embeddings

Embeddings are a representational construct in machine learning and information retrieval. An embedding maps discrete, symbolic objects — words, items, users, or categories — into a continuous vector space of real numbers such that semantic, functional, or relational similarity between objects is reflected as geometric proximity in that space. The parameters defining an embedding are: (1) the vocabulary or item set being mapped, (2) the dimensionality of the vector space (typically 50–5000 dimensions), (3) the training objective or loss function that shapes the space (e.g., predicting co-occurrence, minimizing reconstruction error, or ranking based relevance), and (4) the optimization procedure (e.g., stochastic gradient descent) that adjusts vector values. The persistence mechanism is the learned weight matrix stored as model parameters in neural network architectures, persisted as serialized tensors in model files. The representation endures across sessions and deployments as long as the model weights are preserved.\n\n[formal: repraesentatio | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]