf retriever and facts with words in common with those facts. their idea is similar to ours, but due to the high number of combinations, they are limited to explanations of only 2 facts. as a second approach, they use bert like @xcite to rank single facts: but das et al. simply rank all facts instead of the top-t initially retrieved ones, which is computationally expensive for the larger 2020 dataset. ## proposed approach this section describes our proposed method, which we call 'autoregressive reasoning over chains of facts' (arcf). arcf consists of an initial retrieval component described in §3.3, a learning-to-rank training scheme and an iterative inference procedure (both in §3.4, fig. 1 shows the latter schematically).