Neural Representational Geometry of Feature Binding Operations

The brain faces the feature binding problem: how are multiple stimulus features and variables combined into coherent representations that support flexible behavior? A key finding from neuroscience is that some brain regions employ factorized representations, where distinct features are encoded in neural state space in such a way that enables independent readout and robust generalization. Various algebraic operations have been proposed to model multi-variable representations, but despite extensive study of their theoretical properties (e.g., capacity, noise robustness), it remains unclear which operations produce the representational geometries observed in neural recordings. We systematically evaluate six binding operations implemented in recurrent spiking neural networks performing a working memory task. We find that only superposition and binding with slot-filler structure produce factorized geometry with favorable scaling, while the alternatives do not. These results provide a taxonomy linking algebraic binding operations to neural representational signatures, offering guidance for both computational modelers and experimentalists.