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Attention is not all you need: pure attention loses rank doubly exponentially with depth

ICML 2021 · Architectures and efficiency › Attention and transformers · approach: Sparse and structured attention · 69 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Remove skip connections and MLPs from a transformer (pure self-attention network) (ablation)Pure attention SAN (depth L) · Real architectures BERT, Albert, XLNet residual analysisRelative residual ||res(SAN_l(X))||/||SAN_l(X)|| across depthHurt
Add skip connections to self-attention network (ablation)Self-attention network (SAN) · Real architectures BERT, Albert, XLNet residual analysisRelative residual across depth (rank collapse)Helped
Add MLP blocks to self-attention network (ablation)Self-attention network (SAN) · Toy 2D circular trajectory taskConvergence of predicted trajectories at inference (rank collapse)Helped
Add MLP blocks to self-attention network (ablation)Self-attention network (SAN) · Real architectures BERT, Albert, XLNet residual analysisRelative residual across depthNo clear effect
Increase weight norm beta (hidden dimension 32 to 128) in single-layer recurrent transformer without skip/MLP (ablation)Single-layer transformer applied recurrently · Toy 2D circular trajectory taskSpeed of rank collapse at inferenceHelped
Add layer normalization (ablation)Self-attention network · Theoretical analysisResidual convergence boundNo clear effect
Use only short paths (length 0 to 2) versus long paths (length up to 6) in trained attention networks (ablation)Trained attention networks on memorization, sorting, convex hull · Sequence memorization, sorting, convex hullPer-token prediction accuracy of path subsetsMixed

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