Equation 7 · Part 1 · Embeddings and the Geometry of Similarity
Symbol varepsilon
What this part means
varepsilon is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Its job in the formula
varepsilon is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol varepsilon→Article meaning
The passage around this formula
for every > 0 [ 11 ] . The condition is on the relative variance of the distance distribution: when distances stop varying much relative to their own mean, the nearest neighbour stops being distinguishable from everything else. The authors call such a query unstable , and their empirical work shows the effect appearing with as few as 10 to 15 dimensions on both synthetic and real data — while explicitly warning that the result does not mean high-dimensional indexing is never meaningful, since particular workloads escape the conditions [ 11 ] .
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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.