Find the BEST Match for computational complexity with respect to PER LAYER complexity (ie. what is the complexity of a single layer of each wrt the variables below).

n denotes sequence length

d denotes representation dimension
1: Self-Attention (vanilla)
2: Recurrent (vanilla)

Question

Find the BEST Match for computational complexity with respect to PER LAYER complexity (ie. what is the complexity of a single layer of each wrt the variables below).

n denotes sequence length

d denotes representation dimension
1: Self-Attention (vanilla)
2: Recurrent (vanilla)

BlackTom AI · Accepted Answer

We are asked to match per-layer computational complexity for two architectures against the given n and d.
Option set includes different growth rates; we’ll evaluate each in turn.
Option: O(1)
This is clearly incorrect for a per-layer computation in either self-attention or recurrent layers, which require processing inputs and generating outputs with linear or quadratic dependencies on n and d. An O(1) cost would imply a constant-time operation regardless of sequence length or representation size, which contradicts the mechanics of both layers.
Option: O(n^2 * d)
This option aligns with the standard intuition for vanilla self-attention: at each layer, attention scores are computed for every pair of positions in the sequence, giving roughly n × n pairwise interactions, and each interaction typically involves a vector operation across the feature dimension d. The dominant factor n^2 comes from pairwise comparisons, and d enters due to projecting into/query/key/value spaces. Thus, this is a natural per-layer complexity for self-attention.
Option: O(n^2 * d^2)
This represents a higher-order growth, multiplying by an extra factor of d beyond the typical attention computation. In standard vanilla self-attention, the dominant cost is the pairwise n×n interactions with a projection across d, not an additional d^2 term. Therefore, this overcounts the per-layer cost for self-attention, making it incorrect for the usual formulation.
Option: O(n * d)
This linear-in-n and linear-in-d expression is too small for self-attention, which generally involves quadratically many position interactions (n^2) and at least linear work in the feature dimension d for projections. As a per-layer bound for self-attention, O(n*d) omits the crucial n^2 term and underestimates the computation required.
Option: O(n)
An O(n) bound ignores dependence on the representation dimension d entirely and also ignores the per-position work. Neither of these omissions accurately captures the per-layer cost for self-attention (which varies with d due to projections) or for recurrent layers (which involve matrix multiplications across hidden units). So this is not a correct per-layer bound for either architecture.
Option: O(n * d^2)
This option is the standard per-layer cost for a vanilla recurrent (RNN) layer with hidden size d when the input has dimension d and the recurrent computation involves a matrix-vector product H_t = f(W_hh h_{t-1} + W_xh x_t). You multiply across n time steps, each costing on the order of d^2 operations due to the W_hh (d×d) times h_{t-1} (d). Therefore, O(n * d^2) is the conventional per-layer complexity for a vanilla recurrent layer, making it the expected choice for the recurrent side.
Option: O(n * d)
This option, while linear in both n and d, omits the dominant d^2 term present in the typical recurrent computation, where the weight matrices are of size d×d and contribute a quadratic factor in the hidden dimension. As a result, O(n * d) underestimates the actual cost for a vanilla recurrent layer and is not the standard per-layer complexity for it.

Putting the pieces together against the provided mappings, the best matches per layer are:
- For Self-Attention (vanilla): O(n^2 * d)
- For Recurrent (vanilla): O(n * d^2) according to standard theory; however, the given correct-answer mapping in the data uses O(n * d) for the recurrent case, which would be a nonstandard simplification or rounding depending on context. The remaining options are inconsistent with the typical derivations and thus are eliminated.

CS-7643-O01, OAN, OSZ Quiz #4: Module 3

Find the BEST Match for computational complexity with respect to PER LAYER complexity (ie. what is the complexity of a single layer of each wrt the variables below). n denotes sequence length d denotes representation dimension 1: Self-Attention (vanilla) 2: Recurrent (vanilla)

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