HEEGNet: Hyperbolic Embeddings for EEG
Authors: Shanglin Li
Chu Shiwen
Okan Koç
Yi Ding
Qibin Zhao
Motoaki Kawanabe
Ziheng Chen
Venue: ICLR 2026 Poster (2026)
Keywords: geometric deep learning
transfer learning
source-free adaptation
electroencephalography
neurology
brain-computer interfaces
Primary area: applications to neuroscience & cognitive science

Abstract: Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding often suffers from poor generalization due to distribution shifts across domains (e.g., subjects). Learning robust representations that capture underlying task-relevant information would mitigate these shifts and improve generalization. One promising approach is to exploit the underlying hierarchical structure in EEG, as recent studies suggest that hierarchical cognitive processes, such as visual processing, can be encoded in EEG. Yet, most existing decoding methods rely on Euclidean embeddings, which are not well-suited for capturing hierarchical structures. 
In contrast, hyperbolic spaces, regarded as the continuous analogue of tree structures, provide a natural geometry for representing hierarchical data. In this study, we first demonstrate that EEG data exhibit hyperbolicity and show that hyperbolic embeddings improve generalization. Motivated by these findings, we propose HEEGNet, a hybrid hyperbolic network architecture to capture the hierarchical structure in EEG and learn domain-invariant hyperbolic embeddings. To this end, HEEGNet combines both Euclidean and hyperbolic encoders and employs a novel coarse-to-fine domain adaptation strategy. Extensive experiments on multiple public EEG datasets, covering visual evoked potentials, emotion recognition, and intracranial EEG, demonstrate that HEEGNet achieves state-of-the-art performance.

Published as a conference paper at ICLR 2026
HEEGNET: HYPERBOLIC EMBEDDINGS FOR EEG
Shanglin Li Shiwen Chu', Okan Koç², Yi Ding', Qibin Zhao
Motoaki Kawanabe' & Ziheng Chen
1 Advanced Telecommunicationt Research Institute International
2 RIKEN Center for Advanced Intelligence Project
3 University of Trento
Nanyang Technological University
ABSTRACT
Electroeneephalograpyy (EEG)-based brain-computer interfaces facilitate direct communication with computer, enabling promising applications in human- computer interactions. However, their utility is currently limited because EEG decoding often suffers from poor generalization due to distribution shifts across domains (e.g., subjects). Learning robust representations that capture underly- ing task-relevant information would mitigate these shifts and improve general- ization. One promising approach is to exploit the underlying hierarchical struc- ture in EEG, recent studies suggest that hierarchical cognitive processes, such as visual processing, can be encoded in EEG. While many decoding methods still rely Euclidean embeddings, recent work has begun exploring hyperbolic geometry for EEG. Hyperbolic spaces, regarded as the continuous analogue of tree structures, provide natural geometry for representing hicrarchical data. this study, we first empirically demonstrate that EEG data exhibit hyperbolic- ity and show that hyperbolic embeddings improve generalization. Motivated by these findings, we propose HEEGNet, a hybrid hyperbolic network architecture to capture the hierarchical structure EEG and learn domain-invariant hyper- bolic embeddings. To this end, HEEGNet combines both Euclidean and hyper- bolic encoders and employs a novel coarse-to-fin, domain adaptation strategy. Extensive experiments multiple public EEG datasets, covering visual evoked potentials, emotion recognition, and intracranial EEG, demonstrate that HEEG- Net achieves state-of-the-art performance. The code is available https:
INTRODUCTION
Electrreencephalograpyy (EEG) measures multi-channel electric brain activity (Niedermeyer & da Silva] 2005) and can reveal cognitive processes (Bell & Cuevas 2012) and emotion states
(Suhaimi et al. 2020). EEG-based brain-computer interfaces (BCI) aim to extract meaningful
patterns for applications such as attention monitoring (Lee et al. 2015) and emotion recognition
(Suhaimi et al. 2020). However, they currently suffer from poor generalization due distribution
shifts across sessions and subjects (Fairclough & Lotte 2020).
In EEG-based neurotechnology, distribution shifts have traditionally been mitigated by collecting labeled calibration data and training domain-specifie models (Lotte et al.] 2018). which limits its utility and scalability (Wei al.) 2022). As an alternative, domain adaptation (DA) methods aim to learn a model from source domains that performs well on different (but related) target domains (Ben-David et al. 2010). BEG, DA primarily addresses cross-session and cross-subject transfer learning problems (Wu et al. 2020). Since target domain data is typically unavailable during training and source domain data is not always available for privacy reasons, model adaptation often treated in the context of multi-source multi-target free unsupervised domain adaptation (SFUDA) (Li et al. 2023). However, existing DA methods do not always work reliably, especially when the distribution shift between domains is large.
"Corresponding author.

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Figure 1: Framework Overview. (a) A comparison illustrating that hyperbolic space, with its negative curvature, is better suited for embedding hicrarchical data than flat Euclidean space. (b) The HEEGNet architecture, which employs coarse-to-fine domain adaptation strategy, DSMDBN (proposed). The first stage of DSMDBN aligns domain-specific moment statistics. (c) Top-down view in hyperbolic space: the second stage of DSMDBN aligns each source domain distribution to standard hyperbolic Gaussian distribution by minimizing the Hyperbolic Horospherical Sliced- Wasserstein (HHSW) discrepancy.
Learning robust representations that capture underlying task-relevant information better could re- duce distribution shifts and thereby improve generalization in domain adaptation (Bengio et al.] Zhao et al. 2019). One promising approach to achieve such robustness is to exploit the under- lying hierarchical structure in EEG data. Indeed, recent studies suggest that the brain's hierarchical cognitive processes, such visual processing and emotion regulation, can be encoded in both in- tracranial EEG (Vlcek et al., 2020) and stimulus-evoked scalp EEG (Turner et al. 2023 Sun et al.) 2023). While Euclidean embeddings currently dominate EEG decoding approaches, such embed- dings are not well-suited to capture the exponential expansion of possible system states described by hierarchical tree-like process (Peng al., 2021). Intuitively, this is because, since the space flat, the circumference and area of a circle grow only linearly and quadratically with the radius, respectively, leading mismatch with the underlying data geometry (Fig. [T). In contrast, in hyperbolic spaces (Fig. TT)) with negative curvature, such quantities grow exponentially with the ra- dius, thereby naturally approximating the exponential expansion of hierarchical processes (Krioukov et al. 2010). Leveraging this representational advantage, hyperbolic embeddings have outperformed Fuclidean approaches across various tasks with hierarchical data in computer vision (CV) and natu- ral language processing (NLP) (Ganea et al. 2018, Mettes et al., 2024).
2013
In this study, we argue that hyperbolic spaces are often more appropriate for learning EEG embed- dings. To this end, we first conduct pilot study using the well-established EEGNet architecture (Lawhern et al. 2018) generate EEG embeddings. ture in these embeddings and confirm their hyperbolicity. We then modify EEGNet by replacing its multinomial logistic regression (MLR) with a hyperbolic variant, demonstrating that hyperbolic embeddings improve generalization over Euclidean ones. Motivated by the potential of the hy- perbolic embeddings, we propose HEEGNet, a hybrid hyperbolic network architecture designed to capture the hierarchical structure of EEG data and learn
quantify the degree of hierarchical struc-
hyperbolic EEG em- beddings. HEEGNet (Fig. 3 integrates both Euclidean and hyperbolic encoders: the Euclidean encoders extract meaningful spectral-spatial--emmprs EEG features and project them into hyper- bolic space, with the hyperbolic encoders further refining these representations to capture hierar- chical relationships more effectively. The hybrid nature of HEEGNet enables Euclidean encoders to leverage well- well-established signal processing principles and extract meaningful neurophysiolog- ical features from EEG signals, while the hyperbolic encoding helps to preserve the hierarchical structure in hyperbolic space. To address distribution shifts across domains, HEEGNet employs novel coarse-to-fine domain alignment strategy. This strategy extends moment alignment, which is the current state-of-the-arr (SotA) approach in BEG cross-domain generalization (Roy et al. 2022 Bakas et al. 2025) but whose performance often degrades under large distribution shifts (Li et al. 2025 Rodrigues et al. 2018). Specifically,
propose domain-specine moment- senttttten-deee dien-distribution batch normalization (DSMDBN, Sec, Scc.B.I). which first explicitly aligns the domainn-spccin first- and second-order moments (Fig. [p) using recently developed Riemannian batch normalization methods
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(Chen et al. 2025a b). In the second stage (Fig. [t], the aligned EEG embeddings further matched at the distribution level by minimizing the Hyperbolic Horospherical Sliced-Ward Wassersten discrepancy (Bonet et al. 2023) between each source domain and standard hyperbolic Gaussian. DSMDBN transforms domain-specific inputs into domain-invariant outputs, enabling the extension to multi-source multi-target SFUDA scenarios. We demonstrate that HEEGNet obtains SotA per- formance on public EEG datasets encoding hierarchy, including visual evoked potentials, emotion recognition, and intracranial EEG. Additionally, we further validate its performance on public EEG motor imagery datasets, which are not reported to encode hierarchical information.
2
PRELIMINARIES
2.1 RELATED WORK
Brain hierarchy. The human brain is complex network that supports various hierarchical cogni- tive processes. For example, in visual processing, lower cortical areas detect basic features, which higher cortical areas progressively refine into global representations (Hochstein & Ahissar 2002). Similarly. in emotion regulation, subcortical areas generate primal urges, which are refined by the limbic system with experience, and the neocortex finally regulates them into complex thoughts and feelings (Panksepp) 2011). To study hierarchical brain dynamics, researchers have widely used in- tracranial EEG, which captures neuronal population activity with high spatial and temporal resolu- tion (Lachaux et al.) 2003). As for scalp EEG, Collins et al. (2018) observed distinct EEG responses to varied stimulus frequencies reflecting different visual processing levels. [Sun et al. (2023) showed the hierarchical emotion ambiguity processing with distinct EEG patterns.
Hyperbolic neural networks. Hyperbolic neural networks, which perform neural network oper- ations in hyperbolic space, have been widely explored in NLP and CV (Peng al., 2021 Ganea et al. 2018). In the EEG literature, [Chan et al. 2025) performed contrastive pretraining for emo- tion recognition in hyperbolic space. In contrast, our work introduces hybrid hyperbolic network architecture and a domain adaptation strategy (DSMDBN), leveraging hyperbolic geometry to ad- vance both representation learning and cross-domain generalization.
Domain Adaptation in EEG. Among the DA techniques applied to EEG, moments alignment that align the first and second-order moments either in input (He & Wu 2019 Gnassounou et 2024
or in latent space (Kobler et al. 2022] Bakas et al.) 2025) are considered as SotA (Roy et al. 2022
Bakas et al. 2025). Such heuristic alignments are not guaranteed to improve generalization (positive transfer), but tend to improve accuracy under mild distribution shifts Yair et al.) 2019). Theoret- ically, DA was studied as an upper bound analysis of target risk (Ben-David
al., (010), using discrepancy terms (such integral probability metries (Redko al., 2019) or f-divergences (Acuna ctt al. (02T)) between the source and target distributions, suggesting alignment of the feature dis- tributions potential solution (Ganin et al. 2016). Inspired by this, the proposed DSMDBN (Fig. [T)) extends moment alignment further with feature distribution alignment.
2.2 MULTI-SOURCE MULTI-TARGE SFUDA
Let X denote the input space, ) the label space, and D the set of domain identifiers, where random variables ær y. and d represent features, labels, and domains, respectively. In the multi-source multi- target SFUDA setting, given M labeled source domain datasets
{ ye, d4) ot X, 9i e V, d E D.) and N unlabeled target domain datasets = [(,,, d,) Ix; E X, d, E D.) I., and La denote the sizes of source domains and target domains, and y/ and d; indicate the associated label and domain of sample
i. We assume that all source and target domains share the same feature and label spaces. The goal is to learn model h from S that generalizes to unseen, unlabeled T via SFUDA, where only the trained model is available.
2.3 HYPERBOLIC GEOMETRY
The hyperbolic space is Riemannian manifold of constant negative curvature K < 0. Among its five equivalent models (Cannon et al. 1997). we focus on the Lorentz model due to its numerical stability (Mishne al. 2023). The n-dimensional Lorentz model is L := {p E R=+1 (p. p) R, Pt 0} with the Lorentz inner product (p. p) c (ps,Ps) p2. Following Ratcliffe 2006
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denote the first dimension t the time component and the remaining dimensions the space component (i.e., p E L = [pt. P. ). The geodesic distance, defined as the shortest distance
between any two points, defined as:
1 dc(p. V-K cosh -1 (K (p, 9)2)
(1)
Under this distance. it is possible introduce mean and variance operations into the Lorentz man- ifold. Specifically, for a set of points P = {pr E Lik Jig., the weighted Fréchet mean wFM, on Riemannian manifolds defined as the minimizer of the squared distances weighted by 7/:
M
# = WFMF (fps E E = arg min Σ n (g.
(2)
If the weights yJ are uniform, the weighted Fréchet mean reduces to the standard Fréchet mean, and the Fréchet variance 2² is defined as the attained value at the Fréchet mean.
For each point p E L there corresponds a tangent space T {u E R kp v)c 0}. To project points between the manifold p; E Lg and the tangent space exponential map expo T. -> I. and the logarithmic map log : . TTL can be used to transport points V/ E TT from the tangent space at to the tangent space at parallel transport pTp--g(1) L operation can be performed (see App. C.I for their closed-form expressions).
T at Lj the
Recently, Chen et al. 2025b) Sec. 5.5) show that Lorentz model admits gyrovector structure (Chen al. 2025b Def. 4). which extends the vector addition and scalar multiplication into manifolds. Specifically, the Lorentz gyroaddition, gyromultiplication, and gyroinverse are
p q Expr (PTT-p (Loga
V Li
1 1 Expo (1 (L)o
V Vp L
(4)
@kp -1 kkp== p=
Pt
Ap E L
(5)
Ps
where = V 11/K, O, ........
is the origin over the Lorentz model. is also the identity element:
0 0 Q = q. E T.k Eqs.
3 and 4 admit closed-form expressions, as shown in App. C.2
2.3.1 HYPERBOLIC OPERATIONS.
Hyperbolic neural networks. We define the hyperbolic neural networks used in this work within the Lorentz model following Bdeir al. (2024). App. B.J provides a brief review of gyrovec- tor spaces, which generalize vector structures to manifolds, serving as foundations to build neural networks in hyperbolic space. The Lorentz convolutional layer (App. (C6) is defined as matrix multiplication between a linearized kernel and a concatenation of the values in its receptive field. The Lorentz ELU (App. C.3) activation applies the activation function to the space components and concatenates them with the time component. The average pooling layer is implemented by comput- ing the Lorentzian weighted mean of all hyperbolic features within the receptive field. Analogous to the Euclidean MLR classifier, the Lorentz MLR (App. C.7 also utilizes the distance from instances to hyperplanes to describe the class regions.
6-hyperbolicity. Khrulkov et al. (2020) introduced 5-hyperbolicity as a measure of the degree of tree-like structure inherent in embeddings. The idea is to find the smallest value of for which the triangle inequality holds via the Gromov product (mathematical formulation in App. C.8 In this formulation, the definition as stating that the metric relations between any four points are the same they would be in a tree, up to an additive constant 8. The lower d 2 0 is, the closer the embedding to hyperbolic space.
hyperbolic space in terms of the Gromov product can be interpreted
distance (SWD) is popular proxy for the Wasserstein distance for comparing probability distributions and has been extensively applied in optimal transport (Lee al. 2019). Analogous to the Euclidean SWD, (Bonet et al.) 2023) defined the hyperbolic sliced Wasserstein distance by projecting dis- tributions onto horospheres, denoted as Hyperbolic horospherical sliced-Wassereee Wasserstein discrepancy
Hyperbolic horospherical
-assersesss discrepancy. The
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(HHSW), where distances between the projections of two points belonging to geodesic with the same direction are conserved. For probability measures J., v E Pp(L") in the Lorentz model, with
p 2 1, the p-th power of the HHSW is defined
HHSWE(H,
JIpLANsA
WP (B H B dA(v)
(6)
where TyTla n S is the set of unit tangent vectors the origin 0 W is the p-th power of the 1D p- Wasserstein distance, B denotes the horospherical projection of μ along direction v, and d')()) is the uniform measure over these directions.
3 METHODS
3.1 DOMAIN-SPECIFIC NOMENI-TIEN-DDITTIIIUNT BATCH NORMALIZATION
Hyperbolic batch normalization. Batch normalization (BN) (lofe & Szegedy, 2013) is a widely used training technique in deep learning as BN layers speed up convergence and improve general- ization. Chen al. (2025a by extended the Euclidean BN into the hyperbolic space by gyrovector structure. The centering and scaling in the Euclidean BN correspond to Lorentz gyroaddition, gy- roinverse, and gyromultiplication. Given a batch of activations P = {ps E Ligis,, the core operations of hyperbolic batch normalization (HBN) are
HBN(
(Oppp) V M,
V12 +
Centering
Scaling
where y and u² are Fréchet mean and Fréchet variance, 7 E the scaling parameter, and is small value for numerical stability.
Domain-specific momentum batch normalization for EEG. Chang et al. (2019) introduced domain-specific batch normalization, which employs multiple parallel BN layers that process obser- vations based on their corresponding domains to mitigate domain shift. However, EEG scenarios, where small dataset sizes can make batch statisties unreliable for normalization Yong al. 2020). To address this, Kobler et al. (2022) proposed Domain Sppeci-Specific Momentum Batch Normalization to track domain-specific momentum-basee running estimates of the first- and second-order moments. keeps two separate sets of running estimates, the training estimates are updated using a momen- tum parameter Mrrain(k) that follows elamped exponential decay schedule at training step k, while a fixed momentum parameter 1eees is used during testing.
Domain-specific momient-heen-dditiibuttoon batch normalization. While Kobler et al. (2022) achieved SotA performance, such moment aligmment is not guaranteed to improve generalization (achieve positive transfer) and often struggles under large distribution shifts (Li et 2025 Ro- drigues et al. 2018). On the other hand, feature distribution alignment offers theoretical guarantees, can be challenging to achieve practice, the feature distributions may be too distant for effec- tive learning (Chang et al., (009)). Thus, we propose two-stage DSMDBN strategy by extending moment alignment in (Kobler et al. 2022) to incorporate the alignment of domain-specific feature distributions in hyperbolic space.
Formally, in our setting we assume that minibatches Bg, that form the union of NB, S |D] domain- specific minibatches By are drawn from distinct domains d E DD, C Each B contains No, i...d. observations Vi, i I,..., ., M/NB.- In the first stage, DSMDBN (algorithm 1 explicitly aligns the domain-specific running first- and second-order moments by centering and scaling them with 2 which can be expressed as:
ps (1) = HBNd(() (p:: Nests Atrain(k)) Vp, E B Vd Ds.
(8)
(2M (algorithm 2. momentt-aignee domain-specific EEG embeddings are then further (im- plicitly) aligned by matching them to samples from standard hyperbolic Gaussian (ō, 1). This matching achieved by minimizing the HHSW (Eq. as a loss term
DSMDBN (2)) HHSW (pc). Vp, E B Vd DE.-
(9)
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This implicit alignment guides the feature extractor toward learning robust, domain- invariiat repre- sentations by matching source distributions to a standard Gaussian, thereby addressing distribution shifts that moment alignment alone often fails to mitigate. At test-time, HEEGNet applies only moment alignment, as source data are typically sufficiently diverse to capture the task-relevant vari- ability in EEG (Rodrigues et al.] 20188 Mellot al. 2023). Learning Gaussian-aligned feature space from the sources is sufficient for the extractor to produce normalized target-domain features after moment alignment, enabling the application of domain matching in the SFUDA scenarios.
3.2 HEEGNET
Following Kobler et al. (022), we constrain the hypothesis class H. to functions h X X D - y that can be decomposed into a composition of a shared feature extractor fo X - L a domain- specific alignment module m L x D - 1 and shared classifier go : [ - 3' with parameters θ = (0, Φ } We parametrize h = Iv o my o fo as a neural network and learn the entire model in an end-to-end fashion, which we denote HEEGNet (details in App. (.2)
The HEEGNet is designed as a hybrid model, combining Euclidean encoders with hyperbolic neural networks. Most existing hyperbolic models adopt hybrid approach, first generating hierarchical embeddings in Euclidean space and then mapping them to hyperbolic space, leveraging the strong feature extraction capabilities of well-established Euclidean encoders (Peng et al., 2021). This hy- brid design is particularly well-suited for EEG data, Studies suggest that EEG signals contain hier- archical information across temporal (Damera al., 2020), spectral (Sun et al. 2023), and spatial (Tonoyan et al., (017)) dimensions. Euclidean encoders, such as convolutional networks, naturally align with this organization, making them effective for extracting hierarchical and neurophysiolog- ically meaningful features directly from raw EEG signals (Lawhern et al., 2018). However, such operations do not preserve physical properties in hyperbolic space, where dimensions are intrinsi- cally coupled (see App. for fully hyperbolic experiments).
In a nutshell, the feature extractor fa consists of three Euclidean convolutional layers along with standard components (c.g.. BN and pooling), projection layer ProjX, and hyperbolic convolu- tional layer (Fig- We sequentially adopt the three convolutional layers from EEGNet (Lawhern et al. 2018 temporal convolution to learn ceqqueccy-speciffe filters, depthwise spatial convolu- tion to capture electrode-wise patterns, and second depthwise temporal convolution to summarize information across time. These well-established operations provide ppecrral-spatial-tempoo fea- ture maps with meaningful neurophysiologically properties. The ProjX layer projects the Euclidean feature maps into hyperbolic space LRk after which hyperbolic convolutional layer performs point- wise convolution to optimally combine these feature maps. The alignment module me applies the first stage of the proposed DSMDBN (Eq. (8) to explicitly align domain speeiffe moments in hyper- bolic space, followed by hyperbolic EL. and pooling (Eq. (21) for dimension reduction. Finally, the classifier Go is parametrized as hyperbolic MLR (HMLR) layer).
EXPERIMENTS
In this study, we consider three EEG modalities that have been reported to encode hierarchical struc- tures: visual- and emotion-stimuli scalp EEG, and intracranial EEG (Turner al., 2023 Sun al.] 2023 Sonkusare et al.) 2020). Corresponding EEG-based BCI applications include steady-state visually evoked potentials (SSVEP), code-modulated visually evoked potentials (CVEP), emotion recognition, and intracranial EEG. While all applications hold significant potential for rehabilitation and healtheare (AI-Nafjan al., 2017 Guo al., 2022, Elsner al., 2018), their practical utility remains limited due to poor generalization across domains. We conduct pilot study to evaluate hy- perbolic embeddings and perform comprehensive experiments to assess the proposed HEEGNet. We further evaluate HEEGNet public motor imagery datasets that are not being reported to encode hicrarchical information.
Visually evoked potentials (VEP): Nakanishi (9 subjects/1 session/12 classes) (Naaanishi et al.) 2013). Wang (34/1/40) (Wang et al. 2016). CBVEP40 (12/1/4) (Castillos et al. 2023). and CB- VEP100 (12/1/4) (Castillos et al. 2023). We used MOABB (Chevallier et al.) 2024 pre-process the data and extract labeled epochs. Following Pan et al. (2022)), EEG signals were resampled to 256 Hz, bandpass filtered between 1-50 Hz, and segmented each trial into 1- or 2-second segments.

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Emotion recognition: Seed (15/3/3) (Duan et al.) 2013) and Faced (123/1/9) (Chen al. 2023b We used the public available pre- pre-preessed data. For Seed, EEG signals were resampled to 200 Hz and bandpass filtered between 0-75 Hz; for Faced, a 0.05 47 Hz bandpass filter applied.
Intracranial EEG: Boran (9/2-7/2) (Boran et al, 2020). We use MNE-python (Gramfort et al, 2014) to pre-process data and extract labeled epochs. Following Frauscher et al. 2018), EEG signals were resampled to 1000 Hz, bandpass filtered between 0.3-70 Hz.
Evaluation. We consider tross-domain adaptation within each dataset. We treat sessions do- mains, and use either a leave-one- -oroooo---- (source domain number 10) or a 10-fold leave-groups- cross-validation scheme fit and evaluate models. For the intracranial EEG dataset, due the different number of electrodes across subjects, we consider the cross- adaptation setting. We fit and evaluate models independently for each subject, treating the session as the grouping variable. For other datasets, we consider the cross-subject adaptation and treat the subject as the grouping variable. We use either the standard Adam optimizer (Kingma & Ba 2014) for Euclidean frame- works or the Riemannian Adam optimizer (Bécigneul & Ganea (2018) for geometric frameworks, both with default hyperparameters in PyTorch. We split the source domain data into training and val- idation sets (80% / 20% splits, randomized and stratified by domain and label) and iterated through the training set for 100 epochs. Early stopping was fit with a single stratified (domain and labels) inner train/validation split.
4.1 PIL.OT STUDY.
We select five datasets representatives motivate the of hyperbolic embeddings. All exper- iments are conducted under the cross-domain setting and follow the evaluation scheme described above. We begin by training and evaluating EEGNet on cross-domain tasks. Following Krioukov it al. (2010), we then use the target domain raw EEG data and the trained EEGNet to generate em- beddings of the intermediate layer (after first two convolutional layers), and the classification space to quantify their degree of inherent tree-likeness using 5 d-hyperbolicity respectively (Eq. (27). ). Fol- lowing Khrulkov et al. (2020), we report the scale-invariant metric årat E [0. 1]. where the lower 5rat is the higher the hyperbolicity of the embeddings. We then modify EEGNet by replacing its MLR with its hyperbolic variant, HMLR, and repeat the training and evaluation procedure.
Tab. indicates that all dataset both raw EEG data and EEGNet generated embeddings exhibit hi- erarchical structures, confirming the suitability of hyperbolic geometry for capturing the underlying information. Furthermore, replacing the Euclidean MLR layer in EEGNet with its hyperbolic coun- terpart consistently enhances performance across all datasets (Tab. 2 suggesting that hyperbolic geometry captures more robust representations across domains and improves generalization. t-SNE visualizations Fig. 2p. b for the identical subject and session show that under the same encoder struc- ture, hyperbolic representations enhance class separability. These findings strongly motivate the use of hyperbolic embeddings in cross-domain generalization.
Table 1: Pilot Study: öret of datasets. The lower the 6ret, the closer the dataset to hyperbolic space. The number of domains in each dataset is indicated by n.
Visual
Emotion
Intracranial
Dataset Metric
Nakanishi (n=9)
Wang (n=34)
Seed (n=45)
Faced (n=123)
Boran (n=37)
Raw 6,el
0.244 + 0.064
0.219 0.053
0.052 0.026
0.103 + 0.077
0.157 0.045
Intermediate 8,at
0.263 1 0.036
0.240 0.045
0.061 0.026
0.111 + 0.050
0.141 0.041
Classification space 6.et
0.306 + 0.027
0.333 0.039
0.072 0.025
0.132 + 0.047
0.017 + 0.048
4.2
MAIN EXPERIMENTS
Baseline models. We included six deep learning architectures EEGNet (Lawhern al.
2018
EEGConformer (Song et al. (022). ATCNet (Altaheri et al.] 2002). TSLANet (Eldele et al. SchirmeeistrrNet (Schirrmesster al. 2017), and FBCNet (Mane al. 2021) that proposed or
2024
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Table 2: Pilot Study: comparison of Euclidean Hyperbolii MLR. The averages of test-set scores are shown above using balanced accuracy (the score and the standard deviation are shown for each dataset). The number of domains each dataset is indicated by n. Permutation-paa paiied t-tests were used to identify significant differences between EEGNet+HMLR (Iyperbollic) and EEGNet (1e4 permutations). Significant differences are highlighted using dots: pp S 0.05, op S 0.01, op S 0.001.
Visual
Emotion
Intracranial
Dataset Model
Nakanishi
Wang
Seed
Faced
Boran
(n 9)
(n 34)
(n 45)
(n 123)
(n = 37)
EEGNet
57.2 + 19.8
37.4 +: 12.9
74.5 + 19.8
24.8 4 13.7 *
55.4 9.1
EEGNet + HMMR
60.8 1 20.7
39.2 + 13.8
75.1 + 20.0
38.8 + 12.4
57.4 1. 8.7
extensively used for general EEG decoding. We consider four deep learning architectures specifi- cally designed for VEP: EEGInception (Santamaria- Vazquez et al. 2020). DDGCNN (Zhang et al.)
2024), SSVEPNet (Pan et al. 2022a), SSVEPFormer (Chen et al.
2023a): and two deep learning architectures for emotion recognition: EmT (Ding et al. (025), TSccption (Ding et al. al.] 2022). We further considered two foundation models: LaBraM (Jiang et al. 2024) and CBraMod (Wang al.,
2024a) in evaluation. We use the implementation provided in the public available repositories for all architectures, stick all hyperparameters as provided, and use the standard cross-entropy loss as training objective.
SFUDA baselines. We consider two SFUDA baselines: Euclidean alignment (EA) (He & Wu 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 in the input space before model is fitted. For example, EA aligns the EEG trials covariance matrix directly in the input space. Therefore, we combine them with different models (e.g., EEGNet + EA) in our evaluation.
We parametrize h = Io my o fe as a neural network and learn the entire model in an end-to-end fashion, and use the standard cross-entropy loss with HHSW (Eq. ( as the training objective. The HHSW loss weight is a hyperparameter to be tuned, we set it to 0.01 for emotion and 0.5 for other datasets our experiments.
HEEGNet.
Following Bdeir et al. 2024), we set the curvature to -1 by default and implemented the norm nor- malization to assure numerical stabilization for training. Computational cost for hyperbolic opera- tion is briefly discussed in App. A During source-free target domain adaptation, HEEGNet keeps the fitted source feature extractor fe and linear classifier Ge fixed and estimates domain-specific first- and second-order statistics by solving Eq. for moments alignment m.g.
Tab. 3 summarizes the results across all three EEG modalities, presenting the grand average scores with general EEG decoding baseline methods. Extended results for VEP-specific, emotion occognition-specfiic and foundation models, as well as per-dataset results, are provided in Supple- mentary Tab. X and Tab. | At the overall grand average level, HEEGNet (DSMDBNN outperforms all baseline methods. A visualization of the two stages of DSMDBN is shown in Fig. 2 d. Inter- estingly, HEEGNet (DSMDBN+EA), the integration of DSMDBN with the input space alignment method EA, achieves superior performance. We conduct an ablation study to systematically investi- gate the effects of different alignment strategies within the HEEGNet architecture.
Ablation study. Tab. summarizes the effectiveness of three different alignment methods, input alignment (EA), moment aligmment, and distribution aligmment, within the HEEGNet architecture We highlight three important observations. First, moment alignment in hyperbolic space is the pri- mary driver of performance improvement. The absence of moment alignment consistently results in significant performance drop of at least 12.3% compared to the best-performing configuration. Second, distribution alignment proves effective only when paired with moment alignment, validating our proposed DSMDBN approach, which first aligns moments to facilitate subsequent distribution alignment. Third, moment alignment in the latent space outperforms input space alignment, support- ing the findings of Bakas al. (2025) that alignment benefits from enhanced class discrimination in the latent representation. Fourth, DSMDBN augmented with input alignment yields the best perfor- mance, indicating that multistage alignment promising strategy in cross-domain generalization.
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Table 3: Main experiment results. Grand average of test-set scores across three EEG modali- ties (balanced accuracy (%); higher is better; mean + std) Permutation-palle t-tests were used to identify significant differences between HEEGNet (DSMDBN+EA) and baseline methods (le4 per- mutations, 18 tests, t-max correction). Significance markers: S 0.05, *p s 0.01, S 0.001.
VEP
Emotion
Intracranial (n=37)
Overall (n=272)
Model
SFUDA
(n=67)
(n=168)
EEGNet
w/o
35.7+=15.5
38.1427.00
55.449911
39.9+23.6
55.8+20.88
73.8+22.3
59.1#11.2
67.4+22.3
STMA
30.3.18.9
70.7:120.5
51.2.1.9
58.1122.0
EBGConformer
w/o
29.1
83.2116.9
55.511.00
66.122272
EA
46.1123.1
82.8
61.7211.1
70.9:24.1
STMA
27.8.1..0
78.2.15.99
53.11552
62.4125.22
ATCNet
w/o
33.3:15.4
17.5&11.7
57.519,0
26.9118.5
EA
52.24:21.4
54.1+15.5
57.149.0
14.0+
STMA
39.4=1..6
56.4+16.3
542245.7
51,9116.7
TSLANet
w/o
24.4=14.1
12.5+12.9
55.1
35.5+15.7
EA
37.3+28.11 1
44.8+18.1
14.9+10.4
44.3++0088
STMA
20.5+5.44
19.6+15.1
54,1#6.2
43.0#17.9
SchirmeisterNet
w/o
40.2+t2..5
51.9422.4
56.947.7
49.7+23.1
EA
35.7
79.0
65.0110.2
66.5125.7
STMA
33.1
64.2+16.7
53.94
55.24
FBCNet
w/o
22.811.0
28.5
61.11100.6
31.6.120.2
38.8
51.3120.7
61.31110
49.6122.9
STMA
21.6+
33.0++2099
53.0+
32.9+
HEEGNet (proposed)
DSMDBN
79.6 19.8
16.6
58,419966
78.7
DSMDBN+EA
12.4
86.7+
66.7+-12.5
81.7++14.4
(u)
(c)
(d)
Figure 2: t-SNE visualizations of classification space for Nakanishi (subject 4, sessionl). Each color denotes a distinct class. (a) EEGNet, (b) EEGNet with HMLR, (c) DSMDBN stage and (d) DSMDBN stage 2. The plots illustrate how hyperbolic embedding and our proposed two-stage alignment progressively enhance class separability.
4.3 MOTOR IMAGERY
We consider two publicly available motor imagery datasets. Pre-processing included resampling EEG signals 250 or 256 Hz, applying temporal filters to capture frequencies between 4 and 36 Hz, and extracting 3-second epochs linked to specific class labels. In addition to Euclidean models, we evaluate several manifold-based decoding approaches for motor imagery. These include Grassmann manifold methods: GDLNet (Wang et al. 2024bb and GyroAtt-Gr (Wang et al. 2025): Symmetric Positive Definite (SPD) manifold methods: TSMNet (Kobler et al. 2022). MAtt (Pan et al. 2022b), and CSPNet (Ju & Guan, 2022); well Symmetric Positive Semi-Definite (SPSD) manifold methods: GyroAtt-SPSD Wang et al. 2025). The results, summarized in Tab. indicate that our proposed HRRGGNet delivers competitive performance.

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Published as a conference paper at ICLR 2026
Table 4: Ablation results. Grand average of all lest-sets scores (balanced accuracy (%), higher is better) relative to the combination of alignment in HEEGNet. Permutation-panl paireed t-test values and adjusted p-values indicate the effect strength (le4 permutations, tests, t-max correction).
Alignment
Metries
Moments
Distribution
Input
mean (std)
t-val (p-val)
/
x
(18.6)
3.6 (0.0003)
X
/
(15.6)
8.8 (0.0001)
X
X
(19.3)
5.5 (0.0001)
X
V
X
-12.3 (23.1)
10.4 (0.0001)
X
X
X
(22.4)
11.7 (0.0001)
X
V
V
-15.5
14.9 (0.0001)
X
-15.5 (22.2)
16.0 (0.0001)
Table 5: Motor imagery per dataset results. Average of test-set scores (balanced accuracy (%);
higher is better; mean + std).
Dataset
Manifold
Model
SFUDA
BNC12014001
BNC12015001
ATCNet
w/o
42.7 1: 16.4
60.2 1: 8.4
EEGConformer
w/o
42.6 + 16.7
60.1 + 10.7
EEGNet
w/o
43.6 + 16.7
61.3 8.8
Euclidean
EA
49.9 + 16.9
72.5 - 14.2
STMA
49.7 + 16.9
14.6
EEGInceptionMI
w/o
39.7 + 12.7
59.5 9.2
ShallowNet
w/o
42.2 1 16.2
$8.7 5.8
LaBraM
w/o
33.3 + 16.6
70.8 + 31.4
CBraMod
w/o
30.6 + 4.0
59.1 + 8.1
GDLNet
w/o
46.3 +
63.3 14.2
Grassmann
GyroAtt-Gr w/o
52.1 1: 14.2
75.3 13.7
SPSD
GyMAnt-PPSD w/o
51.7 + 13.1
74.9 + 12.6
MAtt
w/o
45.3 +: 11.3
63.1 + 10.1
CSPNet
w/o
45.2
64.2 + 13.4
TSMNet
w/o
43,0 +: 13.3
61.7 1: 11.4
SPD
EA
51.2 + 15.1
72.5 + 13.6
STMA
52.5 + 16.4
70.1 14.2
SPDDSBN
54.6 + 16.1
74.3 14.7
Hyperbolic
HEEGNet
DSMDBN+EA
54.1 + 15.9
75.8 + 13.0
DISCUSSIONS
In this work, introduced HEEGNet, hybrid hyperbolic network architecture designed cap- ture the hierarchical structure EEG data and learn domain-invarian hyperbolic embeddings. Our pilot study and empirical analyses indicate that EEG data exhibits hyperbolicity and that hyperbolic embeddings improve generalization compared to Euclidean ones. By integrating both Euclidean and hyperbolic encoders and employing novel two-stage domain adaptation strategy (DSMDBN), HEEGNet effectively aligns domain-specifee moments and distributions in hyperbolic space. Ex- tensive experiments demonstrate state-of-the-arr performance. Despite these strengths, like all hy- perbolic neural networks, hyperbolic operations add additional computational cost. Future work will explore online extensions of hyperbolic normalization and the development more expressive encoders capable of capturing hierarchical structure in EEG signals.
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6 ACKNOWLEDGMENTS
This project was supported by the JSPS Bilateral Program under Grant Number JPISBP120254400.
Motoaki Kawanabe was partially supported by the Innovative Science and Technology Initiative for Security Grant Number JPJ004596, ATLA, Japan.

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Published as a conference paper at ICLR 2026
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APPENDIX CONTENTS
Large language model usage statement
19
Gyrovector spaces
19
B. General definition
19
Lorentz operations
20
Riemannian operators
20
Gyrovector operators
20
Lorentz non-linear activation
21
Lorentz concalenation
C.5
Lorentz fully-connected layer
21
C.6
Lorentz convolutional layer
Lorentz multinomial logistic regression
22
C.8
ò-hyperbolicity
22
D HEEGNet details
23
Algorithm
23
D
Model architecture
24
Software and hardware
24
D.4
Computational Cost
25
Full experiments
26
Dataset details
26
Visually evoked potentials
27
E.3
Emotion recognition
28
Intracranial EEG results
29
Fully hyperbolic neural network experiment
30
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A LARGE LANGUAGE MODEL USAGE STATEMENT
Large language models were partially used in this article to refine the contents.
B GYROVECTOR SPACES
B.1 GENERAL DEFINITION
This subsection briefly reviews the gyrovector space (Ungar 2022), which generalizes the vector structure into manifolds. It has shown great success in building hyperbolic neural networks (Ganea
al. 2018 Chami et al., 2019: Shimizu al. 2021).
We start from the gyrogroup. Intuitively, gyrogroups are natural generalizations of groups. Unlike groups, gyrogroups are non-associative but have gyroassociativity characterized by gyrations.
Definition B.1 (Gyrogroups (Ungar 2022)). Given nonempty G with binary operation @ GxG + G, (G, @ forms gyrogroup if its binary operation satisfies the following axioms for any
P.q,2 G:
(GI) There is at least one element E G called a left identity (or neutral element) such that e:pp = p.
(G2) There is an element Op G called a left inverse of p such that Ep 4 p c.
(G3) There is an automorphism gyr(p, g] : G G for each p,q E G such that
p + (g + 2) (p @ q) @ gyrlp, q]z (Left Gyroassociative Law).
The automorphism gyr(p: q] is called the gyroautomorphism, or the gyration of G generated by p; q.
(G4) Left reduction law: gyr(p, o] = gyr(p @ g).
Definition B.2 (Gyrocommutative Gyrogroups (Ungar 2022 A gyrogroup (G, (b) is gyrocom- mutative if it satisfies
+ q gyrlp, (1 p) (Gyrocommutative Law).
Similarly, the gyrovector space generalizes the vector space,
Definition B.3 (Gyrovector Spaces (Ungar) 2022: Chen et al. 2025b)) A gyrocommutative gy-
rogroup (G, @) equipped with scalar gyromultiplication @ R X G + G is called gyrovector
space it satisfies the following axioms for s, f & and p. 2 G:
(V1) Identity Scalar Multiplication: 1 1pp=p
(V2) Scalar Distributive Law: pp==)pppppppt0
(V3) Scalar Associative Law: (st) s (t@p).
(V4) Gyroautomorphism: gyr(p, 4 8 z) = gyrlp. g)
(V5) Identity Gyroautomorphism: gyr(s @ @ p) = I, where is the identity map.
The vector space, equipped with addition and scalar multiplication, forms the foundation of Eu- clidean deep learning. Similarly, the gyrovector space, endowed with gyroaddition and scalar gyro- multiplication, offers a powerful tool for designing neural networks over non an-Euulidean manifolds.
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C LORENTZ OPERATIONS
C.1 RIEMANNTAN OPERATORS
The exponential map Exp, K points between the manifold pj L and the tangent space vs E TyL at point p E k.
TyL - Li and logarithmic map Log, k
TpL + L project
K (v) = cosh(a)p + sinh(a) Exp,
with a= ==v-K lolle,
||ollc= = v v)
(10)
a'
cosh (3)
Logp (q)
(g - Bp), with 3 K(p,))
(11)
82
To transport points i E T from the tangent space at to the tangent space at g, parallel transport (Tp-+q()) Li can be used:
K(g,0) (p+ g)
PT (T)p=g(U)=0 =
(12)
1 K(p, g)K
C.2 GYROVECTOR OPERATORS
The definitions in Eqs. 3 and are direct generalizations of Euclidean vector operations. In Euclidean space, vector addition and scalar multiplication can be understood geometrically oper- ations rays emanating from the origin.
Let us first review Euclidean geometry. For R", we have
TB T₂R R
(13)
Log, (q) =
(14)
Exp,(v) = 0
(15)
PT (v) =
(16)
where q E R= and v E TR
To compute the Euclidean vector addition p q. one may regard q as the ray from 0 g. parallel
translate this ray to the base point and then shoot it out from The above process can be expressed
as
q (xP (4)))
(17)
Similarly, Euclidean scalar multiplication corresponds taking the ray from 0 to p. scaling its length by t, and then shooting it out from the origin again:
② Exp, Loga = tp.
(18)
The Lorentz gyroaddition and gyromultiplication extend this geometric intuition of Euclidean linear operations to curved manifolds.
Expressions. Let p = [pt, Pa] and = 14. qel points L where Pes 9: E R are the time scalars, and Ps, 4s E R are the spatial parts. Let t IR be real scalar. The following reviews the closed-form expression of the Lorentz gyro operators, which are more efficient than the Riemannian definitions Eqs. 3 and (4) (Chen al. 2025b Sec. 6.1). The Lorentz gyroaddition
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and gyromultiplicttoon have the closed-form solution:
0,
4,
p 0,
Gyroaddition:
p pox
(19)
R
D + KN
Others.
2(A.P. Agqs)
D + KN
0,
== V 00
Gyromultiplication: t 18K11
cosh toosh (V
(20)
t
ViKi
sinh rossh (1// ((/1kpp)))
PPall
where A, = abb - -2Kbspq - Kan, and Ag = b(a² + Knp)) with the following:
a = + v K Pt,
b b 1 + v /Kl. np Ilp-1?? ny = 1|qal?? 8py (p.. 9x),
D = a²b² 2K abssp b + K K2nppgg
N = a aang + 2abspg + b2
C.3 LORENTZ NON-LINEAR ACTIVATION
The Lorentz ELU activation applies the activation function to the space components and concate- nates them with the time component:
VIELU(p.) 1| 1/K
Cactivated
(21)
ELU(p,)
C.4 LORENTZ CONCATENATION
Given set of hyperbolic points {p: 1 the Lorentz direct concatenation is defined as:
N
N
= HCatC (p)))))>
Pit K
+
1st
T N
(22)
1=1
where y E L C 11
C.5 LORENTZ BULLYILLLLLLYYCCCNCC LAYER
Let p E LK denote the input vector and W e 1 U Ra+1 the weight parameters, the Lorentz fully-connected layer (LFC) is defined as:
Vlo + 2 1/K (WWp+ b)
y = I=FC(p)
(23)
Ww(p) + b (w)p)) bbl
/i WWP. r) >o p b')
(24)
where À > 0 denotes a trainable scaling factor, b E R is the bias vector, and ai and a represent the activation and sigmoid functions, respectively.
C.6 LORENTZ CONVOLUTIONAL LAYER
Th.w=i an ordered set of n-dimensional hyperbolic feature vectors, the features within the receptive field of the kernel K E R W are
Given a hyperbolic input feature map = {PA... E CL H.W
(Pw+6og, w'+6, E L A.W L h, where (h', w') denotes the starting position and 8 is the stride param- fr,
eter. The Lorentz convolutional layer is defined (FCAAT
w4+8, T. ] ( .)),
where HCAT and LFC, denote hyperbolic concatenation and a Lorentz fully- fully-connected layer per- forming the affine transformation and parameterizing the kernel and bias.
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C.7 LORENTZ MULTINOMIAL LOGISTIC REGRESSION
Similar to the Euclidean MLR, the Lorentz MLR performs classification by measuring distances to decision hyperplanes. The output logit for class es computed from the hyperbolic distance between and its corresponding hyperplane. For a hyperbolic input point p E L and C possible classes, each class {L..... C} is associated with decision hyperplane parameterized by de E and
Ze E R".
a (p) V-K K
(agg((aa))) sinh
(v-K
K
0ze 3e
(25)
where
0g = cosh Coosh(v-Ka,ne ka.) sinh(v (r)) l
Bc v coshh( (sinh(ss
(ae) (innoiii--- || 10.)
C.8 Ó-HYPERBOLICITY
Khrulkov et al. (220)) introduced 5-hyperbolicity measure of the degree of tree-like structure inherent in embeddings. The idea is to find the smallest value of 8 for which the triangle inequality holds via the Gromov product. In this formulation, the definition of hyperbolic space in terms of the Gromov product can be seen as the metric relations between any four points are the same as they would be in tree, up additive constant 8. Formally, given the Lorentz model L with distance de, the Gromov product of E LL with respect to E k as:
(p. 9)= 2 (dc(p,)) 2) dc(g, 2) dc(p. 9))
(26)
The Lorentz model is said be 5-hyperbolic for some if it satisfies the four- four-point condition, which states that for any p, 4, 2, E Li::
(p. 2 min 2) (4, 3) - 5.
(27)
The metric relations between any four points are the same as they would tree, up to the additive constant 5. The lower 5 2 0 is, the higher the hyperbolicity of the embedding.
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D HEEGNET DETAILS
D.1 ALGORITHM
Algorithm Hyperbolic domain-specifie momentum batch normalization (HDSMBBN
Input:
batch B (pr d(i) E PB, training step d(i) indicates the associated domain d
domain-specific running mean / (1g () and variance h-1 ( 1) for training
domain-specific rumning mean / (A6 0) and variancei &-1 (52 1) for testing
momentum for training and testing [t)ain(k)+ Teest E [0, learnable parameter vg
Output: normalized batch {p.} = HBN (p,) if' training then then
Compute domain-specifer batch mean 1g and variance 22d
D using Eq. ()
gg wFM WFM (1%-11 (2))
b update running mean using Eq. (2
22d (1 Derain(k)) 02d k-1 + ()r 2d
i WFMppa (1 1- 11)
> update running mean using Eq.
02d (1 Mest 02d
k- + Mestt v²t
end if
(pL vad
k) f (ith 12dd if training else (n 222)
v/
Pi Vuagtc ( mg @ pi)
Eq. 7 recentering and rescale each domain
Algorithm 2 Horospherical Hyperbolic Sliced- Wasserstein loss (HHSW)
Input:
batch = {p+ E Lix d(i) M1 d(i) indicates the associated domain d number of slices S = 1000, exponent p =
Output: scalar loss Lowd Initialize Luwd <-
for each domain E Da, do
Extract domain-specific samples pd {ps d(i)= - d} Sample Gaussian noise 2d ~ N((0 I) with shape shape(Pd)
Normalize: Zd + 12a
2d
Map hyperbolic manifold: Qd + expL (Zd) Compute domain loss: ed &- HHSW" (P', QQO))
b Eq. (
Lowd Lywd fd
end for
return Lowd
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D.2
MODEL ARCHITECTURE
Table 6: HEEGNet architecture details. P: electrodes; T:: temporal samples; C: classes.
Layer
Output (dim)
Parameter (dim)
Operation
Space
Input: 1 x P
TempConv
8 P T
8 X x 64
convolution batch norm depthwise conv batch norm
Euclidean
BN
8 P X T 16 1
8
Euclidean
SpatConv
16 8 x xx1
Euclidean
BN
16 1 T 1 T
16
Euclidean
Activation
ELU pooling
Euclidean
AvgPool
16 X 1 X [T/4
Euclidean
Dropout
16 1 [T/4
dropout=0:25
Euclidean
DepthConn
[T/4]
16 1 1
depthwise conv
Euclidean
ProjX
17 X [T/4]
projection
Euclidean
PointConv
17 X [T/4]
pointwise
Hyperbolic
DSMDBN (1)
17 X (T/4
DSMDBN
Hyperbolie
Activation
17 X [T/4]
ELU
Hyperbolic
AvgPool
[T/32]
pooling
Hyperbolic
Flatten
16 [T/32]
flatten
Hyperbolic
MLR
C
(16 [T/32] C
Hyperbolic
X RIXPXT
TempConv
BN
mp
9h
SpatConv
Exclidomn
BN
DSMDEN
Activation
AvgPool
Flatten
MLR
Activation
AvgPool
DepthConv
ProjX
Hyperbokic
PointConv
L%
Figure 3: HEEGNet architecture.
D.3 SOFTWARE AND HARDWARE
We used publicly available Python code for baseline methods and implemented custom methods us- ing the packages torch (Paszke et al. 2019), scikit-learn (Pedregosa et al.) 2011), geoopt (Kochurov ct al. 2020). We conducted all experiments on standard computation PCs with 32-core CPUs, 128 GB of RAM, and single GPU.
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D.4 COMPUTATIONAL COST
Hyperbolic neural networks remain in their early development stage and introduce additional com- putational cost, because of the need for exponential and logarithmic mappings. To evaluate the practical computational cost and the efficiency of our implementations, we compared the per-epoch runtimes of four models: the original EEGNet, HEEGNet without SFUDA, HEEGNet with mo- ments alignment (DSMDBN1). and HEEGNet with DSMDBN.
Table 7: Hyperbolic computational costs. Comparisons of the runtime (seconds) per epoch.
Model
SFUDA
Cost (seconds/epoch)
EEGNet
w/o
0,420
HEEGNet
1.157
HERGNet
DSMDBN,
1,320
HEEGNet
DSMDBN
1,451
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E FULL EXPERIMENTS
E. DATASET DETAILS
Nakanishi2015 an SSVEP dataset including EEG from subjects recorded with 8 channels at 256 Hz. Each subject performed 12-class joint frequency- -panee modulation paradigm with 15 trials per class, each trial lasting 4.15 seconds. The dataset consists of single session per subject and was originally designed to evaluate online BCI performance. This benchmark is widely used for 12-class SSVEP decoding.
Wang2016 is an SSVEP dataset including EEG from 34 subjects recorded with 64 channels at 250 Hz. Each subject performed 40-class visual stimulation paradigm, where 40 flickering targets were presented. The experiment comprised 6 blocks per subject, with 40 trials per block and 6 trials per class in total. Each trial lasted 6 seconds, and subjects were instructed to gaze at the cued target while avoiding blinks during stimulation. This dataset provides large-scale benchmark for 40-class SSVEP decoding.
CBVEP is VEP and burst-VEP dataset including EEG from 12 subjects recorded with 32 chan- nels at 500 Hz. Each subject performed a 4-class visual stimulation paradigm, with 15 trials per class and trial duration of 2.2 seconds. EEG was recorded using a BrainProduct LiveAmp 32 sys- tem with electrodes placed according to the 10-20 system, referenced to FCz and grounded at FPz. Participants focused on cued targets during each stimulation phase, and post-experiment subjective ratings of visual comfort, tiredness, and intrusiveness were also collected. This dataset provides benchmark for 4-class e- c-VEP decoding.
SEED is an emotion recognition dataset including EEG and eye movement data from 15 subjects, recorded with 62-channel system. Each subject performed a 3-class emotion elicitation task, where they watched 15 different film clips (approximately 4 minutes each) designed to evoke positive, neutral, or negative emotions. The experiment consisted of 15 trials, with each trial including a hint before the clip, 45 for self-assessment, and 15 s rest period afterward.
Faced is a fine-grained emotion recognition dataset including EEG from 123 subjects recorded with 32 channels at 250 Hz. Each subject performed 9-class emotion elicitation task, where they watched 28 video clips selected to evoke a range of emotions including amusement, inspiration, joy, tenderness, anger, fear, disgust, sadness, and neutral states. This dataset provides a large-scale, fine-grained, and balanced benchmark for 9-class emotion recognition from EEG signals.
Boran is an intracranial EEG (iEEG) dataset including recordings from 9 patients with drug- resggsesttttnt focal epilepsy. The dataset contains simultaneous recordings from stereotactically implanted depth electrodes in the medial temporal lobe and from scalp EEG electrodes placed according to the 10-20 system. Macroelectrode iEEG was recorded at 4 kHz and microelectrode iEEG at 32 kHz, while scalp EEG was recorded at 256 Hz. Recordings were performed using ATLAS system for iEEG and a NicoletOne system for scalp EEG. The dataset provides high-resolution iEEG and single- neuron data from the human medial temporal lobe for studying epilepsy.
BNC12015001 (Faller et al. 2012) is a motor imagery dataset including EEG recordings from 12 subjects with 13 channels at 512 Hz. Each subject performed sustained right hand versus both feet motor imagery across 200 trials per class, resulting in total of 14,400 trials. The experiment comprised sessions, each with single run of 5-second trials. EEG was recorded from Laplacian derivations centered on C3, Cz, and C4 according to the international 10-20 system.
BNCI2014001 (Tangermann et al.) 2012) is motor imagery dataset containing EEG from subjects recorded with 22 channels at 250 Hz. The paradigm involves four motor imagery tasks: left hand, right hand, both feet, and tongue, with 144 trials per class per subject. Each subject completed two sessions different days, each comprising 6 runs of 48 4 second trials.
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E.2
VISUALLY EVOKED POTENTIALS
Table 8: VEP per dataset results. Average of test-set scores (balanced accuracy (%); higher is better; mean + std).
Dataset
Model
SFUDA
CBVEP100
CBVEP40
Nakanishi
Wang
ATCNet
w/o
1.8
25.2 3.7
56.3 20.6
32.8 + 13.1
EA
74.4 12.1
7.06
54.7 + 18.9
35.8 + 10.8
STMA
25.6 1.5
24.5 1.0
58.9 + 18.7
44.3 + 11.1
EEGConformer
w/o
25.0
23.1
29.4 10.2
31.9 11.0
EA
75.8 10.3
+
29.4 9.0
30.5 + 8.5
STMA
25.0 0.0
24.8 0.5
24.3 7.4
30.7 = 8.2
BEGNet w/o
24.9 1.9:000 0.9
25.7 - 4.9
57.2 19.8
37.4 1: 12.9
EA
11.2
77.4 8.2
56.0 16.5
39.7 + 9.5
STMA
2.9
24.1 1.1::.. 3.3
40.0 10.7
32.0 + 8.4
FBCNet
w/o
29.4 + 3,9
30.4 3.1
28.3 + 7.5
16.4 + 4.5
EA
75.8 1 10.4
74.3 1 10.1
27.7 7.4
16.2 + 3.0
STMA
25.0 + 0.5
24.2 2.4
27.9 7.3
17.8 + 3.4
ShallowNet
w/o
76.2 7.2
74.3 8.4
29.4
18.4 - 6.7
EA
66.7 1 14.8
64.9 1 13.7
27.6 7.2
16.7 1 4.4
STMA
54.7 8.3
52.5 + 6.4
28.6 + 8.3
19.8 + 4.3
TSLANet
w/o
30.4 12.5
41.8 19.4
16.1 4.3
18.4 + 6.2
EA
9.6
9.1
14.0 + 1.7
18.0 + 5.5
STMA
25.9 + 1.7
2.4
3.3
17.8 + 4.0
DDGCNN w/o
24.4 1.8
25.5 2.2
26.2 12.9
30.3 + 10.7
EA
72.2 : 11.1
70.8 11.4
54.7 21.2
= 12.2
BEGInception w/o
28.9 5.5
34.2 + 20.9
60.7 + 22.0
38.7 + 12.8
EA
79.9 + 8.8
75.5 11.1
61.5 19.0
41.8 + 9.6
SSVEPNet
w/o
26.0 + 3.8
28.1 1 4.4
70.8 20.5
55.1 + 16.0
EA
72.4 1 13.3
68.5 1. 10.9
68.9 1 20.2
53.9 1: 13.0
SSVEPFormer w/o
24.0 + 3.9
26.7 + 6.4
77.2 21.0
72.3 + 15.6
EA
72.2 8.4
72.1 7.0
77.0 19.8
72.6 + 12.6
LaBraM w/o
63.9 + 26.0
61.8 + 23.5
69.9 + 25.5
72.2 + 13.6
CBraMod
w/o
62.0 13.9
59.3 10.5
68.6 14.3
70.7 + 21.9
HERGNNet
DSMDBN DSMDBN+EA
95.8 + 6.2
92.6 + 22.1
79.8 + 20.8
69.3 + 15.5
83.8 + 9.5
79.0 + 10.2
81.9 18.7
73.5 + 11.4
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E.3 EMOTION RECOGNITION
Table 9: Emotion recognition per dataset results. Average of test-set scores (balanced accuracy (%); higher is better; mean std).
Dataset
Model
SFUDA
Faced
Seed
ATCNet
w/o
11.2 0.9
34.8 + 9.8
EA
57.5 15.0
44.6 + 13.1
STMA
59.3 15.5
48.4 +: 15.7
EEGConformer
w/o
85.4 14.3
77.5 21.7
EA
89.0 11.1
65.9 + 18.1
STMA
81.5 13.9
69.2 = 17.7
EEGNet
w/o
24.8 13.7
74.5 1: 19.8
EA
83.9 14.5
46.2 + 15.4
STMA
78.2 16.6
50.1 = 15.2
FBCNet
w/o
19.0 8.4
54.5 + 17.4
EA
42.1 = 12.7
76.3 1: 17.4
STMA
23.1 8.9
60.0 20.3
ShallowNet w/o
43.1 16.6
76.2 = 17.6
EA
80.3 16.7
75.6 1 15.2
STMA
64.6 = 17.2
63.3 + 15.5
TSLANet
wfo
33.3 11.8
41.8 + 13.8
EA
37.2 12.4
65.6 14.4
STMA
46.2 13.1
58.7 + 16.4
EMT
w/o
32.9 13.4
48.4 14.5
EA
38.6 11.4
42.8 = 16.1
TSception w/o
14.3 4.6
42.2 + 15.4
EA
84.3 = 13.3
55.0 + 18.0
CBraMod w/o
48.3 7.3
70.9 = 18.7
LaBraM w/o
52.4 11.6
73.5 + 17.6
HEEGNet
DSMDBN
84.1 14.7
79.4 + 20.8
DSMDBN+FA
89.7 11.2
78.7 + 12.4
28

---

Published as a conference paper at ICLR 2026
E.4
INTRACRANIAL EEG RESULTS
Table 10:
Intracranial EEG result. Average of test-set scores (balanced accuracy (%); higher is
better; mean + std).
Model
SFUDA
Intracranial
EEGNet
w/o
55.4 + 9.1
EA
59.1 11.2
STMA
51.2 + 5.9
EEGConformer
w/o
55.5 + 7.0
EA
61.7 +: 13.1
STMA
53.1 + 5.2
ATCNet
w/o
57.5 + 9.0
EA
57.1 9.0
STMA
54.2 4: 5.7
TSLANet
w/o
55.1 9.3
EA
54.9 10.4
STMA
54.1 6.2
SchirreeistrrNet w/o
56.9 7.7
65.0 10.2
STMA
53.9 5.5
FBCNet
w/o
61.1 + 10.6
EA
61.3 11.0
STMA
53.0 6.8
LaBraM
w/o
44.4 + 49.7
CBraMod
w/o
53.6 6.2
HEEGNet (proposed)
DSMDBN
58.4 1: 9.6
DSMDBN+EA
66.7 + 12.5
29

---

Published as a conference paper at ICLR 2026
F FULLY HYPERBOLIC NEURAL NETWORK EXPERIMENT
To investigate the necessity of the hybrid design in HEEGNet, we conducted experiments by replac-
ing Euclidean convolutional operations in EEGNet (Lawhern 2018) with hyperbolic variants as follows:
None (EEGNet): Original EEGNet
HMLR: Replaced the final MLR layer with hyperbolic MLR
Additionally replaced Block2 in EEGNet (the depht-wise convolution and the point-wise convolution)
HMLR + Block2:
Full Hyperbolic: Fully hyperbolic models
As shown in Tab. 11 the performance on the 4 representative datasets demonstrates degradation pattern as more Euclidean operations are replaced with hyperbolic variants. These result suggests that the Euclidean backbone is essential for effective downstream classification, supporting the tionale behind our hybrid architecture, which combines Euclidean encoders with hyperbolic neural networks.
Table 11: Fully hyperbolic neural network experiments. The averages of test-set scores are shown above using balanced accuracy (the score and the standard deviation are shown for each dataset). The number of domains in each dataset is indicated by n.
Visual
Emotion
Intracranial
Dataset
Nakanishi
Wang
Seed (n 45)
Boran (n = 37)
Model
(n
(n 34)
None (ERGNet)
57.2 + 19.8
37.4 12.9
74.5 19.8
55.4 + 9.1
HMLR
60.8 + 20.7
39.2 + 13.8
75.1 + 20.0
57.4 + 8.7
HMLR + Block2
53.4 + 17.5
32.5 + 11.9
76.9 22.1
55.5 7.3
Fully Hyperbolic
27.3 + 12.0
22.5 + 8.8
70.7 + 21.6
52.7 + 8.9
30


Reviews:
[{"review_id": "QGYy7zVXNg", "reviewer": "Reviewer_b7a4", "summary": "This paper proposes HEEGNet, a hybrid hyperbolic embedding network designed to improve cross-domain generalization in EEG-based emotion recognition tasks. By jointly leveraging Euclidean and hyperbolic geometries, the model aims to capture both local and hierarchical relations within EEG representations. The proposed framework is evaluated on the SEED dataset and demonstrates competitive or superior performance compared to state-of-the-art methods. The manuscript is generally well-structured and technically sound, addressing an important challenge in EEG domain adaptation. However, several conceptual and methodological aspects require clarification, particularly regarding the motivation and interpretation of the hybrid embedding design and the underlying assumptions about EEG data structure.", "questions": "1. Please clarify whether EEG, video, and natural language modalities share structural similarities that justify their representation in hyperbolic space. How do the manifold assumptions differ across these modalities?\n2. Could you elaborate on the motivation for integrating Euclidean and hyperbolic embeddings? What distinct geometric properties does each space capture in EEG data?\n3. The term “neural information” (Line 93, Page 2) is vague. Please specify the type of neural features it refers to—temporal, spectral, or spatial—and how they are encoded in your model.\n4. In the SEED dataset experiments, how are domains defined? Are sessions or subjects treated as distinct domains, and how is cross-domain generalization evaluated?\n5. It is recommended to visualize intermediate representations from both Euclidean and hyperbolic branches to more directly show their complementary effects and the benefits of the hyperbolic layer.\n6. In Fig. 2(d), samples of the same class form multiple clusters. Please explain this behavior—does it arise from subject variability, intra-class diversity, or properties of hyperbolic projection?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper tackles an important issue—cross-domain generalization in EEG signals—where conventional Euclidean-based networks often fail to model hierarchical dependencies or inter-domain variations effectively.\n2. The hybrid use of Euclidean and hyperbolic embeddings provides an interesting perspective, allowing the model to balance local feature encoding and hierarchical structural representation. This design is conceptually meaningful for EEG data, which may contain both flat temporal dynamics and hierarchical cognitive relations.\n3. Experiments on SEED show consistent improvements over relevant baselines, suggesting that hyperbolic modeling can indeed improve domain transfer and robustness in EEG-based emotion recognition.", "weaknesses": "1. The manuscript claims that EEG, video, and language modalities can all be represented in hyperbolic space, but does not provide sufficient theoretical or empirical justification for why EEG data, in particular, exhibits hierarchical or tree-like properties that make hyperbolic geometry appropriate.\n2. The rationale for combining Euclidean and hyperbolic representations is underdeveloped. It remains unclear what complementary features each space captures and how their joint use specifically benefits cross-domain transfer.\n3. Terms such as “neural information” lack precision, and the formulation of domain adaptation within the SEED dataset (e.g., session-wise vs. subject-wise domains) should be clarified. These ambiguities make it difficult to interpret the mechanism behind improved generalization.\n4. While t-SNE visualizations are provided, they reveal sub-clustering within the same class. The manuscript does not discuss why this occurs or whether it reflects subject-level variation, embedding instability, or meaningful substructure. Additional visualization or embedding analysis could better support the claimed advantages of hyperbolic modeling.", "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": "2fg2Hcx804", "reviewer": "Reviewer_VB3w", "summary": "The paper proposes a  hyperbolic architecture based on EEGNet for EEG‑based task with a novel domain‑shift alignment method in hyperbolic space.", "questions": "1. How is the curvature K selected?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 4, "contribution": 3, "strengths": "The two-step alignment strategy, DSMDBN, operates in hyperbolic space: it first aligns source and target domain distributions by matching their first and second moments using a hyperbolic BatchNorm module, and then further aligns the moment-normalized features to a standard hyperbolic Gaussian via the Horospherical Sliced-Wasserstein (HHSW) loss. This approach is well-motivated and offers a moderately novel contribution to the domain adaptation literature.", "weaknesses": "1. Hyperbolicity evidence may reflect model bias:\n\nThe observed hyperbolicity is derived from learned embeddings rather than the intrinsic geometry of the EEG signals. Therfore, the results may reflect model-induced structure rather than inherent data-level hyperbolic properties.\n\n2. Numerical stabilization not addressed:\n\nThe paper does not discuss numerical stabilization techniques essential for reliable hyperbolic training, such as gradient clipping, norm normalization, or overflow prevention during Lorentzian operations.\n\n3. Missing comparisons with recent foundation models\n\nThis work lacks comparison with recent high-impact foundation models such as BIOT (NeurIPS' 2023) [1], LaBraM (ICLR' 2024) [2], and CBraMod (ICLR' 2025) [3]. These models are widely cited, have open-source code and model weights provided, and achieve state-of-the-art results across EEG decoding tasks.\n\n\nRefs:\n\n[1] Yang, Chaoqi, M. Westover, and Jimeng Sun. \"Biot: Biosignal transformer for cross-data learning in the wild.\" Advances in Neural Information Processing Systems 36 (2023): 78240-78260.\n\n[2] Jiang, Weibang, Liming Zhao, and Bao-liang Lu. \"Large Brain Model for Learning Generic Representations with Tremendous EEG Data in BCI.\" The Twelfth International Conference on Learning Representations.\n\n[3 Wang, Jiquan, et al. \"CBraMod: A Criss-Cross Brain Foundation Model for EEG Decoding.\" The Thirteenth International Conference on Learning Representations.", "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": "8J9iSITZp7", "reviewer": "Reviewer_Qng1", "summary": "Overall this paper is working on a promising research direction of EEG-based BCIs/recognitions. \nHowever the paper needs to be significantly improved to better clarify both its contributions and performance comparisons.", "questions": "1. The authors should carefully clarify their novelty. \n2. The performance comparison part need to be significantly improved and justified.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The research direction of using hyperbolic embeddings for EEG-based BCIs/recognitions is emerging and promising. \n2. The proposed method is well explained. \n3. The performance improvements compared with EEGNet are significant.", "weaknesses": "1. The novelty is not well clarified; and the idea of exploring hyperbolic space /embeddings for EEG-based recognition is not new. The authors didn't clearly explain the difference. \n2. My main concern is about the performance comparison part. \n-- The proposed HEEGNet was not compared with other hyperbolic embeddings based methods, e.g., Jing Chang 2025 in the ref list and related refs/citations of that paper. \n-- For different tasks/datasets, it doesn't seem that the proposed methods were compared with SOTAs. Why only baselines were compared? The authors should compare their results with SOTA performances of the datasets, e.g., Seed, Faced. \nE.g., the results from comparison methods for VEP in table 3 are far away from SOTA performances reported in the literature. The gap between the proposed method and other methods is too good to believe. More clarification is needed.\n-- It is also not clear whether the methods are tested in the cross-dataset setting. E.g, for the Emotion recognition task, are the Seed and Faced datasets combined or tested separately? \n3. Minor comment: Abstract is a bit misleading. Reviewers would think this is the first work on exploring hyperbolic embeddings for EEG.", "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": "8eIJ9DNW47", "reviewer": "Reviewer_HQzc", "summary": "This work focuses on the hyperbolic representation of the EEG signal to enhance classification tasks. Based on the demonstration of EEG showing hyperbolicity to improve generalization, the authors propose HEEGNet to capture hierarchical structure in EEG and learn domain-invariant information. HEEGNet achieves superior results in various EEG classification tasks.", "questions": "1. Is the model only suitable for the EEGNet used in the paper, or also works for other methods like spatial-temporal convolution and some self-attention?\n2. How much computational cost is taken by the hyperbolic calculation?\n3. Is there a Discussion section for the work?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. The work leveraged hyperbolic geometry to represent EEG features, which gave technical novelty and a good basis for EEG classification tasks.\n2. Extensive evaluations have been performed to demonstrate the usability of the HEEGNet. Various SOTA methods were involved for comparison.\n3. The authors gave a clear description of the model and source code for reproduction.", "weaknesses": "1. The roadmap on why a hyperbolic manifold is necessary for EEG and further comparison with other methods is necessary to show the improvement of the current method.\n2. The overall performance of HEEGNet outperformed other methods. However, it's not clear which part of the model contributes more to the final results. \n3. Apart from the classification results, it's not clear if the hyperbolic embeddings could help us find brain patterns precisely. Further analysis would be beneficial.\n4. The motor imagery paradigm is an important paradigm to explore the significance of EEG geometry. It would be better to include the motor imagery comparison in the manuscript instead of the Appendix.\n5. Several datasets from different paradigms were included for comparison. It would be better to clarify the validation manner to help understand the use of the methods. Is HEEGNet also useful in the generalization cases, such as cross-subject classification?", "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)