{"id":"79ab358f-c2f4-4ec4-8ca3-ff299bbe02cf","arxiv_id":"2505.09205","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"HMamba is an architecture that runs Mamba's selective state space model in hyperbolic space for sequential recommendation, claiming 3-11% gains over baselines on four benchmarks.","lead":"This paper proposes HMamba, a sequential recommendation model that combines Mamba's linear-time state space processing with hyperbolic geometry embeddings. It reports 3-11% accuracy gains over existing recommenders on four datasets, but the method description and experiments contain inconsistencies that call the results into question.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The hyperbolic state update degenerates at the stated curvature: Algorithm 1 uses log(1/c), and §3.1.4 sets c=1.0, so \\bar A=I and HMamba-Full's claimed curvature-aware SSM is not the mechanism evaluated.","rationale":"I read the central claim as: adding hyperbolic geometry to Mamba's selective SSM yields 3–11% gains while retaining linear-time efficiency. For that to be true, the paper must specify a working curvature-aware state-space update and must evaluate that update. The most load-bearing flaw is that it does not. The reader's weakest assumption identified the curvature-sign contradiction (c<0 vs c=1.0); I agree with that diagnosis and sharpen it: with c=1.0, the explicit log(1/c) factor in Algorithm 1 makes \\bar A=I and the recurrence loses the A-dependent dynamics that the hyperbolic SSM is supposed to contribute. With c<0, the algorithm's log term is undefined. Eq. 13 provides a different formula, but at k=1 its curvature factor is also identity, so the two published definitions do not agree. The theoretical guarantees in Section 2.7 have unspecified constants and are secondary; the empirical tables are self-reported and no code is provided, so they cannot independently confirm which formula was used. I am not objecting to the research direction: hyperbolic recommenders are a plausible area, and a properly specified Lorentz-Mamba model could be useful. The issue is that this paper, as written, does not provide a consistent specification of its central mechanism, so the reported accuracy gains are not attributable to the claimed hyperbolic state-space design. The reader's REJECT verdict is retained; my read does not move it, and I do not see a basis for ACCEPT or CONDITIONAL without code and a corrected, self-consistent statement of the model.","tokens_in":22200,"tokens_out":12402,"duration_ms":128012,"concrete_test":"Analytically instantiate Algorithm 1 line 12 and Eq. 13 at the reported c=1.0 (k=1): line 12 gives \\bar A = exp(0) = I, while Eq. 13 gives \\bar A = exp(ΔA) with K=I. Then run the Texas HMamba-Full configuration with c=1.0 and with c=0.1, keeping all other hyperparameters fixed. If the two runs differ, the paper's formulas do not determine the implementation actually evaluated; if they do not differ, the curvature-aware transition is inert and the reported gains are not evidence for the claimed mechanism. Either outcome would settle the concern.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim requires a working curvature-aware selective state-space mechanism, but the method as written does not define one. §3.1.4 fixes the curvature parameter at c=1.0, while Algorithm 1 line 12 defines the fully hyperbolic variant's discretized transition matrix as \\bar A = exp(ΔA · log(1/c)). Since log(1/1.0)=0, this gives \\bar A = I, so the A-dependent decay that Eq. 12's PTrans(Ah) is supposed to provide vanishes. Eq. 13 gives a different formula, \\bar A = exp(ΔA ⊙ K(k)) with K(k) = diag(sqrt(|k|),1,...,1); at k=1/c=1, K is the identity, so no curvature-dependent factor appears there either. The complexity table's log(1/c) factor is therefore zero at the reported setting, contradicting the claimed O(log(1/c)) overhead. Meanwhile, Eq. 1 and Table 1 require c<0 with k=1/c, but then log(1/c) is undefined over the reals and the standard Lorentz hyperboloid condition is not met. Thus no value of c makes the paper's description internally consistent: a negative c makes the algorithm's log factor undefined, and c=1.0 makes the curvature-aware transition inert. Because no code is released, the reported 3–11% gains cannot be attributed to the stated hyperbolic SSM; they may come from an implementation that silently uses a different curvature or a different discretization. This is an internal inconsistency, not a disagreement with external consensus.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"HMamba proposes to combine Mamba-style selective state space models with hyperbolic geometry for sequential recommendation. The paper defines a Lorentz-model embedding layer, a 'hyperbolic selective state space' with curvature-aware discretization, gyrovector processing, and two model variants (HMamba-Full and HMamba-Half), and reports 3–11% improvements over baselines on ML-1M, New York, California, and Texas datasets. It also provides complexity analysis and several theoretical guarantees (Theorems 2.1–2.4 and Corollary 2.5). The central claim is that adding hyperbolic structure to Mamba yields consistent accuracy gains while retaining linear-time efficiency.","tokens_in":22619,"tokens_out":5796,"duration_ms":56093,"significance":"If the central claim were correct, the paper would introduce a useful architectural direction: extending selective state space models beyond Euclidean geometry for hierarchical sequential data. The idea is timely, and the paper explicitly positions itself against both Transformer-based and Euclidean-Mamba recommenders. The authors also ship a reasonable set of baselines and datasets. However, the paper is not currently publishable because the method's core mathematical formulation is internally inconsistent: the curvature parameter is defined as c < 0 but set to c = 1.0 in the experiments, the discretized transition matrix degenerates to the identity under that setting, the hyperbolic loss function has contradictory sign conventions, and the theoretical guarantees rely on unconstructed constants. The empirical comparison is also underspecified. These are not presentational issues but load-bearing defects that prevent attribution of the reported gains to the claimed hyperbolic mechanism.","major_comments":[{"comment":"The curvature parameter is internally inconsistent. §2.1 and Table 1 define the hyperbolic space with c < 0 and set k = 1/c, so k < 0. With k < 0, the factors √k appearing in Eqs. (2), (11), and (17) are imaginary, and log(1/c) in Algorithm 1 line 12 is undefined over the reals. In §3.1.4 the paper instead sets c = 1.0, for which log(1/c) = 0; Algorithm 1 line 12 then gives \\bar A = exp(ΔA·0) = I, and the K(k) factor in Eq. (13) is the identity. Thus no value of c makes the equations both well-defined and curvature-active: a negative c makes the algorithm's log factor undefined, while c = 1.0 makes the curvature-aware transition inert. The reported 3–11% improvements therefore cannot be attributed to the stated hyperbolic selective state space mechanism.","section":"§2.1/§3.1.4/Algorithm 1"},{"comment":"The hyperbolic loss is not a valid training objective as written. Eq. (17) defines dL with an explicit negative sign relative to the distance in Eq. (2), making the 'distance' non-positive, and Eq. (18) then sets Lfull = -2k - 2·dL. With the positive distance from Eq. (2), minimizing Lfull would drive the distance to +∞; with the signed quantity from Eq. (17), the loss is proportional to the magnitude but the notation is contradictory. Additionally, Eq. (17) uses '⊗' for elementwise multiplication where the Lorentz inner product is required, and the subscript/superscript placement (e.g., 'ˆ(E_u^h, E_w^h)') is not standard. The objective needs to be re-derived and stated with consistent sign conventions.","section":"§2.5, Eqs. (17)–(18)"},{"comment":"The formula labeled 'Möbius Gyrovector product' is actually the standard Möbius addition formula for gyrovector spaces, not a product operation. As written, Eq. (14) applies this operation to an SSM output and a SiLU-projected linear transformation, but no definition is given for how these real-valued vectors are mapped to the hyperboloid H^{d+1}_k or how the operation should be interpreted as a layer. This makes the gyrovector processing layer ill-defined and not implementable from the text.","section":"§2.4, Eq. (14)"},{"comment":"The theoretical guarantees are vacuous as stated. The constants C1–C10 are never constructed or bounded, and the proofs never connect them to the model's hyperparameters (A, B, C, Δ, c). Theorem 2.3's proof is a generic covering-number and Rademacher-complexity argument that does not reference the proposed architecture, so the sample-complexity bound cannot be instantiated. Theorem 2.1's proof uses Eq. (23), but Eq. (23) is trivially zero because \\bar A = exp(ΔA) by definition in Eq. (5). These results do not establish the claimed sample-efficiency or convergence properties of HMamba.","section":"§2.7, Theorems 2.1–2.4 and Corollary 2.5"},{"comment":"The evaluation protocol is underspecified and the headline improvement range is not supported by the reported numbers. No data-split strategy, negative-sampling scheme, or number of random restarts is given, although HR@10, NDCG@10, and MRR@10 all depend on the candidate set used for evaluation. Table 4 marks results with '*' for p-value < 0.01, but no significance test, standard deviation, or number of runs is reported. Moreover, the abstract's '3–11% improvement' claim is inconsistent with Table 4: HMamba-Full improves over the best baseline by only 0.9% HR@10 on New York and 2.5% on California, while on New York HR@10, HMamba-Half ties Mamba4Rec at 0.0544. The experiments need a clearly specified protocol and a presentation of results that matches the claimed range.","section":"§3.1.3/§3.2"}],"minor_comments":[{"comment":"The manuscript contains numerous typos and formatting errors, including 'frequently' for 'frequently' (Table 1 caption), 'Varnilla Mamba' for 'vanilla Mamba' (§3.2), and 'fraquently' for 'frequently' (§2.2); a thorough proofreading pass is needed.","section":"Throughout"},{"comment":"The caption says 'the second corresponds to an unspecified region,' but both subplots are labeled 'Texas'; the caption and the figures are inconsistent.","section":"Figure 3 caption"},{"comment":"The ablation study in Figure 4 reports 'EMamba,' but EMamba is not defined in §3.1.2 and does not appear in Table 4; the variant should be defined and its results reported in a consistent table.","section":"§3.3/Table 4"},{"comment":"The expression for \\bar B, ΔA^{-1} exp(ΔA)·ΔB, is not the standard zero-order-hold discretization; the usual formula is (ΔA)^{-1}(exp(ΔA) − I)ΔB. Please correct the formula or explicitly state the convention.","section":"Eq. (5)"},{"comment":"The notation in the theorems is informal: the norm ∥·∥_H, the domain of F, and the relationship between Y and the model output are never precisely defined, and the angle-bracket markup (e.g., in Eq. (17)) appears to be leftover LaTeX formatting.","section":"Theorems 2.1–2.4"}],"recommendation":"reject","confidential_remarks":"This manuscript reads as an incomplete draft: the notation and equations change between sections, the curvature parameter setting in §3.1.4 makes the central mechanism degenerate or undefined, and the loss and gyrovector operations are not consistently defined. The issues are load-bearing rather than cosmetic, and no code is provided to resolve the ambiguity. I would not encourage resubmission without a fundamentally rewritten method section and a complete, well-documented experimental protocol."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: HMamba is the first Mamba-plus-hyperbolic combination for sequential recommendation I've seen in the cited literature, and the two-variant design is sensible. But there is a load-bearing inconsistency in the core mechanism, and without code or evaluation details, the reported 3-11% gains are not yet evidence.\n\nWhat's genuinely new: the idea of putting selective SSMs inside the Lorentz model, with a fully hyperbolic variant and a half-hyperbolic variant, plus an ablation against an Euclidean variant (EMamba). The experiments span four datasets, use standard HR/NDCG/MRR, and include a hyperparameter study. That is a reasonable empirical skeleton.\n\nThe soft spots are not minor. Section 2.1 and Table 1 define curvature c < 0 and k = 1/c. Algorithm 1 line 12 computes \\bar A = exp(\\Delta A * log(1/c)), and Section 3.1.4 fixes c = 1.0. Then log(1/c) = 0, so \\bar A = I and the curvature-adjusted transition is inert. The other formula in Eq. (13), \\bar A = exp(\\Delta A * K(k)) with K(k) = diag(sqrt|k|,1,...,1), is also the identity at k=1. No value of c makes the description coherent: a negative c makes log(1/c) undefined over the reals, while c=1 makes the mechanism vanish. The complexity table's log(1/c) factor is zero at the reported setting. Since no code is released, we cannot guess what was actually implemented; whatever ran is not the mechanism the paper derives.\n\nThe empirical section also omits split and negative-sampling details, and the 3-11% gains are against a single run of Mamba4Rec without code. The theoretical guarantees are mostly decoration: constants C1-C10 are never constructed, and the sample-complexity proof is a generic covering/Rademacher argument not tied to the architecture. Theorem 2.4 is a known hyperbolic-embedding result repackaged.\n\nCredit where due: the ablation with EMamba is a good idea, and the authors correctly include Mamba4Rec and HSASRec as baselines. The related work is engaged with the immediate literature.\n\nBottom line: as submitted I would desk reject. The central mechanism is internally inconsistent, not just missing empirical support. If the authors fix the curvature/log issue (or say what curvature they really used), release code, and spell out the evaluation protocol, the combination could become a publishable paper. Until then, the main claim is not attributable to hyperbolic geometry.","headline":"Clever combination of Mamba and hyperbolic geometry, but the paper's own math makes the curvature-aware mechanism vanish at the stated hyperparameter, so the empirical claim is unattributable as submitted.","tokens_in":23069,"tokens_out":3228,"would_cite":false,"duration_ms":32037,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"HMamba runs Mamba's selective state space on a hyperbolic manifold and claims 3-11% accuracy gains over Euclidean and attention-based sequential recommenders at linear-time cost.","keywords":["sequential recommendation","hyperbolic geometry","state space models","Mamba","Lorentz model","hierarchical representation learning","recommender system efficiency","next-item prediction"],"falsifier":"Run HMamba-Full on ML-1M and Texas with $c=-1$ (negative curvature) and $c=+1$ (positive curvature) under identical hyperparameters and compare HR@10 and NDCG@10; if negative curvature does not improve on positive curvature, or if the positive-curvature run reproduces the reported gains, the claim that hyperbolic geometry drives the results is falsified.","tokens_in":21981,"feed_emoji":"📐","tokens_out":6576,"duration_ms":65803,"temperature":0.7,"pith_summary":"The paper argues that recommendation histories carry a hierarchical structure—genres over items, categories over genres—that Euclidean sequence models flatten, and that Mamba's selective state-space machinery is the right vehicle to exploit that hierarchy if it is run on a hyperbolic manifold instead of in Euclidean space. It proposes HMamba, which lifts item embeddings into the Lorentz model of hyperbolic space, performs curvature-aware discretization of the state-space matrices, mixes features with Möbius gyrovector operations, and scores candidates by hyperbolic distance. On four benchmarks, including ML-1M and three location datasets, the authors report 3-11% improvements over state-of-the-art baselines, with fewer parameters and roughly 3.2x faster training than attention-based recommenders. A hybrid variant that processes in hyperbolic space but scores in Euclidean space performs in between, which the paper reads as evidence that the geometric component, not the extra parameters, drives the gains.","feed_headline":"Hyperbolic Mamba lifts recommendation accuracy by 3-11%","feed_subtitle":"Lorentz-geometry state space claims hierarchy-aware, linear-time next-item prediction","key_machinery":"The load-bearing object is the Lorentz model of hyperbolic space, $H^d_k = \\{x \\in \\mathbb{R}^{d+1} : \\langle x,x\\rangle_L = -k,\\ x_0>0\\}$, with curvature parameter $k=1/c$ and Lorentz inner product $\\langle x,y\\rangle_L = -x_0y_0 + \\sum_j x_jy_j$. The construction depends on three operations that keep the state-space model geometrically consistent: the exponential map $\\exp_o(v)$ projecting tangent vectors onto the manifold, parallel transport that preserves Lorentz orthogonality during hidden-state updates, and the Möbius gyrovector product used for nonlinear feature mixing. The curvature-aware discretization $\\bar A = \\exp(\\Delta A \\odot \\operatorname{diag}(\\sqrt{|k|},1,\\dots,1))$ is the step that nominally imports the geometry into the state-space dynamics, and the complexity analysis attaches a $\\log(1/c)$ factor to it. Together these operations let the hidden state evolve along the manifold instead of in a flat ambient space, which is what the paper claims preserves tree-like preference hierarchies.","core_discovery":"HMamba is a sequential recommender whose encoder is a Mamba selective state-space model transplanted onto the Lorentz hyperboloid $H^d_k$ rather than Euclidean space. The pipeline is: zero-pad Euclidean item embeddings to $\\mathbb{R}^{d+1}$, apply the exponential map at the origin to obtain points on the hyperboloid, evolve the hidden state through a curvature-aware discretization $\\bar A = \\exp(\\Delta A \\odot \\operatorname{diag}(\\sqrt{|k|},1,\\dots,1))$ with parallel transport preserving Lorentz orthogonality, mix features through Möbius gyrovector products, and score the next item by hyperbolic distance to item embeddings lifted onto the same manifold. HMamba-Full performs both representation and scoring in hyperbolic space; HMamba-Half returns to Euclidean space for scoring. The paper's central discovery claim is that this geometric relocation consistently improves next-item prediction over Euclidean Mamba, attention transformers, and the previous hyperbolic attention model HSASRec across four datasets, with the largest margins on the sparser location datasets, while retaining Mamba's linear-time complexity.","pith_inferences":["A fair test of the paper's geometric claim would run HMamba-Full with a genuinely negative curvature constant and compare it against a positive-curvature setting; the reported implementation fixes $c=1.0$, which makes $k=1$ and leaves the Lorentz form with a signature different from the one the paper's theory describes.","If the curvature parameter is not actually negative in the reported configuration, the 3-11% gains could be attributable to the Mamba-style architecture rather than to hyperbolic geometry, and the EMamba ablation is consistent with that reading.","A testable extension is to sweep $c$ across negative values and check whether gains correlate with $|c|$, which would isolate the curvature mechanism from the architectural mechanism.","The complexity argument's $\\log(1/c)$ overhead term vanishes at $c=1$, so the paper's complexity comparison implicitly assumes a different curvature setting from the one used in its experiments."],"forward_implications":["If HMamba's reported gains hold, sequential recommenders can reach or exceed attention-based accuracy while scaling linearly with sequence length, making very long user histories practical in production.","The Full-versus-Half performance gap implies that scoring in hyperbolic space, not just representing in it, contributes part of the accuracy gain.","HMamba would extend selective state-space modeling beyond recommendation to any sequence with intrinsic taxonomy, such as clinical event histories or inventory movements, as the paper itself suggests.","The ablation against EMamba indicates that the architectural refinements help even in Euclidean space, so the hyperbolic component is the marginal difference that the paper credits for the improvement."],"supporting_citations":[{"why":"Supplies the selective state-space backbone that HMamba relocates into hyperbolic space.","marker":"[9]"},{"why":"Provides the Euclidean Mamba baseline whose accuracy and efficiency HMamba must beat.","marker":"[17]"},{"why":"Prior hyperbolic sequential recommender built on self-attention; the main hyperbolic comparison baseline.","marker":"[7]"},{"why":"Source of the Lorentz model formulation and its stability advantages, which the method relies on.","marker":"[22]"},{"why":"Cited as foundation for the Lorentz-model exponential map and hyperbolic embedding construction.","marker":"[30]"},{"why":"Supports the claim that hyperbolic spaces embed hierarchies with $O(\\log h)$ dimensions, underpinning the parameter-efficiency theorem.","marker":"[8]"}],"fun_headline_variants":["Hyperbolic Mamba: 3-11% better recommendations, linear time","Curved-space Mamba: 3-11% recommendation gains","Linear-time hyperbolic recommender boosts accuracy 3-11%","Hyperbolic Mamba: efficiency plus geometry for recommendations"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the model is actually operating in a constant-negative-curvature hyperbolic space; the paper defines $c<0$ but fixes $c=1.0$ in its experiments, and if the implemented geometry is not the negative-curvature one, the source of the reported gains is unproven.","fun_headline_variants_meta":{"raw":{"variants":["Hyperbolic Mamba: 3-11% better recommendations, linear time","Curved-space Mamba: 3-11% recommendation gains","Linear-time hyperbolic recommender boosts accuracy 3-11%","Hyperbolic Mamba: efficiency plus geometry for recommendations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000999,"raw_usage":{"total_tokens":4234,"prompt_tokens":953,"completion_tokens":3281,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":569,"completion_tokens_details":{"reasoning_tokens":3208}},"tokens_in":569,"tokens_out":3281,"duration_ms":23612,"temperature":1.0,"reasoning_tokens":3208,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:37:00.571569+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run HMamba-Full on ML-1M and Texas with $c=-1$ (negative curvature) and $c=+1$ (positive curvature) under identical hyperparameters and compare HR@10 and NDCG@10; if negative curvature does not improve on positive curvature, or if the positive-curvature run reproduces the reported gains, the claim that hyperbolic geometry drives the results is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior hyperbolic sequential recommender built on self-attention; the main hyperbolic comparison baseline."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Source of the Lorentz model formulation and its stability advantages, which the method relies on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Cited as foundation for the Lorentz-model exponential map and hyperbolic embedding construction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports the claim that hyperbolic spaces embed hierarchies with $O(\\log h)$ dimensions, underpinning the parameter-efficiency theorem."}],"review_version":1}