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Determining Position Index from a Sine Vector
In a computational model that encodes sequential data, a 'sine vector' is constructed for each position i using a set of frequency parameters θ. The formula for the k-th element of this vector is sin(i * θ_k). If the frequency parameters are θ = [π/6, π/2] and the resulting sine vector for a certain position is [1, -1], what is the smallest positive integer for the position index i? Explain your reasoning.
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i = 2and a set of frequency parametersθ = [π/2, π/4], what is the resulting 2-dimensional sine vector, defined as[sin(iθ₁), sin(iθ₂)]?Consider a method for encoding positional information where a
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