Functionsattention

Functionsattention is a term used to describe an attention-based mechanism that assigns weights to a set of candidate functions or function-like modules when processing an input. The goal is to dynamically select or compose function components to produce an output, enabling flexible, compositional computation within a neural model.

Formally, given input x and a pool of functions F = {f1, ..., fk}, each fi is a parametric function that can operate on x. A scoring network computes si = score(x, fi) and the attention weights αi = softmax(si). The final output is y = sum_i αi fi(x) in soft attention, or y equals fi*(x) where i* = argmax si in hard attention. This framework allows the model to blend multiple functional perspectives or select a single, most relevant function for a given instance.

Variants include multi-head attention over functions, hierarchical function graphs, and differentiable function composition where the output passes through a sequence of selected functions with learned composition order. Training typically uses standard backpropagation with differentiable attention, though hard attention can use reinforcement learning or straight-through estimators.

Applications include neural program synthesis, differentiable interpreters, neural module networks for visual question answering, meta-learning, and algorithmic tasks that benefit from reusable functional building blocks. The approach emphasizes modularity and interpretability, enabling models to reason about which functions to apply in different contexts.

Relation to broader concepts: functionsattention builds on attention mechanisms from transformers and neural module networks, and relates to differentiable programming and neural function composition. While not as standardized as other attention forms, it is discussed in research focused on modular and interpretable neural architectures.