Introduction

Linking and modifying previously acquired knowledge, through Transitive Inference (TI) processes, is an efficient skill found in numerous animal species, allowing them—for example—to make decisions in social interactions while avoiding potentially dangerous trial-and-error strategies1. This mental skill has been studied in laboratory settings using various types of TI tasks. During a typical TI task, subjects undergo training to learn the hierarchical relationships between a set of items, such as A > B > C > D > E > F. This training involves presenting the reciprocal relations of adjacent items, such as A > B, B > C, and so on. During the subsequent test, subjects are required to infer the hierarchical relation between novel pairs of items, such as B > D or C > E. The observation of a Symbolic Distance Effect (SDE) indicates that comparing items with adjacent ranks is more difficult than comparing items with more distant ranks.

Several lines of evidence indicate that when animals engage in TI, they rely on organized mental schema where learned premises have been previously mapped2,3,4,5. However, no definitive evidence excludes the use of simpler cognitive processes in these tasks (for deeper considerations see Supplementary Note 1). For example, associative models, such as the ones proposed by the Value Transfer Theory (VTT6) and Reinforcement-based learning models (RL7,8), suggest that non-cognitive processes underlie TI9. According to this state of the art, the mental processes underlying the solution of the proposed inferential problems are largely unknown. As a result, while there is agreement that forming inferential insights involves actively rehearsing learned premises, the neural processes underpinning these cognitive operations remain unclear5,10. The prefrontal cortex (PFC) is a potential candidate area for investigating the underlying neuronal mechanisms. Studies have shown that this brain area in monkeys is modulated by the difficulty of the comparisons and premises rehearsal (i.e., they are modulated according to the SDE) and encodes the rank of items in a TI task2, like how numerical quantities are encoded during numerical comparison tasks11. Interestingly, comparing the latencies of activation between the PFC and PMd neuronal activities revealed that the PFC engagement in the task, on average, anticipated the PMd12. This finding suggests these areas are part of a neural circuit in which the PFC provides earlier top-down information to guide subsequent motor choices. In this respect, the difficulty in solving the task, evident from the SDE, likely reflects the involvement of the cognitive operations that vary according to the difficulty of pair comparison.

To better understand the role of PFC neural computation on TI capabilities, we conducted a study analyzing local field potentials (LFPs) in the same dataset of Brunamonti et al. 2 with two monkeys performing a TI task. We focused our analyses on exploring the interplay between the beta and gamma bands of LFPs, which have been shown to underpin the level of top-down demands during goal-directed behavior13,14,15,16,17. Given the different levels of difficulty proposed by the task, we hypothesize a variation in cognitive effort depending on the symbolic distance (SD; see Methods) of the proposed inferential problems and, therefore, a different interaction between the beta and gamma bands in PFC.

We identified distinct SD-dependent beta and gamma anticorrelated oscillatory patterns emerging during the inferential problem-solving epoch. Our results indicate that lasting beta-gamma modulations underly prolonged cognitive computations related to solving a more difficult inferential problem. Remarkably, while the beta band showed a constant relationship with the SDE throughout the trial, the gamma band exhibited a flexible and dual relationship: negative during the latter part of the delay epoch, when TI computations are supposed to operate, and positive when monkeys reached the chosen symbol. We discuss our results in line with the view that PFC hosts neural cognitive pathways supporting diverse cognitive operations underlying inferential reasoning18,19,20,21,22.

Results

Symbolic distance effect modulated the monkeys’ behavior

The structure of the experimental trials was identical for both the learning and the test phases (Fig. 1A). On each trial monkeys must choose the higher-ranking item on the presented pair to receive a liquid reward (see Methods, for details). Overall, both monkeys performed the task accurately during the test phase (Monkey 1: accuracy = 0.90 ± 0.017; Monkey 2: accuracy = 0.90 ± 0.013) when novel pairs were presented (Fig. 1B). We also show their ability to solve TI problems improved as the symbolic distance (SD) between two items increased. This was supported by an increase in accuracy (Fig. 1C - p(accuracy) <0.001 for both Monkeys; Kruskal-Wallis nonparametric test) and faster response time (ResT; Monkey 1: p(ResT) < 0.001; Monkey 2: p(ResT) <0.01; Kruskal-Wallis nonparametric test). Using the same dataset, we explored whether the SDE (see Methods) also characterized the performance in comparing individual items. Supplementary Fig. 1 illustrates that both pairs with extreme rank items (always (“A”) or never (“F”) reinforced during training) and those with middle-rank items show a similar accuracy benefit with larger SD. This finding contrasts the exclusive use of “anchoring” strategies on the extreme items due to reward history to solve the task23.

Fig. 1: TI task and behavioral performance.
figure 1

A Schema of task events during the learning and test phases and example of ranked items in a session (bottom). The monkeys reached a central cue, which prompted the display of a pair of items after an initial holding. To obtain a reward, the monkeys were required to touch the item with the higher rank after the Go signal presentation. During the learning phase, the monkeys were tested on adjacent items only (SD1). In the testing phase, both learned and novel problems were presented. The delay epoch was present only in the test phase. B All possible combinations of pairs from the items in the ranked series, along with their symbolic distances (SDs). Pairs are labeled as “learned” (gray boxes) or “novel” (green boxes). C Symbolic distance effect (SDE) on performance (left) and mean response time (ResT; right), for each monkey. Error bars represent ± SE.

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Beta and Gamma bands dynamics in TI task

Figure 2 shows the grand average—among electrodes—time-frequency plot of correct trials, aligned at Pair Onset presentation (Pair ON – Fig. 1A), separately for each monkey. In response to this event, the beta band shows an initial phasic power desynchronization (negatively peaking at ~330 ms in Monkey 1 and ~140 ms in Monkey 2), which was followed by a tonic synchronization that constantly increases until the completion of movement ending on the selected symbol. The gamma band shows an early activation in response to the pair presentation (peaking at ~140 ms in Monkey 1 and ~230 ms in Monkey 2), more robustly in Monkey 1, followed by a tonic desynchronization that lasted until the end of the trial. In Monkey 1, the positive gamma peak emerges before the negative beta peak, whereas in Monkey 2, the positive gamma peak follows the negative beta peak. Given the close temporal contingencies observed between the powers of these two frequency bands, two distinct modulatory phases can be identified in both monkeys. The first period is characterized by phasic gamma synchronization and beta desynchronization (i.e., beta(-)/gamma(+)), while the second period is characterized by beta tonic synchronization and gamma desynchronization (i.e., beta(+)/gamma (-)). Thus, beta and gamma activities were characterized by an opposite trend, roughly showing mirror images of one another (Fig. 2, right panels). Notably, the signals from the beta and gamma bands exhibit a strong anti-correlation throughout the trial duration (from 0 to 1800 ms, Pair ON aligned) in both monkeys (Monkey 1: r = −0.86, p < 0.001; Monkey 2: r = − 0.87, p < 0.001).

Fig. 2: LFP dynamics following pair presentation.
figure 2

Left Panels: Grand average spectrogram of correct trials aligned at pair presentation (Pair ON), obtained by combining data from all selected channels. Lateral colored curly brackets represent the frequencies that encompass beta (in blue) and gamma bands (in red). Right Panels: Average relative power time-series across the beta and gamma bands, separately for each monkey. The vertical dashed lines show the mean ± standard error (SE) of the task events (GO = Go onset; Mov ON = Movement onset; Touch = target touch). The time interval between the GO and the Touch corresponds to the response time.

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If the interaction between these two signals is crucial for resolving the task, we expect this relationship to be more prominent in correctly solved trials versus wrong trials. To this aim, we analyzed the relation between the two signals both in Correct trials (i.e., where the monkey chose the item with the higher rank) and in Wrong trials (i.e., where the monkey chose the item with the lower rank). To better focus on actual inferential processes, we considered only trials containing non-adjacent items. We found that while Correct trials show significant anticorrelated signals (Monkey 1: r = − 0.95, p < 0.001; Monkey 2: r = − 0.99, p < 0.001) in the second part of the delay epoch (i.e., time window 400–620 ms from pair onset, shaded gray areas in Supplementary Fig. 2), such type of anticorrelation is absent in the Wrong condition, even showing a positive correlation in Monkey 2 (Monkey 1: r = − 0.13, p = 0.55; Monkey 2: r = 0.80, p < 0.001). This result thus supports the idea of a specific link between the opposite trend of the two oscillatory signals and the ability of the animals in solving the proposed task.

Beta and Gamma bands are modulated by the Symbolic Distance

As shown above, TI trials consistently exhibit an anti-correlation between beta and gamma activity. To study the role of these two frequency bands in the task, we assessed their relationship across different epochs and with respect to the SDE. Specifically, we tested whether the signals associated with each SD significantly differed for each time bin (time step 50 ms), for both beta and gamma bands. In doing that, we focused on four critical epochs (Fig. 3) of the task by aligning to four specific events: Pair Onset (ending at the minimal delay duration, 600 ms), Go-signal presentation (-200 ms before and +200 ms after), Movement Onset (-200 ms before and +200 ms after) and Touch (-200 ms before and +200 ms after). Exploring the signal along these alignments will allow us to thoroughly investigate the extent to which these bands are involved in the task.

Fig. 3: Beta and gamma bands are modulated by the symbolic distance.
figure 3

Average time-series of beta (blue) and gamma (red) bands as a function of SD ± SE, shown separately for each monkey. Signals for each SD are represented using different shades of color, with dark shades indicating low SD and light shades indicating high SD. The timeline is aligned to: pair presentation (Pair ON), Go onset (GO), and Movement onset (Mov ON), and target touch (Touch). The colored blue and red lines at the bottom indicate significant differences between the SD conditions for each frequency band (permutation test, with significance p < 0.05).

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Permutation tests (see Methods) revealed significant SD-dependent beta modulations (p < 0.05) following Pair Onset in both monkeys: from 240 ms in Monkey 1 and 320 ms in Monkey 2. However, in Monkey 1, strong modulations were still present across most of the subsequently analyzed time windows. In contrast, in Monkey 2, beta modulations remained high only during the periods surrounding the presentation of the Go-signal (from -200 ms to 200 ms) and the target touch (from -30 ms to 40 ms). On the other hand, significant SD-dependent gamma modulations were observed after Pair Onset (starting from 510 ms), around the Go-signal presentation (from -90 ms to 200 ms), and around target touch (from -180 ms to 190 ms) in Monkey 1. In Monkey 2, significant gamma modulations emerged after Pair Onset (starting from 350 ms) and around the Go-signal presentation (from -200 ms to 200 ms). Notably, during the delay epoch, beta modulations appeared earlier than gamma modulations in both monkeys.

After observing the emerging of significant beta and gamma modulations at the end of the delay epoch, we wandered if the duration of these changes was related to symbolic distance. In particular, we focused on the beta(-)/gamma(+) modulation as it is the one that most characterize this early epoch of the task. The beta(-)/gamma(+) modulations were calculated as follows: for each symbolic distance condition and for each recorded channel, we measured the time during the delay period ([0 0.65]) in which the power in the beta (gamma) range was lower (higher) than the power calculated during the baseline period ([−0.15 0]). We then calculated the total duration of these changes by adding up the absolute values of these two time periods. The results show significant differences between these modulation lengths (Kruskal-Wallis nonparametric test, p < 0.05). Post hoc multiple comparisons revealed significantly longer durations for the SD1 condition compared to the SD5 condition in Monkey 1. A similar trend was also observed in Monkey 2 (Kruskal-Wallis nonparametric test, p = 0.05; Supplementary Fig. 3).

Beta and Gamma activities show different relationships with the SDE

In the above paragraph, we observed the emerging of significant power modulations of beta and gamma during the late part of the delay epoch, which is the period when inferential problem-solving reasoning is supposed to occur. Here, we investigated the strength of the relationship of beta and gamma frequency bands with the performance accuracy (i.e., the SDE shown in Fig. 1). Specifically, for each time bin (time step 50 ms), we tested whether the signals associated with each SD and the corresponding SD accuracies resulted in a linear correlation, focusing on the same epochs as in Fig. 3.

The Pearson correlation analysis revealed strong correlations (R > 0.75) between the average beta powers and SD accuracy before the Go signal presentation in both monkeys (Fig. 4, first row). These correlations were significant (p < 0.05, permutation test) for most of the time windows, indicating a robust relationship. This relationship continued to be high (R > 0.6) throughout most of the trial timeline in both monkeys. Monkey 1 exhibited significantly positive relationships around the Movement onset (range from 0 to 50 ms) and the Touch (range from −50 to 100 ms), while Monkey 2 showed similar positive relationships around 200 before Movement onset.

Fig. 4: Relationship of Beta and Gamma with behavioral performance over time.
figure 4

Evolution of Pearson’s correlation coefficient (R) between mean SD signals and behavioral performance across the trial. The timeline is aligned to: pair presentation (Pair ON), Go onset (GO), Movement onset (Mov ON), and target touch (Touch). The mean SD signal values were computed every 50 ms using a 100 ms sliding window while the performance remained constant over time. The black lines at the bottom of the graph show statistically significant correlations (permutation test, with significance p < 0.05).

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On the other hand, the average gamma powers exhibited an early positive relationship with accuracy in response to the Pair presentation in Monkey 1 which rapidly turned into a negative relationship with accuracy within the delay period (Fig. 4, second row). This negative correlation also emerged in Monkey 2. Following the Go-signal presentation, the strength of the negative gamma/ accuracy correlations gradually diminished, turning positive in both animals at the time of the selected item touch (Touch), with both monkeys showing significant (p < 0.05, permutation test) positive relationships before the Touch, from -100 ms to −50 ms. In both monkeys, we thus observed significant but opposite correlations of the beta and gamma signals with the SDE in the last portion of the time (delay epoch) preceding the Go-signal presentation. However, later in the trial, while beta maintained its functional link to task demands, the correlation of gamma with the SDE exhibited an inversion from negative to positive.

Beta and Gamma signals modulation in relation to Response time changes

As shown, the difficulty of the proposed inferential problems is also expressed through different lengths of response time (ResT; Fig. 1C). Here, we investigated the strength of the relationship between beta and gamma frequency bands and the ResTs. Our analysis focused on the epochs immediately preceding the presentation of the Go-signal and Touch. During these epochs, the gamma signal more evidently showed opposite relationships with the SDE (see Fig. 4). For each session, we categorized neuronal activity into five categories based on normalized ResTs, ranging from fastest to slowest. Then, we investigated whether the average signals obtained from these categories correlated linearly with the average ResTs across the five categories.

When analyzing the average power before the Go-signal presentation (time window: [−100 ms 0 ms]), we observed significant negative Pearson correlations between the beta signal and ResT in both monkeys (Monkey 1: R = − 0.96, P < 0.01; Monkey 2: R = − 0.97, p < 0.01), while the gamma signal exhibited a positive relationship with ResT (Monkey 1: R = 0.99, p < 0.001; Monkey 2: R = 0.93, p < 0.05). Before the Touch (time window: [−100 ms 0 ms]), the analysis revealed a negative relationship between beta and ResT only in Monkey 1 (Monkey 1: R = − 0.98, P < 0.01; Monkey 2: R = −0.59, p = 0.29). Similarly, the gamma/ResT relationship was negative only in Monkey 1 (Monkey 1: R = −0.90, p < 0.05; Monkey 2: R = −0.08, p = 0.90).

In summary, our data indicate that before the Go-signal presentation, at the end of the delay epoch, both monkeys showed negative beta/ResT correlations and positive gamma/ResT correlations. Before the Touch, after response completion, while in Monkey 2 the signal correlations with the ResT were not significant, in Monkey 1, both beta/ResT and gamma/ResT correlations expressed negative relationships.

The Beta-Gamma combined signals account for the Symbolic Distance Effect

We have identified strong relationships between the power of the beta and gamma bands and the SDE in different epochs of the TI task. In the following, we aim to investigate 1) whether the combined modulation of beta and gamma frequency bands acts as a stronger predictor of behavioral performance than the activity of the two bands considered separately and 2) whether this coupled activity demonstrates a stronger association with behavior at the very end of the delay period, when TI computations are supposed to operate, or in the epoch preceding the motor execution. To address these questions, we conducted a correlation analysis (Pearson correlation analysis) between the SD-dependent beta-gamma signals power difference and the SD accuracies in two specific epochs: the period preceding the presentation of the Go-signal, at the very end of the delay (from −100 ms to 0 ms) and the epoch before the Movement onset (from −100 ms to 0 ms).

We found that, before the Go-signal presentation (Fig. 5A), the relationship with the behavior of the absolute relative power difference between beta and gamma bands has the same shape and is highly correlated with the SD accuracy (Monkey 1: R = 0.93, p = 0.02; Monkey 2: R = 0.92, p = 0.03), suggesting a tight functional link between these two measures (Fig. 5A, right panels). In contrast, this relationship was not significant in the epoch preceding the Movement onset (Monkey 1: R = 0.84, p = 0.08; Monkey 2: R = 0.83, p = 0.08) (Fig. 5B, right panels). Interestingly, the beta-gamma differences that emerged before the Go-signal presentation were found to be the strongest predictor of behavioral performance, outperforming the predictive ability of the beta and gamma bands considered individually. This pattern held true both in the epoch preceding the Go-signal presentation (Beta correlation: Monkey 1: r = 0.92, p = 0.03; Monkey 2: r = 0.87, p = 0.06; Gamma correlation: Monkey 1: r = −0.62, p = 0.26; Monkey 2: r = −0.86, p = 0.06) and at the Movement onset (Beta correlation: Monkey 1: R = 0.76, p = 0.13; Monkey 2: R = 0.50, p = 0.39; Gamma correlation: Monkey 1: R = 0.34, p = 0.58; Monkey 2: R = −0.72, p = 0.17).

Fig. 5: The Beta-Gamma signal difference accounts for the Symbolic Distance Effect before the Go-signal.
figure 5

A Left columns display the mean normalized signals of Beta and Gamma activity before Go signal presentation (time window: −100 ms, 0 ms). Symbolic distances (SDs) are represented using different shades of color, with dark shades indicating low SD and light shades indicating high SD. Error bars represent ± standard error (SE). Right columns show the absolute differences between Beta and Gamma activities calculated before Go signal presentation, plotted against the overall behavioral performance. Error bars represent ± SE. B Same conventions as in panel A; alignment to movement onset (MOV onset) (time window: −100 ms, 0 ms).

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Discussion

We investigated the neural mechanisms that underpin TI processes in PFC by analyzing LFP signals recorded in two monkeys during TI’s problems solving. Our findings reveal a characteristic interplay between beta and gamma oscillations15,24, providing insights into the neural dynamics involved in TI and the possible role of PFC in the process. Typically, models underlying inferential reasoning are divided into cognitive (e.g., spatial-based models) and non-cognitive models (e.g., associative models). However, although spatial-based models involving more complex cognitive processes compared to associative strategies (see5, for a review), no definitive evidence excluding the use of simple cognitive processes in the latter has been found yet25. In the present work, we investigated the neural correlates underlying the resolution of inferential processes, without making specific assumptions about the cognitive complexity involved in these operations. Our results show a SDE even in pairs containing extreme items (Supplementary Fig. 1), allowing us to exclude ‘anchoring’ strategies reliant on the reward history of the task5,8. This finding supports the idea that the SDE in our animals mainly derives from a SD-dependent cognitive operations26,27,28,29.

The beta and gamma powers consistently exhibit a strong anti-correlation pattern throughout the resolution of the inferential task. This anti-correlation shows two distinct modulatory phases. The first phase involves an early beta(-)/gamma(+) modulation, followed by a late opposite tonic beta(+)/gamma(-) modulation. During the delay period, power band modulations related to the task emerge, with both signals displaying a strong relationship with the SDE, albeit in opposite directions (Fig. 4). These opposite signal/SDE associations result in lasting beta(-)/gamma(+) modulations in the late part of the delay for trials with smaller SD, suggesting a combined participation of these bands during inferential decision-making processes. Our data support the importance of these bands’ interaction in TI, showing that the absolute relative power difference between beta and gamma bands serves as a stronger predictor of behavioral performance than considering beta and gamma signals individually. Moreover, the relationship of both beta and gamma with the SDE diminishes its strength before the start of the reaching movement towards the selected stimulus, highlighting a specific involvement of these bands during a period typically associated with inferential problem-solving computations.

Together, these findings align with the idea that lasting beta/gamma anticorrelated oscillatory patterns in the delay epoch underly prolonged cognitive computations related to solving a more difficult inferential problem. In other words, the more difficult the task, the longer the beta(-)/gamma(+) modulation duration. While this may seem to diverge from studies demonstrating a correlation between task difficulty and beta/gamma power strength30,31,32,33, it is essential to consider that in these works the task difficulty was related to the number of items to be processed. In our task, the number of elements to be dealt with remains the same across the TI conditions. This aligns with the idea that when processing the same number of elements, as in our task, the overall cognitive load remains constant, with cognitive effort focused on sustaining problem-solving processing for the necessary duration to solve inferential computations.

Numerous studies have shown that beta oscillations play a critical role in top-down control, purportedly acting as an inhibitory mechanism for controlling information management across the cortex. In the prefrontal cortex (PFC), low beta oscillations are associated with working memory (WM) engagement34, predictive coding35, attention16,36, and social observation15, whereas high beta levels are associated with cognitive inhibition. This pattern also holds true for the areas governing motor control, as the premotor regions, suggesting a possible functional similarity between cognitive and motor control processes operating at beta frequencies (for a review, see37). According to this view, it has been hypothesized that simultaneous and opposite beta and gamma activations are expressions of an integrative mechanism involved in processing task-relevant information across various cognitive tasks15, where reduced beta activity facilitates the emergence of gamma oscillations for sustained information encoding34,38.

Considering also the observations in the previous paragraph, the overall picture thus suggests a top-down control role of the beta band during TI, which allows for longer cognitive processing depending on the difficulty of TI problems. The constant positive relationship with the SDE until the late part of the trial, indicates that the beta band maintains this functional role throughout the trial. Differently from the beta band, the relationship between the gamma band and the SDE changes throughout the trial. Specifically, while we observe a negative relationship between gamma and SDE at the end of the delay epoch, this relationship turns positive upon motor output execution, becoming significant around the completion of the reaching movement. This inversion of correlation may underly a switch in the functional role played by gamma. For instance, the link of gamma activity occurring in trials with higher SDs—conditions associated with faster response times (ResTs)—may reflect an involvement of this band during motor response execution. As partial support for this hypothesis, we found that in one monkey, higher gamma levels during the movement execution, before target reaching, are associated with faster ResTs.

Overall, we report evidence suggesting that while the beta activity governs the top-down access to cognitive processing relevant to inferential reasoning, the gamma band exhibits a more flexible coding. Initially, it is involved in inferential cognitive processing; however, after initiating the motor response, we have indications of its participation in the control of the reaching movement toward the chosen symbol.

Paralogical models, proposing that logical abilities are not obligatory for inference, suggest that inferential problem-solving involves implementing multiple interconnected cognitive processes. In particular, many emphasize processes related to the retrieval and active manipulation of a spatial mental model3,4,29,39,40,41,42. The implementation of these functions in TI tasks implies the utilization of a mental workspace that involves recalling visuospatial memory traces for information maintenance and manipulation—a theoretical framework commonly used to conceptualize working memory (WM) functionalities43. A series of studies conducted by Lundqvist and colleagues (2016, 2018, 2023)17,34,44 and Miller and colleagues (2018)38 demonstrated an association between the anti-correlated beta-gamma signals and WM access, maintenance, and control in PFC. These authors describe how PFC beta and gamma power and spiking activity relate to top-down executive control, facilitating WM access. WM episodes trigger gamma oscillations and reduce inhibitory beta activity, leading to temporary synaptic weight changes without sustained spiking. Periodic bursts of spiking and gamma activity refresh these changes, creating an oscillatory dynamic where beta regulates the neural PFC firing times. Although, the mechanisms from Miller et al. 38 do not directly apply to our findings, given the uncertain use of WM in the TI task45, the PFC might use these neural dynamics as an efficient mechanism for processing task-related information, being less metabolically costly, less prone to interference, and suitable for encoding multiple items. In line with these considerations, the observed beta and gamma power modulations may reflect cognitive computations commonly encountered in various cognitive tasks. Thus, not only specific for inferential reasoning.

This hypothesis leaves open the potential existence of functionally flexible beta/gamma neural pathways dedicated to recalling and maintaining of a unique representation encompassing the rank of the stimuli—critical for the hypothesized cognitive inferential operations. If this holds true, the resolution of TI tasks may depend on the same neural circuits implicated in the context of WM45. However, in our task, unlike WM tasks, the stimuli remain available to the subject until a choice is made. Representational recall in our task would specifically involve retrieving the spatially organized mental schema of the proposed items. Further exploration, using modified version of the TI task, is needed to test this hypothesis.

Methods

Animals

Two male, head-restrained rhesus monkeys (Macaca mulatta) weighing 5.50 Kg (Monkey 1) and 6.50 Kg (Monkey 2) were tested while neural activity was recorded extracellularly from the dorsal portion of the PFC (dPFC) using a 5-channel multielectrode system (Thomas Recording, Giessen, Germany). The recordings used in this study were previously utilized in a work that focused on single-unit analysis2. Recording chambers were surgically implanted on the left frontal lobe at known stereotactic coordinates (anterior: 32, lateral: 19 in monkey 1; anterior: 30, lateral: 18 in monkey 2), with head restraints. The position of the electrodes in the PFC was confirmed at the end of the neurophysiological experiments by structural MRI (Monkey 2) or visual inspection after surgical opening of the dura during implantation of a chronic matrix (Monkey 1). See also Fig. 4 in Brunamonti et al. 2. Animal care, housing and experimental procedures conformed to the European (Directive 210/63/EU) and Italian (DD.LL. 116/92 and 26/14) laws on the use of non-human primates in scientific research. The research protocol was approved by the Italian Health Ministry (Central Direction for the Veterinary Service). The housing conditions and the experimental procedures were in accordance with the recommendations of the Weatherall report (use of non-human primates in research). We have complied with all relevant ethical regulations for animal use.

Experimental set-up

A 17-inch PC monitor (LCD, refresh rate 85 Hz, 800 × 600 resolution) that was equipped with a touchscreen (MicroTouch, sampling rate of 200 Hz) was placed in front of the monkeys to present stimuli and record touch positions (monitor-eye distance 21 cm). A non-commercial software package, CORTEX (http://www.nimh.nih.gov), was used to regulate the stimuli and behavioral responses and collect behavioral data. An RX6 system (Tucker-Davis Technologies, Alachua, FL, USA) synchronized to the behavioral events detected the neural activity (saved as raw signal, unfiltered, 24 KHz sampling rate) during each behavioral trial. Eye movements were recorded using an infrared tracking system (Arrington Research, Scottsdale, AZ, USA) at a sampling rate of 220 Hz.

Test stimuli and task design

The stimulus dataset consisted of 80 abstract images that were black and white bitmaps, measuring 16° x 16° of visual angle, and had an equal proportion of white area over a black background. In each session, the monkeys underwent two learning phases to acquire knowledge about the relationships between six ranked items, which were randomly selected from the original set of stimuli and ordered by the authors (Fig. 1A, bottom, for an example of ranked items). The distance between symbols in each rank is known as symbolic distance (SD). Adjacent symbol pairs have SD = 1, while non-adjacent symbol pairs have SD > 1. To prevent repetition and ensure long-term memory retention, the same item was never assigned the same rank between sessions, and a minimum of two weeks passed before reusing any item.

In learning phase 1 (learning 1), the pairs of items with adjacent rank (Fig. 1B – SD1) were sequentially presented to the monkey. The monkey had to identify the higher-ranking item in each pair through trial and error in blocks of 15 (Monkey 1) or 20 (Monkey 2) trials. Each block was repeated until the monkey reached a learning criterion of at least 90% correct choices for the pair. Once this criterion was met for all pairs, the second learning phase (learning 2) began. In this phase, all 5 previously experienced pairs of adjacent ranked items were presented intermingled in a random order (not sequentially), and the monkey had to achieve a criterion of > 60% overall correct trials, with additional blocks of trials presented until the criterion was reached. During the test phase (test), the monkeys were presented with a block of at least 14 trials for each inferential problem, as shown in Fig. 1B. The test included both learned pairs (pairs with SD1) and novel pairs (pairs with SD > 1).

At the beginning of each trial (Fig. 1A, top), a red spot (13.5° x 13.5° of visual angle) appeared at the center of the screen, signaling the start of the trial. The monkeys were given 5 s to push a button to initiate the task. After a button press, and the holding period, a pair of items was presented (Pair Onset) for a variable delay period, ranging from 620 to 1200 ms (during the learning phase, this delay period was absent). The disappearance of the central spot (Go-signal) indicated to select the item of the pair with the higher rank (i.e., the one associated with reward) by performing a reaching movement. The rewarded item of each pair was randomly presented on either the left or right side of the central spot.

Data analyses

To ensure that the monkeys were using the learned premises to compare pairs of items based on their rank, we checked whether the SDE followed a positive linear trend, as suggested by computational models46. In our original sample of 37 recording sessions (Monkey 1: n = 18; Monkey 2: n = 19), all sessions exhibited a positive regression slope. However, we excluded 1 session from Monkey 1 and 2 sessions from Monkey 2 because they didn’t meet the required minimum of 15 trials for each SD condition. Overall, we proceeded with 17 sessions for Monkey 1 and 17 sessions for Monkey 2.

For the LFP signal analyses of each selected session, we only included artifact-free channels in the voltage ___domain (Monkey 1 = 39; Monkey 2 = 34). Time-frequency analysis was computed using the multi-taper algorithm with the freeware toolbox “Chronux” (cronux.org; version 2.00). For each trial, the mean value and linear trend (detrend) were removed from the raw signal, and spectrograms were generated in a window of 300 ms with 10-ms steps, using a frequency bandwidth of 5 Hz and 2 Slepian tapers. We set the maximum frequency to 120 Hz. Relative spectrograms were defined as the ratio (in dB) between the power spectrum in each time-frequency bin and the mean power spectrum across all trials of baseline activity between 0 ms and 300 ms before the presentation of the pair of items to judge (Pair ON). Each relative spectrogram corresponds to the average across all trials under the same condition. Although these averaged signals might reflect bursting activity across trials, the well-documented high correlation between burst rate and across-trial power17 indicates that they can be considered a reliable measure of the oscillatory dynamics observed in the various conditions.

The LFP bands were calculated by measuring the mean relative power belonging to the frequency range of the beta and gamma bands from the corresponding relative spectrograms. The gamma band was selected in the range 50 Hz to 120 Hz. Within the frequency range of 18 to 50 Hz, we observed similar power modulations between the monkeys (Supplementary Fig. 4), characterized by initial desynchronization followed by subsequent synchronization. These modulations do not seem to occur at overlapping frequencies between monkeys. To determine beta band frequency ranges in each monkey, a null distribution was generated by randomly shuffling the time-frequency bins 1000 times within the frequency range of 18 Hz to 50 Hz. Real time-frequency bins that exceeded the 99.9th percentile of the null distribution were considered significant, corresponding to a p-value < 0.01. The upper and lower limits of the beta bands are defined by the maximum and minimum frequencies that exhibit significant time bins. As a result, the beta band frequency ranges spanned from 19 to 28 Hz for Monkey 1 and 25 to 48 Hz for Monkey 2 (as shown in Supplementary Fig. 4). It is not uncommon to find variations among different animals expressing the beta neural network in distinct frequency ranges47,48,49. Here, despite the different frequencies of these bands, we demonstrate that similar modulations have similar properties.

To investigate the relationship between behavioral performance and LFP activity, correlation analyses were performed between SD accuracies and the power of the beta and gamma frequency bands. The data that support the findings of this study are available in the repository reported in the Data Availability section.

When comparing signals across the five SD conditions over time, the large number of consecutive statistical comparisons necessitates controlling for the family-wise error rate (FWER)50. To address this, we used a nonparametric random permutation approach, in which the signals were randomly reassigned to a SD condition. This process was repeated 1000 times, generating 1000 data points representing the statistical distribution for each statistical distribution. The statistics for real non-permuted data were considered significantly above chance if they fell within the 5% of their respective random permutation distributions. We only considered clusters with significant effects lasting more than 50 ms51.

Statistics and Reproducibility

All data curation and statistical analyses were implemented in MATLAB (MathWorks, R2020a). Data comparisons between monkeys were performed using a nonparametric ANOVA test (Kruskal-Wallis). Correlation analyses were performed using Pearson’s linear correlation coefficient. To compare Beta and Gamma signal modulations over time, a cluster-based permutation test was applied, as described in the Methods section.

Reporting summary

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