{"id":"ea510eb3-3934-49fd-888f-7307bb8d7950","arxiv_id":"2507.20490","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"HIAL selects labels for hypergraph neural networks by maximizing a dual feature-and-topology influence function, and reports improved accuracy on seven datasets.","lead":"HIAL proposes a new way to choose which nodes to label when training hypergraph neural networks, by turning node selection into an influence-maximization problem that uses both feature structure and high-order connections. The authors report accuracy gains over existing active learning baselines on seven public datasets and claim a (1-1/e) approximation guarantee for their greedy selection procedure.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Surrogate objective F(S) is not connected to the active learning objective in Eq. (1); the (1-1/e) guarantee does not apply to generalization error.","rationale":"The reader's weakest assumption correctly identifies the alignment between the influence objective and downstream model accuracy as the load-bearing point. The paper provides no derivation connecting F(S) to the expected loss in Eq. (1), and the only supporting evidence is a single correlation plot on Cora. This is the central vulnerability: even if all submodularity proofs are correct, the greedy approximation guarantee applies to a function whose relevance to the actual active learning goal is assumed, not established. The proposed concrete test—checking rank correlation of F(S) with accuracy, including a feature-shuffle control—would directly settle whether the assumption holds across datasets. I agree with the reader's conditional verdict: the work is promising and the gap is empirical, but the central claim should not be accepted without this validation. The concern is addressable, so no change to the conditional recommendation is needed.","tokens_in":11183,"tokens_out":4407,"duration_ms":50501,"concrete_test":"On a small hypergraph (e.g., Cora with budget B=10), enumerate or randomly sample many distinct seed sets S of size B. For each set, compute F(S) and the test accuracy of an HNN trained on S (with fixed hyperparameters). Measure the Spearman rank correlation between F(S) and accuracy. Then repeat after randomly permuting node features (breaking feature-label alignment while keeping graph structure and labels fixed). If the correlation is not consistently positive, or if it disappears or reverses under feature shuffle, the assumption is load-bearing and HIAL's performance is not justified as a guarantee for active learning.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper defines the true active learning objective in Eq. (1) as minimizing expected test loss of the HNN trained on the selected set. HIAL instead maximizes F(S) = gamma*MoI(S)/MoI_hat + (1-gamma)*EDV(S)/EDV_hat. Theorems 1-3 show F is monotone and submodular, so the greedy algorithm achieves F(S) >= (1-1/e) F(S*). However, this guarantee is only for the surrogate F, not for the objective in Eq. (1). The only bridge between them is the 'reasonable assumption' before Definition 5 that nodes close in feature space share labels, plus the empirical correlation in Figure 2. That figure is a single anecdotal plot on Cora without details on how the seed sets were sampled or how theta, k were set; it also shows that equal activation scale |sigma(S)| can yield substantially different accuracies, explicitly acknowledging the gap. The addition of MoI and EDV is heuristic, not derived from any model of HNN training or label propagation. Consequently, if feature-space proximity does not align with labels, or if one-hop diffusion in EDV does not capture how HNNs assimilate label information, then a near-optimal set for F need not be near-optimal for the actual labeling objective. The central claim of state-of-the-art accuracy is therefore contingent on an untested alignment between the surrogate and the true objective, which is the weakest link in the argument.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript proposes HIAL, a hypergraph active learning method that selects nodes for annotation by maximizing a dual-perspective influence objective. The first component, MoI, measures feature-space coverage of nodes activated by a high-order-aware feature propagation scheme; the second, EDV, estimates one-hop probabilistic diffusion over hyperedges. The authors claim both components are monotone and submodular, and hence the greedy algorithm achieves a (1-1/e) approximation of the surrogate objective. They evaluate HIAL on seven datasets against seven baselines and report improved accuracy, efficiency, and robustness.","tokens_in":11651,"tokens_out":7101,"duration_ms":70182,"significance":"The framing is attractive: it is genuinely native to hypergraphs and avoids clique expansion, the objective is model-agnostic, and the greedy selection with a formal guarantee would be a useful tool if the theoretical claims are correct. The empirical evaluation is broad in terms of datasets and ablations, including generalization across four HNN architectures. However, the core theoretical results are stated without proof, the link from the surrogate objective to the actual active learning objective is only anecdotal, and several of the reported advantages are not significant under the reported error bars. The contribution is therefore conditional on substantial revision.","major_comments":[{"comment":"Theorems 1, 2, and 3 are stated without proofs, and the surrounding text only says that the functions 'exhibit desirable properties' or are 'provably' monotone and submodular. Since the (1-1/e) guarantee in Algorithm 1 is the paper's central theoretical claim, the proof of monotonicity and submodularity for each of σ(S), MoI(S), and EDV(S) must be supplied. This is especially important for Theorem 3 because the sum in Eq. (10) is over N(S), which changes as S grows, so the standard argument for a fixed set of nodes does not apply verbatim.","section":"Influence Function (Theorems 1-3)"},{"comment":"The objective F(S) in Eq. (11) is not connected by derivation to the active-learning objective in Eq. (1). The paper relies on the 'reasonable assumption' before Definition 5 and on Figure 2, which is a single Cora plot with no details on how seed sets were sampled or how θ and k were set; moreover, Figure 2 itself shows that equal |σ(S)| can yield substantially different test accuracies. Adding EDV addresses one of those failures, but the alignment between F(S) and downstream HNN accuracy remains an empirical conjecture. A paired analysis across all seven datasets (e.g., correlation between F(S) and test accuracy for many random and greedy sets) or a derivation from the HNN training objective is needed before 'near-optimal for F' can be claimed to imply near-optimal active learning.","section":"Influence Function and Figure 2"},{"comment":"The manuscript describes the HOI-Aware propagation mechanism as 'parameter-free' in the introduction of the framework section and again before Eq. (5), but the method has at least six hyperparameters: α in Eq. (5), the activation threshold θ in Definition 4, the feature-ball radius r in Definition 5, β in Eq. (10), γ in Eq. (11), and the propagation depth k. The paper states that parameter settings are in Appendix A.5 and sensitivity analyses are in the supplementary material, but neither is included in the submitted version. The authors must report the chosen values and the tuning protocol for every dataset, or the reported results cannot be reproduced or compared fairly.","section":"HIAL Framework and Hyperparameters"},{"comment":"In Table 1 the claim that HIAL 'significantly outperforms' all baselines on all seven datasets is not supported by the reported error bars. On Mushroom, HIAL is 96.35 ± 6.31 while RIM is 95.50 ± 1.88 and GRAIN is 94.51 ± 3.76; on Recipe200K, HIAL is 59.13 ± 1.09 while GRAIN is 57.86 ± 0.98 and ACGNN is 56.93 ± 1.20. In both cases the intervals overlap. The authors should report paired or repeated-measures significance tests, or at least per-seed results, before claiming significance on these datasets.","section":"Table 1"},{"comment":"The evaluation section repeatedly defers to Appendix A.2-A.5 for dataset statistics, baseline implementation details, HNN model descriptions, and parameter settings, and the robustness section defers to 'the supplementary material' for the sensitivity figures. None of these materials is present in the submitted version, so the empirical claims cannot currently be verified. Please include the appendices and supplementary material in the submission.","section":"Experimental Settings and Appendices"}],"minor_comments":[{"comment":"There is a typo in the affiliation block: 'Guoren Wag1' should be 'Guoren Wang'.","section":"Author affiliations"},{"comment":"The caption of Table 1 contains 'Hightlighted' instead of 'Highlighted'.","section":"Table 1 caption"},{"comment":"Definition 3 is imprecise: the expectation in Eq. (6) is not defined, and the L1 norm of a Jacobian matrix is ambiguous. Please specify the distribution over which the expectation is taken and the exact matrix norm used.","section":"Definition 3, Eq. (6)"},{"comment":"Algorithm 1 line 6 computes MoI(V) as a normalization factor, but Definition 5 defines MoI(S) via a union over σ(S); for S=V this should be clarified, especially because σ(V) depends on the threshold θ.","section":"Algorithm 1"},{"comment":"The text refers to Figure 2(a), 2(b), and 2(c), but the figure and its caption are not present in the text version; please ensure all panels are visible and described.","section":"Figure 2"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You can skip the hype, but you should look at this one if you care about active learning on hypergraphs. HIAL is the first method I've seen that does influence-maximization-based selection directly on hypergraphs, without clique expansion, and the main idea is clean: propagate features over the hypergraph with a high-order-aware transition matrix, then score nodes by a weighted combination of feature-space coverage (MoI) and a one-hop expected diffusion value (EDV). That is a genuine contribution — it gives you a non-iterative, model-agnostic query rule, which is practically appealing, and the ablations show both terms and the propagation mechanism each pull their weight. The generality experiments across different HNN backbones are a nice touch as well.\n\nBut the theory section is the soft spot. Theorems 1–3 state that MoI and EDV are submodular, and then the paper just moves on. No proofs, no appendix pointer in the visible text. That is not acceptable for the claim \"formal approximation guarantee,\" because the guarantee only applies to the surrogate F(S), not to the actual active learning objective in Eq. (1) (expected test loss). The paper never connects the two. The \"reasonable assumption\" that feature-space neighbors share labels is doing a lot of work, and Figure 2 actually shows that same-size activation sets can produce very different accuracies — an honest but awkward admission that the surrogate is imperfect. The EDV term is also justified partly by the empirical results on the same datasets, so there's a hint of circular motivation there.\n\nThere are also reproducibility gaps: at least six hyperparameters (α, θ, r, β, γ, k) are left unspecified in the main text, and no code is released. Some of the headline SOTA claims are on shaky error bars — Mushroom (96.35±6.31 vs RIM's 95.50±1.88) and Recipe200K (59.13±1.09 vs GRAIN's 57.86±0.98) overlap. The citation pattern looks fine; the relevant influence-maximization and hypergraph learning literature is covered.\n\nOverall, the core idea is sound and worth developing, but the paper currently overclaims. I would send it to peer review with the expectation of major revision: provide the missing proofs or clearly state that the guarantee is only for the surrogate, add a sensitivity analysis for all hyperparameters, release code, and tone down the error-bar-overlapping success claims. The paper deserves serious referee time — it's a solid contribution with addressable weaknesses.","headline":"HIAL is a plausible, natively hypergraph take on influence-based active learning with strong empirical wins, but the paper's formal guarantees are only for a surrogate objective and the proofs are missing, so treat the theory claims as provisional.","tokens_in":12010,"tokens_out":2107,"would_cite":true,"duration_ms":22417,"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":"HIAL turns hypergraph label choice into an influence-maximization problem, where greedy seed selection is provably near-optimal.","keywords":["hypergraph active learning","influence maximization","submodularity","hypergraph neural networks","active learning","node selection","feature propagation","high-order interactions"],"falsifier":"Run HIAL on a hypergraph whose node features are shared across classes while class labels follow hyperedge membership, at a fixed labeling budget, and compare downstream HNN accuracy with random selection and an entropy-based uncertainty baseline. If HIAL's chosen seed set does not beat those baselines, then maximizing the dual influence function does not track what actually helps the model learn.","tokens_in":11040,"feed_emoji":"🎯","tokens_out":11350,"duration_ms":102935,"temperature":0.7,"pith_summary":"Hypergraph neural networks learn from data in which one connection can link many items at once, but obtaining labels for enough items is expensive. This paper works out how to do active learning—choosing which few items to label—directly on the hypergraph, instead of flattening it into pairwise edges and losing higher-order structure. The key move is to reformulate the choice as an influence-maximization problem: pick seed nodes whose labels, once known, would spread farthest through both hypergraph topology and feature space. The paper proves the objective is monotone with diminishing returns—a property called submodularity—so a greedy picker is guaranteed to reach at least $1-1/e$ of the optimal value. This gives hypergraph active learning a native, model-agnostic selection rule with a formal approximation guarantee and, on the seven datasets tested, consistently higher downstream accuracy.","feed_headline":"One greedy rule for hypergraph labeling is provably near-optimal","feed_subtitle":"HIAL scores seeds by feature coverage plus hyperedge spread and outdoes flattening baselines on seven datasets.","key_machinery":"The load-bearing object is the dual-perspective objective $F(S)=\\gamma\\,MoI(S)/\\hat{MoI}+(1-\\gamma)\\,EDV(S)/\\hat{EDV}$. $MoI$ counts feature-space nodes covered by the activated seed set, using the propagation $X^{(k+1)}=\\alpha\\tilde{L}X^{(k)}+(1-\\alpha)X^{(0)}$ built on a common-neighbor weighted transition matrix $\\tilde{L}$. $EDV$ computes the probability that one-hop neighbors are activated by seeds sharing hyperedges with them. All three pieces—activated-set size, $MoI$, and $EDV$—are proved non-decreasing and submodular, meaning adding a seed never decreases influence and marginal gains shrink as the seed set grows, and a nonnegative linear combination preserves those properties. Therefore Algorithm 1's greedy marginal-gain selection inherits the $(1-1/e)$ approximation guarantee.","core_discovery":"HIAL's central claim is that hypergraph active learning should be solved natively as an influence-maximization problem rather than by flattening hyperedges into pairwise edges. The paper proposes a parameter-free propagation mechanism, driven by a common-neighbor weighted transition matrix, that treats hyperedges as group interaction units. On top of it, HIAL maximizes $F(S)$, a weighted combination of $MoI(S)$, the size of the feature-space neighborhood covered by nodes activated by seed set $S$, and $EDV(S)$, the expected number of one-hop neighbors activated through shared hyperedges. The paper shows that the activated-set function, $MoI(S)$, and $EDV(S)$ are all non-decreasing and submodular, so greedy marginal-gain selection returns a seed set with $F(S)\\ge (1-1/e)F(S^*)$. On seven public datasets across labeling budgets, with a budget of $20C$ labels, HIAL is reported to beat both graph-flattening and native hypergraph active learning baselines, with the largest gains on citation networks.","pith_inferences":["Beyond the paper, the same dual-perspective objective could be carried to other higher-order architectures, such as simplicial complexes or set-based models, whenever one has a propagation matrix and a feature-space distance; the submodularity proof would have to be re-checked for each new propagation.","A natural stress test is to replace the heuristic threshold $\\theta$ and ball radius $r$ with calibrated quantities; if monotonicity and submodularity survive, the guarantee could extend to adaptive or budget-aware selection.","The paper's correlation between high $F(S)$ and high accuracy is empirical; a formal learning-theoretic link between the influence objective and the HNN's expected test loss would turn the approximation guarantee into a statement about generalization."],"forward_implications":["Greedy node selection carries a formal $(1-1/e)$ approximation guarantee relative to the best seed set for the combined objective, so the selected labels are near-optimal for that objective.","Selection is learning-free and oracle-free, so the labeling budget can be spent in one pass before training, avoiding the repeated retraining loops of model-dependent active learning baselines.","At a budget of $20C$ labels, HIAL's reported gains over the strongest learning-free baseline on citation networks are $1.82$ to $8.38$ percentage points, and up to $8.62$ percentage points over RIM, meaning higher accuracy at the same labeling cost.","Replacing the HOI-aware propagation with the message passing of HGNN, UniGCN, VilLain, or AHGAE still beats the baselines, so the selection logic transfers across HNN architectures.","HIAL's steeper learning curves mean fewer labels are needed to reach a given accuracy; on Citeseer, HIAL passes 55% with 48 labeled nodes, a level RIM needs 108 nodes to reach."],"supporting_citations":[{"why":"Defines the influence-maximization problem and the cascade model that HIAL reuses as the seed-selection framing.","marker":"Kempe, Kleinberg, and Tardos 2003"},{"why":"Supplies the $(1-1/e)$ guarantee for greedy maximization of monotone submodular set functions that HIAL invokes for its theorems.","marker":"Nemhauser, Wolsey, and Fisher 1978"},{"why":"Introduces GRAIN, the diversified influence-maximization active learning method on graphs that motivates HIAL and serves as a primary baseline.","marker":"Zhang et al. 2021b"},{"why":"Introduces RIM, the reliability-aware influence-based graph active learning baseline HIAL compares against on test accuracy.","marker":"Zhang et al. 2021a"},{"why":"Introduces the HGNN layer whose node-to-edge-to-node message passing HIAL's propagation mechanism extends to high-order interactions.","marker":"Feng et al. 2019"},{"why":"Models random walks on hypergraphs and supports treating a hyperedge as a fundamental interaction unit, the basis of HIAL's HOI-aware propagation.","marker":"Carletti et al. 2020"},{"why":"Shows that direct generalizations of cascade models to hypergraphs can be non-submodular, motivating HIAL's design of a submodular $EDV$ term.","marker":"Zhu et al. 2018"},{"why":"Unifies graph convolution and label propagation and informs the definition of feature influence through propagation Jacobians used by HIAL's $MoI$.","marker":"Wang and Leskovec 2020"},{"why":"Supplies the Jacobian-based feature influence perspective that HIAL adapts for $MoI$.","marker":"Xu et al. 2018"}],"fun_headline_variants":["Hypergraph AL as influence maximization: provable and fast","Native hypergraph active learning: no flattening, near-optimal","HIAL: greedy submodular selection for hypergraph labels","Influence spread picks seeds for hypergraph labeling","From hyperedges to seeds: provable AL without expansion"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that feature-space proximity and one-hop hyperedge diffusion track label informativeness; the paper asserts this correlation and supports it empirically, but does not derive it from the HNN's generalization error.","fun_headline_variants_meta":{"raw":{"variants":["Hypergraph AL as influence maximization: provable and fast","Native hypergraph active learning: no flattening, near-optimal","HIAL: greedy submodular selection for hypergraph labels","Influence spread picks seeds for hypergraph labeling","From hyperedges to seeds: provable AL without expansion"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000229,"raw_usage":{"total_tokens":1522,"prompt_tokens":1030,"completion_tokens":492,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":646,"completion_tokens_details":{"reasoning_tokens":409}},"tokens_in":646,"tokens_out":492,"duration_ms":4997,"temperature":1.0,"reasoning_tokens":409,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:42:51.758590+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run HIAL on a hypergraph whose node features are shared across classes while class labels follow hyperedge membership, at a fixed labeling budget, and compare downstream HNN accuracy with random selection and an entropy-based uncertainty baseline. If HIAL's chosen seed set does not beat those baselines, then maximizing the dual influence function does not track what actually helps the model learn.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the influence-maximization problem and the cascade model that HIAL reuses as the seed-selection framing."},{"cited_title":"L.; Wolsey, L","cited_arxiv_id":null,"evidence_quote":"Supplies the $(1-1/e)$ guarantee for greedy maximization of monotone submodular set functions that HIAL invokes for its theorems."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the HGNN layer whose node-to-edge-to-node message passing HIAL's propagation mechanism extends to high-order interactions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Models random walks on hypergraphs and supports treating a hyperedge as a fundamental interaction unit, the basis of HIAL's HOI-aware propagation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that direct generalizations of cascade models to hypergraphs can be non-submodular, motivating HIAL's design of a submodular $EDV$ term."}],"review_version":2}