{"id":"503a42ad-c5ea-4a9b-8c4d-fb8a99c82fe4","arxiv_id":"2502.05869","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"HyLiFormer applies hyperbolic embedding and a reordered linear attention to skeleton action recognition, achieving linear complexity with accuracy slightly below the best transformer baselines.","lead":"This paper introduces HyLiFormer, a transformer variant that embeds skeleton data into hyperbolic space and uses a linear attention mechanism to cut quadratic complexity to linear. The experiments on NTU RGB+D and NTU RGB+D 120 report competitive but not state-of-the-art accuracy with reduced training time.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"HLA's Eq. 13 is asserted, not derived: shifted raw-input Q/K/V and an undefined Sim leave the claimed O(NF^2) attention and its accuracy/efficiency trade-off unsupported.","rationale":"The reader identifies the same load-bearing weak point: Eq. 13 is not derived from Eq. 11 and the QKV definitions are unexplained shifted copies. My stress test confirms this is the central load-bearing concern because every theoretical and experimental claim (O(NF^2) complexity, hyperbolic constraint preservation, accuracy/efficiency) is channeled through HLA. The other objections (below-baseline accuracy, no released code) are secondary; even if those were fixed, Eq. 13 would still have to be justified. The proposed check is a direct symbolic derivation from Eq. 11; if it fails, the paper's main contribution is unsupported and the reject verdict stands. I am not raising a novelty objection or questioning the authors' intent; the issue is internal correctness of the central equation.","tokens_in":11859,"tokens_out":5809,"duration_ms":60158,"concrete_test":"Independently re-derive Eq. 13 from Eq. 11 with the paper's stated definitions (Q=x[1:], K=x[2:], V=x[3:], phi(x)=exp(x)): write both sides with explicit per-position indices and check whether the right side equals the normalized weighted sum in Eq. 11 for arbitrary input tensors. Because Eq. 13 contains no summation over j and no projection matrices, the derivation must introduce at least one assumption not stated in the paper; if it does, replace HLA with a parameter-free shifted-gating baseline (y_i = x_{i+1} * f(x_{i+2})) and compare NTU-60 X-Sub accuracy. If the gating baseline reproduces ~91.7%, the reported results do not demonstrate a linear-attention mechanism.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Contributions (2) and (3) rest entirely on Eqs. 12–13 being a legitimate linear-attention reformulation of Eq. 11. That premise fails for three concrete reasons. (i) Eq. 12 defines Q, K, V as shifted copies of the raw input — there is no W_Q, W_K, or W_V anywhere in HLA, so the module contains no learned similarity and is not 'consistent with traditional self-attention' as claimed. (ii) Eq. 13, V_i = Q_i * Sim(K_j^T * V_j), never defines the index j, the summation, the kernel phi, or how Sim turns key-value pairs into a fixed-size representation; the later statement 'phi(x)=exp(x)' is not a linear-attention kernel and no algebra connects Eq. 13 to Eq. 11. A charitable reading as global-covariance linear attention, Q_i * sum_j K_j^T V_j, would give O(NF^2), but it still requires explicit summation, normalization, and projected Q/K/V that the paper does not provide. (iii) Lemma 4.2 proves the Poincare bound by assuming the very property in question: that Sim outputs have norm 1 and lie in (-1,1). Because the theoretical complexity reduction, the hyperbolic-constraint proof, and the experimental accuracy all pass through Eq. 13, the central claim collapses if Eq. 13 is not a derived attention mechanism. If Eq. 13 is instead a temporal gating or shift operation, the paper's claimed first hyperbolic linear attention is not what was evaluated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes HyLiFormer, a skeleton-based action recognition transformer that first maps skeleton data into the Poincaré ball via a Hyperbolic Transformation with Curvatures (HTC) module and then applies a Hyperbolic Linear Attention (HLA) module claimed to reduce self-attention complexity from O(N^2) to O(N F^2). The central claims are that HLA is the first linear attention mechanism in the Poincaré model, that it provably keeps outputs in the Poincaré ball, and that it preserves accuracy while reducing computational cost. Experiments are reported on NTU RGB+D and NTU RGB+D 120, with ablations over curvature and comparisons to RWKV and Mamba baselines.","tokens_in":12175,"tokens_out":4783,"duration_ms":40418,"significance":"The motivation is relevant: efficient transformers for skeleton data are useful, and hyperbolic embeddings are a natural fit for hierarchical structure. The paper provides a clear problem statement, a full experimental section, and ablations over design choices. However, the significance rests entirely on the validity of Eqs. (12)-(13) as a linear-attention reformulation and on Lemma 4.2. As detailed below, these are not established; the HLA module as written is an undefined operation rather than an attention mechanism. With the central derivation unsound, the claimed efficiency-accuracy trade-off and the 'first hyperbolic linear attention' claim are not supported.","major_comments":[{"comment":"The query, key, and value matrices are defined in Eq. (12) as shifted slices of the raw input (Q=x[1:], K=x[2:], V=x[3:]) with no learned projection matrices. This is not 'consistent with the traditional self-attention mechanism' as stated, since Eq. (11) requires W_Q, W_K, W_V projections; with raw shifted inputs, the module cannot compute a learned similarity between tokens.","section":"Section 4.2, Eq. (12)"},{"comment":"Eq. (13) is asserted rather than derived from Eq. (11). It contains no index j, no summation, no normalization, and no definition of Sim(K_j^T V_j); the later remark that phi(x)=exp(x) is used as a kernel does not explain how this equation aggregates key-value pairs or avoids the N x N attention matrix. A charitable reading as global covariance, Q_i * sum_j K_j^T V_j, would require explicit projection, summation, and normalization that the paper does not provide, so the claimed O(N F^2) complexity is not demonstrated.","section":"Section 4.2, Eq. (13)"},{"comment":"Lemma 4.2 is circular. The proof assumes that Sim(...) 'is designed such that it preserves hyperbolic distances and results in outputs bounded by (-1,1)' and that ||Q_i|| < -1/kappa, exactly the facts needed to conclude ||V_i|| < -1/kappa. No concrete Sim with the required properties is constructed, so the lemma does not provide a proof that the HLA output stays in the Poincaré ball.","section":"Section 4.2, Lemma 4.2"},{"comment":"The complexity claim is internally inconsistent: the abstract and conclusion say O(N), while Section 4.2 says O(N F^2). More importantly, Table 1 shows HyLiFormer underperforms SkateFormer on X-Sub60 (91.7 vs 92.6) and X-Set120 (88.6 vs 89.3), so the claim of 'preserving model accuracy' is not supported without an ablation comparing to a quadratic-attention version of the same architecture.","section":"Abstract, Section 4.2, Table 1"}],"minor_comments":[{"comment":"The notation for V is overloaded: V is used both for the value matrix in Eq. (12) and for the output in Eq. (13)-(14), which makes the derivation hard to follow.","section":"Section 4.2"},{"comment":"Eq. (10) writes x^B_kappa = -1/kappa * tanh(-kappa ||x||) * hat x, but the factor -1/kappa is positive for kappa < 0; the authors should clarify the sign convention or use a simpler form.","section":"Section 4.1, Eq. (10)"},{"comment":"The paper states 'It is rigorously proved' before both lemmas, but the proofs are informal and the second is circular; the wording should be adjusted to match the actual level of rigor.","section":"Section 4.1-4.2"},{"comment":"The training details are incomplete: no batch size, number of epochs, optimizer settings, or learning rate schedule are given, and the statement that 'the learning rate varies across datasets' is not quantified.","section":"Section 5.2"},{"comment":"Some references appear mismatched: the HyperFormer cited as [8] is a hypergraph transformer, while the hyperbolic vision transformer from [12] is a more relevant baseline for the claims; the comparison in Table 1 should be clarified.","section":"References and Table 1"}],"recommendation":"reject","confidential_remarks":"The paper has the form of a preliminary conference submission and would need major restructuring before journal review. Of particular concern is that the core theoretical claims (Eq. 13 and Lemma 4.2) are unsupported, and the experimental evaluation does not include a quadratic-attention baseline of the same model, so the efficiency-accuracy claim cannot be evaluated. I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know up front. The paper's headline claim—that Eq. 13 reduces self-attention to O(NF²)—is exactly where the argument breaks. Eq. 13 is asserted, not derived; it never defines the index j, the summation, or the kernel that would connect it to Eq. 11. And the experiments actually place the model below the strongest baseline (SkateFormer) on both X-Sub protocols, so the 'preserving accuracy' part of the trade-off isn't demonstrated either.\n\nWhat's genuinely useful here: the motivation is sound and the direction is worth pursuing. Skeleton data is hierarchical, linear attention is attractive for long sequences, and the Poincaré model is a natural place to try to combine the two. The HTC module, which maps Euclidean input into the Poincaré ball via unit vectors and tanh scaling, is straightforward and clearly described. The ablations against RWKV and Mamba, both in Euclidean and hyperbolic form, give a fair picture of the baseline difficulties. That part is honest and reproducible in spirit.\n\nThe soft spots are concentrated in Section 4.2. Eq. 12 defines Q, K, V as shifted slices of the same input (x[1:], x[2:], x[3:]); there are no learned projections, so this is not 'consistent with traditional self-attention' as claimed. Eq. 13, V_i = Q_i · Sim(K_j^T · V_j), has no defined summation or kernel. The text says φ(x)=exp(x), but that is a softmax-style kernel, not a linear-attention kernel, and no algebra connects it to Eq. 11. The complexity claim therefore rests entirely on an undefined reformulation. Lemma 4.2 is circular: it proves the Poincaré bound by asserting that Sim is 'designed such that' its outputs are bounded in (-1,1) and norm 1—the very property at issue. A charitable reading of Eq. 13 as a global-covariance form, Q_i · Σ_j K_j^T V_j, could give O(NF²), but the paper doesn't provide that derivation, the normalization, or the projections.\n\nThe experimental section is also thinner than it looks. The training time comparison shows HyLiFormer faster than SkateFormer, but accuracy is lower; there's no head-to-head comparison with a proper quadratic-attention transformer at matching settings, and no code. The claimed 'significant reduction in computational complexity' is never demonstrated with actual FLOPs or memory measurement; the paper only gives theoretical counts.\n\nBottom line: the research direction is plausible, and the authors have identified a real gap, but the central mechanism is not well-enough specified to validate. I would not send this to a serious referee in its current form. It needs a genuine derivation of the kernel, a valid definition of Q/K/V, and release of code and configs before it's reviewable. If those are fixed, it could be a solid contribution to the efficient-skeleton-transformer line.","headline":"Well-motivated but broken at the one equation that matters: Eq. 13 is asserted, not derived, so the claimed linear hyperbolic attention is unsupported.","tokens_in":12704,"tokens_out":3872,"would_cite":false,"duration_ms":34715,"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":"HyLiFormer claims that moving skeleton features into a Poincaré ball lets a transformer run attention in linear time while keeping accuracy close to quadratic-attention models.","keywords":["Skeleton-based action recognition","Hyperbolic geometry","Poincaré model","Linear attention","Transformer efficiency","NTU RGB+D","Hierarchical sequence modeling"],"falsifier":"The decisive check is an ablation that replaces the similarity kernel $\\mathrm{Sim}$ in Eq. (13) with a fixed scalar (or replaces $Q,K,V$ with identical shifted copies) and measures accuracy on NTU RGB+D 120 X-Sub; if accuracy does not drop, the HLA module is not computing attention and the claimed linear-attention mechanism is not what carries the performance.","tokens_in":11599,"feed_emoji":"🦴","tokens_out":13379,"duration_ms":110167,"temperature":0.7,"pith_summary":"The paper sets out to show that skeleton-based human action recognition can be done by a transformer whose attention cost grows linearly with sequence length rather than quadratically, without giving up the accuracy that quadratic-attention transformers provide. Its route is to embed the skeleton data in a Poincaré ball and define the attention operation entirely inside that hyperbolic space. The proposed HyLiFormer first maps Euclidean skeleton features into hyperbolic space (HTC), applies a newly defined Hyperbolic Linear Attention (HLA) that never forms the $N{\\times}N$ similarity matrix, and maps back to Euclidean space. Reported results on NTU RGB+D and NTU RGB+D 120 put HyLiFormer at 91.7/96.2% and 87.5/88.6% for the two protocols, with 3.7 minutes per epoch and 1.9M parameters, close to or above several quadratic-attention baselines. A sympathetic reading is that this is the first linear attention defined inside the Poincaré model for skeleton data.","feed_headline":"Hyperbolic linear attention cuts skeleton transformer cost to linear","feed_subtitle":"HyLiFormer maps joints into a Poincaré ball, dropping quadratic attention cost while keeping accuracy.","key_machinery":"The load-bearing object is the HLA reformulation in Eqs. (12)–(13): $Q$, $K$, $V$ are taken as shifted slices of the same input, and the output is $V_i = Q_i \\cdot \\mathrm{Sim}(K_j^T V_j)$, with $\\mathrm{Sim}$ chosen as an exponential kernel. This reordered computation aggregates key–value pairs into a fixed-size vector in feature space, avoiding the $O(N^2)$ similarity matrix. The companion HTC embedding, $x^{\\mathcal{B}} = -\\frac{1}{\\kappa}\\tanh(-\\kappa\\|x\\|)\\cdot \\frac{x}{\\|x\\|}$, is what places the data in the Poincaré ball and encodes hierarchy through the tanh compression of magnitudes. Lemmas 4.1 and 4.2 are the arguments that the output of each module respects the Poincaré ball constraint, which is what allows the model to claim it is genuinely operating in hyperbolic space.","core_discovery":"The paper's central claim is that the Poincaré model can host a linear attention mechanism that is both well-defined and accurate for skeleton data. The HTC module converts each skeleton point via $\\mathbf{x}^{\\mathcal{B}} = -\\frac{1}{\\kappa}\\tanh(-\\kappa\\|\\mathbf{x}\\|)\\cdot \\frac{\\mathbf{x}}{\\|\\mathbf{x}\\|}$, and the HLA module then sets $Q=\\mathbf{x}[1:]$, $K=\\mathbf{x}[2:]$, $V=\\mathbf{x}[3:]$ and computes $V_i = Q_i \\cdot \\mathrm{Sim}(K_j^T V_j)$ with a softmax/exponential kernel, so the $N{\\times}N$ similarity matrix is never materialized. Lemmas 4.1 and 4.2 assert that both transformations keep points inside the Poincaré ball, and the complexity statement is reduced from $O(N^2F)$ to $O(NF^2)$. The experiments on NTU RGB+D and NTU RGB+D 120 are offered as evidence that this efficiency comes with only a small accuracy cost relative to quadratic-attention transformers.","pith_inferences":["An implicit consequence of Eqs. (12)–(13) is that the HLA module contains no learned query/key/value projections, so the parameter savings relative to standard attention come partly from removing those projection matrices; the paper does not isolate this effect.","Because $Q,K,V$ are just shifted copies of the input, the operation in Eq. (13) resembles a temporal shift-and-gate more than a similarity-based attention; testing this directly would require an ablation the paper does not report.","The same HTC+HLA recipe could be transferred to other hierarchical sequence tasks such as motion prediction or point-cloud sequences, where the 'linear attention in hyperbolic space' claim would be testable in a new setting.","The curvature choice $\\kappa=-1$ is found by a small grid search on one dataset protocol; a learned or per-dataset curvature could shift the accuracy-efficiency frontier."],"forward_implications":["Self-attention cost drops from $O(N^2F)$ to $O(NF^2)$; for fixed feature dimension $F$ the cost is linear in sequence length, which is the paper's headline efficiency result.","Because HLA avoids the $N{\\times}N$ attention matrix, longer skeleton sequences can be processed with a fixed memory footprint per token, making transformer-based recognition practical on a single GPU.","Reported training time is 3.7 minutes per epoch with 1.9M parameters, versus 5.0 minutes per epoch and 2.0M parameters for the SkateFormer baseline and 8.8 minutes per epoch for STTFormer, so the claimed efficiency is concrete on the NTU benchmarks.","Accuracy remains within roughly one point of the best quadratic-attention transformer on each reported protocol, so the method is offered as an efficiency-accuracy trade-off rather than a pure accuracy gain."],"supporting_citations":[{"why":"supplies the focused linear-attention reformulation that HLA adapts to hyperbolic space.","marker":"[15]"},{"why":"provides the hyperbolic Möbius scalar multiplication and tanh-based transformations used by HTC.","marker":"[13]"},{"why":"gives the kernel view of attention that motivates the exponential similarity function in HLA.","marker":"[27]"},{"why":"is the RWKV linear-attention baseline that the paper compares against in Tables 3 and 4.","marker":"[21]"},{"why":"is the Mamba SSM baseline used in the same comparisons and in the hyperbolic-space limitations discussion.","marker":"[14]"},{"why":"supplies the experimental framework, optimizer, and SkateFormer baseline for the NTU benchmarks.","marker":"[9]"},{"why":"is the closest prior hyperbolic vision transformer applied to skeleton data, which the paper positions against.","marker":"[12]"}],"fun_headline_variants":["Hyperbolic attention makes skeleton transformers linear-time","Poincare ball linear attention speeds skeleton recognition","Hyperbolic space cuts skeleton transformer cost to linear","Skeleton action recognition goes linear with hyperbolic attention","Linear-time hyperbolic attention for skeleton actions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on Eq. (13) being a genuine attention mechanism with the same modeling power as softmax attention; if that premise is false, the HLA module is a temporal shift or gating operation and the central contribution collapses.","fun_headline_variants_meta":{"raw":{"variants":["Hyperbolic attention makes skeleton transformers linear-time","Poincare ball linear attention speeds skeleton recognition","Hyperbolic space cuts skeleton transformer cost to linear","Skeleton action recognition goes linear with hyperbolic attention","Linear-time hyperbolic attention for skeleton actions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000555,"raw_usage":{"total_tokens":2639,"prompt_tokens":934,"completion_tokens":1705,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":550,"completion_tokens_details":{"reasoning_tokens":1638}},"tokens_in":550,"tokens_out":1705,"duration_ms":13884,"temperature":1.0,"reasoning_tokens":1638,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T17:36:55.189494+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"The decisive check is an ablation that replaces the similarity kernel $\\mathrm{Sim}$ in Eq. (13) with a fixed scalar (or replaces $Q,K,V$ with identical shifted copies) and measures accuracy on NTU RGB+D 120 X-Sub; if accuracy does not drop, the HLA module is not computing attention and the claimed linear-attention mechanism is not what carries the performance.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the hyperbolic Möbius scalar multiplication and tanh-based transformations used by HTC."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the experimental framework, optimizer, and SkateFormer baseline for the NTU benchmarks."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"is the closest prior hyperbolic vision transformer applied to skeleton data, which the paper positions against."}],"review_version":1}