Double Sum

Essential AI Math Excel Blueprints

\(\sum_{i=1}^{n} \sum_{j=1}^{m} a_{ij}\)

The purpose of a double sum is to aggregate contributions that naturally vary along two dimensions into a single scalar. In AI models, these dimensions often correspond to features and data points, or inputs and outputs. By summing across both indices, a double sum ensures that every pairwise interaction is accounted for, rather than emphasizing only one dimension. This makes it a natural tool for computing total loss, regularization terms, and weight updates during training.

Excel Blueprint

This Excel Blueprint is available to AI by Hand Academy members. You can become a member via a paid Substack subscription.