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Equation 16 · Part 1 · Embeddings and the Geometry of Similarity

Symbol L_3

L3L_3
L3L_3

What this part means

L3L_3 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

L3L_3 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

with C constant, while typical distances themselves grow like d1/kd^{1/k} . Relative contrast therefore decays with dimension, and the constant shrinks as k rises — which is why they conclude that L1L_1 is preferable to L2L_2 in high dimensions, L2L_2 to L3L_3 , and that fractional norms preserve contrast better still [ 12 ] .

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