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REVIEW 5 major objections 6 minor 58 references

Entropy measures as indicators of connectivity paths in the human brain

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Pith's one-line read Entropy measures alone can pick out task-active brain regions from binarized fMRI signals.

desk verdict Entropy-based fMRI activation mapping with a data-derived threshold that needs external validation before the central claim is credible. read the letter →

arxiv 2507.04442 v2 pith:FCZ5RSA7 submitted 2025-07-06 q-bio.NC cs.ITmath.IT

Ania Mesa-Rodríguez , Ernesto Estevez-Rams , Holger Kantz This is my paper · ORCID
classification q-bio.NCcs.ITmath.IT
keywords entropydensityLempel-Zivcomplexityeffectivemeasurecomplexity-entropymaptask-basedfMRIbrainactivationinformationdistanceresting-stateasymmetry
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 claims that two Lempel-Ziv-based entropy measures, the entropy density $h_{LZ}$ and the LZ-effective complexity $E_{LZ}$, computed from mean-binarized fMRI time series, separate active from inactive cortical regions during motor, working-memory, emotion, and language tasks. This matters because the separation is achieved without a hemodynamic model, a network model, or pre-set parameters, so the same pipeline could be used as an exploratory probe for tasks where the expected activations are unknown. The paper also claims that task conditions produce symmetric entropy-density maps across hemispheres, while the resting state is strongly asymmetric, and that LZ-distance dendrograms cluster functionally related regions. Directed connectivity between regions, which the title promises, is explicitly deferred to a forthcoming paper.

What carries the argument

The carrying object is the complexity-entropy map built from Lempel-Ziv factorization of each binarized fMRI time series: entropy density $h_{LZ}$ estimates randomness through the number of new patterns in the exhaustive history, and LZ-effective complexity $E_{LZ}$ estimates memory by comparing the original sequence with randomly shuffled versions. A third quantity, the LZ-distance $d_{LZ}$, estimates the normalized information distance between pairs of regions and is used to build distance matrices and Neighbor-Joining dendrograms. The underlying identity is the coding theorem that the Lempel-Ziv complexity divided by $N/\log N$ converges to the entropy density for ergodic sources, which licenses the estimates on the short, discretized fMRI sequences.

What would settle it

Recompute the active-region lists after replacing each task time series with a phase-randomized surrogate that preserves the power spectrum but destroys nonlinear pattern structure; if the same regions still land left of the threshold, the entropy measures are responding to trivial autocorrelation rather than task-related dynamics.

Watch

Extended reading notes

Core claim

On the paper's own terms, active regions present lower entropy density and higher effective complexity than inactive regions: their binarized BOLD (blood-oxygenation-level-dependent) time series are less unpredictable and more patterned, while inactive regions keep a noisy background. Plotting every cortical region as a point in the $(h_{LZ}, E_{LZ})$ plane yields a linear trend with a data-derived residual threshold, and the regions to the left of that threshold match large parts of the known activation maps for each task, including visual areas for visually cued tasks, motor and sensory cortices for movement, face- and object-selective areas for emotion and memory, and auditory, language, and arithmetic areas for language. The LZ-distance dendrograms group active regions together at low hierarchy levels, and the resting state shows an asymmetry index of 0.41 compared with 0.078 to 0.11 across tasks.

Load-bearing premise

The load-bearing premise is that the data's own residual curve, with its ten-neighbor window, gives a true boundary between active and inactive regions, with no independent ground truth, and that mean-value binarization preserves the task-relevant dynamics even though it is admitted to discard information.

Editorial extensions

If this is right

  • If active regions really are the low-entropy, high-complexity points in the $(h_{LZ}, E_{LZ})$ plane, then task-activation maps can be produced directly from binarized fMRI time series without fitting a hemodynamic response or specifying a network model.
  • The consistency of the visual, motor, face, and language clusters across tasks means the same unparameterized measures can be applied to new tasks where the expected activation pattern is not known.
  • The interhemispheric symmetry of entropy density during tasks and its breakdown at rest suggests a simple scalar summary of hemispheric coordination that could be tracked across cognitive states.
  • Because the method also flags regions not usually reported as active and misses subcortical structures, it offers a complementary activation map rather than a replacement for conventional task contrasts.
  • The finding that active regions appear far from inactive ones in LZ-distance while inactive regions cluster tightly suggests that shared pattern redundancy, not just correlation, is a usable signal for functional grouping.

Reading between the lines

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

  • Extension: the same two-number entropy summary could be tested on other coarse physiological recordings such as EEG or calcium imaging, where binarization is less drastic and ground-truth activation is available; the paper does not run that test.
  • Extension: the resting-state asymmetry index suggests a testable prediction that entropy-density asymmetry grows with mind-wandering or low arousal and shrinks with focused external attention, which the authors do not investigate.
  • Robustness check: rerunning the full pipeline with different window sizes for the residual threshold (for example $k=5$ or $k=15$ instead of $k=10$) and with median rather than mean binarization would show how much of the active-region list depends on those choices.
  • The authors defer directed connectivity, but the time-symmetric LZ-distance matrices could be extended to time-shifted or conditional versions that assign a direction, which would test whether the 'connectivity paths' of the title are actually recoverable.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 6 minor

Summary. The paper proposes using Lempel-Ziv estimates of entropy density (h_LZ) and effective measure complexity (E_LZ), computed from mean-binarized fMRI time series of 360 Glasser regions, to identify task-active regions in HCP task-fMRI data (motor, working memory, emotion, and language, plus resting state). Active/inactive status is assigned by a threshold that is the maximum of the mean residual of each point's ten nearest h_LZ neighbors with respect to a linear fit to the (h_LZ, E_LZ) cloud. The paper reports that active regions have lower h_LZ and higher E_LZ, interprets these as less unpredictable and more patterned, and uses an undirected LZ-information-distance with dendrograms to claim functional groupings. The Conclusion states that the present results are a consistency check and that directed connectivity analysis is left to a forthcoming paper.

Significance. If the activation classification were validated, the approach could offer a relatively simple, entropy-based way to screen task-active regions from fMRI without an explicit hemodynamic or network model, and the use of a large public dataset (N=153, HCP) with multiple tasks is a genuine strength. The manuscript is also transparent about its limitations, including information loss from binarization and the undirected nature of the distance measure. However, the central scientific claim is not currently established because the activation threshold is fit to the very data it labels, with no independent calibration, cross-validation, or null-model testing. The paper therefore reads as a promising but unvalidated proposal rather than a demonstrated result.

major comments (5)
  1. [Section III, Figure 3, and Supplementary B] The threshold separating active from inactive ROIs is defined as the maximum of the mean residual of each point's ten nearest h_LZ neighbors with respect to a linear least-squares fit to the same (h_LZ, E_LZ) data it partitions. Consequently, the statement that active regions have lower h_LZ and higher E_LZ is true by construction: the left-of-threshold set is selected by that property. The overlap with prior literature in Supplementary Table I is a qualitative sanity check, not an independent validation. To support the claims, the authors must calibrate or validate the threshold against an independent activation measure from the same data (e.g., HCP task-fMRI contrast maps) and provide stability analyses with respect to k, the fit model, and the binarization threshold, together with confidence intervals or null-model results.
  2. [Section II (Data preprocessing) and Abstract] The Abstract's claim that the tools detect dynamics 'without relying on pre-established parameters, models, or prior assumptions' is contradicted by the method's own choices: mean-value binarization per ROI (which the authors admit is 'a drastic procedure resulting in the loss of information'), the nearest-neighbor count k=10, the linear-fit model, and the residual-maximum threshold rule. These are ad hoc parameters that materially affect the classification; the parameter-free claim should be removed or substantially qualified.
  3. [Title, Section III.B, and Conclusion] The title promises 'connectivity paths,' but the paper explicitly defers directed connectivity analysis to a forthcoming study and states that 'it is possible to assign a time arrow to information distances, this was not done in the present analysis.' The LZ-distance is an undirected, time-symmetric similarity measure, and the dendrograms are descriptive hierarchical clusterings without statistical support. No evidence of information flow or directed paths is presented. The title should be revised, or the directed connectivity analysis must be included and validated.
  4. [Section II (Methods) and Figure 5] The paper reports one (h_LZ, E_LZ) tuple per ROI but does not describe how the N=153 subjects' time series are combined (concatenation, averaging, or per-subject analysis followed by pooling), nor does it provide error bars or subject-level variability. Without this information, the reader cannot assess whether the separation left and right of the threshold is statistically meaningful. The authors should specify the subject-pooling scheme and provide per-subject or bootstrap confidence intervals for h_LZ and E_LZ.
  5. [Section III (active region lists)] The reported percentages of active ROIs are inconsistent with the enumerated lists. For example, the motor task reports 8.61% of 360 regions (about 31 regions) but the listed entries correspond to 27 regions; the memory task reports 11.4% (about 41) but lists 23; the language task reports 13.61% (about 49) but lists 20. These discrepancies make the active-region results difficult to reproduce and must be resolved.
minor comments (6)
  1. [Section III] A stray '1.' formatting artifact appears before 'Areas that are identified as active in this study but are not typically considered activated,' which should be removed.
  2. [Figure 6] The dendrogram labels are too small to read; a zoomed panel or a separate list of cluster members would improve clarity.
  3. [Section III.2] The resting-state 'active' set is selected manually from the low-h_LZ grouping ('22 regions can be considered in the far left end'), and this ad hoc criterion should be clearly distinguished from the threshold-based task analyses.
  4. [References] Reference 28 is incomplete: 'Wu-Minn and HCP' is not a proper author list for the HCP reference manual.
  5. [Page 2] The in-text arXiv identifier and submission date ('arXiv:2507.04442v1 [q-bio.NC] 6 Jul 2025') should be removed from the body text.
  6. [Section III.2] The asymmetry index is reported without a significance test or confidence interval, so the resting-state symmetry contrast is not statistically supported.

Circularity Check

1 steps flagged · score 6.0 of 10

The central entropy-activation relationship is true by construction: active regions are defined as the low-hLZ side of a threshold fitted to the same complexity-entropy cloud; external overlap does not break the circularity.

  1. self definitional [Section III (Results), threshold-selection paragraph and Figure 3 caption; Supplementary B]
    "From the plot of the residuals, a threshold can be computed by taking for each point, the mean value of its 10 hLZ neighbors and using as threshold the maximum value. ... we take the lower entropy side (left of the vertical threshold line) to correspond to activated regions. ... The active regions during each task present lower hLZ and higher ELZ, which points to less unpredictability and more patterned behavior than the rest of the regions."

    Activated is operationally defined as the low-hLZ/high-ELZ side of a threshold fitted to the same (hLZ, ELZ) scatter (10-neighbor mean residual maximum), with no independent activation measure such as a GLM contrast. Therefore the reported result that active regions have lower hLZ and higher ELZ is a restatement of the labeling rule, not an empirical finding; the same holds for 'inactive regions have higher randomness.' The later comparison with prior literature is an external plausibility check, but it does not calibrate the threshold, so every active-region list changes with k or the residual criterion and the association remains true by construction.

full rationale

The only load-bearing circular step is the activation threshold: active is defined as lower entropy, and lower entropy is then reported as a property of active regions. This is a genuine self-definitional reduction, so the score is 6 rather than 0. The paper's Lempel-Ziv estimators are cited partly from the authors' prior work, but those citations are not circular: LZ complexity is anchored in Ziv's coding theorem (ref. 58) and the shuffling-based complexity estimate is an established procedure, so the self-citations are not load-bearing. The abstract's 'no parameters' claim is contradicted by the mean-binarization choice, the k=10 neighborhood, and the residual-maximum threshold, but that is an overstatement/correctness issue rather than a circularity. The paper itself calls the activation results 'a consistency check' and defers directed connectivity to a forthcoming paper, confirming that the title's 'connectivity paths' are not derived here; that limitation is consistent with a partial-circularity verdict rather than a fully circular derivation.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

No new physical or mechanistic entities are introduced. The only ad hoc construct is the residual threshold rule, which is listed as an axiom; the 'connectivity paths' phrasing in the title is an interpretation of an undirected distance matrix, not a new entity.

free parameters (3)
  • Binarization threshold per ROI = mean BOLD value of each region's time series
    The discretization threshold is set to the temporal mean of each region, which is data-dependent and discards amplitude information; the paper admits binarization loses information.
  • Nearest-neighbor count k in residual threshold = 10
    The activation threshold uses each point's 10 nearest h_LZ neighbors to compute mean residuals; k is not justified and changes the active region sets.
  • Fit model for complexity-entropy cloud = linear (first-order polynomial)
    Residuals are measured against a linear fit of E_LZ versus h_LZ; a nonlinear fit would change residuals and the resulting threshold.
assumptions (7)
  • domain assumption Binarized BOLD signal preserves task-relevant information
    The paper states 'What is hoped for is that the binary sequence still carries enough information to grasp relevant features of the dynamics of the system.' This is assumed, not tested.
  • domain assumption LZ entropy estimate is valid for these finite, non-stationary fMRI sequences
    Ziv's theorem (Eq. 3) holds for ergodic processes in the infinite limit; applicability to short task-fMRI windows is assumed.
  • domain assumption Shuffle-based LZ effective complexity approximates the true excess entropy
    E_LZ is defined via random shuffling following refs 31,32; no validation on fMRI data is provided.
  • standard math LZ information distance approximates normalized information distance
    Standard use of LZ complexity as a surrogate for Kolmogorov complexity (Li et al. 2004); finite-sequence bias is not assessed.
  • domain assumption Low entropy density indicates task activation
    The mapping from low h_LZ to active regions is justified by citing Ito et al. (ref 36) on quenching of variability, assumed rather than tested in these data.
  • ad hoc to paper Maximum of the 10-neighbor mean residual curve is the active/inactive boundary
    This threshold criterion is introduced for this analysis and has no independent justification; all activation lists depend on it.
  • domain assumption Glasser 360 parcellation is a valid ROI definition
    Glasser atlas is used without checking its appropriateness for individual HCP task data.

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Pith. "Pith review of Entropy measures as indicators of connectivity paths in the human brain." pith.science (2026). https://pith.science/paper/FCZ5RSA7

@misc{pith2026250704442,
  author       = {Pith},
  title        = {Pith review of: Entropy measures as indicators of connectivity paths in the human brain},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FCZ5RSA7}},
  note         = {Machine review of arXiv:2507.04442}
}
read the original abstract

How does the information flow between different brain regions during various stimuli? This is the question we aim to address by studying complex cognitive paradigms in terms of Information Theory. To assess creativity and the emergence of patterns from a Shannon perspective, we applied a range of tools, including Entropy Density, Effective Measure Complexity, and the Lempel-Ziv distance. These entropic tools enable the detection of both linear and non-linear dynamics without relying on pre-established parameters, models, or prior assumptions about the data. To identify connections between different brain regions, we analyse task-based fMRI data from subjects during motor, working memory, emotion recognition, and language stimuli to gain insight into these complex cognitive processes. Since this method does not rely on prior knowledge, it is particularly well-suited for exploratory research, facilitating the discovery of previously unidentified connections or patterns in the brain. The capacity to identify non-linear dynamics is especially important for studying brain connectivity, as the brain exhibits significant non-linear interactions across multiple functional levels.

Figures

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Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
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Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
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Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
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Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.