Equation 11 · Part 1 · Embeddings and the Geometry of Similarity
Symbol d^1/k
What this part means
the while typical distances themselves grow like.
Its job in the formula
/k 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 d^1/k→Article meaning
Where the article explains it
with C constant, while typical distances themselves grow like .
The passage around this formula
with C constant, while typical distances themselves grow like . Relative contrast therefore decays with dimension, and the constant shrinks as k rises — which is why they conclude that is preferable to in high dimensions, to , and that fractional norms preserve contrast better still [ 12 ] .
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.