Stability of Brain Functional Network During Working Memory Using Structural Balance Theory

Masoud Lotfalipour; Reza Jafari; Reza Khosrowabadi; Sepehr Gourabi

REVIEW 4 major objections 6 minor 10 references

Stability of Brain Functional Network During Working Memory Using Structural Balance Theory

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Using structural balance theory on fMRI connectivity, this paper claims that the brain's functional network becomes more stable during working memory than at rest, measured by more balanced triads and lower balance energy.

desk verdict A plausible first SBT application to working memory, but the memory-specific stability claim is untested because 0-back and 2-back are pooled; still worth a serious referee. read the letter →

arxiv 2411.16558 v1 pith:EDQXXTJI submitted 2024-11-25 q-bio.NC

Sepehr Gourabi , Masoud Lotfalipour , Reza Khosrowabadi , Reza Jafari This is my paper · ORCID

classification q-bio.NC

keywords structuralbalancetheoryworkingmemoryfMRIfunctionalconnectivityN-backtasksignednetworkbrainstabilitytriadic

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether the brain as a whole shifts toward a more stable configuration when it performs a working memory task. Treating fMRI correlations between brain regions as positive or negative links, it counts triads—three-region motifs—and classifies them as balanced or imbalanced using structural balance theory. Across 138 healthy adults, balanced triads were significantly more numerous during an N-back working memory task than at rest, imbalanced triads were fewer, and the balance energy was lower. The authors read this as evidence that working memory processing pushes the functional network into a more stable, less frustrated state, with the largest sign changes occurring in temporal, parietal, and prefrontal cortices.

What carries the argument

The signed functional connectivity matrix: for each of 360 cortical regions from a multimodal parcellation, pairwise Pearson correlations of BOLD time series are turned into positive or negative links. On this signed network, structural balance theory classifies every three-node motif by the product of link signs: balanced triads have positive product (all-positive or one-positive-two-negative), imbalanced triads have negative product. The four types T0, T1, T2, and T3 are tabulated separately. Balance energy is defined as $$E = -\frac{1}{\binom{N}{3}} \sum_{i<j<k} S_{ij} S_{jk} S_{ik},$$ so lower energy means fewer imbalanced triads. Negative tendency-to-make-hub measures whether negative links concentrate around particular nodes. The resting-state versus working-memory comparison uses Wilcoxon signed-rank tests on each of these structural balance parameters across subjects.

What would settle it

Run the same analysis on an active control task with matched sensory input and motor responses but no memory load, and compare balanced-triad counts and balance energy to the N-back values; if the control shows the same or larger effect, the shift is not memory-specific. A second check would be to recompute correlations after regressing out head motion and physiological noise and see whether the rest-versus-task difference survives.

Watch

Extended reading notes

Core claim

The central claim is that a signed functional brain network built from resting-state fMRI is less structurally balanced than the same network during an N-back working memory task. The paper reports that the number of balanced triads increases, the number of imbalanced triads decreases, and the global balance energy decreases during the task relative to rest. It attributes this to a conversion of weakly balanced (T1) and strongly imbalanced (T2) triads into strongly balanced (T3) triads as negative correlations between regions turn positive, especially in temporal, parietal, and prefrontal cortex. The paper concludes that the working-memory brain state is more stable in the sense defined by structural balance theory.

Load-bearing premise

The load-bearing premise is that positive and negative links between brain regions, read directly from correlation of fMRI time series, reflect working-memory-specific neural coordination; if instead those sign changes come from general arousal, head motion, or blood-flow effects, the claim that working memory creates a more balanced network collapses.

Editorial extensions

If this is right

During working memory, the number of balanced triads in the signed fMRI network is significantly higher than at rest, and the number of imbalanced triads is significantly lower.
The shift is carried mainly by weakly balanced (T1) and strongly imbalanced (T2) triads turning into strongly balanced (T3) triads, meaning negative correlations flip to positive.
Balance energy is lower during the working memory task than at rest, which the paper interprets as the network occupying a more stable state.
Negative tendency-to-make-hub decreases with the task, indicating that negative links become less organized around individual nodes.
The largest rest-to-task sign changes occur in temporal, parietal, and prefrontal cortical regions, linking the stability shift to the known working memory network.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper compares both 0-back and 2-back to rest but never directly contrasts the two loads; a natural extension would test whether balanced-triad counts scale with memory load, which would separate mnemonic demand from general task engagement.
Because the balance-energy drop could be produced by any global increase in positive correlations, a control task matched for sensory and motor demands would be needed to decide whether the stability shift is working-memory-specific; the paper does not include such a control.
An individual-differences extension is available: if balance energy during 2-back correlates with reaction time or accuracy across subjects, the stability measure would earn a functional interpretation beyond group-level comparison.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things. First, this is the first structural balance theory (SBT) analysis of working memory, and the basic observation—balanced triads increase, imbalanced triads decrease, negative hub tendency drops, all with decent p-values in 138 HCP subjects—is internally consistent. Second, the headline claim that working memory specifically drives the brain to a more stable state is not actually tested. The task data concatenates all blocks, so the only contrast is rest vs. pooled task. That leaves a generic task-engagement confound wide open: any global shift toward positive correlations, from arousal, attention, or motion, would mechanically produce more T3 triads, fewer T1/T2, and lower balance energy. The 0-back vs. 2-back contrast is sitting right there in the HCP WM task and they never run it.

What the paper does well: it uses a well-preprocessed public dataset, applies paired nonparametric tests, reports exact p-values, and the region-level findings (temporal, parietal, prefrontal) line up with prior WM work. That is genuine credit. The authors also clearly build on their own earlier SBT papers, which is appropriate, not a flaw.

The soft spots, in proportion. The energy result is redundant: balance energy is a deterministic function of the balanced-triad fraction (E = 1 - 2B/T), so 'lower energy' adds no independent evidence. No null model is provided, so we cannot tell whether the triad shift exceeds what a degree-preserving or correlation-reshuffling null would produce. There is no multiple-comparison correction across the many link-level tests, and the IQR outlier rule is a free parameter. The sign construction—presumably sign of Pearson r—is never explicitly stated, and code is only 'available upon request.' The causal 'forced the network' language in the abstract overstates what a rest-vs-task comparison can show.

None of these flaws are fatal to the core descriptive finding, but they do mean the working-memory-specific stability interpretation is not yet established. A serious referee could fix this with a 0-back vs. 2-back contrast, a null model, correction for multiple comparisons, and a code release.

Who this is for: cognitive neuroscientists working on signed network analysis or WM network dynamics. It is a legitimate new application, not a new theory, and it deserves a real peer review rather than a desk reject. I would read the revision, but I would not cite it as evidence until the specificity question is answered.

Referee Report

4 major / 6 minor

Summary. The paper applies structural balance theory (SBT) to signed functional connectivity networks derived from HCP fMRI data, comparing resting state to the N-back working memory task in 138 healthy right-handed male participants. Connectivity is computed with Pearson correlation across Glasser 360 parcels; task time series are concatenated across runs and all task conditions into one array. The authors report a significant increase in positive links and balanced triads (T3), a decrease in negative links and imbalanced triads (T1, T2), a decrease in negative tendency-to-make-hub, and a decrease in balance energy during the task, and they identify temporal, parietal, and prefrontal regions as the main drivers of negative-to-positive link changes. The paper interprets these results as evidence that the brain shifts toward a more stable functional state during working memory.

Significance. If the reported effects survive appropriate controls, this would be a novel application of structural balance theory to working memory and a useful addition to the network-level literature on cognitive states. The paper has clear strengths: it uses a publicly available dataset, applies paired nonparametric tests, states the SBT formulas explicitly, and grounds its regional discussion in prior working-memory findings. However, the central interpretation as working-memory-specific stability is currently under-supported: the task/rest contrast pools 0-back and 2-back, no null model or global-correlation control is reported, and one of the headline findings (balance-energy decrease) is mathematically equivalent to another (balanced-triad increase) rather than an independent confirmation.

major comments (4)

[Functional Connectivity and Results] The task connectivity matrix is computed by concatenating all task runs and both 0-back and 2-back conditions into a single time series (`task_data`), so every reported contrast is rest versus this pooled task state. This design cannot distinguish working-memory-specific effects from generic task engagement due to arousal, attention, motion, or hemodynamic shifts. This is load-bearing for the abstract's claim that working memory specifically forces the network into a more stable state. Please add a within-task contrast (0-back vs. 2-back) computed with condition-specific concatenation, or a non-memory control task, and report whether the triad and balance measures track memory load; at minimum, explicitly discuss this confound and its bearing on the conclusions.
[Balanced Energy] As defined in the manuscript, balance energy is a deterministic function of the balanced-triad fraction: E = (N_imbalanced - N_balanced) / N_triads = 1 - 2*N_balanced / N_triads. Therefore the reported 'decrease in balance energy' (p = 6.19e-5) and 'increase in balanced triads' (p = 6.19e-5) are the same measurement expressed in two ways, not independent evidence. The causal wording in the abstract ('The increase of balanced triads forced the network to a more stable state with a lower balance energy level') is not supported by the correlational rest/task design. Please reframe energy as a derived quantity and soften or remove the causal language.
[Statistical Analysis and Functional Connectivity] No null model or global-signal control is reported. Because signed links are derived from Pearson correlations and the paper reports a task-related increase in positive links, the triad shifts could in principle be trivially explained by a global increase in positive correlations during task performance (for example, from arousal or motion), with no specific bearing on working memory or network stability. Please report the mean correlation (or distribution of correlations) in rest vs. task, and include null models such as sign-permutation or edge-shuffle that preserve the number of positive/negative edges or the degree sequence, to show that the balanced-triad excess is not a byproduct of the global correlation shift.
[Statistical Analysis] The outlier-removal step is described in a single sentence ('we employed the Interquartile Range (IQR) method to eliminate outliers for extracting the components of SBT') without specifying what variable was filtered, at what level (links, subjects, or triads), and whether the procedure was applied separately to rest and task conditions. Differential outlier handling across conditions could bias the paired comparisons. Please specify the procedure in detail and demonstrate robustness of the main results to the inclusion or exclusion of this step.

minor comments (6)

[Results] The Results state that positive links increased 'during the working memory task in all conditions, both 0-back and 2-back,' but the Functional Connectivity section concatenates all conditions into one array and computes a single connectivity matrix; this is inconsistent and should be clarified, or per-condition analyses should be provided.
[Statistical Analysis] The text says 'We applied the nonparametric Wilcoxon signed-rank test... We used p < 0.05 (Fisher permutation) as a significant threshold,' which mixes two different testing frameworks; please state exactly which test was used and how the p-values were computed.
[References] The reference to the HCP preprocessing pipeline is listed as 'Perprocess' and appears to be a typo; please correct the entry and provide full citation details.
[Figures] Figure 2 shows the four triad types, but the caption is only 'Types of Balanced and Imbalanced Triads'; please add a legend or labels identifying T0, T1, T2, and T3 directly in the figure.
[Abstract and Discussion] The words 'forced' (abstract) and 'induce a demand' (Discussion) imply causation; given the rest/task contrast, please replace these with correlational phrasing such as 'was associated with'.
[Data Availability] The manuscript states that data and code are 'available upon request'; depositing the analysis code in a public repository would strengthen reproducibility, especially given that the preprocessing and IQR steps are not fully specified.

Circularity Check

1 steps flagged · score 6.0 of 10

Balance-energy decrease is the balanced-triad increase restated by construction; the primary triad-count finding is not circular.

self definitional [Methods, 'Balanced Energy' section; Results, Balance Energy paragraph]
"The formula for calculating Balance Energy is as follows: E = −1&!"'(𝑆#$#$%𝑆#%𝑆$% ... As one of the SBT parameters, Balance Energy exhibited differences between the response to the working memory task and the resting state. We observed a decrease in energy levels during the task compared to the resting state, indicating a more stable functional performance during task response, and this difference was statistically significant (p-value = 6.19×10-5)."

Marvel et al.'s E is defined as -(1/C(N,3)) times the sum of triad sign products. A balanced triad contributes +1 to the product and an imbalanced triad contributes -1, so E = (N_imbalanced - N_balanced)/C(N,3) = 1 - 2*N_balanced/C(N,3). Hence E is a deterministic decreasing affine function of the balanced-triad count. The reported 'decrease in balance energy' and the 'increase of balanced triads' are the same comparison expressed in two variables, which is why both tests carry the identical p-value (6.19e-5). Presenting the energy drop as a separate SBT outcome 'forced' by the triad increase is thus a restatement of the definition rather than an independent prediction or confirmation.

full rationale

The paper's central measurement—that the number of balanced triads increases from rest to working memory—is an empirical result from signed Pearson-correlation fMRI networks and is not itself derived from the hypothesis. The circular component is the balance-energy claim: because E is defined as the normalized negative sum of triad sign products, any change in balanced triads mechanically produces the reported 'lower energy level'; the energy result carries the same p-value and adds no new evidence. The stability interpretation ('forced the network to a more stable state') is a definitional consequence of SBT rather than an independent verification. Other weaknesses, such as pooling 0-back and 2-back conditions into a single task connectivity matrix and the absence of a non-memory control task, are validity threats to the working-memory-specific interpretation but are not circularity and do not further raise the score. Weighing the one definitional redundancy against the independent triad-count finding, the appropriate score is 6 (partial circularity), not 8 or 10.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central empirical result does not rest on fitted constants; the main choices are the sign mapping, the energy-stability interpretation, the task-time-series concatenation, and the outlier-removal rule. No new physical or biological entities are introduced.

free parameters (1)

IQR outlier-removal rule = not reported
The paper removes outliers from SBT components before statistical testing but does not state the multiplier or how many subjects were excluded; this choice can affect p-values.

assumptions (4)

domain assumption Signed edges are defined by Pearson correlation signs without a disclosed threshold or null model (Functional Connectivity section).
The triad counts depend entirely on this mapping, and task-evoked BOLD can inflate positive correlations.
domain assumption Minimizing balance energy corresponds to neural/cognitive stability (SBT and Explanation Brain Stability sections).
The paper applies a social-balance energy metaphor; no independent neural evidence connects low balance energy to stability.
ad hoc to paper Concatenating all task runs and conditions into one time series yields a valid connectivity estimate comparable to rest (Functional Connectivity section).
This ignores block type, 0-back vs 2-back differences, nonstationarity, and potential task-related autocorrelation.
ad hoc to paper Outlier removal does not bias the rest-versus-task comparison.
No details on excluded subjects are given, so selection effects cannot be ruled out.

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Cite this review

Pith. "Pith review of Stability of Brain Functional Network During Working Memory Using Structural Balance Theory." pith.science (2026). https://pith.science/paper/EDQXXTJI

@misc{pith2026241116558,
  author       = {Pith},
  title        = {Pith review of: Stability of Brain Functional Network During Working Memory Using Structural Balance Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EDQXXTJI}},
  note         = {Machine review of arXiv:2411.16558}
}

read the original abstract

Working memory plays a crucial role in various aspects of human life. Therefore, it has been an area of interest in different research studies, especially neuroscience. The neuroscientists investigating working memory have primarily emphasized the brain's functional modularity. At the same time, a holistic perspective is still required to investigate the brain as an integrated and unified system. We hypothesized that the brain should shift towards a more stable state during working memory than the resting state. Therefore, based on the Structural Balance Theory (SBT), we aimed to address this process. To achieve this, we examined triadic associations in signed fMRI networks in healthy individuals using the N-back as the working memory task. We demonstrated that the number of balanced triads increased during the working memory task compared to the resting state, while the opposite is true for imbalanced triads. The increase of balanced triads forced the network to a more stable state with a lower balance energy level. The increase of balanced triads was crucially related to changes in anti-synchrony to synchronous activities between the Temporal Cortex, the Prefrontal Cortex, and the Parietal Cortex, which are known to be involved in various aspects of working memory, during the working memory process. We hope these findings pave the way to a better understanding the working memory process.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

10 extracted references · 8 canonical work pages

[1]

Therefore, it has been an area of interest in different research studies, especially neuroscience

Stability of Brain Functional Network During Working Memory Using Structural Balance Theory Sepehr Gourabi 1, Masoud Lotfalipour 1, Reza Khosrowabadi 1, Reza Jafari 1,2,3 1 Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran 2 Department of Physics, Shahid Beheshti University, Evin, Tehran, Iran 3 Center for Communications...

work page 2000
[7]

L., Garcia Caraballo, N

https://doi.org/10.3389/fnhum.2017.00085 Hempel, A., Giesel, F. L., Garcia Caraballo, N. M., Amann, M., Meyer, H., Wüstenberg, T., Essig, M., & Schröder, J. (2004). Plasticity of Cortical Activation Related to Working Memory During Training. American Journal of Psychiatry, 161(4), 745–747. https://doi.org/10.1176/appi.ajp.161.4.745 Hooker, D. (1960). Plan...

arXiv 2004
[8]

Henry Holt and company, New York. 226 pp. Journal of Comparative Neurology, 115(2), 217–217. https://doi.org/10.1002/cne.901150208 Jimura, K., Chushak, M. S., Westbrook, A., & Braver, T. S. (2018). Intertemporal Decision-Making Involves Prefrontal Control Mechanisms Associated with Working Memory. Cerebral Cortex, 28(4), 1105–1116. https://doi.org/10.1093...

work page doi:10.1002/cne.901150208 2018
[11]

Mini-mental state

https://doi.org/10.3389/fpsyt.2020.512761 Cartwright, D., & Harary, F. (1956). Structural balance: A generalization of Heider’s theory. Psychological Review, 63(5), 277–293. https://doi.org/10.1037/h0046049 Constantinidis, C., & Klingberg, T. (2016). The neuroscience of working memory capacity and training. Nature Reviews Neuroscience, 17(7), 438–449. htt...

work page arXiv 1956
[1200]

Tendency to make hub (TMH)

We filtered the available data so that all our final subjects were healthy, male, and right-handed. After selecting male subjects, using the results of the Edinburgh Handedness questionnaire employed to assess handedness in this dataset, we specifically chose right-handed individuals(Oldfield, 1971). In the final stage, we examined the participants' menta...

work page 1971
[1952]

Although it has not only been limited to the frontal cortex, other brain areas have also been investigated (Brooks et al., 2020)

and confirmed it through studies using electrophysiological signals (Fuster & Alexander, 1971; Kubota & Niki, 1971). Although it has not only been limited to the frontal cortex, other brain areas have also been investigated (Brooks et al., 2020). For instance, the impact of working memory exercises has been shown to increase fractional anisotropy, a measu...

work page 1971
[1960]

or be implied in complex cognitive abilities such as learning and reasoning (A. D. Baddeley & Hitch, 1974). Therefore, understanding the working memory process in the brain has been an area of interest in many studies, especially in cognitive neuroscience. Neuroscientists have mainly focused on identifying the brain regions and their interactions in worki...

work page 1974
[1966]

https://doi.org/10.1038/s41598-020-80330-0 Oldfield, R. C. (1971). The assessment and analysis of handedness: The Edinburgh inventory. Neuropsychologia, 9(1), 97–113. https://doi.org/10.1016/0028-3932(71)90067-4 Olesen, P. J., Westerberg, H., & Klingberg, T. (2004). Increased prefrontal and parietal activity after training of working memory. Nature Neuros...

work page doi:10.1038/s41598-020-80330-0 1971

Show all 10 references

[2016]

tendency to make hub

and mapping the 360-defined points in this atlas to each individual's data, we calculated Pearson correlation coefficients. These coefficients measure the strength and direction of linear relationships between different pairs of variables. In functional connectivity, higher co...

1996
[2176]

https://doi.org/10.1038/s41598-021-81767-7 Saberi, M., Khosrowabadi, R., Khatibi, A., Misic, B., & Jafari, G. (2022). Pattern of frustration formation in the functional brain network. Network Neuroscience, 6(4), 1334–1356. https://doi.org/10.1162/netn_a_00268 Saikia, M. J. (20...

2022

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Therefore, it has been an area of interest in different research studies, especially neuroscience

Stability of Brain Functional Network During Working Memory Using Structural Balance Theory Sepehr Gourabi 1, Masoud Lotfalipour 1, Reza Khosrowabadi 1, Reza Jafari 1,2,3 1 Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran 2 Department of Physics, Shahid Beheshti University, Evin, Tehran, Iran 3 Center for Communications...

work page 2000

[2] [7]

L., Garcia Caraballo, N

https://doi.org/10.3389/fnhum.2017.00085 Hempel, A., Giesel, F. L., Garcia Caraballo, N. M., Amann, M., Meyer, H., Wüstenberg, T., Essig, M., & Schröder, J. (2004). Plasticity of Cortical Activation Related to Working Memory During Training. American Journal of Psychiatry, 161(4), 745–747. https://doi.org/10.1176/appi.ajp.161.4.745 Hooker, D. (1960). Plan...

arXiv 2004

[3] [8]

Henry Holt and company, New York. 226 pp. Journal of Comparative Neurology, 115(2), 217–217. https://doi.org/10.1002/cne.901150208 Jimura, K., Chushak, M. S., Westbrook, A., & Braver, T. S. (2018). Intertemporal Decision-Making Involves Prefrontal Control Mechanisms Associated with Working Memory. Cerebral Cortex, 28(4), 1105–1116. https://doi.org/10.1093...

work page doi:10.1002/cne.901150208 2018

[4] [11]

Mini-mental state

https://doi.org/10.3389/fpsyt.2020.512761 Cartwright, D., & Harary, F. (1956). Structural balance: A generalization of Heider’s theory. Psychological Review, 63(5), 277–293. https://doi.org/10.1037/h0046049 Constantinidis, C., & Klingberg, T. (2016). The neuroscience of working memory capacity and training. Nature Reviews Neuroscience, 17(7), 438–449. htt...

work page arXiv 1956

[5] [1200]

Tendency to make hub (TMH)

We filtered the available data so that all our final subjects were healthy, male, and right-handed. After selecting male subjects, using the results of the Edinburgh Handedness questionnaire employed to assess handedness in this dataset, we specifically chose right-handed individuals(Oldfield, 1971). In the final stage, we examined the participants' menta...

work page 1971

[6] [1952]

Although it has not only been limited to the frontal cortex, other brain areas have also been investigated (Brooks et al., 2020)

and confirmed it through studies using electrophysiological signals (Fuster & Alexander, 1971; Kubota & Niki, 1971). Although it has not only been limited to the frontal cortex, other brain areas have also been investigated (Brooks et al., 2020). For instance, the impact of working memory exercises has been shown to increase fractional anisotropy, a measu...

work page 1971

[7] [1960]

or be implied in complex cognitive abilities such as learning and reasoning (A. D. Baddeley & Hitch, 1974). Therefore, understanding the working memory process in the brain has been an area of interest in many studies, especially in cognitive neuroscience. Neuroscientists have mainly focused on identifying the brain regions and their interactions in worki...

work page 1974

[8] [1966]

https://doi.org/10.1038/s41598-020-80330-0 Oldfield, R. C. (1971). The assessment and analysis of handedness: The Edinburgh inventory. Neuropsychologia, 9(1), 97–113. https://doi.org/10.1016/0028-3932(71)90067-4 Olesen, P. J., Westerberg, H., & Klingberg, T. (2004). Increased prefrontal and parietal activity after training of working memory. Nature Neuros...

work page doi:10.1038/s41598-020-80330-0 1971