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When replacing the activation function at test time (as described in Section 5.3.2), here's what happens:

What stays the same:

  • All trained weights: encoder weights WencW_{\text{enc}}, decoder weights WdecW_{\text{dec}}
  • All biases: bencb_{\text{enc}}, bpreb_{\text{pre}}
  • The overall architecture: encoder → activation → decoder

What changes:

Only the activation function itself is swapped out. For example:

  • If trained with TopK(k=32), you might test with TopK(k'=64) or JumpReLU(θ)
  • If trained with ReLU, you might test with TopK(k') or JumpReLU(θ)

Where JumpReLU parameters come from:

The threshold parameter θ\theta for JumpReLU is chosen at test time as a hyperparameter. The authors sweep across different values of θ\theta to generate the curves in Figure 10. Specifically:

For JumpReLU: Jθ(x)=x1(x>θ)J_\theta(x) = x \cdot \mathbf{1}_{(x>\theta)}

The process is:

  1. Train autoencoder with original

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