Riemannian High-Order Pooling for Brain Foundation Models
Authors: Chen Hu
Ziheng Chen
Rui Wang
Yefeng Zheng
Nicu Sebe
Venue: ICLR 2026 Poster (2026)
Keywords: EEG
brain-computer interface
representation learning
manifold learning
Primary area: applications to neuroscience & cognitive science
TL;DR: A Riemannian high-order pooling classification head for EEG foundation model

Abstract: Electroencephalography (EEG) is a noninvasive technique for measuring brain electrical activity that supports a wide range of brain-computer interaction applications. Motivated by the breakthroughs of Large Language Models (LLMs), recent efforts have begun to explore Large EEG foundation Models trained on broad unlabeled corpora. However, most advances focus on improving the backbone while neglecting the classification head. Existing models often rely on a single class token, underutilizing the spatiotemporal structure and second-order statistics that are crucial for EEG decoding. We propose Riemannian High Order Pooling (RHOP), a plug-and-play module that injects principled Riemannian statistics into the classifier. RHOP maps each token to a quotient Gaussian jointly encoding mean and second-order information, yielding scale-invariant descriptors. Tokens are then aggregated by estimating a Riemannian Gaussian on the SPD manifold, where the Fréchet mean and covariance are embedded into an SPD descriptor. The resulting normalized vector is fused with the class token for prediction. RHOP is backbone-agnostic and integrates with modern EEG foundation models, \textit{e.g.}, BIOT and LaBraM. Across diverse EEG benchmarks, it improves accuracy and efficiency under full fine-tuning, linear probing, and from-scratch training settings. The code is publicly available at github.com/ChenHu-ML/RHOP.

Published as a conference paper at ICLR 2026
RIEMANNIAN HIGH-ORDER POOLING FOR BRAIN FOUNDATION MODELS
Chen Hu Zihenng ; Rui Wang"! Yefeng , Nicu Sebe
School of Artificial Intelligence and Computer Science, Jiangnan University
2 Medical Artificial Intelligence Lab, Westlake University
3 Department of Information Engineering and Computer Science, University of Trento
ABSTRACT
Electroeneephalogrpphy (EEG) is a noninvasive technique for measuring brain electrical activity that supports wide range of brain-computer interaction applica- tions. Motivated by the breakthroughs of Large Language Models (LLMs), recent efforts have begun to explore Large EEG foundation Models trained on broad un- labeled corpora. However, most advances focus improving the backbone while neglecting the classification head. Existing models often rely on a single class to- ken, underutilizing the spatiotemporal structure and second-order statistics that are crucial for EEG decoding. We propose Riemannian High Order Pooling (RHOP), plug-and-play module that injects principled Riemannian statisties into the clas- sifier. RHOP maps each token to quotient Gaussian jointly encoding mean and second-order information, yielding scale-invariant descriptors. Tokens are then aggregated by estimating a Riemannian Gaussian on the SPD manifold, where the Fréchet mean and covariance are embedded into SPD descriptor. The re- sulting normalized vector is fused with the class token for prediction. RHOP is backbone-agnostic and integrates with modern EEG foundation models, e.g. BIOT and LaBraM. Across diverse EEG benchmarks, it improves accuracy and efficiency under full fine-tuning, linear probing, and from- nom-scraachh training set- tings. The code is publicly available at hwwpeeeooo/cheoLLL//CC
INTRODUCTION
Eleetroenncephallgraphy (EEG), which records cortical electrical potentials with millisecond preci- sion, provides dynamic insights into brain function. It has enabled advancements in seizure detec-
tion (Ahmad et al. 2022 Cherian Kanaga 2022). sleep staging (Aboalayon et al. 2016 Phan
& Mikkelsen 2022, Zhou et al. (025), motor imagery (Altaheri et al., [023] Ju & Guan, 2023
Roy et al. ),, abnormality screening (Roy et al. 2019), emotion analysis (Suhaimi et 2020
Biesmans et al. 2016 Dadebayev et al. 2022), and auditory attention (Biesmans et al. 2016).
How-
ever, EEG's s practical deployment remains challenging due to issues like low signal-to-noie ratio,
inter-subject variability, and task meskddepnddent non-stationarity (Hine et al. 2017).
Early EEG decoding pipelines relied on traditional machine-learning methods (Lotte et al.) 2007). With the rise of deep learning (LeCun et al.) 2015 Zhao et al. 2024; Liu et al. 2024 Gao et al. 2025b Hu et al. 2025b), classic architectures such Convolutional Neural Networks (CNNs) (Lawhern et al. 2018) and Long Short-Tera Memory (LSTM) networks (Phan et al. 2019) adapted to EEG tasks, followed by transformer backbones (Peh al. (022b). In parallel, ge- ometric learning approaches have gained traction in EEG decoding tasks, most notably those lever- aging Riemannian geometry. The power and spatial distribution of multi-channel EEG segments can be encoded into covariance matrices, which are symmetric positive definite (SPD) matrices. By operating on the SPD manifold, Riemannian methods exploit metrics that are robust outliers and noise (Congedo et al. 2017), leading to broad success in practice (Pan et al.) 2022 Kobler al. 2022, Ju et al. 2024 Li et al. 2025). More recently, inspired by the rise of self-supervision and foundation models in vision and language, research has followed this paradigm (Devlin et al.
"Equal contribution.
1 "ooresponniig author; es wr@ wr@@jangnan.cdu.com

---

Published as a conference paper at ICLR 2026
2018 Radford et al. 2021: Bommasani al. 2021). EEG foundation models are pretrained on large unlabeled corpora with contrastive learning, masked reconstruction, or self relf-prediction and then transferred to diverse downstream tasks (Yang et al. 2023 Jiang et al. 2024 2025).
Despite these advances, many foundation models still apply Global Average Pooling (GAP) or con- catenate tokens before the final classification, which discards valuable second-order information and underuses global spatiotemporal dependencies. Intuitively, EEG features exhibit dependencies in- herently across temporal and channel dimensions (Song et al. 20 Wang al. (025a). Global Covariance Pooling (GCP) replaces GAP by summarizing activations with a covariance descrip- tor (Lin et al. 2015 Wang et al. 2017). partially closing this gap. However, typical GCP compresses all tokens into single covariance matrix, thereby overlooking the intrinsic spatiotemporal structure of EEG features (Lin et al. 2015 Li et al. 2017b) 2018). This raises a central question for applying EEG foundation models to downstream decoding: Can we design global pooling head that is both statistics-aware and geometry- aware while respecting the underlying spatiotemporal structure?
We answer this question with Riemannian High-Order Pooling (RHOP), plug-and-play module for EEG foundation backbones and, to our knowledge, the first geometric pooling head tailored for this setting. RHOP motivated by two empirical properties of EEG features: significant spa- tiotemporal structure and pervasive scale variation across temporal segments. First, we introduce quotient- embedding that normalizes per-token covariances to correlation form and jointly encodes first- and second-orde statistics, removing temporal scale discrepancies while preserving dependency structure (Lovrić et al. 2000a Thanwerdas & Pennec 2022). Second, we aggregate in- formation across tokens by estimating a Riemannian Gaussian on SPD manifolds and embedding it into an SPD descriptor, efficiently capturing high-order interactions (Pennec 2006). Finally, a sparse ieverse-covarinne layer emphasizes partial correlations and yields compact vector, which is fused with the classification (CLS) token for prediction (Rahman et al. 2023). RHOP is architecture- agnostic and can be attached modern EEG backbones such as BIOT and LaBraM (Yang al.) 2023 Jiang et al. 2024). RHOP bridges EEG foundation models with Riemannian statistics by em- bedding token-level representations into SPD manifolds and preserving their spatiotemporal infor- mation and high-order dependencies in a pooling head. In summary, our contributions are threefold:
Quotient-Gaussin embedding. A scale-invariant embedding that transforms per-token co- variances into correlation form and jointly encodes first- and second-order statistics, addressing variance differences across temporal segments.
Riemannian High-Order Pooling. A geometry-aware pooling head that preserves token- level spatiotemporal structure and captures high-order interactions via a Riemannian Gaussian- embedded SPD descriptor.
Comprehensive empirical validation. RHOP delivers consistent gains and robust generaliza- tion across EEG decoding tasks under state-of-the-art EEG foundation backbones (BIOT and LaBraM) and three training regimes (full fine-tuning, linear probing, and training from scratch).
2
RELATED WORKS
SPD sanifold-based EEG decoding. Methods that operate on the SPD manifold achieve strong EEG decoding by respecting covariance geometry and improving robustness across subjects (Con-) gedo al. 2017 Ju et al. 2025). For example, |an et al. (2022; Wang al. (2025b) built manifold attention directly on SPD manifolds and captures spatiotemporal dependencies, outperforming deep baselines. SPDDSMBN (Kobler et al. 2022) learns fomain-invariann tangent-space mappings for unsupervised adaptation with an interpretable normalization scheme. DGCCA (Ju et al., 2024) introduces geodesic correlation with an SPD latent space align paired covariance modalities. SPDIM (Liet al. 2025) addresses source-free adaptation with conditional and label shift through an SPD-constrained parameterization. Taken together, these works show that geometry-aware learning on SPD manifolds is powerful and motivate pairing such geometric bias with large-scale pretraining.
Brain foundation models. Foundation models are large self-superviser systems trained on broad data and adapted to many tasks via fine-tuning (Bommasani et al. 2021). with BERT (Devlin et al.) 2018), CLIP (Radford et al. 2021), and GPT-4 (OpenAl, 2023) This paradigm is extending to brain signals. Recent EEG studies pretrain with contrastive learning. masked reconstruction, or self- prediction to learn transferable representations (Banville et al. [022 Kostas et al. 2021 Chien et al.) 2022 Wang et al. 2023) Zhang et al.) 2023 Mohammadi Foumani et al. 2024). BIOT learns generic
biosignal representations for joint pretraining and cross-dataset transfer (Yngg et al. 2023). LaBraM
2

---

Published as a conference paper at ICLR 2026
predicts masked neural tokens for general EEG features (Jiang et al. 2024). CBraMod decouples spatial and temporal modeling with a criss-cooss transformer and masked reconstruction for strong cross-dataset generalization (Wang al. 2025a and MeuroLM tokenizes EEG signals and uses an L.M with multi-channel autoregression and instruction tuning to unify diverse tasks (Jiang et al.) Despite progress, many backbones compress EEG features into a single CLS token catenate tokens before the final classification, leaving the global spatiotemporal structure underused, which motivates our geometry-aware high-order pooling head.
2025).
Gaussian embedding. Gaussian embedding offers geometric route to compare distributions. The Fisher-Rao metric formalizes information geometry (Rao) 1945), but closed-form geodesics are challenging for multivariate Gaussians. A practical remedy identifies each Gaussian with an SPD) matrix by viewing the Gaussian family as a Riemannian symmetric space, which enables affine- invariant tools for learning (Lovrić et al., 2000a| Pennec 2006). Alternative lines embed Gaussians
into the Siegel domain to define distances (Calvo & Oller 1990). or relate Gaussians to affine matrix subspaces (Gong al., 2009). Bog-Euclidean mappings linearize SPD structure and yield efficient Gaussian descriptors for vision (Arsigny et al.] 2005a Li et al.) 2017a). Deep architectures have adopted these ideas, for example, a global Gaussian layer that maps images to SPD features (Wang er al.)) 2017) and a Lie-group embedding of Riemannian Gaussians for sets of SPD matrices (Nguyen 2021 This geometric toolbox naturally connects to second-order pooling.
Global covariance pooling. GCP replaces global average pooling with second-order covariance descriptors (Lin et al.) 2015 Wang et al. 2017). which can be viewed as modeling feature activa- tions with Gaussian statistics. Early works mainly focused on numerical stabilization of covariance matrices through matrix logarithm backpropagation (Ionescu et al. 2015), matrix power normaliza- tion such as MPN-COV (Li et al. (017b), and iterative matrix square root as iSQRT-COV (Li et al. 2018). Subsequent methods improved conditioning and scalability, introduced graph-aware formulations (Rahman et al., 2020; Zhu et al., 2024), and enhanced discriminability via sparse inverse covariance estimation (SICE) (Rahman et al. 2023). More recently, matrix functions in GCP have been interpreted from a Riemannian perspective, relating covariance transformations to non-Euclidean classifiers (Chen et al., 2024cc 2025). Despite these advances, standard GCP on EEG flattens all spatiotemporal tokens into a single feature dimension before covariance estima- tion, thereby overlooking intrinsic temporal structure. This limitation motivates Riemannian high-order pooling module.
3 PRELIMINARIES
This section provides a brief overview of the foundations of SPD geometry and the concept of Fréchet Mean (FM). For detailed discussions, please refer to Pennec 2006 Arsigny et al. (2005b).
SPD manifold. The space of x n SPD matrices denoted S (P E R P
PT, P > 0}. It forms a Riemannian manifold when endowed with the Affine-Invarinn Metric (AIM) [Pennee 2006). For two points P, Q S, the AIM distance defined as
dAIM P. Q) || log P #*QP=t)]l=
(1)
where || || is the Frobenius norm and log(.) denotes the matrix logarithm. The associated expo- nential and logarithm maps are given by
(S) pt exp t
Se SETS
(2)
Logp(Q) = p
(P P 1) Q st
(3)
where exp(-) denotes the matrix exponential, and S is the tangent space at P.
Fréchet Mean. Given set of points [P:).N C M, the FM is the point S that minimizes the average sum of squared distances all points. The FM (Karcher 1977b) defined as
FM((P.)) arg min SEM
Σ s),,
(4)
N
where d(P,, S) is the distance between them. The FM is locally unique on general manifolds Afsari
2011]. In the case of (S, dAIM), it is globally well-defined and unique (Chakraborty et al. 2022
3

---

Published as a conference paper at ICLR 2026
Lincar
Lievec
Classifier
Classification token
EEG Foundation Model
S+,1
T+k
Ri Siemannnian Gaussian Embedding
Segment loken
Quotient QuotientGGaxiin Gaussian Embedding
ISICE
y
(Y 1nn=1
Figure 1: Overview of our RHOP framework. The EEG backbone outputs CLS token and token- wise features. Each token transformed into quotient Gaussian and embedded as Yn E S on SPD manifold. The set {Y,) is then aggregated into Riemannian Gaussian, whose FM ym and covariance are jointly embedded into SPD descriptor G. Finally, iSICE + utvec block produces a sparse precision vector, which is fused with the CLS branch for classification.
4 RIEMANNIAN HIGH-ORDER POOLING
In this section, we introduce Riemannian High-order Pooling (RHOP). plug- aoug-and-pll and--lay geometric pooling head for EEG foundation models. The overall RHOP framework consists of three parts: quotient Gaussian embedding, Riemannian Gaussian embedding, and sparse inverse covariance estimation (iSICE) module (Rahman et al. 2023).
4.1 QUOTIENT GAUSSIAN EMBEDDING
Let (E, μ)) (n) denote Gaussian with covariance E and mean μ. Previous methods often used raw covariance matrices as EEG descriptors (Pan et al. 2022 Li et al. 2025), capturing second- order temporal dependencies but highly sensitive to scale variations. Two tokens with similar tem- poral dynamics may yield substantially different covariance matrices if their amplitudes differ (Hu) al. 2025a). To address this, introduce quotient Gaussian distributions, which normalize tem- poral covariances to eliminate scale dependence. This ensures that the representation focuses on correlation rather than raw magnitudes, thereby providing a celee-nnvrriant descriptor of temporal dynamics.
Definition 4.1 (Quotient Gaussian Distributions). Let (E, E (M)) be Gaussian distribution.
The Quotient Gaussian distribution QN(n) is defined as
@N(n) ( ((n) (n)
[>, p4] = (DD HDD +, ()) D E Diag (m) Diag*(n)
(5)
For the quotient Gaussian QN(n), each element is an equivalence class of Gaussians [Σ, μr] sharing the same mean and whose covariances differ only by positive diagonal scalings. Within each class, the canonical representative C' = diagg(E) - EdiaggEE)= is exactly the correlation matrix, which invariant to scaling. We thus denote each quotient element by (C, p). where C' is the normalized covariance, ie., correlation matrix. Then, to facilitate end-to-end optimization,
embed the
quotient Gaussian into SPD matrices as shown Thm. 4.2 (see App-[[for the proof).
Theorem 4.2 (Quotient Gaussian Embedding Let S n+tk
T be the space of SPD (n + k) x (n + k))
matrices with determinant 1. quotient Gaussian (C, (1) E QN(m) can be identified as
[ + kppp
(e( Is
(det C*) n-
(K)T
E St1
(6)
where Iş is the k x l identity, and y! repeats μ across l identical columns.
This embedding maps quotient Gaussians into the SPD manifold, enabling the joint representation of mean and normalized covariance within a unified form. Following Nguyen (20T): Lovrič et al. 20000)), endow this space with the AIM introduced in Sec.
4

---

Published as a conference paper at ICLR 2026
Algorithm 1: RHOP over SPD manifolds
Input: BEG features X E RXTxN from fo: CLS token
Output: Class probabilities p
for n <- 1 N do
Compute temporal statisties (un, En) across channels;
C, diag(2i,,) -1, (2..) -1/2;
Yn + quotient- quotient-Gaussian Gaussian embedding via Eq.
end
ym
<- FM((Y
y <- covariance as in Eq. 12
G embed (Y )²) using Eq. 9
g Utve ASICE):
p softmax [[v( g]));
return p;
4.2 RIEMANNIAN GAUSSIAN EMBEDDING
Motivated by Euclidean covariance pooling, we extend first- and second-order statistics on St via Riemannian Gaussians. Given / E S the FM (Fréchet 1948) is given as
N d(Y,
pm = FM((P.) arg min
YESt
It can be computed via the Karcher flow (Karcher 1977a), which iteratively maps P. to T SpSt calculates the mean the tangent space, and maps back onto S, until convergence (Moakher) 2005). Due to the computational cost of FM, we follow the previous work (Brooks et al. [219]] et al. 2024b) and set the number iterations to one. The implementation steps are provided App. F
where dana(..)) is the AIM distance defined in Eq.
Similarly, given FM Pm, the covariance of {P.) E S is defined as
Σ fo pLog (P.)) fo (P.))((P.))
(8)
where fe(.) vectorizes the lower-triangular entries of a symmetric matrix with off-diagonal terms scaled by v2 [Penee et al. 2006). Then, Riemannian Gaussian is parameterized by the pair (Pme po) E S S.... As shown by Nguyen (2021), this pair lies on a product SPD manifold that forms Lie group, and the following block-matrix construction provides a ttw-ggouu--isooropp embedding that preserves its algebraic and geometric structure. Let p = LL denote the Cholesky decomposition. The embedding is formulated
L
Opixk]] I
(pm Po)
(Pm))
Shitke
where IN is a k' x k identity matrix and 0w' is zero block. Here is chosen ; fu o log, with lPg(P) (og(Z)) representing the matrix logarithm by eigenvalue decomposition of P.
4.3 THE OVERALL FRAMEWORK OF RIEMANNIAN HIGH-ORDER POOLING
In this section, we detail the whole framework of RHOP. An EEG foundation backbone So (e.g., BIOT or LaBraM) first extracts spatiotemporal features X E RDxTxN where /) is the number of channels, T the number of temporal segments, and N the token length. For convenience we permute to X E NXTXDD We then compute temporal first- and second-order statistics for each token n,
1 D
1 D
Un I
X ai ERT. Σ, = D D- Σ
(X 1z)) (X mm)) E TXXT
(10)
To ensure that Σ,, is an SPD matrix, we stabilize by adding small multiple of the identity matrix Le., En, + En aT, where set 0.001 in all experiments. Let D, diag(E.,) and
5

---

Published as a conference paper at ICLR 2026
Cn Dí = D,,1/ Dm, be the correlation matrix which removes per-time scaling. According to Thm. 4.2 each token then encoded as quotient Gaussian embedding, given below
Co + k uoll (k) Mn
Y (det C.) 7+E
pun Ix
STTH
(11)
To aggregate information across tokens, we estimate Riemannian Gaussian the SPD manifold based on the set [Yn)a= The FM and empirical Riemannian covariance are given by
N
Ym = FM ((rm) y = N
Σ ==1
(Logrm (Yn)) fo (oogrm (Kw))
(12)
The obtained product manifold (Ym, ye) is embedded into an SPD matrix G uuing Eq.
Finally, RHOP integrates global semantics with statistical structure to enhance prediction. The backbone outputs a CLS token yo E _R for global semantics, while the statistical branch applies iSICE (Rahman et al. 2023 to G. followed by upper-triangular extraction and vectorization, i.c.
= utvee (iSICE(G)).
(13)
The final prediction is obtained by concatenating yo and g and passing them through linear layer with softmax activation. This design enriches the CLS token with quotient- and Riemannian-base high-order statistics, yielding more discriminative representation.
EXPERIMENTS
This section evaluates RHOP on four EEG benchmarks under training from scratch, full fine-tuning, and linear-head tuning settings. We compare our method against state-of-the-art foundation models and representative GCP heads.
5.1 EXPERIMENT SETUP
Datasets. We evaluate RHOP four EEG benchmarks spanning abnormal detection, event classification, motor imagery, and event-related potentials. TUAB (Oheid & Picone (016) con- tains 23-channel EEG 256 Hz labeled as normal or abnormal, with 409,455 ten-second seg- ments. TUEV (Obeid & Picone 2016) includes 112,491 five-second segments from 23 channels 256 Hz across six classes: spike sharp wave (SPSW), generalized periodic epileptiform dis- charges (GPED), periodic lateralized epileptiform discharges (PLED), eye movement (EYEM), arti- fact (ARTF), and background (BCKG). BCIC2B (Steyrl et al. 2016) records EEG from 10 subjects on three bipolar channels (C3, Cz, C4) at 250 with two-class motor imagery (left vs. right hand). Each subject two no-feedback sessions (120 balanced trials each) and three feedback sessions. PhysioP300 (Goldberger al. 2000) is Donchin-style 6x6 row/column speller, where rows/columns are flashed for 100 ms with m0 inter-stimulus intervals (=20 flashes cach), and each subject spells 20 characters per
We evaluate RHOP on two widely used EEG foundation models: BIOT Yang et al., 2023) and LaBraM (Jiang al.) 2024). Since public checkpoints are only available for LaBraM- Base, we fine-tune this configuration in all experiments. To further assess robustness beyond foun- dation pretraining, we also train BIOT from scratch without any pretraining-
Backbones.
Preprocessing. For TUAB and TUEV, strictly follow the original backbone preprocessing without any additional modifications. For BCIC2B, we use uniform units, apply 0-38 Hz band- pass filter, resample the data 200 Hz, and perform EA normalization (He & Wu (019) within each session. For PhysioP300, we also use uniform units, apply 20 Hz low-pass filter, downsample to 200 and extract 2s epochs starting -0.7 relative to the onset of the flicker stimulus. For more details, please refer to App.
Baselines. We compare RHOP with both non-foundation and foundation baselines. For non-
foundation baselines, we include widely used EEG models such as EEGNet (Lawhern et al. 2018 EEGConformer (Song et al. 2022), SPaRCNet (Jing et al. (202)), ContraWR (Yang et al. 2021
CNN-Trame TeN-Transformer (Peh et al. 2022a), FFCL L al. 2022). and ST-Transformer (Song et al.
2021a), implemented following the BIOT repository ( (Yagg et al. 2023) unless official results are available. For coundation-mode baselines, evaluate BIOT Yang et al. 2023) and LaBraM (Jiang

---

Published as a conference paper at ICLR 2026
Table 1: Results on TUEV with different models and model complexity.
Methods
Model Size (#Params)
Time Epoch
Balanced
Cohen's Kappa
Weighted
SPaRCNet
0.79M
0.06
0.4161 =: 0.0262
0.1233 # 0.0181
D. 0,7021 = 0.0101
ContraWR
1.6M
0.07
0.4384 1: 0,0349
0.3912 4: 0.023T
0.6893 0.0136
Transformer
3.2M
0.12
0,4087 = 0.0161
0,3815 # 0.0131
0.6831 0.0293
FFCL
2.4M
0.12
0,3979 1: 0.0104
0,3732 4 0.0188
0.678 0.0120
ST-Transfomer
3.5M
0.03
0,0228
0.0306
0.0190
BIOT (non-preirained)
BIOT
3.2M
0.12
0.4682 1: 0.0125
0.4482 4: 0.0285
0.7085
0.0184
BIOT+ISORT-COV
3.2M+A33.J
0.81
0,4480 1: 0.0131
0,3344 =: 0.0121
0.6323
0.0203
BIOT=SVD.Paa
3.2M | A11.
10.61
0.4347 1: 0.0133
0,4091
à: 0.0290
0.6906
0.0137
BIOT+iSICE
II
4.71
0.0143
0.0197
0.0167
BROP
3.2M A1.3K
0.53
0.5355
0.0189
0.5177
0.0252
0.7466
0.0084
BIOT (pretrained)
BIOT
3.2M 3.2M I A33.1
0.12
0.5281 1: 0.0225
0.5273 1: 0.0249
0.7192 = 0.0182
BIOT-iSQRT-COV
0.81
0.4683 + 0000146
0.3563 + 0.0218
0.6530
0.0187
BIOT-SVD.
3.2M+ I3
0.0176
0.0162
0.7398
0.0171
BIOT+iSICR
3.2M I A3
4:73
0.5358 + 0.0241
0.5245 + 0.02113
0. 0.7534
0.0094
BIOT-RHIP
3.2 A1.3K
0.73
0.5572 1 0.0201
0.5480
0.0212
0.7565
0.0074
LaBrraM-Base (pretrained)
LaBraM-Base
S.MM
1.03
0.6409 + 0. 00.0065
0.6637 + 000000
0.8312 + 0.0052
LaBraM-Buse BiS--SOQ
5
3.23
0.0226
0.0234
0.0094
5.M++220.
6.93
0.5605 + 00.0217
0.5798 + 0.0288
0.70000
0.0101
LaBraM- Buse+iSICE
5.8M 32
13.67
0.6405 4: 0.0220
0.6134 : 0.0337
0.8182 0.0091
BtraM-Base-RHOP
58M-A00KK
2.25
0.6380 + 0.0056
0.6785
0.0079
0.8420
O. 0.0038
Table 2: Results on TUAB with model complexity.
Methods
Model Size (#Params)
Epoch
Balanced
AUC-PR
AUROC
SPaRCNet
0.79M 66
0.43
0,7896 : 0.0018
0,8414 = 0,0018
0.8676 = 0.0012
ContraWR
0.48
0.7746 0.0041
0.8421 0000104
0.8456 0.0074
WUNN-Taasformes
3.2M
0.76
0.7177 : 0.0022
0,8433 : 0.0039
0.8161
0.0113
FFCL
2.4M
0.86
0.7848 + 0.0038
0,84-88 # 0.0065
0.8569 0.0051
ST-Transfomer
3.5M
0.24
0.0023
0.0026
0.0111
BIOT (non-prcirained)
3.2M
1.36
0.7925 0.0025
0.0087
0.8691
0.0033
BIOT+ISORF-COY
A.3MI
4.78
0.7983 1: 0.0045
0,8684 + 0.0051
0,8639 = 0LOUSS
BIOT-SVD-Pad
3,2M+
50.71
0.7303 = 0.0051
0,8271 = 0.0058
0.8270
0.0066
BIOT+iSICE
3.2M+A331IK
10.47
0.0057
0.0021
0.01143
BIOT-RHOP
3.2M-&LO0
3.64
0.7993 1: 0 0031
0.8719 = 0.00084
0.8765
O. 0.0031
BIOT (pretrained)
BIOT
3.2M
1.09
0.7959 1: 0.0057
0.8792 1: 0.0023
0.8815 -: 0.0143
BIOT-ISQRI-COV
3.2M+A33JE
4.78
0.7819 1: 0.0011
0.8390 = 0 0.0028
0,8598
01.0139
BIOT+SVD.
3.2M ARL.K
54.38
0.7532 0.0064
0.0043
0.0056
BIOT-iSICE
10.50
0.7976 1: 0.0097
0,8617
= 0.0046
0.8739 = (100
BIOT-RHOP
3.2M A1.3K
3.69
0.8102 1: 0.00
0.8833
0.0079
0.8864
O. 0.0033
LaBraM-Base (pretrained)
LaBraM-Base
5.8M
11.5c 11.54
0.8140 + 0.0019
0.8965 + 0.0016
0.9022 0.0000
LaBraM- -.S-RTCT
5.M A20.3K
19.07
0.9039 0.0018
0.0012
5.8M+-20.33 3K
31.23
0.8202 + 0.0017
0.9062
#: 0.0014
0.9072 = 0.0011
LaRraM-Buree BuseviSICF.
5.8M 1.8.322033 320.3K
67.77
0.8183 + 0.0018
0.9037 0.0016
0.9059 0.0016
BBaaM-Bas--RHOP
5.8M-24.6
21.48
0.8244 + 0.0012
0.9078
0.0012
0.9105
0.0011
et al. 2024), using their released code and checkpoints. Since only LaBraM-Bass provides public weights, we fine-tune this variant in all experiments, while BIOT tested both with and without pre- training. In addition, we compare RHOP against several representative global covariance pooling (GCP) heads, including iSICE (Rahman et al. 2023), iSQRT-COV (Li al. 2018). and SVD- Padé (Song et al. 2021b). For fairness, given EEG inputs, all backbones produce spatiotemporal tokens and a CLS token. GCP variants then compute covariance descriptors, which we vectorize via the upper triangular (including the diagonal) before classification with linear layer.
Metrics. We report results using five widely adopted evaluation metrics: (1) Balanced Accu- racy, defined as the mean recall across classes, applied to both binary and multi-class settings. (2) AUC-PR, the area under the precision-recall curve, for binary classification. (3) AUROC, the area under the receiver operating characteristic curve, also for binary classification. (4) Cohen's Kappa, which measures agreement beyond chance by comparing observed and expected accuracies a contingency table, is used in multi-class tasks. (5) Weighted F1, the weighted harmonic mean of precision and recall, used for multi-class evaluation. For monitoring, AUROC is adopted in binary classification experiments, while Cohen's Kappa is used in multi-class settings.
7

---

Published as a conference paper at ICLR 2026
Table 3: Results on BCIC2B with different models and model complexity.
Methods
Model Size (#Params)
Epoch
Balanced
AUC-PR
AUROC
LaBraM-Basc
3.8M
0.04
0.68 + 0.0059
0.7405 #: 0.0087
0.7172 = 0.0054
LaBraM- Bue+iSQRT-COV
3.8M+A22.55
0.38
0.6842 1: 0.0061
0.7210 4: 0.0079
0.7285 0.0055
-.BraM-Bae+SSD--- Basc+SVD-Pade
5.8M+-220.36
0.15
0,6829 + 0.0056
0.7198 # 0.0083
0.7267 0.0061
LaBruM- Bae+iSICE
5.8M + 32
0.97
0.6877 1: 0.0058
0.7433
4 0.0082
0.7510
- 0.0055
LoBraM-Buc++HHOP
0.05
0.6901 0.0057
0.7485
0.0079
0.7587
Table 4: Results on PhysioP300 with model complexity.
Methods
Model Size (#Params)
Time / Epoch (m)
Balanced Acc.
AUC-PR
AUROC
LaBraM-
0.05
0.6327 0.019
0.6565 0.024
0.6893
58M+A20.08
0.08
0.6170 = 0.016
0.6560 0.019
0.6813 :: 0.012
LaBraM-Base- Sase-
3RM4-20.38
0.16
0.6323 0.015
0.6400 0.0020
0.6751
0.014
LaBraM BSsc.
38M+AA20.1
0.41
0.6138 0.018
0.6350 0.022
0.6427 0.017
LaBraM Base-RHOP
5.8M+A004K
0.08
0.6517 0.018
0.6630
0.016
0.7044
0.024
5.2 EVALUATIONS
Training from seratch. On TUEV, as reported in Tab. I RHOP yields larger gains: balanced accuracy increases from 46.82% to 53.55% Cohen's Kappa from 44.82% % to 51.77%, and Weighted F1 from 70.85% to 74.66%, with only 0.53 minutes per epoch. On TUAB, as shown in Tab. 2 BIOT with RHOP improves balanced accuracy from 79.25% to 79.93% and AUROC from 86.91 % to 87.65% while reducing per-epoch time to 3.64 minutes compared with 10.47 minutes for iSICE and 50.71 minutes for SVD-Padé. These results highlight that RHOP is particularly effective without pretraining, as it preserves spatiotemporal structure and high-order statistics.
Full fine-tuning. On TUEV, as shown in Tab D RHOP reaches a higher Cohen's 's Kappa of 67.85% and a Weighted F1 of 84.20%, while maintaining strong balanced accuracy. On TUAB, as ported in Tab. 2 LaBraM-BB Maase with RHOP improves balanced accuracy from 81. 40040% to 82.44% and pushes AUROC to 91.05 91.05%. These improvements confirm that even strong pretrained backbones benefit from RHOP, which captures dependencies overlooked by conventional heads.
Linear-head tuning. With frozen backbones, RHOP still surpasses all baselines. On BCIC2B, LaBraM-Base with RHOP reaches 69.01% % balanced accuracy and 75.87% AUROC, outperforming all GCP heads, as given Tab. 3 On PhysioP300, it improves balanced accuracy from 63.27% to 65.17% and AUROC from 68.93% to 70.44%, presented in Tab. 4 These results demonstrate RHOP's ability to deliver discriminative representations even when backbone weights are frozen, which makes it suitable for rapid adaptation with minimal compute.
Why RHOP outperforms GCP? Classical GCP methods such as iSQRT-COV, iSICE, and SVD- Padé collapse all tokens into a single covariance matrix, which discards temporal and channel hier- archy. RHOP instead normalizes tokens' covariances to correlation form, embeds both means and normalized covariances on the SPD manifold, and aggregates via a Riemannian Gaussian defined by Fréchet mean and tangent-space covariance. This preserves ecale-invarian dependencies, aligns computation with manifold geometry, and emphasizes direct relationships through a sparse inverse- covariance layer. The result is more faithful global representation that consistently outperforms GCP, especially in challenging setups such as TUEV with training from scratch.
Efficiency. RHOP delivers accuracy gains with minimal overhead. On TUAB, LaBraM- -ase with RHOP trains in 21.48 min per epoch with only 4.6K additional parameters, compared with 67.77 min for iSICE and 31.23 minutes for SVD-Padé as reported in Tab. 2 BIOT with RHOP requires just 3.69 min per epoch when pretrained, and only 0.53 min per epoch when trained from scratch on TUEV, far below iSICE and SVD-Padé, as shown in Tab. I On BCIC2B and PhysioP300, RHOP adds less than IK parameters and only 0.01 min per epoch, while still improving all metries, as shown in Tabs. 3 and 4. Overall, RHOP combines strong accuracy, scale robustness, and geometric fidelity with thousand-level parameter overhead and negligible training cost, making it practical plug-and-play head for EEG foundation backbones.
5.3 A ABLATION STUDY
Quotient Gaussian Embedding vs Gaussian Embedding. Fig. 2 compares quotient Gaussian embedding with conventional Gaussian embedding. The only difference is that conventional em-
8

---

Published as a conference paper at ICLR 2026
Table 5: Ablation study on different components, where QGE denotes Quotient Gaussian Embed- ding, RGE denotes Riemannian Gaussian Embedding, and CLS indicates whether concatenation with the classification head is applied.
QGE
RGE
SICE
CLS
TUAB
TUEV
Halanced
AUC-PP
AUROC
Ralaneed Ace.
Kappa
Weighted
0.0065
+000053
0.8312 0.00062
0.8175
0.9002
0,6325
0.0051
0.820
6.0016
0.0031
0.0044
039029
0.0010
0.6300
0.0000
0.6712
0.0067
0.8365 0L004)
0.0014
0.9058
0.0013
0.9083 0.0010
0.6311
0.0058
0.6789
0.0084
0.850
0.0047
0.8244
0.0012
0.9078 0.0012
0.9105 0.0011
0,6380 2: 1.0056
0.6785
0.0079
0.5420
0.0038
Table 6: Ablation of (k, k') on LaBraM- BBsse.
k:
TUAB
TURY
Ralanced Acc.
AUC-PR
AUROC
Balanced Acc.
Cohen's Kappa
Weighted F1
0,8065 = 0.0019
0,8973 : 0.0017
018988 + 0.0012
0.6157 = 0.0121
0.5772 + 0.0203
0.7876 = 0.0114
0.8193 0.0021
0.9064 0.0016
0.9064 + 0.0013
0.6339 0.0184
0.6078 0.0227
0.5062 0.0
3
0,8199 = 0.0020
0 :: 0.0015
0.9060 + 0.0012
0.6726 = 0 0.0137
0.6156 + 0.0181
0.8221 = 0.0097
0,8975 0.0018
0.0116
0.6471
0.0193
2
2
0.8249 = O. 0.0022
0,9044 1: 0.0014
(.9071 + 0.00011
0.6159 : 0.0128
0.60088 1 0.0251
0.7970 = 0.1085
0.0016
0.9037
0,6110 0.0137
0.6196 0.0228
0.8183 1 0.0019
0.9035 0.0015
0.9062 1. 0.0011
0.6859 1 0.0123
0.6317 0.0273
0.8176 1. 0.0135
0.00266
0.6220 0.0234
0.8241 = 0.0012
0.9078 = 0. 0012
0.9105 + 0.0011
0.6380 = 0.0056
0. 0.6785 + 0.0079
0.8420 = O. 0038
Embcoling
LaBraM (TUAB)
LaBraM (TUEV)
BIDT ITUAB]
BIOT (TUEV)
33-
6.-
35
65
65
Aronnty
AUC
Asdcc
Oecncee Acotect
comns Apps
Regindrl
Esanced Scdonde
ASC-F
Belagel Acional
Covos Kappl
Reginad
Figure 2: Quotient Gaussian embedding vs Gaussian embedding on TUEV and TUAB.
bedding (Nguyen 1 directly uses the covariance matrix without normalization. On both TUAB and TUEV, the quotient form consistently outperforms the raw covariance representation, confirm- ing that scale normalization is essential for robust EEG descriptors.
Component analysis. Tab. 5 evaluates the contribution of each RHOP component. QGE alone improves performance, RGE further enhances high-order modeling, and SICE highlights partial correlations. The best results are obtained when CLS fusion is added, which combines semantic and statistical cues. Overall, each component provides complementary gains, and the full RHOP yields the strongest improvements.
Embedding dimensions. The parameters and k control the augmentation of mean vectors and the embedding of Riemannian statisties in Eqs. (9) and (TT). Tab. repoorts their influence TUAB and TUEV. Non-trivial choices with k. k' > consistently outperform the baseline, and the optimal configuration varies across datasets. TUAB achieves the highest AUROC with A 3, k' 3, while TUEV obtains the best Cohen's Kappa with A = 3, k' = 3 and the best balanced accuracy with A k 3. Increasing k or k'' expands the SPD embedding dimension and amplifies the mean-related terms, which reduces the relative influence of the covariance structure and introduces additional computational and numerical burdens. As result, moderate settings such as (A: R 3) achieve the best trade-off between representational expressiveness and model stability.
Covariance normalization. Tab. 7 examines why iSICE is selected as the final covariance nor- malization method. Replacing iSICE with iSQRT-COV SVD-Padé reduces performance, while iSICE achieves the best results on TUAB and TUEV. The reason is that iSICE imposes sparsity during normalization, which regularizes high-dimensional features. This property is particularly ef-

---

Published as a conference paper at ICLR 2026
Table 7: Comparison of different GCP heads on LaBraM-Base.
Normalization
TUAB
TUEV
Balanced Acc.
AUC-PR
AUROC
Bulanced Ace.
Cohen's Kappa
Weighted F1
SVD-Padk iSORT-COV ISICE
0.8190 0.0016
0.9012 0.0014
0,9058 = 0. 0.0010
0,6308 + 0.0071
0.6710 = 0. 0.0085
0 0,8365 0,0019 0.5350
0.0011
0.9001
0.0011
0.6375 0.0068
0.0091 0.6785 = 0.0079
0.8244 = 0.0012
0.9078 + 0.0012
0 9105 0.0011
0.6380 + 0.0056
0.8420 = 0038
Table 8: Gaussianity statistics of token features after random projection. SW-p: Shapiro-Will p-
value; Prop.: fraction of projections with 0.05 (non-rejection of Gaussianity).
RHOP compora--sggment features.
(b) GCP token-level aggelllgggeee aggregated features.
Model
Dataset
SW-p
Prop.(t > 0.05)
Skew
Kurt
Model
Dataset
SW-p
Prop-6p > 0.05)
Skew
Kurt
LaBraM
TUAB
0.49
0.94
-0.13
0.19
LaBrMM
TUAB
0.01
0.05
0.14
18.94
TUEV
0.47
0.89
-0.10
0.15
TUEV
0.01
0.03
0.25
19.54
BIOT
TUAR
TUEV
0.46
0.85
0.91
-0.07
0.10
0.12
BIOT
TUAB
0.02
0.03
0.22
0.14
19.16
19.97
fective for EEG decoding, where signals noisy and correlations are often spurious, making iSICE a more robust choice than dense normalization approaches.
5.4 GAUSSIANITY ANALYSIS
In this section, we evaluate the Gaussianity of token features extracted from LaBraM and BIOT on TUAB and TUEV, aiming to understand the statistical behavior of foundation model activations.
Testing procedure. For each dataset, we randomly sample 10000 data samples, extract their token representations, and assess the distributional properties of the temporal feature vectors. Each token feature is projected onto multiple random dieedinesio directions, standard approach for test- ing multivariate normality. For each projection, we compute the Shapiro-Wii Wilk p-value, skewness, and excess kurtosis, and then average these quantities.
Discussion. As summarized in Tab. 8 8a), we evaluate Gaussianity along the temporal dimension where RHOP computes covariance. The resulting temporal-segmect features exhibit near-Gaussian behavior: Shapiro-Wilk v-values are moderate, 85%-94% of projections satisfy p > 0.05, skewness close to zero, and excess kurtosis remains small. These results indicate that RHOP's temporal- segment representations follow a Gaussian suitable for second-ordes modeling. In contrast, the GCP features in Tab. ()) exhibit strong non-Gaussian behavior. GCP computes covariance after flatten- ing and aggregating spatial and temporal tokens, thereby mixing heterogeneous EEG components within a single representation. When Gaussianity is assessed along this mixed token axis, the statis- ties deviate markedly from normality: the Shapiro-Wilk p-values are near zero, fewer than 5% of projections satisfy p > 0.05, and the excess kurtosis reaches extremely high values. These results indicate heavy-tailed, asymmetric, and multimodal structure, reflecting the statistical complexity introduced by combining spatial and temporal information in a single representation. By contrast, RHOP evaluates covariance within coherent temporal segments rather than across mixed tokens. operates on statistically well-behaved representations, leading to more stable covariance estimates and improved downstream performance.
6 CONCLUSION
This work introduced Riemannian High-Order Pooling (RHOP), a geometry-aware classification head designed to complement large EEG foundation backbones. By embedding per-token quo- tient Gaussians on the SPD manifold and aggregating them into a Riemannian Gaussian descriptor, RHOP preserves scale-invariant dependencies and captures high-order spatiotemporal interactions. Extensive experiments across abnormal detection, epileptic event classification, motor imagery, and event-related potentials demonstrated that RHOP consistently improves accuracy, robustness, and efficiency over global average pooling and classical covariance pooling. These gains persist across different training regimes, including training from scratch, full fine-tuning, and linear probing, con- firming that RHOP provides principled and effective bridge between Riemannian statistics and foundation models. More broadly. this study highlights the value of geometric inductive bias in large-scale EEG modeling and supports geometry- analysis of brain signals.
10

---

Published as a conference paper at ICLR 2026
ETHICS STATEMENT
This work adheres to the ICLR Code of Ethics. All experiments were conducted on publicly avail- able datasets with appropriate licenses, and no personally identifiable or sensitive information was involved.
REPRODUCIBILITY STATEMENT
We have made every effort to ensure reprodueibility. The datasets used are publicly available. Model architectures, training procedures, and evaluation metrics detailed in Sections 4 and 5, with additional implementation details and hyperparameters provided in the appendix. Upon acceptance, we will release the complete source code and instructions for reproducing all experiments.
ACKNOWLEDGE
This work was supported in part by the National Natural Science Foundation of China (62306127, 62332008), the Natural Science Foundation of Jiangsu Province (BK20231040), the Fundamental Research Funds for the Central Universities (JUSRP124015), the Postgraduate Research & Prac- tice Innovation Program of Jiangsu Province (SJCX25_131) (101214398) the FIS project GUIDANCE (F1S2023-03251), the National Key R&D Program of China (2023YFFI 105102, 2023YFFI 105105), the Zhejiang Leading Innovative and Entrepreneur Team Introduction Program (2024R01007) and the "Pioneer" and "Leading Goose" Research and Development Program of Zhejiang (2025C02077).
the EU Horizon project ELLIOT
REFERENCES
K. A. Aboalayon, M. Faczipour, W. S. Almuhammadi, and S. Moslchpour. Sleep stage classifi- cation using eeg signal analysis: A comprehensive survey and new investigation. Entropy, 18(9): 272, 2016.
Bijan Afsari. Riemannian 1" center of mass: existence, uniqueness, and convexity. Proceedings of the American Mathematical Society, 2011.
Ijaz Ahmad, Xin Wang. Mingxing Zhu, Cheng Wang, Yao Pi, Javed Ali Khan, Siyab Khan, Oluwarotimi Williams Samuel, Shixiong Chen, and Guanglin Li. Eeg-based epileptic seizure detection via machine/deep learning approaches: A systematic review. Computational Intelli- gence and Neuroscience, 2022:98 4248, 2022.
H. Altaheri, G. Muhammad, M. Alsulaiman, U. Amin, G. Altuwaijri, W. Abdul, M. A. Bencherif, and M. Faisal. Deep learning techniques for classification of electroencephallggamm (eeg) motor imagery (mi) signals: A review. Neural Computing and Applications, 35(20): 14681 14722, 2023.
Vincent Arsigny, Pierre Fillard, Xavier Pennec, and Nicholas Ayache. Fast and simple computations tensors with log-euclidean metrics. Research Report RR-5584, INRTA, Sophia Antipolis, France, 2005a.
Vincent Arsigny, Pierre Fillard, Xavier Pennee, and Nicholas Ayache. Fast and simple computations on tensors with log- Englliddn metrics. PhD thesis, INRIA, 2005b.
Hubert Banville, Omar Chehab, Aapo Hyvärinen, Denis-Alexander Engemann, and Alexandre Gramfort. Uncovering the structure of clinical EEG signals with self-supervised learning. Journal of Neural Engineering, 18(4):046020, 2021. doi: 10. (0100//11111252///1
Wouter Biesmans, Neetha Das, Tom Francart, and Alexander Bertrand. Auditory- -editory-inspired speech envelope extraction methods for improved eeg-based auditory attention detection in cocktail party scenario. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 25(5): 402-412, 2016.
Rishi Bommasani et al. On the opportunities and risks of foundation models. arXiv preprint 108. 2021.
11

---

Published as a conference paper at ICLR 2026
Daniel Brooks, Olivier Schwander, Frédéric Barbaresco, Jean-Yves Schneider, and Matthieu Cord. Riemannian batch normalization for SPD neural networks. In NeurIPS, pp. 15463- 15474, 2019.
Miquel Calvo and Josep M. Oller. A distance between multivariate normal distributions based in an embedding into the siegel group. Journal of Multivariate Analysis, 35(2):223-22 242, 1990. doi:
Rudrasis Chakraborty, Jose Bouza, Jonathan H Manton, and Baba C Vemuri. Manifoldnet: A deep neural network for manifold-valued data with applications. IEEE Transactions Putlern Anal- ysis and Machine Intelligence, 44(2)799-810,, 2022. doi: 10. 1009/PAAM..20000005544 URL 3003846
fittps://do.... woo./r///0 1109 TPAMT
Ziheng Chen, Yue Song, Gaowen Liu, Ramana Rao Kompella, Xiao-Jun Wu, and Nicu Sebe. Rie- mannian multinomial logistics regression for SPD neural networks. In CVPR, 2024a.
Ziheng Chen, Yue Song, Yunmei Liu, and Nicu Sebe. A Lie group approach to Riemannian hatch normalization. In ICL.R, 2024b.
Ziheng Chen, Yue Song, Xiaojun, and Nicu Sebe. RMLR: Extending multinomial logistic regression into general geometries. arXiv preprint (ati:22499.943333 2024c.
Ziheng Chen, Yue Song, Xiaojun Wu, Gaowen Liu, and Nicu Sebe. Understanding matrix function normalizations in covariance pooling through the lens of Riemannian geometry. In The Thirteenth International Conference on Learning Representations, 2025.
R. Cherian and E. G. Kanaga. Theoretical and methodological analysis of eeg based seizure de- tection and prediction: An exhaustive review. Journal of Neuroscience Methods, 369:109483, 2022.
Hsiang-Yuu Yun Sherry Chien, Hanlin Goh, Christopher M. Sandino, and Joseph Y. Cheng. MAEEG: Masked auto-encoder for EEG representation learning. arXiv preprint arXiv:221 1.02625, 2022.
Marco Congedo, Alexandre Barachant, and Rajendra Bhatia. Riemannian geometry for eeg-based brain-computer interfaces; primer and a review. CompuCCr Interfaces, 4(3):155-174, 2017.
D. Dadebayev, W. Goh, and X. Tan. Eeg-based emotion recognition: Review of commercial eeg devices and machine learning techniques. Journal of King Saud Universiry-Compuee and Information Sciences, 34(7):4385 4401, 2022.
Jacob Devlin, Ming- Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint 1rXiv:1810.04800 2018.
Maurice Fréchet. Les éléments aléatoires de nature quelconque dans un espace distancié. In Annales de l'institut Henri Poincaré, 1948.
J. Y. Gao, Y. N. Sun, Y. C. Liu, Y. H. Tang, Y. H. Zeng, D. Qi, K. Chen, and C. R. Zhao. Styleshot: A snapshot on any style. IEEE Transactions on Pattern Analysis and Machine Intelligence, 48 12):1215-1228, 2025a.
Zeyu Gao, Anyu Mao, Yuxing Dong, Hannah Clayton, Jialun Wu, Jiashuai Liu, ChunBao Wang, Kai He, Tieliang Gong, Chen Li, et al. Smmile enables accurate spatial quantification in digital pathology using multiple-instance learning. Nature Cancer, pp. 1-17, 2025b.
Ary L Goldberger, Luis AN Amaral, Leon Glass, Jeffrey M Hausdorff, Plamen Ch Ivanov, Roger G Mark, Joseph Mietus, George B Moody, Chung-Kan Peng, and Eugene Stanley. Physiobank, physiotoolkit, and physionet: components of new research resource for complex physiologic signals. circulation, 101((2):e215-2220 2000.
Liyu Gong, Tianjiang Wang, and Fang Liu. Shape of gaussians feature descriptors. In 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp. 2366-2371. IEEE, 2009. doi:
12

---

Published as a conference paper at ICLR 2026
He He and Dongrui Wu. Transfer learning for brain computer interfaces: A euclidean space data alignment approach. IEEE Transactions on Biomedical Engineering, 67(2):399 410, 2019.
Gabriel Emile Hine, Emanuele Maiorana, and Patrizio Campisi. Resting-state eeg: A study on its
non-stationarity for biometric applications. Proceedings of the 2017 International Conference of the Biometrics Special Interest Group (BIOSIG), pp. 1-5. IEEE, 2017.
Chen Hu, Rui Wang, Xiaoning Song, Tao Zhou, Xiao-Jun Wu, Nicu Sebe, and Ziheng Chen. correlation manifold self-attention network for eeg decoding. In IJCAI, 2025a.
Ming Hu, Chenglong Ma. Wei Li, Wanghan Xu, Jiamin Wu, Jucheng Hu, Tianbin Li, Guohang Zhuang. Jiaqi Liu, Yingzhou Lu, et al. A survey of scientific large language models: From data foundations to agent frontiers. arXiv preprint arXiv:2508.2 148, 2025b.
Catalin Ionescu, Orestis Vantzos, and Cristian Sminchisescu. Matrix backpropagation for deep net- works with structured layers. Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp.
2015. doi: 10. 10.1109//CC22215.333999
Wei-Bang Jiang, Li-Ming Zhao, and Bao-Liang Lu. Large brain model for learning generic repre- sentations with tremendous EEG data in BCI. arXiv preprint 1rXi::2405.18765, 2024.
Weibang Jiang, Yansen Wang, Bao-liang Lu, and Dongsheng Li. NeuroLM: universal multi- task foundation model for bridging the gap between language and EEG signals. In International Conference on Learning Representations (ICLR), 2025.
Jin Jing, Wendong Ge, Shenda Hong, Marta Bento Fernandes, Zhen Lin, Chaoqi Yang. Sungtae An, Aaron F. Struck, Aline Herlopian, Ioannis Karakis, Jonathan J. Halford, Mareus C. Ng. Emily L.. Johnson, Brian I.. Appavu, Rani A. Sarkis, Gamaleldin Osman, Peter W. Kaplan, Mon- ica B. Dhakar. Lakshman Arcot Jayagopal, Zubeda Sheikh, Olga Taraschenko, Sarah Schmitt, Hiba A. Haider, Jennifer A. Kim, Christa B. Swisher, Nicolas Gaspard, Mackenzie C. Cer- venka, Andres A. Rodriguez Ruiz, Jong Woo Lee, Mohammad Tabaeizadeh, Emily Gilmore, Kristy Nordstrom, Ji Yeoun Yoo, Manisha G. Holmes, Susan T. Herman, Jennifer A. Williams, Jay Pathmanathan, Fábio A. Nascimento, Ziwei Fan, Samaneh Nasiri, Mouhsin M. Shafi, Syd- ney S. Cash, Daniel B. Hoch, Andrew J. Cole, Eric S. Rosenthal, Sahar F. Zafar, Jimeng Sun, and M. Brandon Westover. Development of expert-level classification of seizures and rhythmic and periodic patterns during eeg interpretation. Neurology, 100(L7):E750-EII E17677000-117.....11 2023. doi: 10. 21120N..000000000201212
Ce Ju and Cuntai Guan. Graph neural networks spd manifolds for motor imagery classification: A perspective from the time-frequency analysis. IEEE Transactions on Neural Networks and Learning Systems, 34(12):10955-1096 2023.
Ce Ju, Reinmar Kobler, Liyao Tang, Cuntai Guan, and Motoaki Kawanabe. Deep geodesic canon- ical correlation analysis for covariance-based neuroimaging data. In ICIR, 2024.
Ce Ju, Reinmar J Kobler, Antoine Collas, Motoaki Kawanabe, Cuntai Guan, and Bertrand Thirion. Spd learning for catriancc-basee neuroimaging analysis: Perspectives, methods, and challenges. arXiv preprini orXiv:2504. /8882, 2025.
Hermann Karcher. Riemannian center of mass and mollifier smoothing. Communications on Pure and Applied Mathematics, 30:509-541, 541, 1977a.
Hermann Karcher. Riemannian center of mass and mollifier smoothing. Communications on pure and applied mathematics, 30(5):509-541, 1977b.
Reinmar Kobler, Jun-ichiro Hirayama, Qibin Zhao, and Motoaki Kawanabe. SPD domain-specitn batch normalization crack interpretable unsupervised domain adaptation in EEG. NeurlPS, 35: 6219-6235, 2022.
Dimitrios Kostas, Stéphane Aroca- Ouellette,, and Frank Rudziez. BENDR: Using transformers and a contrastive sulf-super learning task to learn from massive amounts of EEG data. Frontiers in Human Neuroscience, 15:653659, 2021. doi: 10.3389/fnhum.2022 wtw.hhm.m..22.655..0 665369..
13

---

Published as a conference paper at ICLR 2026
Vernon J Lawhern, Amelia Solon, Nicholas R Waytowich, Stephen M Gordon, Chou P Hung, and Brent Lance. Eegnet: A compact convolutional neural network for eeg-based based brain- comp-rr interfaces. Journal of Neural Engineering, 15(5)056013,, 2018.
Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learnin. Nature, 521(7553):436 444, 2015.
Hongli Li, Man Ding, Ronghua Zhang, and Chunbo Xiu. Motor imagery eeg classification algorithm based enn-lstm feature fusion network. Biomedical Signal Processing and Control, 72: 12:103342, 2022. doi: 10.
Peihua Li, Qilong Wang. Hui Zeng, and Lei Zhang. Local log-euclidean multivariate gaussian descriptor and its application to image classification. IEEE Transactions Pattern Analysis and Machine Intelligence, 39(4):803887, 2017a. doi: 10.1 10001TTAM..201.255500
Peihua Li, Jiangtao Xie, Qilong Wang, and Wangmeng Zuo. Is second-order information helpful for large-scale visual recognition? In Proceedings of the IEEE International Conference Computer Vision (ICCV), pp. 2070-2078, 201 7b. doi: 10.1109/CCV220117.22
Peihua Li, Jiangtao Xie, Qilong Wang, and Zilin Gao. Towards faster training global covariance pooling networks by iterative matrix square root normalization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition (CVPR), pp. 947-955, 2018. doi: 10.
1109/CVPR.2218.0001.6
Shanglin Li, Motoaki Kawanabe, and Reinmar Kobler. Spdim: Source-free unsupervised conditional and label shift adaptation in eeg. In International Conference on Representation Learning, volume 2025, pp. 101907-101931, 2025.
Tsung- Yu Lin, Aruni RoyChowdhury, and Subhransu Maji. Bilinear CNN models for fine-grained visual recognition. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pp. 1449-144 1457, 2015. doi: 10.110//CC2.2015..110
Jiashuai Liu, Anyu Mao, Yi Niu, Xianli Zhang, Tieliang Gong, Chen Li, and Zeyu Gao. Pamil: Prototype attention-basee multiple instance learning for whole slide image classification. In In- ternational Conference on Medical Image Computing and Computer-Assisted Intervention, pp- 362-372. Springer, 2024.
Fabien Lotte, Emmanuel Congedo, Aurélien Lécuyer, François Lamarche, and Bruno Amaldi. A review of classification algorithms for eeg-based compucr interfaces. Journal of Neural Engineering, 4(2):R1, 2007.
Miroslav Lovrić, Maung Min-Oo, and Ernst A. Ruh. Multivariate normal distributions parametrized as a riemannian symmetric space. Journal of Multivariate Analysis, 74(1):36-48, 2000a. doi:
Miroslav Lovrić, Maung Min-Oo, and Erast A. Ruh. Multivariate normal distributions parametrized as a riemannian symmetrie space. Journal of Multivariate Analysis, 74(1) 74844436-48, 2000b.
Maher Moakher. A differential geometric approach to the geometric mean of symmetric positive- definite matrices. SIAM Journal on Matrix Analysis and Applications, 26(3):735-747, 2005. doi:
10111337700095477844443377
Navid Mohammadi Foumani, Geoffrey Mackellar, Soheila Ghane, Saad Irtza, Nam Nguyen, and Mahsa Salchi. EEG2Rep: Enhancing self-supervised EEG representation through informative masked imputs. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '24), pp. 5544 5555, Barcelona, Spain, 2024. ACM. doi: 10.1145/
3637528.3671600
Xuan Son Nguyen. Geomnet: A neural network based on riemannian geometries of spd matrix space and cholesky space for 3d skeleton-based interaction recognition. In Proceedings of the JEEE/CVF International Conference on Computer Vision (ICCV), pp. 13779113399, 2021.
Iyad Obeid and Joseph Picone. The temple university hospital eeg data corpus. Frontiers in Neuro- science, 10(196), 2016. doi: 20..0000..
14

---

Published as a conference paper at ICLR 2026
OpenAl. GPT-4 technical report. arXiv preprint arXtv:2303.08774, 2023. doi: 10.48550/arXiv. 2303.08774.
Yue-Ting Pan, Jing-Lun Chou, and Chun-Shu Wei. MAtt: A manifold attention network for EEG decoding. In NeurIPS, pp. 31116-31129, 2022.
Wei Yan Peh, Yuanyuan Yao, and Justin Dauwels. Transformer convolutional neural networks for automated artifact detection in scalp eeg. In Proceedings of the 2022 44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 3599-3602,
2022a. doi: 10.1 1.11009//BC482229 202.999799....
Wei Yan Peh, Yuanyuan Yao, and Justin Dauwels. Transformer convolutional neural networks for automated artifact detection in scalp eeg. In Proceedings of the 2022 44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 3599-3602, 2022b.
Xavier Pennec. Statistical computing on manifolds for computational anatomy. Habilitation à diriger des recherches, Université Nice Sophia Antipolis, December 2006. Mémoire présenté pour l'obtention de l'habilitation à diriger des recherches.
Xavier Pennec, Pierre Fillard, and Nicholas Ayache. Riemannian framework for tensor computing. International Journal of Computer Vision, 66(1 (6(1))441-66 2006.
H. Phan and K. Mikkelsen. Automatic sleep staging of eeg signals: Recent development, challenges, and future directions. Physiological Measurement, 43(4):04TR0,, 2022.
Huy Phan, Fernando Andreotti, Navin Cooray, Oliver Y Chen, and Maarten De Vos. Seqsleep- net: End-to-end hierarchical recurrent neural network for sequence-to-sequuee automatic sleep staging. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 27(3):400-410, 2019.
Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agar- wal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever. Learning transferable visual models from natural language supervision. Meila and Tong Zhang (eds.), Proceedings of the 38th International Conference on Machine Learning. volume 139 of Proceedings of Machine Learning Research, pp. 8748 8763. PMLR, 18 24 Jul 2021.
Marina
Saimunur Rahman, Lei Wang, Changming Sun, and Luping Zhou. Redro: Efficiently learning large-sized SPD visual representation. In Computer Vision - ECCV 2020, Proceedings, Part XV, volume 12360 of Lecture Notes Computer Science, pp. 1-17. Springer, 2020. doi: 10.1007/
Saimunur Rahman, Piotr Koniusz, Lei Wang, Luping Zhou, Peyman Moghadam, and Changming Sun. Learning partial correlation based deep visual representation for image classification. In Proceedings of the JEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 6231-6240, 2023. doi: 10.1 11119//VR522992222.0000
C. R. Rao. Information and the accuracy attainable in the estimation of statistical parameters. Bul- letin of the Calcutta Mathematical Society, 37(3):81-9) 1945.
Subhrajit Roy, Isabell Kiral-Kornek, and Stefan Harrer. Chrononet: A deep recurrent neural net- work for abnormal eeg identification. In Artificial Intelligence in Medicine: 17th Conference on Artificial Intelligence in Medicine, AIME 2019, pp. 47-56. Springer, 2019.
Yonghao Song, Xueyu Jia, Lie Yang, and Longhan Xie. Transformer based learning for eeg decoding. arXiv preprint arXiv: 200.:22006111770 2021a. URL https://axxiv.. httg/abs2110e 11170 Preprint.
feature
Yonghao Song, Qingging Zheng, Bingchuan Liu, and Xiaorong Gao. Beg conformer: Convolu- tional transformer for eeg decoding and visualization. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 31:710-719, 2022. doi: 10. N0.100//NSSEE.22223322555
15

---

Published as a conference paper at ICLR 2026
Yue Song, Nicu Sebe, and Wei Wang. Why approximate matrix square outperforms accurate svd in global covariance pooling? In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 1115 1115-1123, 2021b.
David Steyrl, Reinhold Scherer, Josef Faller, and Gernot R MüllerrPutz. Random forests in non- invasive sensorimotor rhythm brain-computer interfaces: a practical and convenient non-linear classifier. Biomedical Enginneriing/Bomddiinissk Technik, 61(1):77-86, 2016.
Nazmi Sofian Suhaimi, James Mountstephens, Jason Teo, et al. Eeg-based emotion recognition:
A state-of-the-art review of current trends and opportunities. Computational Intelligence and Neuroxcience, 2020:981 4248, 2020.
Yann Thanwerdas and Xavier Pennec. Theoretically and computationally convenient geometries on full-rank correlation matrices. SIAM J. Matrix Anal. Appl., 2022.
Christopher Wang, Vighnesh Subramaniam, Adam Uri Yaari, Gabriel Kreiman, Boris Katz, Ignacio Cases, and Andrei Barbu. BrainBERT: Self-supervised representation learning for intracranial recordings. International Conference on Learning Representations (ICLR), Poster, 2023.
Jiquan Wang, Sha Zhao, Zhiling Luo, Yangxuan Zhou, Haiteng Jiang, Shijian Li, Tao Li, and Gang Pan. Cbramod: A criss-cross brain foundation model for EEG decoding. In International Con- ference on Learning Representations (ICLR), 2025a.
Qilong Wang, Peihua Li, and Lei Zhang. G2DeNet: Global gaussian distribution embedding net- work and its application visual recognition. In Proceedings of the IEEE Conference Com- puter Vision and Pattern Recognition (CVPR), pp. 2730-2739, 2017.
Rui Wang. Chen Hu, Xiaoning Song. Xiaojun Wu, Nicu Sebe, and Ziheng Chen. Towards a gen- eral attention framework on gyrovector spaces for matrix manifolds. The Thirty-ninth Annual Conference on Neural Information Processing Systems, 2025b.
Chaoqi Yang, Danica Xiao, M. Brandon Westover, and Jimeng Sun. Sele-supe eeg repre- sentation learning for automatic sleep staging. arXiv preprint arXiv:2110.15279, 2021. URL https: //8 w/t.//vavvvv///.////v//eee/..wvv org/ wtwg//as/////. abs/21100 15278 Preprint.
Chaoqi Yang, M. Brandon Westover, and Jimeng Sun. BIOT: Biosignal transformer for cross- data learning in the wild. In Advances in Neural Information Processing Systems (NeurIPS), volume 36, pp. 78260, 2023.
Daoze Zhang, Zhizhang Yuan, Yang Yang, Junru Chen, Jingjing Wang, and Yafeng Li. Brant: Foundation model for intracranial neural signal. In Advances in Neural Information Processing Systems (NeurIPS), volume 36, pp. 26304-26321, 2023.
C. R. Zhao, Y. B. Wang, X. Y. Jiang, F. Shen, K. T. Song, D. Li, and D. Q. Miao. Learning domain invariant prompt for vision-language models. IEEE Transactions on Image Processing, 33:1348-1360, 2024.
Y. Zhou, S. Zhao, J. Wang, H. Jiang, S. Li, B. Luo, T. Li, and G. Pan. Personalized sleep staging leveraging source-free unsupervised domain adaptation. Proceedings of the AAAI Conference on Artificial Intelligence, pp. 44599-14537, 2025.
Pengfei Zhu, Jialu Li. Zhaowei Dong, Ling Shao, et al. CCP-GNN: Competitive covariance pooling for improving graph neural networks. JEEE Transactions on Neural Networks and Learning Systems, 36(4))6395-644))) 2024. doi: STT.1///NNNNS22222333990
16

---

Published as a conference paper at ICLR 2026
A THE USE OF LARGE LANGUAGE MODELS (LLMS)
We used large language models (LLMs) only for limited assistance in language polishing and for implementing minor parts of the code. All research ideas, experiment design, analysis, and conclu- sions were conceived and validated by the authors, who remain fully responsible for the content of this work.
B NOTATIONS
For better clarity, we summarize all the notations used in this paper in Tab.
Table 9: Notations used in this paper.
Symbol
Meaning
S
of n n symmetric positive definite matrices Affine invariant Riemannian distance S Exponential map E S for langent vector S TpStt Logarithm map E St for Q St Tangent space S at
dAIM Q)
ESpr(S)
Logp(Q)
TpS
Frobenius
WFM((a)),
Weighted Fréchet mean on S with weights {w) Nonnegative weights with Σ, Wi Family of n- n-ddimensionl Gaussians parameterized by (E, Covariance matrix and mean vector of a Gaussian Hyperparameters for quotient and Riemannian embedding dimensions
Wy (m)
k, k
C DATASET DESCRIPTION AND PREPROCESSING
In this section, we provide additional implementation details to ensure full reproducibility of our experiments, including dataset descriptions, preprocessing steps, and training configurations that were not covered in the main paper.
C.I THE TUAB DATASET
Description. The TUAB datase is large clinical EEG corpus in which each recording is labeled as either normal abnormal. The raw EEGs are 23-channel clinical recordings sampled at 256 Hz. After segmentation into non-overlapping 10-second windows, the corpus provides 409,455 samples for binary normal/abnormal classification.
Preprocessing. For experiments using the BIOT model, adopt the preprocessing pipeline pro- vided in BIOT (Yang et al.) 2023). All recordings are processed using 16 bipolar montage channels defined under the 10-20 system. Each EEG signal first resampled to 200 Hz and then transformed into a standardized set of 16 bipolar derivations (Yang et al. (023). which specify fixed electrode pairs (c.g., FP1-F7, F7-T3, T3-T5, etc.). Segments shorter than 10 seconds are discarded. For experiments using LaBraM, we adopt the preprocessing protocol defined in (Jiang et al.) 2024). The EEG signals are first band-pass filtered between 0.1 Hz and 75 Hz remove low-frequency drift, followed by a 50 Hz. notch filter to suppress power-line interference. All recordings are then re- sampled to 200 Hz. Since raw EEG values typically lie within [-0.1, 0.1] mV, we normalize the amplitude by scaling the unit to 0.1 mV such that the resulting signals fall approximately within [-1, 1]. Each valid 10-second window inherits the normal/abnormal label of its source recording and is stored as individual sample for downstream training, validation. and evaluation.
Experimental Configuration. We adopt subject-independent evaluation protocol. Since the official subject-wise split already provides separate training and test partitions, we further divide the training portion into 80%-20% train-validation split, following prior work (Yang et al. 2023 Jiang et al. 2024h. The model achieving the highest validation performance is selected for final testing. Each method is evaluated using own preprocessing pipeline and corresponding channel configuration: 16 channels for BIOT and 23 channels for LaBraM. To improve statistical reliability, all experiments are repeated three times with different random seeds, and we report the mean and standard deviation across runs.
https://isip. htt.ppppppeeeesscce/crcaaaatttaa /dwwn oads. shtm"
17

---

Published as a conference paper at ICLR 2026
C.2 THE TUEV DATASET
Description. The TUEV corpus is clinically annotated subset of TUEG that categorizes EEG segments into six event types: spike and sharp wave (SPSW), generalized periodic epileptiform dis- charges (GPED), periodic lateralized epileptiform discharges (PLED), eye movement (EYEM), arti- fact (ARTF), and background (BCKG). All recordings contain 23 EEG channels sampled at 256 Hz, and the dataset provides 112,491 non-overlapping 5-sccond segments for multiclass classification.
Preprocessing. We adopt the same preprocessing pipeline in TUAB. Each EEG recording is resampled to 200 Hz and transformed into the standardized 16-channel bipolar montage used in shorter than 5 discarded. Each 5-second segment inherits
BIOT Yang al. the event label of its source annotation and is stored as an individual sample for downstream training, validation, and evaluation.
Experimental Configuration. Following the official subject- wise split, the training portion is fur- ther divided into an 80%-20% train-vall valin-vaiiation split, and the model with the best validation accuracy is used for final testing. All experiments are repeated three times with different random seeds, and the mean and standard deviation are reported.
C.3 THE BCIC2B DATASET
Description. The BCIC2B motor-imagery datase recordings from 9 participants and in- cludes both EEG and EOG modalities. EEG signals were collected from three bipolar channels (C3, Cz, C4) at sampling rate of 250 Hz, while ocular activity monitored using three monopolar EOG electrodes with a dynamic range of +1 mV. Each participant completed five experimental runs: the first were screening sessions without feedback, and the remaining three provided feedback. The motor imagery task involved imagining either left-hand or right-hand movements (class 1 and class 2). For the screening phase, each subject was recorded on two separate days within two-weck interval, and every session consisted of 120 trials evenly distributed across the two classes.
Preprocessing. We discard all ocular channels (h0G:ch01, BOG: ch02, EOG: ch03) prior to further processing. The EEG signals are band-pass filtered within 0-38 Hz, resampled to 200 Hz, and subsequently normalized using EA normalization He & (219), which widely adopted for notor-imagery datasets.
Experimental Configuration. We employ a subject-independent evaluation. Since the BCIC2B dataset contains recordings from 9 subjects, the experiments follow 9-fold LOSO cross-validation protocol. In each fold, one subject (e.g.. subl) is designated the test set, and the remaining subjects (sub2--sube are used for training. To enhance statistical reliability, every experiment is repeated 3 times with different random seeds, and the mean and standard deviation are reported.
C.4 THE PHYSIOPP00 DATASET
Description. The PhysioNetP300 datase includes recordings from 12 participants performing a P300-based character-spellingg task using Donchin speller. EEG was acquired with 64-channel BioSemi ActiveTwo system at sampling rate of 2048 Hz. Each subject was asked to spell 20 characters. For each run, target character standard 6x6 matrix were intensified for 100 ms with 50 ms intervals (SOA 150 ms), resulting in roughly 20 flashes of the target per run. During the sequence, subjects focused the designated character and counted its occurrences.
randomly chosen, and the rows and columns of
Preprocessing. We retain all 64 EEG channels from the BioSemi montage and first convert the raw signals into uniform units. The data are band-pass filtered within 0-120 Hz and resampled to 200 Hz. For each trial, we use a 2-second window beginning 0.7 before the flash onset, which corresponds approximately to [-0.1, 2] peri-stimulus interval after resampling. Each extracted epoch is assigned a binary label (target or non-target) depending on whether the intensified row or column contains the designated character.
htterr///shhaiioooeessssssscssst http:///......ee..ee./o/oooooo.. shtml
18

---

Published as a conference paper at ICLR 2026
Table 10: Dataset-backbone specific hyperparameters for downstream training.
TUAB/TUEY
BCIC2B
PhysioNetP300
Hyperparameters
LaBraM
BIOT
LaBraM
BIOT
LaBraM
BIOT
Batch size
64
64
64
64
64
64
LR scheduler
Cosine
Cosine
OneCycle
OneCycle
OneCycle
OneCycle
Start learning rate
1.5e-5
1.5e-5
3.0e-5
3,0e-5
Peak/Max learning rate
5e-4
2.5e-3
4.0e-4
4.0e-4
8.0e-4
8.0e-4
Minimal learning rate
le-6
le-6
1.5e-7
1.5e-7
3.0e-7
3.0e-7
Optimizer
AdamW
Adam
AdamW
AdamW
AdamW
AdamW
Adam B
0.9. 0.999
0.9, 0,999
0.9. 0.999
0.9, 0.999
0.9. 0.999
0.9, 0.999
Weight decay
0.05
0.0005
0.05
0.05
0.05
0.05
Total epochs
100
100
100
100
Warmup epochs
Dropout
0
0.2
0
0.2
0
0.2
Drop path
0.1
0
0
Layer-wise decay
0.65
Label smoothing (multi-class)
0.1
0.1
0.1
Sliding-windood window step
125 ms
125 ms
Experimental Configuration. We follow the configuration used in BENDR Kostas et al. (2021) and exclude subjects 8, 10, and 12, leaving data from the remaining participants. A subject- independent evaluation is employed, using a 9-fold LOSO cross-validation protocol in which one subject held out for testing while the others are used for training. During fine-tuning, the Phys- ioNetP300 data are processed using 125 ms sliding window to extract temporally localized ERP segments for classification.
D HYPERPARAMETERS SETTING
Unless otherwise stated, the saanset-backbone specific configurations summarized in Tab. TO For TUAB and TUEV, models are fine-tuned for 50 epochs with batch size 64 and cosine scheduling: LaBraM uses A with peak learning rate 5e-4, minimal le-6, 5 warmup epochs, drop path 0.1, and layer-wise decay 0.65; BIOT uses Adam with peak learning rate 2.5e-3, minimal le-6, no warmup, and dropout 0.2. For BCIC2B and PhysioNetP300, we adopt LOSO validation and OneCycle schedules for 100 epochs with batch size 64. BCIC2B starts at 1.5e-5, peaks at 4.0e-4, and decays to 1.5e-7, while PhysioNetP300 starts at 3.0e-5, peaks 8.0e-4, and decays to 3.0e-7. Other optimizer settings follow Tab. 10 to ensure fair comparison across heads.
E
MORE RESULTS
E.
COMPARISONS USING THE CBRAMOD BACKBONE
Table 11: Comparison on TUAB using the CBraMod backbone.
Methods
Model Size (#Params)
Time / Epoch (m)
Balanced Acc.
Coben's Kappa
Weighted F1
CBruMid (Original)"
4.0M
10.42
0.7973 1 0.0024
0.8805
0.0043
0.8745
D.0031
CBraMed GAP"
4.0M
0.0031
0.8719
0.8774
0.0143
CBraMod + iSQRT-COV
4.M++
17.89
0.8046 + 0.0047
0.8873 = 0.0064
0.8841
0.0022
CBraMod SVD-Padi
4.0M 402.-220.3
29.97
0.5069 + 0.0051
0,8010
0.0053
0.8885
0.0025
CBraMod 1SICE
4.0M+
65.38
0.8027 + 0.0054
0.8858
0.0019
0.8823
0.0021
CBraMod RHOP
24.66
20.14
0.8131 + 0.0019
0.8972
0.0052
0.8913
0.0024
Re-implemented following the official CBraMod preprocessing protocol.
The original CBraMod (Wang et al. 2025a) employs multi-layer nonlinear classifier rather than a GAP head. To enable fair comparison, we replaced this classifier with GAP, RHOP, and sev- eral existing siaarinnce-bsell pooling heads, while keeping all remaining components unchanged. Because the exact subject-level data partitions used in CBraMod cannot faithfully reproduced, follow the authors' official preprocessing protocol and re-implement the model according to
19

---

Published as a conference paper at ICLR 2026
their recommendations All models are trained from scratch under the same experimental settings. As shown in Tab. [T] RHOP consistently outperforms both the original classifier and other pool- ing baselines across all evaluation metrics, highlighting its clear advantage when integrated into the CBraMod backbone.
E.2 ABLATION ON THE NUMBER OF FRÉCHET MEAN (FM) ITERATIONS
We evaluate the impact of the number of Fréchet Mean (FM) iterations on both TUAB and TUEV. The results are summarized in Tabs. 12 and 13 where the iteration count is set to 1, 2. 3, and oo, with oo denoting iteration until convergence (i.e., the matrix norm change falling below 1 x 10-5),
Across both datasets, performance improves noticeably from 1 to 2 iterations, but the gains saturate quickly thereafter: configurations using 2, 3, indicates that a small number of FM iterations is sufficient for stable and effective Riemannian ag- gregation. Additional iterations incur significant computational overhead without providing further benefits. Consequently, we adopt I iteration as the default setting, achieving a strong balance be- tween accuracy and efficiency. This observation also consistent with prior studies Brooks et al. 2019 Chen et al. )2024b; Chakraborty et al. (2022).
iterations yield nearly identical results. This
Table 12: Ablation of FM iterations TUAB.
Methods
#lter
Time/Epoch (min)
Balanced Acc.
AUC-PR
AUROC
LaBraM-Baal
1
21.48
0.8244 + 0.0012
0.9078 + 0.0012
0.9105 + 0.0011
LaBraMM-B Buss
2
24.59
0.8261 + 0.0011
0.9086 1 0.0011
0.9110 + 0.0010
LaBraM-Band
3
27.71
0.8263 0.0012
0.9085 1 0.0011
0.9111 + 0.0010
LaBraM-Band -Base
26
40.19
0.8239 0.0013
0.9077 + 0.0011
0.9107 = 0.0010
Table 13: Ablation of FM iterations on TUEV.
Methods
#Iter
Time/Epoch (min)
Balanced Acc.
Cohen's Kappa
Weighted Fl
LaBraM-Base
1
2.25
0.6380 + 0.0056
0.6785 + 0.0079
0.8420 + 0.0038
LaBraM--BB -Base
2
3,38
0.6401 + 0. 0.0054
0,6802 1 0.0077
0.8447 + U 00006
LaBraM-BB -Bsse
3
5.02
0.6400 + 0.0053
0.6803 + 0.0076
0.8451 + 0.0037
LaBraM-Ba
26
10.21
0.6360 + 0.0054
0.6783 # 0.0076
0.8414 + 0.0037
E.3 MORE ABLATION ON kk,
We further investigate the influence of the embedding dimensions and k' on model performance. As shown in Tab. 14 in the Quotient-GGassian embedding. increasing & expands the SPD dimension from to d + k, which amplifies the first-order term k/4pa T. As k grows, the embedding becomes more mean-dominated, weakening the relative contribution of second-order statistics that are known to be highly informative for EEG decoding, Moreover, enlarging d + k introduces quadratic growth in matrix size, leading to increased computational burden and potential numerical instability. These effects collectively explain why excessively large k tends to degrade performance.
A parallel interpretation applics to K', which controls the dimensionality the embedded mean vector: larger values introduce additional first-order information but also increase representation size, resulting in diminishing returns and eventual performance decline. As summarized in Tab. [4] performance improves initially as (k, K') increases, but the gains plateau and then decrease for overly large values. Notably, (k = 2, k' 2) and (k 3, k' 3) consistently lie at or near the optimum across TUAB and TUEV, indicating that moderate dimensionality provides the balance between representational richness, computational efficiency, and numerical stability.
F FRÉCHET MEAN ON SPD MANIFOLDS
As shown in Alg. the Karcher flow algorithm computes the weighted Fréchet mean (WFM) on the SPD manifold through an iterative process. In each iteration, the data points are projected onto the tangent space the current estimate G using the logarithmic map, weighted average is
https:
www.tht..b...wjppooooooe com learni http:h/www..ggggaaaa...eeeetetta
README md
20

---

Published as a conference paper at ICLR 2026
Table 14: Ablation on embedding dimensions (kc k*) for LaBraM-Base.
TUAB
TUEV
K
Balanced Acc.
AUC-PR
AUROC
Balanced Ace.
Cohen's Kappa
Weighted F1
0.8065 10.0019
0.8973.0.0011
0.8988_0.0011 0.0002
0.6457.0.0122
0.5772.10.023
0.7876.0000114
2
0.0093110.0021
0.905410.0016
0,9064-0.0013
0.6339:10.0184
0.6078::0.0227
0.8062+100102
0.0099
0.9054+0.0015
0.9060-0.0012
16726++0.013
0.6456+
0.8224+0..0999
0..0011
0.9017.100016
0.9042_0.0012
0.632510.0012
0.635910.0200
0.0184
0.8171++00.011
0.8975+0.0018
0.9013-0.0012
0.6631
0.6471+0.0199
0.8252++0.000
0.0002
0.904411.0014
0.9071=000011
0.645911.0012
0..005
0.7970
2
0.8163-10.0017
0.905810.0016
0.9057-0.0011
0.6440.10.0137
0.619610.0228
0.814510.0011
0.8164++0.0018
0.9043+0.0015
0.9046-0.0012
0.6409+0.0135
0.6302+-0.0221
0.8129+00.0100
0.81831000019
0,903510.0015
0.9062-000011
0.6659..0.012
0.631710.0273
0.8176.1001335
0.8193+-0.0000
0.9008+0.0016
0.9039=0.001
0.6372=000161
0.6220=-0.0234
0,8135+00.002
0.0014
0.9078+0.0012
0.9105-0.0011
0.6080+0.00.66
0.6785+0.0079
0.8420+ 0.0038
0.8187:+0.0021
0.902440.0017
0.9041=0.0013
0.6484::000388
0.6116=00.0217
0.8123++0.019
0.8181++000000
0.9017+0.0016
0.9042-0.001
0.6475+000022
0.6341+0.0200
0.8188+0.0107
2
0.8164:10.0019
0.904311.0015
0.9046-0.0011
0.6362::0.0141
0.6193-00.022
0.8127
0.8187++0.001
0.9024=0.0017
0.9041-0.0013
0.6484::0.0138
0.6116=000217
0.8123+0.0109
0.8190++0.0020
0.9031+0.0016
0.9050=0.0012
0.6100+-0.0132
0.6250+00.025
0.8150+0.0110
Algorithm 2: Karcher Flow Algorithm on the SPD Manifold under AIM
Input : set of SPD matrices X X1...N E St Number of iterations K
Output : The FM Gk E S
Initialize Go = > X;
for k + 1 too K do
G + ExPo
(E Loger- (Xi)
end
calculated this tangent space, and the result is mapped back to the manifold using the exponential map. This algorithm guaranteed converge on manifolds with non-positive curvatures, such as S Karcher 1977a). In practice, we initialize Go with the arithmetic mean and set the number of iterations K I, which provides stable and efficient approximation.
G LIMITATION
RHOP involves batched SVD to compute matrix logarithms and update sparse inverse covariance. While such operations generally less optimized than convolutions and attention current GPUs, in our case, the matrix size is very small (at most 15x 15x15), making the actual overhead negligible. Thus, this limitation is mainly implementation detail rather than a practical concern.
H FUTURE WORK
RHOP is primarily motivated by EEG decoding, but its basic framework and statistics based princi- ples general. The Quotient Gaussian Embedding and Riemannian Gaussian Embedding capture two key characteristics that are particularly salient EEG signals, i.e., spatiotemporal dependency and scale variation. RHOP employs second-order pooling across temporal segments, which pre- serves fine-grained temporal relations that are lost in first-order pooling schemes. More importantly, the quotient Gaussian provides scale-invarian representations, allowing the model focus on rela- tional structure rather than absolute amplitude. These theoretical properties make RHOP naturally well-suited for EEG foundation models, which typically rely on mean- mean-based pooling.
However, the RHOP head can also be extended to other multi-channel temporal modalities that exhibit similar structural characteristies, such ECG, MEG, and fMRI-derived time series. In these domains, the high-order pooling framework may enhance representation ability, while the degree of quotient Gaussian be adapted to reflect the discriminative role of signal amplitude. Investigating
21

---

Published as a conference paper at ICLR 2026
these directions may help understand when quotient-basee basedd modeling is advantageous and shed light on how RHOP could generalize beyond EEG.
I PROOF OF THE THM. 4.2
Proof of Thm. 4.2. We construct V @V(n)) + Sittk and show it is a smooth embedding. Fix k 2 and define
[C + kpue [((k] (CC.p)
(0
M.....
(14)
Ik
columns
Observe that @(C, (i) is SPD and det @(C, (1) = det C. Indeed, with
In
(k)
T(p)
(15)
0 Tk
a direct multiplication gives
C
0
M), = T(u)
0
In
T())
(16)
Since C' E S and T(u) is invertible, (bC, 14) is SPD. Also det T(₁) = 1, hence det $ μd) det C.
Set s(C) (det C) n+* and define
(),,
(17)
Then det (CC = 1, p) $ matching Eq. 6
For injectivity and smooth inverse on the image, suppose (1) VV(C,, μ2) X, and write
X11
X22 By construction X22 s(Ci)Is, s(C)) s(C2) Then X12 p (k)
X12
X
X21
implies μl 12 μ4, and X11 =(C, kuqu T) yields C1 = C2.
Conversely, given X in the image, recover s = 1 tr (r(222). then = s X1201 (with e1 the first basis vector in R,, and finally C = - X11 kpp These depend smoothly on X and satisfy (C, X. Hence
&
smooth embedding.
remains to situate this within the affine action. Let N St As shown in Nguyen (2021): Lovrić et (2000)), Eqs. (41)-(47), the transitive Aff (n)- action on ((n) and the embedding J: AJJ (n)
(n) ) be the space of Gaussians (E, with E E
+ SL(n k) induce
Σ + kpye" (B)
(E. b (det Σ) n+*
St.1
(18)
I
A quotient Gaussian identifies (E, n1) up to positive scalar multiple on Σ. Choosing the canonical representative C' = (det Σ) E yields exactly vi (C, μd). Therefore, V is the natural embedding for quotient Gaussians.
22


Reviews:
[{"review_id": "ckWd6O493a", "reviewer": "Reviewer_Pf1i", "summary": "The paper highlights a shortcoming of existing foundation models trained on EEG signals: they ignore the informative geometry of the underlying spaces. The paper addresses this by proposing a simple module that can be added to (even pre-trained) existing foundations models to allow them to make use of Riemannian geometry, which is well-known in the BCI community to capture important task-relevant information.", "questions": "1. are there other applications of this besides EEG?\n2. L058: Is it really about scaling, or more about applying/tailoring/tuning?\n3. L070: What does CLS stand for?\n4. L089 and 094: SPD is an adjective, so what's the missing noun it's modifying here? Matrices? Manifold?\n5. L104 and 106: A word is missing after EEG here. Maybe \"signals\" or \"measurements\"?\n6. L127: Can the authors more precisely and mathematically explain what is meant here (and elsewhere in the section) by \"collapses all spatiotemporal tokens into a single global discriptor\"? Isn't the proprosed method also doing that via eq. (9), but in a geometry-aware way?\n7. L185 and 189: $\\mathcal{Q}\\mathcal{N}(n)$ isn't a single distribution but the space of all distributions, isn't it? And then eq. (5) is a specific (quotient) distribution that is also a representative of the equivalence class of the nonquotient distributions? So each element $[\\Sigma, \\mu]$ is an equivalence class of distributions $(\\Sigma^\\prime, \\mu)$ where ${\\Sigma}, {\\Sigma^\\prime}$ have the same corresponding correlation matrix?\n8. L194: why not use something more informative and accessible than \"↓\", like \"Appendix F\"?\n9. L210: is eq. (7) here the same as (4)?\n10. Tables 3 and 4: why does the param count for LaBraM-Base+iSICE drop by over 20k here, while all other methods have little or no drop?", "limitations": "", "rating": 8, "confidence": 2, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- comprehensive, compelling experiments\n- open source code and applications on public datasets\n- well written\n- clear theoretical motivation\n- nice translation of the theory into a practical method", "weaknesses": "- the clear performance gains of the method are nevertheless modest\n- the focus is a bit limited (compared to the broader ICLR community), focusing on EEG applications", "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": "5vbDlQjm0V", "reviewer": "Reviewer_VvTH", "summary": "This paper proposes RHOP, a pooling module for EEG foundation models that uses quotient Gaussian embeddings and Riemannian aggregation on SPD manifolds. While the geometric approach is conceptually interesting, the paper suffers from multiple critical flaws: missing the current SOTA baseline (CBraMod in ICLR'25), potential rank deficiency issues, unjustified Gaussian assumptions, and marginal empirical gains.", "questions": "See comments above.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The method is conceptually interesting and represents a novel approach to token-level aggregation in EEG foundation models. The paper is well-written with clear methodology and good presentation.", "weaknesses": "1.Missing Backbone (CBraMod in ICLR'25): \n\nThe paper cites CBraMod [1] in page 2 but did not evaluate on it. CBraMod outperforms LaBraM, BIOT, and other EEG foundation models, as well as backbone + RHOP proposed in this work, while being substantially lighter in terms of trainable params. Moreover, CBraMod[1] is open‑source and provides pretrained checkpoints, which makes it directly compatible as a plug‑in backbone for RHOP. Ignoring CbraMod as backbone limits the paper's contribution.\n\n2. Rank Deficiency Not Resolved:\n\nThe paper does not clearly specify the values of $D$, $N$, $T$, used by each baseline on each dataset. This prevents proper assessment of issues such as rank-deficiency.\nWhen \\( D < T \\) (common in EEG), the covariance matrix \\( $\\Sigma_n \\in \\mathbb{R}^{T \\times T}$ \\) is rank-deficient, with \nrank($\\Sigma_n) \\leq D $.\n$C_n = D_n^{-1/2} \\Sigma_n D_n^{-1/2}\\$ preserves rank and therefore cannot convert a semi-definite matrix into a strictly positive definite (SPD) one.\nMoreover, in Equation (11), $\\mu_n^{(k)} (\\mu_n^{(k)})^\\top = k \\mu_n \\mu_n^\\top$, leaving the Schur complement as\n$S = C_n$. This will leave $Y_n$ in Eq. 11 not SPD, therefore, Riemannian geometry should not be used.  \nThis severe rank deficiency fundamentally limits the informativeness of the SPD representation.\nParticularly, In BCIC2B, where $D=3$, the resulting covariance matrix has very low rank, limiting its capability to capture informative SPD structure.\n\n3. Gaussian Assumption Unjustified:\n \nRHOP applies Quotient‑Gaussian embedding to learned token features, not to raw EEG. However, these features are outputs of deep encoders (LaBraM or BIOT), including non-linear activations, normalization layers, and attention mechanisms, making Gaussian distribution highly unlikely, leaving the SPD embedding theoretically questionable. Covariance is not a sufficient statistic for non-Gaussian data, and QGE may discard essential structure.\n\n4. Across several datasets, the improvement of baseline + RHOP over the corresponding baseline is marginal (often less than 1%).\n\nRefs:\n\n[1] Wang, Jiquan, et al. \"Cbramod: A criss-cross brain foundation model for eeg decoding.\" arXiv preprint arXiv:2412.07236 (2024).\n\n\nI would be willing to raise my score if the authors address any concerns outlined above.", "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": "hAknLvWYOl", "reviewer": "Reviewer_sQZN", "summary": "This paper presents an exploratory attempt to integrate recent large brain foundation models with second-order pooling techniques originally developed in computer vision. The authors claim that their proposed neural layer captures second-order information and global spatiotemporal dependencies from EEGs, and evaluate their approaches on several EEG-BCI scenarios.", "questions": "1. What is the physiological or theoretical motivation for the covariance of the temporal-segment tokens to carry class-discriminative information? Has any prior literature demonstrated its effectiveness for the EEG-BCI classification?\n\n2. Can the authors clarify the experimental protocol in detail? Were the experiments subject-dependent or subject-independent? How many folds or runs were used for cross-validation? What preprocessing steps were applied to the EEG signals (e.g., band-pass filtering, normalization, artifact removal)?\n\n3. Please specify all experimental settings in all experiments. Regarding the \"BCIC2B\" dataset, please specify: Which exact dataset version or competition subset was used (e.g., BCI Competition IV-2a or II-2b)? Provide a download link or public reference for reproducibility. What measures were taken to mitigate overfitting, such as early stopping, data augmentation, dropout, or weight decay?\n\n4. Although the EEG-BCI classification inspires the proposed architecture, its design, particularly the covariance of the temporal-segment token and Riemannian high-order pooling, seems more general and not specific to EEG. Could the authors discuss whether their model can be effectively applied to other domains where temporal dependencies and non-Euclidean structure exist (e.g., video, speech, or physiological time series)? If so, what properties of those modalities would make the approach more suitable or interpretable than in EEGs?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "Overall, the work is conceptually interesting. It aims to transfer second-order modeling paradigms from vision to EEG-based brain signal analysis. The motivation is creative, and such cross-domain adaptation deserves attention.", "weaknesses": "1. The paper frequently cites SPDNet approaches where SPD matrices are computed as spatial covariance matrices derived from multichannel EEG time series. However, the current work constructs SPD representations from tokens derived from the backbone model on temporal segment EEGs, i.e., covariances across temporal-segment tokens rather than across spatial channels. This formulation deviates from existing literature on Riemannian EEG analysis, where spatial covariance carries physiologically meaningful information about inter-channel connectivity. Since reaction time and task onset vary substantially across trials, temporal alignment is inconsistent, making temporal-segment covariance unlikely to encode stable or discriminative features. The marginal performance gains across datasets and backbones (Tables 1–4) further support this concern. Without a clear justification, the connection between the proposed SPD representation and neural dynamics remains weak.\n\n2. The experimental setup is under-specified. It is unclear whether the experiments are subject-independent or subject-dependent, how many cross-validation folds were used, and what preprocessing pipeline (e.g., filtering, artifact rejection, normalization) was applied. These details are critical, as EEG performance is highly sensitive to preprocessing and evaluation protocols. Moreover, the description of the BCIC2B dataset is ambiguous; it is not stated which BCI Competition dataset (e.g., IV-2a, II-2b, etc.) was used. Given that such datasets are relatively small, large-scale models like LaBraM-Base are highly prone to overfitting. Without explicit regularization or validation strategies, the reported performance may not generalize.", "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": "rGYkJTDnkj", "reviewer": "Reviewer_88CQ", "summary": "This paper introduces a plug-and-play classification head module named Riemannian High-Order Pooling , specifically designed for Electroencephalography foundation models. The core thesis is that while state-of-the-art EEG foundation models like BIOT and LaBraM have made significant strides in their feature extraction backbones, their classification stages are underdeveloped. These models typically rely on simple pooling mechanisms  or a single class embedding  for prediction, a process that discards second-order statistics and spatiotemporal structure crucial for EEG decoding. RHOP aims to address this deficiency by injecting principled Riemannian statistics and geometric priors into the classifier, thereby making fuller use of the rich features extracted by the foundation model.", "questions": "See Weakness", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "S1: Significant Problem & Principled Methodology\nThe paper addresses a well-motivated and significant problem. The proposed solution, RHOP, is not an ad-hoc engineering trick but is built on a solid theoretical foundation.\n\nFirst, Quotient-Gaussian Embedding  achieves scale invariance. The use of quotient spaces to achieve invariance is a classic approach in geometric machine learning. Applying it to normalize covariance matrices into correlation matrices elegantly addresses the challenge of amplitude variations across EEG segments, a more principled solution than simple normalization techniques.   \n\nSecond, Riemannian geometry preserves the intrinsic data structure. The long-standing success of Riemannian methods in EEG analysis demonstrates the power of operating on the SPD manifold. By modeling the set of tokens as a Riemannian Gaussian distribution, the method captures not only the central tendency of the features in a geometrically faithful way  but also their dispersion.   \n\nFinally, the iSICE layer serves as a feature refiner. Standard covariance captures all pairwise correlations, which can be misleading due to confounding factors. The inverse covariance  captures partial correlations. By using a sparse inverse covariance, iSICE explicitly models and emphasizes the most direct and robust relationships, which is highly beneficial for dealing with noisy EEG data.   \n\nThese three components are not independent but form a logical, progressive hierarchy of statistical refinement. This structure is a core strength of the method, as it demonstrates a deep understanding of the problem by tackling different statistical challenges at different stages of the pipeline.\n\nS2: Comprehensive and Rigorous Experimental Validation\nThe experimental evaluation is a major highlight of this paper. The authors have gone to great lengths to demonstrate the effectiveness and generalizability of RHOP.\n\nDiverse Benchmarks: Evaluation on four different and widely-used EEG tasks—abnormality detection on TUAB, event classification on TUEV, motor imagery on BCIC2B, and event-related potentials on PhysioP300—shows that the method is not overfitted to a single problem type. These are standard and challenging benchmarks.   \n\nMultiple Backbones: Testing on both BIOT and LaBraM, two state-of-the-art EEG foundation models, proves that RHOP is, as claimed, a truly \"backbone-agnostic\" module.   \n\nMultiple Training Paradigms: The evaluation across full fine-tuning, linear probing, and training from scratch is comprehensive. The strong performance in the \"from scratch\" and \"linear probing\" settings is particularly impressive, suggesting that RHOP can both impose useful structure early in training and effectively extract discriminative information from fixed representations.   \n\nStrong Baseline Comparisons: The comparison against multiple representative global covariance pooling heads is fair and pits RHOP against its most direct competitors.   \n\nS3: Clarity of Exposition & Reproducibility\nThe paper is well-written, well-structured, and easy to follow. The introduction clearly lays out the motivation. The methods section builds logically from preliminaries to the final framework. Figure 1 provides an excellent visual overview of the entire pipeline. The appendix includes detailed hyperparameters , the Karcher flow algorithm , and a proof for the key embedding theorem , which greatly enhances the work's reproducibility. The authors also promise to release the code upon acceptance, which is in line with academic best practices.", "weaknesses": "While the overall methodology is strong, several key design choices lack sufficient justification or analysis.\n\n- Approximation of the Fréchet Mean: The paper states that for efficiency, the Fréchet Mean is computed using only a single iteration of the Karcher flow. While the desire for efficiency is understandable in a deep learning context, this is a significant approximation. The Fréchet Mean is defined as the minimizer of the variance function, and a single step from an arithmetic mean initialization does not guarantee convergence or proximity to the optimum.\n\n- Sensitivity to Hyperparameters ($k, k'$): The embedding dimensions $k$ and $k'$ are crucial hyperparameters.1 Table 6 shows that performance varies with their setting, but no intuition or methodology is provided on how to choose them or set them for a new task. Were they tuned on a validation set? Is there a theoretical reason why $k=3, k'=3$ is optimal on TUAB?\n\n- Choice of Riemannian-Gaussian Embedding (Eq. 9): The specific method for embedding the Riemannian-Gaussian pair $(P^m, P^c)$ into a single SPD matrix $G$ is drawn from the work of Nguyen. While citing prior work is appropriate, a sentence or two explaining why this particular block matrix form involving the Cholesky decomposition of the covariance is a good choice would be highly beneficial to the reader. What properties does this embedding preserve?", "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)