Learn Before
General Equivalence Formula for Modified RoPE
A modified Rotary Positional Embedding (RoPE) function, denoted , can be defined through its equivalence to the original function. Applying the modified function to a token embedding with position parameters is identical to applying the original function to the same embedding but with a transformed set of position parameters, . This relationship is formally stated as:
0
1
Tags
Ch.3 Prompting - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
Related
Application of RoPE Rotation to a 2D Vector
RoPE Frequency Parameters
Definition of the 2x2 RoPE Rotation Matrix Block
RoPE Parameter Vector Definition
Definition of RoPE Parameter Vector (θ)
A language model encodes token positions by applying a unique, position-dependent rotational transformation to each token's initial embedding. The final, position-aware embedding for a token is the result of this transformation. If the exact same token (e.g., 'model') appears at position 4 and later at position 12 in a sequence, which statement best describes the relationship between their final embeddings, and ?
RoPE 2D Vector Rotation Formula
Formula for RoPE-Encoded Token Embedding
Uniqueness of RoPE-based Embeddings
Debugging a RoPE Implementation
General Equivalence Formula for Modified RoPE
Learn After
Formula for RoPE with Linear Positional Interpolation
A researcher defines a new rotary position embedding function,
Ro_new, for a tokenx_iat positioni. The new function is defined asRo_new(x_i, iθ) = Ro(x_i, (i+c)θ), whereRois the original function andcis a constant offset. According to the general equivalence principle, this can be written asRo_new(x_i, iθ) = Ro(x_i, iθ'). What is the correct expression for the transformed position parameteriθ'?RoPE Scaling Transformation Equivalence
Equivalence of RoPE Modification Strategies
Analysis of a Flawed RoPE Modification