Dissociation of Attentional State and Behavioral Outcome Using Local Field Potentials

Effect of attention and behavior on firing rate and LFP power

We found that differences in target-onset times for hits versus miss conditions had a strong effect on our results, especially at low frequencies (as discussed below in more detail). Therefore, we analyzed the data after matching the target-onset time distributions of the hit and miss trials of the respective attention conditions (see Materials and Methods for details). Extended Data Figure 2-1A–G shows the same analyses as Figure 2A–G but before matching the target-onset time distribution (Extended Data Fig. 2-1H).

Figure 2A shows the average peristimulus time histogram (PSTH) across 643 electrodes across 21 sessions for the four validly cued conditions during 500–0 ms before the target onset (see Materials and Methods for details). Neurons fired at both the positive and negative phases of the counterphasing stimulus to produce a strong oscillatory signal at 20 Hz (De Valois et al., 1982). The average firing rates over this 500 ms interval are shown in the inset. The firing rate was higher when the monkeys attended and detected (hit) the target presented inside the RF (Attend-In Valid Hit condition; blue) than when they attended and detected the target outside the RF (Attend-Out Valid Hit condition; red; Bonferroni corrected p = 0.01; Wilcoxon rank-sum test). This recapitulates the classic effect of visual attention on the firing rates of cortical neurons, whereby the responses to attended stimuli in the RF are enhanced, on average, relative to unattended stimuli (McAdams and Maunsell, 1999). The conditions when the monkeys missed the target (Attend-Out Valid Miss, magenta, and Attend-In Valid Miss, cyan) produced a response that was intermediate between the two hit conditions since attention is expected to be on the uncued side leading to the miss.

Event-related potential (ERP), obtained by averaging the LFP traces for different conditions, showed similar trends across four conditions (Fig. 2B). However, these traces showed a pronounced difference between the hit and miss conditions when the target-onset time distributions were not matched (Extended Data Fig. 2-1B). These differences could be largely explained based on differences in target-onset times for hits versus miss conditions because monkeys tended to miss the targets that appeared earlier after stimulus onset than later (Extended Data Fig. 2-1H). Stimulus onset produced a transient elevation in firing rate and a dip in the ERP which reached a steady-state value over several hundred milliseconds [Prakash et al. (2021), their Fig. 1A,B]. Thus, because our analysis window was from 500 to 0 ms before the target onset (which could appear between 500 and 5,500 ms of stimulus onset), earlier target-onset times captured the transient activity for the trials in which the target appeared between 500 and 750 ms after the stimulus onset.

We next examined the effect of attention and behavioral outcomes on LFP power. Figure 2C shows the change in power of each condition from the Attend-Out Valid Hit condition. Attention suppressed the power in lower frequencies (≤14 Hz; blue trace; Benjamini–Yekutieli FDR controlled p < 0.05; Wilcoxon sign-rank test) and increased power in the gamma and high-gamma range (>36 Hz; Benjamini–Yekutieli FDR controlled p < 4.4 × 10⁻¹⁶; Wilcoxon sign-rank test) as well as the steady-state visually evoked potential (SSVEP) frequency of 20 Hz (Benjamini–Yekutieli FDR controlled p = 0.001; Wilcoxon sign-rank test). The effect of behavioral outcome (hit vs miss) was observed when attention was outside the RF and the monkey missed the target (magenta trace; Attend-Out Valid Miss vs Attend-Out Valid Hit) or by comparing the corresponding conditions for the Attend-In condition (i.e., blue vs cyan traces; Attend-In Valid Hit vs Attend-In Valid Miss). Upon visual inspection, low frequencies captured differences in activity related to behavioral outcome, while frequencies closer to gamma distinguished attentional state.

To better dissociate the effects of attentional location and behavioral outcome and examine how the effect of one is influenced by the other, we compared the power spectral densities separately by taking the difference between the attention conditions (attend-in vs attend-out) for the two behavioral outcomes: hit (Fig. 2D, green trace; Fig. 2C, same as the blue trace) and miss (Fig. 2D, yellow trace; Fig. 2C, cyan minus magenta traces). Attention-related suppression of low-frequency power (8–14 Hz; Benjamini–Yekutieli FDR controlled p < 0.01; Wilcoxon sign-rank test) and enhancement of the high-frequency power (>44 Hz; Benjamini–Yekutieli FDR controlled p < 0.05; Wilcoxon sign-rank test) was also observed for the miss condition, albeit the effect was weaker than the hit condition (Fig. 2D, compare green vs yellow traces). Similarly, for behavioral effects, we took the difference between the behavioral outcomes (hit − miss) for the two attention conditions: attend-in (Fig. 2E, blue trace; Fig. 2C, blue minus cyan traces) and attend-out (Fig. 2E, red trace; Fig. 2C, same as the negative of the magenta trace). For the behavioral comparison (Fig. 2E), the power was different mainly in the low-frequency range for both attend-in and attend-out cases, whereas high-frequency power showed only minor differences mainly for the attend-out condition.

Overall, our results show only a modest effect of behavior on LFP data that is mainly in the low-frequency range. But this is largely due to the target-onset matching procedure described above. The difference in power in the very low-frequency range for the missed condition relative to the hit condition was much larger for the nonmatched case (Extended Data Fig. 2-1E) compared with the matched case (Fig. 2E). For example, the change in 4 Hz power of attend-in valid miss (AIVM) relative to attend-in valid hit (AIVH) reduced by more than threefold in distribution matched (0.75 dB) compared with nonmatched case (2.4 dB; Fig. 2E, Extended Data Fig. 2-1E). This shows that the pretarget low-frequency power can spuriously dominate and lead to an overestimation of its behavioral decoding performance if the differences in the distribution of target-onset times between the conditions are not accounted for. For all the analyses, we therefore used trials only after matching target-onset time distributions.

Attentional and behavioral discriminability using firing rate and LFP power

Since the main aim of the study was to compare the ability of different neural measures (such as spiking activity, LFP power, and LFP phase) to discriminate attentional conditions and behavioral outcome, we converted the LFP power and spike responses to d′ values to compare the discriminability across neural measures (Fig. 2F,G; see Materials and Methods for details). Attention discriminability using firing rates (indicated by dashed lines in Fig. 2F) was higher for hit condition (green dotted line) than miss (yellow dotted line), reflecting a larger separation in the means for the hits compared with miss cases (as in Fig. 2A inset). Attention discriminability with LFP power was highest in the gamma band (40–80 Hz), comparable to that of firing rate, and decreased slowly at higher frequencies (Fig. 2F, solid green and yellow traces). Lower frequencies (<30 Hz) had negative d′ (i.e., the attend-in condition had lower power than attend-out as shown in Fig. 2D), but the magnitude of the discriminability was lower than that of the firing rate. On the other hand, very low-frequency (<14 Hz) power was best suited for discriminating the behavior (Fig. 2G) since it had the highest magnitude of discriminability, reflecting the changes in power observed in Figure 2E.

To summarize, two salient results so far are as follows: (1) d′ values for LFP power for attentional discriminability (Attend-In vs out; Fig. 2F) for hit (green trace) and miss condition (yellow trace) were highest in the gamma band, where it was comparable to d′ of firing rate, and decreased in the high-gamma range. It was negative at low frequencies, although the magnitude was less than the gamma range. (2) For behavioral discriminability (Fig. 2G) for attend-in condition (blue solid trace), d′ values were negative at low frequencies, became positive at SSVEP frequency and in high-gamma range, comparable to the discriminability using firing rate (blue dashed line). The highest d′ was observed for the SSVEP frequency. The effect flipped for the attend-out condition in the high-gamma range (red solid trace).

We previously showed that the single-electrode LFP power in the gamma (42–78 Hz) and high-gamma (122–198 Hz) bands performed better than firing rate in decoding attention (Prakash et al., 2021). However, in our present analysis, the power in the gamma and high-gamma ranges did not perform better than firing rate in discriminating the attention condition (Fig. 2F, green trace). This discrepancy is due to the variability in the spectral estimator at individual frequency bins (Jarvis and Mitra, 2001), which decreases d′ values as observed here. However, spectral variability is uncorrelated across frequencies and therefore can be reduced by summing or averaging the power over the frequencies of interest, which can improve the decoding performance (Prakash et al., 2021). We illustrate this fact by performing similar averaging by smoothening over a frequency window using the multitaper method. The extent of frequency smoothening is controlled by the time-bandwidth product (TW) which determines the number of tapers (K) to use (K = 2TW − 1) for maximal spectral concentration. Increasing TW increases the frequency window over which the power is smoothed. As expected, as we increased TW, the attentional d′ in the gamma and high-gamma bands increased and exceeded the d′ of firing rate (Fig. 2H). However, smoothing improves performance only when nearby frequencies are modulated in a similar fashion by attention/behavior. For example, note that the enhanced discriminability at SSVEP was eliminated by this smoothing because the nearby frequencies around the SSVEP frequency did not show this discriminability. Thus, frequency smoothing improves the discriminability only when the neighboring frequencies also perform comparably well. The TW parameter is usually chosen depending on the length of the signal and frequency band of interest. For relatively wider frequency bands like gamma and high-gamma choosing TW of five (which smoothens over a frequency bin of ±10 Hz for a 0.5 s signal) or more is appropriate whereas for a narrower band like alpha (8–12 Hz) and SSVEP, the TW should be kept to low values. For a case where different frequency bands of varying bandwidths are used, TW should be chosen such that the wider and narrower frequency activity is captured sufficiently well. We have used TW = 3 (i.e., five tapers) when analyzing the effect of attention/behavior on the power spectrum, as shown in Figures 2, 3. In the final comparison over different frequency bands shown in Figure 6, power is averaged over different frequency ranges prior to the computation of d′, which is essentially equivalent to using different numbers of tapers for different frequency ranges depending on the bandwidth of the signal of interest.

The neutral cueing condition showed similar results (compare Fig. 2A–H and Extended Data Fig. 2-1I–P). The results are shown after matching the target-onset times because we found similar artifacts as the valid condition when target-onset times were not matched (data not shown). As in the valid condition, firing rates in neutral condition were higher when the target appeared inside the RF than when it appeared outside (Fig. 2A, Extended Data Fig. 2-1I inset), and the ERPs were comparable across conditions (Extended Data Fig. 2-1J). However, there were some important differences as well. Firing rates were different for hits versus misses when the target was inside the RF (Extended Data Fig. 2-1I, blue and cyan dots that correspond to Target-In Neutral Hit vs Target-In Neutral Miss conditions, respectively), but not when the target was outside the RF (Target-Out Neutral Hit vs Target-Out Neutral Miss). This trend was also reflected in the LFP power, with large discriminability in behavior in the gamma range (which was further comparable to the firing rate discriminability) when the target was in the RF (Extended Data Fig. 2-1O, blue trace) but not when outside (Extended Data Fig. 2-1O, red trace). The discriminability between target-in and target-out conditions for hit trials was highest in the gamma range and was comparable to the firing rate (Extended Data Fig. 2-1N, green trace), and the traces were essentially inverted for the miss condition for both firing rate and LFP power (Extended Data Fig. 2-1N, yellow traces). Unlike the valid condition, frequency smoothening did not improve discriminability beyond firing rates (Extended Data Fig. 2-1P). Overall, the behavioral discriminability pattern of the neutral cue was similar to the attentional discriminability of the valid condition (in other words, the effect observed in Fig. 2F was similar to that in Extended Data Fig. 2-1O, while Fig. 2G was similar to Extended Data Fig. 2-1N).

Discrimination of attentional state and behavioral outcome using LFP phase

EEG studies have shown that phases at frequency bands such as alpha (8–12 Hz) are modulated by attention and are informative about behavioral performance (Thut et al., 2006; Busch et al., 2009). We therefore examined the ability of the LFP phase to discriminate the attentional and behavioral states. If the LFP phases at which monkeys detect the target are consistently different from the phases at which they miss, the difference should be reflected in the ERPs, which we did not observe (Fig. 2B; although note that the presence of strong SSVEP may have affected the endogenous alpha rhythm). Because phase is a circular variable, we used the sine component of the phase vector to make it linear (like firing rate and LFP power) in order to calculate d′. This transformation should not affect our results since we are interested in the differences between conditions rather than their absolute values. For valid trials, the phase values were only consistent at the SSVEP frequencies (Fig. 3A), but we did not find a consistent difference across conditions at any frequency, resulting in low attentional and behavioral discriminability compared with the firing rate (Fig. 3B,C). Similar results were obtained when the cosine component was used instead of the sine component (data not shown).

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Figure 3.

Comparison of LFP phase and pairwise phase consistency of individual electrodes and trial-wise firing rate correlation, LFP power correlation, and pairwise phase consistency (PPC) of electrode pairs across validly cued attention and behavioral conditions. A, Mean sine of the LFP phase angle for Attend-In Valid Hit (AIVH; blue), Attend-Out Valid Hit (AOVH; red), Attend-In Valid Miss (AIVM; cyan), and Attend-Out Valid Miss (AOVM; magenta) conditions. B, Mean d′ of firing rate (dashed color lines) and sine of the LFP phase angle (solid lines) between attend-in and attend-out conditions for hit (green) and miss (yellow) conditions. The horizontal dashed black line marks the zero of the y-axis. The horizontal green and yellow patches at the bottom indicate the frequencies at which the d′ of LFP phase angle for hit and miss conditions, respectively, are significantly greater than zero (Wilcoxon signed-rank test, Benjamini–Yekutieli FDR controlled p < 0.05 under unknown dependency). The horizontal black and gray patches at the bottom indicate the frequencies at which the d′ of the LFP phase angle is significantly different from the d′ of firing rate for hit and miss condition, respectively (Wilcoxon rank-sum test, Benjamini–Yekutieli FDR controlled p < 0.05 under unknown dependency). Negative d′ values were multiplied by −1 before performing the significance test. C, Mean d′ of firing rate (dashed color lines) and sine of the LFP phase angle (solid lines) between hit and miss conditions for attend-in (blue) and attend-out (red) conditions. The horizontal dashed black line marks the zero of the y-axis. The horizontal blue and red patches at the bottom indicate the frequencies at which the d′ of LFP phase angle for attend-in and attend-out condition, respectively, are significantly greater than zero (Wilcoxon signed-rank test, Benjamini–Yekutieli FDR controlled p < 0.05 under unknown dependency). The horizontal gray patches at the bottom indicate the frequencies at which the d′ of the LFP phase angle is significantly different from the d′ of firing rate for attend-out condition. (Wilcoxon rank-sum test, Benjamini–Yekutieli FDR controlled p < 0.05 under unknown dependency). Note that the difference between d′ for the LFP phase angle and firing rate for attend-in condition was not significant at any frequency (Wilcoxon rank-sum test, Benjamini–Yekutieli procedure for FDR control under unknown dependency); hence, no patch is shown for that comparison. Negative d′ values were multiplied by −1 before performing the significance test. D, Mean single-electrode pairwise phase consistency (PPC; see Materials and Methods for details) for the four conditions as in A. E, Mean change in single-electrode PPC between attend-in and attend-out conditions for hit (green) and miss condition (yellow). The horizontal dashed black line marks the zero of the y-axis. The horizontal green and yellow patches at the bottom indicate the frequencies at which the change in PPC for hit and miss condition, respectively, is significantly greater than zero (Wilcoxon signed-rank test, Benjamini–Yekutieli FDR controlled p < 0.05 under unknown dependency). F, Mean change in single-electrode PPC between hit and miss conditions for attend-in (blue) and attend-out condition (red). The horizontal dashed black line marks the zero of the y-axis. The horizontal blue and red patches at the bottom indicate the frequencies at which the change in PPC for attend-in and attend-out conditions, respectively, are significantly greater than zero (Wilcoxon signed-rank test, Benjamini–Yekutieli FDR controlled p < 0.05 under unknown dependency). In A–F, mean and SEM are computed like in Figure 2A,G. G, Mean change in trial-wise firing rate correlations for the four conditions relative to the Attend-Out Valid Hit (AOVH) condition. The dashed black line indicates the zero of the y-axis. The asterisks indicate the conditions between which the differences in trial-wise correlation are significant (Wilcoxon rank-sum test; Bonferroni corrected p < 0.05) between the conditions. H, Mean change in trial-wise LFP correlations (solid lines) and firing rate correlation (dashed color lines) between attend-in condition and attend-out condition for hit (green) and miss trials (yellow). The dashed black line indicates the zero of the y-axis. I, Mean change in trial-wise LFP correlation (solid lines) and firing rate correlation (dashed color lines) between hit condition and miss condition for validly cued attend-in (blue) and attend-out (red) conditions. The dashed black line indicates the zero of the y-axis. J, Mean pairwise phase consistency (PPC) across trials for the four conditions as in (A). K, L, Same as E and F but for pairwise phase consistency (PPC) across trials. In G–L, the mean was taken across 50 bootstrap samples of mean across 5,754 pairs, and the shaded lines and error bar indicate the bootstrap mean of SEM across 5,754 electrode pairs. In H, I, K, and L, the significance lines shown at the bottom are calculated using the same approach as B, C, E, and F. A similar comparison of single-electrode phase measures, trial-wise correlations, and PPC for neutrally cued condition is shown in Extended Data Figure 3-1.

Previous studies have shown that pairwise phase consistency (PPC) across pairs of electrodes, which reflects the consistency of the phase difference between electrodes across trials, varies with attentional condition (Rohenkohl et al., 2018; Prakash et al., 2021). We next tested whether the absolute phase of a single electrode also showed any consistency across trials. For this analysis, we computed the PPC, which is an unbiased estimator of the square of the coherence (Vinck et al., 2010), but replaced the phase difference between a pair of electrodes with the absolute phase of one electrode for each trial. This single-electrode PPC is expected to be high if the absolute phase is consistent across trials. However, PPC was high only at the SSVEP frequency (the peak is seen at 24 Hz instead of 20 due to the smoothening effect of multitaper) and its harmonics (Fig. 3D). No consistent trends were observed when we compared across conditions (Fig. 3E,F). Note that since PPC is computed across trials, it is not a single-trial measure, and therefore we cannot obtain d′ values like above. In summary, the absolute phase of the LFP was much less informative about the attentional location or behavioral state than firing rates, and no difference in the consistency of the phase across trials was observed across conditions. Similar results were obtained for the neutral cue (Extended Data Fig. 3-1A–F).

Effect of attention and behavioral outcome on pairwise measures

Conventional measures based on pairs of electrodes, such as correlation and phase consistency, are computed across trials. Before exploring single-trial estimates of such measures, which are required to estimate discriminability, we evaluated the effects of attention and behavior in the traditional way by computing these measures across trials. Consistent with previous studies (Cohen and Maunsell, 2009; Mitchell et al., 2009; Mayo and Maunsell, 2016), attention reduced correlations in firing rate across pairs of electrodes (Attend-Out Valid Hit vs Attend-In Valid Hit; Fig. 3G). The correlation for missed conditions was intermediate to the hit condition (Attend-Out Valid Miss and Attend-In Valid Miss; Fig. 3G), consistent with the changes in firing rate as shown in Figure 2A inset. Correlations between LFP power recorded from two electrodes increased with attention at SSVEP frequency (20 Hz) and its harmonic but reduced for frequencies higher than 50 Hz for valid hit condition (Fig. 3H, green trace). Such modulations were not observed when the animals missed the trials (Fig. 3H, yellow trace). Differences between behavioral outcomes (hit vs miss; Fig. 3I) were small in the high-gamma range, mirroring the small changes observed in firing rate correlations as well. Interestingly, lower frequencies including the SSVEP frequency showed larger differences for the Attend-out condition (Fig. 3I, red trace), which is similar to the strong effect of behavioral differences on SSVEP power observed earlier (Fig. 2G). Overall, these results are consistent with previous studies that showed a reduction in spike count correlation (Cohen and Maunsell, 2009; Mitchell et al., 2009) and LFP power correlation except at SSVEP (Prakash et al., 2021).

Next, we analyzed the PPC between the LFP signals from pairs of electrodes (Fig. 3J–L). PPC increased for valid condition when attention was cued into the RF over a broad range of frequencies between 36 and 106 Hz (Fig. 3K, green trace), although we did not observe much difference beyond 120 Hz even though LFP power was elevated in that range (compare with Fig. 2D, green trace). The reason for this difference between high-frequency power and PPC could be the poor sensitivity of phase synchronization measures at higher frequencies (Ray, 2022). Interestingly, PPC was more sensitive to attentional differences (Fig. 3K) than behavioral differences (Fig. 3L).

For neutral condition (Extended Data Fig. 3-1G–L), the effect of target location (Extended Data Fig. 3-1H,K) was somewhat similar to the behavioral effect of the valid condition (Fig. 3I,L), and the behavioral effect (Extended Data Fig. 3-1I,L) was similar to the attentional effect of the valid condition (Fig. 3H,K), as observed previously with LFP power (Extended Data Fig. 2-1N is similar to Fig. 2G with the two traces flipped horizontally, while Extended Data Fig. 2-1O is similar to Fig. 2F with one trace showing salient effect and the other one close to zero).

Discrimination of attentional state and behavioral outcome using pairwise measures

Modulation of pairwise measures by attentional state and behavioral outcome motivated us to develop methods to obtain the same measures in single trials, which could then be used to obtain discriminability values (d′) like the power and phase measures we used earlier. We devised two independent methods to estimate correlation and phase consistency within a single trial. In the first method, we divided the spiking and LFP signal of a single trial into ten nonoverlapping bins of 50 ms each and computed the firing rate, LFP power, and phase in each bin. We then calculated the correlation and LFP–LFP phase consistency between electrode pairs across bins (Fig. 4, left panel). In the second approach, we used the multitaper method where a single-trial LFP signal was multiplied by nine orthogonal Slepian tapers to obtain nine independent estimates of LFP power and phase (Fig. 4, right panel) and computed their correlation and phase consistency (see Materials and Methods for more details). The first method is more direct because power and LFP values are obtained from nonoverlapping segments of data, although the frequency resolution (reciprocal of the analysis duration in seconds) becomes 20 Hz. The second method uses the same length of data (500 ms) to get several estimates of power and phase (which are independent because the tapers are orthogonal) and therefore has a frequency resolution of 2 Hz. We also used a method based on the Hilbert transform method to estimate instantaneous power and phase at each time point within a trial and then computed correlation and phase consistency across time (Spyropoulos et al., 2024).

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Figure 4.

Illustration of methods used for estimating correlation and pairwise phase consistency within a trial. Binning method (left panel), A single-trial LFP signal of 500 ms duration from two electrodes is first divided into 10 nonoverlapping bins of 50 ms each. Then, the power and phase of each 50 ms LFP segment of the two electrodes were estimated by Fourier transform. Subsequently, we estimated the power correlation and pairwise phase consistency across the ten bins between the pair of electrodes at each frequency between 0 and 200 Hz with 20 Hz resolution. Similarly, the spikes from the two electrodes were also binned and firing rate correlations between the two electrodes were computed across bins (bottom left panel). These correlations were subsequently shuffle corrected (see Materials and Methods). Multitaper method (right panel), We used an alternate method to obtain multiple estimates of power and phase using the multitaper method. LFP signal of 500 ms duration of two electrodes was first multiplied by nine orthogonal Slepian tapers of the same length, and then power and phase of these nine tapered LFP signals were obtained by Fourier transform. Power correlation and PPC were calculated between electrode pairs across tapers at frequencies between 0 and 200 Hz with 2 Hz resolution. The black dot in the PPC vs frequency and correlation versus frequency plots indicates the frequency whose amplitude and phase are shown in the polar plot in the top panel and whose power scatter plot is shown.

Firing rate correlations were reduced with attention for hit trials even when computed over a single trial (Fig. 5A, dashed green line), but not reduced in miss trials (Fig. 5A, dashed yellow line), consistent with the across-trial correlation measures (Fig. 3H). Because these were single-trial measures, we could now calculate and compare the discriminability by calculating d′ values in the same way as before (Fig. 5B). LFP correlations in the high-gamma range could distinguish the attention conditions slightly better than firing rate correlation when the targets were correctly detected (Fig. 5B, green trace), although these d′ values were considerably lower than the ones obtained using firing rate/LFP power (compare with similar traces in Fig. 2F). Similar trends were obtained for behavioral comparison: (1) magnitude of discriminability (Fig. 5D) was higher in the high-gamma range where it was comparable to firing rate correlations for the attend-in condition (Fig. 5D, blue traces), and (2) for the attend-out condition, the low-gamma frequencies were more discriminable (Fig. 5D, red trace) than the firing rate for that condition. In summary, we found that the discriminability of high-gamma and firing rate correlations were comparable. Interestingly, the magnitude of d′ values of bin-wise PPC was considerably higher (Fig. 5F,H) compared with that of correlations in firing rate/power, suggesting that single-trial PPC, especially in the gamma range, was a useful measure to discriminate attention or the behavioral outcome.

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Figure 5.

Comparison of single-trial bin-wise firing rate correlation, bin-wise and taper-wise LFP power correlation, and pairwise phase consistency (PPC) across validly cued attention and behavioral conditions. A, Mean change in single-trial bin-wise LFP power correlation (solid lines) and firing rate correlation (dashed color lines) between validly cued attend-in and attend-out conditions for hit (green) and miss (yellow) conditions. Single-trial bin-wise correlation was measured by dividing the analysis period of 500 ms into 10 nonoverlapping bins and measuring the firing rate or power correlation across bins. Since power was estimated for signals of 50 ms duration, the frequency resolution is 20 Hz. The dashed black line indicates the zero of the y-axis. B, Mean d′ of bin-wise LFP power correlation (solid lines) and firing rate correlation (dashed color lines) between validly cued attend-in and attend-out conditions for hit (green) and miss (yellow) conditions. The dashed black line indicates the zero of the y-axis. C, Mean change in bin-wise LFP power correlation (solid lines) and firing rate correlation (dashed color lines) between hit and miss conditions for validly cued attend-in (blue) and attend-out (red) conditions. The dashed black line indicates the zero of the y-axis. D, Mean d′ of bin-wise LFP power correlation (solid lines) and firing rate correlation (dashed color lines) between hit and miss conditions for validly cued attend-in (blue) and attend-out (red) conditions. The dashed black line indicates the zero of the y-axis. E–H, Same as A–D but for single-trial bin-wise PPC. Single-trial bin-wise PPC was computed across the same 10 nonoverlapping bins used to compute power correlations. In A–H, the colored patches at the bottom indicate significance like that in Figure 3, but here the FDR was controlled using the Benjamini–Hochberg procedure. I–P, Same as A–H but for single-trial taper-wise power correlation and PPC. Here power correlation and PPC are computed by using the multitaper method. Specifically, we use TW = 5 to get 9 (2TW-1) estimates of power and phase values per trial and compute the power correlation or PPC between electrode pairs across these nine values. Unlike A–H, FDR was controlled by using the Benjamini–Yekutieli procedure under unknown dependency. In A–P, the mean was taken across 50 bootstrap samples of mean across 5,754 pairs and shaded lines indicate the bootstrap mean of SEM across 5,754 electrode pairs. A similar comparison of single-trial measures for neutrally cued condition computed using the binning method and multitaper method are shown in Extended Data Figure 5-1 and those computed using the Hilbert transform method for valid and neutral conditions are shown in Extended Data Figure 5-2.

Although the binning method showed some discriminability, it was inherently limited in its frequency resolution. To overcome this limitation, we used the multitaper method and computed correlation and PPC across tapers (Fig. 4, Method 2). The binning and multitaper methods produced similar results, validating our approaches. For correlations (Fig. 5I–L), while the trends were generally similar to the bin-wise approach (compare with Fig. 5A–D), we found two important differences. First, while the high-gamma band beyond 100 Hz essentially reflected the trends observed in firing rates for the bin-wise method (Fig. 5A), the multitaper method produced negligible correlation differences above 100 Hz (Fig. 5I). On the other hand, the difference in LFP correlations between the conditions improved remarkably in the gamma band and below (<60 Hz) for taper-wise method, and hence the discriminability index increased threefold compared with the binning method (compare Fig. 5B,D with Fig. 5J,L; note the difference in scales). In contrast, the PPC measure (Fig. 5M–P) remained comparable across both methods (Fig. 5E–H). Among the electrode pair measures, PPC in the low-frequency to mid-frequency range was the most useful measure to discriminate attention and behavior. The neutral conditions (Extended Data Fig. 5-1), reflected the same results as observed for valid trials. Single-trial estimates of power correlation and phase consistency calculated using the Hilbert transform method (Extended Data Fig. 5-2) yielded largely comparable results.

Finally, because our analyses in Figure 2H demonstrated that discriminability differs as a function of smoothening over frequency ranges, we computed all the LFP measures within the frequency bands of alpha (8–12 Hz), SSVEP (18–22 Hz), gamma (40–80 Hz), and high-gamma (120–200 Hz) and then computed their d′ values. Note that the d′ values obtained this way are not similar to the simple average of d′ values of individual frequencies computed earlier (Figs. 2, 5). There are two reasons for this. First, as discussed above, averaging the LFP power across frequencies reduces the variability due to the spectral estimator which improves d′, as shown in Figure 2H where increasing the number of tapers increases d′. Second, the total power in a band is dominated by lower frequencies within the band, since power falls with increasing frequency, and hence the d′ values are biased toward that of lower frequencies rather than reflecting average d′. We summarized our results in Figure 6. The same results for the neutral condition are shown in Extended Data Figure 6-1. Our key findings are summarized as follows: (1) LFP power in the high-gamma and gamma bands were best suited for discriminating “attend-in” versus “attend-out” attentional state (d′ of 0.32 ± 0.01 and 0.3 ± 0.01; Fig. 6A). Firing rate was the next most informative measure (d′ of 0.23 ± 0.01; Fig. 6A), but discriminability using gamma was significantly greater than that of firing rate (p = 4.6 × 10⁻⁵; Wilcoxon rank-sum test). Alpha power also had strong discriminability (d′ of −0.14 ± 0.01), although the magnitude was significantly less than the firing rate (p = 1.1 × 10⁻⁶; Wilcoxon rank-sum test). (2) While gamma, high-gamma, and spiking activity could all be reliably used to discriminate attentional state, alpha power, SSVEP power, and SSVEP phase were the most informative measures for discriminating behavioral outcome (Fig. 6B). In general, firing rates and high-frequency LFP (gamma and high-gamma) were not very useful to discriminate behavior. (3) Among the phase-based measures, single-trial PPC in the gamma band was the most informative of the attentional state, especially when calculated using the multitaper method (d′ of 0.23 ± 0.004; Fig. 6A, purple bar), on par with the firing rate (p = 0.95; Wilcoxon rank-sum test). (4) The performance of the neural measures in the discriminating behavioral outcome for neutral condition (Extended Data Fig. 6-1B) was similar to the discrimination of attentional conditions for valid condition (Fig. 6A).

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Figure 6.

Summary plot comparing across the d′ values of all the measures for spikes, LFP power, and phase in different frequency bands for validly cued attention and behavioral comparison. A, d′ of firing rate/LFP power (red), sine of the phase angle (blue), firing rate/LFP power correlation across the bins (green), LFP power correlation across the tapers (magenta), pairwise phase consistency (PPC) across bins (brown), and PPC across tapers (purple) for spikes, alpha (8–12 Hz), SSVEP (18–22 Hz), gamma (40–80 Hz), and high-gamma (120–200 Hz) power between attend-in and attend-out conditions for hit trials. Note that for spikes, only d′ values of firing rate and bin-wise correlation exist because the rest of the measures cannot be computed for the spike data whereas for alpha-band, d′ of bin-wise measures (Correlation_Bin and PPC_Bin) are absent because the frequency resolution in the binning method was 20 Hz. “***” indicates p-value < 0.001, “**” indicates 0.001 < p-values < 0.01, “*” indicates the 0.01 < p-values < 0.05, and no asterisks are shown for p-values > 0.05. Negative d′ values were converted to positive values by multiplying with −1 before performing the significance test since we were comparing only the magnitude. All the p-values are Bonferroni corrected for multiple comparisons. B, Same as A but for the d′ between the hit and miss conditions of the attend-in condition. A summary plot comparing the d′ values of all the measures for neutrally cued condition is shown in Extended Data Figure 6-1.