Solve for the rotary frequency index at a chosen rotation count

Read the equation

At index i, the unscaled angular frequency is base^(−2 i/dim). Over orig_max positions it completes orig_max*base^(−2 i/dim)/(2π) rotations. Setting that count equal to rot and solving logarithmically for i gives the displayed correction coordinate. The caller rounds and clamps coordinates to form a blending interval.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

dim,
                             base=10000,
                             max_position_embeddings=2048):
    return (dim * math.log(max_position_embeddings /
                           (num_rotations * 2 * math.pi))) / (2 *
                                                              math.log(base))


# Find dim range bounds based on rotations

return (dim * math.log(max_position_embeddings /
                           (num_rotations * 2 * math.pi))) / (2 *
                                                              math.log(base))

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