To communicate, to ground hypotheses, to analyse data, neuroscientists often refer to divisions of the brain. Here we consider atlases used to parcellate the brain when studying brain function. We discuss the meaning and the validity of these parcellations, from a conceptual point of view as well as by running various analytical tasks on popular functional brain parcellations. the brain anatomy, the problem is even more pronounced for the choice of functional units. Yet, the 23 choice of functional parcellation impacts models of brain functions that are learned from these [26] . 24 Here, we discuss principles to guide these choices. We first consider the meaning and construct 25 validity of functional brain units. We then conduct an empirical study using analytic questions that 26 probe different aspects of functional parcels, on 6 popular brain-imaging functional parcellations. seen as implementing an elementary operation, analogous to layers of an artificial neural network [9] . In an ideal world, a functional brain parcellation would capture such units. Can a large-scale division of the brain true, or merely useful? There is very active research on properties [11] . One goal is to reflect intrinsic brain structure with parcels that characterize better functional-connectivity models. An independent validation of such a model is whether it can be 77 well associated with variations of behavioral or clinical traits across subjects [7] . Popular functional atlases We investigate 6 popular atlases derived from fMRI, detailed in Table 1 . The atlases differ in their number of regions, whether these regions are defined with continuous or 80 binary maps, and which method was used to extract them. Performance for functionalconnectivity biomarkers for 6 traits across various cohorts as in [7] . usefulness of continuously defined node reported in [7] . captures well anatomical boundaries (Figure 2 ). But the evidence to ground the choice of a functional atlas is subtle and there is not simple story. From a pure signal-processing point of view (Figure 1 a and c) , the best option at low dimensionality 112 are ICA-derived modes, and at higher dimensionality the BASC atlas, built by clustering fMRI with 113 weak spatial constraints. Decoding performance (Figure 1b) gives a useful measure of the functional 114 specificity of the units defined [24] . In this respect, for higher dimensionalities the Schaefer atlas [20] -built from clustering with more spatial constraints-appears to give the most useful functional 116 units. Finally, the best option to build brain-connectivity models (Figure 1d ) is the BASC atlas. Continuously-defined modes, as opposed to hard parcellations, give excellent expressive power for 118 low dimensionality, however no such atlas is currently available at high dimensionality. It is unclear how close any of these atlases get to actual functional units, when these exist. In 120 some regions for which functional organization is well known, [25] confirmed the face validity of 121 parcels extracted from clustering fMRI. When an atlas is used to define the units of models of brain 122 dynamics and function, these units should ideally capture coherent neural populations. Yet, when the 123 data modeled are fMRI, these come with many measurement imperfections, including intersubject 124 variability. Multimodal approaches promise to define parcellations that capture this variability [11] . Yet, as they entail a significant increase in complexity, most studies prefer to use a predefined atlas. Such an atlas is a simplified view on brain architecture at the population level. Its choice should be 127 guided by its suitability to an analytic task, as studied here: all atlases are wrong, some are useful.
All functional brain parcellations are wrong, but some are useful