SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG
Authors: Shanglin Li
Motoaki Kawanabe
Reinmar J Kobler
Venue: ICLR 2025 Poster (2025)
Keywords: geometric deep learning
transfer learning
source-free adaptation
electroencephalography
neurology
brain-computer interfaces
Primary area: applications to neuroscience & cognitive science

Abstract: The non-stationary nature of electroencephalography (EEG) introduces distribution shifts across domains (e.g., days and subjects), posing a significant challenge to EEG-based neurotechnology generalization.
Without labeled calibration data for target domains, the problem is a source-free unsupervised domain adaptation (SFUDA) problem.
For scenarios with constant label distribution, Riemannian geometry-aware statistical alignment frameworks on the symmetric positive definite (SPD) manifold are considered state-of-the-art.
However, many practical scenarios, including EEG-based sleep staging, exhibit label shifts.
Here, we propose a geometric deep learning framework for SFUDA problems under specific distribution shifts, including label shifts.
We introduce a novel, realistic generative model and show that prior Riemannian statistical alignment methods on the SPD manifold can compensate for specific marginal and conditional distribution shifts but hurt generalization under label shifts.
As a remedy, we propose a parameter-efficient manifold optimization strategy termed SPDIM.
SPDIM uses the information maximization principle to learn a single SPD-manifold-constrained parameter per target domain.
In simulations, we demonstrate that SPDIM can compensate for the shifts under our generative model.
Moreover, using public EEG-based brain-computer interface and sleep staging datasets, we show that SPDIM outperforms prior approaches.

Published as a conference paper at ICLR 2025
SPDIM: SOURCE-FREE UNSUPERVISED CONDI- TIONAL AND LABEL SHIFT ADAPTATION IN EEG
Shanglin Li Motoaki Kawanabe & Reinmar J. Kobler
1 Nara Institute of Science and Technology (NAIST), Nara, Japan
2 Department of Dynamic Brain Imaging, ATR, Kyoto, Japan
3 Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan
f Equal contribution
(s (shangl iinngliniin in, kawanabe, re nmmr. koble e koblereeatrrr......
ABSTRACT
The non-stationary nature of eletrrencephallgraphy (EEG) introduces distribu- tion shifts across domains (e.g.. days and subjects), posing significant challenge to EEG-based neurotechnology generalization. Without labeled calibration data for target domains, the problem is source-free free unsupervised domain adaptation (SFUDA) problem. For scenarios with constant label distribution, Riemannian geometry-aware statistical alignment frameworks the symmetric positive defi- nite (SPD) manifold are considered state-of-the-art. However, many practical sce- narios, including EEG-based sleep staging, exhibit label shifts. Here, we propose a geometric deep learning framework for SFUDA problems under specific dis- tribution shifts, including label shifts. We introduce a novel, realistic generative model and show that prior Riemannian statistical alignment methods on the SPD manifold can compensate for specific marginal and conditional distribution shifts but hurt generalization under label shifts. As a remedy, we propose parameter- efficient manifold optimization strategy termed SPDIM. SPDIM uses the informa- tion maximization principle to Iearn a single per target domain. In simulations, we demonstrate that SPDIM can compensate for the shifts under our generative model. Moreover, using public EEG-based brain-come orain-computer interface and sleep staging datasets, we show that SPDIM outper- forms prior approaches.
parameter
INTRODUCTION
Electroenncepaalography (EEG) measures multi-channel electric brain activity from the human scalp NNiedermeyer & da Silva 2005) and can reveal cognitive processes (Pfurtscheller & Da Silva 1999). emotion states (Suhaimi et al. 2020). and health status (Alotaiby et a 2014). Neurotechnologg and brain-computer interfaces (BCI) aim extract patterns from the BEG activity that be utilized for various applications, including rehabilitation and communication (Wolpaw et al. 2002). Despite their capabilities, they currently suffer from a low signal-to-noise ratio (SNR). low specificity, and non-stationarities manifesting as distribution shifts across days and subjects (Fairclough & Lotte 2020).
For EEG-based neurotechnology, distribution shifts have been traditionally mitigated by collecting labeled calibration data and training domain-
models (Lotte et al.) 20188. limiting neurotech- nology utility and scalability (Wei et al., 2022). As an alternative, domain adaptation (DA) learns model from one or multiple source domains that performs well on different (but related) target do- main(s), offering principled statistical learning approaches with theoretical guarantces (Ben-David ctt al.) 2010; [offfman et al.) 2018). Within the BCI field, DA primarily addresses cross-session and cross-subject transfer learning (TL) problems (Wu al., 2020), aiming to achieve robust general- ization across domains (e.g., sessions and subjects) without supervised calibration data.
BCIs that generalize across domains without requiring labeled calibration data challenges in EEG-based BCI research (Fairclough & Lotte (2020) Wolpaw et al. (002). Since target domain data is typically unavailable during training, the problem corresponds to source-free unsu-
of the grand

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generative model
b multl-source domain training (2% M4 D.
source-free UDA with SPDIM (r. ~ Dr
label
noiss
step 1: estimate domain-specifor statistics SPD batch norm layer Tito step 2: fit SPD bias parameter $ Ex
y Cau mT
source-
fo
m
CcB
covariance
J
effacts Sp
Jabel
Sp
class labels
source domains statistics
label priors
22
fo
m
I
LIM
9
target domainn statistics
M w/o SPDIM 7g with SPÒIM
Cov(z) =E
EEG
m
domain
allgn stats on S
9
EEG A
R PxT
Figure 1: Framework Overview. a, EEG data is generated by mixing source signals with unknown, linear forward models A₁. A submanifold Sh of the sources' covariance matrices E E Sp encodes information about the label y. Domain-specifie label priors иj and forward models Aj introduce label and conditional distribution shifts, respectively. b. Multi-source domain training, utilizes balanced batch sampling and the end-to-end latent alignment framework proposed in (Kobler) et al. (0022a). c, Proposed SPDIM framework. After latent alignment of marginal distributions (step 1), SPDIM uses the information maximization (IM) loss to fit bias parameter @ E S (step 2), and thereby counteract over-corrections in step that are driven by label shifts.
pervised domain adaptation (SFUDA) problem (Liu et al.
2021 Yang al. (021). For this problem
class, Riemannian gcometry-aware statistical alignment frameworks (Barachant et al., 2011 oper- ating with symmetric, positive definite (SPD) matrix-valuee features are considered of-te-ot-theann
(SoA) in cross-domain (Roy et al., 2022 Mellot et al. 2023) generalization. They offer several advantageous properties, such invariance linear mixing, that are suitable for EEG data (Con- iedo et al. 2017). as well as consistent (Sabbagh et al.
2020) and inherently interpretable (Kobler
al. 2021) estimators for generative models with log-linear relationship between the power of latent sources and the labels. Additionally, Collas et al. (024) suggests that linear mapping exists between the source and target domains Riemannian geometry framework. To facilitate gener- alization across domains, statistical alignment frameworks aim to align first (Zanini et al., 2017 Yair et al. 2019) and second (Rodrigues al., 2019 Kobler al., (202a)) order moments, denoted Fréchet mean and variance on Riemannian manifolds. Once the moments are aligned, model
trained on source domains typically generalizes to related target domains (Zanini et al. 2017 Wei
ct al. 2022 Kobler et al. 2022a Ju & Guan 2022. Mellot et al. 2024).
Although infrequently studied, many applications, including EEG-based sleep staging, exhibit la- bel shift (Thölke et al. 2023). Under label shift, aligning the moments of the marginal feature distributions can increase the generalization error (Bakas et al.] 2202)). To address various sources of distribution shifts in EEG, an SFUDA approach that can deal with additional label shifts is quired. Machine learning literature offers several frameworks for SFUDA problems with label shift (Li al. 2021] Liang et al.) 2024), but few have been applied EEG data. For example, Li al. 2023) employed the information maximization (Shi & Sha 2012) objective for cross-domain gen- eralization. Within Riemannian geometry methods, Mellot al. (0024) studied an BEG-based age regression problem and proposed framework to facilitate generalization across populations with different prior distributions.
Here, we propose geometric deep learning framework to tackle SFUDA classification problems under distribution shifts, including label shift. We introduce a realistic generative model with a log- linear relationship between the covariance of latent sources and the labels (Figure [p.. We provide theoretical analyses showing that prior Riemannian statistical alignment methods (Figure (pp) on the SPD manifold can compensate for the conditional distribution shifts introduced in our model but hurt generalization under additional label shifts. As a remedy, we propose a parameter- efficcient manifold optimization strategy termed SPDIM. SPDIM employs the information maximization principle to leam a domain-speciff HPD-manifold conrrfooid-ostttiinedd bias parameter to compensate over-corrections introduced via aligning the Fréchet mean (Figure Te).
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2 PRELIMINARIES
2.1 SFUDA SCENARIO
Let y and denote random variables representing the true lahels and associated features, and let (y))) and Py (xly) be the prior and conditional probability distributions for domain j. In the transfer learning scenario considered here, we assume that the class priors тÿ = py(y) can be different from each other, as well as specific shifts in the conditional distributions Pj (x]y). We consider labeled source dataset D, ((r1, Ji) E X, E Va.hi E J. and an unlabeled target dataset Dj { 2: E Xr. Us Ne. JT where y: and js (or j(i) if used suffix) indicate the associated label and domain for each example i. We additionally assume that both datasets share the feature space (i.e., X contain the same classes (i.e., V.- ----), and comprise examples from different domains (i.e., T. n ((=)). The goal is to transfer the knowledge learned from D, to D, via first learning a source decoder h, within hypothesis class H. and then use h, and the unlabeled target dataset D. to learn h, E H.
2.2 RIEMANNIAN GEOMETRY ON SD
The SPD manifold S = {C E DDD cT==CC > 0} together with an inner product on its tangent space ToSp at each point C E St forms a Riemannian manifold. Tangent spaces have Euclidean structure with casy-to-compute distances, which locally approximate Riemannian distances on Sp (Absil et al. 2008). In this work, we consider the affine invariant Riemannian metric (AIRM) CIRR (S) S2 TT(C TTCC-1S S as the inner product, which gives rise to the
following distance (Bhatia 2009):
((C1,C) = Iog(CT+
(I)
where Ci and C2 are two SPD matrices, Tr(-) denotes the trace, log(-) the matrix logarithm, and ||- le the Frobenius norm. For set of points C {O₂ E Shlis, the Fréchet mean is defined as the minimizer of the average squared distances:
M Σ (G,
Č = arg min uG(C) = arg min GES
(2)
GESD
M
1=1
For M 2, there exists a closed form solution:
Ö arg min vo(1Ci, C. = c ( ( GES,
c
(3)
where parameter E [0, 1] smoothly interpolates along the geodesic C1# C2 (i.e., the shortest path) connecting both points.
The logarithmic map Logo St TeSt and exponential map Expe : TeSt + St project points between the manifold and the tangent space point C:
(C,) O¹ log - Expa(S.) T exp(O-
(5)
To transport points S, E ToSD from the tangent space at Ö to the tangent space C.. parallel transport on SD can be used as:
re-c (S:) PC
(6)
While parallel transport is generally defined for tangent space vectors (bssi et al. 2008). for (S+ g AIRM) it can be directly applied without explicitly computing tangent space projections (i.c.. Expo, o Ic-cc o Logg Tc-c.) (Brooks et al. 2019: Yair et al. 2019).
If C' lies along the geodesic connecting C' with the identity matrix Dp there exists step-size R so that C₂ ID, and 6 simplifies to Mellot et al. (2024):
T (C= -o-cCt1 (Q==
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3 METHODS
3.1 GENERATIVE MODEL
In the case of EEG, the features 2; & R comprise epochs of multivariate time-series data with P spatial channels and 7'' consecutive temporal samples. Propagation of brain activity to the EEG electrodes, located at the scalp, is typically modeled linear mixture of sources (Nunez & Srinivasan 2006):
I3 == Az(1)
where Ag() E E EREPP
rank(A)=P) is domain-specifts forward model and 2, E RRPT the activity of latent sources. Utilizing the uniqueness of the polar decomposition for invertible matrices, we constrain the model to
RPP,
A₁ = Qexp(P3)
where Q E e QTQ=IT) is a orthogonal matrix modeling rotations and exp(P;) E Sp SPD matrix modeling dppein-sp scalings.
Like (Sabbagh et al. 2020; Kobler et al., [021] Mellot et al. 2024), we consider zero-mean (i.e., [(z) Op Vi) signals, and log-linear relationship between the spatial covariance E, Cov(zi 2.) E sp of the latent sources 24 and the target Vi. As graphically outlined in Figure we model the source covariance matrices as:
E, = exp oupper oupper (s:)
(10)
where the linear mapping upper PP(44)/2 + Sp transforms vector to a symmetric matrix while preserving its norm (i.e., S E Sp : llupper (s)l and latent log-space features E 1P/42 are generated as:
8; == Bij + Ez: Di y, マ
(11)
where Ln, represents one-hot-coded labels, TΙ Ip, (y-(y:))l contains the class priors for domain j. E, P(((41)/2 is zero-mean additive noise, and {B (F((+)///2X1111 : rank DD|}. We assume that the matrix B is sparse and structured so that label information in log( E,) only encoded in its first D-dimensional block (F).
Proposition 1 Given the specified generative model and a set of examples E₁ = ((E,.0 yi, ST. W1 E Y)s,, of domain j E J, we have that the Fréchet mean of Ej. defined in 2 converges to the identity matrix Tp with Mj - co for all domains E J.
Our proof, provided in appendix A.1 relies on the uniqueness of the Fréchet mean for AIRM) and that y, and e in (11) are zero-mean.
For the generated multi-variate time-series features I; E X' the empirical covariance matrix C, is:
1 T 2G E Sp
C Cov(z,)
(12)
Due to the linear relationship between observed features and latent sources 8 we obtain a direct relationship to the latent source covariance matrices E,:
C Ant
(13)
Since E; encodes the target y E y and A₁ invertible, C, are sufficient descriptors to decode yi-
Remark Note that for each domain the covariance matrices of the generated data (C₃ : Js = j are not necessarily jointly diagonalizable. Depending on the structure of B and E,. the proposed gen- erative model reduces to a jointly diagonalizable model if all the off-diagonal elements in log F.))
are zero Vi.
3.2 DECODING FRAMEWORK
Given source domain data D, and a hypothesis class H. we aim to learn a decoder function h, E H, and once the unlabeled target data D, is revealed use Dj and h2 to learn hy H. Following
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Kobler al. (022a). constrain the hypothesis class 7- to functions h X x J + y that can be decomposed into a composition of a shared feature extractor fo : X - Sb, latent alignment m. S x J + D(D+1)/2 and a shared linear classifier De : D(D++1) - Y with parameters O {0, Φ, 3 (Figure[p) Within this section, we focus on theoretical considerations for ms under our generative model.
Tangent space mapping (TSM) to recover log( Ex) Considering set of labeled data D {<., V1) I2 E X, yr E j.j=j Vi} obtained from a single domain j. TSM (Barachant et al, 2011 provides an established (Lotte et al., 2018; Jayaram & Barachant 2018 decoding approach to infer y/- TSM requires SPD-matrix valued representations. For the considered generative model, covariance features C, as defined in (22. are a natural choice (i.e., fo Cov). nutshell, TSM first estimates the Fréchet mean C' of C {Cov(z;) (24, E "D} projects each C; to the tangent space at C, and finally transports the data to vary around Ip. Formally,
(C:) upper PC-, (C,) upper (log (C+C))))) x=
(C}
(14)
where the resulting representations of m. have linear relationship to log( (E)) (Sabbagh et al. 2020 Kobler et al. 2021) and through (TO) and (T also to the labels ye-
RCT+TSM compensates marginal and conditional shifts In the context of functional neu- roimaging data, the recentering (RCT) transform (Zanini et al., 2017 Yair et al. 2019) and its extensions (Rodrigues et al. 2019: He & Wul 2019; Kobler et al. 2022a Mellot et al. 2023] ad- dress source-free UDA problems. Combined with TSM, RCT+TSM essentially applies (14) inde- pendently to each domain j. The outputs Majitt)) (Ct), where Φ()) {C₁}, are treated domain- invariant and passed on to the shared classifier Iv-
Although RCT+TSM is established method to address SFUDA problems for neuroimaging data (Lotte et al. 2018 Wei et al. 2022 Roy et al. 2022), there is a lack of understanding of what kind of distribution shifts RCT+TSM can compensate.
RCT+TSM compensates condi- tional distribution shifts introduced by the invertible linear map Aj. defined in (8) and recovers domain-invariant representations if there are no label shifts (i.e., p5
Proposition 2 For the generative model, specified in section 3.1
(tte,,,(())))(ss p-(y=))-p(y-u) Vy E y, Vj e
J. U Tt).
A detailed proof is provided in appendix A.2 Starting with mo(r)) (C.), as defined in 14 and utilizing the unique polar decomposition (9) of A, into rotational Q and scaling exp(P;) transfor- mations along with proposition
| we obtain:
log (C C3GGT
log FT)QT== Qupper (B (1,, v: TT(O) + ++) Q*
(15)
j(6)
If there are no label shifts we have x, Vj. k E J. U Jr. Then (1) only contains domain- invariant terms on the right hand side. Thus, RCT+TSM compensates the conditional shifts intro- duced by exp(P;).
Remark If all sources in S can be partitioned into relevant and irrelevant sources 2|=(=!], , 2 E DxT , ((() E R(P-D)XT that are independent from each other, then the source covariance matrices E, have a block-diagonal structure. Consequently, RCT+TSM compensates marginal shifts in 2 and conditional shifts in z. introduced by exp(P,).
Alignment under label shifts We aim to extend RCT+TSM to extract label shift invariant repre- sentations. Specifically, we aim to apply additional transformations on (St g. A.IRMM that attenuate the effect of class priors T, in (15) We first rewrite 15 as:
J.C. = exp log(
(Qlog(E:))))) (Fa)())) = exp (Qupper -1 (B (1,, T(0)) + & Q²)
(16)
exp
uupper -1 (B1,, ei) QT of -Q Qupper (BT Q"
e:)
(17)
log(E.)
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where we split log(E), E,) into domain-invariant log( E,) and label shift Pa(e) terms. To separate both terms into products of matrices, we utilize exp(o(A A + B)) = exp(aB/2) exp(()))xx((aBB) + (aa²) Higham 2008 Theorem 10.5), resulting
GO 30) = exp (Pa))) QT exp (Pr()) Q" + (0()))g((E))1
(18)
with the approximation error O(I log(E;))(?) decaying cubically for (log(E))lle < 1. In this form, straightforward see that an additional bilinear transformation on the left hand side in 18) with an SPD matrix can approximately compensate the effect of exp( Pa(e)) We denote this parameter domain-specife bias parameter ( E ESh: and generalize RCT+TSM to:
mzG()) (C2) = upper o log (o C C, C, (.)) .((() = [C 250) a(t)
(19)
Note that (P)(P)) and cxp(P;) share the same eigenvectors, they commute and lie on the same geodesic connecting exp(P;) with Tp. Consequently, the combined effect of exp(P,) and exp(P)) constrained the geodesic connecting Cj with Ip. Then, the solution space be constrained to Ø { + S + #, ID. PP R), and ( used to simplify (19 to:
# o((t))
(C.) upper log of
In (Ci), o(((1) {C,()) (20)
where the geodesic step-size parameter P9(() E IR needs be learned.
Latent alignment with domain-specific SPD batch norm. Parametrizing the feature extractor So - *D as neural network naturally extends the decoding framework to neural networks with SPD matrix-vall valued features (Huang & Gool 2017). In this end-to-end learning setting, SPD batch norm (SPDBN)(rook) et al., 2019; Kobler et al. (202b)) and domain-spectie batch norm (Kobler al. 2022a) layers be utilized to implement m... m...
3.3 SPD MANIFOLD INFORMATION MAXIMIZATION
We utilize the labeled source domain dataset D, to learn the shared feature extractor for Pej- and m for the source domains j E J, with the cross-entropy loss as the training objective (p))
For the target domains, we keep fo and fu fixed and learn ((j) Vj Te (Figure Ic). For each domain j E Jr, we use 2 to compute the Fréchet mean C5(0) of Cj [fo(zs) (xx,) (i)) E Dr, j(i) j)- To estimate P in an unsupervised fashion, we employ the information maximization (IM) loss (Shi & Sha 2012) to ensure that target outputs are individually certain and globally diverse. The IM loss is a popular training objective for SFUDA and test-time adaptation frameworks (Liang et al. 2020 2024). In practice, when the target domain data is revealed, we initialize P)()) with T and Pi(() with We then minimize the following LOEM and bMM that together constitute the LIM loss:
LIM
LCEM + LMEM
(21)
|
(e(( T
(he(zers)) T
CCEM = - (E,,)))E
log 8x
D'
he he(Waag
LMEM Σ de log pr: Pk BeeeSNED,
T
where &g is the k-th element of the softmax output, LCEM conditional entropy minimization, LMEM is marginal entropy maximization and factor 7 is temperature scaling. IM balance is more effective than conditional entropy minimization because minimizing only the conditional entropy may lead to model collapse with all test data allocated to one class (Grandvalet & Bengio 2004). We additionally employed a temperature scaling factor to adjust the model's 's prediction confidence on the target data, common technique for calibrating probabilistic models (Li al. 2023 Guo et al. (017). Temperature scaling uses a single scalar parameter > 0 for all classes, and it increases the softmax output entropy when T > 1 and decreases it when T 1.

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4 EXPERIMENTS
We conducted simulations and experiments with public EEG motor imagery and sleep stage datasets to evaluate our proposed framework empirically.
Multi-source domain training Following Kobler et al. (022aa), we parameterize h2 Pe m as a neural network and fit the source decoder hg in an end-to-end fashion (Figure (Tp), denoted as TSMNet. We used the standard-cross entropy loss training objective, and optimized the param- eters with the Riemannian ADAM optimizer (Bécigneul & Ganea 2018). We split the source do- mains' data into training and validation sets (80% / 20% splits, randomized, stratified by domain and label) and iterated through the training set for 100 epochs. We stick to the TSMNet hyper-parameters as provided in the public reference implementation (for implementation details see Appendix A.7.1)
SPDIM Source-free domain adaptation SPDIM keeps the fitted source feature extractor So and linear classifier Py fixed and estimates a domain-specific bias parameter for latent alignment m (Figure ( Depending on the choice of the bias parameter, we distinguish between SPDIM(bias), defined in (19). and (gDdM(ge defined in (20). We use the entire target domain data to estimate gradients for the IM loss 21 and Riemannian ADAM to optimize the bias parameter for 50 epochs.
SFUDA Baseline Methods. We consider several multi-source (-target) SFUDA baseline methods, including Recenter (RCT) (Zanini et al. (017), Euclidean alignment (EA) (He & Wul 2019), and spatio-temporal Monge alignment (STMA) (Gnassounou et al., 2024). These alignment methods are model-agnostic techniques that are applied to the EEG data before a classifier is fitted. Among the end-to-end learning SFUDA methods, was introduced together with the TSMNet architecture. Lastly, we compare SPDIM to classic IM approaches (Shi & Sha 2012) that adapt parameters in fo or 9ø-
consider SPDDSBN (Kobler et al. 2022a) which
No DA Baseline Methods. Methods in this category, denoted w/o SFUDA, treat the problem as a standard supervised learning problem; they do not utilize the domain labels J. U J. during training and testing. In models that perform TSM, all data are projected to the tangent space at the Fréchet mean of the entire source dataset DD,-
We used publicly available Python code for baseline methods and implemented custom methods using the packages torch (Paszke al., 22019) seikit-learn (Pedregosa et al. 2011), braindecode (Schirrmeister et al. 2017), geoopt (Kochurov et al., (2200) and py pyRiemann Barachant et al. (202)). We conducted the experiments on standard computation PCs with 32-core CPUs, 128 GB of RAM, and single GPU.
4.1 SIMULATIONS
To examine the effectiveness SPDIM, we simulated binary classification problems under our gen- erative model (implementation details in Appendix(A.6) We used balanced accuracy as evaluation metric and examined the performance of SPDIM(hias) and SPDIM(geodesic) against RCT (Zanini et al. over different label ratios. [ggumrrssmmmrizess the results for different class separability levels. Supplementary Figures display the methods' performance over parameters [J,] (Figure M, (Figure/A2). P (Fig.re/A3p. and D A4].
The simulation results empirically confirm Proposition 2 That is, RCT can compensate the condi- tional shifts introduced by A, if there are no labels shifts (i.e., label ratio 1.0). They also demon- strate that as the label shifts become more severe (i.c., lower label ratio), the average performance of SPDIM decreases while the variability increases. Still, SPDIM outperforms RCT across almost all considered parameter configurations.
4.2 EEG MOTOR IMAGERY DATA
Almost all public motor imagery datasets are generated in highly controlled lab environment and desgined to be balanced. However, in realistic brain-computer interface application settings, the variability of human behavior and environmental factors likely cause label shifts across days and subjects. To bridge the gap between controlled research settings and real-world scenarios, we artifi- cially introduced label shifts in the target domains.

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low
class separabilityp(ss/
high
100
postr
source domain
balanced accuracy
95
target domain
90
RCT
85
SPDIM (geodesic)
80
p
plln)
M
PSM
M
SPDIM
(bias)
10-1
100 10-1
100 10-1
100 10-1
10
label ratio
label ratio
label ratio
label ratio
Figure 2: Simulation results. Balanced accuracy scores (higher is better) across target domain label
ratios (i.e., majority to minority label ratio) on the x-axis and class separability p(s|y) across panels.
Source domain labels were balanced.
(Tngerraann et al. 2012) (9 sub- jects/2 sessions/4 classes/22 channels), BNCI201 5001 (Faller et al. (012)) (12/2-3/2/13), Zhou2016 (Leeb et al. 2007) (9/5/2/3). We used MOABB (Jayarmm & Barachant 2018 Chevallier et al. 2024) to pre-proect process the continuous time-series data and extract labeled epochs. Pre-processing included resampling EEG signals to 250 or 256 Hz, ap- plying temporal filters to capture frequencies between and 36 Hz, and extracting 3-second epochs linked to specific class labels. Following Kobler et al. (2022a), we use TSMNet as model archi- tecture and treat sessions as domains, and use a leave-one-group to fit and evaluate the methods. To evaluate cross-session transfer, we fitted and evaluated models independently per subject and treated the session as the grouping variable. To evaluate cross-subject transfer, we treated the subject as the grouping variable. After running pilot experiments with the ACC12014001 dataset, we set the temperature scaling factor in (21) to T = 2 for binary classifica- tion problems and 7 0.8 otherwise. Early stopping were fit with a single stratified (domain and labels) inner arin/validatton split. We used balanced accuracy the metric to examine the perfor- mance of each method at label ratios of 1.0 and 0.2 for the source and target domains, respectively.
We considered 4 public motor imagery datasets: BNCI201400)
(Zhou et al. 2016) (4/3/3/14), and BNCI20 40044
cross-validation (CV) scheme
Grand average results across all 4 datasets are summarized in Figure 3 and grouped by the transfer learning scemario (cross-session, cross-subject). To attenuate large variability across subjects, we report scores relative to the score obtained with SPDDSBN w/o label shifts (i.e., 1.0 label ratio). Detailed results per dataset are listed in Table[A4] (w/ label shifts) and Table (w/o label shifts) along with the ones of relevant baseline methods. Although method artificially introduced label shifts, SPDIM(bias) consistently at the top (cross-subject) or among the top (cross-session) performing methods. Significance testing (n=34 subjects), summarized in Ta- Alc[A4] revealed that the performance of (bDIM(bias) is significantly higher than w/o, SPDDSBN, IM(llassiiier) and IM(lll) in the cross-subject setting as well as SPDDSBN, IM(classifier), and IM(llI) in the cross-session scenario.
perfectly compensate the
SFUDA
balanced accuracy (%)
w/o
SPDDSBN
-5
SPDIM(geodesic)
SPDIM(bias)
-10
IM(classifier bias)
IM(classifier)
-15
subject
outlier(upper)
20
outlier(lower)
session
subject
Figure 3: Motor-imagery results (0.2 label ratio). Average of test-set scores (balanced accuracy: higher is better; error bars indicate 95% confidence interval) relative to SPMNNN+ (Kobler al. 2022a) w/o label shifts. For extended results per dataset, see Tables A4 and A5
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4.3 EEG-BASED SLEEP STAGING
The aim of this experiment is to demonstrate the effectiveness of our method on datasets with inher- ent label shifts. Due to the inherent variability of sleep, most sleep stage datasets exhibit label shifts across subjects (Eldele al. 2023). Sleep stage classification plays a key role in assessing sleep quality and diagnosing sleep disorders (Perez-Pozuelo et al., 2020). Yet, automated frameworks lack aceuracy and suffer from poor generalization across domains, resulting accuracy drops compared to expert neurologists.
We considered public sleep stage datasets: CAP Terzano et al. 2001: Goldberger et al. 2000), Dreem (Guillot et al. 2020), HMC (Alvarez-Esteeer & Rijsman [2021a b), and ISRUC (Khalighi ct al., 2016). A detailed description is provided in Supplementary Table Al We consider sleep stages following the AASM (Berry et al. 2012) standard (W, NI, N2, N3, REM). If data was orig- inally scored following the K&M (Wolpert 1969) standard (W, S1, S2, S3, S4, REM), we merged stages S3 and S4 into single stage N3. EEG data pre-processing followed (Guillot & Thorey) 2021] and was implemented with MNE-python (Gramfort et al. 2014). First, all EEG channels were retained, and IR band-pass filter ranging from 0.2 30 Hz was applied. The signals were then resampled to 100 Hz, and non-overlapping 30-second epochs were extracted together with the associated labels. To attenuate the effects of gross outliers, each recording was scaled to have unit inter-quartile range and a median of zero, and values exceeding 20 times the inter-quartile range were clipped Perslev et al. (202T). Lastly, subjects with corrupted data (e.g., mismatched labels and elippedPerslev epochs) were excluded, resulting in total of 426 remaining subjects.
Since label shifts occur in the source domains of sleep stage data, the considered models are trained with balanced mini-batch sampler, which is popular method to compensate for label shifts during training in deep learning (Cao et al. 2019). The balanced sampler over-sampled minority classes to ensure that the label distribution per domain is balanced within each mini.
To evaluate the methods, we employed a 10-fold grouped cross-validation scheme, ensuring that each group (i.e., subject) appears either in the training set (i.e., source domains) the test set (i.e., target domains). As before, we set the temperature scaling factor T = 0.8 and used stratified (labels and domains) inner train/validation splits for early stopping. In addition the TSMNet architecture, we included four baseline deep learning architectures specifically proposed for sleep staging: Chambon (Chambon et al., 20 Usleep (Perslev et al. [021], DeepSleepNet (Supratak et al. 2017). and AttnNet (Eldele et al. (023) (implementation details in Appendix (.7.2)).
Table summarizes the results across datasets along with the grand average results of published baseline methods. Extended results for all considered baseline methods are listed in Supplemen- tary Table A2 TSMNet+SPDIM(bia) significantly outperforms all other methods for the patient and healthy (except TSMNet+STMA) subject groups. Overall, the margin to TSMNNt+SPDDSEN was approx. 5% in the patient group, which indicates that SPDIM has great potential for clinical applications.
A Ablation Study Table grand average test scores relative to (hDIM We highlight four observations. First, all considered ablations lead to significant performance drop of at least 3% compared to SPDIM(bias), suggesting the combined importance of IM paired with the manifold- constrained bias parameter. Second, in the presence of label shifts, fitting m. per domain (i.c., TSM- Net+SPDSBN) hurts generalization compared to global my (i.e., TSMNet+w/o). Third, fine-tuning the classifier bias parameter yields approximately the same performance as SPDIM(geodesic,, tending the finding of (Mellot et al., (024) from regression to classification scenarios. Fourth, IM methods obtained the top 3 scores, but two variants failed improve upon the global method, which underscores the importance of regularization (i.e., via selecting the right parameter) to prevent the IM loss from overfitting.
5 DISCUSSION
We proposed a geometric deep learning framework, denoted SPDIM, to address SFUDA prob- lems with conditional and label shifts and demonstrated its utility in highly relevant baGebased neurotechnology application scenarios. We first introduced a realistic generative model, and pro- vided theoretical analyses showing that prior Riemannian statistical alignment methods that align

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Published as a conference paper at ICLR 2025
Dataset:
CAP
Dreem
HMC
ISRUC
Overall
Group: SFUDA
patient (n=82)
healthy (n=22)
patient (n=50)
patient (m=154)
healthy (n=10)
patient (n=108)
healthy (n=32)
patient
Model
(n=394)
Chamhon
w/o
64.7
65.2
53.4
64.0
72.7
68.9
67.5
64.2
(10.7)
(9.1)
(16.2)
(9.6)
(3.9)
(8.2)
(8.6)
(11.5)
EA
63.8
64.7
54.5
63.4
74,9
70.7
67.9
64.3
(11.3)
(10.3)
(14.4)
(10.7)
(4.8)
(9.3)
(10.0)
(12.0)
STMA
65.2
67.1
51.3
63.8
74.8
70.8
64.4
(10.0)
(7.7)
(19.0)
(9.1)
(4.4)
(7.6)
(7.7)
(12.1)
USleep
w/o
19.1
55.9
48.4
66.6
72.9
68.8
61.3
63.3
(10.3)
(8.3)
(8.2)
(9.3)
(6.1)
(8.3)
(11.0)
(11.3)
Deep-
w/o
68.1
68.6
68.7
64.9
75.8
72.7
70.9
68.2
SleepNet
(11.3)
(9.9)
(10.3)
(10.3)
(4.5)
(9.1)
(9.1)
(10.7)
AttnSleep
w/o
68.9
65.4
61.77
67.7
75.4
73.1
68.5
68.7
(10.3)
(10.7)
(14.2)
(10.0)
(4.0)
(8.6)
(10.2)
(10.9)
TSMNet
w/o
68.0
65.9
66.7
63.6
73.4
68.7
68.3
66.3
(11.2)
(9.6)
(12.4)
(11.3)
(3.9)
(9.3)
(8.9)
(11.1)
SPDDSBN
68.2
68.9
64.2
62.2
72.8
66.6
70.1
64.9
(8.8)
(5.8)
(8.5)
(6.0)
(2.8)
(6.4)
(5.3)
(7.5)
SPDIM(bias)
71.0
72.1
68.1
68.6
76.7
71.6
73.5
69.9
(proposed)
(9.6)
(8.0)
(9.8)
(8.5)
(3.4)
(6.9)
(7.2)
(8.6)
Table 1: Sleep-staging results per dataset. Average of test-set scores (balanced accuracy: higher is better; standard-deviatin in brackets). Permutation-paired t-tests were used to identify significant differences between SPDNM (proposed) and baseline methods (le4 permutations, 14 tests, t-max correction). Significant differences are highlighted (. 0.05, s 0.01, p 0.001). Extended results are provided in Table A2
Alignment
Fréchet mean
LIM
θIM
mean (std)
[-val (p-val)
m
19
per domain j
4
m
20
domain j
/
-3.6
-1744 (0.0001)
77
per domain j
X
.4.8 (4.5)
-22.1 (0.0001)
m
global (i.c., D.))
X
(8.5)
-9.0 (0.0001)
m
per domain j
V
bias in x/
(3.8)
-16.1 (0.0001)
m
per domain j
(5.4)
-18.5 (0.0001)
per domain
0 DU
22.11 (13.5)
-4.55 (0.0001)
Table 2: Sleep-staging ablation results. Balanced accuracy scores (higher better) relative to the proposed method. Averages and standard deviation summarize the individual (n=426 subjects) test- set scores. Student's values and adjusted values indicate the effect strength (permutation-pall I-tests, le4 permutations, tests, t-max correction). Table lists results per dataset and group.
the Fréchet mean can compensate for the conditional distribution shifts introduced in our gen- erative model, but hurt generalization under additional label shifts. As a remedy, we proposed SPDIM to learn a domain-specifie SPD manifold-constrainee bias parameter to compensate for over- corrections introduced via aligning the Fréchet means by employing the information maximization principle. In simulations and experiments with real EÉG data, SPDIM consistently achieved the highest scores among the considered baseline methods.
limitation of our framework that the IM loss, due to large noise and outliers, can sometimes estimate inappropriate bias parameter, leading to the data being shifted in the wrong direction. While generally improves average performance, it also increases variability. We expect future work to explore more robust way estimate the bias parameter.
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6 ACKNOWLEDGMENTS
Motoaki Kawanabe and Reinmar J Kobler were partially supported by the Innovative Science and Technology Initiative for Security Grant Number JPJ004596, ATLA and KAKENHI (Grants-in-Aid for Scientific Research) under Grant Numbers 21K JSPS, Japan.
7 AUTHOR CONTRIBUTIONS
Shanglin Li contributed to the study under the co-supervision of Motoaki Kawanabe and Reinmar Kobler. Shanglin Li and Reinmar Kobler developed the decoding methods. Reinmar Kobler contributed the theoretical analysis. Shangling Li and Reinmar J. Kobler performed the simulation experiments. Shanglin Li conducted the experiments with EEG data. The draft of the manuscript was written by Shanglin Li and Reinmar Kobler. All authors read and approved the final manuscript.
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Xiaoxi Wei, A. Aldo Faisal, Moritz Grosse- Wenttrup, Alexandre Gramfort, Sylvain Chevallier, Vinay Jayaram, Camille Jeunet, Stylianos Bakas, Siegfried Ludwig, Konstantinos Barmpas, Mehdi Bahri, Yannis Panagakis, Nikolaos Laskaris, Dimitrios A. Adamos, Stefanos Zafeiriou, William C. Duong, Stephen M. Gordon, Vernon J. Lawhern, Maciej Šliwowski, Vincent Rouanne, and Piotr Tempezyk. 2021 BEETL Competition: Advancing Transfer Learning for Subject In- dependence and Heterogenous EEG Data Sets. In Douwe Kiela, Marco Ciccone, and Barbara Caputo (eds.), Proceedings of the NeurIPS 2021 Competitions and Demonstrations Track, vol- ume 176 of Proceedings of Machine Learning Research, pp. 205-219. PMLR, 2022.
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Paolo Zanini, Marco Congedo, Christian Jutten, Salem Said, and Yannick Berthoumieu. Trans- fer learning: A riemannian geometry framework with applications to brain-compen interfaces. IEEE Transactions on Biomedical Engineering, 65(5): 107-1116, 2017. doi: 10. 109//TBM. 2017.2742541.
Bangyan Zhou, Xiaopei Wu, Zhao Lv, Lei Zhang, and Xiaojin Guo. A fully automated trial selection method for optimization of motor imagery based brain-computer interface. PloS one, 11(9): e0162657, 2016. doi: 10.137 1.o 0166677
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Published as a conference paper at ICLR 2025
A APPENDIX
A.1 PROOF OF PROPOSITION 1
Proposition [ stats that given the generative model specified in section 3.1 and a set of examples E = {[E, Ma E; E Sp, E J',, of domain j E J, we have that the Fréchet mean of Ej, defined in converges with Mj - 30 to the identity matrix Ip for all domains j E J.
Since (Sp.g) g. AIRM) forms a Cartan- Bartan-Hadamart manifold with global non- non-positive sectional curvature, a unique Fréchet mean exists (Bhatia 2013). At the global minimum, we have:
M₁ Σ 0 VEEE(E) VE M,
M, Σ
( = 1
(,)
= EV
Σ
Log
(22)
M2 i=1
M, i=1
i=1
1 M₁
Mj
Σ
m log Lo
E
Σ
log E 1 E,
E
(23)
Mj
Mj
F log(F
log
F
(24)
where we used the derivative of the Riemannian distance (Moakher 2005 For E Ip. (24) simplifies to:
Pennec
2018 in
22
log E.) - 0 = Eloog( E.)) 1
(25)
BiBü, + e;} ( + B(a,) -
(26)
which holds true because by definition T and 6; are zero-mean. Therefore, Ej Ip the global minimizer of (E(E, for all domains j E TTD
A.2 PROOF OF PROPOSITION 2
RCT+TSM compensates conditional distribution shifts introduced by the invertible linear map Aj. defined in ( and recovers domain-invariant representations if there are no target shifts (i.e., p5 = p(y= vy E 3/ Vjj E
Proposition 2 states that for the generative model, specified in section 3.1
J. JT.
Due to the congruence invariance of the Fréchet mean BBhatia 2013) we have
C = arg min Ma(C,) GEST
A,E,
(27)
where E, is the Fréchet mean of Eg. Utilizing proposition (i.e., E, Ip f) and plugging (9) for Aj. (27) simplifies to:
C = AjlnA Q (xx)(P3) exp exp(P,)Q0 = =(xp((
(28)
+ + = -
(29)
The RCT+TSM transform, as defined in 14 recenters the data C₁ E C, for each domain j. Ex- cluding the invertible mapping upper, RCT+ computes:
log (c,tc.0, +)
log (Q=
(30)
log (Qexp(P))~AA,, exp(P))
(31)
log (Qexp(())) (xp(P))E exp(P)) (ex((()))))'''""
(32)
log (QE.QT) Q log(
(33)
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Published as a conference paper at ICLR 2025
where used 13 for C., the fact that Q is orthogonal matrix and log(ACA-1)
A log(C)A-1 for non-singular A and C' E Sp. Plugging 11 for log( Ei), we obtain a direct relationship to the label y/s
log (c,80,088) - Qupper (1y: - mT)) + Ei) Q"
(34)
there are no target shifts the class priors are constant (y- = p(y=y) by E y for all domains j E U Jr, and consequently иj n. Then (34) simplifies to:
log (g, C Qupper ( (1 σ) Ex) Q"
(35)
which contains only the conditional shifts introduced by Aj. D
terms on the right hand side. Thus, RCT+TSM compensates
A.3
SLEEP STAGE DATASET DETAILS
Dataset
Recordings
Subjects
Channel numbers
Patients
Scorer
Scoring rule
ISRUC-SGI
100
100
6
Scorer1
AASM
ISRUC-SG2
16
6
Scorerl
AASM
ISRUC-SG3
10
10
6
x
Scorerl
AASM
Dreem-SGI
22
22
12
X
Scorerl
AASM
Dreem-SG2
50
50
8
Scorerl
AASM
HMC
154
154
4
AASM
CAP-SGI
36
36
13
K&M
CAP-SG2
34
34
9
K&M
CAP-SG3
22
K&M
Table A1: Sleep stage dataset details. Overview of datasets and their subgroups (SG), including the number of recordings, subjects, channel numbers, patient status, scorer (the chosen scorer if there are multiple scorers), and scoring rule.
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A.4 EEG-BASED SLEEP STAGING RESULTS
Datasct:
CAP
Dreem
HMC
ISRUC
Overall
Group:
patient (n=82)
healthy (n=22)
patient (n=50)
patient (m14
bealthy (n= 10)
patient 10=)
healthy (m=32)
patient (m=394)
Model
SFUDA
Chambon
w/o
mean
64.7
65.2
53.4
64.0
72.7
68.9
67.5
64.2
std
10.7
9.1
16.2
9.6
3,9
8.2
11.5
t-val
-6.8
5.3
-6.1
-7.0
-2.6
.4.6
-5.8
-1..3
EA
mean
63.8
64.7
54.5
63.4
74.9
70.7
67.9
64.3
std
11.3
10.3
14.4
10.7
4.8
9.3
10.0
12.0
t-val
-7.5
-3.8
-6.1
-7.5
-1.2
-1.3
-3.8
-10.7
STMA mean
65.2
67.1
51.3
63.8
74.8
70.8
69.5
64.4
std
10.0
7.7
19.0
9.1
4.4
7.6
7.7
12.1
t-val
-8.5
550
-6.0
-8.6
-1.3
-1.4
-4.7
-0.44
USleep w/o
59.1
55.9
48.4
66.6
72.9
68.8
61.3
63.3
10.3
8.3
8.2
9.3
6.1
8.3
11.0
11.3
-12.1
-8.0
13.3
-2.2
.4.3
-6.8
12.1
DeepSleepNet w/o mean
68.1
68.6
68.7
64.9
75.8
72.7
70.9
68.2
std
11.3
9.9
10.3
10.3
4.5
9.1
9.1
10.7
t-val
-3.3
-3.1
0.5
-5.1
-0.5
1.7
-2.8
-3.9
EA
mean
66.3
62.3
67.1
68.8
68.0
11.7
10.3
11.4
10.2
4.6
9,9
t-val
-5.1
-3.1
-3.6
-2.3
-4.1
2.1
-3.6
-4.1
STMA mean
67.7
70.5
64.2
64.8
74.5
72.9
71.8
67.6
std
10.1
8.5
11.4
10.2
4.0
7.8
7.5
10.3
t-val
-4.7
-1.4
-2.7
-5.5
-1.3
2.5
-1.9
-5.8
AttnSleep w/a
mean
68.9
65.4
61.7
67.7
75.4
73.1
68.5
68.7
std
10.3
10.7
14.2
10.0
4.0
8.6
10.2
10.9
t-val
-2.6
. -..4
-3.1
-1.4
-1.3
2.2
-4.3
-2.6
EA
mean
68.6
65.5
59.6
65.7
75.4
74,2
68.6
67.9
std
11.7
11.1
15.3
11.1
4.5
7.1
10.5
11.9
t-val
-2.9
-3.4
-3.9
-3.9
-1.0
4.5
-3.44
44,0
STMA
mean
69.9
69.0
61.8
66.8
75.7
74.6
71.1
68.9
std
10.2
8.8
14.8
9.4
3.9
7.0
8.2
10.7
t-val
-1.7
-2,9
-3.0
-3.3
-0.8
5.2
-2,9
-2.2
TSMNet
68.0
65.9
66.7
63.6
73.4
68.7
68.3
66.3
11.2
9.6
12.4
11.3
3.9
9.3
8.9
11.1
3..7
-6.5
-3.44
-3.8
-7.0
-8.2
EA
mean
67.5
66.7
67.0
62.1
73.3
68.1 1
68.7
65.5
std
9,9
11.2
11.1
12.0
2.2
9.7
9.8
11.2
t-val
-4.3
-3.4
-0.8
-8.2
-3.3
-4.3
-4.2
-9.5
STMA mean
70.7
68.2
65.0
73.4
71.5
67.6
9.6
7.7
10.6
9.0
5.1
7.9
I-val
-1.8
-1.5
-7.3
-1.9
-4.8
-2.4
-7.3
SPDDSBN mean
68.2
68.9
64.2
62.2
72.8
66.6
70.1
64.9
std
8.8
5.8
8.5
6.0
2.8
6.4
5.3
7.5
t-val
-6.3
.4.8
-8.6
-15.3
+3.8
13344
-6.2
-21.4
SPDIM(bias) mean
71.0
72.1
68.1
68.6
76.7
71.6
73.5
69.9
9.6
8.0
9.8
8.5
3.4
6.9
7.2
t-val
Table A2: Sleep-staging results dataset. Summary statistics of the test-set scores (balanced accuracy; higher better) across public sleep staging datasets. Parameters that were adapted the test-data with the IM loss are indicated in brackets. Permutation-paires t-tests were used to identify significant differences between our proposed (i.e., SPDMMia)) and baseline methods (1e4 permutations, 10 tests, t-max correction). Student's values summarize the effect strength. Significant differences are highlighted (+ p < 0.05, & 0.01, < 0.001).
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Dataset:
CAP
Dreem
HMC
ISRUC
Overall
Alignment/ Mean
Group:
patient (n=82)
healthy (n=22)
patient (n=50)
patient
healthy
patient (m=108)
healthy (n=32)
patient
LIM 1mm
(n= 154)
(n=10)
(n=394)
my per domain
mean
72.1
68.6
76.7
71.6
73,5
69.9
9.8
8.5
7.2
8.6
m 20
11
68.6
70.0
66.8
64.7
74.6
68.3
71.4
66.8
per domain
7.1
t-val
-6.4
-3.9
-3.7
-12.2
-3.9
10.00
-5.3
me 14
X/-
mean
68.2
68.9
64.2
62.2
72.8
66.6
70.1
64.9
per domain
std
8.8
5.8
8.5
6.0
2.8
6.4
5.3
7.5
t-val
-6.3
-.88
-8.6
-15.3
-3.8
13.4
-622
-21.4
my [4]
X/-
mean
68.0
65.9
66.7
63.6
73.4
68.7
68.3
66.3
global
12.4
11.1
v-l
-3.7
-6.5
-1.0
-6.8
-3.8
-7.0
-8.2
m 14
bias in
mean
69.8
70.3
65.7
64.1
74.7
68.9
71.7
66.8
per domain
std
9.5
6.8
9.2
6,9
2.7
6.8
6.1
8.1
t-val
-3.3
4.00
-7.4
13..0
-3.9
-8.1
-5,4
-1.66
my
mean
68.8
63.1
73.2
67.7
70,2
64.9
per domain
10.5
10.9
10.1
t-val
-5,9
-311
-4455
+388
-4.3
-88.0
me 14 per domain
VIOU
mean 54.8
46.9
36.2
35.8
$3.6
45.9
49,0
42.5
std
14.8
13.8
11.4
11.2
13.4
12.5
13.8
14.5
t-val
-13.3
-9.6
17.1
-32,8
-6.4
23.0
111.6
-39.9
Table A3: Sleep-staging ablation study results per dataset. Summary statisties (mean, std, t-val) of the test-set scores (balanced accuracy; higher is better) across public sleep staging datasets. All statisties computed at the subject level. Permutation-paired t-tests were used identify signifi- cant differences (1e4 permutations, 6 tests, t-max correction). Significant differences are highlighted (.p < 0.05, p 0.01. p 0.001). For summary across datasets and groups see Table in the main manuscript.
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A.5
EEG-BASE BASED MOTOR IMAGERY BCI
label rutio = 0.2
Evaluation
session
xubject
Dataset:
2014001 (n=9)
2014004
2015001
Zhou2016 (m=4)
Overall (o=34)
2014001 (n=9)
2014004
2015001
Zhou2016 Overall
Model
SFUDA
(i=9)
(n=12)
(i=9)
(n=12)
(m=4)
(o=34)
EEGNet
w/O
74.5
72.4
71.7
64.6
42.6
69.0
61.4
72.6
59.7
V-4
sid
17.9
14.6
16.3
5.8
20.6
16.6
10.7
8.3
3.7
15.6
L-val
4,88
0.2
-4.1
4.44
5.0
4,3
-1.7
-2.3
-3.4
..2
EA
mcon
53.2
75.3
76.0
71.2
69.9
48.6
72.0
70.7
70.6
65.2
21.8
15.4
18.3
2.9
19.7
17.2
11.1
14.7
6.8
16.7
L-val
5.2
-2.7
-8.9
4.44
-1.9
-0.1
-0.5
-3.2
-1.5
std
5.5
14.4
9.5
14,5
20.2
16.1
12.4
14.3
2.2
16.0
t-val
-7.3
-8.3
-2.4
-6.8
-1.6
-0.8
-1.5
EEG-
w/o
mean
48.6
75.0
71.6
73.9
66.7
41.7
69.4
60.6
74.6
59.6
Conformer L-val
17.0
18.5
3.8
18.4
11.7
6.0
-6.1
0.5
-4.0
-6.2
-5.5
+4.1
-1.7
-2.4
-2.8
-4.1
74.7
68.4
59.8
sid
18.7
13.8
16.3
4,3
18.1
16.3
10.9
8.7
8.7
15.5
-4.0
EEGlo
w/o
47.7
71.5
72.6
75.1
66.0
39.4
67.0
59.2
63.1
56.5
ceptionMI t-val
17.0
12.1
15.8
9.4
18.0
13.8
9.5
6.4
14.8
+6.1
-1.2
.4.9
-1.9
-6.1
-3.5
-2.3
-2.5
-6.9
4.99
TSMNet w/o
mean
68.6
74.8
82.7
81.0
76.7
41.1
69.5
61.1
77.8
60.0
12.9
11.1
13.4
2.5
12.8
12.7
9.6
10.9
2.6
16.2
t-val
-0.5
-0.6
-1.8
-0.9
...3
-2.0
-1.3
EA sid
67.2
76.0
83.6
81.9
77.0
50.0
73.0
68.2
73.3
65.3
13.7
12.0
9.5
5.2
12.6
16.9
10.6
13.7
4.3
15.9
t-val
-1.2
2.1
-0.1
-0.9
-0.6
-1.4
0.5
-0.9
-2.4
-1.5
STMA
mcon
69.9
74.7
83.0
83.3
77.3
50.2
71.9
66.9
7688
65.0
16.0
13.1
7.7
6.3
12.7
17.5
11.5
13.0
5.5
16.0
t-val
0.1
-0.3
.0.4
.0.2
-1.4
-0.2
-1.2
-1.2
-1.7
IM sid
74.2
83.2
78.3
76.7
70.6
73.0
75.4
(classifier
17.5
12.5
10.1
3.0
13.3
15.0
9.9
15.1
3.8
15.3
bias) Lvaal
0.2
-0.0
-0.6
-11.2
-1.7
0.4
-0.7
-1.7
-1.7
IM mcon
66.6
70.9
78.2
77.0
73.0
50.5
67.0
69:7
69.0
63.8
(classifier)
17.2
9.5
6.6
1.7
11.5
14.9
12.4
7.5
14.1
vval
-311
-3.8
117.2
6.8
-1.1
-4.1
3399
.2.9
5.0
50.4
(all)
std
10.9
1.7
7.8
6.4
15.1
7.5
1.7
8.3
4.1
12.5
t-val
-6.6
-6.1
.4.0
-7.5
-9.5
+4..0
-5.2
-2.5
-10.3
-7.3
SPDDSBN mean
69.3
73.5
81.2
80.6
76.0
52.1
69.6
71.5
76.2
66.4
16.2
8.6
2.4
12.0
13.9
13.5
3.1
t-val
-0.3
-0.9
-2.4
-7.0
-2.8
-0.3
-1.9
-2.6
-1.9
.3.2
SPDIM
74.7
70.9
(goodesic)
std
16.5
11.9
10.3
3.5
13.1
15.1
10.9
15.2
3.6
16.0
0.4
0.1
SPDIM
mean
69.7
74.3
83.6
84.1
77.5
52.6
72.2
73.6
80.4
68.5
(bias)
2.4
E-val
Table A4: Motor imagery BCI results for a label ratio of 0.2. Average and standard deviation of test-set scores (balanced accuracy; higher is better) across public motor imagery BCI datasets. For IM and SPDIM variants, the parameters that were tuned to the test-data with the IM loss indicated in brackets. Permutation-paired t-tests between the proposed (i.e., TSMNNt=SSDDM(bias and baseline methods (1e4 permutations, 14 tests, t-max correction). Student's 's values summarize the effect strength. Significant differences are highlighted (+ & 0.05, < 0.01. s 0.001).
used to identify significant differences
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label ratio
Evaluation
session
subject
2014001 (n:9)
2014004
Zhou2016
2014001
2014004
Zhou2016 Overall
Model
SFUDA
(n-9)
(m=12)
(m=4)
(o:34)
(n=9)
(n=9)
(n=12)
(m:4)
(o:34)
EEGNet
W/O
mcan
73.1
73.5
70.6
64.4
43.6
69.6
61.3
75.1
v4
16.6
15.0
15.8
6.5
20.3
16.7
8.1
8.8
3.2
15,4
t-val
665
-3.66
-4.7
-3.8
5500
-2.1
-2.4
-2.8
+44
EA
54.5
76.3
75.7
79.6
70.7
49.9
74.0
72.5
73.9
67.1
19.9
15.5
17.1
2.9
18.7
16.9
10.4
14.2
3.7
t-val
4.3
-1.0
-3777
-4,9
-5.5
-3.4
1,5
-0.3
-4,8
-1.2
STMA mean
30.1
74.4
55.9
55.4
49.7
72.6
69.9
75.0
4.7
15.8
8.0
16.8
20.1
16.9
10.6
14.6
2.4
16.4
t-val
-9.4
-9.9
-1.8
-7.6
-3.7
-0.7
-.9
FRG-
w/o
46.9
73.8
73.1
66.1
42.6
68.8
60.1
74.5
59.5
Conformer
sid
17.2
12.8
17.2
3.2
18.7
16.7
10.0
10.7
4.4
t-val
4..9
-3.6
-4.5
-8.5
-7.2
5500
-2.8
-2.6
4.11
-4.7
ATCNet w/o
mean
51.6
74.3
73.2
77.9
68.3
42.7
68.5
60.2
69.8
58.9
18.4
13.6
4.3
8.4
6.3
t-val
-5.6
-3.0
-4.7
-3.0
-6.3
-5.7
-3.6
-2.8
-4.6
-5.5
ERGIne-
eptionMI
sid
17.9
12.6
15.7
8.5
17.7
12.7
8.1
9.2
5.4
14.6
-2.6
-2.5
TSMNet w/o
mean
69.7
75.1
82.2
80.0
76.8
43.0
68.0
61.7
77.5
60.3
E-val -2.6
-2.4
-2.0
-5.3
44.6
-6.0
-3.2
-2.0
-1.7
-3.9
EA
mean
71.1
77.1
85.2
79.2
51.2
73.1
72.5
75.0
67.3
std
13.3
12.8
9.7
2.6
12.2
15.1
11.1
13.6
1.8
15.6
STMA
71.9
76.3
84.9
82.8
78.9
52.5
72.5
70.1
77.1
66.9
L-val -1.6
-2.4
-0.3
-4.3
-2.0
-1.7
-1.3
-0.7
-4.0
-1.3
SPDDSBN
meun
73.7
77.4
85.3
84.6
80.0
$4.6
73.3
74.3
80.9
69.6
15.3
12.5
10.4
2.3
12.5
16.1
11.1
14.7
1.5
15.9
t-val
Table A5: Motor imagery BCI results for balanced data (i.e., label ratio of 1.0). Average and standard deviation of test-set scores (balanced accuracy; higher is better) across public motor im- agery BCI datasets. For all IM and SPDIM variants, the parameters that were tuned the test-data with the IM loss are indicated in brackets. Permutation-painn cant differences between the SSMNe++SPDDSBN and baseline methods (1e4 permutations, tests, t-max correction). Student's s values summarize the effect strength. Significant differences are high- lighted (- p < 0.05, < 0.01, s 0.001).
t-tests were used to identify signifi-
22

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Published as a conference paper at ICLR 2025
A.6 SIMULATIONS
A.6.1 IMPLEMENTATION DETAILS
We generated covariance matrices C E Sp with P To do so, first generated log-space features s/RP((41)/2 defined in 11 using the scikit-learn function make classi fosiffinn fiaaaiiiii i with 2 dimensions encoding label information. The data were then normalized to have zero mean and unit variance. To obtain F, E Sp, applied upper-1 and Expı,- defined in (5) At this level, the data were split across source domains and the target domain, with each domain receiv- ing 500 observations. Finally, the data were projected the channel space using domain-specific mixing matrices Aj. as defined in (9). To introduce label shifts, we artificially varied the label ratio (LR), defined as the proportion of the minority class the majority class, in the target domain via randomly dropping samples.
We used balanced accuracy as evaluation metric and examined the performance of SPDIM(bias) and SPDIM(geodesic) against RCT (Zanini et al. (017) over different label ratios. Figure summarizes the results for different SNR levels. To control the SNR, we varied the class separability parameter of the make_clas makecclassifi ciasifiiaaii diccaiion function. Additional Figures summarize the methods' performance over parameters Jal (Figure Al
M, (Figure A2 0, P (Figure A3), and (Figure A4)
Us1 1
Usl =
Vsl =
Usl =
balanced accuracy (%)
100
source domain
95
target domain
RCT SPDIM
90
(geodesic)
SPDIM
85
(bias)
"T
10
10" 10-1
10a 10-1
10a 10-1
label 10
label
label ratio
label ratio
Figure Al: Performance over the number of source domains. Same parameters in Figure
(panel 3) but for a different number of source domains [Tal E 3,,
Mj 100
M, 200
Mj = 400
Mj 800
100
source domain
balanced accuracy
95
target domain
RCT SPDIM (geodesic)
90
85
SPDIM
(bias)
10-1
10 -0-1
10a 10-1
10a
10-1
10
label ratio
label ratio
label ratio
label ratio
Figure A2: Performance over the number of samples per domain Mj. Same as Figure (panel 3) but for a different number of samples per domains M2 {100, 200, 400, 800).
A.7 IMPLEMENTATION DETAILS
A.7.1 TSMNET
We used the TSMNet as provided in the public reference implementation as follows:
Architecture The feature extractor fo has two convolutional layers, followed by covariance pooling AAchary et al. 2018). BiMap (Huang & Gool 2017), and ReEig [Huan & Gool (2017) layers. The first convolutional layer operates convolution along the temporal dimension, implementing
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Published as a conference paper at ICLR 2025
P 2
p=4
P = 8
balances accuracy (%)
100
source domain
target dom ain
RCT
90
SPDIM (geodesic)
85
SPDIM
(blas)
10-1
10a 10-1
10 10-1
10
label ratio
label ratio
label ratio
Figure A3: Performance over the number of dimensions P. Same parameters as in Figure
(panel 3) but for a different number of dimensions P {2, 4,8
n_ __informativee
n_informative 2
n_informative =
balancad accuracy (%)
source domain
95
target domain
90
RCT
SPDIM
(geodesic)
SPDIM
(bias)
10-1
10" 10
10" 10-1
10"
label ratio
label ratio
label ratio
Figure A4: Performance over the number of informative sources. Same as Figure (panel 3) but for different number of informative dimensions encoding label information in 8, defined in (TT). The m_informad ivve parameter of the scikit-learn function mak make_clase c effectively defines the dimensionality of the label encoding subspace D.
finite impulse response (FIR) filter bank (4 filters) with learnable parameters. The second convo- lutional layer applies spatio-spectral filters (40 filters) along the spatial and convolutional channel dimensions. Covariance pooling is then applied along the temporal dimension. A subsequent BiMap layer projects covariance matrices to a D-dimensional subspace (D-20) via bilincar mapping. Next, ReEig layer rectifies all eigenvalues lower than threshold 10-4, We varied the alignment and tangent space mapping layer m as specified in the main text. Finally, the classification head Jy is parametrized linear layer with softmax activations.
Parameter estimation We used the cross-entropy loss as the training objective, employing the Py- Torch framework (Paszke al. 2019) with extensions for structured matrices (Tonescu et al. 2015) and
gradients (Absil et al.) 2008) to propagate gradients through the layers. We stick to the spper-parameters provided in the public reference implementation. Specifically, gradients were estimated using fixed-size bini-bbtches (50 observations; 10 per domain across 5 do- mains) and updated parameters with the Riemannian ADAM optimizer (Bécigneul & Ganea (aanea)201)) (0188) (10-3 learning rate, 10 weight decay, 31 0.9, 3n = 0.999). We split the source domains' data into training and validation sets (80% / 20% splits, randomized, stratified by domain and label) and iterated through the training set for 100 epochs using exhaustive minibatch sampling. After training, the model with minimal loss on the validation data was selected.
A.7.2 SLEEP STAGING MODEL
We considered four baseline deep learning architectures Chambon (Chambon et al. 2018). Usleep (Perslev et al., 2021). DeepSleepNet (Supratak et al.) (2017). and AttnNet (Eldele et al.) (023) here. Although DeepSleepNet and AttnNet are initial proposed for single-channel EEG data, there are many related studies (Guillot et al. 2020 Ji et al. 2023 Ma et al. 2024 Guillot & Thorey 2021) use the model proposed for single-channn implementation provided in braindecode (Schirmeister et al. 2017) for all architectures above, and stick to all model aaper-parametes as provided in the braindecode. We used similar learning- related hyper-parameters with an Adam optimizer (e.g., early stopping, LR scheduler, same batch size,
data as a baseline for multi-channels data. We use the
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Published as a conference paper at ICLR 2025
similar number of epochs) to TSMNet A.7.1 We split the source domains' data into training and validation sets (80% / 20% splits, randomized, stratified by domain and label), and the model with minimal loss the validation data was selected after training.
25


Reviews:
[{"review_id": "Csl8kZWaDK", "reviewer": "Reviewer_PCcy", "summary": "This study focuses on the realistic issue of label shifts in EEG across subjects and/or sessions (relative class proportions in target domains when source domains are class-balanced). Using theoretical analysis, it extends the SotA statistical alignment framework for handling distribution shifts in EEG to also include label shifts. The proposed SPDIM includes a domain-specific bias parameter estimated from unlabeled target data that reduces over-corrections done by the current SotA framework. Results on synthetic data and real-world EEGs demonstrate the value of SPDIM over baselines.", "questions": "- Q: Does this framework treat one subject or one EEG recording as one source/target domain containing both/multiple class labels?\n- Q: How does this framework for \"latent space alignment\" compare/relate to non-reimannian approaches for SFUDA for EEGs/multivariate timeseries? See [1] for a recent example. The \"test-time adaptation\" (Section 3.2) studies listed in [2] might also be relevant.\n- Q: What factors other than dataset size and label shifts could account for the high variability/stdev in Table 1? In most cases, handling label shift (either with RCT or SPDIM) decreases variability compared to \"w/o\", but its still seems high.\n- Minor comments: 1) pixel resolution of Figure 1 can be improved, 2) typo in citations at line 218 and 236., 3) line 443 remove \"standard-deviation in brackets\"\n- The anonymous code link is broken?\n\n[1] He, Huan, et al. \"Domain adaptation for time series under feature and label shifts.\" International Conference on Machine Learning. PMLR, 2023.\n\n[2] Garg, Saurabh, et al. \"Rlsbench: Domain adaptation under relaxed label shift.\" International Conference on Machine Learning. PMLR, 2023.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- Rigorous and clear presentation of technical details and full analytic workflow.\n- This work is a great example of theory-guided methods design for EEG.\n- Impactful choice of research problem - performance of EEG models under label shifts will remain a ubiquitous concern, both clinically and in the BCI space.", "weaknesses": "- (line 166) Q: Is the assumption of number of latent brain sources = number of observed scalp channels = P necessary or realistic?\n- No discussion of study limitations and/or future directions.", "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": "lOqoAbLXoE", "reviewer": "Reviewer_CvWN", "summary": "The study addresses a source-free unsupervised domain adaptation problem and proposes SPDIM, a framework based on the SPD manifold. \nSPDIM compensates for label shifts using proposed generative models, which prior Riemannian statistical alignment methods do not effectively handle. \nAdditionally, SPDIM applies the information maximization principle to learn domain-specific parameters. \nSimulation experiments demonstrate its superiority under various levels of label shift, and empirical analysis on real EEG datasets shows that it outperforms previous approaches.", "questions": "- Is the domain-specific formard model $A_{j}$ learned from features of a specific domain, or is it predefined? \n- How are domain specific parameters $\\Phi_{j(i)}$ and the geodesic step-size parameters $\\varphi_{j(i)}$ learned according to the proposed information maximization principle described in Section 3.3?\n- Is there any relationship between the adaptation performance and predefined hyperparameters, such as the rank of $A$ and the number of domains within $\\mathcal{D}_{s}$?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The motivation is clear and easy to follow. SPDIM aims to address adaptation under label shifts, a common challenge in real-world EEG datasets. \n  Theoretical analysis further explains the causes of deviations under label shifts.\n\n- Simulation experiments qualitatively validate the benefits of SPDIM in the presence of label shifts. \n   Cross-subject and cross-session experiments on motor and sleep-staging EEG datasets illustrate its superiority over existing alignment methods based on the SPD manifold.", "weaknesses": "- Some notations in equations seem confusing. For example, the index $j$ under $\\sum$ may need to be $i$ in Eq. (2). The invertible mapping $upper$ is defined on $S$, but $upper^{-1}$ appears in Eq.(10). \nAdditionally, $j_i$ and $j$ use the same letter but with different meanings, which could lead to ambiguity. The notation $Q$ in Eq.(15) seems to appear without prior introduction. \n\n- Some aspects of the method require further clarification. As mentioned in Line 249, the right-hand side of Eq. (15) is claimed to contain only domain-invariant terms. However, from my perspective, $C_i$ depends on the domain-specific \nmatrix $A_{j}$, as suggested by Eq. (13). According to Proposition 1, $ \\bar{C} _ {j(i)} $ converges to $I_P$. These indicate that $Q$ is linked to $A_{j}$, which may not be domain-invariant. Additionally, the relationship between the information maximization approach introduced in Section 3.3 and SPDIM (bias) / SPDIM (geodesic) is unclear. \n\n- To better demonstrate SPDIM’s effectiveness, it would be beneficial to compare it with additional statistical alignment methods beyond those based on the SPD manifold. This would provide a more comprehensive evaluation against existing approaches.", "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": "tBDXy4frRt", "reviewer": "Reviewer_ASJZ", "summary": "The \"SPDIM\" paper introduces a novel geometric deep learning framework aimed at enhancing source-free unsupervised domain adaptation (SFUDA) for EEG data under both conditional and label shifts. By leveraging the symmetric positive definite (SPD) manifold and employing a parameter-efficient manifold optimization strategy, the proposed method, SPDIM, addresses significant generalization challenges in EEG data processing, especially where traditional Riemannian geometry methods fall short due to label shifts. SPDIM shows promising improvements across multiple EEG-based applications, including brain-computer interface tasks and sleep staging, demonstrating its efficacy over prior alignment frameworks", "questions": "Plz go and check weaknesses", "limitations": "", "rating": 5, "confidence": 2, "soundness": 3, "presentation": 1, "contribution": 3, "strengths": "1.\tThe introduction of an SPD-manifold-constrained bias parameter is an advancement for tackling SFUDA in EEG.\n2.\tThe framework has been applied effectively across different tasks, showcasing broad applicability.\n3.\tSPDIM outperforms conventional methods, showing its resilience under varying label distributions.", "weaknesses": "1.\tThe motivation behind addressing label shifts and domain gaps with SPDIM is somewhat implicit, without clearly laying out why these challenges necessitate the proposed framework. \n2.\tThe paper contains an extensive number of equations and mathematical formulations in the main text, which can make the methodology difficult to follow. \n3.\tAlthough the paper compares SPDIM with several baselines, a broader set of comparisons, especially with newer unsupervised or semi-supervised EEG methods, could provide further insights into SPDIM’s performance and robustness.\n4.\tWhile SPDIM improves accuracy under domain shifts, the model’s interpretability remains limited. \n\nI will reconsider my assessment after checking rebuttual.", "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": "ZDlhpGR5qQ", "reviewer": "Reviewer_ocKU", "summary": "The paper introduces SPDIM, a framework for source-free unsupervised domain adaptation (SFUDA) in EEG-based applications, which are challenged by distribution shifts across sessions or subjects. SPDIM leverages the geometry of symmetric positive definite (SPD) matrices to handle conditional and label shifts, aligning EEG data across domains without requiring labeled target data. The approach introduces a domain-specific SPD-manifold bias to counteract label shifts, and optimizes alignment using an information maximization principle, which prevents mode collapse by ensuring class diversity and prediction confidence. Experimental results on EEG datasets for motor imagery and sleep staging show that SPDIM outperforms baseline SFUDA methods, demonstrating robust generalization across domains even under significant label distribution changes.", "questions": "- You mention there are conditional shifts in EEG data (p_j(x|y) changes between domains). Can you relate this with your modelization?\n- What is D in the Remark 1?\n- Does the Propostion 2 still hold when M_j does not tend to the infinite?\n- You train your model on the target domain (in an unsupervised manner). Did you train/test split the target domain?\n- How easy to train are the methods you use? e.g. USleep is rarely used as a baseline in other sleep staging papers. Providing infos the lr scheduler, batch size, … would be valuable.\n- I am surprised that the spatial covariance is enough to classify sleep stages. Usually, the temporal information is used but not the spatial one. Can you comment on this?\n\nA few typos:\n- D and P are both used for the data dimension\n- There are “?” in lines 218 and 236.\n- Q and U are both used for domain-invariant par of the mixing matrix.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper is well written.\n- The modelisation is original and insightful. I really enjoyed reading the modelisation part of the paper.\n- The developed methods are tested on 3 setups: synthetic data, Motor-Imagery and Sleep-Staging.", "weaknesses": "- At the time of reviewing the paper, the code is not available: “The repository is not found.” is returned by anonymous.4open.science\n- A modelisation per domain of EEG data was proposed in [1] which could be worth citing in your introduction. Indeed, the authors mention there exists a linear mapping per domain to get domain-invariant tangent vectors (and without assumption on the mixing matrix (9)).\n- The experiment on motor imagery is limited since you artificialy unbalance the labels. Finding real world data which are naturally unbalanced would add value to the paper.\n- The mean accuracy of the 2 proposed methods are within the standard deviation of the recenter for the motor imagery application.\n- On the sleep-staging setup, you do not compare with adaptation methods expect recenter. You should compare at least to STMA or TMA (Spatio-Temporal Monge Alignment) which is presented in [2].\n- The presentation of the results is not homogeneous between the two applications. In particular, it is strange to me to call an “ablation study” a comparison with other methods.\n\n[1] Collas, Antoine, Rémi Flamary, and Alexandre Gramfort. \"Weakly supervised covariance matrices alignment through Stiefel matrices estimation for MEG applications.\" arXiv preprint arXiv:2402.03345 (2024).\n\n[2] Gnassounou, T., Collas, A., Flamary, R., Lounici, K., & Gramfort, A. (2024). Multi-Source and Test-Time Domain Adaptation on Multivariate Signals using Spatio-Temporal Monge Alignment. arXiv preprint arXiv:2407.14303.\n\n\nI put a rating of 5 but I am open to increasing it.", "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": "yCZEPGojOG", "reviewer": "Reviewer_GP1Q", "summary": "Due to the difficulty of the SPD method in handling label shift issues, this paper proposes a geometric deep learning framework, SPDIM, for SFUDA problems under specific distribution shifts, including label shifts. SPDIM employs the information maximization principle to learn a single SPD-manifold-constrained parameter per target domain. Using public EEG-based brain-computer interface and sleep staging datasets, we demonstrate that SPDIM outperforms prior approaches.", "questions": "Please see the weakness.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "This paper investigates the label shift problem in SFUDA, with a very strong motivation and significant practical relevance.\n\nThe method proposed in this paper has a certain theoretical foundation, and the derivation of some propositions may provide inspiration for solving the label shift problem.", "weaknesses": "**The clarifications and revisions have addressed most of my concerns.**\n\n---\n\nAlthough this paper focuses on EEG SFUDA problems, the proposed method does not appear to be specifically designed for EEG but seems to be a more general approach applicable to any label shift scenario. From the perspective of EEG research, the method lacks specificity for EEG data, while from the perspective of SFUDA research, the paper only validates the method on EEG data, lacking more reliable experimental verification.\n\nThe experiments are not solid. The paper does not clearly present the experimental setup, such as the hyperparameters of the models, the partitioning method of the source and target domains, etc. Additionally, the EEG decoding methods compared in the experiments are not sufficiently strong. The paper does not compare some classic EEG decoding models, such as EEGNet and EEG Conformer, nor does it compare some sleep staging models, such as DeepSleepNet. The domain adaptation methods only compare Information Maximization (IM), and such insufficient comparisons are not enough to prove the superiority of the proposed method.\n\nThe writing of this paper still has some room for improvement. For example: Figure 1 has low resolution, and the four sub-figures in Figure 2 lack sub-titles.", "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)