  Comparing spoken segments is a central operation to speech processing.
Traditional approaches in this area have favored frame-level dynamic
programming algorithms, such as dynamic time warping, because they require no
supervision, but they are limited in performance and efficiency. As an
alternative, acoustic word embeddings -- fixed-dimensional vector
representations of variable-length spoken word segments -- have begun to be
considered for such tasks as well. However, the current space of such
discriminative embedding models, training approaches, and their application to
real-world downstream tasks is limited. We start by considering ``single-view"
training losses where the goal is to learn an acoustic word embedding model
that separates same-word and different-word spoken segment pairs. Then, we
consider ``multi-view" contrastive losses. In this setting, acoustic word
embeddings are learned jointly with embeddings of character sequences to
generate acoustically grounded embeddings of written words, or acoustically
grounded word embeddings.
  In this thesis, we contribute new discriminative acoustic word embedding
(AWE) and acoustically grounded word embedding (AGWE) approaches based on
recurrent neural networks (RNNs). We improve model training in terms of both
efficiency and performance. We take these developments beyond English to
several low-resource languages and show that multilingual training improves
performance when labeled data is limited. We apply our embedding models, both
monolingual and multilingual, to the downstream tasks of query-by-example
speech search and automatic speech recognition. Finally, we show how our
embedding approaches compare with and complement more recent self-supervised
speech models.
