{"id":"c60ab064-da6e-4fb9-a457-ec7d60d24a70","arxiv_id":"2411.16582","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A DCM extension models time-varying effective connectivity as a Gaussian process using temporal basis functions in the design matrix, validated on simulations and an oddball MEG dataset.","lead":"This paper presents a method to model how brain connections change slowly over time in neuroimaging data, using temporal basis functions inside the Dynamic Causal Modelling framework. It could give researchers a practical tool to study learning, adaptation, and disorders where synaptic strengths drift.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The recovery claim is only tested for trajectories generated inside the same cosine basis; the basis-expressivity assumption is acknowledged but never stress-tested, so the real-data trajectory could reflect model misspecification.","rationale":"The mathematical construction in Equations (3)-(5) is sound: a linear combination of Gaussian modulatory parameters defines a Gaussian process over connectivity, and the DCM machinery can estimate it. The central empirical claim, however, is that time-varying connectivity is recovered from data. The simulations support this only in a matched regime: the generative and inversion models share the same temporal basis and smoothness assumptions. The paper explicitly acknowledges that the basis determines which trajectories can be expressed, but it does not provide any experiment in which the true trajectory violates the basis assumption. The real-data application is also consistent with this concern: the analysis is restricted to 0.11-0.55 Hz, and no model comparison against a static DCM is reported, so the estimated trajectory is not statistically distinguished from noise or from a constant-connectivity model. The reader's weakest assumption correctly identifies the band-limited representability of the trajectory; my concern sharpens this by noting that the missing test is precisely what would establish whether the assumption is injurious. I do not see a reason to change the CONDITIONAL verdict: the method is plausible and well described, with code and demo scripts, but the recovery claim needs to be qualified by an explicit misspecification test. If such a test shows graceful degradation, the paper's claims stand substantially as written; if not, the real-data interpretation would need to be moderated. A minor additional observation is that the analytical Fourier basis in Equation (7) appears to index frequencies inconsistently with the stated 'frequency 1 to M/2,' but this does not affect the implemented DCT-based results and is not the primary concern.","tokens_in":14097,"tokens_out":9204,"duration_ms":91411,"concrete_test":"Generate synthetic evoked and spectral data with a true time-varying connectivity that is not in the sixth-order cosine span—for example, a step change at the sequence midpoint or a Gaussian-process trajectory with a Matérn covariance whose correlation time is shorter than the basis cutoff—then invert with the proposed model and report recovery error (mean squared error and posterior coverage of the true trajectory) alongside the same metrics for an in-span trajectory. If recovery degrades substantially or the posterior excludes the true trajectory, the paper must qualify its central recovery claim to band-limited trajectories and add this negative result as an explicit limitation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (3) defines time-varying connectivity as a linear combination of M temporal basis functions, so the method can only represent trajectories in the span of that basis. The paper states this limitation ('The temporal basis functions that compose the design matrix determine the type of trajectory that can be expressed'), but it never tests what happens when the generative trajectory is outside that span. In both simulations, the true fluctuations are generated through DCM modulatory effects and the recovery model uses a sixth-order cosine set, so the generative and inversion models are matched; this is a face-validity check, not a test of recovery under misspecification. The OPM-MEG application uses an order-5 cosine basis limited to 0.11-0.55 Hz, so any true connectivity change with spectral content outside this band—or with a non-cosine shape such as a sharp switch at the oddball—is unidentifiable and will be projected onto the basis, potentially creating the apparent trajectory. Because the central claim is that the approach 'recovers time-varying connectivity,' the missing out-of-basis test is load-bearing: it determines whether the method is merely a self-consistent estimator or actually robust to its main stated limitation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes an extension of Dynamic Causal Modelling (DCM) to time-varying effective connectivity. The authors define the connectivity trajectory as a linear combination of temporal basis functions via the standard modulatory B-matrix mechanism, so that the modulatory weights provide a spectral expansion of the trajectory and the whole time course is treated as a matrix-valued Gaussian process (Eqs. 3-6). The method is validated with simulations of evoked and spectral responses using a two-region canonical microcircuit model, and applied to an OPM-MEG auditory roving oddball experiment, where a 5th-order cosine basis is used to estimate connectivity fluctuations between 0.11 and 0.55 Hz. The paper discusses design choices, connections to parametric empirical Bayes, and computational efficiency.","tokens_in":14321,"tokens_out":6115,"duration_ms":51037,"significance":"The methodological idea is simple and natural: it reuses the existing DCM modulatory mechanism and turns the design matrix into a temporal basis, thereby avoiding bespoke algorithmic changes. If the approach is robust, it offers a computationally efficient middle ground between fixed-shape regressors and adiabatic DCM, with potential applications across EEG, MEG, and fMRI. The derivation of the Gaussian-process representation (Eqs. 3-6) is correct and transparent, and the availability of SPM demo code is a practical strength. However, the current evidence is internal: simulations use the same model family for generation and inversion, the recovery assessment is visual and qualitative, and the real-data results are limited to a single subject and a narrow frequency band. The significance of the contribution is therefore conditional on additional validation under model misspecification and on quantitative recovery metrics.","major_comments":[{"comment":"The validation is a matched-model exercise: the data are generated with the DCM modulatory mechanism and inverted with a model whose design matrix is a sixth-order cosine set, and no attempt is made to assess what happens when the true trajectory is outside the span of that basis. The paper itself states in the 'Technical details' section that the basis functions determine the type of trajectory that can be expressed, but it never tests the consequences of this limitation. This matters because the empirical trajectory in the Application section is interpreted as reflecting true connectivity dynamics, whereas any misspecified component with spectral content outside 0.11-0.55 Hz would be projected onto the basis and could create spurious structure. I request at least one simulation in which the true time-varying connectivity is not representable by the estimation basis (e.g., a step function or a higher-frequency oscillation) and a quantitative report of recovery error (e.g., mean squared error or correlation between true and estimated posterior mean) for both in-basis and out-of-basis conditions.","section":"Results, Numerical validation (Simulation setup)"},{"comment":"The recovery results are assessed only qualitatively, by visual inspection of Figures 1.C and 2.C. There is no quantitative summary of how well the posterior mean tracks the generative trajectory or whether the posterior intervals have appropriate coverage, and there is no comparison against existing approaches such as adiabatic DCM or the fixed design-matrix method of Auksztulewicz and Friston (2016). Because the paper positions the method as a middle ground between constrained and over-parameterized alternatives, a quantitative comparison is directly relevant to the central claim of recovering time-varying connectivity. Please add numerical recovery metrics for the simulations and, if feasible, a model comparison or recovery comparison against at least one alternative method.","section":"Results, Numerical validation (Evoked responses; Spectral responses)"},{"comment":"The band-limited nature of the empirical analysis is stated explicitly: the fifth-order cosine set restricts fluctuations to 0.11-0.55 Hz and the Nyquist criterion prevents analysis of faster fluctuations. As a result, the estimated trajectory in Figure 3 is a projection of the true (unknown) trajectory onto a low-dimensional cosine basis, and interpretations such as a 'negative gain ... at the onset of the oddball, returning to a small positive value' are conditional on that basis. The manuscript should either temper these interpretive statements or provide model evidence comparisons (e.g., free-energy comparison against a no-modulation model or against a higher-order basis) to support the claim that the temporal modulation is present in the data rather than an artifact of the chosen basis.","section":"Application, Model specification and Results"}],"minor_comments":[{"comment":"The Introduction contains several grammatical errors, e.g., 'slow fluctuations changes in neural activity and confounds neuronal coupling will are expected to impact' and 'buildinggenerative models'; these should be corrected.","section":"Introduction"},{"comment":"In the sentence following Figure 1, 'We also note that the model to recover the first and last 0.5 seconds for the self-inhibition of superficial pyramidal neurons in region 1' appears to be missing a word; the text likely means 'failed to recover' or 'was unable to recover'.","section":"Results, Evoked responses"},{"comment":"The notation in Eq. (1) uses condition index k, while Eq. (3) switches to time t without explicitly defining how the design matrix rows are constructed from epoch mid-times; a brief notational clarification would help.","section":"Technical details"},{"comment":"The statement that 'the interval between stimuli is too large to analyse these fluctuations – following the Nyquist criterion' is slightly confusing because the Nyquist criterion concerns sampling rate rather than interval length; please rephrase to clarify that the inter-stimulus interval limits the resolvable frequency range.","section":"Application, Results"},{"comment":"The claim that log-Bayes factors computed from free-energy differences are 'guaranteed to be always equivalent to the most powerful test across all levels of sensitivity' is strong and would benefit from a qualification or a more careful citation, as stated it could be misleading.","section":"Discussion, Design choices"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a method paper squarely within the journal's scope. The derivation is correct and the implementation is open source. The main deficiency is the absence of a misspecification test and quantitative recovery metrics, which I view as fixable within a revision. I would not require a full re-derivation, but I would like to see the additional simulations and quantitative comparisons in the next version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one. It is a clean, honest extension of DCM: model time-varying connectivity by putting temporal basis functions in the design matrix so the modulatory B matrices become coefficients of a spectral expansion. That generalizes Auksztulewicz and Friston (2016) from two fixed basis functions to an arbitrary basis set, and the Gaussian-process reading falls out naturally. The math (Eqs. 3-6) is straightforward and correct, and the practical packaging is good: the method works through the existing modulatory mechanism, and they ship SPM demos for evoked, spectral, and real MEG data. That is a real contribution for DCM users who want to model slow fluctuations without the cost or brittleness of adiabatic DCM.\n\nThe soft spots are in validation, not in the derivation. Both simulations generate the true connectivity trajectory inside the same cosine basis used for inversion, so recovery is a self-consistency check rather than a test under misspecification. The paper explicitly says the basis determines what trajectories can be expressed, so the authors know this; but they never stress-test it. If a real trajectory has a non-cosine shape or higher-frequency content, the method will project it onto the basis and can produce apparent structure that is partly artifact. The real-data application inherits this: the fifth-order cosine set only covers 0.11–0.55 Hz, so anything faster or sharper is unidentifiable. I would not call this fatal, because the claim is qualified as slow, band-limited fluctuations, but it means the empirical trajectory should be read as 'the best in-basis representation' rather than a validated recovery. Also missing: no quantitative recovery errors, no comparison against adiabatic DCM or a static DCM despite free-energy model comparison being available, and some sloppy prose in the introduction.\n\nWho is this for? DCM practitioners who want a drop-in method with SPM support. As a methods paper it deserves a serious referee; the core idea is useful and the authors are not overselling it much. The referee should ask for an out-of-basis simulation and some form of baseline comparison, but the work is publishable after that.","headline":"Useful incremental DCM extension with honest self-consistency validation; needs an out-of-basis test before the recovery claim is fully credible.","tokens_in":14832,"tokens_out":1611,"would_cite":true,"duration_ms":15631,"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":"Reinterpreting Dynamic Causal Modelling's design matrix as temporal basis functions turns modulatory effects into a spectral expansion of time-varying connectivity.","keywords":["time-varying connectivity","dynamic causal modelling","Gaussian process","temporal basis functions","spectral expansion","effective connectivity","OPM-MEG","roving oddball"],"falsifier":"Simulate an experiment in which the true effective connectivity changes abruptly, for example as a step change or a fluctuation above the basis order's Nyquist frequency, then invert the model with a low-order cosine design matrix and inspect whether the posterior trajectory tracks the ground truth; failure to do so would confirm that the method recovers only the band-limited component of connectivity.","tokens_in":13912,"feed_emoji":"🧠","tokens_out":8074,"duration_ms":79153,"temperature":0.7,"pith_summary":"The paper sets out to establish that Dynamic Causal Modelling, a Bayesian framework for estimating the directed influence between brain regions, can track slow changes in those influences without changing its estimation machinery. The trick is to read the design matrix as a set of temporal basis functions evaluated at the midpoint of each time bin; then the modulatory-effect matrices that DCM already estimates become coefficients in a spectral expansion of the connectivity trajectory. Because those matrices are Gaussian, the trajectory is a matrix-valued Gaussian process with an explicit mean and covariance, so one inversion returns a whole posterior distribution over connectivity over time. The authors support this with simulations of two coupled cortical regions, for both evoked and spectral responses, and with an OPM-MEG auditory roving oddball dataset, where a transient loss of self-inhibition in primary auditory cortex at deviant onset resolves over the stimulus sequence.","feed_headline":"Time-varying brain connectivity becomes a Gaussian process","feed_subtitle":"Putting temporal basis functions in the DCM design matrix turns modulatory effects into a spectral expansion of connectivity.","key_machinery":"The load-bearing object is the DCM design matrix $X$, re-read as a temporal basis set: each column is a basis function evaluated at the mid-time of each epoch, and each modulatory matrix $B_m$ weights one basis function. This is what turns a model of condition-specific effects into a model of slow parameter trajectories, with the Fourier or cosine case making the spectral-expansion interpretation explicit. The Gaussian distribution over the $B_m$ matrices then makes the connectivity a Gaussian process, whose posterior mean and covariance are obtained by projecting the modulatory-effect posterior through the basis set.","core_discovery":"The central claim is that time-varying effective connectivity can be written as $E_c(t)=A_c+\\sum_{m=1}^{M}B_mX_m(t)$, where $X_m(t)$ are temporal basis functions and $B_m$ are the modulatory matrices that DCM already estimates. Since the modulatory effects have Gaussian priors, the implied trajectory is a matrix-valued Gaussian process, and estimating the $B_m$ via standard variational inversion yields a posterior distribution of connectivity at every time point. The basis order controls the fastest allowed fluctuation, making the model an explicit band-limited prior; with Fourier or cosine bases, this is precisely the spectral expansion of the trajectory. Simulations on evoked and spectral responses from two canonical microcircuit regions show the recovered mean tracks the simulated trajectory, and the roving-oddball application reveals a transient decrease of self-inhibition in primary auditory cortex after deviant onset that subsides over repeated stimulus presentation.","pith_inferences":["The same logic invites second-level designs in which connectivity trajectories are contrasted across groups or conditions; the paper sketches this possibility with Kronecker-product designs but does not demonstrate it on data.","Because the recovered trajectory is band-limited by the basis order, apparent connectivity dynamics in resting-state data will depend on the chosen basis; model comparison across orders could separate genuine synaptic modulation from slow artefacts, a test the paper leaves for future work.","The spectral-coefficient reading suggests a natural coupling to time-frequency DCMs, where the same basis expansion could parameterize how oscillatory power drifts over time; this is not implemented in the present paper."],"forward_implications":["With one inversion, users obtain a posterior distribution over the full temporal trajectory of each modulated connection, rather than a set of per-window estimates.","The trajectory is a Gaussian process, so it can be passed to hierarchical Bayesian models such as parametric empirical Bayes for group-level analysis.","Free-energy comparison gives a principled way to choose the basis set and its order, and to test whether connectivity fluctuates at all by comparing against a static model.","Because the approach uses the existing modulatory mechanism, it applies to most DCM variants and modalities, including fMRI, with slower timescales.","The number of parameters scales with basis order rather than number of time points, giving better statistical efficiency than window-by-window methods."],"supporting_citations":[{"why":"Introduces Dynamic Causal Modelling and the variational Bayesian inversion scheme that the proposed method reuses unchanged.","marker":"Friston et al., 2003"},{"why":"The design-matrix modulatory-effects approach this paper extends, with phasic and monotonic covariates for slow connectivity changes.","marker":"Auksztulewicz and Friston, 2016"},{"why":"Window-based DCM estimation with parametric empirical Bayes, the approach the paper contrasts with its single-inversion design.","marker":"Rosch et al., 2018"},{"why":"Formalizes adiabatic DCM, the per-window baseline used for comparison in the paper.","marker":"Jafarian et al., 2021"},{"why":"Supplies the five-region auditory roving oddball DCM architecture used in the real-data application.","marker":"Garrido et al., 2008"},{"why":"Provides the openly available OPM-MEG roving oddball dataset analyzed in the application.","marker":"Mellor et al., 2023"}],"fun_headline_variants":["Time-varying brain connectivity goes Gaussian","Gaussian processes model slow shifts in brain connectivity","DCM enters the time domain with Gaussian process priors","Deviance onset triggers transient inhibition drop in auditory cortex"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method's load-bearing assumption is that the chosen temporal basis functions can express the true connectivity trajectory; the paper itself notes that the basis set determines what trajectories can be expressed and restricts the real-data analysis to fluctuations below 0.55 Hz, so any faster or non-smooth change in connectivity lies outside what this model can recover.","fun_headline_variants_meta":{"raw":{"variants":["Time-varying brain connectivity goes Gaussian","Gaussian processes model slow shifts in brain connectivity","DCM enters the time domain with Gaussian process priors","Deviance onset triggers transient inhibition drop in auditory cortex"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000334,"raw_usage":{"total_tokens":1808,"prompt_tokens":856,"completion_tokens":952,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":472,"completion_tokens_details":{"reasoning_tokens":893}},"tokens_in":472,"tokens_out":952,"duration_ms":10460,"temperature":1.0,"reasoning_tokens":893,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:57:04.324712+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate an experiment in which the true effective connectivity changes abruptly, for example as a step change or a fluctuation above the basis order's Nyquist frequency, then invert the model with a low-order cosine design matrix and inspect whether the posterior trajectory tracks the ground truth; failure to do so would confirm that the method recovers only the band-limited component of connectivity.","supporting_citations":[{"cited_title":"J., Harrison, L., and Penny, W","cited_arxiv_id":null,"evidence_quote":"Introduces Dynamic Causal Modelling and the variational Bayesian inversion scheme that the proposed method reuses unchanged."},{"cited_title":"and Friston, K","cited_arxiv_id":null,"evidence_quote":"The design-matrix modulatory-effects approach this paper extends, with phasic and monotonic covariates for slow connectivity changes."},{"cited_title":"E., Hunter, P","cited_arxiv_id":null,"evidence_quote":"Window-based DCM estimation with parametric empirical Bayes, the approach the paper contrasts with its single-inversion design."},{"cited_title":"C., Walker, M., and Friston, K","cited_arxiv_id":null,"evidence_quote":"Formalizes adiabatic DCM, the per-window baseline used for comparison in the paper."},{"cited_title":"I., Friston, K","cited_arxiv_id":null,"evidence_quote":"Supplies the five-region auditory roving oddball DCM architecture used in the real-data application."},{"cited_title":"M., Seymour, R","cited_arxiv_id":null,"evidence_quote":"Provides the openly available OPM-MEG roving oddball dataset analyzed in the application."}],"review_version":1}