{"id":"0129274f-f6ea-42c3-a98f-4eba18487bed","arxiv_id":"2608.05315","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"OSPDIM applies online information maximization to a manifold-constrained bias parameter, correcting label-shift-induced geometric misalignment for source-free EEG adaptation.","lead":"This paper proposes an online method that adjusts the geometric alignment of EEG brain-signal features as data streams in, correcting distortions caused by uneven class frequencies. The method, OSPDIM, is tested on two motor-imagery datasets and reports accuracy gains over standard Riemannian alignment baselines under simulated class imbalance.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"At ρ=0.1, N=32, the buffer has ~29 majority and ~3 minority samples; Eq. 4's marginal-entropy term can only be satisfied by predicting majority samples as minority, so IM may distort geometry rather than recover the balanced center.","rationale":"The reader correctly identifies the weakest assumption: the IM objective must recover the true class-balanced center. My concern sharpens this into a concrete, arithmetic failure mode under the paper's own configuration (ρ=0.1, N=32, K=5). Because the buffer is heavily imbalanced, LMEM and LCEM in Eq. (4) are in direct tension: the minority samples alone cannot raise p̄_minority toward uniform, so the optimizer must either misclassify majority samples or leave marginal entropy far from its maximum. The paper provides no fixed-point analysis, no diagnostic of predicted-label distribution, and no comparison to the closest IM-based test-time baseline (T-Time). The empirical gains could therefore be explained by a generic entropy-minimization effect rather than by the claimed geometric bias correction. This does not invalidate the empirical results, but it does mean the central causal claim is not established. The reader's CONDITIONAL verdict remains appropriate: the paper should provide the requested diagnostic or an explicit analysis of the IM fixed point under imbalanced buffers. I chose UNCHANGED because this concern reinforces the existing CONDITIONAL verdict rather than moving it. Credit is due for the online protocol design and the consistent positive gains over Online RCT, which are genuinely useful; the issue is specifically the explanatory mechanism.","tokens_in":7397,"tokens_out":8528,"duration_ms":79974,"concrete_test":"Run the synthetic 2×2 SPD simulation at imbalance ratio ρ=0.1 with buffer size N=32, and after OSPDIM converges inspect the predicted labels on the buffer. Count how many of the ~29 majority-class samples are assigned to the minority class by the frozen classifier after adaptation. If more than 10 of the 29 majority samples are predicted as minority, the IM objective is forcing majority samples into the minority class to satisfy marginal entropy, contradicting the claim that IM recovers the true class-balanced geometric center. Also report the post-adaptation gap between corresponding class centroids (as in Fig. 1, Right) to directly measure geometric correction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that OSPDIM's information maximization (Eq. 4) corrects the geometric skew caused by label shift by recovering the true class-balanced geometric center. The load-bearing assumption is that the IM optimum for the bias Φ_t corresponds to that balanced center. The paper does not analyze this, and under its own experimental parameters the assumption is questionable. For ρ=0.1 and buffer size N=32, the sliding buffer contains on average about 29 majority and 3 minority samples. The marginal-entropy term LMEM in Eq. (4) pushes the average prediction vector p̄ toward uniform (p̄_c ≈ 0.5). The three true minority samples can contribute at most 3/32 ≈ 0.094 to the minority-class mean even if each is predicted with probability 1. To increase p̄_minority toward 0.5, the optimizer must therefore assign substantial minority-class probability to roughly 13 of the 29 majority samples, directly conflicting with the conditional-entropy term LCEM that demands each sample be predicted confidently. The fixed point of this tension is unexamined; the bias may satisfy the IM objective by flattening majority-class confidence instead of by correcting the geometric displacement. If that happens, the large reported gains over Online RCT may stem from generic entropy minimization rather than from the manifold-constrained bias recovering the class-balanced center. The paper's synthetic 2×2 visualization is suggestive but does not quantify the centroid gap after IM convergence, and no experiment measures whether the estimated bias matches the true balanced-center offset.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes OSPDIM, an online source-free unsupervised domain adaptation method for EEG classification under label shift. The method introduces a manifold-constrained bias parameter Phi_t into the tangent-space mapping of SPD covariance features and optimizes it via an information-maximization loss computed on a sliding buffer of recent unlabeled target samples. The authors argue that this corrects the geometric misalignment caused by imbalanced target streams, where standard Riemannian centering (RCT) fails. They support the claim with a 2D SPD-manifold visualization and with motor-imagery experiments on BNCI2014001 and BNCI2015001 under simulated imbalance ratios from 0.1 to 0.4, reporting consistent balanced-accuracy gains over Online RCT and related baselines.","tokens_in":7663,"tokens_out":3492,"duration_ms":33921,"significance":"If the central claim holds, OSPDIM would be a practically valuable plug-and-play component for online BCI systems that face non-stationary class priors, because it adapts without target labels and without storing large target batches. The paper has clear strengths: experiments on two public datasets, multiple imbalance ratios, 10 random seeds per condition, bootstrap confidence intervals, and an ablation on the adaptation learning rate. The proposed mechanism is intuitive and the visual simulation is helpful. However, the central claim that information maximization recovers the class-balanced geometric center is not established analytically or diagnostically, the most relevant IM-based test-time baseline (T-Time [28]) is not compared, and a key implementation detail -- the update rule for the reference center C_t in Eq. (2) -- is left ambiguous. These issues are load-bearing for the paper's main contribution.","major_comments":[{"comment":"The IM objective is the sole supervision for Phi_t, and the paper claims that it recovers the true class-balanced geometric center. Under the paper's own experimental parameters this is not self-evident: at rho=0.1 and buffer size N=32, the buffer contains about 29 majority and 3 minority samples, so the marginal entropy term L_MEM can only push the mean prediction toward uniform if the optimizer assigns substantial minority-class probability to majority samples, which conflicts with the conditional entropy term L_CEM. The paper does not analyze this fixed point, nor does it report diagnostics such as the centroid gap after adaptation or per-class confidence. Please add either a theoretical analysis of the IM fixed point under severe imbalance or a diagnostic experiment that directly measures whether the optimized Phi_t recovers the balanced class centroids, since this is the mechanism on which the central claim rests.","section":"III-B, Eq. (4)"},{"comment":"The paper cites T-Time [28] as a relevant IM-based test-time adaptation method for BCIs but does not include it in the experimental comparison. Figure 2 compares only Riemannian baselines and an offline reference. Without a comparison against T-Time, the conclusion that OSPDIM 'significantly outperforms standard Riemannian baselines' does not address the most directly relevant IM-based competitor, and the reader cannot judge whether the gains come from the manifold-constrained bias or simply from applying information maximization at test time. Please add T-Time (and, if feasible, one or two other source-free/test-time adaptation baselines) under the same online protocol and imbalance conditions.","section":"IV-B, Experiments"},{"comment":"The reference center C_t in Eq. (2) is never defined for OSPDIM. The text says C_t represents the 'reference center for tangent space mapping at time t', but the online adaptation protocol only describes how Phi_t is updated, not how C_t is obtained or updated. Is C_t the Riemannian mean of the current sliding buffer, an exponential moving average of target covariances, or a fixed source statistic? This is not a cosmetic issue: the inner term performs standard centering, and its bias is exactly what Phi_t is supposed to correct. Without a precise update rule, the method is not reproducible and the interpretation of the bias parameter is ambiguous. Please specify the update rule for C_t and state whether it differs from the Online RCT baseline.","section":"III-B, Eq. (2)"}],"minor_comments":[{"comment":"The caption of Figure 1 is internally inconsistent: the Left panel is described as 'Blue dots represent Source, Red dots represent Target', but the Middle and Right panels refer to Orange and Green target colors. Please harmonize the color descriptions.","section":"IV-A, Fig. 1"},{"comment":"The notation in Eq. (2) mixes C_i and C_t without a clear definition of the sample index i versus the time index t. Please define C_i explicitly as the SPD covariance of the incoming trial and clarify the relationship between i and the buffer index.","section":"III-B, Eq. (2)"},{"comment":"The paper uses the phrase 'significantly outperforms' but reports only bootstrap confidence intervals, not a paired significance test across subjects. A paired test (e.g., Wilcoxon signed-rank or permutation test) at each imbalance ratio would make the claim more precise.","section":"IV-B, Results"},{"comment":"The details of Online RCT and Offline RCT are sparse; in particular, the exponential moving average parameter for Online RCT is not reported. Please provide these settings so that the comparison is fair and reproducible.","section":"IV-B, Baselines"},{"comment":"The offline reference SPDIM [30] is described as an upper bound, but [30] is a self-cited manuscript whose public availability is not stated. Please clarify whether SPDIM results are taken from the cited paper or reimplemented, and provide enough detail to assess the comparison.","section":"IV-B, SPDIM reference"},{"comment":"The conclusion states '>15% improvement on BNCI2014001' without specifying the imbalance ratio or the baseline used for the comparison. Please report the exact condition to which this number refers.","section":"V, Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is built substantially on the authors' own SPDIM framework [30], which is cited as an offline reference but is not publicly available; this makes the novelty assessment somewhat difficult. The missing comparison against T-Time [28] is particularly important because T-Time is also an IM-based test-time adaptation method for BCIs and is cited but not benchmarked. I would encourage the editor to request the authors to release code and to include the T-Time baseline in the revision; without those, the empirical claims are hard to verify."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper tackles a real problem—Riemannian centering fails when online EEG streams are class-imbalanced—and OSPDIM's sliding-buffer bias correction is a sensible, if incremental, extension of the authors' offline SPDIM. The experiments are honestly run (two public datasets, multiple imbalance ratios, 10 seeds) and show consistent positive gains over RCT baselines. The adaptation-speed analysis is a nice addition. I'd send it to review, but the authors need to tighten the interpretation.\n\nWhat's actually new: the online protocol—FIFO buffer, retraction-based SPD bias updates, and the hyperparameter sensitivity study. The bias parameter and IM objective come straight from SPDIM [30], so novelty is incremental, but the online machinery is not in the prior work.\n\nWhere the paper is soft: first, no comparison against T-Time [28], which is the most relevant IM-based online/plug-and-play EEG baseline. That omission undercuts the \"significantly outperforms\" claim. Second, no code; for a methods paper that's a real gap. Third, the update rule for the reference center C_t in Eq. (2) is left ambiguous—it's not clear whether OSPDIM also updates C_t online or keeps it fixed.\n\nThe bigger concern is the interpretive claim. The stress-test note is right: at rho=0.1 with N=32, the buffer has ~29 majority and ~3 minority samples. The marginal-entropy term wants p-bar near uniform, so the optimizer has to label a dozen-odd majority samples as minority to balance the mean, which conflicts with the confidence term. The paper never analyzes this fixed point, and the 2x2 simulation only shows the desired outcome, not whether the learned bias actually matches the true balanced-center offset. So the statement that IM \"recovers the true class-balanced geometric center\" is unproven. The empirical gains are plausible, but they might come from generic entropy minimization rather than from correcting the geometric displacement. That's a moderate concern, not fatal—the method can still work—but the paper should either prove the fixed point, add a diagnostic, or soften the interpretation.\n\nAlso, \"significantly outperforms\" is based on bootstrap CIs, not formal tests; minor, but worth flagging.\n\nWho's this for? BCI researchers using Riemannian geometry and test-time adaptation folks. A serious referee should engage with it. My recommendation: accept with major revision; require the T-Time comparison, clear C_t update, and an analysis or experiment showing the bias actually aligns the class centroids.","headline":"OSPDIM is a plausible online extension of the authors' own offline SPDIM, with consistent gains on two EEG datasets, but the central claim that information maximization recovers the balanced geometric center is not actually shown and is strained under severe imbalance.","tokens_in":8230,"tokens_out":2915,"would_cite":true,"duration_ms":25714,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A Riemannian bias term restores EEG alignment under class imbalance.","keywords":["EEG","brain-computer interface","Riemannian geometry","source-free domain adaptation","label shift","information maximization","online adaptation","SPD manifold"],"falsifier":"Run OSPDIM on a source-free EEG adaptation stream in which the frozen source classifier's softmax outputs are deliberately miscalibrated (for instance, by temperature scaling), or in which the buffer size is reduced below the number of classes; if balanced accuracy falls to the level of online RCT, the information-maximization objective is not recovering the true class-balanced center.","tokens_in":7149,"feed_emoji":"🧠","tokens_out":3881,"duration_ms":33459,"temperature":0.7,"pith_summary":"The paper argues that in online brain-computer interface streams, label shift makes standard Riemannian centering—aligning the empirical Fréchet mean to the source center—actively harmful, because the mean is dominated by the majority class. To fix this, OSPDIM introduces a time-varying SPD bias parameter $\\Phi_t$ into the tangent-space mapping, optimized by information maximization on a small sliding buffer. Simulations on $2\\times 2$ SPD matrices show the corrected class centroids overlap with the source, and on two motor-imagery datasets OSPDIM outperforms both online and offline Riemannian centering baselines, with improvements over $15\\%$ on BNCI2014001. The paper concludes that decoupling geometric centering from distribution alignment recovers the true class structure on-the-fly without target labels.","feed_headline":"Online EEG adaptation fixes label-shift skew, beating baselines by 15%","feed_subtitle":"Riemannian centering fails when classes are imbalanced; a manifold-constrained bias restores alignment without target labels.","key_machinery":"The central object is a manifold-constrained bias parameter $\\Phi_t \\in \\mathcal{S}_+^D$, introduced into the tangent-space mapping as $m_\\phi(C_i) = \\operatorname{upper}\\circ\\log\\big(\\Phi_t^{1/2}(C_t^{-1/2} C_i C_t^{-1/2}) \\Phi_t^{1/2}\\big)$, where $C_t$ is the empirical target reference center. This bias is updated online by approximate Riemannian gradient descent with retraction onto the SPD manifold, using the information-maximization loss on a FIFO buffer of recent target features.","core_discovery":"The central claim is that standard Riemannian alignment fails under class imbalance because it performs geometric over-correction: centering the imbalanced target mean to the identity pulls the majority class centroid away from the source decision boundary. OSPDIM corrects this by learning a manifold-constrained bias $\\Phi_t$ that acts after standard centering, and the information-maximization objective—minimizing conditional entropy while maximizing marginal entropy over a causal buffer—steers this bias toward the class-balanced geometric center. The result is that target class centroids realign with source centroids, restoring the decision boundary structure without any target labels.","pith_inferences":["The same manifold-bias-plus-information-maximization trick could transfer to other SPD-based test-time adaptation settings, such as MEG or fNIRS, whenever class priors drift over time.","A likely failure mode is that a miscalibrated frozen classifier makes the IM objective lock onto a confident but wrong class structure; a direct test would use deliberately temperature-scaled source classifiers.","The reported buffer size $N{=}32$ and optimal learning rate $\\eta{\\approx}0.005$ suggest a practical rule that adaptation speed should scale inversely with buffer noise, matching the stability-responsiveness trade-off shown in the ablation.","Comparing the learned $\\Phi_t$ against the true class-balanced Fréchet mean computed from labeled target data would directly measure how well the IM objective recovers the intended center."],"forward_implications":["Online BCI decoders can keep working during severely imbalanced command streams without recalibration or target labels.","Standard Riemannian centering (RCT) and TSMNet-style batch normalization should be avoided under label shift, since they distort class clusters.","A purely causal sliding buffer is sufficient to bridge most of the gap between a failing online baseline and the offline full-batch oracle.","The method remains stable when label shift is absent, so enabling the learnable bias does not appear to hurt balanced streams."],"supporting_citations":[{"why":"Defines the Riemannian Centering Transformation that OSPDIM extends and that serves as the key failing baseline under label shift.","marker":"[16]"},{"why":"Provides TSMNet, the source model architecture and geometric alignment setup that OSPDIM modifies with the bias parameter.","marker":"[19]"},{"why":"Introduces the offline SPDIM framework that OSPDIM adapts to the online setting and uses as the offline upper-bound reference.","marker":"[30]"},{"why":"Supplies the information-maximization objective (conditional entropy minimization plus marginal entropy maximization) used to fit the bias without labels.","marker":"[29]"},{"why":"Provides the BCI competition IV motor-imagery datasets, including BNCI2014001 and BNCI2015001, used for the main empirical evaluation.","marker":"[31]"},{"why":"Supports the claim that aligning marginal feature distributions can be detrimental under label shift.","marker":"[25]"}],"fun_headline_variants":["OSPDIM: online EEG fix for label shift beats baselines","Fix EEG label shift on the fly with OSPDIM","Beating Riemannian baselines by 15% with OSPDIM","Realign imbalanced EEG online without target labels"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method relies on the information-maximization objective, computed on a small imbalanced buffer, to pull the bias parameter to the true class-balanced geometric center; if the source classifier is poorly calibrated or the buffer is too short, the bias can lock onto a wrong center.","fun_headline_variants_meta":{"raw":{"variants":["OSPDIM: online EEG fix for label shift beats baselines","Fix EEG label shift on the fly with OSPDIM","Beating Riemannian baselines by 15% with OSPDIM","Realign imbalanced EEG online without target labels"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000641,"raw_usage":{"total_tokens":2934,"prompt_tokens":911,"completion_tokens":2023,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":527,"completion_tokens_details":{"reasoning_tokens":1951}},"tokens_in":527,"tokens_out":2023,"duration_ms":13753,"temperature":1.0,"reasoning_tokens":1951,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T15:27:39.629459+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run OSPDIM on a source-free EEG adaptation stream in which the frozen source classifier's softmax outputs are deliberately miscalibrated (for instance, by temperature scaling), or in which the buffer size is reduced below the number of classes; if balanced accuracy falls to the level of online RCT, the information-maximization objective is not recovering the true class-balanced center.","supporting_citations":[{"cited_title":"Transfer learning: A Rieman- nian geometry framework with applications to brain–computer inter- faces,","cited_arxiv_id":null,"evidence_quote":"Defines the Riemannian Centering Transformation that OSPDIM extends and that serves as the key failing baseline under label shift."},{"cited_title":"SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG,","cited_arxiv_id":null,"evidence_quote":"Provides TSMNet, the source model architecture and geometric alignment setup that OSPDIM modifies with the bias parameter."},{"cited_title":"SPDIM: Source-free unsuper- vised conditional and label shift adaptation in EEG,","cited_arxiv_id":null,"evidence_quote":"Introduces the offline SPDIM framework that OSPDIM adapts to the online setting and uses as the offline upper-bound reference."},{"cited_title":"Information-theoretical learning of discriminative clusters for unsupervised domain adaptation,","cited_arxiv_id":null,"evidence_quote":"Supplies the information-maximization objective (conditional entropy minimization plus marginal entropy maximization) used to fit the bias without labels."},{"cited_title":"Review of the BCI competition IV,","cited_arxiv_id":null,"evidence_quote":"Provides the BCI competition IV motor-imagery datasets, including BNCI2014001 and BNCI2015001, used for the main empirical evaluation."}],"review_version":1}