Rhythmic temporal structure organizes recurrent dynamics to support sequential working memory

Reviewer #1 (Public review):

Summary:

This manuscript investigates how rhythmically presented stimuli support working memory by using task-trained recurrent neural networks (RNNs) endowed with short-term synaptic plasticity. RNNs trained with rhythmic sequences have a marginal performance increase (0.4%) over models trained with jittered input and show increased phase-locking and oscillatory organisation during the sample period. While the question addressed in this paper is highly relevant, the core conclusion that regular temporal structures provide a functional scaffold for sequence working memory lacks evidence. The extensive post-hoc filtering pipeline obscures whether there is phase coding or not, and whether or not the found oscillatory phenomena are truly emergent or a mathematical artefact of the analytical selection criteria.

Strengths:

(1) The manuscript addresses a highly relevant question.

(2) The introduction is nicely written and presents relevant background work.

(3) The authors' results are robust in the sense that they analysed and trained an ensemble of models instead of single networks.

Weaknesses:

(1) Misalignment between analysis epoch and core claims. The manuscript argues that temporal regularity supports sequence working memory. However, the majority of analyses focus on the sample/encoding period rather than the delay period during which memory maintenance occurs.

(2) Ambiguity in the neural code (rate vs. phase). The decoding accuracies suggest that the memory can be well decoded from the instantaneous activity, implying a rate (not a phase) code. This raises two questions:
a) Can memory-related information be decoded directly from the oscillatory phase, particularly during the delay period?
b) What would be the mechanism with which the increase in phase organisation improves a representation that seems otherwise decoded/represented from activity levels?

(3) Absence of any RNN activity plots. The manuscript would benefit from showing, e.g., single neuron response plots, raster plots, phase histograms of units, etc. Are there actually spontaneous oscillatory dynamics as the paper writes (line 243)? Can the authors show baseline activity (which is also supposed to be oscillatory, line 219)?

(4) Potential concerns in the analysis pipeline: The data undergo an intensive, selective pipeline that might be susceptible to introducing circularity and selection bias. I highlighted some points here:
a) Many analyses are performed on (summed) data projected on demixed PCs (extracted from time-warped data). Crucially, dPCAs are not unsupervised; they already explicitly maximise the variance of interest.
b) For the phase extraction during sample encoding: after dPCA percentile clipping, z-scoring, and z-score clipping are applied (lines 762-764), low-amplitude trials are excluded (lines 779-781), and there is further selection based on a valid-point criterion and r2 thresholding (lines 804-805). Do all of these selection criteria risk introducing bias?
c) Some statistical assumptions are not explicitly evaluated. E.g., the sign-flip permutation test (lines 735-742) relies on sign-exchangeability.
d) For selectivity analysis of oscillatory organisation (Figure 4C, lines 893-896): Units are first selected by ANOVA, and then on the selected units further stats (Power and PLV) are computed. Unless the further stats are completely independent of the ANOVA, this may introduce selection bias.
e) The finding of stronger power around f0 given rhythmic inputs of that exact frequency seems somewhat circular (Figure 3A)?
f) The dPCA description seems a little odd, e.g., line 674, for the ordinal component you would normally actually average (i.e., marginalise out) everything except the ordinal axis.

(5) Conflation of RNN learning dynamics with working memory mechanisms. The authors show that rhythmic input makes learning marginally easier, but in principle, both RNNs reach full performance (so working memory can be done as well with either case). To avoid the findings depending on learning dynamics, it could be of interest to test the RNNs trained with jittered input on fixed input (or retrain RNNs with both jittered and non-jittered input). It is also unclear if the small increase in performance (0.4%) can be expected to hold across different initialisations and/or learning rate /regularisation strengths.

(6) STSP. It is unclear if the findings rely on STSP being present or not (or what the role of STSP is in the model at all currently). Note that in Liebe et al. 2025, RNNs were trained on an almost identical task without STSP, and phase-coding was demonstrated in the models.

(7) Writing redundancy. The methods subsections "Population signal construction for oscillatory analysis" and "Oscillatory phase organization during sample encoding" seem to define exactly the same quantity with different characters (activity projected in dPCA space), which leads to confusion (in one section, z is the PC component, in another, it's the complex signal). There are also slightly different definitions of the wavelets in either section, for which the reasoning is unclear.

Reviewer #2 (Public review):

Summary:

The authors train E-I recurrent networks with short-term synaptic plasticity on a sequential delayed match-to-sample task, comparing regular versus jittered sample timing. They report a small accuracy gain under rhythmic input, a more separable population geometry during encoding, organization of internal oscillations around the dominant input frequency, a preference for temporal order over feature encoding, and improved decodability and persistence of stimulus information in both activity and synaptic efficacy. A delay-period perturbation shows synaptic efficacy contributes more than activity to maintenance.

Strengths:

The model is well-specified. Dale's law, the STSP formulation, the training objective, and the hyperparameters are all reported clearly enough to reproduce, and code is shared. The statistical machinery is appropriate, with cluster-permutation tests for the spectral analyses and across-network sign-flip tests rather than naive pooling. The temporal-order versus stimulus-direction dissociation in Figure 4C is the most interesting result. The negative association between phase locking and direction selectivity is non-trivial and argues against a simple global-gain reading, and it connects to Liebe et al. 2025. The serial-position decoding curves and the synaptic-versus-neuronal perturbation are well-motivated tests of the maintenance claim.

Weaknesses:

The behavioral effect is very small. Match accuracy is 0.991 versus 0.987, and non-match is 0.973 versus 0.969, on networks already at the ceiling. The entire mechanistic analysis is built to explain a roughly 0.4 percentage point difference, and the paper does not establish that this difference is functionally meaningful rather than a marginal byproduct of the timing manipulation. The IOI-dependence result meant to support it is weak, with an R-squared of 0.071 at a p-value of 0.029 on n of 67.

The core spectral and phase results are close to definitional and should be framed that way. The regularity index R is computed from IOI variability, the dominant frequency f0 is computed from the same IOIs, and the oscillatory metrics in Figures 3 and 4 are then measured relative to f0 and correlated against R. This shows that more regular input produces internal phase progression closer to the input-derived reference frequency, partly restating the input statistics rather than uncovering an independent network mechanism. The phase-locking-increases-with-regularity finding is the clearest case. This does not invalidate the analyses, but the manuscript currently reads them as a mechanism when much of the signal is built into the measurement.

The only genuinely causal manipulation is the delay-period shuffle, and it is underpowered at n of 15. Its main conclusion, that synaptic efficacy matters more than activity for maintenance, largely recovers prior STSP results (Mongillo et al. 2008, Masse et al. 2019) rather than establishing something specific to rhythm. The result the authors most want, that disrupting synaptic state removes the rhythmic advantage, is predicted in the Discussion but not tested.

The authors should add a control that breaks the circularity (a held-out f0/phase reference, or shuffling R against the metric) and run the causal STSP-disruption test that is mentioned in the Discussion.

The oscillatory framing is stronger than the model supports. Phase locking to a periodic input can reflect temporal predictability or repeated preparation without self-sustained entrainment, and the authors acknowledge this once but then use entrainment-style language throughout. The signals are extracted from firing-rate units and should not be read as LFP or EEG oscillations.

The authors should show raw single-unit and population activity so readers can verify the oscillations before the filtered pipeline. The delay perturbation largely recovers Mongillo 2008 / Masse 2019 rather than anything rhythm-specific, and the relationship to Liebe et al. 2025 should be addressed in the Results.

Appraisal and impact:

The authors largely achieve their stated aim of describing how temporal regularity constrains recurrent dynamics in this model, and the temporal-order preference is a useful prediction. The reach of the conclusions exceeds the evidence in two places: the functional importance of the behavioral effect and the degree to which the phase results are independent of the input construction. With the framing corrected and one causal test added, this would be a useful contribution to the modeling literature on timing and working memory rather than a definitive account.

Author response:

We thank the editors and the two reviewers for their careful evaluation of our study, as well as for their positive assessment of the research question, model reproducibility, and the results concerning temporal-order representations. We also agree with the core issues raised in the reviews: the current manuscript has not yet sufficiently distinguished descriptive changes in recurrent dynamics from the functional mechanisms underlying the behavioral advantage; the behavioral effect itself is small and close to the performance ceiling; the phase analyses require more stringent controls; and the specific role of short-term synaptic plasticity in the rhythmic advantage has not yet been directly tested. We plan to add the corresponding analyses in the revised manuscript and to temper several mechanistic claims.

First, we would like to clarify three aspects of the study design and analysis pipeline. First, the rhythmic and arrhythmic conditions were not performed by two separately trained groups of networks. Each network was jointly trained using balanced batches containing rhythmic-match, rhythmic-non-match, arrhythmic-match, and arrhythmic-non-match trials. Therefore, the behavioral differences were compared within the same independently initialized network. We will revise the relevant descriptions in the Abstract, Results, and Methods to make this joint-training procedure more explicit. Second, Figures 2 and 3–4 used different dimensionality-reduction approaches because they addressed different analytical questions. In Figure 2, dPCA was applied to time-aligned population activity to separate task-related variance into temporal, ordinal-position, and stimulus-related components, allowing us to examine how rhythmicity affected each representational component. In contrast, Figures 3 and 4 used standard PCA to construct a low-dimensional population signal for spectral and phase analyses without explicitly demixing task variables. We will clarify this distinction and the rationale for the two analysis pipelines in the revised Methods. Third, STSP was not introduced as an auxiliary module. Previous theoretical and computational studies have suggested that STSP can contribute to working-memory maintenance (Mongillo et al., 2008; Masse et al., 2019). Based on previous studies, we incorporated STSP alongside persistent neural activity to examine how synaptic and consistent neuronal activities jointly support sequential working memory. Under the current architecture and training settings, our ablation experiments showed that RNNs without STSP had difficulty successfully learning the task. We will emphasize this result and further distinguish the roles of STSP in task learning, delay-period maintenance, and the rhythmic advantage. We will also explore whether vanilla RNNs can successfully learn the same task under alternative hyperparameter settings.

Our core hypothesis is that temporal regularity improves the encoding of sequential information by organizing recurrent population dynamics and phase structure during the encoding period, and that this organization subsequently influences information maintenance during the delay period and behavioral performance. The current results establish a relationship between temporal regularity and encoding-period dynamics, but direct validation of how this organization influences subsequent working-memory maintenance remains insufficient. In the revision, we will focus on strengthening the link between the encoding and delay periods and test whether population dynamics and phase organization during encoding are associated with subsequent information maintenance and behavioral performance.

To provide a more direct view of the network dynamics, we plan to add intuitive visualizations of network activity and phase structure, allowing readers to evaluate the reported temporal organization with less dependence on dimensionality reduction, filtering, and complex statistical processing.

The current behavioral advantage of approximately 0.4 percentage points is small, and network performance in both conditions is close to ceiling. Following the reviewers’ suggestions, we plan to evaluate the stability of this effect across learning, random initializations, and representative hyperparameter settings, and to examine whether the rhythmic advantage becomes more pronounced under higher memory load when ceiling effects are reduced. We will also avoid equating statistical significance directly with functional importance.

Although the manuscript already includes decoding and perturbation analyses of neural activity and synaptic efficacy during the delay period, we will perform additional delay-period analyses to more directly examine whether the temporal organization established during encoding is associated with subsequent working-memory maintenance. These analyses will help distinguish the contributions of rhythmic input to stimulus encoding and memory maintenance.

We will also test the role of STSP more directly. The current delay-period shuffle results show that synaptic efficacy makes a functional contribution to delay-period maintenance, but this does not yet demonstrate that STSP specifically supports the rhythmic advantage. We will further illustrate the roles of STSP during encoding and delay-period maintenance. In the revision, we plan to increase the number of independent networks in the perturbation analysis and test the interaction between temporal regularity and STSP disruption.

Finally, we will further tighten the conceptual framing of the manuscript by more clearly distinguishing stimulus-driven phase organization from self-sustained oscillations, and by clarifying that the analyzed signals are model population signals derived from firing-rate population activity rather than LFP or EEG field potentials. Where the current evidence is insufficient to support interpretations in terms of entrainment or self-sustained oscillations, we will adopt more cautious terminology and revise the corresponding conclusions accordingly. We will also clarify the relationship between our phase-organization results and the findings of Liebe et al. (2025) in the revised Results.

Overall, the revised manuscript will more precisely frame the study around how temporal regularity improves sequential working memory and how this behavioral advantage is associated with the organization of recurrent population dynamics and synaptic-state representations during encoding. After completing the additional training and analyses, we will also make the corresponding model weights, training configurations, and necessary analysis files publicly available to improve reproducibility.

We again thank the editors and the two reviewers for their detailed and constructive comments. We will revise the manuscript carefully on the basis of these suggestions.

References

Mongillo, G., Barak, O., & Tsodyks, M. (2008). Synaptic theory of working memory. Science, 319(5869), 1543–1546. https://doi.org/10.1126/science.1150769

Masse, N. Y., Yang, G. R., Song, H. F., Wang, X.-J., & Freedman, D. J. (2019). Circuit mechanisms for the maintenance and manipulation of information in working memory. Nature Neuroscience, 22(7), 1159–1167. https://doi.org/10.1038/s41593-019-0414-3

Liebe, S., Niediek, J., Pals, M., Reber, T. P., Faber, J., Boström, J., Elger, C. E., Macke, J. H., & Mormann, F. (2025). Phase of firing does not reflect temporal order in sequence memory of humans and recurrent neural networks. Nature Neuroscience, 28, 873–882. https://doi.org/10.1038/s41593-025-01893-7