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arxiv: 2605.18085 · v1 · pith:J2FMNNV3new · submitted 2026-05-18 · 📡 eess.SP

PRiSE-EEG: A Prior-Guided Foundation Model with Depth-Stratified Experts for Cross-Paradigm EEG Representation Learning

Wei Xiong , Jiangtong Li , Kun Zhu , Jie Li This is my paper

Pith reviewed 2026-05-20 01:01 UTC · model grok-4.3

classification 📡 eess.SP
keywords EEG foundation modelcross-paradigm representation learningmixture of expertsCKA similarityprior-guided patchingdepth-stratified expertstransformerbrain signals
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The pith

PRiSE-EEG learns reusable EEG representations by patching signals with cortical priors and allocating experts according to layer-wise CKA sharedness.

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

The paper seeks to build a foundation model that works across different EEG recording paradigms without separate fine-tuning protocols. It starts by showing that dense Transformers face optimization conflicts between paradigms and that similarity across paradigms drops with depth. This motivates PRiSE-EEG, which creates continuous multi-channel patches from static priors and short-time interactions, then routes through shared and specialized experts in a depth-dependent way using a sigmoid function on CKA values. The result is stronger performance on twelve public benchmarks when protocols are matched, outperforming both standard Transformers and simpler MoE variants.

Core claim

By analyzing gradients and CKA similarities, the authors establish that shallow layers capture shared EEG features while deeper layers specialize. They then design PRiSE-EEG to form patches using weak static cortical and network priors along with dynamic channel interactions, and to place shared and specialized experts in MoE blocks via a sigmoid mapping of layer-wise CKA sharedness. This yields strong cross-paradigm results on 12 benchmarks.

What carries the argument

CKA-calibrated Depth-Stratified Experts, which allocate shared versus specialized experts across MoE Transformer blocks based on a sigmoid function of layer-wise CKA similarity.

If this is right

  • Common EEG regularities are preserved in early blocks while later blocks gain specialized capacity.
  • Optimization conflicts among EEG paradigms are reduced through the depth-dependent expert allocation.
  • Performance improves on heterogeneous benchmarks under consistent evaluation protocols.
  • Compact models can outperform dense Transformers by using CKA-derived routing instead of uniform or manual expert ratios.

Where Pith is reading between the lines

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

  • Similar CKA-based routing might reduce conflicts in other heterogeneous signal domains such as multi-site recordings.
  • Checking whether the depth transition stays stable when more datasets are added would test how general the allocation rule is.
  • Replacing the fixed sigmoid with a learned router could further adapt the sharing pattern during training.

Load-bearing premise

The depth-wise pattern of decreasing cross-paradigm similarity seen in CKA analysis on the six training datasets will hold for other EEG data and justify using a fixed sigmoid-based expert split.

What would settle it

A new set of EEG benchmarks where the CKA sharedness does not decrease consistently with depth, or where the PRiSE-EEG model fails to improve over dense baselines, would challenge the central design choice.

Figures

Figures reproduced from arXiv: 2605.18085 by Jiangtong Li, Jie Li, Kun Zhu, Wei Xiong.

Figure 1
Figure 1. Figure 1: Pairwise cosine similarity of downstream fine-tuning gradients across datasets for LaBraM [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The architecture of PRiSE-EEG framework. The Prior-Guided Continuous Tokenizer [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ablation Study. We study the effect of the approaches for three modules in Prior-Guided [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: CKA analysis and shared expert allocation. The left heatmap shows layer-wise CKA [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Gradient subspace affinity (rank=5) and similarity of routed expert distribution among [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Ablation Study of attention bias strength for static path on TUSL, Workload and SEED-V [PITH_FULL_IMAGE:figures/full_fig_p026_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Ablation Study of the stage that the neural prior has been introduced on TUSL, SEED-V, [PITH_FULL_IMAGE:figures/full_fig_p026_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Grad-CAM visualization of PRiSE-EEG on SEED showing the region of model interest for [PITH_FULL_IMAGE:figures/full_fig_p029_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Grad-CAM visualization of our PRiSE-EEG on ADFTD dataset showing the region of [PITH_FULL_IMAGE:figures/full_fig_p030_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Grad-CAM visualization of PRiSE-EEG on Workload dataset showing the region of model [PITH_FULL_IMAGE:figures/full_fig_p030_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Grad-CAM visualization of PRiSE-EEG on Workload dataset showing the region of model [PITH_FULL_IMAGE:figures/full_fig_p031_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: t-SNE visualizations of feature embeddings reduced to 40 dimensions by PCA on different [PITH_FULL_IMAGE:figures/full_fig_p031_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Scaling behavior with model size N and a) Lp; b) HMC balanced accuracy; c) SEED balanced accuracy. Axes are all on a logarithmic scale. 0.005 0.014 0.040 0.12 0.34 1.0 Training Data Size (ratio) 0.6 0.7 0.8 0.9 1.0 1.1 Pretrain Loss Pretrain Loss 0.005 0.014 0.040 0.12 0.34 1.0 Training Data Size (ratio) 0.66 0.68 0.70 0.72 0.74 0.76 Test Balanced Accuracy SEED (B-Acc) 0.005 0.014 0.040 0.12 0.34 1.0 Trai… view at source ↗
Figure 14
Figure 14. Figure 14: Scaling behavior with data partition P and a) Lp; b) SEED balanced accuracy; c) HMC balanced accuracy. Axes are all on a logarithmic scale. of the test Lp with model size (N) is: Lp = −0.034 * ln(N) + 0.786 , where R2 is 0.974. The results on the SEED dataset show that the scaling law of the test balanced accuracy with model size (N) is: BAcc = 0.010 * ln(N) + 0.699, where R2 is 0.940. The results on the … view at source ↗
read the original abstract

EEG foundation models aim to learn reusable representations across heterogeneous paradigms, yet existing approaches often use uniform adaptation mechanisms and are typically reported under separate downstream fine-tuning protocols. In this work, we first analyze dense EEG Transformers from two complementary perspectives. Gradient similarity across six downstream datasets reveals substantial optimization conflicts among EEG paradigms, while CKA analysis on mixed-paradigm batches shows a consistent depth-wise transition: shallow layers preserve stronger cross-paradigm similarity, whereas deeper layers become increasingly specialized. Motivated by these findings, we propose \textbf{PRiSE-EEG}, a prior-guided EEG foundation model with CKA-calibrated Depth-Stratified Experts. PRiSE-EEG forms continuous multi-channel EEG patches using weak static cortical and network priors and dynamic short-time channel interactions, then allocates shared and specialized experts across MoE Transformer blocks according to a sigmoid mapping from layer-wise CKA sharedness. This design preserves common EEG regularities in early blocks while assigning more specialized capacity to later task-specific transformations. Experiments on 12 public EEG benchmarks show strong cross-paradigm performance under matched protocols. Compact ablations further show that CKA-derived expert allocation improves over dense Transformers, uniform MoE, and manually fixed shared-specific expert ratios.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The paper proposes PRiSE-EEG, a foundation model for cross-paradigm EEG representation learning. It constructs continuous multi-channel EEG patches from weak static cortical/network priors combined with dynamic short-time channel interactions, then deploys a MoE Transformer with depth-stratified experts whose shared-versus-specialized allocation is set by a sigmoid mapping of layer-wise CKA similarity. The design is motivated by gradient-similarity analysis revealing optimization conflicts across paradigms and by CKA analysis on mixed batches from six datasets showing a consistent shallow-to-deep transition from shared to specialized representations. Experiments on 12 public EEG benchmarks under matched protocols, together with compact ablations, are reported to demonstrate gains over dense Transformers and uniform MoE baselines.

Significance. If the empirical improvements are shown to be statistically robust and the CKA-derived allocation rule generalizes, the work would supply a concrete, data-driven mechanism for balancing shared and specialized capacity inside EEG foundation models, directly addressing the paradigm-heterogeneity problem that uniform adaptation strategies have left unresolved.

major comments (2)
  1. [Motivation and Method (CKA analysis and expert allocation)] The sigmoid expert-allocation rule is calibrated exclusively on layer-wise CKA values obtained from mixed-paradigm batches drawn from the same six datasets used for the gradient and CKA analysis. No verification is provided that the observed depth-wise sharedness transition (and therefore the same sigmoid parameters) remains near-optimal when the paradigm mix is expanded to the remaining six benchmarks or altered in other ways; if the transition point or slope shifts, the allocation becomes an arbitrary hyperparameter and the performance advantage over uniform MoE cannot be confidently attributed to the CKA calibration.
  2. [Experiments and Ablations] The central performance claims rest on results from 12 benchmarks and compact ablations that are presented without error bars, without statistical significance tests, and without complete training details or hyperparameter specifications. This absence prevents assessment of whether the reported gains are reliable or could be explained by other design choices such as the prior-guided patch construction.
minor comments (1)
  1. [Method] Notation for the sigmoid mapping parameters and the precise definition of 'sharedness' used to compute CKA should be introduced earlier and used consistently throughout the method and ablation sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. We address each major comment below and outline the revisions we will make to improve the manuscript.

read point-by-point responses

  1. Referee: The sigmoid expert-allocation rule is calibrated exclusively on layer-wise CKA values obtained from mixed-paradigm batches drawn from the same six datasets used for the gradient and CKA analysis. No verification is provided that the observed depth-wise sharedness transition (and therefore the same sigmoid parameters) remains near-optimal when the paradigm mix is expanded to the remaining six benchmarks or altered in other ways; if the transition point or slope shifts, the allocation becomes an arbitrary hyperparameter and the performance advantage over uniform MoE cannot be confidently attributed to the CKA calibration.

    Authors: We appreciate this observation on the scope of the CKA calibration. The six datasets selected for the gradient and CKA analyses represent a diverse collection of EEG paradigms (motor imagery, P300, SSVEP, and others) that capture the primary sources of heterogeneity present across the full 12 benchmarks. The consistent shallow-to-deep transition in cross-paradigm similarity appears to reflect a general property of how dense Transformers process mixed EEG data rather than a narrow dataset artifact. To directly verify robustness, we will add CKA analyses on mixed batches that include the remaining six benchmarks, recompute the sigmoid parameters, and report the resulting performance deltas versus uniform MoE in the revised manuscript. This will strengthen the claim that the allocation rule is data-driven and generalizable. revision: yes

  2. Referee: The central performance claims rest on results from 12 benchmarks and compact ablations that are presented without error bars, without statistical significance tests, and without complete training details or hyperparameter specifications. This absence prevents assessment of whether the reported gains are reliable or could be explained by other design choices such as the prior-guided patch construction.

    Authors: We agree that the current experimental reporting lacks the statistical detail and transparency needed for rigorous evaluation. In the revised manuscript we will include error bars (standard deviation over three independent runs with different seeds) for all main results and ablations. We will add paired statistical significance tests (t-tests or Wilcoxon signed-rank) comparing PRiSE-EEG against the dense Transformer and uniform MoE baselines. A new appendix will provide complete hyperparameter tables, optimizer settings, learning-rate schedules, batch sizes, and hardware specifications for every experiment. These additions will allow readers to assess whether the observed gains are robust and attributable to the CKA-calibrated depth-stratified experts. revision: yes

Circularity Check

1 steps flagged

CKA-derived sigmoid expert allocation is a data-informed design choice but does not reduce the central claim by construction

specific steps
  1. fitted input called prediction [Abstract (CKA analysis and PRiSE-EEG proposal)]
    "Gradient similarity across six downstream datasets reveals substantial optimization conflicts among EEG paradigms, while CKA analysis on mixed-paradigm batches shows a consistent depth-wise transition: shallow layers preserve stronger cross-paradigm similarity, whereas deeper layers become increasingly specialized. Motivated by these findings, we propose PRiSE-EEG, a prior-guided EEG foundation model with CKA-calibrated Depth-Stratified Experts. ... allocates shared and specialized experts across MoE Transformer blocks according to a sigmoid mapping from layer-wise CKA sharedness."

    The sigmoid mapping is calibrated directly from the observed CKA transition on the same six datasets used for gradient/CKA analysis and downstream training. While not a direct fit of accuracy, the expert allocation rule is statistically informed by the input data's layer-wise similarity statistics, so performance gains over uniform MoE baselines are partly attributable to this post-observation design choice rather than an independent prior.

full rationale

The paper computes CKA on held-out mixed-paradigm batches from six datasets solely to observe the depth-wise sharedness pattern and then selects a sigmoid mapping to allocate experts. This is a modest data-dependent hyperparameter choice rather than fitting the final performance metric or redefining the result in terms of itself. The core contributions (continuous patch formation with priors, MoE blocks, and cross-paradigm evaluation on 12 benchmarks) retain independent content, so the derivation chain is largely self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The design rests on two empirical observations (gradient conflicts across paradigms and depth-wise CKA transition) that are treated as stable properties of EEG Transformers; the sigmoid mapping introduces at least one tunable functional form whose parameters are not derived from first principles.

free parameters (1)
  • sigmoid mapping parameters
    Controls how CKA sharedness values are converted into the proportion of shared versus specialized experts at each depth; chosen after inspecting CKA curves on the analysis datasets.
axioms (2)
  • domain assumption Gradient similarity across six downstream datasets reveals substantial optimization conflicts among EEG paradigms
    Invoked in the opening analysis paragraph to justify the need for depth-stratified rather than uniform adaptation.
  • domain assumption CKA analysis on mixed-paradigm batches shows a consistent depth-wise transition from shared to specialized representations
    Used to motivate the sigmoid allocation rule; treated as a general property rather than dataset-specific.

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