GoKawiilData structure
We used the International Brain Laboratory (IBL) public data release4. For each experimental session, we collected time-series data on task, behaviour and electrophysiological recordings. These were segmented into trials based on key task events. The task recordings collected for each trial included information on the block prior as well as stimulus contrast and location. The behaviour recordings for each trial comprised the choice made, the outcome/reward received and the time-varying movement such as wheel movement velocity, whisker motion energy and licks. Other behavioural variables, such as paw movement, body motion energy and pupil diameter traces, could be potentially included. However, we did not include them because many sessions had missing values. The electrophysiological recordings for each trial contained time-varying spike trains of recorded neurons. All of these recordings can be accessed directly through the IBL’s open API. The following section describes the steps for preprocessing these raw data into data matrices for the encoding model.
Criteria for session inclusion
We iterated over all cortical regions and downloaded the related sessions. Sessions were included only if all of the behaviour recordings (wheel velocity, whisker motion energy and licks) and electrophysiological data were in place. A maximum of 30 sessions was included per cortical area to encourage a more balanced coverage. Some analyses required additional inclusion criteria, such as a minimum number of trials per condition. These analysis-specific criteria are discussed in the relevant sections below.
Criteria for trial inclusion
All trials from the left or right unbalanced blocks were included except when the animals did not respond to the stimulus in time (the first movement time was longer than 0.8 s). Trials from the 50–50 balanced block were excluded from the analysis to avoid possible time artifacts arising from the fact that all of these trials were exclusively recorded in the first 90 trials of the session.
Criteria for neuron inclusion
All neurons were included in the downloaded data provided that their mean firing rate was higher than 0.5 Hz and lower than 50 Hz. For the selectivity and geometry analyses, we included only neurons whose activity was predicted accurately enough by the RRR model described below (above a minimal threshold of \(\min \Delta {R}^{2}\) with respect to a simple model that assumes that the activity is equal to the average firing rate for all conditions). Unless specified differently, we used \(\min \Delta {R}^{2}=0.015\). This threshold was necessary to avoid confounding effects from neurons that do not encode any relevant variable, including those recorded with a low signal-to-noise ratio. Although the main results of our article remain qualitatively the same for a broad range of values of ΔR2 (Extended Data Fig. 6), it is important to avoid the extreme cases (that is, when no neuron is discarded, or when too few neurons are selected) when studying whether the representations are categorical or not. Indeed, as already noticed previously13, when all neurons are considered, there is the risk that ‘junk’ neurons with very low selectivity to all variables are over-represented, leading to a peak in the distribution around zero selectivity. This distribution would be significantly different from our null distribution (multivariate Gaussian), but that does not mean the representation is actually categorical or that there is any interesting structure in the selectivity distribution. Indeed, in that previous study13, they used as a null distribution the superposition of two Gaussians: one representing the distribution of the selective neurons, and the other, peaked around zero selectivity, to describe the junk neurons. In our case, we decided to discard the worst neurons by selecting only cells that have a large enough ΔR2. Again, the exact value is not important, but keeping all neurons would lead to an extra peak around zero selectivity, and a misleading, inflated number of brain areas that would pass the criterion for being considered categorical. Again, this is not a real, interesting structure and, in general, when performing this kind of analysis, we recommend checking that the structure revealed by a statistical test is not just due to the overrepresentation of junk neurons. Similarly, if only very few neurons are selected, the centre of the selectivity distribution might be depleted, leading again to the misleading conclusion that the representation is categorical.
RRR encoding model
In this section, we describe the RRR model used to analyse the selectivity profiles of single neurons. We start by describing the input and target variables of the model, followed by a description of the model itself and its fitting procedure. Finally, we introduce a few quantities resulting from the fitted model that are key to the follow-up analysis. The notation that will be used is summarized in the ‘Notations’ section. The code for implementing and fitting the encoding model is available at GitHub (https://github.com/realwsq/brainwide-RRR-encoding-model).
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