SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Figure S11: Sensory related info transfer carried by multi unit activity (MUA). (A) Schematic of the experimental setup. MUA was recorded in rats from the Ventral Posteromedial nucleus (VPM) of the thalamus, the Lateral Geniculate Nucleus (LGN) of the thalamus, the primary somatosensory (S1) and visual (V1) cortex simultaneously. During the recording either a unimodal tactile, a unimodal visual, or a bimodal (visual and tactile) stimulus was presented. (B) FIT values averaged across delays for all combinations of transfer direction and stimulation type on the somatosensory pathway (VPM-S1). (C) Same as B but for the visual pathway. (D) FIT from VPM to S1 (mean across subjects) for each value of delay and post-stimulus time. Line plots above and below show Mutual Information (MI) between the presented stimulus and the recorded MUA in the VPM and S1, respectively. Width of shaded errorbars show the SEM of the measure across subjects. The left panel reports values of information and FIT for the tactile-discriminative set, whereas the right panels report values of information and FIT about the visual stimulus set. (E) Directional sensitivity for TE (left) and FIT (right) between VPM and S1, for the Tactile stimulus-set. (F) Comparisons between tactile- and visual-discriminative set, for the TE (left) and the FIT (right) from VPM to S1. (G) Same as panel D but from LGN to V1. (H) Same as panel E but between LGN and V1, for the Visual stimulus-set. (I) Same as panel F but for TE and FIT from LGN to V1.
SM3.3.3 Further details about the information-theoretic results
We first focused on the somatosensory pathway (VPM and S1). We found that, on this pathway, the tactile FIT in the VPM to S1 direction was visibly higher than the visual FIT in the same direction and both tactile and visual FIT in the S1 to VPM direction (Fig. S11B) We found that the timing of tactile FIT from VPM to S1 was consistent with the one of tactile information in neural activity, that was present in the 5-30ms and 15-30ms post-stimulus intervals in VPM and S1, respectively (Fig. S11D left, top and bottom lines). We found that FIT revealed the directionality of tactile information flow, which was significantly larger in the feedforward (VPM to S1) compared to the feedback (S1 to VPM) direction (Fig. S11E right,  $\mathrm{p} = 0.0065$ ). On the contrary, TE computed for the tactile set was not significantly different in the two directions (Fig. S11E left,  $\mathrm{p} = 0.13$ ). FIT also revealed the content of communication from VPM to S1, being significantly larger for the tactile set than for the visual set (Fig. S11F, right;  $\mathrm{p} = 0.0084$ ), while TE from VPM to S1 was not significantly different in the two directions (Fig. S11F, left;  $\mathrm{p} = 0.12$ ).
Complementary results were found in the visual pathway (LGN and V1). On this pathway, the visual FIT in the LGN to V1 direction was visibly higher than the tactile FIT in the same direction and both tactile and visual FIT in the V1 to LGN direction (Fig. S11C). FIT for the visual-discriminative set in the LGN to V1 direction peaked in a time interval of approximately 45 to 65ms after stimulus-onset and with a transfer delay of approximately 10-25ms (Fig. S11G). The visual FIT values were larger in the feedforward than in the feedback direction (Fig. S11H, right;  $p = 0.033$ ), while TE was not sensitive to the directionality of visual information (Fig. S11H, left;  $p = 0.15$ ). Moreover, visual FIT values were significantly larger than the tactile ones from LGN to V1 (Fig. S11I, right;  $p = 0.013$ ), while TE did not capture these sensory modality-specific differences (Fig. S11I, left;  $p = 0.4$ ). Taken together, these results highlight the power of the FIT in revealing feature- and direction-specific transfers of information with high temporal precision, beyond what is achievable using methods that measure the total propagation of neural activity such as TE.
SM3.4 Applications of cFIT to real neural data
We tested the effectiveness of the conditional FIT (cFIT) in the analysis of neurophysiological data by applying it to perform further analyses on the EEG and the MUA datasets (Fig. S12). For simplicity, when computing cFIT from  $X$  to  $Y$  conditioned on the stimulus information of  $Z$ , we always considered the same communication delay (that is, the time difference between the present and past activity used to compute the information theoretic measures) for the past activity of the sender  $X$  and the past activity of the third region  $Z$ . However the definition of conditional FIT holds for an arbitrary representation of  $Z_{past}$ , potentially including multiple time points or a communication delay that is different from the one of  $X_{past}$ .
We first applied cFIT to the EEG dataset. We investigated whether the contra-lateral Occipito-Temporal electrodes used to compute TE and FIT in Figure 4 where the sole senders of eye-specific information across hemispheres. We selected two different sets of putative alternative senders of eye-specific information and used cFIT to remove the contribution of the putative alternative senders from the contra-lateral FIT that we measured. Namely, we selected the third location to be conditioned upon from either a set of weak or a set of strong alternative senders for both the left and for the right eye (Fig. S13). For each participant, we defined the two weak alternative sender locations (one for the left an one for the right eye) as those electrodes carrying the lowest amount of stimulus information about the left or the right eye, respectively, in the frontal lobe of the brain. The expectation was that removing the contribution of these electrodes using cFIT would not change appreciably the results obtained with the contra-lateral unconditional FIT reported in Figure 4.
For each participant, we defined the strong alternative senders locations (one for the left an one for the right eye) as those electrodes carrying the second-largest amount of information about the left eye in ROT or about the right eye in LOT (ROT and LOT defined as in Ref [18]). We found that FIT conditioned on the contra-lateral-eye information of one of the weak alternative senders (the orange lines in Fig. S12A) did not reduce FIT, as the cFIT was virtually equal to the unconditional FIT (the blue trends in Fig. S12A). However, FIT conditioned on the contra-lateral-eye information of one of the strong alternative senders (the green trends in Fig. S12A) was lower than unconditional FIT. However, both cFIT given the weak and the strong alternative senders were significant (cluster statistics over time,  $p < 0.01$ ). The fact that cFIT was lower than FIT when conditioning on informative electrodes but not when conditioning on weakly informative electrodes suggests that cFIT is effective
at removing influences related to similar feature-specific (but not un-specific) information present already in the past activity of other regions. The fact that the inter-hemispheric Occipito-Temporal controlateral-eye-specific cFIT is still highly significant and is only marginally smaller than the original unconditional FIT suggests that most eye-specific information flows across hemispheres through the contra-lateral Occipito-Temporal electrodes selected in [18].
Next, we analyzed the spiking activity dataset. We examined tactile-discriminative information flowing through the somatosensory pathway, and the visual-discriminative information flowing though the visual pathway.
We first used cFIT to test whether the tactile-discriminative FIT from the somatosensory thalamus VPM to the somatosensory cortex S1 could have actually been relayed through the visual thalamus LGN. The neurophysiological expectation is that all tactile-discriminative information flows within the somatosensory pathway, without contributions from visual stations. Consistent with this expectation, we found that the tactile-discriminative cFIT from VPM to S1 conditioned on the visaul thalamus LGN was equal to the unconditional tactile-discriminative FIT from VPM to S1.
We then used cFIT to test whether the visually-discriminative FIT from the visual thalamus LGN to the visual cortex V1 could have actually been relayed through the somatosensory thalamus. The neurophysiological expectation is that all visual-discriminative information flows within the visual pathway, without contributions from somatosensory stations. Consistent with this expectation, we found that the visually-discriminative cFIT from LGN to V1 conditioned on the somatosensory thalamus VPM was equal to unconditional visually-discriminative FIT from LGN to V1.
Together, these results suggest that cFIT is useful to remove contributions from alternative pathways specifically with regard to the transmission of feature-specific information.
SM4 Comparison with other possible or previously published measures
We examine how FIT differs with respect to other possible or previously published algorithms that were designed to identify the information flow across regions about behavioral or stimulus features of interest. We first consider two measures that implement the Wiener-Granger discounting of the information present in the past activity of the sender. We then consider two other methods, that did not implement this principle.
SM4.1 Comparison with variations in transfer entropy  $\Delta TE$
As mentioned in the main text, one simple-minded proxy for identifying feature-specific information flow could be quantifying how the total amount of transmitted information (TE) is modulated by the stimulus-feature [4]. For the case of two stimuli, this amounts to the difference of TE computed for each stimulus-feature value.
We now show, using simulations, that this measure can fail in capturing feature-related information flow. We performed simulations in a scenario having variable degrees of both feature-specific and feature-unrelated information transfer. The encoded and transmitted stimulus feature  $S$  was a stimulus-intensity integer value (1 or 2). The activity of the sender  $X$  was a two-dimensional variable with one stimulus-feature-informative  $X_{stim}$  and one stimulus-uninformative component  $X_{noise}$ . The feature-informative dimension had a temporally-localized stimulus-dependent bump in the activity (from 200 to 250ms) and additive Gaussian noise. The stimulus-unrelated component was, at any time point, a zero-mean Gaussian noise. The activity of the receiver  $Y$  was the weighted sum of  $X_{stim}$  and  $X_{noise}$  with a delay  $\delta$ , plus Gaussian noise. The delay  $\delta$  was chosen randomly in each simulation repetition (N=50) in the range 40-60ms. We tested whether  $\Delta TE$  across simulation repetitions was significantly different from zero using a two-tailed t-test.
As we did in Figs. 2 and S3 for FIT and TE, we studied the behavior of  $\Delta TE$  as a function of the simulation parameters  $W_{stim}$  (which increases the amount of information transferred about the stimulus feature) and  $W_{noise}$  (which increases the amount of feature-unspecific information that is transferred from  $X$  to Y). We found (Fig. S14A) that  $\Delta TE$  had almost no relationship with the values of  $W_{stim}$  and  $W_{noise}$ , unlike FIT which individuated stimulus-feature-specific transfer correctly because it increased with  $W_{stim}$  but not with  $W_{noise}$  (Fig. S3A).
cFIT profiles for different confounders sets
Figure S12: Application of cFIT to experimental data. (A) cFIT application to the EEG data. We conditioned the contra-lateral FIT about the left and the right eye (see Fig. 4) to the activity of two either weak or strong alternative eye-visibility information senders. Temporal profiles of unconditional FIT (in blue) for about the left eye from ROT to LOT (left) and about the right eye from LOT to ROT (right). cFIT temporal profiles when conditioning on weak alternative senders (in orange) and on strong alternative senders (in green). The points where the measures were significant are indicated with a circular marker  $(\mathsf{p} < 0.01$ , cluster statistics). (B) cFIT applied to MUA data. We conditioned tactile- (visual-) discriminative FIT through the somatosensory (visual) pathway (first row) to the activity of the visual (somatosensory) thalamus. The amount of unconditional FIT that was shared with the FIT through the alternative sender (second row) was subtracted from the original FIT to obtain cFIT (third row). The left column shows results for the tactile-discriminative set, the right column for the visual-discriminative set.
Note that we performed also simulations (that were exactly like those of Fig. 2, except that we had 2 rather than 4 stimulus intensity values) in which the noise in  $X$  was multiplicative rather than additive. In this case (results not shown)  $\Delta TE$  increased with both  $W_{stim}$  and  $W_{noise}$ . Thus,  $\Delta TE$  had limited capabilities of identifying some stimulus-feature-specific information transfer in some specific case, but it dot reflect it in general.
The reason that  $\Delta TE$  cannot capture feature-specific information flow is, in our view, that  $\Delta TE$  is a measure of variation of information strength across stimulus-feature conditions rather than a measure of stimulus-feature-specific information transfer.
Figure S13: Sets of electrodes used in the EEG data analysis. (A) Electrodes used to measure FIT and TE and for all the analyses in Fig.4, same electrodes used in [18]. (B) Set of 'strong alternative senders', selected as the electrodes carrying the second maximum amount of information about the left eye in the ROT (left panel) and about the right eye in the LOT (right panel). (C) Sets of 'weak alternative senders', selected as the electrodes in the frontal lobe carrying the minimal amount of information about the left eye (left panel) and about the right eye (right panel).
Additionally, we tested  $\Delta TE$  on MEG data. We first binarized the stimulus feature into two classes (average contrast either greater,  $S = 1$ , or lower,  $S = 0$ , than the reference contrast). We computed TE for all pairs of visual regions in the visual cortical network separately in trials with the same value of the binary stimulus we and computed the difference  $\Delta TE$  between these values. Fig. S14B shows that  $\Delta TE$  in the visual cortical network had the same strength in the feedforward and feedback direction, unlike FIT that showed a clear directionality of communication of stimulus information (stronger in the feedforward than in the feedback direction). Finally, when computing TE on the spiking activity data of the rat thalamocortical network, we found that TE from thalamus to cortex did not vary between the tactile-discriminative and visually-discriminative stimuli set (see Fig. S11E-I).
Figure S14: Performance of the Transfer Entropy Difference across stimuli ( $\Delta TE$ ) on simulated and real MEG data. (A) Simulated data. Values (mean across 50 simulations) of  $\Delta TE$  from  $X$  to  $Y$  computed on the same simulated data used in Fig. S3A as a function of the simulation parameters  $W_{stim}$  (which increases the amount of information transferred about the stimulus feature) and  $W_{noise}$  (which increases the amount of feature-unspecific information that is transferred from  $X$  to  $Y$ ). We found that  $\Delta TE$  had almost no relationship with the values of  $W_{stim}$  and  $W_{noise}$ , unlike FIT which increases only with  $W_{stim}$ . All  $\Delta TE$  values were not significantly different from zero (two sided t-test across 50 simulations, significance threshold at  $\mathfrak{p} = 0.01$ ). (B) Real MEG data. Average across participants, sessions and pairs of regions of the values of  $\Delta TE$  (reported values were obtained taking the average over delays and then the maximum over time in the same time-delay region used for the results in Fig. 3D,E,F).
In contrast, on the same data FIT could distinguish tactile-discriminative from visually-discriminative information flow from thalamus to cortex (see Fig. S11E-I).
SM4.2 Comparisons with Directed Feature Information (DFI)
A previous study [17] defined a measure, Directed Feature Information (DFI), which computes feature-specific information redundant between the present activity of the receiver and the past activity of the sender, conditioned on the past activity of the receiver. However, DFI used a measure of redundancy that actually conflated the effects of redundancy and synergy (see Section SM1.5 where we consider in detail its definition and its PID decomposition). Because of this, DFI can be negative and thus not interpretable as measure of information flow. Moreover, because DFI discounts only past activity of the sender rather than its feature-specific information, it is less precise and less conservative in localizing direction and timing of feature-specific information flow.
The above properties are expected from theoretical considerations but were also demonstrated by us in the following numerical simulations. We computed DFI in the two simulations described in Section SM2.1 (Fig. S15). We found that, in general, DFI had a trend similar to FIT, increasing with the amount of stimulus-feature-related transfer from  $X$  to  $Y$  ( $W_{stim}$ ) and decreasing with the amount of stimulus-unrelated transfer ( $W_{noise}$ ). However, DFI had several false positives (cases when there was no transmission in the ground truth of the simulated data but it was detected as significant by the algorithm) and also had several false negatives (cases when there was transmission in the ground truth of the simulated data but it resulted as non significant by the algorithm). In comparison, FIT under the same conditions and same simulations had none, see Fig. 2A). More importantly, as a consequence of its inability to include only redundancy and discard synergy, DFI values were very often negative, and could be negative over time both at baseline and during stimulus-feature-related transmission (Fig. S15B).
The limitations of DFI for individuating directed well time-resolved flow of information about specific stimulus features were further tested with the bidirectional information transfer simulations described in detail in Section SM2.4. We remind briefly that in these simulations we simulated a scenario with bidirectional communication between  $X$  and  $Y$  with stimulus-feature-related transfer from  $X$  and stimulus-unrelated transfer from  $Y$  to  $X$  (Fig. S5A). In brief, both  $X$  and  $Y$  received information directly from a feature-information-sending node  $S$ .  $X$  received feature information from  $S$  early on (between 50 and 90 ms) and  $Y$  received feature information from  $S$  at a later time (between 110 and 150 ms).  $X$  sent its entire activity to  $Y$  (therefore communicating its feature information when it became available).  $Y$  instead only sent to  $Y$  a part of its activity that did not carry feature information. We found that while DFI had a significant positive bump from  $X$  to  $Y$  in the [60, 100]ms time window, it also had a significant negative bump from  $Y$  to  $X$  in the time window in which  $X$  encoded the feature [50, 90]ms. Crucially, the presence of significant DFI from  $Y$  to  $X$  preceding in time the DFI from  $X$  to  $Y$  would be interpreted that there is a bidirectional flow of stimulus-feature information, occurring first from  $Y$  to  $X$  and then from  $X$  to  $Y$ . Therefore, DFI could not capture correctly neither the directionality nor the timing of the stimulus-feature information flow that we put in the simulations.
For FIT, which is a non-negative measure, we always used one-tailed tests to determine whether the measured values were significantly larger than the 99th percentile of the null hypothesis distribution obtained as described in Section SM1.7.
For DFI, which is an unsigned measure, we implemented a two-tailed test. Analogous to our method for FIT, we computed two null hypothesis distributions: one by shuffling  $S$  across all trials, and one by shuffling  $X$  for fixed values of  $S$ . We then tested whether DFI was either above the 99.5th percentile of the element-wise maximum or below the 0.5th percentile of the element-wise minimum of these two null hypothesis distributions. If one of these conditions was met, we assigned significance to DFI.
Lastly, we computed DFI on the three real datasets (MEG, EEG and spiking activity) presented in the main text. We found (Fig. S5C-E) that the problems with DFI predicted by mathematics (see Section SM1.5) and encountered simulations are also found in the neural datasets. On real data, DFI was very often negative and it did not detect directionality or feature specificity in cases in which we would expect from previous literature that specificity or directionality should exist.
In the MEG dataset (Fig. S5D), DFI had negative values and thus not interpretable as measure of information transfer. Unlike FIT, DFI could not detect that (as predicted by previous studies) stimulus information is stronger in the feedforward than in the feedback direction, and DFI could not detect that feedforward stimulus information is stronger in correct than error trials (an important result found by FIT).
In the EEG dataset (Fig. S5C), DFI was negative and thus not interpretable as measure of information transfer. The comparison of the DFI results between eye visibility features and directionally of cross-hemispheric transfer could not support the conclusion (predicted by findings in previous literature and confirmed by the FIT analysis) that across-hemisphere information transfer is directional from contra- to ipsi-lateral (DFI does not detected a leading direction of RE information transfer) and is feature specific (DFI does not detected a difference between LE and RE information in the R to L hemisphere communication).
In the thalamocortical spikes data (Fig. S5E), DFI has mostly positive values which are thus interpretable in terms of information transmitted. DFI confirms (though with lower statistical power) the FIT results than in both the somatosensory and visual corticothalamic pathway more information is transmitted feedforward about the corresponding sensory modality (more visual than somatosensory information transmitted from visual thalamus to visual cortex, and more somatosensory than visual information transmitted from somatosensory thalamus to somatosensory cortex). However, DFI failed to demonstrate that, as expected from well-established neurophysiological findings, more information about such simple stimulus features is transmitted from thalamus to cortex than from cortex to thalamus.
In sum, our results lead us to conclude that the definition of redundancy used in DFI that, unlike the more refined one arising from PID, conflates synergistic and redundant effects, leads to major problems predicted by theory and confirmed by simulation and in real data. Our results suggest that DFI is not robust or refined enough to be applied generally and systematically to brain data, and that
the advances provided by FIT with respect to DFI are important not only conceptually but also for the analysis of empirical datasets.