SlowGuess/NeurIPS_2023_OCR huggingface dataset:
E
Figure S15: DFI tested on simulated and real brain data. In Panels A,B DFI is tested on the same simulations used for Fig 2A-B. Panel C-E report DFI results on real brain data. (A) DFI as function of stimulus-feature-related  $(W_{stim})$  and -unrelated  $(w_{noise})$  transmission strength. * indicate significant values  $(p < 0.01$ , permutation test) for the considered parameter set. (B) Dynamics of DFI in a simulation with time-localized feature-information transmission. Red area shows the window of feature-related information transfer. Yellow dots show time points with significant information  $(p < 0.01$ , permutation test). Results plot mean (lines) and SEM (shaded area) across 50 simulations (2000 trials each). (C) EEG DFI between L, R hemisphere about L and R eye visibility (cf with FIT in Fig4D of main paper). (D) MEG DFI about stimulus or choice feedback or feedforward and in correct vs error trials (cf with FIT in Fig. 3D-F). (E) Spikes DFI for the thalamocortical pathway and tactile- or visual-discriminative stimulus set (cf with FIT in FigS8E-I). P-values: 2-tailed paired t-test.  $^{*} p<0.05$ ,  $^{**} p<0.01$ .
SM4.3 Comparison with measures not discounting past information in the receiver as in the Wiener-Granger Causality principle
We finally consider the suitability for identifying flow of information about specific features of possible alternative measures that, although have relevance to feature information coding across areas, do not implement the Wiener-Granger discounting of the information present in the past activity of the sender. In brief, methods that do not implement this (and thus just correlate past information of the sender with present information of the receiver), erroneously identify information already encoded in the past activity of the receiver as information transmitted from a sender. This concern would apply in general to all measures that compute time-lagged cross-correlations of activity across areas [14]. In the following, we consider briefly some possible methods that have been used to infer feature-specific information transfer but that do not consider the Wiener-Granger Causality principle.
One possibility would be to measure the presence and timing of feature information (using mutual information between the feature and the activity of the individual area at each instant of time, as in Eq. S1) and then inferring transfer of feature information from  $X$  to  $Y$  if information about  $S$  arises first in  $X$  and  $Y$ . Inferring processing hierarchies on the basis of response selectivity latencies
is a long-established practice in neuroscience [32; 36; 39]. However, the presence of time-lagged information in two areas does not mean that the information in the second area comes from the first area. Indeed, in the simulations to test FIT we created several such simulated scenarios of information present in each area with a different timing but without actual communication between the areas (Fig. S7C, Section SM2.6), and we created non-parametric tests to rule out this possibility based on FIT measures (Section SM1.7). Thus, differential response latencies can be used to hypothesize the presence of processing hierarchies but not to prove transfer of information between specific nodes of the putative information processing network.
Another possibility would be to use PID to measure the presence of shared (or redundant) feature information encoded in both  $X$  and  $Y$  at different temporal lags. PID can specifically isolate only the information about a feature that is the same, e.g., redundantly encoded, in  $X$  and  $Y$ . Thus, measuring time-lagged shared information goes beyond computing a simple time-lagged correlation between the amount of reach-to-grasp information in  $X$  and  $Y$ , which would not consider whether the time-lagged information content is the same. However, this measure would not discount the presence of the same information in the past activity of  $Y$ , and it would thus be prone to detecting false communications in case the information was already present in the past of  $Y$  and thus could not have come from  $X$ . (In other words, it would erroneously identify information already encoded in the past activity of the receiver as information transmitted from a sender.) These types of problems of not discounting the past have been illustrated and discussed extensively in the Granger-Causality literature. These considerations apply to a previous study [29] which used PID to attempt to define feature-specific information transmission using the so-called Intersection Information [28], computing information shared between the past activity of the sender and present activity of the receiver (not considering the information already present in the past activity of the receiver).
SM5 Computational resources
Each of the simulations in Figures 2, S3, S4, S6, S7, S8, S14, and S15 ran in approximately 30 minutes on a personal computer equipped with an Intel i7-10510U processor (4x 1.80GHz CPUs) and 16Gb of RAM, running Windows 10, using MATLAB R2021a. Simulations in Fig. S5 took approximately 3 hours on the same machine.
Real neural dataset analyses ran on a server with an AMD Ryzen Threadripper 3970X processor (32x 3.7GHz CPUs) and 256Gb of RAM, running Ubuntu 18.04, using MATLAB R2019b. The EEG and MEG analyses ran in parallel (using the Parallel Computing Toolbox) over participants or links in the visual cortical network, respectively. Each analysis of the full real datasets (across all participants and experimental sessions) took 12-28 hours depending on the usage of the server.
Our MATLAB codes to compute Feature-specific Information Transfer are provided with this submission and are released under the MIT license. The routines to compute FIT, TE and cFIT are also available at [https://github.com/mcelotto/Feature_Info_Transfer].
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