{"id":"501957f7-925c-49e0-992d-caebeb6db0cb","arxiv_id":"2505.00196","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A decomposed subject-specific layer lets neural manifold models of fMRI capture individual spatial variation with far fewer parameters than per-subject layers.","lead":"This paper introduces a way to give each person their own spatial brain map inside a neural network, while sharing most of the network across people to keep memory use low. It tests the approach on movie-watching and resting-state fMRI, reporting better reconstruction, better label decoding, and schizophrenia-related spatial differences.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The shared U/V decomposition restricts each subject to amplitude-scaled versions of a fixed spatial basis, so the method may not capture true topographical variability; this needs a direct capacity check before the central claim is accepted.","rationale":"The reader's weakest assumption identifies the same load-bearing condition: the Decomposed model's claim to capture subject-specific spatial variation rests entirely on the assumption that subject differences are expressible as diagonal rescaling of shared singular vectors U and V. The central claim would fail if real topographic variability cannot be represented in this parameterization. I agree with the CONDITIONAL verdict: the empirical gains are consistent and the simulation is a legitimate proof of concept, but the clinical and generalization claims require either a capacity comparison against the flexible Subject model or a demonstration that S_i is not dominated by confounds. A direct Decomposed-versus-Subject comparison on already-available ROI data is the cleanest way to settle whether the shared-U/V restriction discards signal. I do not recommend rejection because the paper shows consistent improvements over group baselines on multiple datasets, and the parameter-efficient decomposition is a useful contribution even if the interpretability claims prove to be weaker than stated.","tokens_in":13393,"tokens_out":18864,"duration_ms":214938,"concrete_test":"On the Sherlock and Forrest Gump ROI experiments, where the full Subject model is computationally feasible, train the Subject and Decomposed autoencoders with identical shared MLP architecture and hyperparameters, and compare held-out reconstruction MSE and held-out label classification accuracy. If Subject significantly outperforms Decomposed on held-out data, the shared-U/V assumption discards real subject-specific spatial structure and the Decomposed model's gains cannot be attributed to capturing true individual variation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation 4 parameterizes every subject-specific spatial map as W_i = U S_i V^T with U and V shared across subjects, so the only subject-specific degrees of freedom are the diagonal entries of S_i. Geometrically, all representable W_i lie in a fixed low-dimensional subspace of matrix space; each subject is an amplitude-scaled combination of the same L spatial bases. Real subject differences in fMRI include topographic shifts, shape changes, and component reorientations, none of which are expressible by rescaling a common basis. The paper's only support for this restriction is the qualitative similarity of individual ICA spatial maps, but group ICA/back-reconstruction permits more flexible subject-specific maps, so that citation does not establish that amplitude scaling is sufficient. The whole-brain results cannot distinguish the hypothesis that the Decomposed layer captures true individual spatial variation from the alternative that S_i absorbs global amplitude, site, or motion confounds; Figures 4b and 5 are derived entirely from S_i and frozen shared weights. The paper never directly compares Decomposed with the full Subject model on data where the Subject model is trainable, so the loss of information caused by the shared U/V assumption is never quantified.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a scalable framework for learning subject-specific nonlinear manifolds from fMRI data. It compares three architectures: a Group model with a shared first linear layer, a Subject model with a separate spatial weight matrix per subject, and a Decomposed model in which each subject-specific weight matrix is parameterized as W_i = U S_i V^T with U and V shared and only the diagonal singular values S_i varying across subjects. On simulated rotated half-moons data and on the Sherlock and Forrest Gump naturalistic fMRI datasets, the Subject and Decomposed models improve held-out reconstruction and label classification over the Group model, and the Decomposed model is the only one that scales to whole-brain voxelwise data. On the fBIRN resting-state schizophrenia dataset, the authors report that a VAE with the Decomposed layer can fine-tune subject weights for unseen subjects with as little as one TR of data, that an SVM on the learned subject weights separates patients from controls with 79.16% accuracy, and that subject-specific spatial reconstructions show group differences in basal ganglia, visual, auditory, somatosensory, insula, inferior frontal gyrus, and angular gyrus regions.","tokens_in":13668,"tokens_out":6070,"duration_ms":68842,"significance":"If the central claims hold, the Decomposed layer is a practically useful contribution: it introduces a parameter-efficient way to give each subject a distinct linear spatial map while retaining a shared nonlinear manifold, and it enables whole-brain analysis and generalization to unseen subjects without retraining the shared network. The simulation result that a Group model cannot separate rotated half-moons despite nonlinear layers is a clean illustration of the need for subject-specific spatial conditioning, and the one-TR fine-tuning result is an appealing practical capability. However, the manuscript currently provides only limited evidence for the key representational assumption behind the Decomposed model, and the main quantitative claims are not supported by inferential statistics or confound analyses. The clinical interpretation of the group-difference maps is therefore premature. With additional capacity checks and statistical rigor, the paper could make a solid contribution to manifold learning for neuroimaging.","major_comments":[{"comment":"The parameterization W_i = U S_i V^T restricts all subject-specific spatial maps to a single low-dimensional subspace of matrix space: only the diagonal entries of S_i vary across subjects. This cannot express topographic shifts, shape changes, or component reorientations that differ between subjects, and the paper's supporting argument (the qualitative similarity of ICA resting networks in Section 4.2) is not direct evidence that amplitude rescaling of a common basis is sufficient. Because the whole-brain fBIRN results in Figures 4b and 5 are derived entirely from the frozen shared U and V together with subject-specific S_i, this assumption is load-bearing. The manuscript never quantifies the information loss relative to the Subject model in a setting where the Subject model is trainable, nor does it test a simulation with subject-specific spatial variation beyond global scaling. Please add a direct capacity check, for example a comparison of Decomposed versus Subject on the ROI-level data for reconstruction and classification, and a simulation where subjects differ by local translation or reorientation of spatial maps, to determine whether the Decomposed model recovers the true generating factors.","section":"Section 2.2, Figures 2 and 3"},{"comment":"The text repeatedly states that the Subject and Decomposed models significantly outperform the Group model, and that the Decomposed model significantly improves whole-brain classification, but the paper reports no p-values, confidence intervals, paired-test details, or multiple-comparison corrections. The bar charts show point estimates without error bars. Since these significance statements are central to the claim that subject-specific spatial maps improve nonlinear manifold learning, please report the exact test procedure, the number of paired observations, and corrections for the multiple ROIs and label types, or provide bootstrap confidence intervals. The comparison with MRMD-AE should also state explicitly which settings and data are matched and whether the MRMD-AE numbers are from the original publication rather than re-evaluated under identical conditions.","section":"Section 2.3, Figure 4"},{"comment":"The 79.16% SVM classification accuracy on subject-specific weights is reported without uncertainty, permutation testing, or description of the cross-validation details beyond '20-fold.' The fBIRN dataset is multi-site, and diagnosis can be correlated with acquisition site; the subject-specific singular values could in principle absorb site, motion, or global-signal differences rather than clinically meaningful spatial variation. Please report fold construction at the subject level, class balance, hyperparameter selection details, a permutation null, and confidence intervals. Please also add a confound analysis, such as testing whether an SVM can classify acquisition site from the same weights, or whether the patient-control separation survives regressing out site and motion parameters. This is important because the subsequent spatial interpretation in Figure 5 rests on the assumption that the weights capture diagnosis-related neurobiology rather than acquisition artifacts.","section":"Section 2.4, Figure 5"},{"comment":"The spatial group-difference analysis uses 64 FastICA sources and two-sided t-tests on the whitened unmixing matrix, with FDR correction for 64 tests, but it does not account for covariates such as age, sex, site, medication, or motion, and the effective dependence among the 64 tests is not discussed. The manuscript should clarify how the subject-specific reconstructions are constructed from S_i and the shared matrices, and what exactly is being compared in the t-test (e.g., source amplitudes, spatial maps, or unmixing coefficients). A permutation test in which diagnosis labels are shuffled, or in which site labels are permuted, would substantially strengthen the claim that the observed regions reflect schizophrenia-related differences rather than amplitude or site effects.","section":"Section 2.4, Figure 5"}],"minor_comments":[{"comment":"The phrase 'To test this, we apply the framework to temporally unstructured resting-state fMRI data ... We further apply our method to a large resting-state fMRI dataset ...' describes the same fBIRN application twice and should be condensed.","section":"Abstract"},{"comment":"There are typos: 'approxiation theorem' should be 'approximation theorem,' and 'spatial spatial activation map' should be 'spatial activation map.' In Appendix A, 'the the number' should be corrected, and in Section 4.3.2 'dscribed' should be 'described.'","section":"Section 4.1"},{"comment":"The simulation experiment does not explicitly state what classification label is being predicted. Please clarify that the target is the half-moon cluster label after rotation, and specify how the classification is performed for the Subject and Decomposed models relative to the encoder-decoder formulation used elsewhere.","section":"Section 2.1"},{"comment":"The dimension conventions are unclear: W_i in Eq. (4) is written as an L x N matrix, while Eq. (2) uses W_enc^i in a way that suggests an N x L map for the encoder. Please define the exact shapes of U, S_i, and V for both the encoder and decoder, and clarify which matrices are transposed in the implementation.","section":"Section 4.2, Eqs. (2)-(4)"},{"comment":"The paper would benefit from a code and data availability statement. Several datasets and label repositories are listed, but no implementation, training hyperparameters, or random seeds are provided in the main text or appendices beyond the simulation.","section":"General"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The one thing you should know: this paper introduces a parameter-efficient way to fit per-subject spatial maps in nonlinear autoencoders, and that idea is worth taking seriously. The Decomposed layer (W_i = U S_i V^T with shared U,V and subject-specific diagonal S_i) is new, scales to hundreds of subjects, and the naturalistic fMRI experiments show consistent gains over the group baseline and MRMD-AE. The fine-tuning scheme for unseen subjects is also clean and practical.\n\nBut there is a soft spot that looks load-bearing. The simulation generates each subject as a random rotation of the half-moons dataset. A rotation matrix in 2D has identical singular values (both 1), so under the shared-U/V decomposition every subject should collapse to the same W_i. The paper reports near-perfect classification and a circle in the learned singular values. That is not a minor discrepancy; it suggests either the implementation deviates from Eq. 4 (e.g., S_i not actually diagonal, or U/V not fully shared) or the result is an artifact. The authors need to explain this explicitly, because the simulation is the primary evidence that the decomposition can capture true subject-specific spatial variation.\n\nThe stress-test note about capacity is related: real topographic shifts, shape changes, and component reorientations are not amplitude scalings of a common basis. The paper never quantifies the information lost by the shared U/V assumption, and never compares Decomposed to the full Subject model on data where the latter is trainable. That comparison would directly address the capacity concern.\n\nOther weaknesses are less central but still worth fixing: the 79.16% SVM accuracy on subject weights comes without confidence intervals or a null permutation baseline; the clinical group differences are not controlled for site or motion; and no code is released. The citation pattern looks fine.\n\nWho is this for? Researchers building subject-specific models on unstructured fMRI, especially large resting-state datasets. They would get a useful parameterization and a promising training recipe, but should not trust the clinical spatial maps until the simulation question is resolved.\n\nRecommendation: send this to peer review. The core idea is novel and the naturalistic results are suggestive, but the paper needs major revision—at minimum a clarification of the simulation implementation and a direct capacity check—before the central claims can be accepted.","headline":"The Decomposed layer is a genuinely useful parameterization, but the simulation evidence as reported is questionable because random rotations are outside the capacity of shared U,V with diagonal S_i.","tokens_in":14152,"tokens_out":3342,"would_cite":false,"duration_ms":39253,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Decomposing each subject's spatial layer into shared singular vectors and subject-specific singular values lets a nonlinear autoencoder learn individual brain manifolds that scale to hundreds of subjects and separate schizophrenia…","keywords":["subject-specific manifold learning","fMRI","autoencoder","singular value decomposition","schizophrenia","resting-state fMRI","subject generalization","shared response model"],"falsifier":"Simulate a dataset where each subject's spatial map is generated with a subject-specific rotation applied to shared components (differing $U_i$ and $V_i$ rather than just $S_i$), then compare the Decomposed model's held-out reconstruction error to the Subject model's; if the Decomposed model fails to match the Subject model on such data, the shared-$U,V$ assumption is the limiting factor.","tokens_in":13208,"feed_emoji":"🧠","tokens_out":8638,"duration_ms":70710,"temperature":0.7,"pith_summary":"The paper tries to establish that nonlinear autoencoders trained on fMRI fail to capture individual differences not because of insufficient depth, but because they assume a single group-level spatial map. To fix this, it proposes a subject-specific first/last linear layer decomposed as $W_i = U S_i V^T$, where $U$ and $V$ are shared across subjects and only the diagonal singular values $S_i$ vary per subject, paired with a shared nonlinear network. Across simulated rotated data, two naturalistic movie datasets, and resting-state fMRI from schizophrenia patients and controls, this Decomposed layer matches or beats per-subject linear layers, scales to hundreds of subjects, and generalizes to new subjects by fine-tuning only $S_i$. If correct, the field gains a way to learn individually tailored brain manifolds without temporal alignment or per-subject decoders, making subject-specific modeling feasible on large clinical datasets.","feed_headline":"Shared singular vectors give each brain its own fMRI manifold","feed_subtitle":"A decomposed subject layer scales to hundreds of fMRI scans and exposes schizophrenia-linked spatial differences.","key_machinery":"The load-bearing object is the decomposed subject-specific linear layer $W_i = U S_i V^T$ (Eq. 4), placed as the first layer of the encoder and last layer of the decoder of a shared neural network. $U$ and $V$ are shared across subjects and only the diagonal singular values $S_i$ are subject-specific; this replaces an $N \\times L$ per-subject matrix with $L$ per-subject numbers, shrinking the parameter count from $IS \\times HS \\times NS$ to $IS \\times HS + HS^2 + HS \\times NS$. That reduction is what makes voxelwise whole-brain training possible, allows new subjects to be added by fine-tuning only their singular values, and keeps the subject-specific weights linear and therefore interpretable.","core_discovery":"The central claim is that a decomposed subject-specific spatial map, $W_i = U S_i V^T$ with shared orthonormal $U$ and $V$ and per-subject diagonal $S_i$, is enough to let a shared nonlinear autoencoder represent each individual's spatial variation in fMRI data. The paper demonstrates this on three fronts: the Decomposed model recovers the exact rotation angles of simulated half-moon subjects; it outperforms the Group model and the MRMD-AE baseline in reconstruction and event classification on Sherlock and Forrest Gump, including whole-brain data where per-subject linear layers cannot fit in memory; and on roughly 300 resting-state subjects it scales efficiently, generalizes to unseen subjects (even from a single TR), and learns singular values that separate schizophrenia patients from controls with 79.16% label-free classification accuracy. Spatial maps reconstructed from $S_i$ alone show increased basal ganglia, visual, auditory, and somatosensory activation and decreased insula, inferior frontal gyrus, and angular gyrus activation in patients, matching established schizophrenia findings.","pith_inferences":["As an extension, the same $W_i = U S_i V^T$ decomposition could be applied to temporal layers instead of spatial maps, letting a model capture individual differences in dynamics rather than topography; the paper notes this possibility but does not test it.","The compact per-subject singular values $S_i$ are a natural target for harmonization: if scanner or site effects are present in multi-site resting-state data, regressing them out of $S_i$ could enable cleaner cross-site pooling for clinical studies.","The 79.16% label-free classification accuracy suggests $S_i$ may trace a continuous illness-related axis; correlating $S_i$ with symptom severity, medication dose, or illness duration would sharpen the clinical interpretation beyond binary group separation."],"forward_implications":["The Decomposed model can be trained directly on whole-brain voxelwise data, where per-subject linear layers are memory-prohibitive, enabling subject-specific manifold learning at population scale.","New subjects can be added to a fitted model by fine-tuning only their singular values, even from a single TR, without retraining the shared network or inducing catastrophic forgetting.","Unsupervised subject-specific weights separate schizophrenia patients from controls with 79.16% accuracy, suggesting the singular values carry diagnostic information without label supervision.","Spatial reconstructions driven only by subject-specific weights localize group differences to basal ganglia, sensory, insular, and frontal regions, offering a candidate pipeline for generating interpretable clinical biomarkers.","Because the decomposition is architecture-agnostic, it can be inserted into other autoencoder, variational autoencoder, or foundation-model objectives without changing the training procedure."],"supporting_citations":[{"why":"Provides the MRMD-AE baseline and the autoencoder evaluation protocol (train on first half, classify labels on second half) that the paper compares against.","marker":"[24]"},{"why":"Supplies the shared-response generative model with subject-specific spatial maps that the decomposed layer generalizes to unstructured data.","marker":"[15]"},{"why":"Prior demonstration of subject-specific non-linear manifolds for movie-watching fMRI; its public labels are used for classification evaluation.","marker":"[5]"},{"why":"Earlier approach using a separate linear layer per subject for fMRI decoding, which the paper extends into a parameter-efficient decomposed form for manifold learning.","marker":"[41]"},{"why":"Provides the Sherlock naturalistic fMRI dataset used in the autoencoder and classification experiments.","marker":"[14]"},{"why":"Provides the Forrest Gump 7T audio fMRI dataset used as the second naturalistic testbed.","marker":"[21]"},{"why":"Provides the fBIRN Phase III resting-state fMRI dataset from schizophrenia patients and controls used to test scaling, generalization, and clinical differences.","marker":"[29]"},{"why":"Supports the assumption of shared spatial structure across subjects by showing similarity of individual resting-network maps from ICA.","marker":"[8]"}],"fun_headline_variants":["Shared bases, personal maps: fMRI manifolds at scale","Subject-specific fMRI manifolds without temporal alignment","Scaling individual brain manifolds to resting-state data","From group averages to per-subject fMRI manifolds","Decomposed manifold learning finds schizophrenia-linked patterns"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The model assumes that all subjects' spatial maps share the same singular vectors $U$ and $V$, so every individual difference must be a rescaling of shared components; if two brains differ by rotating a spatial component rather than scaling it, the Decomposed layer cannot represent that difference.","fun_headline_variants_meta":{"raw":{"variants":["Shared bases, personal maps: fMRI manifolds at scale","Subject-specific fMRI manifolds without temporal alignment","Scaling individual brain manifolds to resting-state data","From group averages to per-subject fMRI manifolds","Decomposed manifold learning finds schizophrenia-linked patterns"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000541,"raw_usage":{"total_tokens":2637,"prompt_tokens":1033,"completion_tokens":1604,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":649,"completion_tokens_details":{"reasoning_tokens":1530}},"tokens_in":649,"tokens_out":1604,"duration_ms":13737,"temperature":1.0,"reasoning_tokens":1530,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:48:22.039455+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate a dataset where each subject's spatial map is generated with a subject-specific rotation applied to shared components (differing $U_i$ and $V_i$ rather than just $S_i$), then compare the Decomposed model's held-out reconstruction error to the Subject model's; if the Decomposed model fails to match the Subject model on such data, the shared-$U,V$ assumption is the limiting factor.","supporting_citations":[{"cited_title":"Huang, E","cited_arxiv_id":null,"evidence_quote":"Provides the MRMD-AE baseline and the autoencoder evaluation protocol (train on first half, classify labels on second half) that the paper compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the shared-response generative model with subject-specific spatial maps that the decomposed layer generalizes to unstructured data."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior demonstration of subject-specific non-linear manifolds for movie-watching fMRI; its public labels are used for classification evaluation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Sherlock naturalistic fMRI dataset used in the autoencoder and classification experiments."},{"cited_title":"Hanke, F","cited_arxiv_id":null,"evidence_quote":"Provides the Forrest Gump 7T audio fMRI dataset used as the second naturalistic testbed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the fBIRN Phase III resting-state fMRI dataset from schizophrenia patients and controls used to test scaling, generalization, and clinical differences."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports the assumption of shared spatial structure across subjects by showing similarity of individual resting-network maps from ICA."}],"review_version":1}