HomeNatureDistinguishing externally from saccade-induced motion in visual cortex

Distinguishing externally from saccade-induced motion in visual cortex

Mouse handling

Experiments were conducted in accordance with the regulations of the Institutional Animal Care and Use Committee of the University of California, San Diego, and of the University of California, San Francisco. All mice used in this study were wild-type C57BL/6J males or females from the Jackson Laboratory (JAX 000664) and were of postnatal ages of 3 to 6 months. No statistical methods were used to predetermine sample size. The experimenter was not blind to the experimental conditions.

Animals were familiarized to head fixation for at least 2 weeks before recording. During this time, they were also familiarized to visual stimuli that would be used during recording. Animals were head-fixed on a custom-made passive treadmill, either circular or linear, and were free to run.

Eye tracking

Video-oculography was used to track the movement of the right eye in both freely moving and head-fixed mice, contralateral to the hemisphere in which recordings were conducted.

In freely moving mice, the right eye was tracked using a miniature camera (Arducam Noir Spy Camera) mounted on a custom-designed holder attached to the skull. The eye was illuminated using an infrared LED mounted on the holder. The video was acquired at 90 Hz through Raspberry Pi 3B+ using RPiCamera-Plugin51.

For head-fixed experiments, a high-speed camera (IMPERX, IPX-VGA-210-L) was fitted with a 45-mm extension tube, a 50-mm lens (Fujifilm, Fujinon HF50HA-1B) and an infrared pass filter (Edmund Optics, 65-796). Images were acquired at 200 Hz through a frame grabber (National Instrument, PCIe-1427). An infrared hot mirror (Edmund Optics, 43-958) was placed parallel to the antero-posterior axis of the animal (1 inch from the eye) in between the animal and the LCD monitor, and the camera captured the image of the eye through its reflection. The camera was angled at 59° relative to the antero-posterior axis. Three infrared 880-nm LED emitters (Digi-Key, PDI-E803) were used to illuminate the eye.

Measuring the angular position of the eye

In head-fixed animals, one of the three infrared LEDs (see above) was aligned with the optical axis of the camera and served as a reference to calculate pupil position. The pupil was identified by thresholding and fitting an ellipse. We computed α, the angular position of the eye, according to sin(α) = d/Rp, where d is the projected distance on the camera image between the centre of the ellipse and the corneal reflection (CR) of the reference LED and Rp is the length of the radius that connects the rotational centre of the eye with the centre of the pupil on the plane that harbours the pupil. Note that Rp is shorter than the radius of the eyeball. Rp was estimated before the experiments as follows: the camera, together with the reference LED, was swung by calibration angles γ of ±10° along a circumference centred on the rotational centre of the eye (more precisely, on the rotational centre of the mirror image of the eye, as the eye was imaged through an infrared mirror) such that the CR of the reference LED remained stationary relative to the image frame of the camera. We used different values of d obtained with different γ to estimate Rp. Complicating the issue is the fact that Rp is not fixed but changes with the size of the pupil (that is, the distance from the rotational centre of the eye to the plane that harbours the pupil increases with constriction of the pupil52). We thus computed Rp under various luminance conditions to change pupil diameter (Dp, the long axis of the fitted ellipse) and obtained the following linear relationship: Rp = r – a × Dp, where r is the radius of the eyeball; a typically ranges between 0.05 and 0.25. During eye tracking in both freely moving and head-fixed animals, this relationship was used to determine Rp for every video frame on the basis of pupil diameter. In some mice, Rp was estimated using the relationship obtained from littermates or other similarly sized mice. The details of the eye tracking method during head fixation have been published previously53,54.

In freely moving mice, to delineate the pupil, eight points along the edge of the pupil were tracked post hoc using DeepLabCut55 and were fitted with an ellipse. The centre of the pupil was defined as the centre of the ellipse, and the centre of the projected eye on camera C (equivalent to CR in head-fixed mice; see above) was estimated by using the orientations of the ellipses at multiple pupil positions where d is the projected distance between C and the centre of the pupil. The angular position of the eye, α, was computed as in head-fixed animals according to sin(α) = d/Rp. Rp was estimated from the equation Rp = r – a × Dp obtained under head fixation.


Mice were implanted with either a custom T-shaped head bar (head-fixed experiments) or three threaded screw inserts arranged in a triangle (head-fixed and freely moving experiments; McMaster-Carr, 92395A109). Implantation was done stereotactically using an inclinometer (Level Developments, DAS-30-R) connected to a USB I/O device (National Instruments, USB-6008), such that the axes of the electrode manipulators for acute, head-fixed recordings would be aligned to the antero-posterior, medio-lateral and dorso-ventral axes of the skull. Mice were anaesthetized with 1–1.5% isoflurane and kept on a feedback-regulated heating pad to maintain body temperature at 37 °C (FHC, 40-90-8D). Before surgery, mice were given buprenorphine subcutaneously. Before incision, topical lidocaine cream was applied to the skin. Once the scalp and fascia were removed, the head bar or the screw inserts were cemented using dental cement (Lang Dental, Ortho-Jet for head bars; 3M ESPE, Relyx Unicem2 for screw inserts). Animals were allowed to recover in their home cage for at least 1 week following surgery.

For mice prepared for freely moving experiments, an extracellular electrode (Diagnostic Biochips, P64-4) mounted on a custom-designed hat for chronic recording was implanted 1 d before the recording session using dental cement. This procedure was performed weeks after initial implantation of the screw inserts. Mice were anaesthetized with 1–1.5% isoflurane and kept on a feedback-regulated heating pad. The electrode held by a holder was lowered to 1,100 mm below the pia surface using micromanipulators, and the hat was cemented in place before retracting the holder. The cranial window over V1 was ~200 mm by ~200 mm and was covered with silicone gel after electrode insertion to prevent V1 from drying. A ground wire (A-M Systems) was inserted in the cerebellum. A custom-designed camera mount was also attached to the head using the previously implanted screw threads (see above).

In head-fixed experiments, cranial windows for extracellular recording were made 1 or 2 d before the recording sessions. For all recordings, the size was ~500 µm to 1 mm by ~500 µm to 1 mm. Whiskers that would interfere with eye tracking were also trimmed at this point. Following craniotomy, the window was sealed with biocompatible silicone sealant until the recording session (World Precision Instruments, Kwik-Cast). The cranial windows were centred around the following coordinates that were marked during head bar or screw insert implantation:

V1 recording: 2.7 mm lateral to the midline, 4.1 mm posterior to the bregma

Pulvinar recording: 1.2 mm lateral to the midline, 1.9 mm posterior to the bregma

dLGN recording: 2.4 mm lateral to the midline, 2.2 mm posterior to the bregma

For identification of pulvinar neurons that send projections to V1 through optogenetic antidromic activation, AAV2/1.hSyn.ChR2(H134R)-eYFP.WPRE.hGH (Addgene, 26973P) was injected into the pulvinar in the left hemisphere, before implantation of the head bar or screw heads.

Visual stimulation

Visual stimuli were presented on an LCD monitor running at 240 Hz (Gigabyte, AORUS KD25F) to the right eye, contralateral to the hemisphere in which recordings were performed. The monitor was angled at 31° anticlockwise relative to the antero-posterior axis of the animal and tilted 20° towards the animal relative to the gravitational axis. It was positioned such that the tangent point between the plane of the monitor and a sphere around the centre of the eye was in the centre of the monitor. The distance from the centre of the eye to the tangent point was 133 mm, with the monitor covering 128° of the field of view horizontally and 97° vertically. In the experiment described in Fig. 2g (a full-field flash), an LCD monitor running at 75 Hz was used.

The static vertical grating used in the experiments described in Figs. 2 and 5 was a full-field sinusoidal grating with 70% contrast, a spatial frequency of 0.08 cycles per degree (cpd) and a mean luminance of 40–60 cd m–2 (gamma corrected; fixed luminance for each animal). It was spherically morphed around the centre of the animal’s right eye to maintain the same spatial frequency across different spatial locations on the retina. For pseudo-saccades, the exact same grating was quickly shifted horizontally once every 1.5 s on average, over the span of seven frames (six inter-frame intervals, 25 ms). The speed of the shift over the seven frames was linear. The direction and amplitude of each shift were predetermined by randomly drawing from the distribution of real saccades collected separately from wild-type unmanipulated mice. For a nasal pseudo-saccade, the grating was shifted in the temporal direction, and, for a temporal pseudo-saccade, the grating was shifted in the nasal direction. Post hoc, every pseudo-saccade was checked for display errors such as a dropped frame. All pseudo-saccades that occurred within 500 ms of a real saccade were also discarded from further analysis, which resulted in about 350 pseudo-saccades for each animal over a span of 10 min. We then resampled the pseudo-saccades to match the direction and amplitude of the real saccades collected from the same animal. To increase statistical power, we resampled two matching pseudo-saccade events for every saccade. The mean ± s.d. of the difference in amplitude between a real saccade and its matched pseudo-saccades was 0.18° ± 0.47° (446 pseudo-saccades, 4 mice) for the experiments in Fig. 3e and 0.18° ± 0.45° (942 pseudo-saccades, 9 mice) in Fig. 5a.

For every animal, response to pseudo-saccades was collected at the beginning of the experiment. Response to real saccades using the static grating was collected after the pseudo-saccade session. The two responses were collected separately, to maximize our chances of obtaining saccades whose responses were not contaminated by pseudo-saccade responses.

To verify the absence of visual responses, following either intraocular TTX injection or muscimol injection in dLGN, we used the following visual stimuli: for the intraocular TTX injections, we used a full-field luminance change from 0 cd m2 to 100 cd m–2 lasting 26 ms. For muscimol injection in dLGN, we used a full-field vertical grating (0.02 cpd; contrast, 0.5), presented every 10 s for 32 ms and preceded and followed by a grey screen of the same average luminance of 40 cd m–2.

All visual stimulation protocols were custom written in LabVIEW (National Instruments) and MATLAB (Mathworks) using Psychophysics Toolbox 3 (refs 56,57).

Acute extracellular recording in head-fixed mice

All recordings in this study were performed on the left hemisphere. On the day of recording, animals were first head-fixed and the Kwik-Cast sealant was gently removed. Artificial cerebrospinal fluid (140 mM NaCl, 2.5 mM KCl, 2.5 mM CaCl2, 1.3 mM MgSO4, 1.0 mM NaH2PO4, 20 mM HEPES and 11 mM glucose, adjusted to pH 7.4) was quickly applied to the craniotomy to prevent the exposed brain from drying. Different configurations of silicon probes were used over the course of the study: A2x32-5mm-25-200-177-A64 (NeuroNexus), A1x64-Poly2-6mm-23s-160-A64 (NeuroNexus), A1x32-Poly2-10mm-50s-177-A32 (NeuroNexus) and ASSY-77 H2 (Cambridge NeuroTech). Using a manipulator (Luigs & Neumann), the probes were slowly lowered to the recording site. Probes were lowered to 1,000 μm below the pia for V1, 3,000 μm below the pia for dLGN and 2,900 μm below the pia for the pulvinar. For recordings in the thalamus, the probes were painted with lipophilic DiI before insertion visualization of the recording track. Successful targeting was verified post hoc.

For optogenetic activation of the axon terminals of pulvinar neurons, a glass fibreoptic cable (960-μm core, NA = 0.63; Doric Lenses) connected to a 465-nm LED light source (Doric Lenses, LEDC1-B_FC) was placed ~500 μm above the craniotomy on V1. The light source was driven by an LED driver (Thorlabs, LEDD1B) at 1,000 mA for 1 ms every 6 s for 10 min (100 trials).

Recordings were started 15 min after insertion of the probes. Signals were sampled at 30 kS s–1 using 64 channel headstages (Intan Technologies, C3315) combined with adaptors (NeuroNexus, Adpt.A64-Omnetics32_2x-sm), connected to an RHD USB interface board (Intan Technologies, C3100). The interface board was also used to acquire signals from photodiodes (TAOS, TSL253R) placed on the visual stimulation monitor as well as TTL pulses used to trigger the eye tracking camera and the LED. These signals were used during analyses to synchronize visual stimulus timings, video acquisition timings and LED photostimulation timings with electrophysiological recordings. All raw data were stored for offline analyses. Occasionally, we recorded from the same animal on two successive days, provided no pharmacological manipulation was performed on the first day. In these instances, the craniotomy was resealed with Kwik-Cast after the first recording session. For post hoc histological analysis, brains were fixed in 4% paraformaldehyde (PFA) in PBS overnight at 4 °C.

Extracellular recording in freely moving mice

Mice were habituated in an acrylic open-air recording chamber under ambient light (length × width × height = 13.25 inches × 9 inches × 9.5 inches) for 1 h each day for 3 d before the day of recording. On the day of recording, a miniature camera connected to Raspberry Pi (see ‘Eye tracking’) was mounted on the camera mount, and the implanted electrode was connected to an RHD USB interface board (Intan Technologies, C3100). The TTL pulses from Raspberry Pi, used to synchronize the video frames with the electrophysiological signals, were also acquired through the interface board. Each recording session was 90 min long.


Intraocular injection of TTX (40 μM) was performed 2 h before recording under isoflurane anaesthesia. A typical procedure lasted less than 5 min. Carbachol (0.011% (wt/vol)) was co-injected with TTX to prevent the pupil from fully dilating, as a fully dilated pupil reduces the accuracy of eye tracking. Immediately before the injection, a drop of proparacaine hydrochloride ophthalmic solution was applied to the eye as a local anaesthetic (Bausch + Lomb; 0.5%). TTX solution was injected intravitreally using a bevelled glass micropipette (tip diameter, ~50 μm) on a microinjector (Nanoject II, Drummond) mounted on a manual manipulator. One microlitre was injected in each eye, at a speed of 46 nl s–1. In some animals, the injection solution also contained NBQX (2,3-dioxo-6-nitro-7-sulfamoyl-benzo[f]quinoxaline; 100 μM) and APV ((2R)-amino-5-phosphonovaleric acid; 100 μM). The animals were head-fixed for recording following a 2-h recovery period in their home cage. Suppression of retinal activity was confirmed for every experiment by a lack of response in visual cortex to a full-field flash of the LCD monitor.

Silencing of the dLGN and pulvinar was performed by injecting 30 nl of 5.5 mM muscimol-BODIPY at a speed of 300 nl min–1, using a bevelled glass pipette (tip diameter, ~20–40 μm) on a UMP3 microinjector with a Micro4 controller (World Precision Instruments). The injector was mounted on a micromanipulator (Luigs & Neumann) for stereotactic injection. In two of the pulvinar silencing experiments, TTX was used instead. The concentration of TTX was 60 μM, and 40 μl was injected at a speed of 40 μl min–1. After recording, brains were fixed in 4% PFA in PBS overnight at 4 °C for histological analysis of BODIPY the next day.


Anaesthetized mice were perfused transcardially with 4% PFA in PBS (pH 7.4). Brains were removed and further postfixed in 4% PFA in PBS at 4 °C overnight, after which the solution was replaced with PBS. They were kept at 4 °C until they were coronally sectioned (100-μm sections) with a Vibratome. Sections were mounted in Vectashield mounting medium containing DAPI (Vector Laboratories, H1500) and imaged with a camera (Olympus, DP72) attached to an MVX10 stereoscope (Olympus).


Detection of saccades

For head-fixed mice, saccades were detected post hoc from the eye tracking data, using a custom-written algorithm in MATLAB. The algorithm searched for any event in which the angular position of the eye changed by more than 0.75° along the horizontal axis in one video frame (5 ms). We discarded all events where the eye position did not move in the same direction for at least three successive frames (15 ms) and in which the peak amplitude of the eye movement was below 3°. Furthermore, to eliminate the influence of preceding saccades on V1 responses, we only analysed saccades that occurred in isolation, that is, that were preceded by a period of at least 500 ms during which the eye did not move.

In freely moving animals, a custom algorithm searched for events in which the eye position changed by more than 5.5° in any direction in one video frame (11 ms). This equates to 500° per second, exceeding the speed of most head movements in mice58 and thus ensuring that the detected eye movements were not image-stabilizing movements (that is, vestibulo-ocular reflexes). The beginning of the saccade was defined as the first frame in which eye movement speed exceeded 200° per second. The saccades were required to be at least two frames long (22 ms), and the vectors of the eye movement between successive frames in a saccade event were required to be within 45° of each other.

Unit isolation

Single units from extracellular recordings were isolated using KiloSort59 and visualized using Phy for further manual merging and splitting. The quality of the isolated units was assessed using refractory period violations and stability of amplitude. The depth for each unit was assigned according to the electrode site at which its amplitude was the largest. For V1 recordings, units with trough-to-peak times longer than 0.5 ms were categorized as regular-spiking neurons. Units with shorter trough-to-peak times were categorized as fast-spiking neurons. Multi-units were defined as the collection of all units that remained after excluding noise using Phy. In the main text, we refer to isolated single units as neurons.

We used the spontaneous FR to register the recording depth across experiments. We approximated the border between layer 4 and layer 5 at ~125 μm above the channel with maximum spontaneous FR. Channels within 200 μm below this border were assigned to layer 5, and channels within 150 μm above the border were assigned to layer 4.

Inclusion criteria

Only animals with at least 15 saccades in each direction were analysed. For this study, we focused on the saccade-related activity of V1 neurons. Nonetheless, we found single units in our recordings whose activity correlated with stationary eye position (putative ‘eye position units’), in both control and TTX-blinded animals. Because there is a correlation between the direction of saccades and the position of the eye along the horizontal plane before the saccade (that is, the more temporal the position of the eye before the saccade, the more likely the upcoming saccade will be nasal), some of these units were capable of discriminating the direction of future saccades, regardless of whether they responded to saccade onset. While these units represent a minority of the population, they would introduce a confounder in the current study because, rather than discriminating saccade direction, they code for eye position. Thus, for analyses of single units in head-fixed mice, we excluded putative eye position units, that is, units whose baseline activity (measured 500 ms before the onset of saccades) was significantly different between the two directions of the upcoming saccades (nasal and temporal). These typically accounted for 1–5% of all units in each recording. In freely moving experiments, all units were considered.

Response to saccades and pseudo-saccades

Saccades in freely moving animals were categorized into eight evenly spaced directions. To determine whether a unit was responsive to saccades, we proceeded as follows: we performed a Kruskal–Wallis test using the response and baseline activity of the unit in each of the eight directions (total of 16 categories). Response was defined as the number of spikes within 100 ms of the onset of saccades, while baseline activity was defined as the number of spikes in a 100-ms window from −300 ms to −200 ms with respect to saccade onset. If the unit passed this test (critical value, 0.05), we proceeded to perform multiple comparisons among the 16 categories using Tukey’s honestly significant difference procedure. A unit was considered responsive if the average response to any of the eight directions was 50% above or below the average baseline activity for the corresponding direction and met at least one of the following two criteria: (1) presence of a significant difference between baseline and response for at least one direction and (2) presence of a significant difference between the responses to any two of the eight directions.

In head-fixed experiments, units were considered responsive to saccades if they met either one of the following two criteria: (1) if the number of spikes elicited within 100 ms of saccade onset was significantly different from baseline for either the nasal or temporal direction (baseline was calculated as the number of spikes within a 100-ms window from −300 ms to −200 ms with respect to saccade onset) or (2) if the number of spikes elicited within 100 ms of saccade onset was significantly different between the nasal and temporal directions. Statistical significance was determined by rank-sum test. To account for multiple comparisons, we controlled the false discovery rate to 10% using q values.

All reported responses in the main text are average FRs within the 100-ms window following saccade onset unless otherwise noted.

Direction selectivity and discriminability

The NT discriminability of each single unit was calculated as the area under the receiver operating characteristic curve (AROC), linearly rescaled to range from −1 to 1 (Gini coefficient), that is, 2 × AROC – 1. NT discriminability was calculated on the basis of two directions, nasal and temporal. The order was fixed, such that negative values indicate a preference for temporal saccades and positive values indicate a preference for nasal saccades; that is, the sign of NT discriminability corresponds to the preferred direction. We calculated the discriminability using two series of values: (1) the number of spikes induced by each nasal saccade and (2) the number of spikes induced by each temporal saccade. The number of induced spikes was calculated as the total number of spikes within the first 100 ms of saccade or pseudo-saccade onset without baseline subtraction. In freely moving animals, the preferred direction was defined as the direction with the maximum average FR within the first 100 ms of saccade onset. The discriminability index was calculated as the absolute value of the Gini coefficient between the preferred direction and the non-preferred direction (direction opposite to the preferred direction). The statistical significance of discriminability was calculated using a rank-sum test comparing the two series of values used to calculate discriminability itself, and the false discovery rate was controlled to be below 10% using q values. The direction selectivity index (Extended Data Fig. 1) was defined as (Rpref – Rnon-pref)/(Rpref + Rnon-pref), where Rpref and Rnon-pref are the number of spikes within the first 100 ms of saccade onset in the preferred and non-preferred directions, respectively.

Average PETH with baseline normalization

When generating average PETHs with baseline normalization, neurons with a baseline below 0.5 Hz were excluded to avoid substantial biases resulting from extremely low FR. The baseline of each neuron to saccades or pseudo-saccades was calculated using its mean activity 500 ms to 200 ms before onset. For other visual stimuli, mean activity between −200 and 0 ms relative to saccade onset was used. Note that this process was applied for visualization purposes only, and all statistics such as direction discriminability, the direction selectivity index and the differences in evoked FRs were calculated using all relevant neurons. The statistical significance of the difference between PETHs for the preferred and non-preferred direction was calculated for each 20-ms bin. This was calculated by signed-rank test, and statistical significance was determined by setting the false discovery rate to be below 10% through the Benjamini–Hochberg procedure.

Modelling of saccade response on a vertical grating with visual and non-visual inputs

Saccade responses on a vertical grating (the number of evoked spikes within 100 ms of saccade onset) were predicted from (1) pseudo-saccade response, (2) saccade response on a grey screen or (3) the sum of the two responses. All responses were baseline-subtracted values. The model is a linear regression (fivefold cross-validated) with no intercept, followed by thresholding, which ensured that the predicted FR did not fall below 0 Hz. That is, if the predicted decrease in the evoked number of spikes exceeded the baseline FR, the value was adjusted so that the sum of the prediction and the baseline was zero. The explained variance is calculated as the explained sum of squares divided by the total sum of squares.

Identification of pulvinar neurons with axonal projections to V1 through antidromic activation

V1 was illuminated with 1-ms-long pulses (100 trials) from a 465-nm blue LED to induce antidromic spikes (see above). Success of antidromic activation was defined by two criteria: (1) greater than 20% probability of observing at least one spike within 5 ms of the onset of LED illumination across trials and (2) less than 0.5 ms jitter (that is, the s.d. of the latency distribution of the first spikes occurring within the 5-ms window following LED onset was less than 0.5 ms).

Classification of saccade direction in head-fixed mice

We classified the direction of saccades and pseudo-saccades using quadratic discriminant analysis (QDA) on the response of each single unit. The spiking activity of each unit was counted in 20-ms bins, and the activity at 60 ms after onset for each event was taken as the response. The discriminant analysis was preceded by principal-component analysis (PCA) for dimensionality reduction. Only single units with average FR above 0.5 Hz were used. For each event of saccades or pseudo-saccades, the classifier assigned either nasal or temporal direction.

Training data consisted of the response to selected pseudo-saccades. This set of pseudo-saccades was selected such that the amplitudes and number of events for the nasal and temporal directions were matched. This ensured that the classifier depended on the NT discriminability of each unit, rather than on the difference in pseudo-saccade amplitude or frequency. The training dataset was first standardized and subjected to PCA. We limited the number of principal components to 20% of the total number of saccades in the training dataset to avoid overfitting. We then trained QDA for classification. The resulting models for PCA and QDA were applied to the test dataset, which comprised responses to either real saccades or pseudo-saccades that were excluded from the training dataset (10-fold cross-validation).

To pool single units recorded from multiple animals, we closely matched the direction and amplitude of the pseudo-saccades for each animal (see ‘Visual stimulation’). From this dataset, we further generated a random subset in which the amplitudes for the nasal and temporal pseudo-saccades were closely matched. Ten such datasets were generated to be used as training datasets. For the test dataset, saccade data from different animals were pooled on the basis of the direction and amplitude of saccades, again such that the directions and amplitudes were closely matched between animals.

To calculate classifier performance as a function of the number of single units used for classification, a random subset of units (5, 10, 15, 20, 30, 40, 50, 100, 175 or 250 units) was chosen from the pooled data without replacement, before being subjected to training and testing. Random selection of units was repeated 50 times, for every randomly generated training dataset (see above), resulting in 500 results that were averaged to calculate decoder performance.

To rank the contribution of each unit to the classifier model, we calculated the permutation feature importance. In brief, we permuted the data from one unit at a time in the pseudo-saccade training dataset during 10-fold cross-validation, to break the relationship between unit activity and pseudo-saccade direction. We then calculated the increase in prediction error resulting from the permutation procedure. To calculate the total contribution from single units with the highest feature importance, we permuted the data from the corresponding units at the same time.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.



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