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: $\tilde{x}_i = x + \epsilon_i$, $\epsilon_i \sim N(0, \sigma^2)$.
• Gradients: Compute the gradient $\nabla_x f(\tilde{x}_i)$ for each noisy copy.
• Average: $SmoothGrad = \frac{1}{N} \sum_{i=1}^N \nabla_x f(\tilde{x}_i)$ — 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.