{"id":"12360685-e4c8-4a2a-ba22-6141a8f4f96b","arxiv_id":"2509.17405","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Bayesian optimization, seeded with quasi-Monte Carlo directions for the hybrid variants, gives sliced Wasserstein estimates that are competitive with or slightly better than prior state of the art on three optimization-in-the-loop benchmarks.","lead":"This paper uses Bayesian optimization to pick the projection directions used when estimating sliced Wasserstein distances, instead of random or quasi-random directions. Four variants are tested inside optimization loops such as gradient flows and autoencoder training, where they match or slightly beat existing quasi-Monte Carlo methods at modest extra compute.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Claimed SOTA is not attributed to BO: no control replaces the GP/UCB refinement with random or brute-force direction selection, so the reported gains may come from high-f bias rather than Bayesian optimization.","rationale":"The reader's weakest assumption is the smoothness of the slice landscape and the adequacy of the angular RBF kernel. My concern is more basic and upstream: even if the GP is well specified, the paper's experiments do not isolate the contribution of the BO mechanism itself. ABOSW only modifies at most 10% of a strong QSW seed set, ARBOSW repeats that process, and the reported margins over the strongest QSW baselines are comparable to the noise level of three-seed runs. Appendix D explicitly states that UCB-based BOSW is biased toward the supremum of f and that bounding the finite-L BO-MC error remains an open question. This makes the alternative explanation plausible: the gains may come from the bias introduced by replacing low-f directions with high-f directions, not from GP-informed adaptive sampling. A simple control experiment with random or brute-force non-BO replacement would settle this directly. If the controls match ABOSW/ARBOSW, the central 'state-of-the-art' claim is not supported by the current evidence; if they do not, the claim is substantially strengthened. The paper is honest and clearly written, and I do not see grounds to reject it; the conditional verdict remains appropriate until this attribution question is answered.","tokens_in":19199,"tokens_out":7176,"duration_ms":70420,"concrete_test":"On the deep autoencoder task of Section 4.5, with identical L=100 and training protocol, replace the ABOSW GP/UCB refinement with two non-BO controls: (a) randomly replace the same number of worst QSW directions by uniform draws from the sphere, and (b) replace them with the highest-f directions found by brute force over the same n_c=4096 candidate pool, without any GP or acquisition function. Run at least 10 seeds for ABOSW and each control, and compare final SW2 and W2 losses. If either control matches ABOSW within one standard deviation, the BO-specific contribution is not established; if both controls are clearly worse, the concern is refuted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the GP/UCB-based adaptive selection of directions is what delivers the reported state-of-the-art convergence in Tables 1 and 2. The paper never tests this attribution. ABOSW changes at most 10 of 100 QSW-seeded directions via two BO rounds (Section 3.2), and ARBOSW periodically restarts this process; no experiment compares against a control that spends the same refinement budget without the GP surrogate, such as randomly replacing the worst directions or selecting the highest-f directions by brute-force search over the same candidate pool. This gap is load-bearing because Appendix D concedes that UCB-driven selection is biased toward sup f and that no finite-L error bound is available. The observed optimization-in-the-loop gains could therefore be produced by the bias of replacing low-f directions with high-f directions, rather than by the BO surrogate's ability to model the slice landscape. With only three seeds and overlapping error bars (Table 2: ABOSW SW2 = 1.81±0.02 vs CQSW = 1.84±0.02; Table 1: ARBOSW W2 = 0.003±0.000 vs REQSW = 0.003±0.001), the data do not yet isolate Bayesian optimization as the cause of the claimed advantage.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes four Bayesian-optimization-based selectors (BOSW, RBOSW, ABOSW, ARBOSW) for the projection directions used in estimating sliced Wasserstein distances, and evaluates them on approximation error, point-cloud interpolation, image style transfer, and deep point-cloud autoencoder training, following the QSW benchmark protocol of Nguyen et al. The central claim is that these selectors achieve state-of-the-art convergence in optimization-in-the-loop settings, particularly in gradient flows and autoencoder training.","tokens_in":19649,"tokens_out":5581,"duration_ms":47216,"significance":"The idea of using BO for SW direction selection is novel (per the cited survey) and the drop-in design is clean and potentially useful. The authors are transparent in their appendices, acknowledging the bias of UCB toward sup f, the superior performance of RGQSW on style transfer, and the tuning of hyperparameters on the point-cloud interpolation task. However, the experimental support for the headline claim is thin: the reported gains are small, often within noise, and no control experiment isolates the effect of the GP surrogate. If the results are reproduced with proper controls, the contribution is a modest but interesting extension of the SW toolbox.","major_comments":[{"comment":"The abstract and conclusion claim that the proposed methods 'achieve state-of-the-art performance' and 'state-of-the-art convergence' for point-cloud interpolation and deep autoencoder tasks. The reported numbers do not support this. In Table 1 at step 500, ARBOSW is 0.003±0.000, statistically indistinguishable from REQSW and RCQSW at 0.003±0.001, and RBOSW (0.018) is clearly worse. In Table 2, the best BO variant is BOSW at SW2=1.80±0.01, only slightly below CQSW at 1.84±0.02 with overlapping error bars, and the text's identification of ABOSW as the best is contradicted by the table, where BOSW has the lower value. No significance testing is reported, and three-seed means do not establish superiority.","section":"§4.3 Table 1; §4.5 Table 2"},{"comment":"The image style transfer experiment contradicts the claim that BO hybrids are competitive with the state of the art. At L=100, RGQSW reaches W2=0.12 while ARBOSW reaches 0.65 and ABOSW 18.50; at L=10, RGQSW reaches 1.25 vs ARBOSW 1.37. The main text acknowledges this but describes RGQSW as 'marginally stronger,' which understates a factor-of-five gap. Since style transfer is one of the three core optimization-in-the-loop tasks, this is directly relevant to the central claim and weakens it.","section":"Appendix A.2, Figures 5-6"},{"comment":"There is no control experiment that attributes the observed convergence gains to Bayesian optimization itself. ABOSW changes at most 10 of 100 directions (r=2, b=5) by replacing the worst directions with UCB proposals, and ARBOSW repeats this; a random-replacement control or a brute-force highest-f replacement control would use the same budget. Appendix D explicitly notes that UCB with constant beta=0.7 drives the estimator toward sup f, so the gains could simply reflect high-f bias rather than the GP surrogate's modeling ability. Without such a control, the paper's causal claim about BO is untested.","section":"§3.2, §4.1, Appendix D"},{"comment":"All hyperparameters (acquisition function, beta, cosine cutoff, nc) were selected by ablations on the point-cloud interpolation task of Section 4.3, and Table 1 reports results on that same task. This self-confirming tuning means the interpolation results cannot serve as unbiased evidence for the method. The paper should either tune on a separate validation task or demonstrate robustness across hyperparameter choices on held-out tasks.","section":"Appendix C"}],"minor_comments":[{"comment":"The approximation error plot includes only BOSW, not RBOSW/ABOSW/ARBOSW; adding a sentence in the text or caption explaining this omission would prevent confusion, since the hybrids are claimed to be drop-in selectors.","section":"§4.2, Figure 2"},{"comment":"The kernel uses geodesic distance dS(θ,θ') = arccos⟨θ,θ'⟩, while near-duplicates are suppressed by cosine similarity > 0.98. Please clarify whether the GP is fit after duplicate suppression and whether the candidate pool is sampled uniformly on S^{d-1} independently at each round.","section":"§3.1, Eq. (3)"},{"comment":"The caption states 'Losses are scaled by 10^2 for ease of exposition,' but the table header lists 'SW2(↓) W2(↓)' without indicating the scaling; standardizing the notation and making the scaling explicit in the header would improve readability.","section":"Table 2"}],"recommendation":"major_revision","confidential_remarks":"The paper is honest in its appendices but the main text overclaims. The lack of a control for the BO attribution and the self-confirming tuning are load-bearing issues that can be fixed. If the authors add controls and substantially soften the claims to 'competitive on some tasks,' the paper could be publishable after major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: this is the first application of Bayesian optimization to SW direction selection I'm aware of, and the QSW-seeded hybrid is a new idea. The paper is worth engaging, but the 'state-of-the-art' headline is not yet supported. The main missing experiment is a control that spends the same refinement budget without the GP surrogate.\n\nWhat's good: the method family is clearly described and genuinely drop-in. The authors are honest where things fail: BOSW is bad on approximation error, RGQSW beats them on style transfer, and Appendix D concedes UCB selects toward sup f with no finite-L bound. The ablations on acquisition function, beta, cosine cutoff, and pool size are real work, and the citation pattern looks fair.\n\nThe load-bearing problem: ABOSW replaces worst QSW directions with UCB proposals, but there is no control that randomly replaces worst directions or brute-force picks the highest-f candidates from the same pool. The gains in Tables 1 and 2 may simply come from swapping low-value directions for high-value ones; the GP's modeling of the slice landscape is never isolated. Appendix D makes this more than a quibble: with constant beta, UCB is biased by design. The numbers are also marginal: ARBOSW ties REQSW/RCQSW at step 500, and ABOSW beats CQSW by 0.03 in SW2 with overlapping spread. Hyperparameters were tuned on the Section 4.3 task, which is also a main result, so some of the advantage is selected. Section 4.1 is a BO showcase against static integration rules rather than a fair SW baseline. No code is released.\n\nWho gains: practitioners using SW inside optimization loops who want a clear, adaptive direction selector and an honest map of its strengths. The paper should go to review, but only with the expectation of a revision: add control experiments, untuned results, code, and toned-down claims.","headline":"First real BO-for-SW direction selector, but the claimed SOTA isn't isolated from simple high-value replacement bias.","tokens_in":20013,"tokens_out":2959,"would_cite":false,"duration_ms":26044,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Bayesian optimization can select sliced-Wasserstein projection directions that match or beat quasi-Monte Carlo baselines inside optimization loops.","keywords":["sliced Wasserstein distance","Bayesian optimization","quasi-Monte Carlo","projection direction selection","gradient flows","point-cloud autoencoder","optimal transport","adaptive estimation"],"falsifier":"Construct point clouds whose slice function $f(\\theta;\\mu,\\nu)$ is effectively supported only in a narrow cap of angular radius well below the median pairwise spacing of the QSW seed; if, across many trials, BO-refined sets (ABOSW/ARBOSW) do not match or beat the unrefined QSW seed in the point-cloud interpolation task, the smoothness-informativeness premise fails.","tokens_in":19021,"feed_emoji":"🎯","tokens_out":8880,"duration_ms":66738,"temperature":0.7,"pith_summary":"The paper argues that when the sliced Wasserstein distance (SW) is evaluated repeatedly inside an optimization loop, fixed direction sets—whether Monte Carlo or quasi-Monte Carlo—ignore information already collected from previous slices. It treats the per-direction cost $f(\\theta;\\mu,\\nu)=W_p^p(\\theta_\\sharp\\mu,\\theta_\\sharp\\nu)$ as a black-box function on the unit sphere and selects directions with Bayesian optimization (BO), yielding four drop-in selectors: BOSW, RBOSW, ABOSW, and ARBOSW. The central empirical claim is that task-adapted directions accelerate or match the best QMC-based estimates in optimization-in-the-loop settings: ARBOSW gives the best final Wasserstein-2 distance in point-cloud interpolation, and ABOSW gives the lowest reconstruction loss in a deep point-cloud autoencoder, both compared against the QSW baseline suite. A sympathetic reader would care because this means SW users can replace or complement QMC direction sets with BO-selected ones without changing downstream losses, gradients, or the option of unbiased randomized estimation.","feed_headline":"BO-chosen slices match or beat QMC in sliced-Wasserstein loops","feed_subtitle":"On interpolation and autoencoder tasks, BO-refined direction sets outperform or match the best QMC baselines without changing losses.","key_machinery":"The load-bearing object is the slice landscape $f(\\theta;\\mu,\\nu)=W_p^p(\\theta_\\sharp\\mu,\\theta_\\sharp\\nu)$ on the unit sphere $S^{d-1}$. A Gaussian-process surrogate with the angular RBF kernel $k(\\theta,\\theta')=\\exp\\bigl(-\\tfrac12(d_S(\\theta,\\theta')/\\ell)^2\\bigr)$, $d_S(\\theta,\\theta')=\\arccos\\langle\\theta,\\theta'\\rangle$, uses a median heuristic for the lengthscale $\\ell$; the UCB acquisition $\\alpha_t(\\theta)=\\mu_{t-1}(\\theta)+\\beta\\sigma_{t-1}(\\theta)$ with $\\beta=0.7$ scores a candidate pool of 4096 uniform directions and proposes batches of five. ABOSW and ARBOSW seed the GP with QSW direction sets and replace the $b$ worst directions after each round, so the machinery converts the SW estimator from a fixed quadrature rule into an adaptive selector that exploits feedback from previously evaluated slices.","core_discovery":"The paper's central discovery is empirical: a small set of BO-refined projection directions, seeded from QSW direction sets, can reach the best reported convergence for SW-based optimization loops. Concretely, ARBOSW achieves a final Wasserstein-2 distance of $0.003 \\pm 0.000$ at step 500 in point-cloud interpolation (same mean as the best randomized QSW variants, with smaller variance), and ABOSW achieves the lowest reconstruction loss in the deep point-cloud autoencoder task ($\\mathrm{SW}_2 = 1.81 \\pm 0.02$ versus $1.84 \\pm 0.02$ for CQSW at epoch 400). The paper also establishes the boundary of the claim: on one-shot approximation of the spherical integral, BOSW trails both MC and QSW, so the advantage is specific to settings where SW appears inside an optimization loop and the direction set can be adapted to the task.","pith_inferences":["The same selector machinery could be applied to other families of slice-based divergences (generalized sliced Wasserstein, max-sliced variants) because it only requires a scalar per-direction cost; the paper does not make this extension.","A cheap diagnostic for why ABOSW/ARBOSW help would be to record which seed directions get replaced during refinement; if only the lowest-value slices are swapped out, the gain comes from pruning bad directions rather than from global landscape learning.","The paper's appeal to high-dimensional BO results suggests a concrete testable extension: run ARBOSW on point clouds in dimension $d\\ge 32$ with the same angular RBF kernel, and check whether the median-lengthscale heuristic still yields informative proposals.","The task-dependence of the best variant implies that SW libraries could expose direction selection as a plug-in choice rather than hard-coding QMC, an interface the paper does not propose."],"forward_implications":["QSW direction sets can serve as a seed rather than a finished design: a few BO refinement rounds improve optimization-in-the-loop performance with modest runtime overhead (ARBOSW at roughly 7 s versus 4–4.3 s for QSW baselines in the interpolation task).","SW-based gradient flows and deep autoencoder training can adopt BO selectors without touching the downstream loss, the gradient computation, or the unbiasedness option provided by RQSW-style randomization.","The optimal direction strategy is task-dependent: stable large datasets favor one-shot or seeded hybrids (BOSW/ABOSW), while evolving flows favor refresh or restart hybrids (RBOSW/ARBOSW).","The Appendix D asymptotic note implies the advantage of BOSW is finite-$L$: with constant UCB $\\beta$ the selector would converge toward the supremum of $f$, not its uniform average, so long-run unbiased estimation requires annealing $\\beta$ or switching to MC/RQSW."],"supporting_citations":[{"why":"Supplies the QSW/RQSW direction sets and the full experimental benchmark suite (datasets, metrics, reporting protocol) that the paper adopts for one-to-one comparison.","marker":"Nguyen et al. (2024a)"},{"why":"Defines the sliced Wasserstein distance and the sorting-based O(n log n) computation of 1-D costs that the estimators call per direction.","marker":"Bonneel et al. (2015)"},{"why":"Provides the GP-UCB acquisition rule with the exploration constant beta that the paper tunes and fixes at 0.7.","marker":"Srinivas et al. (2010)"},{"why":"Supplies the standard Gaussian-process posterior and kernel machinery used for the surrogate model.","marker":"Rasmussen & Williams (2006)"},{"why":"Establishes positive-definite functions on spheres, cited to justify the angular RBF kernel on S^{d-1}.","marker":"Schoenberg (1942)"},{"why":"Supplies the O(L^{-1/2}) Monte Carlo convergence rate used in Appendix D to frame the BO-specific error term.","marker":"Nadjahi et al. (2020)"},{"why":"Cited as the information-gain and regret route toward bounding the BO-MC error term left open in Appendix D.","marker":"Vakili et al. (2021)"}],"fun_headline_variants":["BO-refined slices match or beat QMC in sliced-Wasserstein loops","Adaptive BO direction sets rival QMC for SW optimization","ABOSW: BO-refined projections improve sliced-Wasserstein convergence","Bayesian-optimized direction sets match QMC in optimization loops","BO augmentation of sliced Wasserstein matches QMC baselines"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes the slice function $f(\\theta)=W_p^p(\\theta_\\sharp\\mu,\\theta_\\sharp\\nu)$ is smooth enough on the sphere that a Gaussian-process surrogate with an angular RBF kernel and median lengthscale produces informative UCB proposals; if $f$ varies at scales below that lengthscale, the selected directions are no more useful than random or QMC ones.","fun_headline_variants_meta":{"raw":{"variants":["BO-refined slices match or beat QMC in sliced-Wasserstein loops","Adaptive BO direction sets rival QMC for SW optimization","ABOSW: BO-refined projections improve sliced-Wasserstein convergence","Bayesian-optimized direction sets match QMC in optimization loops","BO augmentation of sliced Wasserstein matches QMC baselines"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001163,"raw_usage":{"total_tokens":4834,"prompt_tokens":985,"completion_tokens":3849,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":601,"completion_tokens_details":{"reasoning_tokens":3759}},"tokens_in":601,"tokens_out":3849,"duration_ms":22489,"temperature":1.0,"reasoning_tokens":3759,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:47:24.954728+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct point clouds whose slice function $f(\\theta;\\mu,\\nu)$ is effectively supported only in a narrow cap of angular radius well below the median pairwise spacing of the QSW seed; if, across many trials, BO-refined sets (ABOSW/ARBOSW) do not match or beat the unrefined QSW seed in the point-cloud interpolation task, the smoothness-informativeness premise fails.","supporting_citations":[],"review_version":2}