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REVIEW 4 major objections 5 minor 37 references

Explainable Brain Age Gap Prediction in Neurodegenerative Conditions using coVariance Neural Networks

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A covariance neural network trained only on healthy aging produces elevated brain age gaps for Alzheimer's disease, frontotemporal dementia, and atypical parkinsonian disorders, with each disease's gap traceable to how the network uses…

desk verdict Incremental but useful VNN brain-age extension to FTD/APD/PD with a null PD result; headline significance claims are under-statted and covariance re-estimation needs robustness checks. read the letter →

arxiv 2501.01510 v1 pith:D465DV7Z submitted 2025-01-02 cs.LG eess.SPq-bio.QM

Saurabh Sihag , Gonzalo Mateos , Alejandro Ribeiro This is my paper · ORCID
classification cs.LGeess.SPq-bio.QM
keywords brainagegapcovarianceneuralnetworkscorticalthicknessneurodegenerationexplainableAIAlzheimer'sdiseasefrontotemporaldementiaatypicalparkinsoniandisorders
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

This paper argues that brain age gap (Δ-Age) can be made anatomically interpretable and mechanistically explainable by computing it with a covariance neural network (VNN), a network whose layers filter cortical-thickness measurements through powers of the anatomical covariance matrix. Using 68 cortical regions from a standard brain atlas, the authors show that a VNN trained only on healthy controls detects significantly elevated Δ-Age for Alzheimer's disease, frontotemporal dementia, and atypical parkinsonian disorders, but not for Parkinson's disease. The elevation is traced to disease-relevant regions and to specific eigenvectors of the anatomical covariance matrix that the network weighs differently for each disease. If correct, the result is a biomarker that localizes accelerated aging and says which anatomical modes carry it, rather than giving a single opaque number.

What carries the argument

The coVariance filter $H(C)=\sum_{k=0}^{K} h_k C^k$, with $C$ the $68\times 68$ anatomical covariance matrix of cortical thickness across regions. Since a covariance filter is equivalent to a PCA transform, the VNN's representations are steered by the eigenvectors of $C$; the paper makes this explicit by computing inner products between final-layer regional residuals and those eigenvectors. The residual construction converts the network output into per-region contributions, so elevated Δ-Age can be assigned to specific anatomy and to specific eigenmodes.

What would settle it

Re-run the analysis with the anatomical covariance matrix fixed to the training-set covariance for every disease cohort, or with a perturbed covariance; if the disease-specific eigenvector signatures and regional maps largely disappear or shift to different eigenvectors, the explainability is an artifact of per-cohort covariance re-estimation. An independent cohort with matched preprocessing should reproduce the same significant eigenvector indices (0, 1, 2, 6 for AD; 0, 1, 4, 5 for FTD; 8 for APD).

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Extended reading notes

Core claim

The central discovery is that a VNN pretrained on a healthy-aging population separates neurodegenerative conditions by Δ-Age and by how it uses the eigenspectrum of the anatomical covariance matrix. With the covariance matrix re-estimated from each dataset's own healthy controls, the model gives Δ-Age = 4.67 ± 4.04 years for Alzheimer's disease (healthy controls 0 ± 2.91), 6.17 ± 4.55 for frontotemporal dementia, and 2.49 ± 3.09 for atypical parkinsonian disorders, while Parkinson's disease shows no significant elevation. Regional residuals at the network's final layer map to disease-plausible cortex: medial temporal, entorhinal, and temporo-parietal regions for AD; frontal and temporal regions for FTD; and motor and occipital regions for APD. Inner products of these residuals with the eigenvectors of the anatomical covariance matrix differ significantly between each disease and its healthy controls — eigenvectors 0, 1, 2, and 6 for AD; 0, 1, 4, and 5 for FTD; and 8 for APD — indicating the distinct Δ-Age patterns arise from the network processing each disease along different covariance eigenmodes.

Load-bearing premise

The anatomical covariance matrix that the network uses is re-estimated from each dataset's own healthy control group rather than kept fixed to the one used in training, so the disease-specific patterns could partly reflect differences in covariance estimation or preprocessing rather than neurodegeneration.

Editorial extensions

If this is right

  • A VNN trained only on healthy aging can flag AD, FTD, and APD through elevated Δ-Age, so disease labels are not needed during training for the biomarker to work.
  • Parkinson's disease shows no significant Δ-Age elevation on cortical thickness, so the pipeline separates conditions with cortical accelerated aging from those without.
  • Because Δ-Age distributions overlap across diseases, the anatomical and eigenvector characterizations carry information that the scalar gap alone does not.
  • Differences in which eigenvectors are significant (several for AD and FTD, only one for APD) explain why Δ-Age elevation is smaller for APD than for the other disease groups.

Reading between the lines

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

  • The paper re-estimates the anatomical covariance matrix per dataset; a direct stress test the paper does not report is to hold the covariance fixed to the training set and verify that the same eigenvectors and regions remain significant, separating neurodegeneration signal from covariance-estimation effects.
  • The significant eigenvector sets (0,1,2,6; 0,1,4,5; 8) are candidates for transdiagnostic signatures; an independent study could correlate these eigenvector loadings with clinical severity, cognitive decline, or longitudinal atrophy.
  • The same residual-to-eigenvector accounting could be applied to other morphometric features (volume, surface area, subcortical thickness) to test whether the disease-specific eigenmode signatures are anatomy-specific or generalize across modalities.
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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

4 major / 5 minor

Summary. The paper applies coVariance neural networks (VNNs) to predict brain age gap (Δ-Age) from cortical thickness features in Alzheimer's disease (AD), frontotemporal dementia (FTD), atypical Parkinsonian disorders (APD), and Parkinson's disease (PD), using a VNN pre-trained on healthy controls from OASIS-3. The authors report elevated Δ-Age in AD, FTD, and APD relative to healthy controls, with distinct anatomic patterns, and claim that these patterns are explainable through the inner products between VNN regional residuals and eigenvectors of the anatomical covariance matrix. The paper emphasizes the inherent interpretability of VNNs compared with black-box brain-age models.

Significance. If the central claims hold, the paper would contribute a transparent, anatomy-resolved brain-age-gap biomarker for multiple neurodegenerative conditions, extending prior VNN work beyond Alzheimer's disease. The paper's strengths are its use of publicly available datasets, a transparent architectural prior based on anatomical covariance, and a clear attempt to link model representations to biological structure. However, the load-bearing inferences currently rest on informal comparisons without proper statistical testing, on a single out of ten trained models, and on a covariance re-estimation step whose validity is not established. These issues must be resolved before the significance of the reported findings can be assessed.

major comments (4)
  1. [Section 4] The statement 'For each disease dataset, we used the anatomical covariance matrix estimated only from the respective HC group in the pre-trained VNN model' changes the operator applied at inference: the coVariance filter H(C) = Σ h_k C^k depends explicitly on C, and the filter taps were optimized for the OASIS-3 training covariance. The paper does not verify that the per-dataset HC covariance matrices fall within the stability/transferability bounds established for VNNs [11,15,18], nor does it report any sensitivity analysis with respect to this covariance shift. Since the datasets also differ in preprocessing (FreeSurfer 5.1 for ADNI vs. CAT12 for NIFD/4RTNI/PPMI), the elevated Δ-Age and eigenvector inner-product differences could reflect covariance mismatch or preprocessing artifacts rather than neuropathology. This affects the AD, FTD, and APD claims jointly and is load-bearing.
  2. [Sections 1.3 and 4] The contributions claim 'significantly elevated Δ-Age' for AD, FTD, and APD, but the results only report means and standard deviations (e.g., '4.67±4.04 years' for AD vs. '0 ± 2.91 years' for HC) without p-values, confidence intervals, effect sizes, or explicit statistical tests for the Δ-Age group comparisons. The word 'significantly' is therefore unsupported in the current text. Formal hypothesis tests (e.g., two-sample tests with appropriate corrections) are needed for each disease-vs-HC comparison and for the PD null result.
  3. [Section 3.2] The manuscript states 'The results reported in this paper are derived from one pre-trained VNN model among the 10 that were pre-trained using the above procedure.' Selecting one model post hoc can yield results that are not representative of the model family, especially given the modest age-prediction performance (MAE 7.25 ± 0.51 years, r = 0.44). The authors should either report results aggregated across all 10 models with appropriate uncertainty, or justify why a single model is sufficient for the disease-group comparisons.
  4. [Section 4 and Fig. 5] The explainability analysis computes inner products between regional residuals and eigenvectors of the anatomical covariance matrix, but this same covariance matrix defines the VNN filter applied to the data. The analysis is therefore at least partly self-referential: both the residuals and the eigenvectors are functions of the same estimated C. Moreover, the eigenvectors reported as significant (0,1,2,6 for AD; 0,1,4,5 for FTD; 8 for APD) are selected from 68 eigenvectors without controlling the false discovery rate across the 68 comparisons. The paper should report corrected p-values or FDR, and should discuss the interpretational limits of using the same eigenvectors that define the model.
minor comments (5)
  1. [Figure 3 caption] The caption and text refer to 'AT P' in Figure 3, but the paper uses 'APD' elsewhere; this abbreviation should be made consistent.
  2. [Throughout] The terms 'interpretability' and 'explainability' are used somewhat interchangeably; the paper should clarify whether the anatomic characterization is an interpretation of the model's internal representation or an explanation of the Δ-Age prediction, as the two are conceptually distinct.
  3. [Section 1.1] There is a typo in the sentence 'they rely onlinear-shift-and-sum operators' — it should read 'they rely on linear-shift-and-sum operators.'
  4. [Section 4] The HC group for 4RTNI is taken from NIFD because of acquisition similarity, but this choice is not tested or discussed as a potential confound; a brief justification or sensitivity analysis would strengthen the report.
  5. [Abstract and Section 1] The phrase 'brain age gap gap' appears in the introductory section; one 'gap' should be removed.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity; empirical Δ-Age comparisons are independent, with minor reliance on prior VNN work for the interpretability framing.

full rationale

Walked the derivation chain. The central claim (elevated Δ-Age for AD/FTD/APD) rests on a VNN trained on healthy OASIS-3 cortical thickness data and applied to held-out disease cohorts; the disease-vs-HC contrast is an empirical, out-of-sample comparison, not a fitted quantity. The bias-correction linear regression on each dataset's HC group only forces HC Δ-Age to zero on average; disease values remain unconstrained. The explainability analysis (inner products of regional residuals with eigenvectors of the anatomical covariance matrix) is a spectral decomposition of the model's own output: because the coVariance filter H(C)=Σ h_k C^k is a polynomial in C, the eigenvectors of C are the filter's eigenbasis, so the inner products are, by construction, the coefficients describing how the VNN output varies. This makes the explanation mechanistic rather than an independent biological validation, but it is not circular in a logical sense: the disease labels provide independent grounding, and the group differences in inner products are empirical findings. The self-citations to [10] and [11] supply the mathematical equivalence (VNN filter vs PCA) and the definition of regional residuals; these are algebraic/architectural facts, not unverified premises. The per-dataset re-estimation of the covariance matrix (Section 4) is a potential confound but not a circular step, since Δ-Age remains an out-of-sample prediction. Thus no load-bearing circularity is present.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim depends on one trained VNN with thousands of fitted parameters, per-dataset bias-correction weights, and several domain assumptions about cross-dataset comparability and the meaning of age residuals. No new physical or biological entities are introduced.

free parameters (3)
  • VNN filter taps (22,570 learnable parameters) = trained on OASIS-3; MAE 7.25 ± 0.51 years
    All downstream Δ-Age values and anatomical patterns are computed from one pretrained VNN; the trained tap values are not disclosed.
  • Bias-correction linear regression weights (per dataset) = not disclosed
    Used to map VNN outputs to brain age on each HC group; directly shifts Δ-Age estimates before group comparisons.
  • Hyperparameters (learning rate, batch size, layer taps, width, epochs) = lr=0.15, batch=10, taps 2 and 6, width 61, up to 100 epochs
    Chosen by Optuna on validation; the selected architecture shapes the representations and the eigenvector explainability results.
assumptions (4)
  • standard math VNN-PCA equivalence theorem from [11]: a covariance filter H(C)=Σ h_k C^k processes data by exploiting eigenvectors of C.
    The explainability analysis assumes this theorem to interpret inner products with eigenvectors as evidence of how the model works.
  • domain assumption Chronological age of healthy individuals is a valid training target for brain age, and residuals in disease groups indicate accelerated aging.
    The entire brain age gap paradigm; the paper does not validate this against clinical markers (future work).
  • domain assumption Cortical thickness features from different datasets (Freesurfer 5.1 for ADNI, CAT12 for others) are comparable enough for cross-dataset model transfer.
    The pretrained VNN is applied to features from different preprocessing pipelines without harmonization.
  • ad hoc to paper The VNN remains valid when the anatomical covariance matrix is re-estimated on each dataset's HC group instead of the training covariance.
    The paper relies on VNN transferability but does not test the effect of this covariance shift.

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Cite this review

Pith. "Pith review of Explainable Brain Age Gap Prediction in Neurodegenerative Conditions using coVariance Neural Networks." pith.science (2026). https://pith.science/paper/D465DV7Z

@misc{pith2026250101510,
  author       = {Pith},
  title        = {Pith review of: Explainable Brain Age Gap Prediction in Neurodegenerative Conditions using coVariance Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D465DV7Z}},
  note         = {Machine review of arXiv:2501.01510}
}
read the original abstract

Brain age is the estimate of biological age derived from neuroimaging datasets using machine learning algorithms. Increasing \textit{brain age gap} characterized by an elevated brain age relative to the chronological age can reflect increased vulnerability to neurodegeneration and cognitive decline. Hence, brain age gap is a promising biomarker for monitoring brain health. However, black-box machine learning approaches to brain age gap prediction have limited practical utility. Recent studies on coVariance neural networks (VNN) have proposed a relatively transparent deep learning pipeline for neuroimaging data analyses, which possesses two key features: (i) inherent \textit{anatomically interpretablity} of derived biomarkers; and (ii) a methodologically interpretable perspective based on \textit{linkage with eigenvectors of anatomic covariance matrix}. In this paper, we apply the VNN-based approach to study brain age gap using cortical thickness features for various prevalent neurodegenerative conditions. Our results reveal distinct anatomic patterns for brain age gap in Alzheimer's disease, frontotemporal dementia, and atypical Parkinsonian disorders. Furthermore, we demonstrate that the distinct anatomic patterns of brain age gap are linked with the differences in how VNN leverages the eigenspectrum of the anatomic covariance matrix, thus lending explainability to the reported results.

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Works this paper leans on

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    Explainable Brain Age Gap Prediction in Neurodegenerative Conditions using coVariance Neural Networks

    INTRODUCTION Aging is a complicated biological process that manifests it- self in the form of various progressive physiological and cog- nitive changes [1]. Recent years have seen an exponential increase in the study of brain aging using machine learning algorithms [2]. A common objective of brain age predic- tion strategies is to derive an estimate of br...

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    COV ARIANCE NEURAL NETWORKS We start by providing a brief overview of the architecture of a VNN model. A single layer of VNN is formed by concate- nating a coVariance filter with a pointwise non-linear activa- tion function σ(·) (e.g., ReLU, tanh) that satisfies σ(u) = [σ(u1), . . . , σ(um)] for u = [ u1, . . . , um]. Therefore, the output of a single lay...

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    METHODS AND MA TERIALS 3.1. Datasets for neurodegenerative conditions In this paper, we leverage cortical thickness measures de- rived from structural MRI and curated according to Desikan- Killiany brain atlas (68 cortical regions) for various neurode- generative conditions. All datasets are publicly available at https://ida.loni.usc.edu/. ADNI. This data...

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    RESULTS For each disease dataset, we used the anatomical covariance matrix estimated only from the respective HC group in the pre-trained VNN model. VNN was oblivious to the identity or any information about the disease. Figure 3 illustrates that elevated ∆-Age was observed for AD, ATP, and FTD relative to their respective HC groups. The ∆-Age for AD grou...

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