MnemoDyn: Learning Resting State Dynamics from  $40$K FMRI sequences
Authors: Sourav Pal
Viet Luong
Hoseok Lee
Tingting Dan
Guorong Wu
Richard Davidson
Won Hwa Kim
Vikas Singh
Venue: ICLR 2026 Poster (2026)
Keywords: Dynamical system
Brain Imaging
Primary area: applications to neuroscience & cognitive science

Abstract: We present a dynamical-systems based model for resting-state functional magnetic resonance imaging (rs-fMRI), trained on a dataset of roughly $40$K rs-fMRI sequences covering a wide variety of public and  available-by-permission datasets. While most existing proposals use transformer backbones, we utilize multi-resolution temporal modeling of the dynamics across parcellated brain regions. We show that MnemoDyn is compute efficient and generalizes very well across diverse populations and scanning protocols. When benchmarked against current state-of-the-art transformer-based approaches, MnemoDyn consistently delivers superior reconstruction quality.
Overall, we find that with such large-scale pre-training on (non-proprietary) rs-fMRI datasets, we get a highly performant model for various downstream tasks. Our results also provide evidence of the efficacy of the model on small sample size studies which has implications for neuroimaging studies at large where resting state fMRI is a commonly acquired imaging modality.

Published as a conference paper at ICLR 2026
MNEMODYN: LEARNING RESTING STATE DYNAMICS FROM 40K FMRI SEQUENCES
Sourav Pal
Viet Luong
Hoseok Lee" Tingting Dan
Guorong Wu
Richard Davidson*
Won Hwa Kim²
Vikas Singh
University of Wisconsin-Madison, Madison, United States
2Pohang University of Science and Technology (POSTECH), Pohang, South Korea Univeessity of North Carolina at Chapel Hill, Chapel Hill, United States
(spa19, vhluong, rjdavids (esssiddsexisc.eee... (hs1==0608, wonhwa @postech. ac kr vsingh@biostar www.iiittttttttttts..too..e.eett wisc. edu (Tingting.Dan, guorong wu wangg..w@@mede @med. unc unc.edu edu
ABSTRACT
We present dynamical-systems based model for resting-state functional magnetic resonance imaging (rs-fMRI), trained on a dataset of roughly 40K rs-fMRI sequences covering a wide variety of public and wwailable-y--permisse datasets. While most existing proposals use transformer backbones, we utilize multi-resolution temporal modeling of the dynamics across parcellated brain regions. We show that MnemoDyn is compute efficient and generalizes very well across diverse populations and scamning protocols. When benchmarked against current state-of-the-a
corsfoommmrbbsee approaches, MnemoDyn consistently delivers superior reconstruction quality. Overall, we find that with such large-scale vre-training on (non-prop proprietary) rs-fMRI datasets, we a highly performant model for various downstream tasks. Ourresults also provide evidence of the efficacy of the model on small sample size studies which has implications for neuroimaging studies at large where resting state fMRI a commonly acquired imaging modality.
INTRODUCTION
Understanding the latent dynamics underlying pesting-state hemodynamic signals is central to appli- cations such as surgery planning and epilepsy seizure localization, as well as advancing neuroscience more broadly (Deco et al. [201T Friston 2011). Modalities such as resting-state functional Magnetic resonance imaging (R-I provide temporal signals that encode rich neural processes (Smith et al. 2013). One important goal is to model these dynamics in manner that captures the spatial and temporal structures of these signals (Breakspear 22004). and permits statistical group testing and predictions across subjects, institutions/sites, and protocols Yamashita et al. 2019). Achieving this goal requires producible models capable of learning representations from large-scale neuroimaging data. To this end, recent developments surrounding Foundation models (Bommasani al. 2021) are particularly relevant.
For example, while such models were originally developed for natural language processing, they have been adapted vision (Dosovitskiy et al. 2020), robotics (Brohan et al.
2022) and beyond (Radoval et al. 2025 Wang et al. 2025). Common to most foundation models are attention- based architectures most promieetlly. the Transformer module- which allows flexible context modeling via self-attention Language models (Brown et al. 2020 Chowdhery et al. 2023) achieve strong performance across most natural language tasks and so, Transformer-basee architectures have also been extended sequence
modeling problems, including time series data (Zhou al. 2021 Liu et al. 2023 Chen et al. (025).
Rationale for alternatives. Transformer models serve as good starting point for building foundation models for fMRI. Recent work (Caro et al.) Dong et al. (2044) has shown that attention-basel models can capture temporal dependencies in rs- fs-fMRI sequences (Kim et al. 2023) and model long-range dependencies well. These approaches work well when sufficient computing resources and data available, particularly for standard acquisition protocols that typically collect minutes of resting-
state data (Birn et al. 2013). But there are reasons explore alternatives. First, emerging

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date) dt
f(((()
FMRI Brain Activity Recording
Fine- Tunn-T with Adapter Layers
MyemoDyn
Diverse Sample
Sputtal
Burface
Age
Tomporel
Sxhaciion
Latent Dynamical System
Predicting Clinical Variables
Clinical Variable
rs-fMRI Pre-processing
Data Collection & Pre-processing
Pre-Training Fine- Tuning
Figure 1: Overview of the MyemoDyn framework. Our foundation model for rs-frrs treats temporal signals trajectories in latent dynamical system, parameterized by learnable operators. The pipeline begins with data curation and pre- pee-pooesssing of large-scale rs-fMRI cohorts into standardized ordynnae representations.
The pre-training stage learns multi-resolution non-linear dynamical operator via da(t) fo((=(()). enabling the model to capture cross-scale temporal dependencies while preserving local dynamics. During fine- ine-tuning. lightweight adapter layers adapt pretrained model diverse downstream cohorts. The resulting representations support prediction of clinical variables across heterogeneous populations (age, sex, cognitive traits, neurodegen- eration markers, etc.), highlighting MnemoDyn's 's ability to generalize from large-scale dynamical modeling to scientifically meaningful tasks.
dt
use cases in sleep research and clinical neuroscience (Yang et al. 2024 are increasingly utilizing longer acquisitions (e.g.. up to 8 hours of continuous rs- f-- data). Characterizing rs- rs-fMRI dynamics from whole-nigh night fMRI means being able to process much longer sequences without increasing the computation dramatically. Second, the data requirements for fine-tuning foundation models on smaller datasets, common scenario in practice, will be simpler via a more compute/paramett efficient architecture will be easier to deploy in the clinic.
sample-efficient architectures. Third,
Learning dynamics with operators. In contrast data from neuroimaging can benefit from approaches that seeks to model the underlying dynamical structure of brain activity. Instead of learning autoregressive mappings in the raw signal space latent space, we can attempt to learn the underlying operator governing the observed temporal dynamics. This casting treats the brain as if it generating trajectories in -igg--imensional latent space governed by an unknown but learnable dynamical system. This aligns, at least, partially, with neuroscientific understanding of brain activity as arising from complex dynamical processes (Deco et al. 2011 Breakspear] 2004) (Sazz-Leon et al.) (015). Recent work in state space models (Gu et al.) and liquid- FM (Hasani et al.) has also highlighted the value using dynamical system rsstemiinppire strategies for sequence modeling, Our architecture, MnemoDyn, learns evolution operator rather than relying on autoregressive sequence modeling and implicitly modeling hidden state recurrence. Specifically, the solution (operator) maps initial conditions and inputs to full latent trajectories and we parameterize the evolution kernel using multi-resolution wavelet bases partly inspired by studies in neuroscience (D' Angelo & Jirsal 2022 Basar al.) 1999). This way, the operator can process features across multiple temporal scales while maintaining temporal locality. The interaction between wavelets and pseudo-differential operators yields highly sparse representations (bey 1991), leading computational efficiency. The key contributions are:
inventioo-bbsed sequence modeling, time series
We describe saweelt-paramettriiee evolution operator that captures multiscale temporal dependencies without attention mechanisms, and it scales efficiently to long sequences. This design eliminates the need for positional embeddings tokenization schemes, which are often finicky, domain dependent, and sensitive to hyperparameter tuning.
(ii) We obtain consistent improvements over state of the art transformer-baset baselines across multiple rM-I datasets for reconstruction, classification, and regression tasks. MnemoDyn trained on 40K rs-MMRI sequences will smaller datasets.
(iii) Open-source rs-fMRI foundation model: founddda
be publicly released for use and fine-tuning
Our findings suggest that operator- baased models grounded in multi-ressoltion analysis offer a powerful alternative to attention-heae They open new avenues for data-driven discovery brain dynamics that are principled and practically deployable in resource constrained settings.
architectures for modeling the dynamics associated with rs-fMRI data.
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2 MODELING BRAIN DYNAMICS
We now set up our formulation for modeling the latent dynamics of the rs-IMRI signal. We consider the temporal hemodynamic measurements it is generated by latent dynamical system defined on a cowddimensional multiscale representation of the observed neural signals. We model the evolution using a latent dynamical system (John al. (002)) framework, i.e., decomposing the observed signal into a hidden neural process (McCormick et al. (022) and measurement process.
Let (t)) :t R2 denote the observed time series data (e.g., rs-fMRI) which is high-dimensional. We use 22 E I= to denote the observed signal at the discrete time step t, where n is the number of brain regions (e.g. parcels, voxels, or channels in case EEG). Let 2, E E represent the latent neural state, which is assumed to evolve according to some (potentially nonlinear) dynamics. The general form of the state space model (Gu et al.) Gu & Dao) is given by:
2++1 = f (2,, I2 ====)==;))+++++ +o,,
(latent state transition)
(observation model)
(2)
where ur 1 is an optional exogenous input (e.g., stimulus or task), which may optionally be zero.
Here, f :R x 1 + R defines the transition dynamics with parameters 0 and h: R - R" is function that maps the latent space the observations with parameters d; wa (O,,Q), Vt ~ (t) are
potential process and observation noise, respectively.
Remark 2.1. A growing body of work shows how to extend such state-space models to large-scale sequence modeling (Gu et al., 2020 Gu et al.)). Also related are results describing liquid foundation models (Hasani al.) showing excellent results via input dependent adaptivity. While these approaches also learn state evolution functions, our approach is complementary in that we utilize a special multi-resolution decomposition, which is compute-efficienn and also inspired by empirical studies in neuroscience.
Benefits of continuous time formulation: While the state-space formulation in discrete time is widely used, modeling neural dynamics in continuous time offers some advantages (Billings et al. 2017). Brain signals are inherently continuous, even though the measurements (such as fMRI) are obtained discrete time points. By using a differential equation-based formulation, we seek to better model the temporal evolution of neural states in continuous form. We know that ordinary differential equations (ODEs) (Hartman 2002) provide a principled way to encode smoothness, locality in time, and known structural constraints such as linear relaxation, oscillatory components, or conservation laws that reflect biophysical priors. This continuous- time perspective opens the door tools from control theory and operator learning for analyzing the evolution of latent neural processes (Lee et al.) [022] Cai et al.) 2021). This strategy also allows us to circumvent tokenization and patching strategies required for attention based models.
Parameterized ODEs as Continuous Time Models: We consider the latent state z(t) ERR as evolving according to an ordinary differential equation (ODE) driven by vector field F F:R x Rm + Rd.
dz((t) F' (z(tt)
z z(0) =20-
where u(t) E R. denotes an optional external control or input signal, and @ are parameters governing the dynamics (Chen et al., 2018 Finlay et al. 2020). Starting from state space naturally led us the ODE formulation. This may seem restrictive, but we will soon see the more general form that will nicely deal with mon-Markovian dynamics through an integral operator. We note that while f and F are distinct mathematical objects: one discrete map and the other a differential operator, they are tightly connected. approximates the time-A A/ flow of the ODE defined by F. Note that f can often be derived from F by applying numerical integration scheme. As an example, the Euler method would yield the update:
Ze+1 2 + Al. u:), s.t. f(,, = 2, + At. F(z,
well- that the tiscrete-time dynamies f can be viewed (in this case) as an Fuler step approximation of the continuous flow generated by F.
Remark 2.2. More sophisticated numerical integrators (Dahlquist & Björck 2012) (such as Runge-Kun Kutta methods) yield more accurate discrete update functions f by evaluating F at multiple intermediate points. The continuous-ting time function F defines a vector field that characterizes the instantaneous rate of change of the latent state z(t). In contrast, the discrete-time update function f governs how the latent state evolves from one time step the next.
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ODEs to Operator Learning: The continuous time formulation treats z(-) as function in a suitable function space (e.g., C* :()) and models the evolution as a map from functions to functions. Specifically, the solution z(t) of the ODE (3) can be viewed as the output of parameterized nonlinear operator To acting on function space (Boullé & Townsend 2024 Subedi & Tewari 2025):
To: ())
which maps initial state and control function the full latent trajectory. To denotes the flow operator induced by the vector field F under the initial condition z()) = Zo and denotes the parameters. The observation model in continuous time is typically given by
x x(t) = H(z(t):)))+v
(6)
where H Rd I is the observation function with parameters é. and v(t) (O, continuous-time observation noise (often modeled as white noise or band-limited noise in practice), The foregoing perspective aligns naturally with the framework operator learning (Kovachki et al.) 2023 2024), where the goal is to learn mappings between infinite-din siteite-dmmnssinnll objects such as functions distributions rather than pointwise predictors. We will now describe our choice of the operator and check the potential benefits.
R) denotes
Operators for representing rs-fMRI dynamics: We note that (3) can be expressed in integral form by integrating the vector field F over time. Assuming sufficient regularity of F, the latent trajectory satisfies the Volterra-type integral equation (Brunner 2017):
=(t)=Zo - 1. F()()).u()):0)d
which defines non-linear integral transform governed by F. We emphasize the integral from 0 through t is important: at each time point, the operator Ke has access to the entire history of the input trajectory u(.) from the initial time to the current time. To make the operator structure more explicit, we observe that the integral in 7 can be expressed as a kernel integral operator acting on the control function u(.). Suppose that the vector field F admits the decomposition
((z(t), ([
8
where P Rd Rdd represents an autonomous drift term, and K Rd Rdxm defines
control-dependent (Kidger et 2020) modulation of the dynamics. Substituting into 77) we obtain
z(t) zo /
P(z(T):0)dr+ J.
K ((z(():))u(rddr
(9)
The final term defines non-linear integral operator acting u(-), with the kernel (<<(T):)):
(KGu))t):= = [ K (((()):))u(7ddr
(10)
which allows the latent trajectory to be compactly represented as
z(t) = z / ((a(t))))dd++(Kaa))))
(11)
The above formulation emphasizes the operator- theoretic nature of the system: the trajectory ztt) results from the action of parameterized nonlinear integral operator on the control input u u(-). combined with an autonomous term driven by P.
We can re-trite II as:
(1)=z0+ =0 [ P(=(T)) ((((()))) ( (7),
(12)
where W (((T is the sulti-scale control path associated with the corresponding Controlled Differential Equation (CDE) (Kidger al. 2020). In CDE terminology, the wavelet-trann transfomedd path serves as the "rough path" (Momil et al. 2021) that encodes history beyond point-wiss wise evaluation. MnemoDyn implements CDEs which are generalization of ODE, and can capture mon-Markovian dependencies.
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Remark2.3. MnemoDyn's formulation is an integral equation with learned kernel K. The main design choice is parameterization of the integral kernel which avoids the use numerical solvers otherwise prominent Integral Equation (IE) based formulations like (Zappala et al. 2024). MnemoDyn is contextualized within the broader operator learning literature in Appendix A.5
Multi- RentiiRReol Kernel Parameterization: We focus our attention on parameterizing the kernel (zz (Tz((T):8 r): in a manner that captures the multi-scale structure of neural signals discussed empirical
studies in neuroscience (Friston 2008 Hilgetag & Goulas 2020: Vidaurre et al. 2017 Kiebel et al. analysis (MRA) framework based wavelet bases, enabling the kernel to decompose and act on the input across multiple temporal resolutions. Formally, we represent the kernel as linear combination of separable wavelet bases:
2008). To reflect this hierarchical organization, we adopt a muuli-rrsolutie
k(z(T):0)
ΣΣ (11((T)44)((((7:))) 1=0
(13)
where (T) denotes the wavelet basis function (Malltt 1999) at scale j and translation k. and Ay.: matrix-vvluuee functions parameterized by 8, modulated by the current state z(T). This decomposition provides the kernel with both temporal locality and scale adaptivity, allowing the system selectively attend to features of un-) different temporal resolutions. Substituting this into the operator (10), we obtain:
(Kou) -DEEEE// (1
(14)
The functional role of wavelet basis is better appreciated when we rewrite the operator by regrouping terms so that the wavelets act directly the input signal. We can interpret Φj.k . as localized filters applied to the control signal u(T) at multiple scales and temporal positions. Specifically, we define the modulated input:
u
(15)
and express the integral operator from 14) as:
(KCu)
(16)
j=0
This makes explicit the two-stage nature of the operator: the input signal is first filtered by wavelet functions Φj isolating localized fea- tures different temporal resolutions Chen et al. (2025), and then transformed by matrix-valus operators A conditioned on the latent state 2(r). This decomposition allows the system to learn dynamic responses that are hoth temporally localized and state-dependent. MnemoDyn evaluates the operator on wavelet-integrated summaries of the entire past trajectory, giving non-Markovian property. Finally, these nonlocal integrals are coupled across space (different ROIs) and time together to modulate the latent dynamics of rs-fMRI.
Multi Resolution Decomposition
CP Tensor Decomposition
Signal + Operator
X
Effcient Computation
Figure 2: Wavelet-based multi- celliiiresolution decom- position rs-fMRI signals and operator along with CP tensor factorization of model parameters enable efficient computation in MnemoDyn.
Compute challenge: While the above formulation is grounded in known priors for brain signal modeling, there are few caveats. First, with the parameterization introduced in (16), we notice that needs huge matrices (with increasing sequence length) and a large number of them to cover different scales and locations. Second, rs- rs-fMRI data is inherently high dimensional, and hence we need very large latent dimension to evolve the dynamics. These two issues would render the formulation not very useful, especially if we are targeting compute efficiency. Next, we will discuss how we circumvent these issues in practice Fig.
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My M
Figure 3: Reconstruction of rs-fMRI for UK- -K-BBibaank. Three parcels of unseen data are shown. We show the output of vanilla auto-encoding the left and masked anto-en on the right.
Pseudo-differential operator: Given the inherently non-local and multiscale structure of neural signals, we note that pseudo-differentia operators (Hörmander) 2007) are a potential choice for parameterization of the kernel. Interestingly, wavelets interact in very fascinating way with pseudo differential operators leading to sparse representation (bey] 1991). I). In fact, our choice of representing operators especially attractive choice: (a) the interaction between the model parameters and latent dynamics is now fully expressed in the wavelet domain, and (b) the operator admits a highly compact, block diagonal representation in this
the signal in wavelet space in (1)) and (16), makes pseudo-differentee
basis leading to both expressive and computationally efficient modeling, as shown in (bey) 1991 Pal
al. 2023).
Low-Rank parameter decomposition: Due to the large number of spatial locations (voxels, sensors) dynamics of rs-fMRI, need high-dimensional latent space. This dimensionality poses challenges for learning and generalization, especially when the sample size is limited. To address this, we adopt structured low-rank (Kishore Kumar& Schneider 2017) representation of the model parameters using tensor decompositions, which provide principled way to reduce the number of free parameters while preserving expressivity. Specifically, we employ the Canonical Polyadic (CP) to parameterize the collection of operators parameter matrices in model. The CP decomposition represents tensor E R XlaX""XIN as a sum of rank-one outer products:
R (1) a
Xx
Σ
0a 80 (N)
(17)
where 7, E and (n) ER are mode-n factor vectors. Each term captures a separable interaction across modes. This structure is particularly well-suited for representing the parameter tensors associated with our pssudo-differente of complex latent dynamics associated with brain signals.
operators in the wavelet space, enabling scalable and structured modeling
Remark 2.4. We use the standard latent-space synamical-systems framing for the problem, where BOLD activity is modeled through evolution in a lower- dimensional latent space rather than through explicit neurophysiology. MnemoDyn parameterizes via a muuti-resolution pseudo -efue-difffrential op- erator, which decomposes temporal interactions across scales and offers interpretability in terms of operator spectrum and seale-specific influence. This structure, however, should not be regarded as physiological validation, a limitation shared with existing data-driven baseline rs-fMRI models such as Brain-JEPA (Dong et al. 2024) and BrainLM (Caro et al.).
Implementation details: While the formulation above describes modeling the dynamics via a single latent space, observe that stacking multiple such blocks, with varying latent dimensions, helps improve the representation of the model. Furthermore, adding residual connections akin to the design choice in transformer blocks further enhances performance. The block diagonal parameterization aris- ing from the design choice of applying wavelet transforms on pseudo-differeme above) is implemented using multiple convolution filters and computation parallelized for efficiency. We observe very minor variations when checking the impact of different wavelet families. We use db2 for all experimental results presented in the paper.
operators (mentioned
Remark 2.5. MnemoDyn is positioned as a foundation model within rs-fMRI as it exhibits clear scaling trends with model depth and pre-trat pre-training data, and transfers robustly across heterogeneous datasets and downstream tasks. These are elaborated in Section 3 and in Appendix A.4 A.4
3 EXPERIMENTS
Here, we describe the end to end pipeline for MnemoDyn. We first list the datasets used both in the pre-training and finetuning phases. Then, describe the training procedure for both stages. Finally, we present empirical evidence showing the efficacy of MnemoDyn. variety of additional details are included in the Appendix. Our code and pre-tr model will be publicly available.

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3.1 DATASETS
We performed large-scale self-supervised pretraining using two different datasets. The first is UK Biobank (Miller et al. (0T66), a public resource that provides the largest publicly available resting-state fMRI data for 65k samples. We consider subjects in the age range 44 to 69. The data were collected across multiple sites with a temporal resolution of 0.735s. We trained a separate model utilizing rs-MMRI data from the Human Connectome Project (HCP) (Human Connectome Project (017)) with temporal resolution of 0. 0.7.s. This is a medium size dataset but has much larger sequence lengths, 1200 compared to about 500 in UK Biobank. The sample size is ~ 1000. As we will discuss later, both these models are comparable in terms of representation capability and improved performance when fine-tuned for predictive tasks. In each case, we used 80% of this dataset for pretraining (including computation of normalization statistics) while the remaining 20% was held out for validation purposes and internal downstream evaluations on age and sex prediction.
Remark 3.1. 1. Pre-training MnemoDyn (with 92M parameters) can be performed on a single A100 40 GB GPU in ~ 3 hours with maximum memory usage. This is much cheaper compared to the configuration of 4 GPUs in other baselines (Dong et al.) 2024). We attribute this the efficient design choice of operators in MnemoDyn implemented using convolution kernels. Further, this also enables training a sample efficient foundation model utilizing data from HCP alone which would otherwise be insufficient for attention-based models (Caro et al.) Dong et al. 2024).
In order to demonstrate the effective representation power of MnemoDyn, we use six additional rs-MMRI datasets. The choice of these datasets is based on the two important baseline models we compare with, namely Brain-LM (Caro et al.) and Brain-JEPA (Dong et al. (024). These datasets are as follows: (a) HCP-Aging (Elam et al. (202I). containing rs-iMRI from 656 elderly participants, used for trait (Neuroticism and Flanker score) and demographic (age and sex) prediction. (b) ADNI (Jack Jr et al. 2008), which includes rs-I scans for studies of Alzheimer's 's disease. Following (Dong al. 2024) used 189 participants for normal control (NC) vs. mild cognitive impairment (MCI) classification, and 100 cognitively normal participants for amyloid positive vs. negative (c) Healthy Brain Network (Alexander et al. (017)) which is large-scale pediatric classification. neuroimaging initiative, was used for the classifica- tion of age and sex. (d) ADHD-200 (Bellec et al.) 2016), consisting of rs- fMRI from children and ado- lescents, used for sex classification and attention deficit/hyperacciiity disorder vs. typically devel- oping control classification. (c) ABIDE (Autism Brain Imaging Data Exchange) (Di Martino et al.] 2014), which aggregates data across multiple sites, used for autism spectrum disorder (ASD) versus control classification. (f) NKIR (Tobe et al. 2022 clinical neuro-imaging resource with diverse populations, used for classification of sex.
UK-Biobank (MSE, R²) (MSE, R²)
HCP
Foundation Model
MnemoDyn-UKB 2.36e-5, 0.985 4.52e-08, 0.934
MnemoDyn-HHC HCP 1.86c-09, 0.969 3.94c-06, 0.987
Table 1: Validation reconstruction MSE and l!² score. We see good generalization across founda- tion models trained with different data.
3.2
PROCESSIN
We now describe the pre-processing steps that were performed to convert and standardize the raw rs-MMRI data to the time-series format which the foundation model was trained. (a) NIfTI +
CIFTI: Raw SIDS-formatted rs-MMRI volumes were first converted into HCP-style dense time series space. This step ensures subject-level consistency and enables downstream use of surface-basse atlases. (b) CIF77 - Parcellation: Each dr..erieeee.. ni 1 was then parcellated into region-level time series using the well-established atlases, yielding matrices X E I X where T is the sequence length and <
(. (dtteries ni i), aligning cortical and subcortical signals within the 91 1282-gray-ordiin
N is the number of parcels. Following (Dong et al. 2024). we used N 450 using Schaefer-400 (Schaefer et al. 2018) for cortical regions and Tian Scale (Tian et al.] (020) for sub-cortical regions. (c) Normalization: Finally, parcel-wist signals were robustly normalized based only on training data statistics, using median and interquartile range (IQR). This procedure reduces the influence of outliers and harmonizes input scales across regions and subjects. Complete algorithmic details, including projection steps, atlas handling, and normalization equations, are provided in Appendix A.
3.3 PRE-TNAINING AND FINE-TUNING
Architecture: Our model MnemoDyn were briefly outlined in Sec. 2 Each layer in MnemoDyn operates at a different wavelet scale, enabling the model to capture both fine-scale fluctuations and long-
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range temporal structure in resting dynamics. Layers coupled through residual connections, which progressively integrates information across scales and helps mitigate vanishing signal issues common in long sequences. Many of these layers come together to comprise encoder block which transforms the data from one function space to another (operator). Mnemolyn stacks multiple of these blocks. The input data is of sequence length 1200 (for HCP) and 490 (for UK Biobank) with N = 450 brain regions (ROIS). The backbone first projects these ROI signals into a hidden space, compresses them into low-rank bottleneck. Temporal dependencies are modeled using wavelet bases (cb2) stacked over multiple resolution levels. Unless otherwise specified, nonlinearities are tanh, chosen for their stability in continuous- time operator approximations.
Pre- Tre-Training Strategy: We evaluated several different strategies.
Mnemo Dyn-
Denoise trained using denoising auto-encoding objective outlined in Appendix A.2.2 JinemoDyn-Mase is masked aufoencoder ob- jective that masks temporal and spatial blocks at random and learns to reconstruct them from surrounding context, forcing the model to learn long-range dependencies shown in Fig. and Appendix [A.2.3] We also adapt the masking scheme from (Dong et al. (2024) for MyemoDyn- Mask-JEPA. We mask 70% of the observed sig- nal spanning temporal and spatial dimensions in the models presented here. AdamW is used as the optimizer with cosine annealing and warm restarts, gradient clipping, and early stopping. The objective a combination of mean squared error (MSE) and mean absolute error (MAE).
Laten Bynanios
CR (8-x)
Libee SparEs
Dowmstrom
Pradetio
Figure 4: Masked pre-training and fine-tuning of MyemoDyn. We note that the dynamics are evolved in the latent space followed by the encoder, which is eventually used to fine-tune adapter layers for downstream tasks. In pre-training phase, loss is computed only on the unseen spatio-tempon data.
Fine-Tuning For downstream tasks, we freeze the pretrained backbone and attach suec-fpec regression/classifcaaiii head which trainable. The default head a multi-layer perceptron (MIP) applied to pooled backbone features (averaged over time and ROIs). In particular, inputs are mapped through successive layers, each followed by LayerNorm, GELU, and dropout (p=0, 0.1), before a final linear layer outputs logits. The training objective depends on the task: mean squared error (MSE) for regression tasks (e.g.. age prediction). and cross-entropy for classification tasks (e.g., sex, diagnosis). scheduler. Unless otherwise noted, robust
Adam is used as the optimizer with normalization 1.. is retained while extracting features from our pre-trained MnemoDyn.
NC/MC (ADNI)
Amyloid v (ADNI)
Age (UKB)
Sex (UKB)
Methods
ACC(S)
FI(S))
ACC(S)
F1(S))
MSF.
ACC(S)
F1(%)
BrainNeiCNN
(3.18) (3.50)
(2.00
(1.14)
0.99 (0.03)
77.86 (0.98)
78.17 (0.86)
BrainGNN
(2.93)
71.42 (2.87)
(4.00)
62.61 (3.48)
0,93 (0:04)
77.31 (0.33)
79.23 (0.31)
BNT
(4.12)
83.14 (3.58)
62.00 (2.45)
59.53 (0.58)
0.86 (0.03)
80.78 (0.40)
82.42 (0.36)
BrainLM
75.79 (1.05)
85.66 (1.27)
67.00 (7.48)
68.82 (8.48)
0.61 (0.04)
86.47 (0.74)
86.84 (0.43)
Brain-JEPA
76.84 (1.05)
86.32 (0.54)
71.00 90)
75.97 (3.93)
0,50 (0.03)
88.17 (0.06)
88.58 (0.11)
MnemoDyn-Mau
96.12
95.98 (0.29)
95.27 (0..3)
(l.37)
0.44 (0.05)
88.40 (0.32)
88.27 (0.41)
MnemoDyn-Maske JEPA
93.67 (0.89)
93.32 (1.09)
94.89 (1.09)
94.60
0.42 (0.03)
88.30 (0.36)
88.28 (0.41)
Table 2: Test set performance in terms of mean (standard deviation) of MnemoDyn when fine-tuned on separate predictive tasks. Results include disease diagnosis (NC MCI) and biomarker status prediction (Amyloid +ve/-ve) from ADNI (left), as well as age regression and sex classification from UK Biobank (right). Different fine-tuned variants of MnemoDyn consistently achieve lower error and higher/comparabl accuracy/F1 compared to prior baselines. We report Fl score in addition to accuracy to take into account class imbalance.
3.4 EVALUATION
We evaluate MnemoDyn for its representation capability as well as fine-tuned performance on multiple benchmarks. Here, we present results for UK-Biobank, HCP, HCH--Aiiii and ADNI. Additional results on a broad basket of datasets are in the Appendix. Our choice of baselines follow (Caro et al. Dong al. 2024) and include existing stand-alone deep learning models (BrainCNN (Kawahara et al. 2017 BrainGNN (Li al. 2021). Ka et al. (2022) as well as foundation models (BrainLM (Caro
et al.), Brain-JEPA (Dong al. 2024 ) for rs-fMRi data analysis. We used graph-based and CNN
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Age
Sex
Neuroticism
Flanker
Methods
MSE +
ACC (%) f
FI (%)
MSE +
MSE +
BrainI.M
1.14 (0.22)
75.27 (1.24)
73.19 (1.12)
1.05 (0.12)
0.77 (0.11)
Brain-JEPA
1.02 (0.01)
79.17 (1.29)
76.29 (1.17)
0.99 0.99 (0.01)
1.28 (0.01)
MnemoDyn-Denn Denoise
0.91 (0.02)
80.2 (0.12)
80.11 (0.11)
0.91 (0.02)
0.61 (0.02)
MnemoDyn-
0.90 (0.01)
83.10 (0.57)
82.77 (0.54)
0.90 (0.03)
0.60 (0.01)
MiemeDyyn-Mask-JPAAA
0.90 (0.01)
82.57 (0.35)
82.23(0.41)
0.90 (0.02)
0.60 (0.01)
Table 3: Performance of MyemoDyn when fine-tuned on External tasks of demographics and trait prediction HCP-Aging. We report mean(standard deviation) for each metrie. Our model achieves strong improvements in predicting age, scx, and cognitive/behan hbhhvvooraall traits (Neuroticism, Flanker) on the test set. We report F1 score in addition accuracy account for class imbalance.
models as our simple baselines for whole-brain rs- rs-fMRI. More reduced models require task-specific network extraction or coarse connectivity features, which under-perform the baselines reported here.
Representation capability of MnemoDyn: We demonstratee the representation capacity of MnemoDyn by evaluating the reconstruction performance on held-out test data. In Fig. we can see that after pre- training on IK-BBobank, MyemoDyn can faithfully recover the signal not only for unseen data. These are further numerically demonstrated in Table where we perform a cross- cessuevvalttioon of MyemoDyn models trained on "K-Biobank and HCP to reconstruct held-out data from either dataset.
By comparing performance of fine-tuned MyemoDyn on a variety of predictive tasks on large collection of rs-MMRI datasets, we demonstrate the efficacy of MnemoDyn as foundation model. We report results from two variants trained on UK-Biobank using pre-training strategies (Mask and Mask-JEPA) described above. Additional results are in Appendix.
Predictive Performance on Fine-Tuning Tuning:
(i) Disease Diagnosis and Prognosis (ADNI): We fine-tune MyemoDyn on external prediction tasks using the ADNI cohort, focusing on (a) differentiating normal controls (NC) from mild cognitive impairment (MCI), and (b) predicting amyloid biomarker status +ve-vve ve (Sperling, 2011). Fine-tuned variants of MyemoDyn substantially outperform baselines (Table 2), achieving SOTA accuracy and F1 scores, underscoring its robustness and effectiveness for both diagnostic and prognostic settings.
(ii) Demographic Prediction (UK-Biobank): While MnemoDyn was pre trained using -K-Biobank, we fine-tuned a model on a held-out set for predicting age and sex. We observe (Table[2) that finetuning has comparable/improved performance over baselines, underscoring the effectiveness of pre-training.
(iii) Demographic and Trait Prediction (HCP-Aging): We further evaluate MnemoDyn on demo- graphic (age, sex) and cognitive/behaviora trait prediction (neuroticism, flanker) using the HCP-Aging dataset. Fine-tuned variants of MnemoDyn consistently outperform strong baselines (Table 3), yielding lower MSE and higher correlation for regression tasks (age, neuroticism, flanker) as well as higher accuracy and Fl scores for sex classification. These results highlight the versatility of MnemoDyn across both categorical and continuous prediction settings, suggesting that works well as a gener- alizable foundation model. Here, we also check different variants of MnemoDyn in the pre-training strategy and observe that despite varying objectives the pre-training phase MnemoDyn improves performance in downstream tasks, asserting that the performance driving factor for MnemoDyn is indeed the operator-theoretic parameterization and not merely the pre- pre-training objective.
Summary, These results show the effectiveness of MnemoDyn fine-tuned for a wide-variety of tasks. We also observe that both pre-training strategies perform equally well suggesting the robustness of MnemoDyn small changes in the training algorithm.
foundation model which can be
Discussion. Our analysis shows that pre-training induces a clear multi-scale organization aligned with our wavelet-domain parameterization. Frobenius norms concentrate in operator kernels. This indicates that the dynamics are driven by structured cross-scale filters rather than dense mappings. Dense components shrink rapidly with depth, suggesting later layers rely increasingly the global structure encoded by the operator. Sparsity patterns further support this: the wavelet-operator kernels remain fully dense (as expected for smooth, global transforms), while output-projection projection matrix is ~ 95% sparse. Additional details in Appendix A.3
Our code is available at htlipp//sshhllloommmiighhgoononn

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4 RELATED WORK
Operator learning (Kovachki et al. 2023) has recently emerged as a promising paradigm for learning mappings between diteittedimesiioall function spaces, particularly for modeling dynamics governed by differential equations. Early works such as DeepONet (Lu et al. 2021) and the Fourier Neural Operator (FNO) (Li et al.) demonstrated the feasibility of learning solution operators to parametric PDEs. These approaches have since been extended to irregular domains (Li et al.) 2020). stochastic dynamics, and implicit formulations. State space models (SSMs) explicitly factorize latent evolution and observation mechanisms (Gu et al.). Recent works have focused combining neural networks with structured transition kernels (Mehta et al.) Gu al. 2020). However, majority of existing SSMs are not tailored to the specific properties of neurophystological data, nor have they explored multiscale bases such as wavelets for learning dynamics.
Operator Learning and State Space Models:
Ckention-Based Models for Brain Imaging Data: Transformer architectures have been proposed for modeling spatiotemporal data in neuroscience, including fMRI (Kan et al. 2022), EEG (Song et al.. 202T), and MEG eXu al. 2025). Recent critical evaluations have pointed out several limitations. First, attention-based models often underperform in scenarios involving long-range, noisy, or irregularly sampled signals (Zeng et al. 2023). Second, their inductive biases are often mismatched to brain dynamics, which exhibit strong local temporal correlations, hierarchical structure, and subject-specific variability. Finally, their memory and compute requirements make them impractical for resource- constrained settings. While some transformer variants introduce inductive structure (e.g., temporal sparsity (Gorbett et 2023)), their complexity often remains high compared to classical or recurrent baselines. Finally, attention based models involve tokenization and patching which is a mismatch for brain imaging data derived from inherent continuous processes. Our work offers Nomain--liggne' alternative, avoiding global attention mechanisms entirely while still capturing long-range structure.
Recent works advocate against the overuse of large secention-based or foundation models for structured domains (Xu et al.) such as time series and brain imaging data. Benchmark studies (Zeng al. [202] Tan al. (2024) show that compact, domain-aligned models relying on CNNs/RNNs can outperform Transformers on time series tasks, especially in low-data regimes. Recent evidence also suggests that Transformers
Lightweight Models for Domain-Specitt Sequence Modeling:
be over- parameterized and ill-suited for biomedical time series, where long sequences, noise, and multiscale localized dynamics dominate (Xu et al. Kim et al.)) In biomedical signal processing, convolutional and recurrent architectures have been preferred for their efficiency and robustness (Kiranyaz et al. (0155] Faust et al. 2018). In neuroscience, studies show shallow or linear models perform competitively on TMRI decoding and EEG tasks (Makeig et al. (2004). while offering better interpretability and less risk of overfitting (Haufe et al. 2014). These findings collectively motivate structure-awar architectures in domains where data noisy, multiscale (Vidaurre et al. 2017) and expensive to acquire.
5 CONCLUSIONS
comain-specifii inductive biases and compact architectures often surpass large generic foundation models when data is limited structured. This is especially true in neuroscience, where brain imaging data are noisy, heterogeneous, and expensive to acquire. Moreover, neuroimaging signals emerge from intrinsic dynamical systems with rich multiscale structure, favoring models that emphasize temporal locality and sparsity. Our work proposed a compact dynamical system based model MnemoDyn tailored for r--MMI Unlike attention-based approaches, we frame learning as the identification of governing dynamical laws. We utilize the interaction between wavelets and pseudo-dii -euudddiiffrential operators, and so MnemoDyn achieves efficiency/sparsity through structured decomposition, maintaining the temporal locality essential for modeling brain dynamics.
While our results of fine-tuning MyemoDyn demonstrate strong performance across diagnostic, prognostic, and trait prediction tasks, there are some limitations. First, our experiments are limited to parcellated rs-IMRI data; extending the model to voxel-level or multimodal inputs (c.g., EEG, PET) is an important future direction. Second, extending the framework to longitudinal studies will be an important next step in establishing the full potential of MyemoDyn. Addressing these limitations will help translate compact dynamical system models into robust, domain -ndated foundation models for neuroscience. While MnemoDyn provides interpretable multi-scale temporal structure, establishing genuine neurophysiological correspondence remains open and is natural direction for future work.
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6 REPRODUCIBILITY STATEMENT
Details of model architecture, training, and evaluation are provided in the main text and appendix. Code, pre-proesssing scripts, and pre-trained model weights will be released publicly via Hugging Face upon acceptance to ensure full reproducibility.
ETHICS STATEMENT
This work uses publicly available, de-identified rs-fMRI datasets under appropriate data usage agree- ments. No new human or animal data were collected, and the study complies with institutional and ICLR ethical guidelines. Our methods are designed for scientific research neuroscience and health- care, and we do not foresee any direct negative societal impact. Nonetheless, as with any machine learning model applied health-care data, risks include potential misuse for inappropriate prediction or diagnosis outside clinically validated settings. We stress that our approach is research contribution and should not be directly applied for medical decision-making without further validation.
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A APPENDIX
A.1 PRE-PROCESSING PIPELINE
A.1.1 NIFTI CIFTI ETSERTRS.
We converted raw BIDS-formatter fMRI volumes (ADHD-200) into HCP-style dense time series (dtseries) to enable analysis in standardized grayordinate framework. For each subject/session, volumetric BOLD runs were first mapped to cortical surfaces using ribbon-constrained volume-to- surface projection onto the fs_LR 32k left/rght midthickness meshes, with corresponding white and pial surfaces providing anatomical constraints. Subcortical structures were handled separately by resampling the functional volumes to the Atlas las_ROOss subcortical grid. These surface and subcortical representations were then integrated using the HCP 91, 1.,282-grayordinn ducing series. ni files that preserve the full temporal resolution of each scan while aligning all cortical and subcortical signals to common anatomical space. This standardized conversion ensures subject-level consistency and facilitates direct comparability with HCP-derived methods and parcellations.
template, pro-
A.1.2 CIFTI DESERTES - PARCELLATION
All fMRI dense time series (. dt sitseries nii) were parcellated into N regions of interest (ROIs)
using one of three brain atlases: the Gordon atlas (N 33: Gordon et al. 2014), the Schaefer atlas
(N = 424: (emaaii et al.) 2020). and the Tian atlas (N=450 440: Tian et al. 2000 Schaeferr et al.) 2018). Each dt dtseries first loaded and oriented as T x (timepoints x grayordinates), transposing when the first dimension equals G-91, 99,228 Given atlas dlabel... ni with integer parcel labels over the same grayordinate space, we exclude background (0) and, for each parcel label l O, compute the parcel time series the mean of all grayordinates assigned to f. This yields parcellated matrix X T'N N We verify that the atlas and dt sseries share the same grayordinate dimension and abort otherwise.
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A.1.3 NORMALIZATION
Normalization constants are estimated solely on the training split. Let x ER denote the i-th training sample (I"= 1200 by default), and let
(
X
CR(N-I)X
be the concatenation all training samples across subjects and time. Foreach ROI/feature E (1.....). define the empirical distribution
X, - [ It=,.,N
From X, we compute:
median, -2
Q25.r = (.,anntiee(x,,00222
Q75.r quantilee(,,,0075))
IQR, = Q75. -
Q99,- (X,
The robust scaler retains (median, IQR, |P-1 as fitted statistics. At transform time, new sample R'x normalized ROI-wise
3t, median.
St.r
6 1=10
TQR, +8
for all LE (1,..,,)),r ((...,))
A.2 EXTENDED TRAINING DETAILS
A.2.1 FOUNDATIONAL TRAINING
Backbone: We employ MnemoDyn stacked foundation model based on wavelet multiresolution analysis. The backbone is composed of L=4 blocks, each operating at different latent dimension and coupled through residual refinement. Inputs of dimension N = 450 are projected hidden space of size 150, compressed to low-rank bottleneck of dimensionality 5. Temporal structure is modeled with Neeells 6 wavelet (db2) decompositions. Where required interpolation in continuous-time operators is spline-based, and nonlinearities are tanh.
Training: We pre-train for 50 epochs using the Adam optimizer with learning rate 10-3, weight decay 0.01, and (81, 82) (0.9, 0.95). A cosine annealing schedule with warm restarts (To 10, Tmuit = 2) reduces the learning rate, with Mmin = 10 5_ Batch sizes are fixed at 8/ 8/16/16 for waining/validatiiontest respectively. The objective defaults squared error (MSE) and mean absolute error (MAE). Training employs gradient clipping at 1.0, and checkpoints the two best models (lowest validation MAE) throughout training. Early stopping with patience 30 epochs is applied to prevent overfitting, Below, we describe different strategies used for self-supervised pre-training.
composite loss, combining mean
Hyperparameter Tuning: We tuned the core architectural hyperparameters that govern the capacity, multiscale structure, and locality of the operator using grid search in the range of values that are plausible based on the dimensionality of the data. The parameter controlling the hidden low-rank dimension of the operator which determines how much compression is applied during the learned integral transform was varied between (3. The number of wavelet decomposition levels, which determine the granularity the multiscale representation was varied between (4,5,6,788) The coarse dense operator applied in each block that refines features at each scale varied in (4,6,8 12). The parameter that governs governs how many locally-connected filters remain active within each diagonally banded structure was varied in (4.6).
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A.2.2 DENOISING AUTOENCODER
To encourage robustness and prevent overfitting, we employ a denoising autoencoding objective. Specifically, we corrupt the input signal by adding stochastic Gaussian noise. Given an input sequence I, we construct the noisy version
x 0.1,c, where e e~ (O,II) The autoencoder is trained to reconstruct the original clean input z from ž. This setup forces the encoder to learn representations that are invariant to small perturbations, improving generalization.
A.2.3 MASKED AUTOENCODER
We additionally adopt masked autoencoding strategy. For each training sample, randomly select five disjoint starting indices within the temporal dimension of the sequence. From each starting index, mask a contiguous block of 80 time steps. The model is trained to reconstruct the masked portions of the input given the unmasked context. This approach encourages the encoder to capture long-range dependencies and contextual relationships, since successful reconstruction requires leveraging both local and global sequence information.
Demppoal-Dimmenioonal Masking. Given a sequence of length T with 1) feature channels, construct binary mask M E (0.1) 2 by placing non-overlapping temporal windows independently for each feature. For window length length) and masking ratio mask sariiii., the method computes
Kreq = [mmaak.ratiio],
Keap= [T/p_
(18)
and uses K min K Keeq Keup) windows. Each feature dimension then samples K disjoint start indices from {O...., L), masking the interval [s.s+ L), resulting structured temporal occlusion while keeping feature channels independent.
The model is trained using a masked reconstruction objective that evaluates errors only on the occluded regions. Let x E RT&D be the original input, åt the model's s reconstruction, and AM E {0,1)7*D the binary mask. Here, Mr,d = indicates masked position where the loss will be computed. Before feeding the sequence into the model, all masked positions are replaced with zeros, i.e.,
Masked Reconstruction Loss.
Tiassked = (1 11--M (1-M))r,
(19)
so the model receives no information from the occluded intervals. The reconstruction loss is then defined as
Lymask
[
(20)
|M
where @ denotes element-wise multiplication and ||M llo counts the number of masked entries. By supervising the model solely on the masked regions, the learning objective forces the operator to infer the missing dynamics from surrounding temporal context, encouraging the extraction of meaningful temporal dependencies and multiscale structure rather than trivial copying from visible inputs.
A.2.4 BRAIN-JEPA STYLE SCHEME
We also adopt the training strategy from the Brain-JEPA framework (Dong et al., 2024), which generalizes the masked prediction objective across multiple domains of the input. Concretely, given an input sequence x E R'D we define a masked subset of indices C (1.....T) TT x (1,...,7) D) and construct masked views a by replacing entries in Ω2 with zeros. Masked views are sampled along three complementary axes: (i) temporal masking, where contiguous blocks of time steps are removed; (ii) spatial masking, where subsets of brain regions (ROIs) are occluded: and (iii) cross neatio-temporal masking, where both temporal segments and ROI subsets are jointly masked. This design compels the encoder to capture dependencies across both spatial and temporal dimensions, rather than overfitting to a single axis of variation.
Following the predictive coding paradigm of V-JEPA (Bardes et al. 2024). we train a student encoder fo against targets produced by teacher encoder for, where the teacher parameters are updated as an exponential moving average (EMA) of the student:
0' 70' (1-T)0,
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Sex
Age
Methods
ACC(%) f
F1(%)
MSE.
Brain-JEPA
58.52 (3.72)
29.12 (1.64)
1.02 (0.01)
MnemoDyn
82.37 (2.1)
82.19 (1.9)
0.84 (0.01)
MnemoDyn Mask
81.55 (1.6)
81.35 (1.6)
0.80 (0.01)
Table 4: Performance of fine-tuned MnemoDyn Healthy Brain Network (HBN). We report mean(standard deviation) on the test set. For both regression and classification, we get better perfor- mance than baseline.
with momentum coefficient [0,1). Given masked view 2/ the student produces predictions (target)
= fe (z)e), while the teacher provides the reference z _ = fo (x). The loss is the mean squared error (MSE) over the masked indices:
Lmakk (0)
|
(arggtt) Atr
[2
(t,r)e
By unifying temporal, spatial, and cross spatio-temporal masking, this scheme encourages the emer- gence of latent representations that capture both local and global structure in rs-MRRI time series.
A.2.5 DOWNSTREAM HEAD
For downstream tasks, we freeze the pretrained backbone and attach task-specific regres- sion/classification head. The default head is multi-layer perceptron (MLP) applied to pooled backbone features (averaged over time and ROIs). Concretely, inputs are mapped through successive layers, each followed by LayerNorm, GELU, and dropout 0.11)... before final linear layer outputs logits.
The training objective depends on the task: mean squared error (MSE) for regression tasks (e.g., age prediction), and cross-entropy for classification tasks (e.g., sex, diagnosis). Optimization uses Adam (Ir= 1r=100-3 wd 10 with set to 8/ for train/test. We robust normalization from (Sec. A.1.3) A.1..
scheduler (factor 0.5, patience 5). Batch sizes are retained.
A.3 ANALYSIS OF PRE-TRAINED OPERATOR
To better understand how MnemoDyn uses its multi-resolution operator parameterization, de- composed the learned operator into banded, level-wise components and small dense residual, and examined their Frobenius norms and sparsity patterns after pre-training. The results expose highly stable multi-scale structure.
Norm structure. Across Mylyeeys,ayers,, the Forbenius differential operator kernels derived from the wavelet domain. These components dominate by an order of magnitude (~ 1500), indicating that the learned dynamics are primarily mediated by structured, cross-scale interactions. Dense layers exhibit rapidly decreasing norms (~20), showing that deeper blocks rely less on local, single-scal scale corrections and more on the global structure encoded by the operator. Components that directly process the raw input diminish steadily with depth, consistent with hierarchical abstraction.
mass is concentrated in the pseudo-
Sparsity structure. The wavelet-operator kernels remain uniformly dense across layers, which is expected for smooth, global transformations that do not benefit from element- pruning. In contrast, the output-projection layer is over 95% sparse, revealing highly selective readout from otherwise rich, distributed multi-scale representation. This is consistent with the interpretation that the learned dynamics evolve a structured, lower-dimensional manifold induced by the operator geometry.
Activation and Lg norm visualizations. In Fig. 5 we illustrate the operator output A, (u,) across wavelet levels 0 through 4, capturing how the learned operator responds to progressively coarser temporal representations. Level exhibits the highest temporal resolution and displays large, high-magnitude activation bursts concentrated around specific time segments, reflected by the yellow
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A/a) Level
300
506
Operator Gulput A(aa) Level
86
100
330
Operator Gutput AjUa)
106
Operator
31
200
Operator Output A/uJ) - Level
15
106
Figure 5: Operator output Ay(ug) across wavelet levels 4.
bands. As the scale increases (levels 1 through 4), the temporal length shortens and the operator responses become smoother and notably lower in magnitude. We observe similar behavior, in Fig. 6 where we visualize the L2 norm at each time step over channels across multiple resolution(s) the latent space of the operator output. Overall, this highlights a clear multiscale pattern: strong, localized operator activity at fine scales and progressively weaker, more diffused responses at coarser scales.
A.4 MNEMODYN AS A FOUNDATION MODEL FOR RS-FMRI
In this section, we elaborate how MnemoDyn exhibits foundation-model like characteristics. We include empirical evidence of scaling behavior with model size and pre-training data size, (ii) precise delineation of generality and transfer within the rs-IMRI modality, and (iii) an explicit framing of what is and is not claimed in terms of modality breadth.
A.4.1 SCALING BEHAVIOR: MODEL SIZE AND DATA SIZE
We conducted controlled ablations to quantify the effect of increasing (a) the depth of the model and (b) the size of the pre-training dataset.
Model-size scaling. MnemoDyn consists of stacked operator blocks, analogous to depth scaling in transformer- based architectures. Increasing the number of operator blocks from two to four yields consistent improvements across regression and classification tasks multiple downstream datasets.
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Multiscale Activation Map
1400
1200
Operator Energy
Wavelet Scale
1000
800
400
200
50
100
150
200
Figure 6: L2 norm of operator output Au(u) across wavelet levels -
This trend aligns with standard foundation-model behavior, where additional representational capacity improves both pre-training objectives and fine-tuning performance. The results summarized in T
Data-size scaling. We additionally pre-train MyemoDyn on different subsets of UK-Bioband avail- able subjects. Models trained with more data show uniformly stronger performance across downstream evaluations (T This confirms that MyemoDyn benefits from increased pre-training data coverage, another key requirement for suundation-model-styyl scaling.
The combined findings provide direct, quantitative evidence that both model depth and pre-training data size contribute to improved representational quality.
# Blocks
Age (MSE
Sex (Acc; F1 t)
1
0.914(0.012)
0.768(0.013) O. (..001) 0.8010().016); 0. 00..007000000 (0.014)
2
0.903().014)
Table 5: Model-size scaling: downstream task performance for different numbers of operator blocks for HCP-Aging.
# Subjects
Age (MSE
Sex (Acc; F) 0.
1000
1.023(0.019)
10000
1.021(0.014)
(.77 0.793 0.790
20000
1.012(0.013)
Table 6: Data-size scaling: downstream performance when pre-trained on different fraction of UK- Biobank and finetuned for HCp-Aging.
A.4.2 SCOPE OF TRANSFER: WITHIN-MODALITY GENERALITY AND REUSE
We clarify the exact empirical scope of generality and transfer supported by our experiments.
Within-modality transfer (rs-MMRI.. All experiments in the present work are conducted within the rs-MMRI modality. MnemoDyn is pre-trained once and evaluated across multiple heterogeneous datasets (HBN, ADNI, ABIDE), which differ in scanner hardware. acquisition protocols, demo- graphics, and health conditions. This cross-dataset robustness is non-tri non-trivial: each dataset required separate institutional approvals, data-use agreements, and constrained compute environments governed
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by the respective data custodians. Within these practical constraints, MyemoDyn functions general-purpos purpose, reusable backbone for rs-IMRI, consistently outperforming strong baselines across scientifically relevant tasks. This evaluation strategy is aligned with the protocols established by recent rs-fMRI foundation models such as Brain-I.M eC et al.)) and Brain-JEPA (Dong et al. (022)).
Task generality. Our evaluation setup of supervised regression and classification matches the dominant protocol for rs-fMRT foundation-modes research. These task types enable direct, fair comparison with prior work while focusing on scientifically meaningful variables such as age, cognitive scores, and disease status. Although we do not include non-label pretext tasks (c.g., trajectory forecasting, contrastive objectives, or clustering) in this paper, MyemoDyn is architecturally designed to accommodate them: the latent trajectories produced by the model capture multi-scale temporal dependencies and spatial interactions, and can easily be used with lightweight task task-specific heads for broad family of downstream objectives.
Cross-modality transfer. We explicitly do not claim empirical cross- mods-mmo generalization here. Extending MnemoDyn to EEG or MEG requires its own elaborate process for dataset acquisition, access approval, pre-processing, and compute scheduling. While the architecture is compatible with other modalities in principle, we restrict our claims to demonstrated within-modality transfer and identify cross- moos-ttd extensions future work.
To conclude, we define MnemoDyn as foundation model for rs-fMRI, characterized by the following properties:
Large-scale, self-supervised pre-training tens of thousands of frRI sequences.
General-purpose, reusable representations that support multiple downstream tasks using lightweight heads.
Cross-dataset robustness across diverse scanners, sites, acquisition protocols, demographics, and health conditions within rs-IMRI.
Empirical scaling in both model size and data size, demonstrated in Tables Fables55andd
This framing reflects the prevailing codaalitysspeciff definition used by baseline rs-IMRI foundation models.
A.S DISTINCTIONS BETWEEN MNEMODYN AND CLASSICAL OPERATOR- FRAMEWORKS
Here we discuss the conceptual and architectural differences between MnemoDyn and canonical operator-leaminn frameworks such as the Fourier Neural Operator (FNO) and DeepONet.
Fundamentally different problem formulations. Classical operator-learning methods are designed for supervised operator regression, where the goal is to learn map between input-output function pairs, typically arising from PDE solution operators (e.g., mapping a forcing function to its corresponding solution field). These methods assume access to explicit operator evaluations: given input function u, predict the output function (()), where 9 is the unknown operator to be learned.
MnemoDyn addresses categorically different learning problem. We observe long rs- ---I time series generated by an unknown dynamical system, with no paired input-output fields, no PDE solution maps, and access ground-truth operator evaluations. The learning objective fully self-supervised, relying on reconstructing or modeling the evolution of observed sequences. While MnemoDyn contains an operator-theoretic flavor through integral formulation of latent dynamics, the learned operator is latent: it parameterizes the evolution rule of the hidden trajectory rather than mapping one function to another. The kernel governs temporal modulation of the latent state, not supervised operator- valued regression.
Architectural mismatch induced by the problem setting. The architectural choices in FNO and DeepONet naturally follow from their reliance on paired function data, but they become ill ill-suited when directly applied to long, nonstationary rs-fMRI sequences.
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FNO parameterizes global Fourier symbols, inducing dense global interactions across the entire domain. This is well-aligned with PDE solution operators, which are typically smooth, globally coupled mappings. However, global Fourier bases are less suitable for multi-scale, nonstationary, and locally temporal dynamics which are commonplace in rs-fMRI data. In contrast, MyemoDyn operates in wavelet domain and parameterizes scale-varying pseudo-differente operator whose symbol adapts across resolutions. The compact support of wavelets induces approximate banded- diagonal sparsity for long sequences, yielding both computational benefits and modeling flexibility for dele-ddeenndnt,, nonstationary behavior that Fourier parameterizations do not provide.
DeepONet, on the other hand, constructs operators through two subnetworks (branch and trunk), but does not provide clear interpretability of the resulting basis functions. This makes it difficult to justify its representational structure for multi-scale spatio-tempon brain dynamics and limits alignment with domain-specific inductive biases required for rs- fs-fMRI modeling.
Nature of the learned operator in MnemoDyn. Although MnemoDyn incorporates operator through its integral representation of latent dynamics, it does not aim to approximate a supervised PDE solution operator. Instead, the kernel acts internally to dictate the evolution of the hidden state trajectory in continuous time. This quantity cannot be interpreted as the same object learned by FNO or DeepONet, because no input-output functional mapping is being approximated. The operator in MnemoDyn is, by construction, latent dynamical operator extracted from unpaired, noisy observational sequences.
Why direct comparison is non-trivial. Constructing a version of FNO or DeepONet suited for rs-MMRI would require a substantial redesign, including: (a) developing new objectives tailored to self-supervised sequence modeling rather than supervised operator regression; (b) replacing global Fourier bases or trunk/branch decompositions with structures that respect multi-scale temporal vari- ability. brain parcellations, and nonstationary dynamics;(c) incorporating architectural modifications to accommodate irregular sampling and Nomain-speciffe masking used in ncuroimaging; and (d) regularization schemes and inductive biases.
introducing neuroimaging-speen
Such modifications amount to designing an entirely new aperator-learning architecture for rs- MMRI, rather than applying an existing method unchanged. For this reason, our comparisons focus strong, domain-appropinn appropriate rs- ---MRI foundation modell baselines that align with MnemoDyn's problem setting and data assumptions.
Summary of conceptual novelty. The contribution of MnemoDyn does not lie proposing a new operator-leaming formalism, but in adapting thereto principles to rs- rs-fMRI in a way that both effective and computationally efficient. The key innovations arise from the integration of (i) wavelet-domain pseudo-differential operators, (ii) structured low-rank parameterization suited to high-dimensional time series, and (iii) continuous-time evolution of latent trajectories. Taken together, these components differentiate MnemoDyn architecturally and functionally from FNO and DeepONet, whose problem formulations, assumptions, and training pipelines are fundamentally different.
blue
A.6 IMPORTANCE OF THE MULTI-RESOLUNE ANALYSIS AND Low RANK STRUCTURE
To assess the contribution of the wavelet-based nustiiresooltionn analysis (MRA), we trained a version of MnemoDynin the raw latent space, removing all wavelet transforms and callestructture operators. The "no-waver wavelet" variant shows consistent degradation across all downstream tasks as shown Table
Task
Metric
No-Wavelet
MnemoDyn-MMask
NC/MCT (ADNT)
ACC/F1
75. /4.39 + 1.01
96.12 + 0.31 95.98 + 0.29
Amyloid (ADNI)
ACC/F1
72.19 :: 2.01 /7123 + 1.78
95.27 +: 0.39 / /95661 +: 0.37
Age (UKB)
MSE
0.67 + 0.07
0.44 + 0.05
Sex (UKB)
ACC/F1
0..16-...1/771144
88.40 + 0.32/88.77 + 0.41
88.27
Table 7: Comparison of MnemoDyn with and without multi-resolltion wavelet decomposition.
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ADHD/TDC
Methods
ACC(%)
F1(%)
Brain-JEPA
45.7 (0.89)
46.5 (0.78)
MnemoDyn
54.24 (0.3)
54.07 (0.42)
MnemoDya-Mask
54.36 (1.24)
54.26 (1.27)
MaemoDYya-Maa--IEA
54.70 (0.75)
54.55 (0.80)
Table 8: Performance comparison on the ADHD200 dataset for ADHD vs. TDC classification. Mean accuracy (ACC) and Fl-score (FI) with standard deviations are reported. Fine-tuned variants of MnemoDyn consistently outperform the Brain-JEPA baseline.
The improvements from reintroducing the wavelet-based multi-resolution structure are substantial: classification accuracy increases by 20-23 points on ADNI tasks and by 12 points on UKB sex prediction, while age regression eиrоr decreases by more than 34%. These consistent gains highlight that MRA is not merely an architectural detail but crucial inductive bias suitable for modelling the dynamics associated with rs-fMRI data.
When we remove the low-rank decomposition in the latent space, we observe immediate memory blow up for the dimensionality required to encode the latent dynamics faithfully.
A.7 ADDITIONAL DOWNSTREAM EVALUATION ON RS- RS-FMRI DATASETS
To assess the efficacy of MnemoDyn as foundation model for brain imaging, evaluate its fine-tuned variants across four different neuroimaging datasets spanning both regression and classification tasks. Our goal is to establish whether MnemoDyn provides consistent performance improvements over existing baselines, such as Brain-JEPA, while maintaining robustness across heterogeneous datasets. We report mean accuracy (ACC), Fi-score (F1), and mean squared error (MSE), depending on the task, with standard deviations in parentheses. Across all datasets, MnemoDyn demonstrates clear advantages over the baseline, underscoring its utility as a versatile foundation model for downstream brain-related prediction tasks.
On the HBN dataset, which includes both sex classification and age regression tasks, fine-tuned variants of MnemoDyn achieves significant performance gains as shown in Table For sex classification, MnemoDyn reaches an accuracy of 82.37% and Fl of 12.19% compared to 58.52% and 29.12% for Brain-JEPA. For age prediction, the mean squared error reduces to 0.84, outperforming the baseline error of 1.0163. The masked variant (MnemoDyn-Mass Dyn-Mask) yields similar results, further highlighting the robustness of the approach. These results indicate that MnemoDyn effectively supports both categorical and continuous prediction settings within developmental datasets.
Healthy Brain Network (HBN):
ADHD200: On the ADHD200 dataset, we evaluate the classification of Attention- Defici//Hyperactivity Disorder (ADHD) vs. Typically Developing Controls (TDC) as shown in Table Here. MnemoDyn consistently surpasses the Brain-JEPP baseline, achieving an accuracy of 54.24% and Fl of 54.07%, relative to 45.7% and 46.5% for Brain-JEPA. The masked variants further improve performance, with MnemolDy--Mask-IR ACC, 54.55%F1), Despite the relatively challenging nature of the ADHD/TDC classification task, MnemoDyn when fine-tuned provides clear and reproducible advantage, validating its utility across clinical cohorts.
reaching the best scores (54.70%
On the NKIR dataset for sex classification, fine-tuned variants of MnemoDyn again yields substantial improvements over Brain-JEPA shown in Table While the baseline achieves 66.52% accuracy and 97% F1, MnemoDyn boosts performance to 87.58 57.52% for both metrics. The masked variant (88.37% ACC, 88.36% F1) offers additional increase. demonstrating the effectiveness of the masking strategy. Overall, the NKIR results show that MnemoDyn generalizes strongly across independent cohorts, providing state-of-the-art performance on demographic prediction tasks.
NKIR:
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Sex
Methods
ACC(%) f
F1(%)
Brain-JEPA
66.52 (0.27)
63.97 (0.40)
MnemoDyn
87.52 (0.49)
87.52 (0.48)
MnemoDyn-Mask
88.37 (0.45)
88.36 (0.45)
MaemoDDya-Maa--JEA
$7.70(0.2))
87.70 (0.20))
Table 9: Performance comparison on the NKIR dataset for sex classification. We report mean accuracy (ACC) and Fl-score (FF) with standard deviations in parentheses. Finetuned MnemoDyn significantly outperform the Brain-JEPA baseline.
Autism/ / TSC
Methods
FI(%) 1
MyemoDyn
60.32 (1.44)
59.26 (2.04)
MnemoDyn-Mask
58.93 (1.25)
58.57 (1.24)
Table 10: Classification performance the ABIDE dataset for Autism vs. TSC for fine-tuned MnemoDyn. The table reports mean accuracy (ACC) and Fl-score (FI) with standard deviations in parentheses, averaged across multiple runs.
NO/CI
Amyloid vve/
Methods
ACC(5E)
FI(%)
ACC(%)
FI(9) 7
BrainNetCNN
(3.18)) (3.50)
(2.00))
59.43 (1.14)
BrainGNN
(7.931)
71.42 (2.87)
(4.00)
62.61 (3.48)
BNT
(4.90)
(3.58)
62.00 (2.45)
59.53 (0.58)
BrainLM
75.79 (1.05)
85.66 (1.27)
67.00 (7.48)
68.82 (8.48)
Brain-JEPA
(1.05)
86.32 (0.54)
71,00 (4.90)
75.97 (3.93)
MncmoDyn-HCP-Mo
87.34 (2.1)
89.7 (2.2)
88.20 (1.09)
88.1 (1.23)
MnemoDyn-Hoe HC--HMc--MMMFRPE
89.87 (1.09)
89.04
93.87 (4.05)
93.48 (3.07)
Table 11: Performance of MnemoDyn pre-trained on HCP and fine-tuned ADNI tasks of NC/MCI diagnosis and Amyloid +ve/-ve classification. Results are reported as mean (standard deviation) for accuracy (ACC) and F1-score (F1). F1 is included account for class imbalance across cohorts. MnemoDyn variants substantially outperform prior baselines, highlighting the benefits of pretraining on HCP before transfer to clinical tasks.
On ABIDE dataset for Autism vs. (TSC) classification, we report results for fine-tuned variants of MnemoDyn. Due to reproducibility issues, we were unable to obtain reliable Brain-JEPA baselines on this dataset. Nevertheless, MnemoDyn achieves consistent performance, with the base model reaching 60.32% accuracy and 59.26% Fl, and the masked variant obtaining 58.93% accuracy and 58.57% Fl. While the margins are narrower compared to other datasets, these results underscore MnemoDyn's 's robustness highly heterogeneous clinical cohort.
ABIDE:
A.8 ZERO-SHOT GENERALIZATION TO SMALLER DATASETS
To further assess how MnemoDyn behaves in low-data regimes and to complement the main experi- mental results, conducted additional analyses examining its zero-shot transfer performance. These experiments evaluate whether the pre-trained model and simple downstream heads retain predictive or reconstruction capability when applied to substantially smaller datasets without any fine-tuning.
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Age
Scx
Neuroticism
Flanker
Methods
MSE 4
ACC (%) 1
FI (%) f
MSE.
MSE
BrainI.M
1.14 (0.22)
75.27 (1.24)
73.19 (1.12)
1.05 (0.12)
0.77 (0.11)
Brain-JEPA
1.02 (0.01)
79.17 (1.29)
76.29 (1.17)
0.99 (0.01)
1.28 (0.01)
MnemolDyn-HCP-Mane
0.90 (0.03)
80.90 (0.13)
80.70 (0.12)
0.90 (0.09)
0.58 (0.09)
MnemoDyn-HoC HCa-yyy--C--MMa----E-
0.90 (0.04)
80.98 (2.13)
80.63 (2.12)
0.90 (0.57)
0.60(0.06)
Table 12:
Performance of MnemoDyn pre-trained on HCP and fine-tuned external tasks from HCP-Aging, including age regression, sex classification, and trait prediction (Neuroticism, Flanker). Results are reported as mean (standard deviation) for MSE, accuracy (ACC). and Fl-score (F1). F1 is included for classification tasks to account for class imbalance. MnemoDyn variants achieve consistent improvements over prior baselines across both demographic and cognitive trait prediction.
We performed two analyses feasible within the rebuttal time frame. First, we trained simple downstream MLP heads on the larger Aiiing dataset and applicd them directly to the dataset collected as part of the Healthy Brain Network (HBN) study. For sex classification, the zero-shot performance reached an accuracy of 0.6393 and an Fl score of 0.6390, while for age prediction the MLP achieved an MSE of 0.851 (2.0((0022) indicating moderate transfer for categorical variables but limited transfer for age due to distributional differences.
Second, evaluated the representation capability of pre-trrined MnemoDynon small datasets by measuring reconstruction quality without any adaptation. A model pre-trained on UK Biobank achieved an 12 of 0.98 HBN and 0.96 on HCP-Aging, with corresponding MSEs of 7.89 10-8 and 4.52 x 10 respectively. These results show that MnemoDyn's learned temporal operators generalize extremely well small datasets. maintaining high reconstruction accuracy even in the absence of fine-tuning.
Overall, these findings demonstrate that the architectural design allows the model to retain and transfer substantial portion of its representational benefits even in zero-shot, low-data settings.
A.9 ABLATIONS
We pre-trained MnemoDyn on rs-MMRI data from the HCP dataset, which contains only 1000 subjects with sequence length 1200. Despite the modest scale of this dataset compared to conventional foundation model pretraining regimes, our operator learning formulation allows MyemoDyn to extract transferable dynamical representations that generalize strongly downstream settings. This highlights one of the key advantages of our approach: rather than relying on massive data curation, MnemoDyn leverages inductive biases from multi-resolution operator learning to capture the underlying structure of brain dynamics in a highly data- manner.
Table II reports results on ADNI, where we evaluate clinical tasks such as NC/MCI diagnosis and ve prediction. Fine-tuned variants of MyemoDyn substantially outperform wide range of prior baselines. particular, MnemoDyn-HHCPMnne Ma--MM-aak- JEPA achieves up to 89. 89.9% accuracy and 89.7% F1 on NC/MCI classification, and 93.9% accuracy and 93.5%F. F1 on amyloid prediction, representing sizable improvement over baselines. These results underscore the benefits of pretraining on HCP, even with limited sample size, before transfer to downstream clinical cohorts.
amyloid ve
We further assess transfer to external demographic and cognitive prediction tasks from HCP-Aging (Table[2). Here, MnemoDyn consistently surpasses prior methods age regression, sex classification, and trait prediction tasks (ncuroticism and flanker). Importantly, these gains are observed across both demographic and cognitive dimensions, illustrating the broad generalization capacity of MnemoDyn.
Taken together, these ablations highlight that MnemoDyn can be effectively pretrained on a relatively small dataset such HCP and still transfer with strong performance diverse downstream tasks. This data efficiency is a direct consequence of the operator learning setup, which allows the model to learn evolution rules over brain dynamics rather than memorizing dataset-specific patterns. As
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such, Myn offers a principled path toward building foundation models for neuroscience without requiring prohibitively large pretraining corpora.
ACKNOWLEDGMENTS
Partial support for this work came from a contract to UW-Madison under the DARPA Strengthen program. We thank Tammi Kral for suggestions regarding pre processinn steps in the initial phase of the project.
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Reviews:
[{"review_id": "6FxXjCbTg8", "reviewer": "Reviewer_oX9c", "summary": "This paper introduces MnemoDyn, a multiscale state-space model designed to model resting-state fMRI data. The model uses a wavelet basis to represent temporal dynamics and a structured, learnable transition matrix A to capture latent state evolution. The approach keeps the multidimensional structure of fMRI data and shows notable improvements in fine-tuning tasks compared to existing baselines.", "questions": "1.\tCan you include runtime and memory benchmarks to support the efficiency claims?\n2.\tCould you analyze the learned matrix A to show which frequencies or scales are most predictive?\n3.\tPlease report R² reconstruction results for HCP and UK Biobank, ideally alongside fine-tuning scores.\n4.\tCould you visualize or quantify the trade-off between pretraining difficulty and fine-tuning accuracy?\n5.\tHow sensitive is the model to the choice of wavelet basis or number of scales?\n\n\nSuggestions:\n•\tThe methods section could benefit from a short schematic showing how the wavelet decomposition and latent transition components interact.\n•\tConsider adding an ablation study (e.g., removing multiscale structure or low-rank decomposition).", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "•\tCreative use of multiscale state-space modeling for fMRI signals.\n•\tPreserves spatial correlations across brain regions rather than treating them independently.\n•\tDemonstrates consistent fine-tuning performance gains over strong baselines.\n•\tThe model seems more parameter-efficient than transformers, which is valuable for neuroimaging data", "weaknesses": "•\tThe claimed computational efficiency isn’t empirically supported—there are no runtime or scalability benchmarks.\n•\tMissing interpretability analysis of the learned transition matrix A (e.g., identifying key frequencies or scales).\n•\tTable 1 lacks R² reconstruction metrics for HCP and UK Biobank datasets, which would be a necessary metric for comparisons.\n•\tThe trade-off between pretraining effort and downstream performance is mentioned but not shown.\n•\tWriting could be tightened in the methods section for clarity.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "MmCupMS9HC", "reviewer": "Reviewer_Yupk", "summary": "The paper introduces a continuous-time latent dynamical model that learns an evolution operator over rs-fMRI trajectories, parameterized via multi-resolution wavelet kernels and implemented with pseudo-differential operators to induce sparsity and block-diagonal computation.​\n\nPretrained on ~40K rs-fMRI sequences and fine-tuned with lightweight heads, MnemoDyn improves reconstruction, clinical classification (ADNI), and demographic/trait prediction (UKB, HCP-Aging) versus other approaches, such as Brain-JEPA, BrainLM, and graph CNNs, while requiring less computing power.​", "questions": "- Figure 3 presents parcel reconstructions for unseen data, where the predicted signals show an almost perfect overlap with the measured fMRI time series. Since this is unseen data (ie, not seen during training), this raises concerns about how inference is performed with this model. Are these outputs generated by evolving the latent state from an initial condition (ie, first point of the dynamics)? Is this the result of solving equation 11? If the reconstruction indeed follows the ODE solution over time, it is surprising that the model can reproduce signals with noise-like structure, such as those shown for the UK Biobank example in Fig 3. More details on the inference procedure are necessary to clarify this result.\n\n- The authors motivate their model using a continuous-time ODE formulation. However, modeling brain dynamics as a first-order (Markovian) system may be restrictive, given the nonlocal and temporally dependent nature of neuronal interactions. Could the authors elaborate on why ODEs, which assume locality in time, were chosen over formulations that can capture non-Markovian dependencies, such as integral equation (IE) or delay-based models? Prior work has shown IE formulations can yield superior numerical accuracy even for Markovian dynamics [1, 2, 3]; therefore, additional justification for the ODE assumption would be valuable.\n\n- Since MnemoDyn is conceptually related to Fourier Neural Operator (FNO) and DeepONet—both of which learn functional mappings using spectral or integral representations—it would strengthen the work to include direct comparisons with these models. In particular, given that MnemoDyn operates in the wavelet domain (analogous to Fourier parameterization in FNO), a head-to-head evaluation would help quantify the benefits of the proposed multiresolution pseudo-differential operator design.\n\n- Tables 2 and 3 report MnemoDyn outperforming several transformer and graph-based baselines on clinical and demographic prediction tasks. Were all baseline models fine-tuned under the same conditions and on the same datasets as MnemoDyn? Additional details about training protocols, data splits, and hyperparameter parity are necessary to assess the fairness of these comparisons.\nThe paper refers to MnemoDyn as a “foundation model.” Could the authors clarify the specific criteria under which this designation applies? For instance:\n  - Does MnemoDyn show improved performance with scale (in model or data size)?\n  - Can its representations transfer effectively to other neuroimaging modalities or tasks beyond label prediction?\n  - How does it satisfy the general-purpose, reusable, and cross-domain characteristics typically associated with foundation models? \n\nRef: \n\n[1] Vladimir Rokhlin. Rapid solution of integral equations of classical potential theory. Journal of computational physics, 60(2):187–207, 1985.\n\n[2] Vladimir Rokhlin. Rapid solution of integral equations of scattering theory in two dimensions. Journal of Computational Physics, 86(2):414–439, 1990.\n\n[3] Zappala, Emanuele, Antonio Henrique de Oliveira Fonseca, Josue Ortega Caro, Andrew Henry Moberly, Michael James Higley, Jessica Cardin, and David van Dijk. \"Learning integral operators via neural integral equations.\" Nature Machine Intelligence 6, no. 9 (2024): 1046-1062.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The paper proposes an alternative to the tokenization/positional heuristics problems, which are common to transformer-based methods.\n\n- Efficient multiscale design: wavelet-domain pseudo-differential parameterization and CP tensor factorization exploit sparsity and low-rank structure, enabling single-GPU pretraining and potentially allowing scaling to longer sequences than conventional transformer-based methods can handle.​\n\n- Broad and consistent gains: large improvements on ADNI NC/MCI and amyloid classification, and better age/sex/trait prediction on HCP-Aging and other cohorts (HBN, ADHD-200, NKIR), indicating robust transfer across sites/protocols.​", "weaknesses": "- Operator interpretability is under-explored: the paper motivates pseudo-differential structure and multiscale kernels but provides limited analysis of learned symbols/kernels or neurophysiological correlates of the operator.​\n\n- Pretraining objectives comparison is shallow: masking and JEPA-style training are included, but ablations isolating what aspects of the operator parameterization versus objective drive gains are not fully disentangled.​\n\n- The figures in the paper do not help with clarification regarding model structure, training and inference.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XQ2JnO3VX8", "reviewer": "Reviewer_sskM", "summary": "The paper MnemoDyn: Learning Resting-State Dynamics from 40K fMRI Sequences introduces MnemoDyn, a foundation model for resting-state fMRI that replaces attention mechanisms with operator-based dynamical system modeling. Instead of tokenized sequence learning, MnemoDyn learns multi-resolution temporal operators using wavelet parameterization and pseudo-differential kernels to efficiently capture multiscale neural dynamics. The architecture offers computational efficiency and scalability to long sequences, achieving strong reconstruction and predictive performance across datasets such as UK Biobank, HCP, and ADNI. Fine-tuned versions of MnemoDyn show improved accuracy and robustness on downstream tasks including age, sex, and disease classification. Overall, the paper argues for a biologically grounded, operator-based alternative to transformer models for neuroimaging, highlighting interpretability and compute efficiency but offering only moderate conceptual novelty and limited theoretical validation.", "questions": "1. How sensitive is MnemoDyn to the choice of wavelet basis and parameterization depth?\n\n2. Could the operator-based approach generalize effectively to multimodal or task-based fMRI?\n\n3. Does the model yield interpretable components that map to known neural circuits or physiological rhythms?\n\n4. How does MnemoDyn’s performance scale with smaller datasets without fine-tuning?\n\n5. Would the model retain benefits under voxel-level resolution rather than parcellated inputs?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Proposes an elegant operator-based formulation for modeling brain dynamics, avoiding attention mechanisms.\n2. Achieves state-of-the-art results on multiple large and small-scale fMRI datasets with high compute efficiency.\n3. Presents a comprehensive evaluation pipeline, supporting claims of generalization and scalability.\n4. Aligns with neuroscientific priors regarding multiscale temporal structure, enhancing biological plausibility.", "weaknesses": "1. Conceptual novelty is modest; builds on existing operator learning and neural ODE frameworks without substantial innovation.\n\n2. The connection to neuroscientific principles is largely rhetorical, lacking physiological validation or interpretability analysis.\n\n3. The paper does not sufficiently contrast MnemoDyn against simpler baselines (e.g., recurrent or convolutional models) to justify complexity.\n\n4. Results, though impressive numerically, may be inflated by dataset overlap and lack of external reproducibility tests.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)