Inferring latent behavioral strategy from the representational geometry of prefrontal cortex activity

Domain: chemistry
Published: 2026-02-17
Editorial outcome: major_revision

Abstract
Behavioral tasks can be solved employing various strategies. Sometimes, different strategies result in the same observable behavior, making them latent. In this study, we infer the latent behavioral strategy used by monkeys in a working memory updating task by comparing the representational geometry of two prefrontal regions-the lateral prefrontal cortex (LPFC) and the prearcuate cortex (PAC)-with that of recurrent neural network (RNN) models trained to solve the task using different strategies. We found that neural activity patterns in both LPFC and PAC align with only one of the proposed strategies, suggesting that monkeys employ this latent strategy to perform the task. These findings open avenues for investigating the processes that lead to strategy learning and the decision-making mechanisms that determine which strategies are chosen when multiple options are available.

Introduction
Organisms can respond differently to the same stimulus depending on their internal state, a capability referred to as behavioral flexibility1. Additionally, they can use various internal states to produce a similar response to a stimulus, each of which is referred to as a task strategy2,3. Different strategies are implemented by different neural dynamics4–6 and can be examined mechanistically using simulations4,7,8. Often, different strategies result in noticeable behavioral differences, such as variations in response accuracy3 or reaction times4. However, in some instances, different strategies may not produce any observable behavioral differences (i.e., latent strategies), and they can only be differentiated via the activity signatures in neural systems.

To date, most research of cognitive strategy focuses on the behaviorally observable ones9, while latent strategy has been largely overlooked due to the detection difficulty. Parameterized models fitted to the neural activities, on the other hand, usually only reveal the implementation mechanism of processes rather than cognitive-level strategies10–13. Only recently, a few studies showed that recurrent neural network (RNN) simulations can be used to infer which latent strategy is used by animals, when multiple strategies are available4,7,8. Here, we explored the latent strategies employed by animals in a working memory task by comparing the geometric representational properties of two prefrontal regions—the lateral prefrontal cortex (area 9/46, LPFC) and the prearcuate cortex (area 8a, PAC)—with those of RNN models explicitly trained to utilize different strategies to solve the same task.

Monkeys and RNNs were trained to solve a working memory updating task14. Human behavioral studies have shown that working memory updating tasks can be performed employing different strategies15. One possible strategy is to initially encode memories in the absence of attention, and then transfer the information to an attended format at the time of recall16 (Retrieve at Recall strategy or R@R). Alternatively, another strategy is to rehearse and update the memory online as the items are shown17 (Rehearse and Update strategy or R&U). The Retrieve at Recall strategy would presumably involve initially encoding multiple memories in orthogonal neural activity subspaces until one of them is selectively rotated for readout18. On the other hand, the Rehearse and Update strategy would presumably involve encoding both the initial and the updated memories directly onto the readout activity subspace.

In both LPFC and PAC, we observed activity patterns that were consistent with the RNNs trained to solve the task using the Rehearse and Update strategy, and were inconsistent with the RNNs trained to solve the task using the Retrieve at Recall strategy. Thus, we infer that the monkeys employ the latent Rehearse and Update strategy to solve the task.

Results
Behavioral results
We trained RNNs and two monkeys to perform a working memory updating task (Fig. 1a). In this task, they had to report the location of the last target (red square) seen. The monkeys reported with a saccadic eye movement to the target location. For Target 1/Target 2 (T/T) trials (Fig. 1a top), monkeys had to report the location of Target 2, while for Target 1/Distractor (T/D) trials (Fig. 1a, bottom), monkeys had to report the location of Target 1. On average, monkeys reported the correct location on over 60% of trials (Monkey A: Overall: M(SD)= 0.700(0.021), T/D: M(SD)=0.688(0.022), T/T: M(SD)=0.711(0.032); Monkey B: Overall: M(SD)=0.616(0.037), T/D: M(SD)=0.626(0.034), T/T: M(SD)=0.611(0.063)) (Supplementary Fig. 1a). To get a reward, in addition to reporting the correct location, the monkeys had to respond within 500ms of the go-cue, and maintain fixation on the target for at least 200ms (rewarded trials: Monkey A: Overall: M(SD)=0.533(0.011), T/D: M(SD)=0.506(0.018), T/T: M(SD)=0.559(0.008); Monkey B: Overall: M(SD)=0.563(0.036), T/D: M(SD)=0.563(0.041), T/T: M(SD)=0.569(0.065)) (Supplementary Fig. 1b). The monkeys’ performance tended to decrease towards the end of sessions. We speculate that this decrease is the product of fatigue or loss of motivation. Prior to this decrease in performance the animals were more attentive and motivated, leading to higher performance (Supplementary Fig. 1c–f). For the rest of the error trials, we found that that the animals were most likely guessing where to go, since they had similar likelihood of going to any of the other three erroneous targets (Supplementary Analysis 1., Supplementary Fig. 1g).

For subsequent neural data analysis we only included rewarded trials (i.e., when the animals responded faster than 500ms and fixated on the correct target for longer than 200ms).

RNNs were trained until they reached >95% accuracy (R@R: M(SD)=0.998(0.003); R&U: M(SD)=0.998(0.013)). Of note, this >95% accuracy in the models is higher than the monkeys’ performance (60−80%), because monkeys’ errors are likely driven by factors that are not present in the models (i.e., external distractions or decreased motivation due to satiation). We presume that when the monkeys perform the task correctly, it is because they are correctly following the learned task rules, which would be comparable to a well-trained RNN model. Nevertheless, for comparison, we carried out all the analyses on networks that only reached ~70% of performance. These analyses showed that all the results were qualitatively similar to the well-trained networks (Supplementary Analysis 2, Supplementary Fig. 2).

The inputs to the RNNs could either be Target 1 followed by Target 2 (T/T, Fig. 1c, left), or Target 1 followed by Distractor (T/D, Fig. 1c, right). The R&U strategy was enforced by evaluating the output of the network during both Delays 1 and 2 (Fig. 1d). The R@R strategy was enforced by evaluating the output during Delay 2 only (Fig. 1e).

Full space decoding analysis
Overall, we recorded 89 neurons from LPFC and 129 neurons from PAC in two animals across 11 sessions. in areas 9/46 (LPFC) and 8a (PAC) (Fig. 1b). Out of the recorded neurons, 100% (129/129) of PAC cells and 94% (84/89) of LPFC cells were task responsive, and 100% (129/129) of PAC cells and 87% of LPFC cells were selective at some point during the task (from target onset to go-cue onset). Our main analyses were based on the pseudo population activities pooled from both animals (see Methods), but we also separately analysed individual animals in the real sessions (Supplementary Figs. 3−7). A summary of all statistical analyses can be found in Supplementary Tables 1−3.

To get a rough estimate of how information was coded in the models and cortical regions, we carried out a cross-temporal decoding analysis (Fig. 2). We applied principal component analysis (PCA) to denoise and reduce the dimensionality of data (see Methods), and we defined the space consisting of the first 15 PCs in each pseudo population and RNN, which counted for at least 90% of total variances, as the full space (ΣEVR : R@R: M(SD)=1.000(0.000), R&U: M(SD)=1.000(0.000); LPFC: M(SD)=0.908(0.005), PAC: M(SD)=0.920(0.004)). We evaluated the stability of the code during late Delay 1 and 2 (i.e., the last 500ms of each delay) (Fig. 2b). To do this, we calculated the ratio of the decoding accuracy for time-displaced decoders (i.e., off diagonal) and time-specific decoders (i.e., diagonal). A value of 1 indicates a stable code that does not change across time, while a value lower than 1 reflects a dynamic code. For each model and brain region, we compared the stability ratio distributions to corresponding baseline distributions created by label-shuffled data as well as between Delay 1 and Delay 2 (see “Methods”), with statistical significance and effect size (Hedge’s g, see Methods) measured. During Delay 2, both regions and both models showed stable codes (R@R: M(SD)=0.999(0.003), p=0.740; R&U: M(SD)=0.998(0.006), p=0.640; LPFC: M(SD)=0.996(0.016), p=0.730; PAC: M(SD)=0.995(0.014), p=0.710) (Fig. 2b, light colors). However, while for the LPFC, PAC and R&U RNNs the code during Delay 1 was equally as stable as during Delay 2, that of the R@R RNNs was more dynamic (Code Stability Ratio: R@R: MD=−0.092, p<0.001, g=−1.863; R&U: MD=−0.001, p=0.436, g=−0.114; LPFC: MD=−0.001, p=0.550, g=−0.086; PAC: MD=0.000, p=0.766, g=0.033) (Fig. 2b). To compare the similarities between RNN models and biological observations, we performed pairwise Kolmogorov−Smirnov (K−S) tests (D) and calculated the Kullback-Leibler (KL) divergence (D_KL) as well as the probability of overlap (p) between both models and both cortical regions to quantify the divergence (D and D_KL) or similarity (p) between the two cumulative distribution functions (smaller D implies more similarity). We found that both brain regions were closer to the R&U than the R@R model (R@R-LPFC: D=0.870, D_KL=12.644, p=0.109; R@R-PAC: D=0.870, D_KL=12.859, p=0.119; R&U-LPFC: D=0.420, D_KL=1.108, p=0.990; R&U-PAC: D=0.380, D_KL=0.920, p=0.990).

Second, in T/D trials, we assessed whether the code for the target location changed between Delays 1 and 2 (Fig. 2c). We calculated the degree of code morphing as logarithm of the ratio between the mean within-delay decodability and the cross-delay decodability (see Methods). A low morphing ratio indicates a time-invariant code19–21. Likewise, we compared the distributions against the label-shuffled baselines to test for statistical significance. Target code was generalizable between Delay 1 and 2 in the LPFC, PAC, and R&U RNNs, while it morphed significantly in the R@R RNNs (Code Morphing Ratio: R@R: M(SD)=0.939(0.174), p=0.010; R&U: M(SD)=0.004(0.011), p=0.812; LPFC: M(SD)=0.022(0.022), p=0.673; PAC: M(SD)=0.050(0.026), p=0.485). The pairwise K−S tests, KL divergence and overlap on the code morphing ratio distributions also showed that both brain regions were closer to the R&U than the R@R model (R@R-LPFC: D=1.000, D_KL=23.113, p=0.010; R@R-PAC: D=1.000, D_KL=23.087, p=0.010; R&U-LPFC: D=0.630, D_KL=1.230, p=0.990; R&U-PAC: D=0.880, D_KL=2.328, p=0.257).

Geometry of item-encoding subspaces
Decoding is a valid, but coarse, way of assessing the geometry of the representations in neural networks. To get a more fine-grained assessment of the representational geometry, we analyzed the principal angles and alignment of the activity subspaces that encode target information in the two delay periods (see “Methods”). If two subspaces are identical, then we expect them to have an angle of zero and a perfect alignment, while if they are different (e.g., rotated), then we expect them to have either angles or misalignments larger than zero (Fig. 3a). We also analyzed the transferability of item codes between subspaces (the performance of decoders trained on one subspace and tested on the other), as we expected them to be transferable between identical subspaces, but not so between rotated subspaces. Again, the distributions of all measures were compared to corresponding baseline distributions for statistical significance test (see “Methods”).

In T/T trials, we estimated the activity subspace that encodes item 1 location during the last 500ms of Delay 1 (I1D1_T/T) and the subspace that encodes item 2 location during the last 500ms of Delay 2 (I2D2_T/T). We found that these subspaces in LPFC, PAC and R&U RNNs were coplanar (cosine of the principal angle was not significantly smaller than 1), while the R@R RNNs they were not coplanar (Fig. 3b) (Coplanarity: R@R: M(SD)=0.446(0.471), p=0.030; R&U: M(SD)=0.804(0.493), p=0.380; LPFC: M(SD)=0.789(0.194), p=1.000; PAC: M(SD)=0.931(0.057), p=1.000). Similarly, the subspaces in LPFC, PAC and R&U RNNs were aligned (cosine of misalignment angle was not significantly smaller than 1), while the R@R RNNs were not aligned (Fig. 3c) (Alignment: R@R: M(SD)=0.839(0.400), p=0.040; R&U: M(SD)=0.940(0.253), p=0.970; LPFC: M(SD)=0.994(0.010), p=1.000; PAC: M(SD)=0.998(0.003), p=1.000). Finally, we found the code transferability ratio between I1D1_T/T and I2D2_T/T was significantly lower than baseline in R@R RNNs, but not in R&U RNNs, LPFC, and PAC (Fig. 3d) (Code Transferability Ratio: R@R: M(SD)=0.453(0.108), p<0.001; R&U: M(SD)=0.782(0.172), p=0.200; LPFC: M(SD)=0.889(0.179), p=0.930; PAC: M(SD)=0.816(0.149), p=0.750). The pairwise K−S tests, KL divergence and overlap on the distributions of subspace coplanarity, subspace alignment and code transferability ratio also showed that both brain regions were closer to the R&U than the R@R model (Subspace coplanarity: R@R-LPFC: D=0.470, D_KL=2.106, p=0.663; R@R-PAC: D=0.750, D_KL=14.058, p=0.287; R&U-LPFC: D=0.450, D_KL=1.556, p=0.713; R&U-PAC: D=0.250, D_KL=4.596, p=0.802. Subspace alignment: R@R-LPFC: D=0.520, D_KL=16.069, p=0.515; R@R-PAC: D=0.650, D_KL=20.878, p=0.376; R&U-LPFC: D=0.340, D_KL=11.028, p=0.871; R&U-PAC: D=0.170, D_KL=19.331, p=0.822. Code transferability ratio: R@R-LPFC: D=0.910, D_KL=2.940, p=0.119; R@R-PAC: D=0.860, D_KL=2.473, p=0.188; R&U-LPFC: D=0.260, D_KL=0.181, p=0.871; R&U-PAC: D=0.150, D_KL=0.052, p=0.822). These results indicate that in T/T trials, the subspace that encodes Target 1 information during Delay 1 is equivalent to the subspace that encodes Target 2 information during Delay 2 in both brain regions, as well as in the R&U model, while in the R@R model they are different.

Neural trajectories in the “readout” subspace
The analyses above show that there is a common representational subspace in T/T trials during Delay 1 and Delay 2 for the PAC, LPF, and R&U models, but not for the R@R models. To determine whether the same subspace is also utilized during Delay 2 in T/D trials, we compared the same metrics (coplanarity, alignment, and code transferability) between the representational subspaces that encode the reported item information during Delay 2 in T/T and T/D trials. We found that both brain regions and both models had a common representational subspace during Delay 2 in both trial types (Supplementary Fig. 8). Thus, a single activity subspace encodes target location information during late Delay 2 in both regions and models, akin to the “readout” subspace reported by Panicello and Buschman (2021)18.

In Fig. 2, we used decoding analyses on the full activity space to show that the R&U model and both PAC and LPFC had similar code stability and code morphing properties, while the R@R model behaved differently. Decoding on projections of activity onto the readout subspace led to equivalent conclusions (Supplementary Fig. 9). To get a deeper understanding of the representational properties of the brain regions and models, we analyzed the trajectories of the average population activity projected onto the readout subspace (Fig. 4a). In particular, we focused on the amount of drift observed in the population trajectories between Delay 1 and Delay 2 (Fig. 4b and Supplementary Fig. 10). We found that the drift between delays in the R@R model was similar in T/T and T/D trials (their ratio was close to 1) (Fig. 4b). On the other hand, the drift between delays in the R&U model, PAC and LPFC was primarily present in T/T trials, and almost absent in T/D trials (their ratio was close to 0) (Fig. 4b) (Drift Ratio: R@R: M(SD)=0.834(0.154), p=1.000; R&U: M(SD)=0.166(0.099), p<0.001; LPFC: M(SD)=0.296(0.094), p<0.001; PAC: M(SD)=0.183(0.053), p<0.001). The pairwise K−S tests, KL divergence and overlap on the drift ratio distributions also showed that both brain regions were closer to the R&U than the R@R model (R@R-LPFC: D=0.980, D_KL=18.309, p=0.030; R@R-PAC: D=1.000, D_KL=22.705, p=0.010; R&U-LPFC: D=0.600, D_KL=0.930, p=0.644; R&U-PAC: D=0.280, D_KL=0.861, p=0.683). These observations confirm that the R@R model employs different representational subspaces during Delay 1 and Delay 2, consistent with an initial representation in a subspace (unattended format) during Delay 1 that is rotated to a “readout” subspace (attended format) during Delay 218, while the R&U model employs the same subspace in both delays, consistent with the direct loading onto the “readout” subspace during Delay 1. Both prefrontal regions, PAC and LPFC, show a consistent alignment with the R&U model and consistent differences with the R@R model. Thus, our data strongly support the conclusion that the monkeys employed the R&U strategy to solve the task.

Methods
Subjects and surgical procedures
Two adult male macaques (Macaca fascicularis) were used in this experiment: Monkey A (age 12) and Monkey B (age 12). All animal procedures were approved by, and conducted in compliance with, the standard of the National University of Singapore Institutional Animal Care and Use Committee (NUS IACUC #R18-0295). Procedures also conformed to the recommendations described in Guidelines for the Care and Use of Mammals in Neuroscience and Behavioral Research (National Academies Press, 2003). Each animal was first implanted with a titanium head-post (Crist Instruments, MD, USA) before arrays of intracortical microelectrodes (MicroProbes, MD, USA) were implanted in multiple regions of the left frontal cortex. In Monkey A, two arrays were placed over the dorsal and ventral aspect of the LPFC (Area 9/46), one array was placed over PAC (Area 8A), and one array was placed over the pMA (not included in the analyses here), with 32 electrodes in each. In Monkey B, two arrays of 32 electrodes were placed over the PAC, and two arrays of 32 electrodes each were placed over the LPFC (as shown in Fig. 1b). The arrays consisted of platinum-iridium wires with 200 µm separation, 1−5.5 mm long and with 0.5 MΩ of impedance, arranged in 8×4 grids. For arrays positioned in the pre-arcuate region (PAC), we used standard electrical microstimulation to confirm that saccades could be elicited with low currents in monkey A (however, we could not perform this procedure in monkey B).

Recording techniques
The neural signals in both monkeys were recorded using a 128-channel Grapevine recording system (Ripple Neuro, UT, USA) at 30 kHz sampling rate. The wideband signals were bandpass-filtered between 300 and 3000 Hz, and spikes were detected on each channel separately using an automated sorting algorithm based on Hidden Markov modelling42. We recorded the eye positions of each subject using the Eyelink 2000 (SR Research Ltd, ON, CA) on another standalone computer. We designed and ran the behavioral tasks using the Psychopy in Python43 on a third computer connected to the recording computer using parallel ports for event mark synchronization during recording.

Behavioral tasks
Both monkeys performed a 2-item delayed saccade task. Each trial began with a 0.5 s fixation period, during which the monkey fixated on a white central dot. A first stimulus (Item 1, I1) was then presented at one of four possible locations on the corners of a 3×3 grid (10° visual angle) for a fixed duration (Monkey A: 0.4 s; Monkey B: 0.3 s), followed by a 1 s delay (D1) where the monkey maintained fixation. A second stimulus (Item 2, I2) was then presented at one of the three remaining locations for the same duration. I1 was always a task-relevant target (red square), while I2 was either a task-irrelevant distractor (T/D) or a new target (T/T), with equal probability. The target (red) and distractor (green) were identical in shape and size. After a second 1 s delay (D2), the fixation dot disappeared, signalling the monkey to make a saccadic response to the location of the most recent target (I1 in T/D trials; I2 in T/T trials). In other words, the animal needed to make an eye movement to the location of I1 when I2 was a distractor, or to the location of I2 when it was a new target. A juice reward was delivered for correct responses within 0.5 s after the go cue. I1 and I2 never appeared at the same location within a trial, yielding 24 trial conditions based on I1×I2 locations (4×3) and I2 types (2).

Behavioral performance analysis
The behavioural accuracy was first calculated separately in each real session as the proportion of correct trials of each type among all trials of that type, and then averaged across all sessions. For example, the accuracy of T/T trials in session i is
ACCT=T = N_T=T,correct / N_T=T
where N_T=T,correct and N_T=T represent the number of correct and total T/T trials in session i, respectively, and the mean accuracy across n sessions is
ACCT=T = (Σ_{i=1}^n ACCT=T_i) / n
To measure the accuracy as a function of session stages, we calculated the accuracy over bins of 100 trials and slide at steps of 20 trials from the beginning of each session to the end. For the conservative calculation of accuracy, we counted only the rewarded trials as correct and the remaining to be incorrect. For the liberal calculation of accuracy, we included both the rewarded trials and trials with correct responded locations but failed to either 1. maintain fixation at the location for at least 200ms or 2. produce saccadic response within 500ms post-go-cue.

Neuron firing rates and preprocessing
We recorded a total of 89 neurons in LPFC (Monkey A: 17, Monkey B: 72) and 129 neurons in PAC (Monkey A: 3, Monkey B: 126) across 11 sessions (Monkey A: 3, Monkey B: 8). The number of LPFC cells in each session ranged between 3 and 14 (M(SD)=8.091(3.145)), and the number of PAC cells in each session ranged between 0 to 21 (M(SD)=11.727(7.669)). All cells were used to build pseudo populations. Single-neuron firing rates were computed using a 50ms sliding window (10ms overlap). Firing rates were z-scored relative to the mean and standard deviation of pre-I1 baseline activity (0.2s) across all trials20. Since I1 and I2 display durations differed between Monkey A (0.4 s) and Monkey B (0.3 s), we removed the middle 0.1 s of each delay period in Monkey A for pooled analyses to ensure temporal alignment.

A cell was considered responsive if it had firing rates significantly different from baseline (before the first stimulus onset) in one or more 50ms time bins (10ms overlap) at any point during the trial (from target onset to go-cue onset). Firing rates were time-averaged within each bin, and statistical significance was tested using 1-sample t-test with a statistical significance threshold of p<0.001 with two-sided alternative hypotheses.

Using the same method, we visualized the proportion of responsive neurons among all recorded neurons as a function of time in each session of each animal in the extended analysis (see Supplementary Figs. 6a and 7a).

We also analysed the selectivity of single neurons to the location of I1 and I2. We averaged neuron activities into 50ms time bins for each trial and performed one-way ANOVA on the I1 and I2 locations at each bin. Neurons with p<0.001 were considered location selective at the bin. In the extended analysis (Supplementary Figs. 6b and 7b), we visualized the proportion of I1 and I2 selective neurons as a function of time in each session of each animal.

Percentage of Explained Variance (PEV) analysis
To estimate how much information of the task variables (i.e., I1 and I2 locations) was coded by the activity of each single neuron, we calculated the percentage of explained variance (PEV, or ω^2). ω^2 is defined by
ω^2 = SS_between - (df × MSE) / (SS_total + MSE)
where df is the degree of freedom, and
MSE = (Σ_{i=1}^n (x_i - x_group)^2) / (Σ_{i=1}^n (n_i - 1))
SS_total = Σ_{i=1}^n (x_i - x_total)^2
SS_between = Σ_{group=1}^G n_group (x_group - x_total)^2

We visualized the PEV of all single neurons as well as the averaged PEV from neurons recorded in each session in the Supplementary Figs. 6c,d and 7c,d.

Pseudopopulation
We created pseudopopulations by sampling equal numbers of trials per condition from each session of both monkeys and pooling these trials together, as if these neurons responded together in each pseudo trial. We created 100 pseudopopulations separately for the LPFC (89 neurons) and the PAC (129 neurons). The selectivity of the neurons was as reported in our previous work14. Only correct trials were included in the pseudopopulation. All neural data analyses were conducted on the pseudopopulations.

Models
We trained artificial recurrent neural networks (RNNs) to simulate neural activity under different latent strategies in trials of 60 time steps (I1/I2 display=6 time steps, D1/D2=20 time steps, post-go-cue=8 time steps). Each RNN comprised 9 input units (4 locations × 2 types + 1 fixation), 64 recurrent units, and 4 output units (4 locations). The recurrent dynamics followed:
r_t = ReLU(W_rec r_{t-1} + W_in I_t + σ)
ReLU(x) = max(0, x)
And the output dynamics can be described as:
Y_t = Softmax(W_out r_t)
Softmax(x_i) = e^{x_i} / Σ_{j=1}^N e^{x_j}
where I_t, r_t and Y_t denote the input, recurrent, and output unit activities at time t, and W_in, W_rec, W_out represent the input, recurrent and output weights respectively. σ represents the noise at the recurrent layer and was drawn from N(0, 0.1). Recurrent weights were orthogonally initialized, while input and output weights followed Xavier-normal initialization. We optimized W_in, W_rec, W_out using stochastic gradient descent with NAdam. The loss was computed as the mean square error (MSE) of the outputs over the target time window:
L = 1/n Σ_{t=1}^n (Y_t - Y^_t)^2

For Retrieve at Recall (R@R) RNNs, during Delay 1 all output units were expected to have equal activity (0.25), and during Delay 2 the output of the choice item (I1 in T/D trials, I2 in T/T trials) was expected to be 1, while the non-choice items remained at 0. For Rehearse and Update (R&U) RNNs, the output corresponded to I1’s location during Delay 1 and switched to the choice item’s location during Delay 2. 100 RNNs were trained per strategy, each with different weight initializations.

Principal Component Analysis (PCA)
We applied principal component analysis (PCA) to each pseudo-population to reduce dimensionality before decoding, using the scikit-learn library44. To preserve variance across conditions, we computed mean firing rates per condition, averaging over Delay 1 and Delay 2. The resulting activity matrix X (N_conditions (24) × N_neurons) was used to fit a PCA model, which was then applied to the full time series for dimensionality reduction. We defined the full space of the transformed data as the projections on the first 15 PCs, which counted for at least 90% of the total explained variance (EVR) on average in both regions. The same procedure was applied to the hidden unit activities of task-optimized RNNs.

Decoding Analysis
Cross-temporal Decodability. To measure the decodable stimulus location information across the population of recorded neurons, we used linear discriminant analysis (LDA) based on the algorithm from scikit-learn44 to predict the locations of Items 1 and 2 (Fig. 2 and Supplementary Figs. 2a–4a, 5b, 6e–7e, 9a). Decoding analyses were conducted on neural data from 0.2 s before Item 1 onset to the go cue. A 50ms non-overlapping smoothing window was applied before training and testing decoders. PCA-based dimensionality reduction was applied before decoding, and analyses were performed on projected activities. The same approach was used for RNN hidden unit activities. For full-spacedecodability (Fig. 2), we used projections on the top 15 PCs to train and test decoders. For readout subspace decodability (Supplementary Fig. 9a), we used state projections on the readout subspace.

Within each pseudopopulation and RNN, we randomly sampled half of the trials for training and the other half for testing, iterating 100 times. At each iteration, a decoder was trained using training set activities at one time bin to predict item locations and tested on the test set activities across all time bins. Decoding performance was averaged over 100 iterations to minimize variability from set-splitting. We tested decodability significance at each time bin using a 95th-percentile test (see Statistical Tests), comparing decoder accuracy to baseline distributions generated from data with shuffled location labels (shuffled 100 times per pseudo-population and RNN). We repeated this process until all time bins were trained and tested.

Code Stability. We defined the code stability as the within-time decodability (trained and tested at the same time bin) divided by the mean cross-time decodability (trained and tested at different time bins) across selected time windows21. More specifically, cross-time decodability was calculated at every possible pair of train-test bins that were different from each other, in other words, the off-diagonal bins in cross-temporal decoding plot, while the within-time decodability was the on-diagonal bins, where decoders were trained and tested at the same bin. These decoder performances were averaged across bins and trial type conditions for stability ratio calculation. We calculated this ratio separately for late Delay 1 (last 0.5s) and late Delay 2, followed by statistical comparisons (see Statistical Tests).

The population code of the target may change after the presentation of a distracting stimulus (i.e., code morphing)19. Here, we quantified the code morphing ratio in the T/D trials as the logarithm of the ratio of the mean cross-temporal decodability trained and tested in late Delay 1 over the decodability trained in late Delay 1 and tested in late Delay 2 (and vice versa). A low code morphing ratio indicates a time-invariant code. Baseline distributions were created by decoders trained with label-shuffled data, iterated 100 times, and averaged within each pseudo-population and RNN.

Subspace analysis
Subspace estimation. Low-dimensional geometries can be estimated from the population based on various methods18,20,29,44. We estimated low-dimensional subspaces using methods adapted from Panichello and Buschman (2021)18 and Piwek et al. (2023)29 to obtain 2D planes best fitting the representations of Item 1 and Item 2 during early (first 0.5 s of) and late (last 0.5 s of) Delay 1 and Delay 2. For each pseudo population, we first grouped the trials by conditions (N_conditions = N_location combinations (12) × N_type (2)). We then averaged the neural population states by conditions and projected the N_conditions (24) × N_neurons data to the axes of the top three principal components (PCs). On average, the sum of explained variances by these three PCs reached about 50% of total variances in LPFC and over 60% in PAC as well as in R@R and R&U RNNs (ΣEVR_PC1-3 : R@R: M(SD)=0.995(0.010), R&U: M(SD)=0.994(0.007); LPFC: M(SD)=0.499(0.016), PAC: M(SD)=0.611(0.013)).

Within each time window, we first averaged the activities across all time points, returning us an N_conditions (24) × N_PCs (3) matrix. For item-specific subspaces (Fig. 3 and Supplementary Fig. 8), we separated the matrix by the type condition (T/T and T/D) for analysis clarity, each with a 12×3 matrix. Within each type, we estimated the mean representation by averaging the rows corresponding to conditions with the same location of each item: for example, the representation of I1 presented at location 1 was calculated as the mean of all conditions with I1-location=1, regardless of the location of I2. This returned us an N_locations (4) × N_PCs (3) matrix for each item. Next, we conducted a secondary PCA on this matrix and extracted the first two PCs. These two eigenvectors corresponded to the directions of maximum variances by locations, hence were used to define the best-fitting 2D plane of the locational representation. Finally, we projected the states from the 3-PC space onto these 2D planes and used these projections for subsequent analyses.

The “readout” subspaces (Fig. 4) were estimated based on the same approach, except that we did not separate between trial types, and the mean representation was calculated by averaging the rows with the same location of the final choice item (i.e., I1 for T/D and I2 for T/T). Also, instead of estimating at separate time windows, we only used activities during late D2 to estimate the “readout” axes, as stable outputs were observed during this period in both models and brain regions (as shown in Fig. 2).

Geometry analysis. With the subspace estimated using the approach described above, we then examined the geometric relationships between subspace pairs, specifically the coplanarity and the degree of alignment of the representational configurations between subspaces. Metrics were calculated using methods adapted from Panichello and Buschman (2021)18 and Piwek et al. (2023)29. For coplanarity, we measured the cosine of the principal angle between the normal vectors of the two planes. We applied a correction to the directions of the plane-defining vectors based on the representational configurations to guarantee vectors from two different subspaces were under a common frame of reference, as described below29. This was because the original directions of PC axes generated by the PCA algorithm are ambiguous with respect to their sign, which would result in inconsistent signs of the normal vectors of the 2D planes and interfere with the principal angle calculations. To avoid this problem, we corrected the directions of the eigenvectors by first rotating PC1 vector to be positively collinear (i.e., parallel and in the same direction) to a predefined directional side of the location configurations, creating a PC1_corrected, and then rotating PC2 vector by the shortest angular distance to be orthogonal to PC1_corrected. We then used PC1_corrected and PC2_corrected as the plane-defining vectors as well as for normal vector calculations. Planes with mirror-reflected configurations of one another would lead to angles greater than 90° (cos(θ)<0), whereas the planes of rigid rotation of each other would have principal angles restricted smaller than 90° (cos(θ)>0).

For alignment, we measured the cosine of the minimal rotation angle, minimizing the distances between corresponding representational points on the two subspaces. To calculate the rotation angle, we first forced the two planes to be coplanar. Next, we estimated the representational configuration from each plane by averaging the states by item locations and then projected the configuration points on corresponding planes, giving us two N_locations (4)×2 configuration matrices. We then applied an orthogonal Procrustes analysis on these two matrices, which returned an orthogonal matrix R that could rotate one matrix to most closely match the other, with the R(0,0) as the cosine of the minimal rotation angle.

For both coplanarity and alignment, the baseline hypothesis was the full equivalence between subspaces; in other words, we tested whether the two subspaces were significantly non-coplanar and misaligned. To create the baseline distributions, we first split the data into a training set and a test set and separately estimated subspaces. We then calculated the coplanarity and alignment between the training and test set subspaces at each item and time bin of interest, and finally took the mean of them. The rationale was that a given subspace is perfectly coplanar and aligned to itself, and subspaces estimated from different subsets of the same pseudo-session or recurrent neural network (RNN) should be highly similar, with some variability due to differences between training and test sets. For example, for the comparison between I1D1 and I2D2, we averaged coplanarity and alignment between I1D1_train vs. I1D1_test and I2D2_train vs. I2D2_test. For each pseudo population and RNN, we repeated this process 100 times and took their average. The resulting parallel distributions were then compared to observed values, and empirical p-values were calculated using the 95th-percentile test (see Statistical Tests), and a significant p value indicated consistent deviation from the equivalent hypothesis.

Code transferability ratio. In addition to the geometry analysis, we also examined the code transferability between subspaces. Specifically, we trained LDA decoders with the state projections on one subspace and tested with the projections on the other subspace. The codes were expected to be transferable if the two subspaces were equivalent. Given the noisy nature of neural data, the decoder performances in the LPFC and PAC were generally worse than in the RNNs. To make the quantifications comparable between neural data and RNNs, we calculated the ratio of cross-subspace decodability (i.e., code transferability) over the within-subspace decodability (i.e., trained and tested with the projection on the same subspace), and a high ratio (close to 1) indicates the decodability to be at a similar level cross- and within-subspace. The baseline distributions were created by training the cross- and within-subspace decoders on data with shuffled location labels, and for each pseudo population and RNN, we repeated the process 100 times and took the average.

Drift ratio. To quantify the dynamics of population activity projection onto the readout subspace, for each condition (I1-I2 Combination × Type) we calculated the Euclidean distance between the mean projection points during late (last 0.5s of) Delay 1 and during late Delay 2 and scaled to the range from −1 to 1. We then calculated the drift ratio by dividing the drift distance in T/D trials by the drift distance in T/T trials. A low ratio would indicate the readout projections to be changed only when information updates were required. The baseline distributions were created by estimating the distances from data with shuffled location labels, and were repeated this process 100 times and took the average for each pseudo population and RNN.

Significance tests
For tests compared to baselines, we considered two distributions to be significantly different from baseline if the 95th percentile range of the test distribution did not overlap with the baseline distribution45,46. The p value was calculated as:
p = (1+X) / (N+1)
where X represents the number of overlapping points and N represents the total number of points in the baseline distribution.

For tests comparing between two test distributions, we pooled the data together and randomly re-assigned them to create two new distributions and calculated the mean difference. We iterated this process for 1000 times to create a null distribution. The p value was then calculated as the proportion of points in the null distribution that are larger or smaller (depending on the test direction of interest) than the true mean difference between the test distributions. We additionally calculated the effect size of the comparisons using the measure of Hedge’s g as:
g = (1 - 3 / (4(n1+n2) - 9)) × (x_1 - x_2) / s_0
s_0 = sqrt(((n1-1)s1^2 + (n2-1)s2^2) / (n1+n2-2))
where n and s refer to the number of data points and standard deviations of each distribution46,47.

Kolmogorov-Smirnov (K–S) test
To statistically compare the distributions between RNN models and biological regions, we applied Kolmogorov-Smirnov (K–S) tests on the primary quantification measures between all model-region pairs using Scipy47. The K–S test assesses whether two empirical distributions vary from each other based on their cumulative distribution functions, with a K–S statistic (D) indicating the distance between the two cumulative distribution functions (the smaller the closer) and a p-value (with two-sided alternative hypothesis) indicating the statistical significance.

Kullback–Leibler (KL) Divergence test
An alternative index we used to compare the similarities between the RNN models and biological regions is the KL divergence, which quantifies the dissimilarity between a model-generated probability distribution function and the empirical observation. It is a common measure of the loss of a model in machine learning. Greater KL divergence indicates more differences between the two distributions. Specifically, the KL divergence (D_KL) of a probability distribution Q from a reference probability distribution P is calculated as
D_KL(P||Q) = Σ_{x∈X} P(x) log (P(x) / Q(x))

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the authors present results using data recorded from monkey prearcuate (PAC) and lateral prefrontal cortex (LPFC) while the subject performed a working memory task. Two possible strategies (Retrieve at Recall, Rehearse and Update) were simulated using recurrent neural networks. Based on similarities in decoding neural activity and RNN hidden unit activity, the authors conclude that the data are consistent with a Rehearse and Update strategy. Although this finding may be of potential interest, I have some concerns with the results as presented.\nFirst, the results and conclusions seem fairly limited in scope - the authors find that population in activity in both PAC and LPFC is consistent with R&U. Very well, but why the redundancy? Are both regions doing the same thing, or is there something that distinguishes them? Are we to understand that both regions are controlling the rehearsal and updating processes? Are rehearsal and updating actually distinct processes? It appears that the authors are so intent on showing that the activity is similar to that of an RNN that they miss the larger picture.\nSecond, the logic of their argument is very indirect. Primarily they seem to rely on the following kind of reasoning: the R@R RNN suggests that Code Stability/Morphing/Coplanarity/Alignment/Transferability is significantly different between two conditions, while the R&U RNN suggests no signficant difference, and we find that there is no significant difference in PAC and LPFC, consistent with R&U. This is not as convincing as an argument based on finding significant differences since there could be a number of ways to obtain a null result.\nThird, I am worried about the behavioral difference between the RNNs and the monkeys - the RNNs are almost perfect, the monkeys are quite bad, even if they do score above chance. I can't find information about how long the monkeys were trained in the text of the manuscript, but I'm surprised they weren't overall better at the task. It would have been nice to see a more in-depth discussion of the kinds of errors the monkeys were making (outside of the 'failures of attention' or 'failures of self-control' the authors mention). That is, are the monkeys saccading to the distractor on T/D trials? Are they fixating an irrelevant location?\nWhat would happen if the RNNs were constrained to fit the monkey's behavioral data rather than simply being trained until they reached above 95% accuracy? Would the RNNs under either strategy make the same types of errors as the monkeys? Would the results of the analyses of hidden unit activity change?\nFourth, it seems that the implementation of the Retrieve at Recall strategy is not consistent with the idea noted by the authors of \"passively storing memory items.\" Since the target output of the R@R networks during following the presentation of T1 (i.e. during Delay 1) is uniform, in order to maintain the information about the initial target location, the hidden units are essentially forced to learn weights such that the information was maintained dynamically across multiple hidden units. This seems much more similar to 'rehearsal' than passive information storage.\nMinor:\nBottom of page 3\nThere is something wrong with the accuracy data for monkey B", "reviewer_2": "In the present work, the authors try to infer the strategy that macaque monkeys used to resolve a working memory task in which the exact same behavioral responses result from different strategies. The infer the strategy by comparing the activity of (pseudo)populations of neurons from 2 cortical regions (Prefrontal Cortex - PFC, Prearcuate Cortex - PAC) to the activity of hidden units of artificial Recurrent Neural Networks (RNN) trained to resolve the task using one of two possible strategies. They apply dimensionality reduction and machine learning techniques to find the subspaces in which the neural activity encodes the behavioral outputs and characterize the properties of these subspaces and the dynamics of the neural activity within these subspaces. The conclusion is that the neural activity from animals follows the same pattern of the activity of only one of the RNN, therefore, the strategy on which that RNN was trained is inferred to be the strategy that the animals were using to resolve the task.\nThe paper is well written, and clearly exposes the point the authors try to make. The research question is an interesting one, and the methods used to address that question (inferring the neural basis of behavioral responses that can be produced under different contexts) are sound.\nI have, however, a few concerns. One major concern is that the results seem to come from only one animal. Furthermore, animals had a rather poor performance. I elaborate my concerns below:\n1) The authors jump into tertiary and beyond layers of analysis without showing too much about functional properties of the neurons recorded and used for analysis. I could not even find a clear and unambiguous report of how many neurons were recorded per animal per session. In addition to this, it is unclear if all the recorded units were used to build the pseudopopulations, and thus the sampling was only made over trials. It is also not reported if the recorded units were responsive during the task, or if they exhibited any form of selectivity, and in that case, what proportion of recorded (and analyzed) neurons were responsive and/or selective to task variables.\n2) The previous comment becomes particularly important when we go into the subspace analyses. The activity of the pseudopopulations was passed through dimensionality reduction, and all subsequent analyses were performed on that lower dimensional activity. However, no justification for this procedure is given. I could try to infer what the purpose was: perhaps to work with decorrelated activity, or some sort of feature (i.e. neuron) selection. But that is not a task that should be left to the reader, it should be made explicit. It is also unclear if this initial dimensionality reduction was performed only for the decoding and code stability analyses, or if the low dimensional activity was also used for the subspace analysis.\n3) Related to comment 2: because pseudopopulations pooled over two animals, selecting features through dimensionality reduction (PCA) can hide the fact that most (if not all) of the significant results come from only one of the animals, as it is clear from the results presented in Extended Figures 1 & 2. Given this, without a solid description of the functional properties of the units recorded and its relation to the performance of the animals, it is difficult to accept the claims the authors make.\n4) The activity of area 8A (Prearcuate cortex) is more in line with the Rehearse and Update strategy. This is precisely what O would expect given that activity in this area has been shown to be strongly associated with the preparation of saccadic eye movements. There is also strong crosstalk between PFC and PAC. My question is then, how could we falsify the results, and dissociate the findings from the saccadic movements?\n5) Perhaps I missed it, but I did not see a Data and Code availability statement in the manuscript, or a link to the repository where it is hosted.\nI only saw a link to a code/data repository at the time of writing this review. That information doesn't seem to be included in the manuscript.", "reviewer_3": "This manuscript examines how monkeys solve a working memory updating task by comparing neural activity patterns in two prefrontal regions (LPFC and PAC) with recurrent neural networks (RNNs) trained to implement different computational strategies. The authors propose two potential strategies: \"Retrieve at Recall\" (R@R), which involves passive storage of memory items until recall, and \"Rehearse and Update\" (R&U), which involves active maintenance and updating of information as new items are presented. Through analyses of neural representational geometry, the authors conclude that monkeys employ the R&U strategy, despite both strategies producing similar behavioral outcomes.\nThis manuscript suffers from conceptual framing issues that undermine its conclusions. The paper's core finding—that prefrontal working memory representations align better with a model of active maintenance than with passive storage and later reactivation—is also not novel.\nMajor Concerns\n1. Mischaracterization of \"Strategy\"\nThe central premise of this paper—investigating \"latent strategies\"—is problematic. What the authors are actually studying is not a behavioral strategy but rather the neural implementation of working memory. The two RNN models (R@R and R&U) represent different theoretical mechanisms for implementing working memory. This is not the same as cognitive strategies that an animal might consciously or unconsciously select, as the manuscript tries to imply. I believe that the neural implementation of working memory is more accurately characterized as a mechanism than a strategy. The authors are essentially testing whether working memory is supported by sustained neural activity (R&U) versus activity-silent mechanisms with later reactivation (R@R), which is an important question about neural mechanisms, not strategies.\n2. Limited Theoretical Framework\nThe paper presents a binary distinction between two possible implementations of working memory without adequately acknowledging the rich theoretical literature on working memory mechanisms. The framing of R@R versus R&U oversimplifies complex neural processes that likely involve combinations of persistent activity, synaptic weight changes, and dynamic coding.\nThe authors refer to human behavioral studies on working memory updating tasks but fail to integrate this with the extensive neurophysiological literature on working memory maintenance mechanisms, creating a disconnect between their behavioral framing and their neural analyses.\n3. Overinterpretation of Results\nThe authors make strong claims about inferring \"latent strategies\" based on comparing monkey neural data with artificial neural networks. However, the match between biological and artificial systems might reflect constraints on how neural networks can solve this particular task rather than revealing strategic choices made by the monkeys.\nThe paper concludes that monkeys employ the R&U strategy based on the similarity of neural patterns, but does not adequately explore alternative explanations, such as whether the observed patterns might reflect a hybrid mechanism or whether the distinction is meaningful given the task constraints.\nGiven these concerns, I will skip the technical details unless the editor feels it's necessary.", "reviewer_4": "Qian et al. compared the patterns of neural activity recorded in the monkey lateral prefrontal cortex (LPFC) and pre-arcuate cortex (PAC) and the activity patterns in the recurrent neural networks (RNN) during a working memory update task. The RNN was trained according to two alternative strategies; retrieve at recall (R@R) and rehearse and update (R&U) strategies. They found that the neural activity in the monkey PFC was more consistent with and resembled the activity in the RNN trained with the R&U strategy. The question and approach used to address this question are interesting, but there are several weaknesses.\n1. The authors claim that “no studies have been able to infer which latency strategy is used by animals”, but this is an exaggeration. Many studies that employ mathematical modeling, especially in reinforcement learning (e.g., Daw et al., 2011), have developed techniques that can distinguish between multiple behavioral and learning strategies based on the choice and reaction time data. Even for the working memory update task used in the present study, it may be possible to determine which strategy is more likely, if the authors have analyzed the patterns of errors more carefully. For example, update failures in the R&U strategy might be more likely to produce the errors of selecting T1 in T/T trials compared to the R@R strategy.\n2. The performance of the animals was quite poor and only slightly above the chance level (even considering the errors associated with fixation). This rases two concerns. First, it may be more appropriate to compare the neural activity in the PFC to that of RNN trained to achieve the level of performance more similar to that of monkeys. Second, it may be useful for the authors to analyze the neural activity during error trials. For example, what does the activity associated with errors during T/T trials look like? Does the activity during D1 and D2 reflect the location of I1, hence reflecting the failure of the update?\nMinor:\n3. How the stability ratio (p.20) was calculated should be explained a bit more clearly. In particular, what were the two bins used to calculate the cross-time decodability?\n4. Code morphing ratio was defined as the ratio of two cross-temporal decodability (D1/D2). It may be desirable to take the logarithm of this ratio before computing the mean, because the average ratio tends to be larger than 1 even when the numerator and denominator have the same distributions."}, "author_response": "Responses in blue. Changes to the manuscript in bold.\nReply to Reviewers\nReviewer #1 (Remarks to the Author):\nIn this manuscript, the authors present results using data recorded from\nmonkey prearcuate (PAC) and lateral prefrontal cortex (LPFC) while the subject\nperformed a working memory task. Two possible strategies (Retrieve at Recall,\nRehearse and Update) were simulated using recurrent neural networks. Based\non similarities in decoding neural activity and RNN hidden unit activity,\nthe authors conclude that the data are consistent with a Rehearse and Update\nstrategy. Although this finding may be of potential interest, I have some\nconcerns with the results as presented.\nComment 1: First, the results and conclusions seem fairly limited in scope -\nthe authors find that population in activity in both PAC and LPFC is\nconsistent with R&U. Very well, but why the redundancy? Are both regions\ndoing the same thing, or is there something that distinguishes them? Are we\nto understand that both regions are controlling the rehearsal and updating\nprocesses? Are rehearsal and updating actually distinct processes? It appears\nthat the authors are so intent on showing that the activity is similar to\nthat of an RNN that they miss the larger picture.\nWe would like to thank the reviewer for allowing us to clarify this point.\nFirst, it is important to emphasize that when we talk about strategy we refer\nto the animal’s strategy, rather than a brain region’s strategy. We assume\nthat all cortical regions work together to implement the animal’s strategy.\nSecond, it is not our goal to claim that both PAC and LPFC are redundant.\nRather, our claim is that the activity in both regions is consistent with\nthe rehearse and update strategy, despite their differences.\nWe agree with the reviewer that it is important to discuss the differences\nbetween the PAC and LPFC. We did observe several differences in their dynamics\ndespite their activity being consistent with the rehearse and update strategy.\nA prior study focused on characterizing the differences in timing of signals\nin these two regions (Qian et al., 2024). In that study, we found that the\nPAC population updated target information faster than the LPFC (PAC: ~100\nms, and LPFC: ~400 ms after stimulus onset). In addition, we found that both\nregions briefly encoded the distractor location in T/D trials but this\ninformation was present for longer in the PAC than in the LPFC. We\ninterpreted these differences in timing as suggesting that the PAC encoded\ntarget information faster, but less selectively, to support rapid action,\nwhile the slower LPFC responses relate to the maintenance of working memory.\nIn the current manuscript we provide evidence that, despite the differences\nbetween brain regions, the activity of both regions are consistent with the\nrehearse and update strategy.\nIn order to clarify these points in the manuscript we have added a new\nparagraph in the discussion:\nP16L20: “It is important to highlight that when we use the term \"strategy,\"\nwe are referring to the animal's approach to solve the task, rather than a\nstrategy specific to a single brain region. We assume that brain regions\ncollaborate to implement this animal-level strategy. Therefore, while\nindividual brain regions may have distinct functional roles within the\norganism, their activity should collectively align with the strategy the\nanimal is employing. Thus, our aim is not to suggest that the PAC and LPFC\nare redundant. Rather, we argue that the activity observed in both regions,\ndespite their differences8, is consistent with the rehearse and update\nstrategy.”\nRegarding the distinction between rehearsal and updating, we assumed that\nthey are two distinct processes, based on cognitive models (E.g., Postle,\n2003). We consider rehearsal as the active maintenance of information, and\nupdating as the replacement of one memory for another. Our results show that\nboth PAC and LPFC are involved in both of these processes. In both regions,\ninformation was stably encoded during the delay periods (consistent with\nrehearsal), and this information was replaced by the new target information\nin T/T trials, but not in T/D trials (consistent with updating).\nIn order to clarify these points in the manuscript we have added a new phrase\nin the discussion:\nP17L20: “Prefrontal cortex plays an important role in working memory\nrehearsal19,20, and updating8,21–23.”\nComment 2: Second, the logic of their argument is very indirect. Primarily\nthey seem to rely on the following kind of reasoning: the R@R RNN suggests\nthat Code Stability/Morphing/Coplanarity/Alignment/Transferability is\nsignificantly different between two conditions, while the R&U RNN suggests\nno significant difference, and we find that there is no significant difference\nin PAC and LPFC, consistent with R&U. This is not as convincing as an argument\nbased on finding significant differences since there could be a number of\nways to obtain a null result.\nWe would like to thank the reviewer raising this point. We agree that a\ncomparison of each model and brain region with a shuffled null distribution\nis not as convincing as a direct comparison between models and brain regions.\nThus, to make the direct comparisons, we performed Kolmogorov-Smirnov (K-S)\ntests on the all the measures quantified. The K-S statistic (D) provides a\nmeasure of the divergence or distance between the distribution functions (the\nsmaller D value the closer distributions). We summarized the results in a\nnew extended data table (Extended Data Table 1 in P42) and added in-text\ndescriptions in the results section (see P7L26, P8L12, P11L28, P14L25, and\nP29L3 for the methods description ). Of note, we do not report the p-values\nof the K-S tests since these depend on the number of simulations run in the\nmodels, where more simulations invariably lead to more significant\ndifferences, whereas the D values are stable converge to a stable value. The\np values reported in Extended Data Table 1 correspond to 100 simulations of\neach model (just for reference).\nOverall, across all measures, the R&U models was closer to both PAC and LPFC\ncompared to R@R models. These results provide stronger support to the\nconclusion that the R&U RNNs better approximated the neural responses in both\nregions.\nComment 3: Third, I am worried about the behavioral difference between the\nRNNs and the monkeys - the RNNs are almost perfect, the monkeys are quite\nbad, even if they do score above chance. I can't find information about how\nlong the monkeys were trained in the text of the manuscript, but I'm surprised\nthey weren't overall better at the task. It would have been nice to see a\nmore in-depth discussion of the kinds of errors the monkeys were making\n(outside of the 'failures of attention' or 'failures of self-control' the\nauthors mention). That is, are the monkeys saccading to the distractor on\nT/D trials? Are they fixating an irrelevant location?\nWhat would happen if the RNNs were constrained to fit the monkey's behavioral\ndata rather than simply being trained until they reached above 95% accuracy?\nWould the RNNs under either strategy make the same types of errors as the\nmonkeys? Would the results of the analyses of hidden unit activity change?\nThis are all good points raised by the reviewer, which we address below.\nPoor Performance of the monkeys\nThe chance-level performance in our task is 25% (1 out of 4 possible options),\nand the animals reached a higher than chance performance level (60%). The\nanimals were trained for over 9 months each, and the performance plateaued\nat this level. Unfortunately, our IACUC does not allow us to water restrict\nour animals, which is commonly used in other institutions to motivate animals,\nso we could only use fruit juice on unrestricted animals for motivation. Thus,\nwe speculate that the low level of performance (compared to other similar\nstudies, including our own previous studies) is due to lower motivation,\nrather than a failure to understand the task. It is also unlikely that the\nperformance reflects learning of one trial type but not the other (i.e.,\nlearned T/D but not T/T, or vice versa), since the accuracy for both trial\ntypes (T/T or T/D) were similar. Therefore, we believe that our conclusions,\nbased on the analysis of correct trials, are valid, even if the overall\nperformance of the animals is comparatively low.\nAnalysis of Error Trials\nThe behavioral accuracies that we reported constitute the proportion of\nrewarded trials over all completed trials. For a trial to be rewarded the\nanimal had to fulfill three criteria: (1) saccade to the correct location,\n(2) saccade earlier than 500 ms after the go-cue, and (3) fixate on the\ntarget for at least 200 ms. Trials in which the animals broke fixation before\nthe go-cue were considered aborted trials, rather than error trials, so they\nwere not included in this calculation. To analyze the types of errors that\nthe animals performed, we divided the error trials into 4 types and calculated\nthe proportion of each among all error trials in each session:\n1. Trials in which the monkeys responded to the correct location but\nfailed to meet the additional criteria (#2 and #3): T/T: M(SD) = 0.158(0.120),\nT/D: M(SD) = 0.203(0.109))\n2. Trials in which the saccades were directed to the distractor location\nin T/D trials, or Target 1 location in T/T trials: T/T: M(SD) = 0.196(0.108),\nT/D: M(SD) = 0.194(0.116))\n3. Trials in which the monkeys responded to a non-presented location\n(neither Target 1, Target 2 nor distractor location): T/T: M(SD) =\n0.594(0.052), T/D: M(SD) = 0.531(0.026))\n4. Saccades that went to none of the locations (e.g., outside the screen):\nT/T = 0.052(0.028), T/D = 0.072(0.030))\nIn summary, ~15-20% of “errors” were trials in which the animals saccaded\nto the correct target location, but the animal failed to fulfill the other 2\ncriteria for reward, ~20% or errors were directed to the Target 1 or\nDistractor location (error type 2), ~50% of the errors were directed to one\nof the other 2 possible targets (error type 3), and ~10% to other locations.\nIf we exclude the first type of error (towards the correct target), these\nresults suggest that in the majority of error trials the monkeys were guessing\nthe correct location (similar likelihood to go to either of the three non-\ntarget locations). So, in summary, in ~60% of trials the monkeys reported\nthe correct location, and in the rest of the trials they reported a random\none or moved their eyes out of the screen.\nTo reflect this conclusion, we have added the following statement in the\nbehavioral results section. We do not believe that adding a detailed\ndescription in the manuscript (as we added above) would contribute much\nbeyond the statement added. If the reviewer believes that this would add\nmeaningful information to the goal of the current manuscript, we would be\nhappy to these details in a revision.\nP4L9: “The rest of the error trials suggest that the animals were guessing,\nsince they had similar likelihood of going to any of the other three erroneous\ntargets (data not shown).”\nRNNs with Lower Levels of Performance\nThe reviewer asks “What would happen if the RNNs were constrained to fit\nthe monkey's behavioral data rather than simply being trained until they\nreached above 95% accuracy? Would the RNNs under either strategy make the\nsame types of errors as the monkeys? Would the results of the analyses of\nhidden unit activity change?”\nBelow we show the results of analyses suggested by the reviewer. However,\nbefore presenting those results, we would like to highlight that there is an\nimportant difference between the reasons behind the errors of poorly-trained\nRNNs and the errors of well-trained, but poorly motivated animals. RNN errors\nreflect a lack of convergence onto the best solution (in other words, the\nRNN has not learned the task properly), whereas an animal (including human)\ncan still commit errors in a well-learned task, either due to distraction,\nfailure of self-control, or lack of motivation to engage in the task. Thus,\nwe propose that the best way to infer the animals’ strategy is to compare\ntheir neural activity with well-trained RNNs. With that preamble out of the\nway, below we present the results of RNNs trained to lower levels of\nperformance.\nWe followed the reviewer’s advice and carried out error analyses in RNNs\nwith behavioral accuracy comparable to the animals’ performance. Since type\n1 and 4 errors were not applicable to the RNNs, we recalculated the behavioral\naccuracy in animals after excluding those trials, and the corrected\nperformance approximation was 70%. We then trained another 100 RNNs for each\nstrategy with an early-stopping rule when outputs at the last timepoint were\n70% accurate. All the other parameters remained unchanged.\nIn general, R@R and R&U RNNs had similar error rates by trial types (T/T:\nR@R: M(SD) = 0.355(0.056), R&U: M(SD) = 0.384(0.055); T/D: R@R: M(SD) =\n0.392(0.057), R&U: M(SD) = 0.337(0.055)). In other words, either strategy\ndid not tend to make more errors in T/T or T/D trials than the other. When\nbreaking down the errors into types, specifically error type 2 and 3 mentioned\nabove, we also found the two strategies had very similar proportions (among\nall errors) of type 2 (T/T: R@R: M(SD) = 0.485(0.128), R&U: M(SD) =\n0.544(0.152); T/D: R@R: M(SD) = 0.247(0.072), R&U: M(SD) = 0.283(0.075)) and\ntype 3 errors (T/T: R@R: M(SD) = 0.515(0.128), R&U: M(SD) = 0.456(0.152);\nT/D: R@R: M(SD) = 0.753(0.072), R&U: M(SD) = 0.717(0.075)). For both\nstrategies, the majority of the errors were type 3 errors, which did not\ncorrespond to the unwanted target or distractor. Since the error patterns\nare similar between both strategies, this analysis cannot be used to infer\nthe animals’ strategy.\nWe also analyzed the neural representations of the hidden units of the 70%-\naccurate RNNs (figures shown in the next page). Since the training was\nstopped early, these RNNs did not strictly obtain the strategic\ncharacteristics as we found in the fully optimized models. Nonetheless,\nmost of the result patterns were still consistent with the observations in\nthe fully optimized RNNs: during D2, both regions and both models showed\nstable codes, although neither model was as stable as when they were fully\noptimized (R@R: M(SD) = 0.968(0.016), p = 0.267; R&U: M(SD) = 0.974(0.014),\np = 0.208). Comparing between delays, the 70%-accurate R&U RNNs the code\nduring D1 was more stable as during D2, while the 70%-accurate R@R RNNs was\nmore dynamic during D1 (R@R: MD = -0.010, p = 0.004, g = -0.402; R&U: MD =\n0.010, p = 1.000, g = 0.704). Code morphing ratios of the 70%-accurate RNNs\nalso showed that target code was generalizable between D1 and D2 in the R&U\nmodels while it morphed in the R@R models (R@R: M(SD) = 0.431(0.234), p =\n0.020; R&U: M(SD) = 0.127(0.100), p = 0.198).\nFor the relationship between I1D1 and I2D2 subspaces, we found that\nT/T T/T\nboth models showed neither good coplanarity (compared to the fully\noptimized RNNs) nor significant deviation from shuffled baseline, but on\naverage the 70%-accurate R&U models still tended to be more coplanar than\nthe R@R ones (R@R: M(SD) = 0.635(0.594), p = 0.644; R&U: M(SD) =\n0.716(0.602), p = 0.644). On the other hand, both models exhibited good\nrepresentational alignment. The 70%-accurate R@R models were more aligned\nthan the R&Us on average, but the difference was marginal (R@R: M(SD) =\n0.903(0.283), p = 1.000; R&U: M(SD) = 0.899(0.371), p = 1.000). The code\ntransferability ratio of 70%-accurate R@R models was also near\nsignificantly lower than the baseline and lower than the R&Us (R@R: M(SD) =\n0.585(0.188), p = 0.059; R&U: M(SD) = 0.805(0.165), p = 0.485). Finally, we\ncalculated the mean drift ratio on the readout subspace of the 70%-accurate\nR@R and R&U models, and the results suggested more readout projection\ndrifts in the R@R models compared to the R&U (R@R: M(SD) = 0.961(0.596), p\n< 0.001; R&U: M(SD) = 0.443(0.595), p = 0.079).\nOverall, despite having some minor deviations from the fully trained RNNs,\nthe results with the 70%-accurate models were consistent with the patterns\nobserved in the fully trained RNNs. We hope these analyses will help\naddress the reviewer’s concerns.\nComment 4: Fourth, it seems that the implementation of the Retrieve at Recall\nstrategy is not consistent with the idea noted by the authors of \"passively\nstoring memory items.\" Since the target output of the R@R networks during\nfollowing the presentation of T1 (i.e. during Delay 1) is uniform, in order\nto maintain the information about the initial target location, the hidden\nunits are essentially forced to learn weights such that the information was\nmaintained dynamically across multiple hidden units. This seems much more\nsimilar to 'rehearsal' than passive information storage.\nThank you for raising this question, as it highlights a point that is unclear\nin our original manuscript. We use the term “passive storage” following\nthe use in prior literature (e.g., Cowan et al., 2005), in which they refer\nto storage of information outside of the focus of attention as “passive”,\nand storage of attended information as “active”. In the Retrieve at Recall\nstrategy, retrieval refers to bringing a memorized item from an unattended\nstate (“passive”) to an attended state (“active”). Rehearsal, on the\nother hand, refers to keeping information under constant attention\n(constantly active). In the context of the RNN models, the “readout”\nsubspace encodes attended information, whereas a subspace orthogonal to the\nreadout subspace encodes unattended information. Hence, our argument is that\ndifferent strategies lead to different ways of maintaining I1 information.\nSpecifically, if the R&U strategy is used, I1 information would be encoded\ndirectly onto the “readout” subspace, whereas if the R@R strategy is used,\nI1 information would be encoded onto a subspace orthogonal to the “readout”\nsubspace. We do realize that the terms “active” and “passive” may lead\nto confusion. Thus, we replaced “passive” with “unattended” and “active”\nwith “attended” throughout the manuscript.\nWe would also like to clarify that although R@R networks were trained not to\nproduce discriminative output during D1, theoretically this could still lead\nto a dynamic code or a stable code (for example, encoded in a stable unattended\nsubspace). This is supported by fact that some (although very few) R@R RNNs\nexhibited code stability ratio close to 1 during D1 (see Fig 2B). Thus,\nwe’re not forcing the hidden units to learn any specific coding mechanism.\nThe key goal of our training procedure for the R@R strategy was to ensure\nthat the format of the memory in D1 was different than in D2, as was observed\nin Panichello et al. (2021) and Piwek et al. (2023). In contrast, the goal\nof our training procedure for the R&U strategy, was to ensure that the format\nof the memory in D1 and D2 was similar, as has been observed in delay movement\ntasks (E.g., Parthasarathy et al., 2019).\nMinor:\nBottom of page 3\nThere is something wrong with the accuracy data for monkey B\nWe are not sure about which part the reviewer is referring to. We’ve added\nthe line number labels to our edited manuscript, and we would appreciate if\nthe reviewer could clarify where there is something wrong.\nReviewer #2 (Remarks to the Author):\nComment 1: The authors jump into tertiary and beyond layers of analysis\nwithout showing too much about functional properties of the neurons recorded\nand used for analysis. I could not even find a clear and unambiguous report\nof how many neurons were recorded per animal per session. In addition to\nthis, it is unclear if all the recorded units were used to build the pseudo\npopulations, and thus the sampling was only made over trials. It is also not\nreported if the recorded units were responsive during the task, or if they\nexhibited any form of selectivity, and in that case, what proportion of\nrecorded (and analyzed) neurons were responsive and/or selective to task\nvariables.\nWe would like to thank the reviewer for pointing out this oversight. We had\nstated the number of cells in each region in the methods section, but we do\nrealize that it would have been helpful to provide more information in the\nmethods, and also some information about the neurons’ responsiveness and\nselectivity in the results section.\nWe have added this information to the methods section:\nP20L21: “We recorded a total of 89 neurons in LPFC (Monkey A: 17, Monkey B:\n72) and 129 neurons in PAC (Monkey A: 3, Monkey B: 126) across 11 sessions\n(Monkey A: 3, Monkey B: 8). The number of LPFC cells in each session ranged\nbetween 3 and 14 (M(SD) = 8.091(3.145)), and the number of PAC cells in each\nsession ranged between 0 to 21 (M(SD) = 11.727(7.669)). All cells were used\nto build the pseudo populations.”\nA cell was considered responsive if it had firing rates significantly\ndifferent from baseline (before the first stimulus onset) in one or more 50\nms windows (10 ms overlap) at any point during the trial (from target onset\nto go-cue onset). Firing rates were time-averaged within each bin, and\nstatistical significance was tested using 1-sample t-test with a statistical\nsignificance threshold of p < 0.001. Under these criteria, all 129 PAC cells\nand 84 out of 89 LPFC cells were task responsive.\nSelectivity was calculated with a 2-way ANOVA (location x trial type).\nSelectivity was calculated in the following epochs: I1 (0-300ms), ED1(300-\n800), LD1(800-1300), I2(1300-1600), ED2(1600-2100), LD2(2100-2600. For I1,\nED1, and LD1, only Location selectivity was considered since the monkey did\nnot know the trial type until I2 was presented. For I2/D2, Location, Type,\nLocation + Type, and Location * Type selectivity were considered. Under these\ncriteria, all 129 PAC cells and 77 out of 89 cells were task selective at\nsome point during the task (from target onset to go-cue).\nWe have added this information to the results section (and the corresponding\nmethods descriptions, which are not shown below):\nP7L2: “Overall, we recorded 89 neurons from LPFC and 129 neurons from PAC\nin two animals across 11 sessions. Out of the recorded neurons, 100% (129/129)\nof PAC cells and 94% (84/89) of LPFC cells were task responsive, and 100%\n(129/129) of PAC cells and 87% (77/89) of LPFC cells were selective at some\npoint during the task (from target onset to go-cue onset)”.\nComment 2: The previous comment becomes particularly important when we go\ninto the subspace analysis. The activity of the pseudo populations was passed\nthrough dimensionality reduction, and all subsequent analyses were performed\non that lower dimensional activity. However, no justification for this\nprocedure is given. I could try to infer what the purpose was: perhaps to\nwork with decorrelated activity, or some sort of feature (i.e. neuron)\nselection. But that is not a task that should be left to the reader, it\nshould be made explicit. It is also unclear if this initial dimensionality\nreduction was performed only for the decoding and code stability analyses,\nor if the low dimensional activity was also used for the subspace analysis.\nWe would like to thank the reviewer for this comment. In the current study,\nwe applied dimensionality reduction (via PCA) to the neural population data\nto denoise the neural data. This is discussed in the results section:\nP7L7: “We applied principal component analysis (PCA) to denoise and reduce\nthe dimensionality of data (see Methods), and we defined the space consisted\nof the first 15 PCs in each pseudo population and RNN”\nWe should point out also that we felt comfortable applying dimensionality\nreduction to this dataset because several prior studies (including from our\nlab) have shown that working memory can be represented in low-dimensional\nmanifolds and subspaces (e.g., Mante et al., 2013; Panichello & Buschman,\n2021; Tang et al., 2021).\nThe dimensionality reduction procedure was applied to all analyses (decoding\nand subspace). In the methods section we noted that subspaces were estimated\nvia a 2-step-PCA method that adapted from Panichello & Buschman (2021), where\nthe 1st-order PCA in this process was calculated in the exact same way as\nused for decoding. The only difference was that we defined the top 15 PCs as\nthe full space for decoding; while only the top 3 PCs were used to construct\nthe 1st-order subspaces for the purpose of conceptualization and\nvisualization.\nComment 3: Related to comment 2: because pseudo populations pooled over two\nanimals, selecting features through dimensionality reduction (PCA) can hide\nthe fact that most (if not all) of the significant results come from only\none of the animals, as it is clear from the results presented in Extended\nFigures 1 & 2. Given this, without a solid description of the functional\nproperties of the units recorded and its relation to the performance of the\nanimals, it is difficult to accept the claims the authors make.\nWe would like to thank the reviewer for pointing this out. As described in\nthe response to question #1, we have now added a solid description of the\nfunctional properties of the units recorded. It is indeed the case that\nMonkey B contributes more to the pooled results than Monkey A, since we\nwere able to record more neurons from Monkey B. However, the neurons that\nwe did record from Monkey A show properties consistent with those of Monkey\nB (and with the R&U strategy). We hope that the further characterization\nprovided of the single neuron responsiveness and selectivity helps address\nthe reviewer’s concern.\nComment 4: The activity of area 8A (Prearcuate cortex) is more in line with\nthe Rehearse and Update strategy. This is precisely what O would expect given\nthat activity in this area has been shown to be strongly associated with the\npreparation of saccadic eye movements. There is also strong crosstalk between\nPFC and PAC. My question is then, how could we falsify the results, and\ndissociate the findings from the saccadic movements?\nThank you for raising this important question. We agree that the activity of\nPAC neurons are associated with saccadic movement preparation, as this has\nbeen extensively shown in the literature, including by our group (Tang et\nal., eLife, 2020). However, we disagree that this observation implies that\nthe animal is employing the R&U strategy. In our task, during Delay 1, the\nanimals do not yet know where they will need to saccade: there is a 50%\nchance that they will have to saccade to Target 1 (if it is a T/D trial),\nand 50% chance that they will have to saccade to one of the other 3 locations\n(if it is a T/T trial). Thus, the animals may decide to employ a strategy\nwhere they immediately start preparing a saccade after Target 1 is shown (R&U\nstrategy), or they may decide to adopt a strategy where they only prepare\nthe saccade once they are sure where the saccade will be directed, after\nStimulus 2 is shown (R@R strategy). Thus, our conclusion, that the animals\nare employing the R&U strategy, would have been falsified if the activity of\nPFC and PAC were more consistent with the representational geometry of the\nRNNs trained using the R@R strategy. Alternatively, if one brain region was\nconsistent with one strategy, and the other brain region with the other\nstrategy, we would not have been able to make any claims about the animals’\nbehavioral strategy.\nComment 5: Perhaps I missed it, but I did not see a Data and Code availability\nstatement in the manuscript, or a link to the repository where it is hosted.\n(Remarks on code availability):\nI only saw a link to a code/data repository at the time of writing this\nreview. That information doesn't seem to be included in the manuscript.\nWe have added the code and data availability information to the end of Methods\nsection. The software submission checklist had also been submitted.\nReviewer #3 (Remarks to the Author):\nThis manuscript examines how monkeys solve a working memory updating task by\ncomparing neural activity patterns in two prefrontal regions (LPFC and PAC)\nwith recurrent neural networks (RNNs) trained to implement different\ncomputational strategies. The authors propose two potential strategies:\n\"Retrieve at Recall\" (R@R), which involves passive storage of memory items\nuntil recall, and \"Rehearse and Update\" (R&U), which involves active\nmaintenance and updating of information as new items are presented. Through\nanalyses of neural representational geometry, the authors conclude that\nmonkeys employ the R&U strategy, despite both strategies producing similar\nbehavioral outcomes.\nThis manuscript suffers from conceptual framing issues that undermine its\nconclusions. The paper's core finding—that prefrontal working memory\nrepresentations align better with a model of active maintenance than with\npassive storage and later reactivation—is also not novel.\nMajor Concerns\nComment 1: Mischaracterization of \"Strategy\"\nThe central premise of this paper—investigating \"latent strategies\"—is\nproblematic. What the authors are actually studying is not a behavioral\nstrategy but rather the neural implementation of working memory. The two RNN\nmodels (R@R and R&U) represent different theoretical mechanisms for\nimplementing working memory. This is not the same as cognitive strategies\nthat an animal might consciously or unconsciously select, as the manuscript\ntries to imply. I believe that the neural implementation of working memory\nis more accurately characterized as a mechanism than a strategy. The authors\nare essentially testing whether working memory is supported by sustained\nneural activity (R&U) versus activity-silent mechanisms with later\nreactivation (R@R), which is an important question about neural mechanisms,\nnot strategies.\nWe would like to thank the reviewer for allowing us to clarify this\nfundamental point.\nThe goal of the current study is to infer the latent strategy employed by\nthe monkeys to solve the task, as explained in detail below. Several previous\nstudies have characterized the neural mechanisms of implementing working\nmemory, including stable coding supported by sustained activity (e.g., Compte\net al., 2000), activity-silent mechanisms supported by short-term plasticity\n(e.g., Lundqvist et al., 2016), and dynamic coding (e.g., Meyers et al.,\n2008). Furthermore, these memories can be encoded in different formats,\ndepending on whether they are attended to or not (Piwek et al., 2023,\nPanichello et al., 2021). Importantly, each one of the strategies hypothesized\n(R@R and R&U) could be implemented with different mechanisms: for example,\nboth strategies could use activity-silent mechanisms, stable coding, dynamic\ncoding or a combination, to solve the task. Thus, it is not our goal to study\nthe specific neural implementation of working memory per se. Rather, using\nour knowledge of the possible neural implementations of working memory (in\nparticular, their representational geometries), we attempted to infer which\nstrategy, out of the two hypothesized ones, is being used by the monkeys.\nThis is a subtle, but important difference.\nWe would also like to clarify that we are not testing in any way the activity-\nsilent hypothesis. The R@R RNNs solves the task without any short-term\nplasticity. Information about Target 1 location is maintained during Delay 1\nin the activity of the neurons (see Figure 2A). What Figure 1D is showing is\nthat this activity is not contributing to the output layer of the network.\nThe precise format of this Delay 1 activity is not controlled for: in some\nRNN simulations the code was dynamic, and in some it was stable (see the\nvariability of Delay 1 code stability in Figure 2B).\nWe have added a concise version of this points to the discussion:\nP18L1: “Several previous studies have characterized the neural mechanisms\nimplementing working memory maintenance, including stable coding supported\nby sustained activity24, activity-silent mechanisms supported by short-term\nplasticity25,26, and dynamic coding27,28. Furthermore, these memories can be\nencoded in different formats, depending on whether they are attended to or\nnot13,18. The strategies considered in this study (R@R and R&U) may be\nimplemented by one, or a combination of these mechanisms. However, it is not\nour goal to study the specific neural implementation of working memory per\nse. Rather, our goal is to compare the representational geometries of RNNs\nand brain regions to infer which strategy was being used by the monkeys.\nRelatedly, our study does not test the activity-silent hypothesis. The R@R\nRNNs solve the task without any short-term plasticity, and information about\nTarget 1 location is maintained during Delay 1 in the activity of the neurons\n(Figure 2A). The precise format of this Delay 1 activity is not controlled\nfor: in some R@R RNN simulations the code was dynamic, and in some it was\nstable (see the variability of Delay 1 code stability in Figure 2B).”\nComment 2: Limited Theoretical Framework\nThe paper presents a binary distinction between two possible implementations\nof working memory without adequately acknowledging the rich theoretical\nliterature on working memory mechanisms. The framing of R@R versus R&U\noversimplifies complex neural processes that likely involve combinations of\npersistent activity, synaptic weight changes, and dynamic coding.\nThe authors refer to human behavioral studies on working memory updating\ntasks but fail to integrate this with the extensive neurophysiological\nliterature on working memory maintenance mechanisms, creating a disconnect\nbetween their behavioral framing and their neural analyses.\nWe hope that the addition of the paragraph discussing neural implementation\nof working memory mentioned in the previous response addresses this comment\nas well.\nComment 3: Overinterpretation of Results\nThe authors make strong claims about inferring \"latent strategies\" based on\ncomparing monkey neural data with artificial neural networks. However, the\nmatch between biological and artificial systems might reflect constraints on\nhow neural networks can solve this particular task rather than revealing\nstrategic choices made by the monkeys.\nThe paper concludes that monkeys employ the R&U strategy based on the\nsimilarity of neural patterns, but does not adequately explore alternative\nexplanations, such as whether the observed patterns might reflect a hybrid\nmechanism or whether the distinction is meaningful given the task constraints.\nWe would like to thank the reviewer for bringing up this interesting point.\nFirst, we would like to clarify that the latent strategies we investigated\nin the present study are the solutions to the given task, but they are not\n“the process of making strategic choices”. This is mentioned as well in\nthe discussion:\nP18L15: “Although this is an important step in understanding how strategies\nare implemented, our findings do not explain why animals prefer one strategy\nover another. To address this, we would need to investigate the learning\nprocess that leads to the selection of a specific strategy, which may itself\ninvolve latent factors29,30. Furthermore, when organisms learn that multiple\nstrategies can be used to effectively solve a task, we must explore the\ndecision-making process —both conscious and unconscious31— that determines\nwhy one strategy is chosen over the others32.”\nSecond, we agree with the reviewer that the solution space is constrained by\nthe task itself. However, given that the artificial networks and the monkeys\nwere trained with an equivalent task, the constraints of strategic options\napply to RNNs and monkeys alike. R@R and R&U strategies were hypothesized in\nthe current study because they have been proposed in existing human behavioral\nliterature. While there may be other possible strategies available, we decided\nto start exploring the most likely ones. Since we saw a good match with the\nR&U strategy, we saw no need to explore further alternatives.\nThird, the reviewer brings up an interesting point about the potential\nexistence of hybrid strategies. As we addressed earlier, the present study\nfocused on the distinctions between strategies rather than working memory\nmechanisms per se. In Reviewer 3 Response 1 we have acknowledged the possible\nco-existence of different mechanistic implementations, even for the same\nstrategy, and we added this to the discussion section. However, instead of\nhybrid mechanisms, we want to discuss the possibility of applying a hybrid\nstrategy. A hybrid strategy would not imply the simultaneous implementation\nof multiple strategies, but rather, it could involve animals applying\ndifferent strategies for different trials, or applying a different strategy\nwith elements of both strategies (i.e., maintaining information during Delay\n1 in a dual redundant format). If the monkeys were applying such mixed\nstrategies we would expect to observe neural representational geometries that\ndo not align well with either model. However, this is not what we observe,\nthus supporting our conclusion that the monkeys employed the R&U strategy.\nReviewer #3:\nGiven these concerns, I will skip the technical details unless the editor\nfeels it's necessary.\nReviewer #4 (Remarks to the Author):\nQian et al. compared the patterns of neural activity recorded in the monkey\nlateral prefrontal cortex (LPFC) and pre-arcuate cortex (PAC) and the activity\npatterns in the recurrent neural networks (RNN) during a working memory\nupdate task. The RNN was trained according to two alternative strategies;\nretrieve at recall (R@R) and rehearse and update (R&U) strategies. They found\nthat the neural activity in the monkey PFC was more consistent with and\nresembled the activity in the RNN trained with the R&U strategy. The question\nand approach used to address this question are interesting, but there are\nseveral weaknesses.\nComment 1: The authors claim that “no studies have been able to infer which\nlatency strategy is used by animals”, but this is an exaggeration. Many\nstudies that employ mathematical modeling, especially in reinforcement\nlearning (e.g., Daw et al., 2011), have developed techniques that can\ndistinguish between multiple behavioral and learning strategies based on the\nchoice and reaction time data. Even for the working memory update task used\nin the present study, it may be possible to determine which strategy is more\nlikely, if the authors have analyzed the patterns of errors more carefully.\nFor example, update failures in the R&U strategy might be more likely to\nproduce the errors of selecting T1 in T/T trials compared to the R@R\nstrategy.\nWe would like to thank the reviewer for the comment. To clarify, there are\nindeed numerous studies modelling the strategies in human and animals, and\nwe cite several of these in the introduction and discussion. However, these\nworks (e.g., Daw et al., 2011) focused on the inference of strategies that\nhave manifest effects on behavior, such as decisions, error types or reaction\ntime. Thus, these strategies are not latent by definition.\nThat being said, we agree with the reviewer’s suggestion that including an\nanalysis of error trials would be recommendable if our goal is to claim that\nthese strategies are truly latent. A difference in the types of errors between\nstrategies would make the strategies manifest, and not latent.\nError Analysis\nWe conducted a thorough analysis of error trials. In summary, we found that\nboth monkeys and both RNNs erred by “guessing” the target location (rather\nthan being biased in different ways by Target 1 in T/T trials or distractors\nin T/D trials). This “guessing” is inferred from an equal likelihood of\nresponding any of the 3 erroneous locations.\nMore specifically, in our task, for a trial to be rewarded the animal had to\nfulfil three criteria: (1) saccade to the correct location,\n(2) saccade earlier than 500 ms after the go-cue, and (3) fixate on the\ntarget for at least 200 ms. Trials in which the animals broke fixation before\nthe go-cue were considered aborted trials, rather than error trials. To analyze\nthe types of errors that the animals performed, we divided the error trials into\n4 types and calculated the proportion of each among all error trials in each\nsession:\n1. Trials in which the monkeys responded to the correct location but\nfailed to meet the additional criteria (#2 and #3): T/T: M(SD) = 0.158(0.120),\nT/D: M(SD) = 0.203(0.109))\n2. Trials in which the saccades were directed to the distractor location\nin T/D trials, or Target 1 location in T/T trials: T/T: M(SD) = 0.196(0.108),\nT/D: M(SD) = 0.194(0.116))\n3. Trials in which the monkeys responded to a non-presented location\n(neither Target 1, Target 2 nor distractor location): T/T: M(SD) =\n0.594(0.052), T/D: M(SD) = 0.531(0.026))\n4. Saccades that went to none of the locations (e.g., outside the screen):\nT/T = 0.052(0.028), T/D = 0.072(0.030))\nIn summary, ~15-20% of “errors” were trials in which the animals saccaded\nto the correct target location, but the animal failed to fulfil the other 2\ncriteria for reward, ~20% or errors were directed to the Target 1 or\nDistractor location (error type 2), ~50% of the errors were directed to one\nof the other 2 possible targets (error type 3), and ~10% to other locations.\nIf we exclude the first type of error (towards the correct target), these\nresults suggest that in the majority of error trials the monkeys were guessing\nthe correct location (similar likelihood to go to either of the three non-\ntarget locations). So, in summary, in ~60% of trials the monkeys reported\nthe correct location, and in the rest of the trials they reported a random\none.\nTo reflect this conclusion, we have added the following statement in the\nbehavioral results section. We do not believe that adding a detailed\ndescription in the manuscript (as we added above) would contribute much\nbeyond the statement added. If the reviewer believes that this would add\nmeaningful information, we would be happy to add further details to the\nmanuscript.\nP4L9: “The rest of the error trials suggest that the animals were guessing,\nsince they had similar likelihood of going to any of the other three erroneous\ntargets (data not shown).”\nFinally, it is possible that animals at earlier stages of learning may make\ndifferent proportions of errors, reflective of the exploration of different\nstrategies. In line with this hypothesis, recent studies reported working\nmemory representations in PFC changed from high-dimensional to low-\ndimensional as learning evolves (Wojcik et al., 2024). Unfortunately, our\nanimals were implanted with the recording electrodes only after the task was\nwell-learned, thus we don’t have evidence to test this hypothesis, but it\nwould be an interesting question for future exploration.\nComment 2: The performance of the animals was quite poor and only slightly\nabove the chance level (even considering the errors associated with fixation).\nThis rases two concerns. First, it may be more appropriate to compare the\nneural activity in the PFC to that of RNN trained to achieve the level of\nperformance more similar to that of monkeys. Second, it may be useful for\nthe authors to analyze the neural activity during error trials. For example,\nwhat does the activity associated with errors during T/T trials look like?\nDoes the activity during D1 and D2 reflect the location of I1, hence reflect\nthe failure of the update?\nPoor Performance of the monkeys\nThe chance-level performance in our task is 25% (1 out of 4 possible options),\nand the animals reached a higher than chance performance level (60%). The\nanimals were trained for over 9 months each, and the performance plateaued\nat this level. Unfortunately, our IACUC does not allow us to water restrict\nour animals, which is commonly used in other institutions to motivate animals,\nso we could only use fruit juice on unrestricted animals for motivation. Thus,\nwe speculate that the low level of performance (compared to other similar\nstudies, including our own previous studies) is due to lower motivation,\nrather than a failure to understand the task. It is also unlikely that the\nperformance reflects learning of one trial type but not the other (i.e.,\nlearned T/D but not T/T, or vice versa), since the accuracy for both trial\ntypes (T/T or T/D) were similar. Therefore, we believe that our conclusions,\nbased on the analysis of correct trials, are valid, even if the overall\nperformance of the animals is relatively low.\nRNNs with Lower Levels of Performance\nBelow we show the results of analyses suggested by the reviewer. However,\nbefore presenting those results, we would like to highlight that there is an\nimportant difference between the reasons behind the errors of poorly-trained\nRNNs and well-trained, but poorly motivated animals. RNN errors reflect a\nlack of convergence onto the best solution (in other words, the RNN has not\nlearned the task properly), whereas an animal (including human) can still\ncommit errors in a well-learned task, either due to distraction, failure of\nself-control, or lack of motivation to engage in the task. Thus, we still\npropose that the best way to infer the animals’ strategy is to compare their\nneural activity during correct trials to well-trained RNNs. With that preamble\nout of the way, below we present the results of RNNs trained to lower levels\nof performance.\nWe followed the reviewer’s advice and carried out error analyses in RNNs\nwith behavioral accuracy comparable to the animals’ performance. Since type\n1 and 4 errors were not applicable to the RNNs, we recalculated the behavioral\naccuracy in animals after excluding those trials, and the corrected\nperformance approximation was 70%. We then trained another 100 RNNs for each\nstrategy with an early-stopping rule when outputs at the last timepoint were\n70% accurate. All the other parameters remained unchanged.\nIn general, R@R and R&U RNNs had similar error rates by trial types (T/T:\nR@R: M(SD) = 0.355(0.056), R&U: M(SD) = 0.384(0.055); T/D: R@R: M(SD) =\n0.392(0.057), R&U: M(SD) = 0.337(0.055)). In other words, either strategy\ndid not tend to make more errors in T/T or T/D trials than the other. When\nbreaking down the errors into types, specifically error type 2 and 3 mentioned\nabove, we also found the two strategies had very similar proportions (among\nall errors) of type 2 (T/T: R@R: M(SD) = 0.485(0.128), R&U: M(SD) =\n0.544(0.152); T/D: R@R: M(SD) = 0.247(0.072), R&U: M(SD) = 0.283(0.075)) and\ntype 3 errors (T/T: R@R: M(SD) = 0.515(0.128), R&U: M(SD) = 0.456(0.152);\nT/D: R@R: M(SD) = 0.753(0.072), R&U: M(SD) = 0.717(0.075)). For both\nstrategies, the majority of the errors were type 3 errors, which did not\ncorrespond to the unwanted target or distractor. Since the error patterns\nare similar between both strategies, this analysis cannot be used to infer\nthe animals’ strategy.\nWe also analyzed the neural representations of the hidden units of the 70%-\naccurate RNNs (figures shown in the next page). Since the training was\nstopped early, these RNNs did not strictly obtain the strategic\ncharacteristics as we found in the fully optimized models. Nonetheless,\nmost of the result patterns were still consistent with the observations in\nthe fully optimized RNNs: during D2, both regions and both models showed\nstable codes, although neither model was as stable as when they were fully\noptimized (R@R: M(SD) = 0.968(0.016), p = 0.267; R&U: M(SD) = 0.974(0.014),\np = 0.208). Comparing between delays, the 70%-accurate R&U RNNs the code\nduring D1 was more stable as during D2, while the 70%-accurate R@R RNNs was\nmore dynamic during D1 (R@R: MD = -0.010, p = 0.004, g = -0.402; R&U: MD =\n0.010, p = 1.000, g = 0.704). Code morphing ratios of the 70%-accurate RNNs\nalso showed that target code was generalizable between D1 and D2 in the R&U\nmodels while it morphed in the R@R models (R@R: M(SD) = 0.431(0.234), p =\n0.020; R&U: M(SD) = 0.127(0.100), p = 0.198).\nFor the relationship between I1D1 and I2D2 subspaces, we found that\nT/T T/T\nboth models showed neither good coplanarity (compared to the fully\noptimized RNNs) nor significant deviation from shuffled baseline, but on\naverage the 70%-accurate R&U models still tended to be more coplanar than\nthe R@R ones (R@R: M(SD) = 0.635(0.594), p = 0.644; R&U: M(SD) =\n0.716(0.602), p = 0.644). On the other hand, both models exhibited good\nrepresentational alignment. The 70%-accurate R@R models were more aligned\nthan the R&Us on average, but the difference was marginal (R@R: M(SD) =\n0.903(0.283), p = 1.000; R&U: M(SD) = 0.899(0.371), p = 1.000). The code\ntransferability ratio of 70%-accurate R@R models was also near\nsignificantly lower than the baseline and lower than the R&Us (R@R: M(SD) =\n0.585(0.188), p = 0.059; R&U: M(SD) = 0.805(0.165), p = 0.485). Finally, we\ncalculated the mean drift ratio on the readout subspace of the 70%-accurate\nR@R and R&U models, and the results suggested more readout projection\ndrifts in the R@R models compared to the R&U (R@R: M(SD) = 0.961(0.596), p\n< 0.001; R&U: M(SD) = 0.443(0.595), p = 0.079).\nOverall, despite having some minor deviations from the fully trained RNNs,\nthe results with the 70%-accurate models were consistent with the patterns\nobserved in the fully trained RNNs. We hope these analyses will help\naddress the reviewer’s concerns.\nAnalysis of error trials\nUnfortunately, we do not have enough type 2 error trials for each condition\n(loc1*loc2*trial type) to build pseudo population for decoding analysis. So\ninstead, we carried out decoding in single sessions, and averaged across\nsessions. Since each session had few neurons, we did not apply PCA to the\ndata, so the decoders were trained and tested using the raw firing rates.\nAll decoders were trained with half the correct trials, and the decoding\nresults are shown for the other half of correct trials, and for all the type\n2 (where the animals responded to Target 1 in T/T trials, and to Distractor\nin T/D trials) and type 3 error trials (where the animals responded to one\nof the 2 location that were neither a target nor a distractor), separately.\nAs can be seen in the plots shown in the next 6 pages the decoding performance\nwas noisier, but qualitatively similar in error, compared to correct trials.\nHowever, due to the noisiness of the data, we are unable to reach any\nmeaningful conclusions about the mechanisms underlying these errors.\nMinor:\nComment 3: How the stability ratio (p.20) was calculated should be explained\na bit more clearly. In particular, what were the two bins used to calculate\nthe cross-time decodability?\nWe apologize for the confusion and would like to explain the calculation of\nthe stability ratio measure in more detail. We have added a more thorough\ndescription in the methods section:\nP24L2: “More specifically, cross-time decodability was calculated at every\npossible pair of train-test bins that were different from each other, in\nother words, the off-diagonal bins in cross-temporal decoding plot, while\nthe within-time decodability was the on-diagonal bins, where decoders were\ntrained and tested at the same bin. These decoder performances were averaged\nacross bins and trial type conditions for stability ratio calculation.”\nComment 4: Code morphing ratio was defined as the ratio of two cross-temporal\ndecodability (D1/D2). It may be desirable to take the logarithm of this ratio\nbefore computing the mean, because the average ratio tends to be larger than\n1 even when the numerator and denominator have the same distributions.\nWe agree with the suggestion. As advised, we transformed the code morphing\nratio to the logarithm and recalculated the statistics. We also fixed in the\ntext and the figures accordingly."}, {"round": 2, "reviewer_comments": {"reviewer_1": "In their revised manuscript, the authors provide additional details and analysis regarding their results finding patterns of brain activity in monkey LPFC and PAC consistent with a Rehearse & Update strategy (R&U) and inconsistent with a Retrieve at Recall (R@R) strategy.\n1) While I appreciate the authors' interest in addressing the points raised by other reviewers and myself, I am not convinced the revised manuscript reaches a level suitable for publication. In particular, while the authors go into a high level of detail in their responses, most of this detail is not included in the revised text itself, but is limited to their response to reviewers.\nFor example: multiple reviewers noted the poor performance of the monkeys, and the author's provided additional detail about possible reasons why the monkeys performed poorly, how the task is decomposed into correct and error trials in different conditions and so on, but they do so only in their comments to reviewers. Any reader of the revised version will be left to wonder why the monkeys are doing so bad at the task because the author's have not included any of that critical information in the main text.\n2) Similarly, the authors conduct additional analyses on RNNs that are halted after reaching a criterion of 70% accuracy - they write two pages of results and include a figure for the 70% accuracy condition, but they never show this in the main text. Again, any reader of the revised version is going to note the discrepancy between RNN and monkey performance and will not be aware of the authors' additional analyses addressing these points because they are not included in the main text.\n3)The authors go into some detail in their response regarding the differences between activity in PAC and LPFC during the task, but, again none of this shows up in the main text. Instead, the text they did at (P16L20, P17L20) is not informative and provides no insight into how these regions differentially contribute to the task. I would have preferred to see more of an effort to delve into the details here.\n4) With respect to the Kolmogorov-Smirnov test, I am not sure I understand what the authors mean in their response when they say that 'more simulations invariably lead to more significant differences' which prevents the authors from undertaking formal statistical tests. This seems important because even if the RNN under a R&U strategy is 'closer' to PAC and LPFC, the D value is still far away from 0 (indicating no difference). That is, the RNN activity for both R@R and R&U seems to be different than lPFC/PAC activity, even if R&U is slightly less different. It doesn't matter if one version of the RNN is 'less bad' than the other if they are both still quite bad at characterizing activity.\nMinor:\nIt is not necessary to thank reviewers for every comment\nRegarding the accuracy for Monkey B, the accuracy data for is given as: Monkey B: Overall: M(SD) = 0.563(0.036), T/D: M(SD) = 0.563(0.041), T/T: M(SD) = 0.569(0.065)). Unless I'm misunderstanding the task conditions, the Overall Mean accuracy (0.563) is the accuracy all trials (both T/D and T/T), yet the accuracy for T/D trials is 0.563 and the accuracy for T/T trials is 0.569. This is mathematically impossible.", "reviewer_2": "The authors have addressed my concerns.\nThe main weakness of this study, however, remains: the main claims of the paper are based on results coming from only 1 animal. The main result does not replicate in the second animal when the analyses are preformed on data split by animal.\nIn an ideal situation, the findings should come from several sessions per animal, and from at least 2 animals. What makes me uncomfortable is that none of those conditions have been met, as different sessions are pooled together to make pseudo-populations. Still, the authors claim that most of the cells used to build the pseudo-populations were responsive (i.e. encode task relevant information) at some point during the trial.\nIt would be good to present this in a more open way as a time resolved analysis. For example, if \"responsivity\" is defined as a significant association between (binned) firing rate and a task factor, the authors could plot the number (or) fraction of cells that cross a significance threshold (y-axis) as a function of time (x-axis) and present 1 curve for each factor. Also, splitting the data by experimental animal.\nThis way, at least, the readers will have a clear sense of the distribution of task-associated information across the pseudo-populations and over trial time. This would at least address the \"elephant in the room\".", "reviewer_3": "Thanks for the authors to clarifying the point about “latent strategy”. I accept that the paper was not about the sustained or dynamic representation of working memory. Yet, I am still not convinced that the current work is an adequate way to investigate latent strategy.\n1. The two RNN models presented are not meaningfully different \"strategies\" but rather networks trained with different output constraints. The R&U network was simply trained to maintain information stably in the output layer, while the R@R network was artificially constrained to not represent the first stimulus in its output during delay periods.\nGiven that stable maintenance of working memory information in DLPFC and PAC is well-established in the literature, the results in Figure 2 are entirely predictable. It's obvious which RNN model would better match the neural data, making this less a discovery of a \"latent strategy\" and more a confirmation of known neural coding properties.\nCharacterizing these different representational schemes as distinct cognitive strategies is problematic. The neural representation geometry likely emerges from fundamental network dynamics rather than reflecting a deliberate strategy choice by the monkeys. It's implausible that animals are consciously or even unconsciously selecting between different neural coding geometries.\n2. The authors claim that \"To date, no studies have been able to infer which latent strategy is used by animals, when multiple strategies are available,\" which is inaccurate. Several prior studies have successfully distinguished between competing models of neural computation in decision-making and other cognitive domains:\n• Churchland et al. (2011, Neuron) used variance signatures in neural activity to distinguish between integration and non-integration strategies in perceptual decision-making.\n• Stine et al. (2020) further developed methods to differentiate between integration and non-integration strategies.\n• Latimer et al. (2015, Science) and subsequent debate with Shadlen et al. (2016) examined competing models of evidence accumulation versus discrete state transitions.\nThese and many other studies have developed sophisticated approaches to infer underlying computational strategies from neural data when behavioral outcomes are similar.", "reviewer_4": "The authors have addressed all the concerns."}, "author_response": "Reviewers' comments:\nReviewer #1 (Remarks to the Author):\nIn their revised manuscript, the authors provide additional details and\nanalysis regarding their results finding patterns of brain activity in monkey\nLPFC and PAC consistent with a Rehearse & Update strategy (R&U) and\ninconsistent with a Retrieve at Recall (R@R) strategy.\n1) While I appreciate the authors' interest in addressing the points raised\nby other reviewers and myself, I am not convinced the revised manuscript\nreaches a level suitable for publication. In particular, while the authors\ngo into a high level of detail in their responses, most of this detail is\nnot included in the revised text itself, but is limited to their response to\nreviewers.\nFor example: multiple reviewers noted the poor performance of the monkeys,\nand the author's provided additional detail about possible reasons why the\nmonkeys performed poorly, how the task is decomposed into correct and error\ntrials in different conditions and so on, but they do so only in their\ncomments to reviewers. Any reader of the revised version will be left to\nwonder why the monkeys are doing so bad at the task because the author's have\nnot included any of that critical information in the main text.\nWe understand the reviewer’s concern about possible confusion. In the\nprevious response to reviewers, we decided to include in the revised\nmanuscript the things that we considered more important for the readers,\nbut we understand that our choice left out important information, which we\nhave included in the current revised version of the manuscript, as described\nbelow.\nWe included an additional figure (Extended Data Fig. 1) in the revised\nmanuscript showing the accuracy of the monkeys as a function of time.\nSpecifically, we calculated the accuracy over bins of 100 trials and sliding\nsteps of 20 trials from the beginning of each session to the end. We see that\nboth monkeys had a consistently high performance (between 60-80% correct,\nsee panels B-F) that decayed close to the end of the session as the animals’\nmotivation to work decreased. We have amended the revised manuscript to\ninclude this more thorough description of the monkeys’ behavior: See page\n4, lines 1 to 18, and Extended Fig. 1.\n2) Similarly, the authors conduct additional analyses on RNNs that are halted\nafter reaching a criterion of 70% accuracy - they write two pages of results\nand include a figure for the 70% accuracy condition, but they never show this\nin the main text. Again, any reader of the revised version is going to note\nthe discrepancy between RNN and monkey performance and will not be aware of\nthe authors' additional analyses addressing these points because they are\nnot included in the main text.\nIn our previous revision, we decided not to include this in the revised\nmanuscript because our simple models don’t get distracted by sensory stimuli,\nand don’t get satiated with juice reward, so we felt that it was not necessary\nto match the performance of the models to that of the monkeys. In other words,\nwe do not believe that the monkeys’ errors are due to a lack of understanding\nor learning of the task, but rather due to distractors and a lack of motivation.\nThus, we felt (and still feel) that a more meaningful comparison would be\nwith a well-trained model. That being said, in the revised version, we have\nadded the 70% performance model results for comparison: See page 4, line 20\nto line 28, page 40, extended analysis 2, and Extended Fig. 2.\n3)The authors go into some detail in their response regarding the differences\nbetween activity in PAC and LPFC during the task, but, again none of this\nshows up in the main text. Instead, the text they did at (P16L20, P17L20) is\nnot informative and provides no insight into how these regions differentially\ncontribute to the task. I would have preferred to see more of an effort to\ndelve into the details here.\nAs we justified in the previous responses, our emphasis in the present\nmanuscript is on the inference of latent cognitive strategies rather than\nexploring the differences between cortical regions. Therefore, we minimized\nthe discussion of differences between LPFC and PAC in the previous version\nto avoid the loss of focus. The differences between PFC subpopulations have\nbeen discussed in our previous work with more details and thorough analyses\n(Qian et al., 2024, J Neurosci).\nThat being said, we agree that adding some additional information would be\nuseful, so in the revised version, we have included additional content about\nthe differences between regions as requested by the reviewer: See page 16,\nline 21 to page 19, line 13.\n4) With respect to the Kolmogorov-Smirnov test, I am not sure I understand\nwhat the authors mean in their response when they say that 'more simulations\ninvariably lead to more significant differences' which prevents the authors\nfrom undertaking formal statistical tests. This seems important because even\nif the RNN under a R&U strategy is 'closer' to PAC and LPFC, the D value is\nstill far away from 0 (indicating no difference). That is, the RNN activity\nfor both R@R and R&U seems to be different than lPFC/PAC activity, even if\nR&U is slightly less different. It doesn't matter if one version of the RNN\nis 'less bad' than the other if they are both still quite bad at characterizing\nactivity.\nWe apologise for the confusion in our previous response, and we want to make\nfurther clarifications to this point. First, “more simulations lead to more\nsignificant differences” means that having a larger sample size of\nmodels/pseudo populations would generally lead to a smaller p-value,\nregardless of the effect size. See the illustration in the figure below,\nwhere we used the full space code morphing distributions as an example. For\neach sample size (i.e., number of RNNs/pseudo populations sampled), we\niterated 1000 times to randomly sample from our models/pseudo populations\nand create cumulative distribution functions (CDF). As the sample size\nincreases, the CDF tends to converge to a stable expectation; thus, it is\nless likely for there to be an overlap between two of the CDFs even when the\nactual difference is very small, consequently leading to smaller p-values.\nThis same rule generally holds in most statistical tests (Thiese, Ronna &\nOtt, 2016). We have not included this figure in the revised manuscript, as\nwe believe it may add more confusion than clarification. However, if the\nreviewer and editor believe that adding this discussion is necessary, we are\nhappy to include it.\nThe primary motivation of conducting K-S tests is to quantify the degree of\nsimilarity between the empirical distributions generated by the models and\nthe biological data based on the D statistic. We chose the K-S test in this\ncase as it is a non-parametric test based on the CDF, which could be applied\nto all metrics and provide comprehensive and fair comparisons. To further\naddress the reviewer’s concern, two additional indices were calculated and\nshown in Extended Tables 2 and 3. To supplement the K-S test results, we\ncalculated: 1. The Kullback–Leibler (KL) divergence between the probability\ndistribution functions of the models and the brain regions, which is a\nstatistical distance measuring the difference between the two distributions\n(Extended Table 2). It is commonly used as the loss between model predictions\nand true observations in machine learning literature. Greater KL divergence\nindicates more differences between the two distributions. 2. We calculated\nthe p-value of the difference between different distributions based on the\noverlaps between model and brain distributions (same test as described in\nMethods, significance test) to index their similarities. A smaller p-value\n(i.e., less overlap) suggests a lower probability of obtaining the brain\nobservations given the model, thus more different, and a p-value smaller than\n0.05 is considered statistically significant. Both indices revealed results\nconsistent with the findings based on the K-S test D statistics, that is,\nR&U was more similar to both LPFC and PAC compared to R@R. These results are\nalso added to the results section of the revised manuscript: e.g., page 8,\nlines 1 to 6.\nIn response to the critique that the R&U models are still significantly\ndifferent from the brain activities, we agree that indeed neither model\nperfectly replicated the brain activity. However, we believe that “all models\nare wrong but some are more useful”, especially given that the two models\nproduced very distinct predictions of activity patterns. Suppose we simplify\nthe strategy space by considering R@R and R&U as the two extremes on a\n“strategy” spectrum (akin to the strategy spectrum recently shown by Pagan\net al., Nature, 2025), with brain activity falling somewhere in between, as\nindicated by those similarity statistics. In that case, we can still identify\nwhich end of the spectrum the measured brain activity is closer to, thus\nstill providing a useful inference of the more likely strategy adopted by\nour animals. It is also not our goal to prove that either model perfectly\nmatched the data, given that: 1. the noisiness of the data, and 2. the two\nstrategies were roughly modelled based on cognitive step expectations rather\nthan precise parameterization of all possible variables to fit the behavior.\nMinor:\nIt is not necessary to thank reviewers for every comment\nWe understand that this repetitive thanking may be too much, so we will tone\ndown our usage. That being said, we really are thankful for the effort by\nthe reviewers :).\nRegarding the accuracy for Monkey B, the accuracy data for is given as:\nMonkey B: Overall: M(SD) = 0.563(0.036), T/D: M(SD) = 0.563(0.041), T/T: M(SD)\n= 0.569(0.065)). Unless I'm misunderstanding the task conditions, the Overall\nMean accuracy (0.563) is the accuracy all trials (both T/D and T/T), yet the\naccuracy for T/D trials is 0.563 and the accuracy for T/T trials is 0.569.\nThis is mathematically impossible.\nWe appreciate the reviewer’s meticulous checking. If we understand correctly,\nthe reviewer considered the results mathematically impossible because the\noverall accuracy was expected to lie between the range of the accuracies of\nT/T and T/D trials. First, we would like to show that this expectation was\nmet when results of Monkey B are rounded to the 5th decimal places or further:\nOverall: M(SD) = 0.56303 (0.03637); T/T: M(SD) = 0.56947 (0.06509); T/D: M(SD)\n= 0.56272 (0.04061). Secondly, we would like to clarify that the accuracy\nwas first calculated separately in each real session as the proportion of\ncorrect trials of each type among all trials of that type, and then averaged\nacross all sessions. For example, the accuracy of T/T trials in session i is\n𝑇/𝑇,𝑐𝑜𝑟𝑟𝑒𝑐𝑡\n𝐴𝐶𝐶 𝑇/𝑇 = 𝑁 𝑖 ,\n𝑖 𝑇/𝑇\n𝑁\n𝑖\nwhere 𝑁 𝑇/𝑇,𝑐𝑜𝑟𝑟𝑒𝑐𝑡 and 𝑁 𝑇/𝑇 represent the number of correct and total T/T\n𝑖 𝑖\ntrials in session I, respectively, and the mean accuracy across n sessions\nis\n∑𝑛 𝐴𝐶𝐶 𝑇/𝑇\n𝐴𝐶𝐶𝑇/𝑇 = 𝑖=1 𝑖 .\n𝑛\nWhile the reviewer’s expectation was met within each session (see\nverification table below), it does not necessarily hold after averaging across\nsessions. Finally, if we calculate the grand accuracy from all trials across\nall sessions, the results also matched the expectation: Monkey A: Overall:\n0.533; T/T: 0.559; T/D: 0.507; Monkey B: Overall: 0.561; T/T: 0.568; T/D:\n0.555. Therefore, we believe that our results are mathematically plausible,\nand we hope they address the reviewer’s concerns. This clarification has\nbeen added to the Methods on page 21, “Behavioral Performance” section.\nVerification Table\nSession, Monkey ACC ACC ACC\nOverall T/T T/D\n20200106, B 0.5137 0.52514 0.50269\n20200108, B 0.55385 0.55085 0.55708\n20200109, B 0.54011 0.46847 0.64474\n20200113, B 0.54574 0.54321 0.54832\n20200115, B 0.61034 0.66467 0.56283\n20200117, B 0.63168 0.67623 0.59286\n20200120, B 0.56278 0.55457 0.57111\n20200121, B 0.54604 0.5726 0.52217\n20210727, A 0.54894 0.56863 0.53008\n20210813, A 0.52434 0.55957 0.48638\n20210823, A 0.52484 0.54825 0.50213\nReviewer #2 (Remarks to the Author):\nThe authors have addressed my concerns.\nThe main weakness of this study, however, remains: the main claims of the\npaper are based on results coming from only 1 animal. The main result does\nnot replicate in the second animal when the analyses are preformed on data\nsplit by animal.\nIn an ideal situation, the findings should come from several sessions per\nanimal, and from at least 2 animals. What makes me uncomfortable is that none\nof those conditions have been met, as different sessions are pooled together\nto make pseudo-populations. Still, the authors claim that most of the cells\nused to build the pseudo-populations were responsive (i.e. encode task\nrelevant information) at some point during the trial.\nIt would be good to present this in a more open way as a time resolved\nanalysis. For example, if \"responsivity\" is defined as a significant\nassociation between (binned) firing rate and a task factor, the authors could\nplot the number (or) fraction of cells that cross a significance threshold\n(y-axis) as a function of time (x-axis) and present 1 curve for each factor.\nAlso, splitting the data by experimental animal.\nThis way, at least, the readers will have a clear sense of the distribution\nof task-associated information across the pseudo-populations and over trial\ntime. This would at least address the \"elephant in the room\".\nWe understand the reviewer’s concern, so we have added the following results\nto Extended Fig. 6-7. For each monkey in each brain region, we visualized:\na. the proportion of significantly responsive neurons (two-sampled t-test\ncompared to the averaged activity during 200 ms pre-I1 baseline, p < 0.001);\nb. the proportion of significantly selective neurons to I1 and I2 locations\n(one-way ANOVA, p < 0.001); c. percentage of explained variances (PEV) to I1\nand I2 locations of individual neurons; d. mean PEV across neurons within\neach session; e. LDA decoder accuracies of I1 and I2 location predictions\n(trained and tested within each session); and f. examples of single neuron\nactivities tuned by whether I1 or I2 was in the preferred location of the\nneuron. Note that all these results were based on real population data without\nany transformation or pseudo-population pooling across animals, and in a, b,\nd, and e, each line represents one real session from an individual animal.\nThese results showed that both Monkey A and B have neurons from multiple\nsessions that were effectively coding the task variables, despite the fact\nthat Monkey B had more such neurons. We also calculated the cross-temporal\ndecodability in each real session (for visualization, we averaged across\nsessions by animal) from both monkeys and estimated the code stability as\nwell as morphing ratio distributions. Similar to what we found with the\nsingle-animal pseudo population (Extended Fig. 5). These results show that,\nwhile monkey A had fewer cells, these tended to behave similarly to those\nrecorded in monkey B. On the other hand, subspace analyses are difficult to\ndo in real sessions, given the scarcity of neurons within each, especially\nfor Monkey A (which is also the reason for unsuccessful replication with its\nindividual pseudo population results shown in Extended Fig. 3), so we did\nnot try to replicate that. We hope these results will help address the\nreviewer’s concern.\nReviewer #2 (Remarks on code availability):\nNo remarks.\nReviewer #3 (Remarks to the Author):\nThanks for the authors to clarifying the point about “latent strategy”. I\naccept that the paper was not about the sustained or dynamic representation\nof working memory. Yet, I am still not convinced that the current work is an\nadequate way to investigate latent strategy.\n1. The two RNN models presented are not meaningfully different \"strategies\"\nbut rather networks trained with different output constraints. The R&U network\nwas simply trained to maintain information stably in the output layer, while\nthe R@R network was artificially constrained to not represent the first\nstimulus in its output during delay periods.\nGiven that stable maintenance of working memory information in DLPFC and PAC\nis well-established in the literature, the results in Figure 2 are entirely\npredictable. It's obvious which RNN model would better match the neural data,\nmaking this less a discovery of a \"latent strategy\" and more a confirmation\nof known neural coding properties.\nCharacterizing these different representational schemes as distinct cognitive\nstrategies is problematic. The neural representation geometry likely emerges\nfrom fundamental network dynamics rather than reflecting a deliberate\nstrategy choice by the monkeys. It's implausible that animals are consciously\nor even unconsciously selecting between different neural coding geometries.\nWe appreciate the further feedback from the reviewer. However, the new comment\nhighlights a misunderstanding that we would like to clarify. First, the\nreviewer argues that, given that we know that PFC neurons have sustained\nactivity, the R&U strategy should always be a better match to the data than\nthe R@R based on its code stability. This claim is problematic because even\nif we accept that the PFC employs stable coding, it could have multiple\ndissociated stable codes of the same information at different stages of the\ntask, for example, before and after the distractor in our previous work\n(Parthasarathy et al., 2017), or that before and after selection of memories\nin (Panichello & Buschman, 2021). In addition, even with output constraints\nduring D1 in the training of R@R RNNs, there is at least one additional\nsolution other than dynamically coding I1 during D1, that is, stably coding\non a subspace independent from the readout. The variation in R@R results also\nsupported this possibility. For these reasons, we disagree with the\nreviewer’s argument that our results are entirely predictable and merely\nconfirmations of known PFC properties.\nA more fundamental reason for the disagreement between the reviewer and us,\nwe believe, is that there is still confusion regarding the definition of\n“strategy” discussed here. Based on the reviewer’s previous comments and\nthe recommended literature in comment 2, it seems that the reviewer considers\ncognitive strategies as something equivalent to the neural processing\nmechanisms, such as the sustained vs. dynamic coding of working memory, or\nintegration- vs. non-integration-based decision-making. While the neural\nmechanisms of cognitive processes are indeed critical questions to be\nunderstood, here we define a strategy as the cognitive-level solution to a\nproblem, which is not equivalent to the neural mechanism implementing the\nstrategy. Multiple strategies can be available for a given problem (though\nthe subject should apply one strategy at a time), while the availability of\nmechanisms largely depends on the biophysical constraints, such as the cell\nproperties and the network connectivity. Also, the implementation of each\nstrategy may require one or more available mechanisms. For example, the\ncognitive model of R@R can be defined as a combination of “maintain\ninformation” and “rotate to the readout after selection” (Cowan et al.,\n2005), whereas the R&U is “maintain information on the readout” and\n“replace when necessary” (Postle et al., 2003). Both the R@R and R&U\nstrategies produced behaviourally equivalent outputs in our task, but\nmechanistically, the R&U strategy appears to rely on the stable coding\nmechanism of WM throughout, while the R@R strategy may be implemented using\nboth stable and dynamic mechanisms.\nIn the present work, we explored the strategy adopted by our animals in our\ntask. The human behavioural literature has suggested two possible cognitive\nstrategies, R@R and R&U. We trained RNNs with output constraints predicted\nby the cognitive models of these strategies, but importantly, no constraint\nabout what specific neural mechanism(s) they should rely on was added to the\ntraining. The rationale is to identify the distinctive characteristics that\nconsistently emerge in artificial systems employing a strategy, and to use\nthese models as a benchmark for inference in the biological brain. In addition,\nthe inference of strategy relies on a comprehensive review of neural\nsignatures from various perspectives (e.g., decodability, code stability,\nrepresentation geometry) rather than the mechanisms at a specific level,\nalthough they are closely related. This approach has been used in several\nrecent works (Ji-An et al., 2023; Tsuda et al., 2023; Fascianelli et al.,\n2024).\nFinally, we agree with the reviewer that the availability of mechanisms is\nnot subject to the choice of the agent but constrained by the biology of the\nsystem. On the other hand, strategies can be chosen by the agent as long as\nthey are biologically plausible. The choice of which strategy, presumably,\nhelps the subjects perform the task (e.g., maximizing gains, minimizing costs,\netc.), but it can also be affected by higher-order factors, such as the task\ndifficulty, learning history, bias of the agent, and so on (e.g., Wojcik et\nal., 2024).\n2. The authors claim that \"To date, no studies have been able to infer which\nlatent strategy is used by animals, when multiple strategies are available,\"\nwhich is inaccurate. Several prior studies have successfully distinguished\nbetween competing models of neural computation in decision-making and other\ncognitive domains:\n• Churchland et al. (2011, Neuron) used variance signatures in neural activity\nto distinguish between integration and non-integration strategies in\nperceptual decision-making.\n• Stine et al. (2020) further developed methods to differentiate between\nintegration and non-integration strategies.\n• Latimer et al. (2015, Science) and subsequent debate with Shadlen et al.\n(2016) examined competing models of evidence accumulation versus discrete\nstate transitions.\nThese and many other studies have developed sophisticated approaches to infer\nunderlying computational strategies from neural data when behavioral outcomes\nare similar.\nWe would like to thank the reviewer for recommending the studies. They indeed\nprovide critical insight into the differentiation between neural processing\nmechanisms, specifically the integration- vs. non-integration-based decision-\nmaking, and we are aware that similar inference methods based on well-\nparametrized computational models can be (and have been) generalized to\nu\nn\nd\ne\nr\ns\nt\na\nn\nd\nw\no\nr\nk\ni\nn\ng\nm\ne\nm\no\nr\ny\np\nReviewer #4 (Remarks to the Author):\nThe authors have addressed all the concerns.\nReferences\nCowan, N., Elliott, E. M., Scott Saults, J., Morey, C. C., Mattox, S.,\nHismjatullina, A., & Conway, A. R. A. (2005). On the capacity of attention:\nIts estimation and its role in working memory and cognitive aptitudes.\nCognitive Psychology, 51(1), 42–100.\nhttps://doi.org/10.1016/j.cogpsych.2004.12.001\nHennequin, G., Ahmadian, Y., Rubin, D. B., Lengyel, M., & Miller, K. D.\n(2018). The Dynamical Regime of Sensory Cortex: Stable Dynamics around a\nSingle Stimulus-Tuned Attractor Account for Patterns of Noise Variability.\nNeuron, 98(4), 846-860.e5. https://doi.org/10.1016/j.neuron.2018.04.017\nJi-An, L., Benna, M. K., & Mattar, M. G. (2023). Discovering Cognitive\nStrategies with Tiny Recurrent Neural Networks. Animal Behavior and\nCognition. https://doi.org/10.1101/2023.04.12.536629\nPanichello, M. F., & Buschman, T. J. (2021). Shared mechanisms underlie the\ncontrol of working memory and attention. Nature, 592(7855), 601–605.\nhttps://doi.org/10.1038/s41586-021-03390-w\nParthasarathy, A., Herikstad, R., Bong, J. H., Medina, F. S., Libedinsky,\nC., & Yen, S.-C. (2017). Mixed selectivity morphs population codes in\nprefrontal cortex. Nature Neuroscience, 20(12), 1770–1779.\nhttps://doi.org/10.1038/s41593-017-0003-2\nPostle, B. R. (2003). Context in verbal short-term memory. Memory &\nCognition, 31(8), 1198–1207. https://doi.org/10.3758/BF03195803\nThiese, M. S., Ronna, B., & Ott, U. (2016). P value interpretations and\nconsiderations. Journal of Thoracic Disease, 8(9), E928–E931.\nhttps://doi.org/10.21037/jtd.2016.08.16\nTrübutschek, D., Marti, S., Ojeda, A., King, J.-R., Mi, Y., Tsodyks, M., &\nDehaene, S. (2017). A theory of working memory without consciousness or\nsustained activity. eLife, 6, e23871. https://doi.org/10.7554/eLife.23871\nWimmer, K., Nykamp, D. Q., Constantinidis, C., & Compte, A. (2014). Bump\nattractor dynamics in prefrontal cortex explains behavioral precision in\nspatial working memory. Nature Neuroscience, 17(3), 431–439.\nhttps://doi.org/10.1038/nn.3645\nWójcik, M. J., Stroud, J. P., Wasmuht, D., Kusunoki, M., Kadohisa, M.,\nMyers, N. E., Hunt, L. T., Duncan, J., & Stokes, M. G. (2023). Learning\nshapes neural geometry in the prefrontal cortex. Neuroscience.\nhttps://doi.org/10.1101/2023.04.24.538054"}, {"round": 3, "reviewer_comments": {"reviewer_1": "I have no further comments on this manuscript.", "reviewer_2": "The authors have added additional supplementary information (Supplementary figures 6-7) to address my main concern, related to the poor results replication in one of the two animals. The analysis performed is convincing.", "reviewer_3": "While there's a formatting error in the rebuttal to my second question, my primary assessment is based on larger, unresolved issues. Unfortunately, my fundamental concerns regarding the manuscript's overall framework and core argument remain.\nI believe we have reached a conceptual impasse, and I do not foresee an additional round of revisions bridging this gap from my perspective. As such, I feel it is best to leave the final decision to the editor's discretion.", "reviewer_4": "The authors have addressed all my concerns."}, "author_response": ""}]

Decision letter