Why does an article created after node2vec training has run have no vector at all?

## Transductive versus inductive, stated properly A **transductive** method produces outputs only for the specific instances present at training time. An **inductive** method learns a function that can be applied to instances it has never seen. DeepWalk and node2vec are transductive in the strongest sense: what training produces is a matrix of free parameters, one row per node id, and every row was fitted independently by gradient descent. There is no weight matrix that maps anything to anything. Ask for the vector of an id that was not in the walk corpus and there is no computation to run — only a missing row. ## The concrete failure Take a Wikipedia hyperlink graph. You sample walks on Monday, train overnight, and ship a table of vectors used by an article-similarity feature. On Tuesday an editor creates a new article with a dozen incoming and outgoing links. That article: - has no row in the table, so the feature cannot be computed for it; - changes the graph, so every existing row is now fitted to a slightly stale structure; - cannot be fixed by any amount of inference, because inference here is an array index. Multiply by the creation rate and the table decays continuously between refits. ## Why you cannot just retrain the one node The tempting patch is to freeze the table, sample fresh walks through the new node, and fit only its row. This is not nonsense — it is a real stopgap — but be honest about what it gives you. The context vectors it is fitted against were optimised without the new node's edges, the number of new training pairs is tiny, and the resulting vector is a noisy point estimate in a space defined by an older graph. It buys you coverage until the next refit; it is not equivalent to a full refit. What you definitely cannot do is train a second full model and mix the two tables. Random initialisation, random walk sampling and stochastic optimisation leave each run in its own arbitrarily oriented space. A vector from run A and a vector from run B are not comparable, and their inner product means nothing. Aligning two runs is a separate procedure and not something to do casually. ## The downstream blast radius This is the part senior candidates are expected to raise unprompted. Because a refit re-orients the whole space, everything fitted on top of the old table is invalidated at the same instant: - a classifier or ranker taking the embedding as input must be retrained on the new table; - a nearest-neighbour index must be rebuilt from scratch, not incrementally updated; - any cached similarity scores, thresholds calibrated on old distances, or monitoring baselines computed from old vectors are void. So the refit is not an embedding job; it is a coordinated release of the embedding table plus every consumer. Treat the table as a versioned artefact and pin consumers to a version. ## Living with it If the graph is essentially static — a product catalogue that changes weekly, a citation graph you analyse offline — transductive embeddings are perfectly fine, and their simplicity is a virtue. Refit on a schedule, version the table, retrain consumers together. If nodes arrive continuously and must be scored on arrival, you need a written cold-start policy: what does the system return for a node with no vector? Options include falling back to non-embedding features, using a neighbour-average stopgap, deferring the node to the next batch, or routing it to a rules path. Silence is not a policy — an unhandled missing row usually surfaces as a zero vector, and a zero vector is not neutral: it has a defined similarity to everything, and it will quietly rank somewhere. The structural fix is to stop storing vectors and start computing them — a model whose parameters are shared weights applied to a node's own features and its neighbourhood, so an unseen node with features and edges gets a vector by running the model forward. That family is a different topic; the point here is to recognise that the missing row is not a bug in node2vec but a property of what it learns. ## Cost of the refit The cost is dominated by walk sampling and by the parameter count, both linear in the node count, so a large graph refit is a scheduled, budgeted job — hours, not seconds. Deciding its cadence is a real tradeoff between staleness and spend, and it belongs in the design document rather than being discovered in production.