In dense retrieval, deep encoders provide embeddings for both inputs and targets, and the softmax function is used to parameterize a distribution over a large number of candidate targets (e.g., textual passages for information retrieval). Significant challenges arise in training such encoders in the increasingly prevalent scenario of (1) a large number of targets, (2) a computationally expensive target encoder model, (3) cached target embeddings that are out-of-date due to ongoing training of target encoder parameters. This paper presents a simple and highly scalable response to these challenges by training a small parametric corrector network that adjusts stale cached target embeddings, enabling an accurate softmax approximation and thereby sampling of up-to-date high scoring "hard negatives." We theoretically investigate the generalization properties of our proposed target corrector, relating the complexity of the network, staleness of cached representations, and the amount of training data. We present experimental results on large benchmark dense retrieval datasets as well as on QA with retrieval augmented language models. Our approach matches state-of-the-art results even when no target embedding updates are made during training beyond an initial cache from the unsupervised pre-trained model, providing a 4-80x reduction in re-embedding computational cost.

Spelling error correction is the task of identifying and rectifying misspelled words in texts. It is a potential and active research topic in Natural Language Processing because of numerous applications in human language understanding. The phonetically or visually similar yet semantically distinct characters make it an arduous task in any language. Earlier efforts on spelling error correction in Bangla and resource-scarce Indic languages focused on rule-based, statistical, and machine learning-based methods which we found rather inefficient. In particular, machine learning-based approaches, which exhibit superior performance to rule-based and statistical methods, are ineffective as they correct each character regardless of its appropriateness. In this work, we propose a novel detector-purificator-corrector framework based on denoising transformers by addressing previous issues. Moreover, we present a method for large-scale corpus creation from scratch which in turn resolves the resource limitation problem of any left-to-right scripted language. The empirical outcomes demonstrate the effectiveness of our approach that outperforms previous state-of-the-art methods by a significant margin for Bangla spelling error correction. The models and corpus are publicly available at https://tinyurl.com/DPCSpell.