arxiv: 2602.09034 · v2 · submitted 2026-01-30 · 🧬 q-bio.NC · cs.AI

Recognition: 2 theorem links

· Lean Theorem

Latent-Space Causal Discovery from Indirect Neuroimaging Observations

Sangyoon Bae , Miruna Oprescu , David Keetae Park , Shinjae Yoo , Jiook Cha

Authors on Pith no claims yet

Pith reviewed 2026-05-16 10:07 UTC · model grok-4.3

classification 🧬 q-bio.NC cs.AI

keywords causal discoveryneuroimagingfMRIlatent spacedirected graphsMambainversionTVB simulations

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The pith

A physics-aware inversion step before graph estimation recovers directed causal structure from indirect neuroimaging signals.

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

The paper shows that neuroimaging signals are distorted by hemodynamics and volume conduction, so statistical dependence in raw data does not equal latent neural influence. It formalizes a setting where inversion of the observation process is possible when modality physics are known and latent dynamics are nonstationary, then derives an error-propagation bound. Building on this, it introduces INCAMA, which performs the inversion and feeds the result into a delay-aware Mamba encoder that uses mechanism shifts to score directed edges. A sympathetic reader cares because better recovery of directed networks could clarify how information flows in the brain during tasks and disease. Controlled TVB simulations show 2-3x higher F1 scores than observation-space or two-stage baselines, while HCP motor-task fMRI yields sparse estimates concentrated in canonical visuo-motor pathways.

Core claim

Under the conditional setting of recoverable inversion from modality physics together with nonstationary latent dynamics, physics-aware inversion coupled with a delay-aware Mamba encoder that treats mechanism shifts as informative variation produces directed graph estimates whose recovery accuracy is 2-3 times higher in F1 than observation-space and two-stage baselines on TVB simulations and yields sparse, anatomically consistent estimates concentrated in visuo-motor pathways on HCP motor-task fMRI.

What carries the argument

INCAMA, which performs physics-aware inversion of the observation process and then applies a delay-aware Mamba encoder that scores directed edges by exploiting shifts in underlying mechanisms as variation.

If this is right

Directed-graph recovery improves when the inversion step is performed explicitly before any graph scoring rather than attempting to work directly on distorted observations.
Nonstationary latent dynamics supply the variation needed to identify directed influences once the observations have been inverted.
The resulting sparse directed estimates align with known functional anatomy such as visuo-motor pathways during motor tasks.
An explicit inversion-error bound can be propagated to quantify uncertainty in the final directed-graph scores.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the same inversion principle holds for other modalities such as EEG, the same encoder architecture could be reused with modality-specific forward models.
Experiments that deliberately induce mechanism shifts (changing task demands or state) may yield stronger causal signals than purely resting-state recordings.
The approach could be coupled with biophysical simulators to generate synthetic datasets that test the limits of the inversion bound before real-data application.

Load-bearing premise

That the observation process can be inverted recoverably when the physics of the recording modality are known and the latent neural dynamics are nonstationary.

What would settle it

A controlled TVB simulation with known ground-truth directed graphs in which the full INCAMA pipeline does not produce at least 2x higher F1 for directed edges than direct observation-space causal methods after the same amount of data.

Figures

Figures reproduced from arXiv: 2602.09034 by David Keetae Park, Jiook Cha, Miruna Oprescu, Sangyoon Bae, Shinjae Yoo.

**Figure 1.** Figure 1: Overview of INCAMA. (a) End-to-end framework. INCAMA decomposes causal discovery from indirect neuroimaging measurements into physics-aware inversion and latent-space causal inference, mapping observed fMRI and EEG signals to latent neural dynamics before estimating directed connectivity. (b) Latent-space causal discovery. Directed, delay-aware causal inference is performed on latent neural trajectories us… view at source ↗

**Figure 2.** Figure 2: Recovered average visuo-motor causal pathways in the (a) left and (b) right hemispheres. Nodes correspond to standard neuroanatomical regions of interest (ROIs) defined by the Desikan–Killiany atlas. Arrows indicate the directional information flow inferred by INCAMA from real fMRI data of the HCP S1200 Motor Task, computed by averaging recovered causal graphs across 1,078 subjects. The resulting group-lev… view at source ↗

read the original abstract

Neuroimaging does not observe causal variables directly: hemodynamics and volume conduction distort signals so that statistical dependence need not reflect latent neural influence. Before estimating graphs, one must specify under what assumptions delayed directed structure can be studied from such indirect observations. We formalize a conditional setting - recoverable inversion under modality physics together with nonstationary latent dynamics - and derive an inversion-error propagation bound under explicit assumptions. Building on this framing, we propose INCAMA (INdirect CAusal MAmba): physics-aware inversion coupled with a delay-aware Mamba encoder that uses mechanism shifts as informative variation for directed graph scoring. We use controlled simulations for quantitative validation and HCP motor-task fMRI as a zero-shot external transfer check based on anatomical and task-network consistency. Across TVB simulations, INCAMA improves directed-structure recovery by 2-3x in F1 over observation-space and two-stage baselines, and on HCP motor-task fMRI it produces sparse directed estimates concentrated in canonical visuo-motor pathways.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

INCAMA pairs physics-aware inversion with a delay-aware Mamba to score directed graphs from indirect observations, with clear simulation gains but unverified inversion on real fMRI.

read the letter

INCAMA is a new pipeline that first inverts indirect signals like fMRI using modality physics, then feeds the result into a delay-aware Mamba encoder that treats mechanism shifts as the variation needed for directed graph scoring. The paper formalizes the recoverable-inversion setting and derives an error-propagation bound under explicit assumptions, which is a useful framing step. The simulation results on TVB data are the strongest evidence: they report 2-3x F1 improvement in directed-structure recovery over observation-space and two-stage baselines, and the controlled setting lets them test whether the inversion step actually helps. That part is concrete and reproducible in principle. The HCP motor-task results are weaker. They show sparse directed estimates that land in expected visuo-motor pathways, but the paper gives no quantitative check that the inversion recovered the latent variables to within the claimed error bound or that nonstationary dynamics supplied enough informative variation. Without those checks, the causal interpretation on real data stays provisional. Error bars and ablations that isolate the inversion component are also missing. This work is aimed at researchers who need causal methods that respect the physics of neuroimaging modalities. A reader already working on latent-variable causal discovery or on bridging biophysical models with sequence architectures would find the architecture and the simulation benchmarks worth examining. It deserves peer review because the problem is important, the proposal is specific, and the simulation evidence is solid enough to justify referee time even if the real-data validation needs tightening.

Referee Report

2 major / 2 minor

Summary. The paper formalizes a conditional setting of recoverable inversion under modality physics together with nonstationary latent dynamics for causal discovery from indirect neuroimaging observations, derives an inversion-error propagation bound, and introduces INCAMA: a physics-aware inversion step coupled to a delay-aware Mamba encoder that scores directed edges via mechanism shifts. It reports 2-3x gains in F1 for directed structure recovery on TVB simulations versus observation-space and two-stage baselines, plus qualitative consistency with canonical visuo-motor pathways on HCP motor-task fMRI as a zero-shot transfer check.

Significance. If the recoverable-inversion assumption holds on real hemodynamics, the work could meaningfully advance causal inference in neuroimaging by supplying a principled error bound and a mechanism-shift scoring approach that exploits nonstationarity, potentially yielding more interpretable directed brain networks than current two-stage pipelines. The controlled simulation gains are a clear strength; the HCP consistency check offers preliminary evidence of external validity.

major comments (2)

[HCP validation] HCP motor-task fMRI results (abstract and corresponding results section): the reported sparse directed estimates concentrated in visuo-motor pathways are presented without any quantitative verification that the physics-aware inversion recovers latent variables to within the derived bound's tolerance or that nonstationarity supplies sufficient informative variation on real data. This verification is load-bearing for transferring the 2-3x F1 simulation gains and for the causal interpretation of the HCP estimates.
[Inversion-error propagation bound derivation] Section deriving the inversion-error propagation bound: the bound is stated under the explicit conditional setting, yet no sensitivity analysis or empirical check is described for how realistic deviations from recoverable inversion (e.g., unmodeled hemodynamic nonlinearities or insufficient nonstationarity) propagate to graph-recovery error. Without this, the bound's practical utility for real-data claims remains unverified.

minor comments (2)

[Abstract] Abstract: the quantitative F1 gains are stated without error bars, confidence intervals, or statistical tests, weakening the strength of the simulation claims.
[Method] Method description: hyperparameters of the delay-aware Mamba encoder and the precise form of the physics model used in the inversion step are not detailed enough to support immediate reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the controlled simulation gains. We address the two major comments point-by-point below, clarifying the scope of our real-data claims and the role of the derived bound.

read point-by-point responses

Referee: [HCP validation] HCP motor-task fMRI results (abstract and corresponding results section): the reported sparse directed estimates concentrated in visuo-motor pathways are presented without any quantitative verification that the physics-aware inversion recovers latent variables to within the derived bound's tolerance or that nonstationarity supplies sufficient informative variation on real data. This verification is load-bearing for transferring the 2-3x F1 simulation gains and for the causal interpretation of the HCP estimates.

Authors: We agree that quantitative verification of latent-variable recovery is impossible on HCP data because no ground-truth neural signals exist. The manuscript explicitly presents the HCP analysis as a zero-shot external transfer check based on anatomical and task-network consistency, not as a quantitative recovery experiment. We will revise the results and discussion sections to (i) restate this distinction more prominently, (ii) add a quantitative assessment of nonstationarity in the HCP time series (e.g., variance of estimated mechanism shifts across task blocks), and (iii) include a brief limitations paragraph noting that causal claims on real data remain conditional on the recoverable-inversion assumption holding sufficiently well. revision: partial
Referee: [Inversion-error propagation bound derivation] Section deriving the inversion-error propagation bound: the bound is stated under the explicit conditional setting, yet no sensitivity analysis or empirical check is described for how realistic deviations from recoverable inversion (e.g., unmodeled hemodynamic nonlinearities or insufficient nonstationarity) propagate to graph-recovery error. Without this, the bound's practical utility for real-data claims remains unverified.

Authors: The bound is derived under the stated assumptions of recoverable inversion and sufficient nonstationarity. The simulation suite already varies inversion error magnitude and nonstationarity level, demonstrating that graph-recovery F1 remains stable inside the assumed regime. We did not, however, include a dedicated sensitivity study for specific unmodeled real-world deviations such as nonlinear hemodynamics. We will add a new subsection that (a) introduces additional TVB simulations with nonlinear Balloon-Windkessel hemodynamics and (b) reports the resulting degradation in both inversion accuracy and downstream graph F1, thereby providing an empirical check on the bound's sensitivity. revision: yes

Circularity Check

0 steps flagged

No load-bearing circularity; derivation uses explicit assumptions and external validation

full rationale

The paper formalizes a conditional setting of recoverable inversion under modality physics together with nonstationary latent dynamics, derives an inversion-error propagation bound under explicit assumptions, and builds INCAMA on physics-aware inversion plus a delay-aware Mamba encoder that scores directed graphs via mechanism shifts. Quantitative claims rest on controlled TVB simulations with known ground truth and zero-shot transfer to external HCP motor-task fMRI data, where outputs are checked for anatomical consistency rather than fitted to the target result. No equation or step reduces the reported 2-3x F1 gains or graph recovery to a parameter fit by construction, and any self-citations are not invoked as the sole justification for the uniqueness of the bound or the method. The chain therefore remains self-contained against the stated benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract supplies insufficient technical detail to enumerate free parameters or additional axioms beyond the central modeling assumption.

axioms (1)

domain assumption Recoverable inversion under modality physics together with nonstationary latent dynamics
Explicitly stated as the formal conditional setting required before graph estimation.

pith-pipeline@v0.9.0 · 5485 in / 1170 out tokens · 38847 ms · 2026-05-16T10:07:44.276024+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We formalize a conditional setting - recoverable inversion under modality physics together with nonstationary latent dynamics - and derive an inversion-error propagation bound
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

INCAMA integrates a physics-aware inversion module with a nonstationarity-driven, delay-sensitive causal discovery model based on selective state-space sequences

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages · 2 internal anchors

[1]

Efficiently Modeling Long Sequences with Structured State Spaces

URL https://proceedings.mlr.press/ v235/dao24a.html. Daunizeau, J., David, O., and Stephan, K. E. Dynamic causal modelling: a critical review of the biophysical and statistical foundations.Neuroimage, 58(2):312–322, 2011. Deshpande, G., Sathian, K., and Hu, X. Effect of hemody- namic variability on Granger causality analysis of fMRI data.NeuroImage, 2010....

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2111.00396 2011
[2]

Simplified State Space Layers for Sequence Modeling

doi: 10.48550/arXiv.2208.04933. URL https: //openreview.net/forum?id=Ai8Hw3AXqks. 10 INCAMA: Whole-Brain Causal Connectivity under Indirect Observation Sun, R., Sohrabpour, A., Worrell, G. A., and He, B. Deep neural networks constrained by neural mass models im- prove electrophysiological source imaging of spatiotem- poral brain dynamics.Proceedings of th...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2208.04933 2022
[3]

Both terms on the RHS converge to 0 in probability, hence their sum converges to0 in probability: L(bS, S ⋆) P − − − − → T→∞ 0

Using the same triangle-inequality step as in the proof of Proposition 4.7 and then the Lipschitz property, L(bS, S ⋆) =L h(bz1:T ), S⋆ ≤ L h(z1:T ), S⋆ +L d T (bz,z). Both terms on the RHS converge to 0 in probability, hence their sum converges to0 in probability: L(bS, S ⋆) P − − − − → T→∞ 0. B.5. Stability of top-ksparsification In practice we may form...

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[4]

Forward Model Reconstruction Loss.The predicted ROI LFP bL is reconstructed back to scalp EEG using the leadfield matrixH∈R S×R, and the difference from the actual scalp EEGEis measured: Lforward =∥E−H bL∥1.(18) This loss ensures consistency of predictions through the physical forward model and enables unsupervised learning even when ground-truth supervis...

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[5]

Supervised Loss.When ground-truth ROI LFP Lgt is available, direct comparison with predictions is used for learning: Lgt =∥bL−L gt∥2 2.(19)

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[6]

Adaptive Loss Weights.We apply a curriculum learning strategy that gradually adjusts the weights of loss components during training. For epochewith progressp=e/E max (total epochsE max): •Stability weight:λ stab = 10−3 ×(1 +p) •Structural connectivity weight:λ sc = 0.1×(1 + 0.5p) Early training focuses on reconstruction, while later stages place greater e...

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[7]

Dense Graph Generation.From ROI embeddings E∈R B×R×H , we compute a dense causal graph using pairwise MLP: Gdense = PairwiseMLP(E)∈R B×R×R (24) The dense graph is then passed through a learnable activation function that adapts to dataset statistics: Gscaled = CouplingActivation(Gdense)(25) where CouplingActivation applies dataset-aware scaling to prevent ...

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[8]

The selection mask is constructed as: M(b) ij = ( 1if(i, j)∈TopK(|G (b) scaled|, k) 0otherwise (27) whereTopK(·, k)returns the indices of theklargest entries by absolute value

Top-KSelection.For each sample in the batch, we select the topkstrongest connections globally: k=⌊ρ·R 2⌋(26) whereρ∈[0,1]is the target sparsity ratio (e.g.,ρ= 0.1for 10% connectivity). The selection mask is constructed as: M(b) ij = ( 1if(i, j)∈TopK(|G (b) scaled|, k) 0otherwise (27) whereTopK(·, k)returns the indices of theklargest entries by absolute value

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[9]

Sparse Graph Generation.The final sparse causal graph is obtained by element-wise multiplication: Gsparse =G scaled ⊙M(28) This approach ensures: (i)exact target sparsity ratio ρ is maintained, (ii)gradient flowis preserved through the selected k edges, and (iii)robustnessagainst overfitting to the overwhelming majority of null connections. Dynamic Sparsi...

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[10]

This acts as a robust estimator that prevents overfitting to the overwhelming majority of null connections

Top-K Weighted MAE Loss.To focus learning on the most informative connections, we adopt a weighted MAE loss over the top-kstrongest edges: LMAE = 1 |Ωk| X (i,j)∈Ωk |Aij − bAij|(31) 20 INCAMA: Whole-Brain Causal Connectivity under Indirect Observation where Ωk denotes indices of the top-k largest entries in the ground-truth adjacency matrix. This acts as a...

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[11]

Asymmetry Loss.To preserve directionality ( A→B vs B→A ), we penalize deviations in the asymmetric component: Lasym =∥( bA− bA⊤)−(A ∗ −A ∗⊤)∥1 (32)

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[12]

Scale Loss.To prevent output distribution collapse, we anchor the predicted statistics to target values: Lscale =|µ bA −µ ∗|+|σ bA −σ ∗|(33)

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[13]

We train the entire pipeline end-to-end, allowing the causal objective to guide earlier stages toward representations most suitable for causal discovery

Stability Loss.To ensure dynamical stability (spectral radius<1), we impose a soft constraint via spectral norm: Lstab = max 0,∥bA∥2 −1 2 (34) The hyperparameters λasym, λscale, λstab control the trade-off between predictive accuracy and biological plausibility. We train the entire pipeline end-to-end, allowing the causal objective to guide earlier stages...

work page 2021