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Perturbational Validity for Foundation Models of Brain Dynamics: A Controlled Proof-of-Principle Simulation
José C. Garcí Alanis, Sarah Alizadeh, Marco Rothermel, Bita Shariatpanahi, Mina Kheirkhah, Stefan G. Hofmann, Tim Hahn, Hamidreza Jamalabadi
TL;DR
Observational benchmarks do not establish whether transferred brain models preserve dynamics under active inputs. The paper frames prospective evaluation across forecast, structural, and perturbational-response layers and tests it in a controlled bistable-system simulation. With few-shot calibration, perturbational pretraining improves recovery of controlled dynamics and intervention outcomes over passive pretraining.
Problem
EEG and fMRI foundation-model benchmarks emphasize observational prediction and downstream tasks, leaving open whether limited-adaptation population models preserve controlled dynamics for new individuals.
Source: §1 · pp. 2–3Method
The paper evaluates intervention transfer through forecasts, dynamical structure, and prospective responses to controlled inputs excluded from calibration.
Source: §2.1 · p. 4, §2.4 · p. 8Results
With two to five system-specific drift evaluations, perturbational pretraining improved recovery of controlled fields, landscapes, stochastic responses, and dose-transition relationships over passive pretraining.
Source: §1 · p. 4, §4 · p. 17Takeaways & Limitations
When intervention-relevant parameters vanish under passive conditions, recovering them requires informative perturbations or equivalent prior assumptions.
Source: §4 · p. 21The simulation used a directly observed, stationary one-dimensional bistable system and analytical drift targets, so it did not test recovering dynamics from noisy, discretely sampled measurements.
Source: §4 · p. 20
Abstract
from arXiv · showhide
Foundation models for human brain recordings are usually evaluated by signal reconstruction, future-state prediction, and transfer to downstream tasks. However, these benchmarks do not establish whether a transferred model remains valid when the system is actively perturbed. We define perturbational validity as the preservation, after limited system-specific adaptation, of the conditional distribution of future trajectories given the current state and a controlled input, and we evaluate it at three levels: time-series accuracy, dynamical-structure similarity, and responses to perturbations excluded from calibration. We demonstrate the framework in an oracle-drift simulation of stochastic bistable systems. Two otherwise identical multilayer perceptrons were trained on drift evaluations from passive or input-driven trajectories. Next, for each held-out system the shared weights were frozen and only a three-dimensional embedding was adapted, with a correctly specified cubic model fitted from scratch as comparator. With two to five system-specific evaluations, perturbational pretraining yielded lower errors in recovering controlled flow, landscape geometry, finite-run occupancy, response distributions, and dose-transition curves. The advantage was reproduced across five independent runs, persisted under full-network adaptation of the passive model, and was attributable to input excitation rather than transition-state coverage: excitation alone lowered controlled-flow error 1.94-fold relative to coverage alone, in five of five runs. The cubic model became competitive as calibration grew, showing that the benefit is specific to few-shot transfer. This controlled demonstration does not test recovery of dynamics from noisy or partially observed brain recordings. It shows why passive prediction should be complemented by prospective evaluation under controlled inputs.
1 From observation to intervention
Observational and downstream-task benchmarks do not establish whether adapted brain models preserve dynamics under controlled inputs. This section motivates prospective perturbation testing and introduces a three-level evaluation framework, demonstrated in a bistable-system simulation.
1 From observation to intervention
- EEG and fMRI foundation-model evaluations emphasize reconstruction, forecasting, and downstream tasks, leaving untested whether adapted population models preserve dynamics under controlled inputs.The unresolved question concerns models adapted to new individuals with limited data.Source: §1 · pp. 2–3
- When the passive condition sets u(t) = 0, input-gain parameters are absent, so systems with identical passive trajectories can imply different intervention responses.Recovering input-response relationships requires sufficiently informative inputs.Source: §1 · p. 3
- Perturbational validity means preserving the conditional distribution of future trajectories given current state and controlled input after limited adaptation.It is tested prospectively with inputs excluded from participant-specific calibration, without implying complete biological identification.Source: §1 · p. 3
- The framework evaluates time-series accuracy, dynamical structure, and perturbational responses, including dose-response relationships under inputs excluded from calibration.No single level or finite metric set establishes equivalence across every state and input.Source: §1 · pp. 3–4
- With two to five system-specific drift evaluations, perturbational pretraining improved recovery of controlled fields, landscapes, stochastic responses, and dose-transition relationships over passive pretraining.The from-scratch cubic model became competitive as calibration increased, so the benefit was specific to few-shot transfer.Source: §1 · p. 4
- The study introduces an evaluation framework, not a new architecture, and tests transfer using oracle-drift training across 60 systems with frozen shared weights and embedding-only adaptation on held-out systems.Observationally pretrained EEG and fMRI models illustrate transfer across participants and downstream tasks, but those evaluations do not test controlled-input validity.Source: §1 · pp. 2, 4
2 A perturbational framework for transfer
The framework treats intervention-oriented transfer as preserving controlled future-trajectory distributions after limited participant adaptation, a property passive data may not identify. It assesses that property through trajectory, dynamical-structure, and held-out-perturbation evidence.
2.1 Problem statement
- With u ≡ 0, passive likelihood contains no information about input-dependent parameters, so systems differing only in input gain can share passive trajectories.Perturbational population data expose input effects and rarely visited states, supporting more efficient transfer when participant-specific calibration is limited.Source: §2.1 · p. 6
2.2 Controlled latent dynamics
- The population model is a stochastic controlled system, and this study adapts only a low-dimensional participant representation while shared parameters remain frozen.The simulation directly observes state and fixes the known diffusion, isolating transfer of controlled drift from latent-state and diffusion recovery.Source: §2.2 · pp. 6–7
2.3 Energy-landscape perspective
- For gradient systems, the effective energy separates the unforced landscape from input coupling, so inputs can deform barriers that passive trajectories leave underdetermined.A unique scalar potential need not exist for higher-dimensional or non-gradient systems; perturbational validity itself is defined on the controlled transition law.Source: §2.3 · pp. 7–8
2.4 Evaluation criteria
- Evaluation uses complementary trajectory, dynamical-structure, and held-out-perturbation layers; drift rollout has an irreducible process-noise floor.The three layers assess forecast state evolution, recovery of the controlled law and path-generating geometry, and prospective intervention outcomes.Source: §2.4 · p. 8
3 Proof-of-principle simulation
This proof-of-principle simulation compares passive- and perturbation-pretrained models on stochastic bistable systems using limited oracle-drift calibration in held-out systems. It evaluates transfer through controlled dynamics, landscapes, occupancy, and intervention responses.
3.1 Generative system and model classes
- The study simulated one-dimensional stochastic bistable systems with participant-varying well shape, asymmetry, and input gain.Every sampled system retained two wells separated by a barrier.Source: §3.1 · pp. 8, 10
- Training and calibration used analytical drift targets, making this an oracle-drift demonstration rather than a test of recovery from noisy state increments.The primary pulse was excluded from participant-specific calibration but remained within the perturbational-pretraining input range.Source: §3.1 · pp. 10–11
- Same-architecture MLPs learned analytical drift from passive or driven trajectories; held-out adaptation froze shared weights and fit a three-dimensional embedding against a correctly specified cubic baseline.The embedding dimension matched the number of participant-varying drift parameters, but its coordinates were not constrained to recover them one-to-one.Source: §3.1 · pp. 10–11
3.2 Coverage and excitation
- Input excitation alone lowered controlled-flow RMSE from 3.12 ± 1.22 to 1.61 ± 0.09 at two evaluations and was lower in five of five runs.Perturbational trajectories also sampled transition-region states; excitation alone improved input-dependent criteria more than transition-state coverage alone.Source: §3.2 · pp. 12–13
3.3 Mechanistic validation in a held-out system
- For the excluded pulse, perturbational pretraining reproduced transition timing but underestimated response spread; passive responses were slower and its dose curve was overly gradual below threshold.The correctly specified scratch model was competitive on the dose-transition relationship with 20 oracle drift evaluations.Source: §3.3 · pp. 14–15, Figure 3 · p. 16
- Perturbational pretraining recovered input-dependent vector-field displacement and the unforced minima and barrier, unlike passive pretraining; the scratch model also recovered the landscape.The comparison used a pulse amplitude excluded from participant-specific calibration.Source: §3.3 · pp. 13–14, Figure 3 · p. 16
3.4 Few-shot transfer across complementary criteria
- Across five runs the few-shot advantage recurred; full-network adaptation of the passive model did not remove the gap, and an out-of-range pulse supported only local extrapolation.The amplitude-3.00 pulse was just outside population-pretraining support.Source: §3.4 · p. 17
- Perturbational pretraining improved controlled flow, landscape, occupancy, response distributions, and dose-transition relations chiefly at two to five evaluations; the scratch model became competitive as calibration increased.The advantage was not a superior asymptotic optimum.Source: §3.4 · pp. 15, 17
4 Discussion
In the oracle-drift simulation, perturbational pretraining improved few-shot recovery of controlled dynamics and intervention outcomes, while its advantage diminished as calibration increased. The discussion argues for prospective, multi-layer evaluation under held-out inputs, while emphasizing that the simulation does not estimate benefits in neural or clinical data.
4 Discussion
- With two evaluations, input excitation alone reduced controlled-flow RMSE from 3.12 ± 1.22 for transition-state coverage alone to 1.61 ± 0.09, a 1.94-fold reduction across five runs.The lower error occurred in all five runs; combining excitation with driven-state coverage gave the lowest error on all six metrics at every calibration size.Source: §4 · p. 17
- With two to five participant-specific evaluations, perturbational pretraining outperformed passive pretraining across controlled-flow, landscape, response-distribution, and dose-transition recovery; the from-scratch model became competitive with more calibration.The comparison spans the six validation criteria in Fig. 4, and the few-shot advantage was reproduced across five runs and persisted after full passive-network fine-tuning.Source: §4 · p. 17, Figure 4 · p. 18
- Because input-coupling parameters disappear when u = 0, passive data cannot identify them without informative input variation or additional assumptions.Resting functional-connectivity measures may constrain relative response magnitude across regions, but do not identify an individual's input coupling.Source: §4 · pp. 18–19
- Intervention-relevant validation should assess time-series accuracy, controlled dynamical structure, and responses to held-out inputs, rather than rely on one forecast or endpoint.In the simulation, a passive model could predict a binary transition correctly despite errors in its controlled field, response timescale, and dose-transition curve; passive-rollout RMSE also contains process noise.Source: §4 · p. 19
- The proposal complements observational foundation-model benchmarks and does not claim that neural models have never predicted perturbation responses.Its proposed transfer target is preservation of the controlled law, evaluated at trajectory, structural, and perturbational levels.Source: §4 · p. 19
- Controllability estimates motivate individualized control models but do not replace prospective validation because they depend on assumed dynamics, connectivity representation, and control objective.The corresponding empirical test is prediction of an individual's response to an input excluded from calibration.Source: §4 · p. 20
- Prospective benchmarks should adapt a population model with limited participant data, then test perturbation types, amplitudes, timings, spatial patterns, or initial states excluded from calibration.The discussion also proposes testing outside population-pretraining support and reporting calibrated predictive uncertainty.Source: §4 · p. 20
- The one-dimensional stationary bistable oracle-drift simulation does not test drift recovery from noisy, partially observed recordings or estimate benefits expected in neuroimaging or clinical data.The out-of-support test used only one nearby amplitude, and the from-scratch comparator was correctly specified for the generating cubic family.Source: §4 · p. 20
5 Conclusion
The conclusion defines perturbational validity as preserving controlled dynamics after adaptation and evaluates it across trajectory, structural, and perturbational-response criteria. A controlled bistable-system simulation supports few-shot transfer with perturbational pretraining and motivates prospective tests on perturbations withheld from participant-specific calibration.
5 Conclusion
- Perturbational validity requires preserving controlled dynamics that determine how inputs alter future trajectories, assessed through time-series accuracy, dynamical-structure similarity, and perturbational-response similarity.The conclusion frames observational accuracy as necessary but insufficient for experimental or clinical intervention.Source: §5 · p. 21
- In the controlled bistable-system simulation, perturbational pretraining enabled few-shot recovery of controlled dynamics and intervention outcomes across repeated runs, full passive fine-tuning, matched ablations, and a local input-extrapolation check.The passage reports the advantage within this proof-of-principle setting.Source: §5 · p. 21
- Models intended for experiment design, stimulation, or treatment selection should be tested prospectively on perturbations withheld from participant-specific calibration.This benchmark proposal follows from the conclusion's distinction between observational accuracy and preserving controlled dynamics.Source: §5 · p. 21
6 Statements and Declarations
The authors report the study's funding sources and state that funders had no role in the research or publication process.
6 Statements and Declarations
- The study received support from DFG grants, a University Hospital of Gießen and Marburg grant, and ERA-NET NEURON JTC 2024; funders had no role in study design, analysis, interpretation, or submission.The passage also states that funders had no role in data generation or manuscript preparation.Source: §6.1 · p. 21
6.2 Competing interests
The declarations report no relevant competing interests and state that the study used synthetic data without human or animal participants.
6.2 Competing interests
- The authors declare no competing interests relevant to the article.Source: §6.2 · p. 21
6.3 Ethics approval
- The study used synthetic simulation data and involved no human participants or animals.Source: §6.3 · p. 21
6.6 Data availability
The data are synthetic and deterministically regenerated from reported seeds; simulation and analysis code is publicly available.
6.6 Data availability
- All analysed data are synthetic and deterministically regenerated from the reported random seeds.Source: §6.6 · p. 22
6.7 Materials and code availability
- The simulation, analysis, and figure-generation code is publicly available, and no other materials were used.Source: §6.7 · p. 22
6.8 Author contributions
The listed contributors span conceptualisation, methodology, validation, analysis, and manuscript preparation.
6.8 Author contributions
- HJ, JCGA, and SA led conceptualisation, methodology, and validation; formal analysis was by HJ and JCGA.Source: §6.8 · p. 22
- HJ, JCGA, and SA drafted the manuscript, while JCGA, SA, MR, BS, MK, SGH, TH, and HJ reviewed and edited it.Source: §6.8 · p. 22
6.9 Use of AI-assisted tools
Coding tools assisted development and validation of the Python simulation implementation and proofreading of the final manuscript.
6.9 Use of AI-assisted tools
- Claude Code and OpenAI Codex helped draft parts of the Python simulation and validation tests and proofread the final manuscript; JCGA and HJ reviewed, executed, and verified all code.Source: §6.9 · p. 22
Supplementary Material
Supplementary checks separate input excitation from state coverage, test robustness and local extrapolation, and document when landscape diagnostics fail.
Supplementary Methods and Robustness Checks
- The evaluations used analytical drift, shared Gaussian innovations for stochastic metrics, and five independent runs averaging results across 20 held-out systems.Fig. S1 panels cover controlled-flow RMSE, response-distribution divergence at amplitudes 2.25 and 3.00, and out-of-support transition-probability error; error bars show standard deviations across run-level means.Source: Supplementary Methods and Robustness… · p. 26, Figure S1 · p. 28
- Full-network adaptation improved the passive model but did not eliminate the few-shot gap, consistent with sparse calibration only partly repairing its unexcited input pathway.Source: Supplementary Methods and Robustness… · p. 26
- Matched ablations isolate state coverage from input excitation: coverage used driven states with unforced targets, while excitation used passive states paired with varied inputs and controlled drift.Source: Supplementary Methods and Robustness… · p. 26, Table S3 · p. 31
- Input excitation alone lowered controlled-flow RMSE 1.94 to 1.99-fold relative to transition-state coverage alone across calibration sizes, with excitation lower in 5 of 5 runs.Source: Supplementary Methods and Robustness… · p. 26, Table S3 · p. 31
- Combining excitation with driven-state coverage gave the lowest error on every metric at every calibration size in 5 of 5 runs; the from-scratch cubic model became competitive as calibration grew.Source: Supplementary Methods and Robustness… · p. 27, Table S3 · p. 31
- With two or three evaluations, the from-scratch cubic model collapsed to one well in every held-out system; perturbational pretraining recovered double wells in 18 of 20 systems.The cubic model's form was correct, but that budget did not determine its five coefficients; perturbational pretraining recovered double wells in all 20 systems from twelve evaluations onward.Source: Supplementary Methods and Robustness… · p. 27, Table S4 · p. 32
- At amplitude 3.00, just beyond population-pretraining support, the perturbational model retained lower response-distribution and transition-probability errors; this supports only local extrapolation.Stronger positive pulses rapidly drove the clipped bistable system toward its state boundary, making them less informative as a graded stress test.Source: Supplementary Methods and Robustness… · p. 27, Figure S1 · p. 28