By Louis Ravn
The terms describing the spaces of deep learning (DL) – including latent space, vector space, feature space, and embedding space – are often used interchangeably. While this rightly betrays a close connection between these concepts, they nonetheless differ in important ways. Hence, this blog posts attempts to explain some of the salient differences and similarities between latent space, vector space, feature space, and embedding space. Please note that these are pragmatic, work-in-progress distinctions.
First, latent spaces are abstract, lower-dimensional representations of essential features of datasets, produced by DL models during training (Munn & Badri, 2025; Munster, 2025). While latent spaces are still high-dimensional, they are significantly compressed relative to the datasets from which they were produced. Although all DL models construct latent spaces, they rose to prominence chiefly in the context of the recent breakthrough of encoder-decoder architectures, centrally entailing variational autoencoders (VAEs) (Kingma & Welling, 2019) and Transformers (Vaswani et al., 2017). Latent spaces were first conceptualised in autoencoders and now enable the division into encoders and decoders. In encoder-decoder architectures, latent spaces are produced as a result of the encoding process; thereafter, they constitute the source from which decoders reconstruct outputs, whether in the form of text, images, or videos. Latent spaces are “latent” in the sense that they encode aspects of data that are not directly observable in the data themselves – what are often called the data’s “hidden” features. In addition to their high dimensionality, this “latency” of latent space is what makes them so counter-intuitive to human modes of comprehension. Specifically, we cannot visualise anything beyond the third spatial dimension.
Second, vector space – which has a long history in mathematics (Salton et al., 1975) – denotes a set of objects whose components (i.e., vectors) can be added and multiplied. In DL, vector space is the foundation of all representation; all vectors exist in the vector space (Lee, 2025). Importantly, vector space forms the overarching mathematical form of which embedding, feature, and latent space form part – all of these operate by vectorizing input data (i.e., turning them into mathematical vectors) during training. While vector space thus constitutes a general mathematical framework, latent space can be seen as a particular vector space which exists within a model and which contains the model’s hidden, implicit representations of training data.
Third, the concept of feature space is often used in ways that indicate a meaning synonymous with that of latent space (e.g., Aradau & Blanke, 2022). In classic, supervised ML, feature space consists of manually constructed features of datasets (e.g., “height”, “occupation”, etc.), which is not the case in DL: here, features are learned automatically. By contrast, latent spaces are lower-dimensional representations of the feature space: not all dimensions of the feature space may be crucial to a task at hand. Accordingly, the production of the latent space entails a selection of which aspects of the feature space are most relevant for specific tasks (Bergmann, 2025) – as well as their combination. Thus, a latent space is a kind of feature space that is more compressed, abstract, and less interpretable (cf. Munn & Badri, 2025). In short, while features can be observed, latent variables cannot.
Finally, embedding space describes a particular type of feature space in which discrete objects (like words, items, or images) are mapped into continuous vectors that preserve semantic relationships (Brunila, 2025). In DL, embedding spaces are particularly important as word embeddings that encode semantic similarities between words (e.g., Kozlowski et al., 2019). We can thus distinguish embedding space and latent space in the following way: while the former encodes discrete entities (characters, words, etc.) into continuous vectors and models the semantic relationships between them (most often in NLP contexts), the latter is a model’s internal representation that constitutes how it “thinks” by means of spatial representations and from which it generates outputs (e.g., via a VAE’s decoder). Put differently, relationality operates differently between embedding and latent spaces: while semantic similarity usually translates to proximity in embedding spaces (Impett et al., 2026, 98), this is not always the case in abstract latent spaces.
Last updated: 30 April 2026