smoothgrad

**SmoothGrad** is an **attribution technique that sharpens gradient-based saliency maps by averaging gradients computed on noisy copies of the input** — reducing the visual noise inherent in vanilla gradient maps by exploiting the principle that true signal survives averaging while noise cancels. **How SmoothGrad Works** - **Noise**: Generate $N$ copies of the input with added Gaussian noise: $ ilde{x}_i = x + epsilon_i$, $epsilon_i sim N(0, sigma^2)$. - **Gradients**: Compute the gradient $ abla_x f( ilde{x}_i)$ for each noisy copy. - **Average**: $SmoothGrad = frac{1}{N} sum_{i=1}^N abla_x f( ilde{x}_i)$ — the average gradient. - **Parameters**: $N$ = 50-200 samples, $sigma$ = 10-20% of the input range. **Why It Matters** - **Noise Reduction**: Vanilla gradients are visually noisy — SmoothGrad produces much cleaner saliency maps. - **Simple**: Can be applied on top of any gradient-based method (vanilla, Integrated Gradients, DeepLIFT). - **Principled**: Averaging is equivalent to computing gradients of a smoothed version of the function. **SmoothGrad** is **denoising by averaging** — computing many noisy gradients and averaging them for cleaner, more interpretable saliency maps.