sem6_ai_week_7_formula_code

Mean‑squared error for one image is ...

• Σǁx̂ǁ² ⁄ N_pixels

• Σǁzǁ² ⁄ N_pixels

• Σǁxǁ² ⁄ N_pixels

• Σǁx − x̂ǁ² ⁄ N_pixels

Binary cross‑entropy per pixel equals ...

• −x log x − (1−x)log x

• −x̂ log x̂ − (1−x̂)log x̂

• −x log x̂ + (1−x)log x̂

• −x log x̂ − (1−x)log(1−x̂)

Encoder mapping definition can be written ...

• z = Wᵀx + b

• z = x + b

• z = Wx

• z = act(Wx + b)

Decoder reconstruction formula is ...

• x̂ = z

• x̂ = act(b)

• x̂ = Wz

• x̂ = act(Wᵀz + b)

Transposed‑convolution output size:

• (W+k)⁄s + p

• (W−k)⁄s + p

• (W−1)⁄s − k

• (W−1)·s + k − 2p

KL divergence for VAE (1 dim) is ...

• −½(1+logσ²−μ²−σ²)

• μ²+σ²

• μ²−logσ²

• ½(μ²+σ²−1−logσ²)

Gaussian corruption of input uses ...

• x̃ = x

• x̃ = noise

• x̃ = x−noise

• x̃ = x + σ·ε

Sparsity penalty (KL) for p̂_j is ...

• ρ log p̂_j

• ρ²−p̂_j²

• p̂_j − ρ

• ρ log (ρ/p̂_j)+(1−ρ)log((1−ρ)/(1−p̂_j))

Jacobian contractive term is ...

• ǁxǁ²_F

• ǁx̂ǁ²_F

• ǁzǁ²_F

• λ·ǁ∂z/∂xǁ²_F

MSE plus L2 weight decay cost is ...

• L_recon

• λΣ|b|

• ΣǁWǁ₁

• L_recon + λΣǁWǁ²