Abstract
Electrophysiological and neuroimaging studies have revealed how the brain encodes various visual categories and concepts. An open question is how combinations of multiple visual concepts are represented in terms of the component brain patterns: are brain responses to individual concepts composed according to algebraic rules? To explore this, we generated "conceptual perturbations" in neural space by averaging fMRI responses to images with a shared concept (e.g., "winter" or "summer"). After thresholding to ensure specificity, we applied these perturbations to the neural pattern associated with a base image, forming new brain patterns that incorporate the added concept. These modified brain patterns were then decoded into images using a pretrained fMRI-to-image decoding model. Qualitative and quantitative inspection of the resulting images provides insight into how the brain might combine visual concepts. For example, adding a "winter" perturbation to the brain pattern of a man on a skateboard yields a new pattern representing a man on a snowboard in a winter scene-even when the perturbation modifies only a small subset of voxels. Our findings reveal that compositional processes in neural representations may lead to predictable perceptual outcomes, as interpreted by our decoding model. This suggests that the brain's combinatory encoding of concepts may follow a systematic, algebraic-like process-what we term "brain algebra." Although our study is model-driven, it opens avenues for future empirical work into the mechanisms of compositionality in the brain.