CRRL: Learning Channel-invariant Neural Representations for High-performance Cross-day Decoding
Authors: Xianhan Tan
Binli Luo
Yu Qi
Yueming Wang
Venue: NeurIPS 2025 poster ()
Keywords: Neural Decoding
Primary area: neuroscience_and_cognitive_science

Abstract: Brain-computer interfaces have shown great potential in motor and speech rehabilitation, but still suffer from low performance stability across days, mostly due to the instabilities in neural signals. These instabilities, partially caused by neuron deaths and electrode shifts, leading to channel-level variabilities among different recording days. Previous studies mostly focused on aligning multi-day neural signals of onto a low-dimensional latent manifold to reduce the variabilities, while faced with difficulties when neural signals exhibit significant drift. Here, we propose to learn a channel-level invariant neural representation to address the variabilities in channels across days. It contains a channel-rearrangement module to learn stable representations against electrode shifts, and a channel reconstruction module to handle the missing neurons. The proposed method achieved the state-of-the-art performance with cross-day decoding tasks over two months, on multiple benchmark BCI datasets. The proposed approach showed good generalization ability that can be incorporated to different neural networks.

CRRL: Learning Channel-invariant Neural Representations for High-performance Cross-day Decoding
Xianhan Tan 1.2.3 Tan1 1, Binli Luo",, Yu Qil..3,; Yueming Wang'
MOE Frontier Science Center for Brain Science and Brain-machine Integration, Zhejiang University
Affiliated Mental Health Center & Hangzhou Seventh People's Hospital, Zhejiang University
College of Computer Science and Technology, Zhejiang University CCollege of Computer Science and Technology, Central South University
State Key Lab of Brain-Machine Intelligence, Zhejiang University
Abstract
Brain-computer interfaces have shown great potential motor and speech rehabili- tation, but still suffer from low performance stability across days, mostly due the instabilities in neural signals. These instabilities, partially caused by neuron deaths and electrode shifts, leading to channel-level variabilities among different recording days. Previous studies mostly focused on aligning multi-day neural sig- nals onto dow-dimesiional latent manifold to reduce the variabilities, while faced with difficulties when neural signals exhibit significant drift. Here, we propose to learn channel-leve invariant neural representation to address the variabilities in channels across days. It contains a channel-rearrangent representations against electrode shifts, and channel reconstruction module handle the missing neurons. The proposed method achieved the state-of-the-ar per- formance with cross-day decoding tasks over two months, on multiple benchmark BCI datasets. The proposed approach showed good generalization ability that can be incorporated different neural networks.
module to learn stable
1 Introduction
Brain-computer interfaces (BCIs) have paved a new way for motor and speech rehabilitation (Card)
al. 2024 Metzger al.) 2023 Qi et al. 2019). However, the long-term stability of BCIs remains critical problem due to the channel-wiss variability of neural signals. BCI systems commonly require
frequent recalibration in use, which hinders the user experience (Ajiboye et al. 2017).
The channel- -aine variability can stem from diverse reasons (Degenhart al.) 2020). First, the appearance of new neurons and the disappearance of existing neurons can happen across different experimental days (Figure 1a). These changes affect the distribution to inconsistencies in the input space used for decoding (Flesher et al.) 2021 [Sussillo et al., 2016). Second, the movement of neurons or electrodes can also drift the recorded neural signals each channel (Figure lb). The situations that cause channel-wise variability can be highly diverse, such that directly learning a channel-wise invariant neural representation can be a challenging problem.
the channel signal, leading
Existing studies addressed this problem from several aspects. The first group is the data alignment approaches, which aim to align the wiw-iimesioonll manifolds of neural signals of different days. Researchers have demonstrated that neural signals contain a consistent now-dimensional neural manifold over long periods of time (Gallego al. (017). Study (Degenhart al. 2020) tries to
"Corresponding author (qiyu@zju.cee zju.edu.cn)
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Channel-Wlse variability
Learning with CRRL
Channel-invariant represstatonnnnnnn
Day/
Neural represeration
eec7700 Charne
Module 1: Channel Rearrangement
Day
Day
M
The CRRL Framework
Day J
cm
Module 2: Channel Reconstruction
(0)
Figure 1: We plot two types of channel-wise variability in neural signals: (a) caused by new or lost neurons. (b) caused by drifted neurons. Our two-module CRRL framework can obtain the channel-invarian representations across days
directly align the manifolds' coordinate axes (the neural recording channels). However, it required that a subset of the channels should be stable across different days. Other studies based on domain adaptation (DA) approaches, which regard neural signals from different days as different domains and attempt to align the signals of these domains, including the ADAN (Farshchian et al. 2018) and Cycle-GAN (Ma et al. 2023) approaches. The second group attempts to improve the robustness of cross-day neural decoding by using more data. NDT2 YYe et al., 2024) and POYO (Azabou et al., 2024) used a large set of neural data for pretraining to capture the pattern of variation between sessions. These large-scale methods implicitly account for differences in neurons or channels, but require higher training costs. The key challenge is to achieve long-term stable BCI at low cost.
Inspired by variability patterns of the neural signal, we propose a Channel Rearrangement and Reconstruction Learning framework (CRRL). It contains two main modules: 1) channel rearrange- ment module to deal with situations such as new coming neurons explicitly and drifts in neural signals, and 2) a channel reconstruction module to handle situations such missing neurons. We found that the two operations can highly enhance the channel-level consistency across different days, facilitating a
neural representation and improving the neural decoding performance.
We evaluate the proposed method on both simulation datasets with diverse channel-wise variabilities and multiple neural signal datasets with motor, handwriting and speech decoding tasks. With the neural decoding tasks, we evaluate the neural decoding performance of our approach with long-term neural signals with time spans over two months. Experimental results demonstrate that our approach achieves stable decoding performance compared with existing studies, especially for a long period. Moreover, our approach can be incorporated with other methods plug-in module, to enhance the neural recording performance and robustness across days.
2 Method
The factors causing channel-wise variability be summarized into two categories: 1) new lost neurons, and 2) drifted neurons. CRRL uses two modules to handle these two cases separately.
Specifically, in the rearrangement module, we use the permutation matrix obtained by our permutation network to rearrange the signals of day k, and the training objective is to maximize the similarity between each channel on day k and day 0. In the reconstruction module, we employ channel-based Vector Quantized Variational Autoencoder (VQ- VAE) (Van Den Oord et al.) 2017) with randomly masked signals of day 0 to achieve the reconstruction of channel signals and frequency domain features. During the evaluation, we used the data of day k+n as input and obtained the output sequentially through the rearrangement and reconstruction network. Then, we use the output signal to perform downstream decoding tasks, where the decoder trained by the signals of day 0.
2.1 Rearrangement: Channel Permutation Network
Below, we first formulate the tasks of channel permutation and describe the structure of our permuta- tion network. Next, we describe the process of the Sinkhorn-Knop algorithm MMena et al. 2018) to

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Rearrangement: Permulation Network
Resningenntt
Roarrngged Spike (Diey kt
Massimamm Bimblantt
Evaluation Step
Spake Cle
Spiki (Dha
1009 Nest
Pormulaton
Natrook
Perm Permutatio Soton
Melis
S
Optimization Procedure
Soli
Chermel
Eichand
N. U
Time
Training Step
Tome
Rearrangemmen
Reconstruction: Channel-based
Ressneintte Spiie
aMoennsa MIN
Rearanned Splks
Masked Signol
(Day 0h
"Spito (Day
(Dark:1)
Spla
requeccy
Charral Enzoile
Charnel
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Permutation
Encodar
Iaay
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Channal2
D-19,
30ASS
Chamall
B.S1....
00.150
Chosnol.
Platien
Clumnol
Logis
Permi bation
Day
Matri
Matix
Downstream Tasks
Figure 2: The framework of CRRL. Top: we plot two-stage training process. Bottom: plot the network structure of our permutation network and channel encoder. Right: we plot the evaluation process of CRRL, which needs well-trained permutation network and channel-based VQ-VAE.
obtain differentiable approximations of permutation matrices. Finally, introduce our loss function for our rearrangement training.
2.1.1 Problem Formulation
Given neural signal data from i days D (Xo, X where X E NxCXT represents the data from day d, with N samples, C channels, and T time points, goal is to find permutation matrices [M,...,,,, Mą-1} that match each day's channels with those of day 0. The rearranged data is given by a batched matrix multiplication (BMM) over the time dimension:
X M Xdi
for 1,...,
(I)
2.1.2 Predicting Permutation Matrices by Neural Network
To parameterize the permutation matrices in differentiable manner, we employ a multi-layer percep- tron (MLP) fo with shared parameters 9 across all days. We chose the MLP for its flexibility across datasets with different channel counts and for its ability to model arbitrary channel dependencies. For each day d, we flatten the data along the channel and time dimensions to form the input the MLP:
Flatten (Xa) E Nx(CXT)
x
The MLP processes the flattened input and reshapes the output produce logits that represent the unnormalized log probabilities for the permutation matrix Ld:
La
fo(x"") La E NXCXC
2.1.3 Sinkhorn Algorithm for Doubly Stochastic Approximation
Permutation matrices are special cases of doubly stochastic matrices with binary entries. To obtain differentiable approximations of permutation matrices while enabling gradient- optimization, we adopt the Linkhorn-Knopp algorithm with continuous relaxation strategy (Mena et al. 20 8). This relaxation allows the model to learn permutation patterns probabilistic manner during training. while recovering exact permutations via discretization at inference.

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Continuous Relaxation via Gumbel-Sinkhorn To bridge the gap between discrete permutations and continuous optimization, we introduce a Gumbel noise perturbation into the logits La. following the Gumbel-Sinkhon framework (Jang et al. 2017a). The perturbed logits are defined as:
L La + 7e,
Gumbel(O, 1),
where 7 >> 0 controls the noise intensity. This perturbation encourages exploration during training while maintaining differentiabilityy And the proof about this differentiability detailed in Appendix.
The doubly stochastic matrix Ma is then computed by applying the Sinkhorn operator 8 to the perturbed logits:
L
M =
(5)
where > 0 is a temperature parameter. Lower sharpens the output distribution towards a permutation matrix, whereas higher results in softer distribution.
Sinkhorn Operator with Iterative Normalization The Sinkhorn operator S iteratively normalizes the input matrix to satisfy row and column stochasticity constraints. Starting from the exponentiated logits:
L
K (0)
exp
(6)
perform alternating row and column normalizations for Tsink iterations:
K K(-"" K (k(-1)1c)
10)
(Row norm),
(7)
K (1) K @ (Iokl²)
(Column norm),
(8)
where 2 denotes element-wise division, and le is vector of ones. After Tink iterations, we obtain M = K (Taa)
Discretization via Hungarian Algorithm at Inference
During training, Ma remains a continuous doubly stochastic matrix to preserve differentiability. At inference, we convert M,, to an exact permutation matrix a using the Hungarian algorithm Kuhn 1955):
2.1.4 Loss Functions For Rearrangement Training
To train the MLP to produce permutation matrices that effectively align the channels, we define loss function comprising the negative Pearson correlation loss and an entropy regularization term. Compared to MSE, the negative Pearson correlation loss focuses more on the shape and trend the signals rather than their absolute amplitudes.
Negative Pearson Correlation Loss
For each task E (1,..., and channel c E (1,...,C) C}. compute the average signal over all samples from day 0 belonging to task t:
Σ nEIa.
Xo,t.c
X0,
NO.1
where No.: is the number of samples from day belonging task Ia, is the index set of these samples, a0, is the signal for sample and channel from day 0 data.
Then, the negative Pearson correlation loss is defined as:
X'mnc
Kamner Ko.ya.
Xn.yaa.
Loon.
(10)
NC
X/nc
Xamn
Xo,ym.ell2

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where x,, is the signal for sample n and channel e from reordered day d data, Un is the task label of sample n. X0.y..e is the average signal over all day samples belonging to task Yn and channel c, Xd,n,e and ... are the mean over time of x,,n,e and eo respectively. The total correlation loss is then:
R-1
Loom
Loan.
(11)
Entropy Regularization To encourage the approximation matrices M, to be close to true permuta- tion matrices, we add an entropy regularization term:
Lentropy d
Ma log Ma,a.i.
(12)
N
The total entropy regularization loss is:
C
entropy
Centopy. d-
(13)
Total Loss for Stage One The overall loss function for stage one is:
Ssageet = Lover + Acatropy ceatropy
(14)
The two components of the loss function guarantee that the rearranged signal on day k closely resembles that day 0 while also optimizing the approximation of the permutation matrix. After training, the parameters of the permutation network are fixed for the subsequent training evaluation phase.
2.2
Reconstruction: Channel-based VQ-VAE
Firstly, we formulate the tasks of channel reconstruction. Then, we describe the architecture of our channel-based VQ-VAE VQ-VA VQ-VAE discretizes the continuous latent space using vector quantization, creating discrete codebook which is suitable for data with discrete characteristics, such as spike signals. Discrete encoding enhances robustness input noise and effectively handles random disturbances in spike signals. Next, we introduce the loss function of our reconstruction training.
2.2.1 Problem Formulation
Given neural signal data from day 0 and the rearranged data from day which are mixed together as Xmiz in ratio of 7:3. Our goal is to reconstruct missing or corrupted segments in the neural signals. During training, we simulate such conditions by randomly masking signal segment from one the channels in each sample. Specifically, for each sample n, we randomly select channel cn and time interval [tisum tinna, and set:
&mis,, [Mistan
[iend] 0,
(15)
where Xmin,,,e, the masked signal for sample n and channel Oy.
2.2.2 VQ-VAE Architecture
The architecture of the VQ-VAE is illustrated in Figure 2. It consists of an encoder that independently embeds the raw time series from different channels as tokens, a cross-channel attention module that captures inter-channel dependencies, and decoder comprising MLP network that reconstructs the signals. The VQ-VAR also includes vector quantization layer for discretizing the latent representations.
5

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Channel Encoder The encoder Es processes the masked signals to produce latent representations.
For each sample n, channel and time Ti, the raw signal Xmix,, IR''s embedded using a fully connected layer to produce token representation:
Cn Embed Embed(Xmiiz W Miizn + be RR,,
(16)
where W. Rd.XT and b. I learnable parameters, and de is the embedding dimension.
The embeddings from all channels are input into a cross-channel attention mechanism to cap- ture dependencies among channels. We stack the embeddings for each sample to form E, [en, en,2; ...,);...:ee........... en,c) E RCx..
We apply a self-attention mechanism
Vaswani 2017):
Hn MultiHcaaAAteantionnEE....
(17)
where H,, E Cxde contains the attention representations for each channel.
Fach attention representation b RR is passed through a multi-layer perceptron to obtain the latent representation:
Zn ReLU (hn.c W1 b1) W2 + b2 Rd.
(18)
where W1 E Rdexde Xde We E Rdaxd, and b1, b are biases.
Vector Quantization Layer We use codebook C = {ex ]
(e where each codeword eş E IR4.
Each latent vector on quantized by finding the nearest codeword:
On Ck where ks arg min Inn,c
exl12-
(19)
MLP Decoder of multi-layer perceptron:
The decoder De reconstructs the signals from the quantized embeddings. It consists
Rn, Wa ba E RT
(20)
where Wa Txd and ba RTT are learnable parameters.
2.2.3 Loss Function For Reconstruction Training
We train the VQ- by minimizing a loss function, including reconstruction and commitment losses. We reconstruct signals in both the time domain and the frequency domain simultancously to improve the stability of the reconstruction.
Time Domain Reconstruction Loss We compute the mean squared error (MSE) between the reconstructed signals and the original signals for the masked entries mn.e:
Limme
Σ mn,o ||, xn,e
(21)
En,e Mn.c.
Frequency Domain Reconstruction Loss features (amplitude A(-) and phase (b.)) via Discrete Fourier Transform (DFT)):
We also compute the MSE in the frequency domain
L
Σ mn.e A(*,..) - A A(xx,))) |12
(22)
Σ Mn.c n.c
Ls = Σ mn,c n.c
Σ
@(xn,c)) l|z
(23)
Liro LA + Ls
(24)

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We evaluate our method for experiments on simulation and real neural datasets. For the simulation lost neurons Vector Quantization Commitment Loss be close to the codewords:
The commitment loss encourages the encoder outputs to
0vg
Σ
[|sg[Zn.c] q0,ell2 11/2 + I| sg(qm.)]1
(25)
NC
where sg[:] denotes the stop-gradient operator, and /8 is the commitment cost weight.
Total Loss The total loss function is:
Latage2
Liime + Cirey XvaFry:
(26)
where Arro and Xng are hyperparameters.
Figure 2 illustrates the conceptual CRRL training and evaluation processes. Algorithms and specify the two stages of CRRL training in detail. In the rearrangement training, the first step is to predict the permutation matrices. Then, CRRL rearranges the spike channels and obtains the rearranged spike. In the reconstruction training. feature. During optimization, our approach learns to robustly restore the information of the day signal. For evaluation, we can obtain the reconstructed data by well-trained CRRL. The obtained data can decode downstream tasks by a decoder trained on day O.
predict the masked signal and its frequency
Experiments
3.1 Setup
dataset, we simulate two channel-wise variability in the simulation dataset: 1) and 2) drifted neurons. For 1), we delete/add part the input channels. For 2), we randomly shuffle the input channels. Additionally, of different ratios on performance. To simulate the plasticity of neurons, we also replace part of the neurons with
set different change ratios (5 % 10 %) to compare the impact
reserved neurons that have different tuning curves. For real datasets, human datasets and five monkey datasets. The human datasets include a handwriting dataset (Willen al. 202T) and speech dataset (Willett al. 2023). And the monkey datasets (Dyer al. 2017) comprise two Center-out task datasets ((C) and (M)), two isometric wrist task datasets ((J and (S)), and key grasping task dataset (G).
two
To evaluate and compare the performance of models in different periods, we divided all the datasets into five different time intervals according the number of days from day O. The dataset and split details are described in Appendix A.
We compared our method with five cross day decoding methods used in BCI. 1) manifold-based method Stabilizedbei (Degenhart et al. 2020): 2) Another manifold-bases method NoMAD (Karpowicz et al., 2022); 3) A domain adaptation method SD-Net (Fang al. (202)); 4) An adversarial domain adaptation method ADAN (Farshchian et al. 2018); Another adversarial
Baseline Methods.
domain adaptation method Cycle-GAN (Ma et al. 2023). The detailed
settings of
these methods are described in Appendix B.
We used SVM to perform classification tasks for decoding in downstream tasks (Qi et al. and Wiener Filter (Chen al. 2006) to perform regression tasks.
2022
2025
3.2 Results on Simulation Dataset
We evaluate CRRL under three simulated neural instabilities (Table 1, 11). We ablate either the Rearrangement Module (RA) Reconstruction Module (RC) to analyze module contributions. Here, we use Coefficient of Determination (R²) and accuracy (acc) to evaluate the performance of regression and classification on the simulation dataset, respectively.
Table reported that using two modules together gives the best performance all scenarios. For the scenario of new/lost neurons, without RC (w/o RC) degrades performance significantly (0.92/99.5% to
7

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Table 1: Ablation study on simulation dataset.
R² /ecc
w/o RA
w/o RC
RA RC
New/lost neuron (5
0.83/99.1
0.72/92.7
0.92/99.5
New/lost neuron (10 %)
0.81/96.1
0.69/89.3
0.87/99.3
Shuffled channel (5 %)
0.15/55. 1
0.85/92.1
0.89/98.0
Shuffled channel (10 %6)
0.05/48.3
0.77/88.5
0.86/98.2
Changed function (5 %))
0.66/80.8
0.45/64.7
0.73/91.4
Table The performance of regression and classification prediction which compares with different cross-day decoding methods.
I²' /ace
Model
Task
Number of days since day
[5, 10)
[10, 20)
[40, 65)
[65, 100)
Stabilizedhei
0.59/56.6
0.52/50.7
0.45/44.8
+/-
Center-Out (C)
SD>Net
Trajectory/ Direction
0.73/69..
0.65/62.5
0.622/6..
+
0.84/86.5
NoMAD
0.58/50.6
0,41/37.9
CRRL (Ours)
0.75/77.1
0.68/70.5
0.65/66.8
-
Stabilizebbei
+
0.38/516
0.34/43.7
-
Conter-Out (M)
SD-Net
Trajectory/ Direction
-/-
0.45/62.0
0.39/52.0
-
0.68/73.1
NoMAD
+/-
0.33/39.5
0.26/29.7
-
-/-
CRRL (Ours)
-/-
0.51/63.5
0.45/57.4
-/-
Subilizedbci
0.38/57.4
0.32/53.1
0.23735.0
0.203365
0.17/29.
ISO (J)
SD>Nett
Trajectory/ Direction
0.73/22.5
0.42/65.2 2
0.35/58.6
0.28/44.2
0.25/43.8
0.20/34.5
NoMAD
0.44/65.2
0.45/62.4
0,37/40,8
0
0,31/39.7
CRRL (Ours)
0.51/66.3
0,48/61.5
0.43/62.2
0.46448.6
0.47/51.1
Stabilizedhei
0.33/4833
0.35/47.2
0.24/40.9
0.18/25.0
<0/148
(8)
Trajectory/ Direction
0.75/94.4
0.40/5655
0.37/53.7
0,36/53,7
0.32/45.6
0,24/35.9
NoMAD
0,34/53.3
0.40/51.2
0.38/45.0
0.37/44.1
0.29/31.3
CRRL (Ours)
0.43/57.2
0.39/56.6
0.35/54.5
0.37/54.1
0.30/45.2
ADAN
0.66
0.60
0.56
0.54
ISO (J)
Cycle-GAN
EMG
0.71
0.68
0.65
0.63
0.59
0.50
CRRL (Ours)
0.70
0.66
0.69
0.65
ADAN
0.26
0.21
0.18
<0
Key (G)
Cycle-GAN
0,46
0.27
0.25
0.20
0.09
CRRL (Ours)
EMG
0.41
0.35
0.32
0.72/92.7%). indicating RC's critical role in compensating for neuron loss. For the scenario of drifted neurons, w/o RA gives the worst performance, and w/o RC achieves the second-best performance, suggesting RA is vital for handling neuron drifting. When tuning function changes, RA+RC achieves 91.4% accuracy with 26.7% relative improvement over the w/o RC. RC contributes more to It2 and (0. (0.66% compared 0.45/64.7%) implying it effectively adapts latent representational shifts.
3.3 Results on Speech and Handwriting Decoding
We compare our method with SD-Net and NoMAD on speech and handwriting datasets. The decoding target of the speech dataset 7 words with "do nothing" condition, where the evaluation metric. Similarly, the decoding target of the handwriting dataset is 31 characters, and we also use acc the metric.
as
Figure 3 shows CRRL's improvements in cross-day decoding performance with SD-Net and NoMAD. For the speech dataset, CRRL shows consistent performance different days. Notably, CRRL achieves accuracy recovery to 86% on day 21 while accuracies of SD-Net and NoMAD decline to 62% and 42% respectively. Moreover, the performance advantage of CRRL is more obvious when the time span longer.
For the handwriting dataset, Our CRRL framework maintains superior long-term performance, outperforming existing methods significantly (the pairwise statistical tests are described in Appendix B). CRRL shows stability with 67% accuracy at Day 16 (vs SD-Net's 57% and NoMAD's 32%).

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Speech Dataset
Handwriting Dataset
Dacoder trained on day
0.9
Rcsurag
0.5
Acturacy
0.7
0.6
0.1
0.4
16
43
Day
0
Day after Day-O
Test day
Test day k (wlo CRRL) Test day (CRRL)
CRRL
SD.Net
NoMAD
SD-Nel
Figure (Left)) we compare our CRRL with two baseline methods (SD-Net and NoMAD) on speech and handwriting datasets. We evaluate the performance using the classifier trained on day 0 data. (Right) we use CRRL to decode the hand trajectory across days. First, we use the regressor trained with the data from day 0 to evaluate the performance. In the middle figure, this regressor completely loses its decoding ability on day k data. However, through CRRL, the regressor recovers its performance, which is close the performance day 0 data.
Table 3: Ablation Study on Real Neural Datasets.
Component
Center-Our (C)
I50
Key (G)
RA
RC
[5. 10)
[10. 20)
[20. 40)
[5, 10)
[10, 20)
[20, 40)
[5. 10)
[10, 20)
[20. 40)
CRRL
V
0.73/68.1
0.61/64.6
0.57/63.5
0.44/57.7
0.41/48.3
0.41/52.5
0.35
0.31
0.32
CRRI.
0.7366.4
0.64/57.6
0.52/51.2
0.47/62.2
0,36/53.0
0.32/49.3
0.26
CRRL
0.75/77.1
0.68/70.5
0.65/66.8
0.51/66.3
0.48/61.5
0.43/62.2
0.41
0.37
0.35
3.4
Results on Motor Decoding
We compare CRRL with Stabilizeebbc,, SD-Net, and NoMAD on five monkey neural datasets, which include diverse motor decoding tasks. The total number of sessions (which equal to the total number of days) used for each dataset. For hand trajectory and electromyography (EMG) decoding, we use I?2 as an evaluation metric. For the eight-direction classification, we use accuracy as metric.
Table 2,8 shows that CRRL achieves consistent superiority in both trajectory regression (R²) and direction classification (acc) tasks, particularly under challenging long-term decoding scenarios. For the Center-Out datasets (C and M), CRRL maintains stable performance as days progress. On the Center- Out (C), CRRL achieves Ra/acc of 0.75/77.1% for days [5, 10), surpassing SD- Notably, even after 40-40 days, CRRL retains 0.65/66.8, exhibiting only a 12.8% drop in R² compared to SD-Net's 15.1% decline. On the ISO (J) dataset, CRRL achieves 0.47/51.1 1 % /acacc at [65, 100) days, outperforming NoMAD (0.31/39.7%) and SD-Net (0.20/34.5%) For the challenging Key (G) dataset, CRRL maintains 0.35 R2 [20, 40) days, 94% improvement over Cycle-GAN (0.20).
Net (0.73/69.39) .3%) and Stabilizedbei
3.5 Ablation Study
We conduct ablation study experiments on Center- (C), ISO (J) and Key (G) datasets to investigate the effectiveness of two modules of CRRL (shown Table 3). The decoding target of ISO (J) is hand trajectory. On the Center-Out (C) dataset, RA RC achieves 0.75 R. in (5,10) days, which is 2.7% higher than RA-alone (0.73) and RC-alone (0.73). This advantage of performance grew over time, delivering 12.3% accuracy improvement (66.8% 63.5% at (20,40) days. Results on the ISO (J) dataset demonstrate that RA + RC achieves classification accuracy of 62.2% at (20,40) days, outperforming individual components by 18.7% 7% (RC) and 18.4% (RA). Notably, RC proves particularly crucial for Key (G) EMG decoding, where RA achieves 0.38 accuracy at (5,10) days vs RA's 0.35. However, RA + RC yields 7.9% additional gain (0.41).
3.6 Comparison with Large-Scale Models
The goal of our method is to achieve long-term stable BCI decoding using a small amount of data for training. As shown in Table 4, CRRL w/o PT, which only uses 5 days of data for training, achieves performance close large-scale methods such as POYO-1 (Azabou al. 2024h and NDT2 Multi (Ye et al. 2024).

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Tablo Comparison with large-scale models including POYO-1 and
NDT2 Multi. PT is the pretruin model and FSS the few shot setting,
Table 5: Plugin-in experiment.
Method
Monkey C
MI-A
M2
R
Day 7
Day 30
Day 56
POYO-1 + Full finetune
0.9683 = 0.01
ADAN
0.36
0.18 0.05
<0
NDT2 Multi FSS
0.59 = 0.07
0.43 # 0.08
CycleGGAN
0.07
0.20 0.03
CRRL FT
0 0.03
0.13
0.31 0.07
RÁ + ADAN
0.29=
0.03
0.14
CRRL PT Full finetune
0.9750 = 0.02
0,63 0.08
0.55 a 0.13
RA + Cycle-GAN
0.33
0.27 0.01
0.20 = 0.02
For a fully comparison, we perform large-scale pretraining using more training data. The pre-training method is conducted as multiple full training runs on different monkeys, but all runs share the same RA and RC module. Specifically, we adopt a sequential training strategy: the RA module is first trained
monkey's s dataset (e.g.. Monkey M), and then its learned parameters initialize training on the next monkey, and so on. (Since two sessions of Monkey C were selected as the test when compared with POYO, the final training was performed on Monkey C). Each training run aligns Day k to Day 0 within the same subject. After the RA module is trained on a given monkey, immediately train the corresponding RC module to reconstruct Day 0 neural activity from the R RA-aligned Day k input.
used to
This progressive training enables the RA and RC modules to accumulate cross-subject channel alignment knowledge while maintaining subject-specife alignment through Day supervision. To mitigate potential forgetting during this sequential training process, adopt a lightweight replay strategy: when training on new monkey, we add a small number of samples (10%) from previously seen monkeys in the training set. As shown in Table 4, the setting of CRRL PT Full finetune achieves a better performance compared to POYO-1 and NDT2.
3.7 Combining CRRL Module into DA Methods
Since our RC module can be regarded as a special domain adaptation method, and RA is a pre- alignment before adaptation, it can be incorporated with the existing DA method as plug-in. We evaluate the performance of plug-ins on the Key (G) dataset. As demonstrated in Table 5. When combined with Sycle-GAN,, the RA module boosts R² scores by 22.2% on Day 7 (0.33 vs 0.27 baseline) and maintains 122% higher accuracy by Day 56 (0.20 vs 0.09). Similar improvements are shown in ADAN. Notably, the RA+Cycle-Gi 6.7% advantage on Day expands to 11.1% by Day 30 and 1 11.0% on Day 56. These results suggest CRRL's effectiveness design enables plug-au sigg-ad-plac enhancement of DA methods.
achieves better performance separation over time:
4 Conclusion
In this work, we propose CRRL, Channel Rearrangement and Reconstruction Learning framework. Our model is inspired by the channel-wise variability in neural signals. By adapting different types of variability in the model, effectively alleviates the damage this variability on the decoder and achieves state-of-the-ar performance on multiple tasks. CRRL has good robustness, which makes its advantage more obvious when the time span long. In addition, CRRL can also be combined with other methods as plug-ins to improve the performance of other methods.
However, although work achieves better performance than the existing methods, still observe a slow decline in performance over time, which may be due to slow changes neuronal population modulation caused by learning or environmental changes. How to accurately capture the modulation change patterns of neuronal populations is another interesting direction for future work. Overall, hope the proposed cross-day decoding framework will inspire new intelligence paradigms and provide a tool for long- terg-termmn stable clinical BCIs.
5 Acknowledgement
This work was supported by grants from the Key Research and Development Program of Zhejiang Province in China (2023C03001), the Natural Science Foundation of China (62276228), and the Zhejiang Provincial Natural Science Foundation (LR24F020002).
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A Experiments Details
A.1 Simulation Dataset Details
We conducted the simulation dataset based on the cosine tuning curve model (Gilja al. 2012): The tuning function links motor cortex signals to hand movement direction. This biological tuning can be simulated using cosine function:
f((t) 01,0 + asst + as.ysing, Et:
(27)
where f denotes the estimated firing rates, 0g,0, 0g Giyy are the coeffcients including baseline, cosPD; and sinPD; respectively. PD means the preferred direction, the means the noise term and 0, means the moving direction at time t.
We simulate 8-direction center-out reaching task, and each trial corresponds to reach toward one of 8 radial targets. We evaluate two tasks: 1) Classification: Predicting the intended reach direction (8 classes). 2) Regression: Reconstructing 2D hand velocity each timepoint.
The simulation dataset consists of: 1) 100 neurons, 2) 50 timepoints per trial, 3) 800 trials total (100 per direction).
A.2 Real Dataset Details
In Section 3, we have described the datasets used in the experiments (Dyer et al. 2017: Willett et al. 2023 2021 Here, give their details and download links:
Isometric wrist (ISO) In the Isometric wrist datasets, Monkeys J and S performed an isometric wrist task, controlling a cursor by applying forces on padded box. Each trial began with a center target hold (0.2-1.0 s), followed by a randomly selected outer target and an auditory cue, EMG data were collected from muscles in Monkey J's left arm (ECU, FCU, ECRI, EDC, FCR, FDP, ECRb) and 8 muscles in Monkey S's left arm and hand (FDP1, FDP2, FCR, 1DI, FPB, EDC, MD, ECRI). Trial lengths varied as no temporal alignment was performed.
Center-out reach + In the Center- Out datasets, Monkeys and M performed a center-out reaching task using a planar manipulandum, moving the handle in parasagittal plane. Each trial began with the monkey moving to the center of the workspace, followed by a random waiting period before one eight outer targets appeared. Trials were extracted from the 'go cue time' to the 'trial end', the monkeys remained stationary before the go cue.
Key Grasping In Key Grasping dataset, Monkey G performed a grasping task, reaching and grasping a small rectangular cuboid under the screen using a key grasp with the thumb and index finger. Each trial began with the monkey resting its hand on touchpad for random period (0.5-1.0 s). Trials were extracted from the 'go cue time' to the 'trial end', as movements were random before the go cue. EMG data were collected from 8 muscles in the left arm and hand (FCR, FDP, PT, FPB, IDI, SUP, HCU, EDC).
Handwriting In the handwritten dataset, the neural activity was recorded from two microelectrode arrays which including 192 channels in the motor area. In the experiments of handwriting dataset, the participant attempted to write 31 different characters in response cues shown on computer screen. The cue list includes the following characters:'a aa,, 'b', 'c. 'd', 'e', 'f', "g', 'h', 'i',, "J', 'k', ',, 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', "comma', "apostrophe', 'tilde', "questionMark'.
zz,, "greaterThan
Speech I In the speech dataset, the neural activity was recorded from four microelectrode arrays (each array includes 64 channels and we only use the first two arrays here). In the experiments of speech dataset, the participant attempted to speak single words (and a "do nothing" condition) in response to cues shown on computer. The cue list includes the following words: 'choice', "day", 'kite', 'though', 'veto", and 'were".
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For every category, we used an equal number of training samples, resulting in balanced number of trials across all classes. More parameters of these datasets are shown in Table 6.
Table 6: Detailed dataset parameters.
Range of days
Num of recordings
Dutaset
Day 0
Decoding target
Decoding Task
ISO (T)
95
20
20150730
EMGs, hand trajectory and 8 directions
Regression Classification
(S)
83
18
20120821
EMGs, hand trajectory and 8 directions
Regression & Classificatin
Center-Out (C)
38
12
20160927
Hand trajectory and directions
Regression Classification
Center-Out (M)
32
11
20140203
Hand trajectory and directions
Regression & Classification
Key (G)
53
8
20190812
EMGs
Regression
Handwriting
51
10
20191125
31 characters
Classilication
Specch
41
9
20220616
words and a "do nothing" condition
Classification
A.3 Dataset usage of Section 3.6
In Section 3.6, we compare CRRL with large-scale methods such as POYO and NDT-2, which can implicitly account for differences neurons or channels (in the multiunit recording case) across days through learnt embeddings. We added two variants: CRRL w/o PT and CRRL PT + Full finetune. The former does not perform additional pre-training, while the latter uses the data that was used in the comparison methods for pre-training and finetuning.
For comparison with POYO-1, we use datasets from seven non-human primates spanning three different labs, with a total 27,373 units and 16,473 neuron-hours for training and finetuning. And we use the two held-out sessions from Monkey C (CO task) for testing. The standard deviation is reported over the sessions.
For comparison with NDT-2, use datasets M1-A, which consists of 4 held-in datasets spanning 5 days, each with 53-61 minutes of calibration data, and 3 held-out datasets spanning 21 days, which have only 1.1-2.2 minutes of calibration data available. And M2 includes 4 held-in datasets over 10 days, with between 5.9-13.3 minutes of calibration data per session available, and 4 held out datasets over 26 days with between 0.8-1.7 minutes of calibration data provided. The FSS (Few Shot Supervised) setting means that it uses a few calibration data in held-out datasets for f inetuning.
A.4 Dataset Split
To investigate the decoder's performance changes over different time periods, we divide all the datasets into five time periods: [5, 10), [10, 20). [20, 40), [40, 65), [65, 100). The data before day 5 includes day 0 as training data (Figure 4). In particular, in the handwriting and Center-Out (M) datasets, there is no data before day 5, and we take the training set to the first day after day For each time period, we compute the average of all data performance in the time period. We average performance across 10 random seeds for each data point. In the cross-day setting, we use data from the first 5 consecutive days for training (held-in data). All data from these 5 days are merged, then randomly split into 90% training and 10% validation. Data from Day and onward is treated as held-out test data. The model is evaluated adaptation, to assess generalization under temporal distribution shift. And the data split ratio used for training the day 0 decoder of all datasets is 8:1:1.
these later days without any additional training or
A.5 Metric Details
We adopt the Accuracy (ACC) metric to evaluate classification tasks (8 directions, phonemes and characters), which measures the proportion of correctly predicted samples. For regression tasks (hand trajectory), we use the Coefficient of Determination (R²) assess the proportion of variance in the target variable explained by the model. In multivariate regression tasks (EMGs), we extend R2 to Multi- Target R to evaluate the model's performance across multiple output variables simultaneously. These metrics are calculated as follows:
Accuracy (ACC):
n ACC
I( = 11)
(28)
n
i=1
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Speech
9800
800
000
00 01
Key
100000
***
Training data
Figure 4: We show the selection of training data for different datasets (black rectangle). Data from day 0-5 were selected as training data for most of the datasets. We divide the different time phases with blue dashed lines, which correspond the time phases of Table 2, 7.
where ii represents the true label, ùs represents the predicted label, T(-) is the indicator function, and n is the total number samples.
Coefficient of Determination (R*):
Σ 1= (1: 0:)²
R² = 1
(29)
Σ 8)2
where y, represents the actual value, ūi represents the predicted value, and ÿj is the mean of the actual values. Multi- Variate R
Th )== i= (16.) Ki.r) )2
Multi- Variate
(30)
ΣØ=1
03)
where Ve, represents the actual value of the j-th target for the i-th sample, fi, represents the predicted value of the j-th target for the i-th sample, Øj is the mean of the actual values for the j-th target, m is the number of targets, and is the number of samples.
These metrics collectively offer comprehensive evaluation of model performance across diverse tasks.
B Additional Experiments
The results of main experiment with error intervals (the standard deviation) are as follow:
Cydle-GAN
CRRL
Cydle-GAN
CRRL
0.5
0.5
0.3
0.1
0.1
64
256
0.001
0.01
0.1
Batch Size
Learning Rate
Figure 5: Comparison on different parameter setting.
B.1 Analysis of Parameter Sensitivity
We compare the parameter sensitivity of our method with Cycle-GAN and ADAN. In the experiment, we selected recording in the ISO (J) dataset (Day 30), and the decoding target was EMG. We compare the performance of the models with different batch sizes (BS) and learning rates (LR),
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Table 7: The performance of regression and classification prediction which compares with different
cross-day decoding methods.
Number of days since day 0
face
Model
Task
10)
[10, 20)
[20,40)
[40,
[65. 100)
Stabilizedbei
56.62 0,027
50.7=0.155
44.8 0.110
-1-
-/-
Conter-Out (C)
SD-Net
Direction
86.52 0.011
0.152
62.5+
63.3+ 0.232
-6-
NoMAD
48.4= 0.023
50.6+ 0.157
37.9+ 0.226
---
-1-
CRRL (Ours)
77.1s 0.117
66.82
-4-
Stabiiizennci
0116+
43.74 0.052
Center-Out (M)
SD-Net
NoMAD
Direction
73.1 0.208
39.5#
29.74 0.140
52.0a
CRRL (Ours)
0.126
57.4
Stabilizedheii
57.4= 0,089
53.1+ 0.205
35.0+ 0.120
36.5t 0. 1.105
29. 19 0.015
ISO
SD-Net
Direction
92.5= 0,240
0.228
0.159
34.5a 0.032
NoMAD
65.22 0.175
62.42 0.023
40,8t 0.111
37.54 0.203
39.72 0.119
CRRL (Ours)
66.3# 0.160
61.5 61.5= 0.204
62.2+ 0.107
48.6t 0.180
51.1= 0.008
Stabilizedbci
43.32 0.023
47.2# 0.229
40.91 0.172
25.02 0.247
14.82 0.176
(S)
SD-Net
56.5= 0.024
53.7= 0.009
53.7+ 0.060
45.6Gt 0.048
35.9= 0.214
NoMAD
94.42 0.072
51.3+ 0.065
51.2+ 0. 188
45.0+ 0. 127
44. 1+ 0.187
31.3+ 0.135
CRRL (Ours)
57.24 0.160
56.62 0.077
54.5+ 0.237
54.1 0.199
45,2s 0.210
ADAN
0.66= 0.152
0.M0+
0. 100
0.364 0.110
0.54 0.106
0.48% 0.0S7
(S)
Cycle-GAN
EMG
0.71# 0.060
0.68= 0.212
0.65= 0.074
0.63+ 0.1
0.59+ 0.183
0.50= 0.036
CRRI (Ours)
0.70# 0.234
0.66+ 0.123
0.69# 0.223
0.684 0.239
0.61 0.070
ADAN
0.262 0.091
0.21= 0.019
0.184 0.145
<0
Key (G)
Cycle-GAN
EMG
0.46+ 0.117
0.27= 0.112
0,25+ 0. 152
0.20+ 0. 146
0.09c 0.234
CRRL (Ours)
0.41= 0.193
0.37s 0.043
0.35I 0.205
0.32+ 0.101
Stabilizedhci
0.592 01224
0.52= 0.163
0.188
Center-Out (C)
NoMAD
SD-Net
Trajectory
0.84 0,186
0.55= 0,123
0.73a 0,239
0.58# 0.234
0.65a 0.070
0.41+ 0.223
0.624 0.176
CRRL (Ours)
0.75e 0.114
0.68: 0.009
0.65# 0.106
Stablizzehhci
0.384 0.199
0.3440.210 0.2T0
Center-Oul (M)
SD-Net
Trajectory
0.682 0.077
0.45a 0.060
0.39a 0.236
NoMAD
0.33# 0.036
0.26 0.183
CRRL (Ours)
0.51# 0.212
0.45+ 0.057
Stabilizedbci
0,382 0,239
0.322 0.223
0.234 0
0.20z 0.117
0.172 0.183
ISO (I)
SD-Net
NoMAD
Trajectory
0.73# 0.070
0.44# 0,166
0,42= 0.228
0.45= 0,1
0,35# 0.032
0.37+ 0.160
0.28+ 0.
0.25+ 0.157
0.28* 0.127
0.20= 0.1
0.31+ 0.187
CRRL (Ours)
0.51# 0.246
0.48: 0.186
0.43+ 0.205
0.46+ 0.043
0.47s
Stabilizedoci
0,332 0,144
0.352 0.152
0.241 0.112
0.18E 0.237
<0
(S)
SD-Net
Trijectory
0.75# 0.193
0,40= 0. 145
0,37: 0.019
0. 0.091
0.32+ 0.117
0.24# 0.234
NoMAD
0.34# 0,069
0.40: 0.061
0.38s 0.136
0.37+ 0.095
0.29+ 0.242
CRRL (Ours)
0.134
0,39
0.35a
0.37
0.30 0.186
respectively. Here LR is only set to the LR of the decoder. When comparing of the parameters, the other parameter is fixed, as shown in the bottom left of Figure 5. Results show that ADAN can fluctuate greatly and even degrade the performance significantly under different parameter Settings. However, our CRRL and Cycle-GAN are more stable. In contrast, our method performs better than Cycle-GAN in all settings.
B.2 Analysis of the Learned Representations
We applied t-SNE and PCA to the output of the Reference Alignment (RA) module. These visualizations showed that neural activity from different sessions, after RA transformation, clusters more tightly by behavioral condition or movement type than the raw neural space. This suggests that the RA module successfully maps inputs from different sessions into shared, behaviorally meaningful latent space.
Visualizing Latent Spaces:
InvarinnInvariaace Analysis: We trained simple linear classifier to predict session identity from the latent representations. The classifier performed close to chance, indicating that the RA outputs carry little information about session- features. This supports the idea that the latent space is aligned across sessions and mostly reflects task-relevant structure
B.3 Analysis of the Sensitivity on Day 0 Data Quality
To evaluate the sensitivity of CRRL under different day 0 qualities, we conducted an experiment in which noise was gradually added to the day 0 signal and observed the changes in performance.
Although CRRL performance affected by the quality of Day data, using average of multi-day effectively reduces this dependency.
23

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Table 8: The sensitivity of CRRL under different day 0 qualities.
Noise Level
ISO J [5. 10)
ISO [10, 20)
ISO J [20, 40)
0.0
0.51/66.3
0.48/61.5
0.46/48.6
0.2 x sld
0,48/62.9
0.43/58 0
0,42/43.0
0.4 x std
0,44/57.5
0.41/52.3
0.37/36.7
0 = 0.6 x std
0.39/50.2
0.36/45.1
0.31/29.6
Table 9: Using the average multiple days as Day
Noise Level
Number of days
I80 [5. 10)
ISO J [10. 20)
ISO J [20, 40)
0.2 std
0.48/62.9
0,45/58.0
0.42/43.0
= 0.4
0.44/57.5
0.41/52.3
0.37/36.7
0.6
0.39/50.2
0.36/45.1
0.31/29.6
0.2 x std
days
0.50/64.7
0,47160.2
0,44/46.1
G 0.4 X std
days
0.46/60.5
0.43/55.4
0,39/40.9
0.6
days
0.42/54.0
0,39/48.8
0,37/33.2
0.2
days
0.51/65.5
0,48/61.0
0,45/47,5
0.4 x std
days
0.49/61.7
0.45/56.8
0,44/46.3
0.6 x std
days
0.48/59.5
0.45/53.7
0.41/43.9
0.51/66.3
0.48/61.5
0.46/48.6
The table shows that averaging over multiple days-especially 3-day averaging- mitigates the degradation of performance and improves both stability and accuracy.
Table 10: Choosing another day as Day O.
0
Performance the data after 20 days
Jango 2015503000000
0.46/48.6 6
Jango_201.500 20155801
0.45/53.0
Jango 20150805
0.45/51.1
Jango_20150905 20150905
0.48/59.2
We randomly selected four different days from the Jango dataset as Day O and trained and evaluated them separately. We found that models trained on different Day 0 all achieved good cross-day alignment performance which shows that it is easy to find day 0 with good quality.
B.4
Additional Ablation Study
B.4.1
Higher Change Ratios
The results of ablation study on simulation dataset show that when the change ratios increase, the performance of the static decoder will rapidly worsen. However, the performance of CRRL will decline slowly.
B.4.2 Parameter Sensitivity
In our parameter sensitivity experiments, we scale the parameters of Cycle-GAN and SD-Net and evaluate the regression R² of EMG and the classification accuracy of directions using the Jango dataset.
Additionally, we reduce the number parameters in POYO-1. As the number of parameters in POYO decreased, performance gradually declined, which is consistent with the report in the paper of POYO.
B.4.3 Loss of Rearrangement Learning
Our RA module is designed to learn permutation matrix that aligns the channels of the re-ordered day k data as closely as possible to those of the day 0 data. Intuitively, using MSE as the loss function like a reasonable choice. However, compared to MSE, the negative Pearson correlation loss focuses more on the shape and trend of the signals rather than their absolute amplitudes, which particularly important for processing time-series data like neural signals. In our experiments,
24

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Table 11: Ablation study simulation dataset with higher change ratios.
R² face
w/o RA
w/o RC
RA + RC
New/lost neuron %)
0.83/99.1
0.72/92.7
0.92/99.5
New/los neuron
0.81/96.
0.69/89.3
0.87/99.3
New/los neuron (15
0.65/84.2
0.69/89.3
0.63/79.5
New/lost neuron (30
0.43/56.9
0.48/51.9
0.87/99.3
Shuffled channel (5 %)
0.15/55.1
0.85/92.1
0.89/98.0
Shuffled channel (10 %)
0.05/48.3
0.77/87.5
0.86/98.2
Shuffled channel (15 %)
<0/25.7
0.52/61.3
0.67/81.8
Changed function (5
0.66/80.8
0.45/64.7
0.73/91.4
Changed function (10 %)
0.32/56.2
0.27/44.2
0.55/75.0
Changed function (15 %)
<0/37.0
<0/28.6
0.33/48.4
Table 12: The performance of baseline methods on the simulation dataset.
Type
Method
RC Ra/ace
New/lost (10 %)
CRRL
0.87/99.3
NoMAD
0.70/91.4
SDNet
0.80/96.3
Stabilized BCI
0.76/91.2
Shuffled Channel (10 %))
CRRL
0.86/98.2
NoMAD
0.58/74.0
SDNet
0.32/60.9
Stabilized BCT
0.18/47.3
Changed Function (5 %)
CRRL
0.73/91.4
NoMAD
0.52/71.5
SDNet
0.68/85.5
Stabilized BCT
0.51/70.2
observed that using negative Pearson correlation loss not only converges more easily but also delivers better performance than MSE.
B.4.4 Backhone of Reconstruction Module
VQ-VAE discretizes the continuous latent space through vector quantization, forming discrete codebook. This makes it more advantageous when dealing with data with discrete characteristics (such spike signals). Specifically, discrete encoding is more robust input noise and is suitable for handling random disturbances in spike signals. Each vector in the codebook represents a potential pattern, which helps separate the activation patterns behavioral states of different channels. Recently, researchers have attempted to use VQ-VAE for encoding on various different signals and have achieved great performance. To further demonstrate the superiority of VQ-VAE in our task, we have conducted a minor experiment to replace VQ-VAE with the original VAE or MLP.
B.5
The Number of Parameters and Computation Time
The two-module design of CRRL results in extra parameters and computation time compared with regular cross-day methods. However, it still outperforms large-scale pre-training methods.
B.6 Different Training Processes
End-to-end training involving both discrete permutation learning (RA) and quantized latent variables (RC) was found to be unstable in the experiments. Training RA and RC separately allows us to analyze their behavior better. This also facilitates model reuse and plug-and and--lay adaptation.
B.7 The Results of Statistical Tests
We conducted a repeated-measure ANOVA followed by post-hoe Tukey HSD tests across all days on the handwriting dataset, where each method trained 10 times with different random seeds.
25

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Table 13: The parameter sensitivity experiments.
Method
Hidden Size
# Params
[5. 10)
20h
[20, 409
[40, 65)
[65,
Cycle-GAN
Dim-112
2.9
0.70=0.14
0.6400099
0.5860
0.57=0.07
0.49:0.06
Dim=226
4.9.M
0.6840.21
0.650.077
06310.11
0.59g0.18
0.5010.01
Dim-384
11.1 M
0.66-0.17
0.6440.12
0.060009
0.61=013
0.48=00.6
SD-Net
Dim-
1.1
51.7=0.22
49 240.14
43.7+0.10
42.8=0.11
33.5:0.06
Dim=256
65.220.23
58.610.16
44.210.06
43.820.18
Dim-384
7.2.
66.1=0.22
58.060.12
43.860.00
39.250.15
34.1=0.06
Table 14: The parameter sensitivity experiments on POYO-1.
Method
Hidden Size
Params
Monkey C
POYO-1
Dim=I 128, Layers=24
13.0 M
0.9683=0.01
Dim=64, Layers=24
5.2M
0.9512=000115
Dim=128, Layersed
3.8 M
0.9469=0.0109
Dim=64, Layersed
0.9403=0.0183
We performed post hoc pairwise comparisons using Tukey's HSD test, which corrects p-values for multiple comparisons and controls the family-wise error rate at a 0.05: CRRI. > SD>Nett (p < .001), CRRL> NoMAD (p .001), SD>-Net NoMAD (p .001)
B.8
The prefraining strategy of CRRL
The choice of a sequential pretraining strategy rather than a more standard joint training approach, such that used in POYO was based on the following considerations:
Challenges of Joint Training. Our model designed to learn a permutation matrix that maps neural representations from day k to day 0 within a single monkey. Extending this training regime to multiple monkeys introduces substantial complexity. Simultancously optimizing permutation matrices for multiple monkeys- without introducing subject-specific modules- would require the model to implicitly resolve both cross-day and cross-subject alignment shared parameter space. This significantly increases optimization difficulty and may lead to unstable or suboptimal training.
Structural Consistency. We chose not modify the core model architecture accommodate multi-subject joint training. Approaches like POYO often require additional components, such as subject encoders subject specific normalization, handle inter-subject variability. Sequential pretraining enabled us to do this without introducing new modules or auxiliary supervision, preserving architectural simplicity and interpretability.
Empirical Support. Sequential transfer learning has been adopted in other machine learning contexts, where models first pretrained general data and then fine-tuned Additionally, our experimental results show that sequential pretraining improves performance over w/o pretraining. This demonstrates both the rationality and effectiveness of the approach in our setting.
domains subjects.
The goal of CRRL is to achieve long-term stable BCI decoding, so we chose pretraining method that is easy to implement. Adding more effective pretraining strategies may further improve model performance, which is promising direction pursue in future work.
B.9 Visualization
As shown in Figure 6, we applied t-SNE the output of the Reference Alignment (RA) module. These visualizations showed that neural activity from different sessions, after RA transformation, clusters more tightly by behavioral condition or movement type than the raw neural space. This suggests that the RA module successfully maps inputs from different sessions into a shared, behaviorally meaningful latent space.
C Related Works
Cross-Day Neural Decoding. The key to cross-day neural decoding is eliminating or alleviating the damage neural signal changes on the decoder which trained on Day The intuitive solution is to align the neural signals from different days. Early studies typically used canonical correlation analysis
26

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Table 15:
Albation Study Key (G) dataset. NPC means the negative Pearson correlation loss. Replaced means that replace with other channels from a different session.
R2
Day 7
Day 30
Day 56
CRRL & MSE
0.26# 0.050
0.18+ 0.079
0.16 + 0.088
CRRL. NPC
0.41# 0.093
0.35+ 0.007
0.32+ 0.091
CRRL & VAE
0.26# 0.105
0.21 0.126
0.224 0. 148
CRRL & MLP
0.362 0.019
0.33# 0.052
0.28 0.091
CRRL & VQ-VAE
0.41# 0.093
0.35# 0.007
0.32 0.091
CRRL wo Replaced
0.41 0.093
0.35# 0.007
0.32+ 0.091
CRRL wi Replaced
0.42# 0.025
0.35+ 0.091
0.32+ 0.056
Table 16: Number of model parameters and iter speed.
Method
#Trainable parameters
Iterations per second
POYO-1
13.0 M
31.9lit's
NDT2
19.1 M
11.2011/s
SD-Net
2.9 M
42,46it/s
ADAN
9.48 MH
26.72t1/4
Cycle-GAN
2.5 M
21.49it/s
CRRL
6.8 M
18.25tv's
(CCA) align Day 0 and Day k (Altan et al. 2021: Naufel et al. 2019), however, this way can only capture linear changes in neural signals. Recently, there has been a great deal of interest in the concept of low-dimensional neural manifold (Gallego et al. 2017). For example, (Degenhart et al. 2020 aligns the signals in the neural manifolds obtained by Factor Analysis, NoMAD (Krrpowicz al. 2022) aligns the neural manifolds of Day 0 and Day k in unsupervised way. While ADAN (Farshchian et al. 2018). Cycle-GAr GAN (Ma et al. 2023). ). and Dynamic-AE (Fang et al. (023) use the idea of domain adaptation to align the signals of Day O and Day k source and target domains. Although these methods have achieved good performance, their high sensitivity to perturbations and different parameters limits their ability for clinical application. NDT2 YYe et al. (024) and POYO (Azabou et al.) 2224) capture the patterns of variation between sessions and sessions by using more data. These methods usually require a large amount of labeled data and are difficult to transfer to other tasks.
Neural Signal Reconstruction and Imputation. Reconstructing missing or corrupted neural signals is critical for maintaining decoding accuracy. Autoencoder-basse models have been employed learn robust representations of neural data. (Vincent al. 2008) introduced denoising autoencoders to reconstruct corrupted inputs by learning latent representations that capture the underlying structure of the data. In the context of neural signals, (Saced et al. [02I] introduces CHAnnel Reordering Module (CHARM) for EEG data. While our Channel Rearrangement (RA) module also learns channel permutations, the two approaches differ significantly in motivation, assumptions, and implementation. (Liu et al.) 2025) proposed BRITS, method for imputing missing time-series data using bidirectional RNNs with temporal masking. These methods demonstrate the potential of leveraging context information for reconstruction but may not fully exploit inter-channel dependencies in neural signals.
D Hyperparameters Settings
D.1 Our CRRL
We undertake several practical considerations to ensure adequate training and inference in our implementation. We adopt the Adam optimizer with learning rate of 0.001 for model training and utilize a batch size of 128/256 samples. The hyperparameters, such as the weights of different loss Arra and Avy are chosen based on validation performance. During masked channel modeling, a masking ratio of 0.05 determines the proportion of channels to mask in each input, and a random channel shuffling rate of 0.1 applied during the training of the permutation network to enhance robustness.
27

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Table 17: The results of ANOVA.
Dataset
p-value
Handwriting
1810.2
<.001
Table 18: The ablation study of different training processes.
Method
ISO J [5, 10)
ISO J [10, 20)
ISO J [20, 40)
End-to-end training
0.51/65.8
0.41/57..7
0.36/40.2
Two-stage training
0.51/66.3
0,48/61.5
0,46/48.6
The embedding size of encoder Eg 128, and the number of attention heads is 4. The codebook size K' is 512, and the commitment cost weight [8 is set to 0.25 to balance expressiveness and computational efficiency. Our model is implemented using PyTorch, enabling flexible model design and training, and training and inference are performed on GPUs to accelerate computation. All experiments were conducted on NVIDIA Tesla A100 GPUs, and the maximum memory usage across all experiments was approximately 22 GB.
D.2 Stabilizedbei
Stabilizedbei (Degenhart al. 2020) aims to stabilize crain-computer interfaces (BCIs) by leveraging the concept of a 'neural manifold," low-dimensional representation of population-level neural activ- ity. The proposed approach addresses the challenge of neural recording instabilities, such as electrode shifts neuron dropout, which can disrupt BCI performance. By aligning the neural manifold across different time points using stable electrodes as reference points, the method maintains a consistent mapping of neural activity to movement intent. This eliminates the need for frequent recalibration, allowing the BCI to provide reliable performance even under severe recording instabilities, and does without requiring knowledge of the user's intent.
D.3 SD-Net
SD-Net (Fang et al. 2023) focuses on extracting both semantic and dynamic features from neural signals, leveraging the idea that low-dimensional dynamics represent high nigh-dimensional neural activity. By embedding these features into a unified space, the method enables recalibration without requiring labeled data from alignment strategy, which aligns both marginal and conditional distributions to handle complex domain shifts in neural data. This approach is validated real and simulated datasets, demonstrating its effectiveness in improving BCI performance across sessions.
sessions. Additionally, the paper introduces joint distribution
D.4 NoMAD
NoMAD (Nonlinear Manifold Alignment with Dynamics) (Karpowiez al. 2022) is novel method to stabilize brain-computer interface (BCI) decoding performance over time. The approach leverages the low-dimensional manifold structure and dynamics of neural activity using unsupervised learning to align neural data across different time periods. By incorporating recurrent neural network (RNN) models to capture neural dynamics and an alignment network map neural data consistent manifold. NoMAD allows the initial decoder to maintain high accuracy without requiring additional labeled data or frequent recalibration. This method was validated on monkey motor task datasets, demonstrating superior decoding stability and performance compared to existing methods, paving the way for more practical and robust BCI systems
D.5 Cycle-GAN
Cycle-GAN (Ma et al. 2023) uses Cycle- Cicle-Consistent Adversarial Networks to align neural activity recorded on different days, enabling fixed decoder trained on an initial day to maintain accurate predictions without requiring frequent recalibration. Unlike previous methods, Cycle-GAN operates directly on full-dimensional neural signals, avoiding information loss from dimensionality reduction and offering greater robustness and case of training. The approach outperforms prior
28

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Space (Coloeed by Dwy)
RA.Aligned Space Day)
HONE Cirwesion
HSNE Dinasori
Figure 6: Visualization of latent space.
Table 19: Hyperparameters for rearrangement training.
Hyperparameters
Values
Batch Size
128
Initial Temperature Tiniial
Shuffling Rate
0.1
Final Temperature Trnall
0.001
Decay Rate y
0.01
Entropy Coefficient Aentropy
0.2
Number of Training Epochs
300
Learning Rate
0.001
alignment techniques like ADAN and Procrustes-baae methods, making it a promising solution for long-term iBCI applications.
D.6 ADAN
ADAN Farshchian et al. 2018) combines deep learning-based neural autoencoder with an EMG pre- dictor to extract low-dimensional representation neural signals while simultancously predicting movement intent. To stabilize the BMI over time, they implement domain adaptation techniques, in- cluding Canonical Correlation Analysis (CCA), Kullback-Leibler Divergence Minimization (KLDM), and new Adversarial Domain A Adaptation Network (ADAN). ADAN, which aligns the probability distributions of residuals from neural signal reconstructions, outperforms other methods and requires minimal data to adapt, offering a more robust and consistent interface for users.
D.7 POYO-1
POYO-1 (Azabou et al., 2024 is large-scale pre-trained model based on Transformer architecture designed for neural population decoding, which aims to integrate neural data across experiments, individuals, and laboratories. The core innovation lies in directly converting each neural spike into Token, preserving the fine temporal structure, and utilizing the PerceiverlO architecture to compress long sequence data to reduce computational cost. The model solves the problem of no correspondence between neurons across sessions by Unit Embedding and Session Embedding, and supports few-shot transfer learning and fast adaptation new datasets. Trained on a diverse dataset covering 27,373 neural units from seven nonhuman primates, POYO-1 significantly improves decoding performance on complex behavioral tasks such as random object tracking, providing an efficient and scalable unified framework for brain-computer interface and neurodynamics research.
29

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Table 20: Hyperparameters for reconstruction training.
Hyperparameters
Values
Batch Size
256
Masking Ratio
0.05
Embedding Size of Encoder
128
Num of Attention Head
Codebook Size
1024,
Commitment Cost Weight /
0.25
Aree
0.1
Xug
0.2
Number Training Epochs
500
Learning Rate
0.001
Table 21: Hyperparameters for Stabilizedbei training.
Hyperparameters
Values
Dim of Latent
10
Num FA models
5
Maximum Num of EM iterations
100000
EM stopping criteria
0.00001
Minimum private variance threshold
0.1
Num of rows of loading matrix
90
Alignment L.2 norm threshold
0.01
D.8 Neural Data Transformer 2 Multi-Context (NDT2 Multi)
NDT2 (Ye et al. 2024 is Transformer-based neural spiking activity model, which significantly improves the adaptation speed and performance of Brain-Computer Interface (iBCI) decoding tasks through multi-context pre-training across sessions, subjects and tasks, combining spatio-temporal attention and context embedding. NDT2 Multi uses neural data from multiple sessions to jointly train the model to enhance the adaptability of the model to inter-session differences.
E
Gradient Propagation Analysis for Gumbel-Sinkhorn Networks
E.1
Problem Formulation
Given log-probability matrix CCC which obtained by our channel permutation network, seek to solve the combinatorial optimization problem:
P = arg max P), PEPE
(31)
where Pc denotes the set of C' C' permutation matrices. Direct differentiation through the discrete arg max operator is infeasible due to non-smooth nature.
E.2
Differentiable Reparameterization with Gumbel Noise
Following (Jang et al. 2017b), we inject Gumbel-distribueed noise f. ~ Gumbel(0, 1) into the logits:
L. = Lif + 765,5
(32)
where 7 > 0 controls the noise magnitude. This reparameterization preserves the original distribu- tional properties while enabling gradient flow.
30

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Table 22: Hyperparameters for SD-Net training.
Hyperparameters
Values
Learning Rate
0.002
Batch Size
10
Dim of Latent
256
Epoch
60
A1; A2
0.1, 0.1
Às A
0.1,
As; A6
0.1,
Table 23: Hyperparameters for NoMAD training.
Hyperparameters
Values
Initial learning rate
10
Batch size
5
NLL cost weight
100000
NLL ramping epochs
0.00001
KL ramping epochs
0.1
KL weight initial conditions
90
KL weight on controller outputs
0.01
E.3
Continuous Relaxation via Entropy-Regularizz Optimal Transport
The cuumeel-pertrbeed logits are transformed into a doubly stochastic matrix M through the Sinkhorn- be temperature parameter:
Knopp algorithm (Cuturi 2013). Let
K (0)
exp
(33)
Alternating row and column normalizations are applied for T iterations:
R diag
K 1K(-
(34)
(1) R (1-1)
(35)
( diag (1)K())
(36)
(0) (t) (())
(37)
where 1 is a column vector of ones. The final doubly stochastic matrix is M = K(T),
E.4 Differentiability of the Sinkhorn Operator
Proposition E.1 (Implicit Gradient Computation). The Jacobian V, M can be computed via implicit differentiation of the Sinkhorn iterations CCttuii 2013 Mena et al. 2018).
Proof. Let S(L/T) denote the Sinkhorn operator. The gradient chain through T iterations is:
T
@K())
ŌK(U)
(0)
(38)
ØL
(-
ØL
(K(()) Fach term SKU yy derived from the row/column scaling operations, which are element-wise differentiable. Full derivations provided in (Mena et al. 2018).
D
31

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Table 24: Hyperparameters for Cycle-GAN training.
Hyperparameters
Values
Batch size
256
Discriminator (D1) learning rate
0.01
Discriminator (D2) learning rate
0.01
Generator (GI) learning rate
0.001
Generator (G2) learning rate
0.001
Number of training epochs
200
Table 25: Hyperparameters for ADAN training.
Hyperparameters
Values
Dim of Decoder Latent
10
Batch Size of Decoder
64
Epochs of Decoder
400
Learning Rate of Decoder
0.0001
Decoder layers
Epochs of ADAN
200
Batch Size of ADAN
Learning Rate of Discriminator
0.00001
Learning Rate of Generator
0.0001
E.5 Convergence to Exact Permutations
Proposition E.2 (Discrete Limit). As - 0t,, M converges almost surely to the permutation matrix obtained by the Hungarian algorithm on L.
Proof. When + 0+, the entries of K
satisfy:
Las
{
if (i.j)= arg max LE.1
lim exp
(39)
otherwise
The Sinkhorn iterations preserve the dominant permutation pattern, recovering the Hungarian solu- tion (Mena al. 2018
32

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Table 26: Hyperparameters for POYO-1 training.
Hyperparameters
Values
Num of Token
512
Hidden Dim
128
Num Attention Head
Num of Layers
24
Len Context
Epochs Batch Size
400
total 1400
Learning Rate of Fine-Tune
0.0001
Learning Rate of Pretrain
0.0003
Table 27: Hyperparameters for NDT2 Multi training.
Hyperparameters
Values
Hidden Dim
512
Num of Attention Head
Transformer Layers
Learning Rate
0.0001
0.0004
Dropout
0.1
Early Stopping
20
Batch Size
Len of Context
600 ms
33


Reviews:
[{"review_id": "7uyfmG37c2", "reviewer": "Reviewer_agK9", "summary": "The paper proposes a framework for decoding neural activity across days under the presence of variability in the measured signals due to electrode drift and other factors. The framework is composed of two modules. The first is a learned permutation network that learns to permute channels on new days to best align them to the baseline day. The second is a VQ-VAE that aims to adapt the permuted neural responses back to the original day by potentially reconstructing the activity of missing neurons. The transformed neural activity after these steps is then passed through a decoder trained on the original day. The paper tests this approach across many different decoding tasks, finding that the combination of both modules often provides the best decoding performance on new days compared to the alternative methods in this space.", "questions": "1. In equation (2), is a fully connected MLP necessary at the input level? This will have $CT$ weights in the input layer. I'm wondering if a more parameter efficient input layer such as temporal/spatial convolutions could also work here. \n\n2. It is not clear to me what the inputs and outputs are for training the VQ-VAE. Could you explain this in additional detail? This will greatly help with clarity. \n\n3. I'm wondering whether the authors have looked at the latent neural representations that the model learns? The right panel of Figure 1 presents a schematic showing how the approach could learn to align representations across days. I think it would be very interesting to see a corresponding plot showing neural representations from one of the tasks and how they are aligned across days.", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Overall, the paper addresses the significant challenge in neural decoding of achieving stable decoding across days. This is a difficult problem as measured neural signals can change due to movement of the electrode, changes in neural representations, and changes in the neural tissue. Methods that can adapt to these changes to achieve good decoding performance in the absence of additional costly supervised data can potentially be very useful for BCIs. The proposed CRRL method appears to generally outperform the alternatives. This is a significant and original contribution. However, the clarity of the paper could be improved. \n\nStrengths\n1. The proposed modules incorporate two very nice ideas. The first is the use of permutation neural networks to learn data-driven permutations of channels. The second is using a VQ-VAE module to adapt neural responses on new days. Both of these innovations are well-motivated.\n\n2. The approach is thoroughly tested on a variety of decoding problems and against strong baselines. Generally, CRRL achieves the best decoding performance on new days across methods and tasks, and it often substantially outperforms the baseline alternatives. Additionally, the authors provide ablation studies showing the importance of multiple model components: the Pearson correlation loss, the use of VQ-VAE compared to VAE, and that both modules are helpful. \n\n3. While the method was primarily applied to neural decoding problems in this paper, it also appears to be a generally useful mechanism for modeling multi-day neural recordings for scientific purposes.  \n\nWeaknesses\n1. The primary weakness is the clarity of the paper is sometimes lacking. There are multiple apparent typos and potential inconsistencies. The paper should be checked for correctness before final publication. I have listed some of these below. \n- It was not clear to me what the inputs and targets are for the VQ-VAE. The paper states that the neural activity at day 0 and day k are mixed together in a 70-30 ratio for input. How does this work? \n- Equation (1) appears to describe the matrix multiplication of 3D arrays $X_d$ and $M_d$.  \n- There is a typo in line 6 in the abstract \n- References are often incorrectly formatted (missing parentheses, etc.)", "was_revised": true, "final_justification": "After discussion with the authors' and reviewers, I am increasing my score by a point to reflect the changes the authors have made to improve clarity and address questions.", "rebuttal": "We thank the reviewer for the detailed and constructive feedback. We are encouraged that you find CRRL to be a significant and original contribution to the challenge of stable cross-day neural decoding, and we appreciate your recognition of both modules’ motivation, thorough experiments, and ablation analyses. We provide detailed responses to your questions and concerns point by point.\n\n> [W] The primary weakness is the clarity of the paper is sometimes lacking\n\nWe appreciate the feedback regarding clarity and have revised the paper to address the following issues:\n* VQ-VAE Inputs and Outputs: Thank you for pointing this out. We apologize for the confusion caused by our earlier description. We clarify here what the inputs and targets are for the VQ-VAE, and what we mean by “mixing” Day 0 and Day k data. \n\n  In our VQ-VAE training, the goal is always to reconstruct Day 0 neural activity, regardless of whether the input comes from Day 0 or Day k. That is, the decoder is trained to output Day 0 signals. The encoder and codebook are shared across inputs from different days, but the reconstruction target is consistently Day 0.\n\n  The “70-30 mixing” refers only to the proportion of training samples drawn from each session during training. Specifically, in each mini-batch, 70% of the inputs are from Day 0, and 30% are from Day k. However, in both cases, the target remains the corresponding Day 0 activity. For Day 0 inputs, this is a straightforward autoencoding objective. For Day k inputs, this setup encourages the encoder to map Day k signals into the same latent space as Day 0, so that the decoder can reconstruct the expected Day 0 activity. In this sense, the model learns to align Day k signals to the Day 0 reference space implicitly.\n\n* Abstract typo (Line 6): We are sorry about the minor typo. We have fixed it and double-checked the paper.\n* Equation (1): We apologize for not clarifying it. Equation (1) involves a batched matrix multiplication (BMM) over the time dimension. We have included a descriptive caption in the revision.\n* Reference formatting: We have corrected all citation formatting for consistency (\\citep{} and \\citet{} now used properly).\n\n> [Q1] In equation (2), is a fully connected MLP necessary at the input level?\n\nWe appreciate this thoughtful question. Indeed, the fully connected MLP in Equation (2) maps the flattened input to a latent representation and introduces a large number of parameters. We chose the MLP for its flexibility across datasets with different channel counts and for its ability to model arbitrary channel dependencies. However, we agree that convolutional or other alternatives (e.g., temporal convolutions or channel-wise 1D convolutions) are promising for reducing parameter count and encouraging structured inductive biases. We have now added a note in the Discussion section regarding this point as an avenue for future work.\n\n> [Q2] It is not clear to me what the inputs and outputs are for training the VQ-VAE.\n\nSame as the response of W\n\n> [Q3] I'm wondering whether the authors have looked at the latent neural representations that the model learns? \n\nThank you for the thoughtful question. Understanding the latent neural representations learned by our model is indeed important, both for interpreting how it achieves cross-session alignment and for evaluating its robustness.\n\nWe have partially explored the learned representations in two ways (have included in our revised Appendix):\n\n* Visualizing Latent Spaces: We applied t-SNE and PCA to the output of the Reference Alignment (RA) module. These visualizations showed that neural activity from different sessions, after RA transformation, clusters more tightly by behavioral condition or movement type than in the raw neural space. This suggests that the RA module successfully maps inputs from different sessions into a shared, behaviorally meaningful latent space.\n* Session-Invariance Analysis: We trained a simple linear classifier to predict session identity from the latent representations. The classifier performed close to chance, indicating that the RA outputs carry little information about session-specific features. This supports the idea that the latent space is aligned across sessions and mostly reflects task-relevant structure.\n\nHowever, we acknowledge that we have not yet performed a full representational analysis—for example, comparing the structure of latent representations to known neural manifolds, or testing whether similar latent trajectories emerge across sessions for the same behavior. These are valuable directions for future work. \n\nWe are grateful for your helpful comments and hope our responses have clarified the key aspects of our work."}, {"review_id": "BkZyQdsvb3", "reviewer": "Reviewer_3qnc", "summary": "Paper proposes a framework to address the problem of performance instability in BCIs across different days. The method explicitly models two sources of neural variability: it uses a permutation network to handle channel drift and re-mapping, and a VQ-VAE-based reconstruction module to compensate for neuron/channel loss, creating a more stable neural representation for downstream decoders.", "questions": "The rearrangement (RA) and reconstruction (RC) modules are trained in two separate stages. Could you please justify this design choice over a joint, end-to-end training paradigm? An ablation would be good.\n\nIt seems like entire framework is anchored to a single `Day 0` recording. How sensitive is the model's performance to the quality of this reference day? What happens if that day is noisy or an outlier session compared to subsequent days?\n\nWhile performance is strong, it still degrades over time. Could you provide a more detailed error analysis? E.g., by inspecting the learned permutation matrices and reconstruction quality, can you determine whether long-term decay is primarily due to failures in the RA module or the RC module?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "The main strength is the direct and a different formulation of the problem, explicitly tackling channel permutations and losses. Evaluation of the approach is also strong across multiple long-term BCI datasets.\n\nMain weakness lies in the clarity of some design choices; the paper presents a two-stage training process without justifying it over a joint end-to-end alternative, and the simulations used to validate the approach feel somewhat simplified compared to the complexity of real neural drift. Also novelty in terms of dealing with different channels in comparison to prior work (e.g., [1]) is weak.\n\n[1] Saeed, A., Grangier, D., Pietquin, O., & Zeghidour, N. (2021, June). Learning from heterogeneous EEG signals with differentiable channel reordering. In ICASSP 2021-2021 IEEE international conference on acoustics, speech and signal processing (ICASSP) (pp. 1255-1259). IEEE.", "was_revised": true, "final_justification": "Thanks for your effort. It seems reliance on day 0 data is crucial and can make or break the model.", "rebuttal": "We thank the reviewer for raising several insightful and important concerns. We are encouraged that the reviewer finds our formulation of the cross-day decoding problem to be direct and well-motivated, and that the reviewer recognizes the strength of our empirical evaluation across diverse long-term BCI datasets. Below, we respond to the main concerns and questions:\n\n> [W1] the paper presents a two-stage training process without justifying it over a joint end-to-end alternative\n\nThanks for your insightful question. We chose a two-stage training paradigm for the following reasons:\n* Training stability: End-to-end training involving both discrete permutation learning (RA) and quantized latent variables (RC) was found to be unstable in preliminary experiments. \n* Interpretability and modularity: Training RA and RC separately allows us to analyze their behavior better. This also facilitates model reuse and plug-and-play adaptation.\n* Ablation Study: We have added the ablation study of different training processes in the Appendix:\n\n|  | ISO J [5, 10)  | ISO J [10, 20)  |ISO J [20, 40) |\n| :----- | :------: | :------: |:------: |\n| End-to-end training |  0.51/65.8  |  0.41/57.7 | 0.36/40.2 |\n| Two-stage training    |  **0.51/66.3**  |    **0.48/61.5**  |**0.46/48.6**  |\n\n> [W2] the simulations used to validate the approach feel somewhat simplified compared to the complexity of real neural drift\n\nWe appreciate this concern. The simulation was to mainly evaluate the situation of channel-wise rearrangement (allows us to validate whether each component behaves as expected), such that we focused on this point and simplified the settings of the neural data. That said, we agree that more realistic simulations (e.g., continuous nonlinear drift) would be valuable. We have included more complex synthetic experiments in the revision.\n\n> [W3]  novelty in terms of dealing with different channels in comparison to prior work (e.g., [1]) is weak.\n\nWe thank the reviewer for pointing to [1], which introduces CHAnnel Reordering Module (CHARM) for EEG data. While our Channel Rearrangement (RA) module also learns channel permutations, the two approaches differ significantly in motivation, assumptions, and implementation:\n\n* CHARM focuses on cross-subject EEG classification, where electrode positions vary across individuals but the channel set is largely consistent and complete. In contrast, RA targets cross-day intracortical recordings, where electrodes may be lost, reordered, or functionally remapped over time within the same subject.\n* CHARM is trained in a task-supervised manner (e.g., EEG classification), with reordering embedded in the end-to-end model. RA is trained in a self-supervised way, using a correlation-based alignment loss between Day 0 and Day k neural activity, independent of the downstream decoder.\n* CHARM assumes full channel observability. RA is designed to work even when a subset of channels is missing or corrupted.\n* CHARM is tightly coupled with its downstream task (e.g., emotion classification). In contrast, RA is trained independently of the decoder, allowing it to generalize across tasks (e.g., speech, handwriting, motor control) using the same realignment.\n\nWe will include it in our related work section and clarify that, although both methods involve channel permutation, RA is designed for a fundamentally different setting: cross-day alignment under dynamic signal instability.\n\n> [Q1] Could you please justify this design choice over a joint, end-to-end training paradigm?\n\nSame as the response of W1\n\n> [Q2] How sensitive is the model's performance to the quality of this reference day? What happens if that day is noisy or an outlier session compared to subsequent days?\n\nThank you for noting this point. We agree that if day 0 recording is an outlier or noisy, it may affect downstream performance. In clinical applications, we typically want the decoder trained on day 0 to perform well, as this forms the basis for cross-day decoding and also requires high-quality day 0 recordings. When there are outliers in the day 0 recordings, we recommend averaging across multiple early sessions (instead of a single Day 0) to improve robustness. \n\nTo evaluate the sensitivity of CRRL under different day 0 qualities, we added an experiment in which noise was gradually added to the day 0 signal and observed the changes in performance. And we have included these experiments and discussions in our revised Appendix.\n\n|  | ISO J [5, 10)  | ISO J [10, 20)  |ISO J [20, 40) |\n| :----- | :------: | :------: |:------: |\n| $\\sigma = 0.0$ |   **0.51/66.3**  |    **0.48/61.5**  |**0.46/48.6**  |\n| $\\sigma = 0.2×std$    |  0.48 / 62.9 |   0.45 / 58.0  |0.42 / 43.0  |\n| $\\sigma = 0.4×std$   |  0.44 / 57.5\t  |    0.41 / 52.3 |\t0.37 / 36.7  |\n| $\\sigma = 0.6×std$    |  0.39 / 50.2\t |   0.36 / 45.1\t   |0.31 / 29.6  |\n\n> [Q3] Could you provide a more detailed error analysis? \n\nMany thanks for your suggestion. We do realize that understanding the source of long-term degradation is important. To this end, we conducted a new analysis where we:\n\n* Visualize learned permutation matrices over time, showing that as sessions become more distant, RA matrices become more diffuse, indicating uncertainty in alignment.\n\n* Measure reconstruction error from RC independently, revealing that it increases for sessions with large channel dropout or tuning drift. However, the reconstruction error of RC did not increase apparently with time.\n\nThese results indicate that the RA module is the primary bottleneck for long-term generalization. We have included these insights in the Discussion section and provided detailed figures in the appendix.\n\nWe hope our response can address your concerns, and we hope that you will consider improving your score. \n\n[1] Saeed, A., Grangier, D., Pietquin, O., & Zeghidour, N. (2021, June). Learning from heterogeneous EEG signals with differentiable channel reordering. In ICASSP 2021-2021 IEEE international conference on acoustics, speech and signal processing (ICASSP) (pp. 1255-1259). IEEE."}, {"review_id": "cCfOyzmqHy", "reviewer": "Reviewer_Uc7c", "summary": "Paper presents a method to learn channel-level invariant neural representation for Brain Computer Interfaces. The authors propose CRRL Channel Rearrangement and Reconstruction Learning (CRRL); a two-module framework to learn channel-invariant neural representations: (1) Channel Rearrangement (RA) which uses a neural network and Gumbel-Sinkhorn relaxation to learn a permutation matrix that aligns channels across different days, and (2) Channel Reconstruction (RC) which uses a channel-wise VQ-VAE (Vector Quantized Variational Auto-encoder) to reconstruct lost or corrupted channel signals, enhancing robustness.", "questions": "No questions.", "limitations": "Can you clarify what the limitations of the work is?", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "STRENGTHS:\n\nQuality\n\n- Strong empirical results across a diverse suite of tasks and datasets: The paper evaluates CRRL on simulated and real datasets, covering speech, handwriting, EMG, and motor tasks (Table 2, p.8), across both human and non-human primates, making the validation broad and robust.\n- Ablation and sensitivity studies: The paper evaluates the contribution of each module (RA and RC) individually and jointly.\n- Comparisons with strong baselines: Includes comparisons with leading BCI alignment and domain adaptation approaches (e.g., StabilizedBCI, NoMAD, SD-Net, ADAN, Cycle-GAN).\n\nClarity\n- Well-structured methodology sections, clear figures.\n\nSignificance\n- Addresses a challenge in BCI: Cross-day instability. \n- CRRL’s ability to generalize across 60+ days represents a meaningful contribution.\n\nOriginality\n- First to show generalization over two months with modular, channel-wise transformation.\n\nWEAKNESS:\nClarity\n- Dense notation in some areas, perhaps formatting smaller equations in-line might be easier to read.\n\nOriginality\n- Method relies heavily on existing components: While the combination is novel, both RA and RC modules draw heavily on existing techniques (e.g. Gumbel-Sinkhorn for permutation and VQ-VAE for reconstruction). The technical novelty is more in composition than invention.", "was_revised": true, "final_justification": "Based on the overall feedback and rebuttals, I believe this work provides meaningful contributions on the topic.", "rebuttal": "We sincerely thank the reviewer for the thoughtful and constructive suggestions. We appreciate your recognition of the practical significance of our work for cross-day generalization in BCIs, the clarity of our methodology, and the thoroughness of our evaluation across multiple tasks.\n\n> [W1] Dense notation in some areas, perhaps formatting smaller equations in-line, might be easier to read.\n\nThank you for this suggestion. We will revise Sections 2.1 and 2.2 to inline some of the smaller equations and reduce formatting overhead, particularly in the rearrangement module. \n\n> [W2] While the combination is novel, both RA and RC modules draw heavily on existing techniques…\n\nThank you for noting this point. We agree that both RA and RC modules build on existing techniques—Gumbel-Sinkhorn and VQ-VAE, respectively. Our key contribution is that we propose a novel, modular, and channel-aware framework that directly addresses long-term BCI instability. In our framework, components can be flexibly replaced or combined with other models. Updating the components of CRRL or adding more effective pre-training strategies may further improve model performance, which is a promising direction to pursue in future work.\n\n> [Limitation] Can you clarify what the limitations of the work is?\n\nOur method has two main limitations. \n\n* First, it relies heavily on the quality of the Day 0 data. If the reference session is noisy or not representative, the performance of RA and RC on later sessions can drop. This means that poor Day 0 recordings may lead to inaccurate alignment and decoding. Using multiple references or filtering Day 0 data could help in future work.\n\n* Second, the RA module can gradually become less effective over time. As neural signals change across weeks or months, a fixed RA model may no longer align well. In such cases, retraining the RA module after a certain period may be necessary to keep performance stable. Future work could explore ways to make RA adapt automatically without retraining.\n\nWe hope our response has answered all your questions and concerns. Thank you again for your valuable feedback."}, {"review_id": "NZkGqktWEL", "reviewer": "Reviewer_rahR", "summary": "In this work the authors present a novel method to solve the problem of cross-day generalization that is faced by current neural decoding approaches. Specifically, they introduce a framework to address 2 reasons that lead to inability of models to generalize across days (1) new or lost neurons, and (2) drifted neurons. Their framework is composed of two steps that are trained separately. Step 1 is a rearrangement module, which attempts to best align the neural activity recorded by each electrode k days after an initial recording with those of the initial recording (by learning a permutation matrix). Step 2 is a reconstruction module, which using a masking regime aims to learn to reconstruct the neural activity of the initial recording using a mixture of the neural activity recorded at the initial recording and the activity recorded k days after. The authors evaluate their approach on 5 real dataset (and perform an ablation study on a synthetic dataset). They show that their method outperforms existing approaches across the board, especially when evaluated on sessions where data was collected many days after the initial recording. They also show that the performance of their method remains more stable over time compared to other approaches. Overall, this work introduces a novel method for enabling cross-day generalization of neural decoders, which is important in real-word BCI applications when long calibration sessions hinder the ability of neural decoders to be useful in practice.", "questions": "Major: \n1. Subsection 3.2 + Table 1. The simulation dataset is ill-defined (even when reading Appendix A.1) and what is the regression and classification tasks reported in this section is also unclear. \n    1. Please give a clear description of the tasks you are simulating.\n    2. Please clarify the size of the dataset (how many neurons, timepoints, and trials are simulated).\n    3. Please explain why you did not evaluate other methods used as benchmarks in this work on the synthetic dataset or evaluate baseline methods on this synthetic dataset as well.\n\n2. Subsection 3.3. Authors in line 250-251 report that \"Our CRRL framework maintains superior long-term performance, outperforming existing methods significantly\". However, no significance testing is performed and error bars are not shown in Figure 3.\n    1. Please justify why significance testing is not performed or compare the performance of your model against that of the rest of the models for statistical significance (e.g. ANOVA followed by multiple comparisons, or use other appropriate statistical testing of your choice). \n    2. Alternatively (for the sake of time during the short rebuttal), please remove any claims pertinent to the statistical significance of your results.\n\n3. Subsection 3.6. From the results reported in Table 4 it looks like pretraining your network markedly improves your model's performance and even surpasses that of state of the art pretrained methods.  \n    1. Please explain in detail how you pretrained your method.\n    2. Which datasets you used to pretrain your method on. \n    3. Please explain why you did not employ this pretraining strategy across all experiments used in this work.\n    4. Table 4: \n        1. Please describe which datasets and sessions are used in these comparisons (clarify which sessions does \"Monkey C, M1-A, and M2-A\" refer to). \n        2. Also describe what the PT and FSS conditions refer to (including the amount of data used in each).\n\n4. Throughout this work, classification tasks have been evaluated using accuracy. However, the authors provide no evidence that the datasets used in this work are balanced.\n    1. Please provide evidence showing that the datasets used in this work are balanced, or report the ROC AUC instead.\n\n5. In Section B.3 the authors report that the number of parameters used for CRRL and baseline models is very different.\n    1. Please explain why the number of parameters used by all models was not matched or train baseline models whose number of parameters approximately match the number of parameters used by CRRL.\n\n\nMinor:\n1. Please correct the use of citep and citet throughout the text. \n2. Section 2.1.2: The dimensions of x_{d}^{flat} are incompatible with those of L_{d}. Please explain how you project x_{d}^{flat} which is a 2-D matrix to a 3-D tensor L_{d} using only an MLP. Aka, is there some reshaping going on, if yes please explain it.\n\n3. Line 43 missing \"2)\" (which is preceded by \"1)\" in line 41).\n4. Line 71-72: Please clarify what \"rearrange each day’s channels with those of day 0\" means. I believe you mean \"match each day’s channels with those of day 0\".\n5. Figure 2 > channel encoder: I believe you have a typo: \"multiheaded attention\" instead of \"multivariate attention\". Please correct if that is the case.\n6. Equation 17, 18 describe single linear layers but are referred to as MLPs in the text. What of the two is it? Please fix text or equations to match.\n7. Figure 3 is missing error bars. Please include the standard deviation or standard error of the mean for each point in the plot.\n8. Line 263 (and wherever else +infinity is used). Please replace +infinity with max number of days. Having an interval end at +infinity is very misleading and suggests that your approach's performance stabilizes after a certain number of days. In contrast the trend suggested by your data is that your performance degrades over time.  \n9. Typo in table 2: row ISO (J), column 6 missing \"/\".\n10. Line 254-255 please specify the total number of sessions used across dataset.\n11. Line 399: Typo in \"gocue time\".\n12. Line 423-424: \"We will average performance across 10 random seeds for each data point\" is unclear. Did you average the performance across 10 seeds or not? Specify.\n13. What are your train/validation/test splits used in this work? Is there a held-out test set or only cross-validation is used? Clarify in A.3.\n14. Line 445. Please explain the metric used in error intervals (e.g. standard deviation, standard error of the mean, or other).\n15.  Caption in Figure 5 is a placeholder. Please fix.\n16. Tables 7, and 8, should be referenced in the main text wherever Table 2 and Table 1 are also referenced, respectively. \n17. The results of the experiment conducted in section B.2.3 are missing. \n18. Please explain what does \"MB\" metric stands for in table 10, if megabytes, please replace all entries in this column with the actual number of trainable parameters for each model.\n19. Line 484 mentions that batch size used in this work is 32 but tables 11 and 12 mention otherwise (128 and 256). Please fix.\n20. Lines 491-492 state \"with specific experiments conducted on NVIDIA Tesla A100 GPUs\". Please specify amount of memory used (for each experiment or max across experiments) and clarify whether all experiments were ran on an A100 GPU or only some of them.", "limitations": "Yes.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n* The problem addressed in this work is of clinical importance and could accelerate progress towards clinically viable BCIs by eliminating the need for frequent calibration sessions that are impractical and frustrating for the user.\n* The authors evaluate their method on a diverse dataset that includes data from multiple NHPs and humans collected across different experimental settings and labs.\n* The authors demonstrate that their methodology outperforms existing approaches across the board, with large performance gaps in many cases.\n* The ablation study demonstrates that both parts of their network are essential for the model's performance.\n\nWeaknesses:\n* The manuscript's claims are not always clear. Experiments are not well described in Section 3.6, 3.7 and results reported in Appendix B.2.3 are missing.\n* The framework introduced in this work is not explicitly placed in the context of existing literature (related work section is missing), which makes it hard to identify the main differences between this work and other existing approaches. \n* There are multiple instances of typographical errors/missing parts of text (see questions), hinting that the submission might have been rushed.", "was_revised": true, "final_justification": "I thank the authors for performing additional experiments during the rebuttal period, which addressed many of my initial concerns. While the issue of cross-day generalization is important for BCIs and thus this paper tackles a significant problem there remain several limitations that should be addressed prior to publication.  \n\nIn particular, key methodological details (e.g., pretraining procedures, synthetic dataset creation) are missing, which limits both the replicability of the work and the transparency of the reported results. Additionally, parameter-matched baselines are not provided by authors.\n\nGiven these issues, I have raised my score to a borderline reject, as I believe they should be resolved before this paper is published.", "rebuttal": "We are glad the reviewer agrees with the clinical importance of the problem our work addressed and the novelty of our framework. We thank the reviewer for their specific feedback and have incorporated all points into our paper to improve clarity and completeness, including:\n\n* We have clarified the experimental design and dataset usage in Sections 3.6 and 3.7, including pretraining details, session selection, and few-shot settings.\n* We have added a related work section to improve the clarity of our work.\n* Typographical issues, missing statistical report, and inconsistencies in the main text and figures have been carefully corrected.\n\nWe hope these improvements address the reviewer’s concerns and help clarify our contributions. Here are our responses to the questions and concerns point-by-point:\n\n> [W1-1] Experiments are not well described in Sections 3.6, 3.7\n\nMany thanks for pointing out the unclear descriptions. And we have added the experimental designs for Sections 3.6 and 3.7 in detail:\n\n* experimental design of 3.6: In Section 3.6, we compare CRRL with large-scale methods such as POYO and NDT-2, which can implicitly account for differences in neurons or channels (in the multiunit recording case) across days through learnt embeddings. We added two variants: CRRL w/o PT and CRRL PT + Full finetune. The former does not perform additional pre-training, while the latter uses the data that was used in the comparison methods for pre-training and finetuning.\n* dataset usage of 3.6: \n  * For comparison with POYO-1, we use datasets from seven non-human primates spanning three different labs, with a total of 27,373 units and 16,473 neuron-hours for training and finetuning. And we use the two held-out sessions from Monkey C (CO task) for testing. The standard deviation is reported over the sessions.\n  * For comparison with NDT-2, we use datasets M1-A, which consists of 4 held-in datasets spanning 5 days, each with 53-61 minutes of calibration data, and 3 held-out datasets spanning 21 days, which have only 1.1-2.2 minutes of calibration data available. And M2 includes 4 held-in datasets over 10 days, with between 5.9-13.3 minutes of calibration data per session available, and 4 held-out datasets over 26 days with between 0.8-1.7 minutes of calibration data provided. The FSS (Few Shot Supervised) setting means that it uses a few calibration data in held-out datasets for finetuning.\n* training method of 3.6: \nIn our method, pre-training is performing multiple full training runs. For example, for comparison with POYO, we train each monkey's dataset separately. In each dataset, we divide the session into day 0 and day k. Lastly, we used the held-in part of Monkey C for finetuning.\n* experimental design of 3.7: In Section 3.7, we aim to evaluate the effectiveness of CRRL as a component when combined with other methods. Considering that the RA module can be regarded as a pre-alignment of the channel, we believe it can assist other cross-day decoding methods, particularly domain-adaptive (DA) methods. We combined the trained RA module with DA to form a pipeline and compared it with the original DA model.\n\n> [W1-2] …results reported in Appendix B.2.3 are missing…\n\nThe results of Appendix B.2.3 have already been reported in Table 9. We apologize for the confusion caused by our unclear description, and have supplemented the references of Table 9 in Appendix B.2.3.\n\n> [W2] The framework is not explicitly placed in the context of existing literature…\n\nWe are deeply grateful for your suggestion. To improve the clarity of our paper, we have added a related work section to further compare the similarities and differences between our method and existing methods.\n\n> [W3] There are multiple instances of typographical errors/missing parts of text…\n\nWe apologize again for the confusion. After careful review, we have corrected these issues and responded to each of your questions as follows:\n\n**Response to Major Questions**\n\n> [Major Q1-1] The simulation dataset is ill-defined…\n\nThank you for this important question. The simulation was to mainly evaluate the situation of channel-wise rearrangement, such that we focused on this point and simplified the settings of the neural data.\n\nHere, wWe provide a clearer description of the simulation setup below:\n\nWe simulate an 8-direction center-out reaching task, and each trial corresponds to a reach toward one of 8 radial targets. We evaluate two tasks: \n* Classification: Predicting the intended reach direction (8 classes).\n* Regression: Reconstructing 2D hand velocity at each timepoint.\n\nThe simulation dataset consists of:\n* 100 neurons\n* 50 timepoints per trial\n* 800 trials total (100 per direction)\n\n> [Major Q1-2] why you did not evaluate other methods ...  on the synthetic dataset\n\nThe primary purpose of the synthetic dataset we used was to evaluate the effectiveness of CRRL’s two main components (RA and RC) under controlled perturbation types. That said, we agree that simulated comparisons could further strengthen the clarity of our work. We have extended our synthetic evaluation to other methods and included these results in the revised Appendix.\n\n> [Major Q2] … no significance testing is performed and error bars are not shown in Figure 3.\n\nWe appreciate this concern. In the revision, we have added the standard deviation bars over 10 seeds to Figure 3. And we have conducted pairwise significance testing (repeated-measures ANOVA followed by post-hoc Tukey HSD tests) to validate performance differences across models.\n\n* Part of standard deviation bars in Figure 3 (handwriting)\n| day |0 |16 |24 |\n| :----- | :------: | :------: |:------: |\n| CRRL|  71.6±0.31 |  68.2±1.37 | 59.8±1.22 |\n| SD-Net|   |  57.3±0.64 | 45.5±0.89 |\n| NoMAD|   |  33.6±0.47 | 29.0±1.14 |\n\n* Part of pairwise significance testing between CRRL, SD-Net and NoMAD (on handwriting)\n\n  ANOVA test: p < 0.0001; post-hoc Tukey HSD test: CRRL > SD-Net > NoMAD\n\n> [Major Q3] Please explain why you did not employ this pretraining strategy across all experiments used in this work.\n\nMany thanks for your concern. The goal of our method is to achieve long-term stable BCI decoding using a small amount of data. And the large-scale pre-training is not the focus of our work.\n\n> [Major Q4] …provide no evidence that the datasets used in this work are balanced.\n\nFor the speech and handwriting datasets we used, the number of categories is balanced (each session performs the same set of tasks). For the CO and ISO datasets we used, the number of trials across different directions is also balanced, for example: the number of trials across directions for Jango_ISO_20150801 is [26, 27, 27, 28, 27, 27, 26, 28]. We will include a table showing class distribution per dataset and add ROC AUC results in the Appendix.\n\n> [Major Q5] …the number of parameters used for CRRL and baseline models is very different\n\nThank you for this thoughtful question. For the methods we compared, we found that increasing the number of parameters did not result in stable performance gains. To ensure the effectiveness of the comparison, we retained the settings in the open-source code of these methods, which led to differences in the number of parameters between methods. We will add the analysis about the sensitivity of the number of parameters in the appendix.\n\n**Response to Minor Questions**\n\n1 & 11. We have corrected it.\n2. Thank you for noting this. We clarify that after the projection of MLP, we reshape the output to the 3D tensor L^{d}. We will revise the description in the paper to clearly state this.\n3. We have added the missing \"2)\" to maintain consistency with the enumeration on Line 41.\n4. We agree that the original description was confusing. We have replaced “rearrange each day’s channels with those of day 0” with “match each day’s channels to those of day 0” for clarity.\n5. We have fixed this in the figure.\n6. Thank you for pointing this out. These are multiple linear layers, and we will revise the equations for consistency.\n7. We have added the error bars (computed across 10 seeds) to Figure 3 and clarified this in the caption.\n8. We agree that using “+$\\infty$” is misleading in this context. We have replaced it with the max number of days used in the experiments for each dataset.\n9. The missing “/” in Table 2, row ISO (J), column 6 has been corrected.\n10. We now explicitly report the total number of sessions (which is equal to the total number of days) used for each dataset in this section.\n12. We confirm that we did average performance over 10 random seeds. The sentence has been revised for clarity.\n13. We have clarified in A.3 that for the training data, we will divide the training set and validation set in a ratio of 9:1, and the data after the training data will be used as our held-out test set.\n14. We specify that all error bars in plots represent the standard deviation of the mean across 10 random seeds.\n15. The placeholder caption has been replaced with a complete and accurate description of the figure content.\n16. We have updated the main text to reference Tables 7 and 8 in the same sections where Table 1 and Table 2 are discussed.\n17. As mentioned above, the results of B.2.3 have been reported but without the correct references. We have added it in the revision.\n18. “MB” stands for megabytes, but we agree that the number of trainable parameters is a more informative metric. Accordingly, we have replaced the entries in this column with the total number of trainable parameters for each model.\n19. The correct batch sizes are those reported in Tables 11 and 12 (128 and 256). We have corrected the statement in Line 484.\n20. We clarify that all experiments were conducted on NVIDIA Tesla A100 GPUs, and the maximum memory usage across all experiments was approximately 22 GB. \n\nWe hope our response can address your questions and hope that you will consider improving your score. we sincerely appreciate the time and effort you have dedicated to reviewing our paper."}]

Author rebuttal:

Meta-review: In the initial review, the paper received numerous questions and concerns. During the rebuttal and subsequent discussion, there was active engagement between the authors and the reviewers. As a result, many of the initial concerns were addressed, and the scores shifted from BR, R, BA, BA → BA, BR, A, BA, meaning that three reviewers raised their scores by one level.

One reviewer, however, maintained a negative evaluation (BR) throughout. Their concern was that key methodological details were missing from the paper, which compromises reproducibility and undermines the transparency of the reported results. They argued that the paper should not be published without these issues being resolved.

These concerns are indeed important, and the position that acceptance should be withheld until an improved version is available is understandable. At the same time, the AC judges that the missing details are of a kind that can reasonably be added in the final version. Given the substantial and constructive exchange between authors and reviewers, the AC wishes not to let this effort go to waste and trusts the authors to prepare a final version that addresses these concerns. On this basis, the AC recommends acceptance.
Decision: Accept (poster)