SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Figure 21: Redundancy about VISp activity between VIS1 and VISal, as a function of time, for flashes corresponding to an image change (blue) and flashes corresponding to a non-change (orange) with an equal number of samples. Data points are across 41 mice. The plot on the left shows the raw redundancy in bits, while the plot on the right shows the redundancy normalized by the total mutual information. The observations made in the other figures continue to hold; the differences seen between the two conditions are, therefore, not a result of differences in sample size.
sample size; however, as noted in Section 5, our bias correction process is not perfect, and may leave some residual bias.
In order to show that the results we observed were not an artifact of differences in residual bias caused by different sample sizes, we randomly subsampled the non-change flashes to produce a dataset with equal numbers of trials for change and non-change flashes. Repeating the analysis as before, we found that our conclusions continued to hold even in the setting where both conditions have equal sample sizes, as shown in Figure 21.
D.7 A Note on Inhomogeneous Poisson Processes
Inhomogeneous Poisson processes are those whose mean firing- (or "emission-") rates change with time. Our method for estimating the PID does not consider the temporal characteristics of the original signal. Rather, the data analyst can choose the random variables  $M$ ,  $X$  and  $Y$  to span some time range (or different time ranges) as they please.
In our analysis of real neural data in Sec. 6, we counted the number of spikes in a 50-125 ms window after stimulus onset. Even if the underlying spiking process was an inhomogeneous Poisson process, this spike count would be Poisson distributed, with a mean given by the integral of the emission rate over the fixed window. In general, while analyzing data and computing PID values, one will have to be aware of severe inhomogeneities (e.g., if the distribution changes not just in the same way in each trial, but changes across trials), and account for them separately. For example, in our analysis, we excluded time periods when the mice were not "engaged" in the task, as defined by not actively consuming rewards at a rate of at least 2 rewards per minute.
E Compute Configuration Used and Code Availability
All analyses were performed on a workstation equipped with an Intel Core i7-10700KF CPU with 8 cores (16 threads), 48 GiB of RAM and data stored on a 1 TB PCIe NVMe solid state drive.
Analysis of the Visual Behavior Neuropixels data (for 84 sessions) with  $d = 20$  took approximately 9 minutes to run. This included loading data for each session and computing 840 PID values on  $60 \times 60$  covariance matrices, implying an average run-time of about 0.64s for each PID estimate (including amortized data-load time).
All code used to compute and estimate the  $\sim_G$ -PID and correct for bias, including all examples in this paper and code for neural data analysis, is available on GitHub [36].
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