pooling by multihead attention

**PMA** (Pooling by Multihead Attention) is an **attention-based aggregation mechanism that pools a set of features into a fixed number of output vectors** — using learnable "seed" vectors as queries that attend to all set elements, replacing simple mean/max pooling with learned aggregation. **How Does PMA Work?** - **Seed Vectors**: $S in mathbb{R}^{k imes d}$ — $k$ learnable query vectors. - **Attention**: $ ext{PMA}_k(X) = ext{MAB}(S, X)$ — seeds attend to all input elements via multi-head attention. - **Output**: $k$ output vectors, each a learned weighted combination of all input elements. - **$k = 1$**: Produces a single set-level representation (like a learned global pooling). **Why It Matters** - **Learned Pooling**: More expressive than mean/max pooling — different seed vectors can capture different aspects of the set. - **Multiple Outputs**: Can produce $k > 1$ outputs for tasks requiring multiple set-level predictions. - **Flexible**: Differentiable and end-to-end trainable as part of any set-processing pipeline. **PMA** is **learned pooling via attention** — using trainable query vectors to extract $k$ informative summaries from a variable-size set.