{"id":"21401e1a-31ef-4a17-95f3-e16f28d71ac5","arxiv_id":"2506.05826","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"HBCT lifts embeddings into Lorentz hyperbolic space, uses entailment cones to keep new embeddings inside old ones' cones, and weights contrastive alignment by an uncertainty estimate, improving backward-compatible retrieval in experiments.","lead":"This paper proposes a training method, HBCT, that uses hyperbolic geometry to make a new embedding model retrieve directly from a database of old-embedding vectors, aiming to avoid re-indexing stored data. It reports large compatibility gains on CIFAR100 and TinyImageNet, but the experiments lack error bars and select hyperparameters on test metrics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The core uncertainty mechanism (Eq. 10) is unvalidated: if hyperbolic norm does not track per-sample old-model error, the adaptive weighting that motivates HBCT is miscalibrated and the claimed compatibility gains cannot be attributed to it.","rationale":"The reader's weakest_assumption is exactly the load-bearing concern: Eq. (10) is borrowed from prior segmentation and action-recognition work without task-specific validation that the Lorentz-norm proxy tracks old-model uncertainty in a retrieval-compatibility setting. The paper's contribution is not merely 'hyperbolic geometry helps'; it is that the time-like dimension supplies calibrated uncertainty that lets alignment adapt. If that premise fails, HBCT collapses to a hyperbolic contrastive method with a fixed q plus an entailment penalty, and the headline numbers lose their mechanistic explanation. The appendix ablates curvature, clipping, alignment weight, temperature, and distance function, but no experiment measures whether Uncertainty(h_o) predicts old-model mistakes per sample. The experimental protocol issues raised by the reader (test-set hyperparameter selection for baselines, no error bars) are serious secondary concerns, but the uncertainty-calibration gap is more specific to the central argument. A per-sample calibration analysis and a random-q control would either validate the mechanism or show the gains come from other components; until then, the conditional verdict is appropriate.","tokens_in":18628,"tokens_out":12812,"duration_ms":139161,"concrete_test":"Run the released code on the CIFAR100 extended-class split. For every old gallery/query embedding, record Uncertainty(h_o) and a ground-truth per-sample error proxy, e.g., whether the old model's nearest-neighbor retrieval for that item is correct, or its hyperbolic softmax confidence. Compute the Spearman rank correlation between Uncertainty(h_o) and old-model error, separately for seen and unseen classes. Then perform a direct causal control: permute the q(ho) values across samples so the marginal distribution of q is unchanged but the assignment to old embeddings is random; if Pcom with permuted q matches the true-q result within seed noise (≥3 seeds), the proposed uncertainty-aware weighting is not the source of the reported compatibility gains.","verdict_should_be":"UNCHANGED","load_bearing_attack":"HBCT's novelty rests on q(ho)=Uncertainty(ho) in Eq. (10) and Section 4.3: old embeddings with small norm are treated as uncertain, downweighted in the RINCE contrastive loss, and given wider entailment cones. But Eq. (10) is an algebraic normalization, not a calibrated estimator, and the only evidence offered is the aggregate histogram in Figure 2 showing that unseen classes have lower norms. Old-model error is per-example, not class-conditional. Because Lbase is a hyperbolic cross-entropy loss and clip ζ_o=1 shapes the norm distribution, a low norm may indicate an out-of-distribution sample, a hard example, or simply a sample near the classifier boundary; it need not correlate with the errors that actually hurt new-to-old retrieval. If the ranking induced by Uncertainty is wrong, the robust contrastive term downweights the wrong positive pairs and the entailment cone widens for the wrong items, so the reported 21.4% CMC@1 and 44.8% mAP gains are not explained by the paper's central mechanism. The ablation in Table 2 narrows but does not resolve this: the Pcom difference between RINCE and InfoNCE is only 0.495 vs 0.475, so the calibration question is more, not less, urgent.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes HBCT, a method for backward-compatible representation learning that operates in hyperbolic space (Lorentz model). The old and new embedding models are mapped to the hyperboloid, and training enforces two geometric constraints: (i) an entailment-cone loss that keeps each new embedding inside the cone defined by its old counterpart, and (ii) a robust contrastive (RINCE) loss in which the per-pair weighting exponent q is set to a hyperbolic uncertainty estimate of the old embedding (Eq. 10). The uncertainty estimate is a monotone function of the old embedding’s norm, and the paper argues that lower-norm old embeddings are less reliable, so they are downweighted and their cones are widened. Experiments on CIFAR-100 and Tiny-ImageNet across four update scenarios report that HBCT improves backward-compatibility metrics (Pcom) over Euclidean baselines, with claimed average gains of 21.4% in CMC@1 and 44.8% in mAP, at small cost to new-model performance. Ablations and appendices probe the influence of curvature, clipping thresholds, alignment weights, and distance functions.","tokens_in":18959,"tokens_out":11021,"duration_ms":105995,"significance":"If the reported gains are robust, the paper would introduce a useful new perspective: hyperbolic geometry provides a principled way to express both representation uncertainty and the ‘evolution’ of an embedding space across model updates, and the entailment cone offers a natural partial-order constraint for compatibility. The paper ships code, which aids reproducibility, and it is among the first to apply hyperbolic geometry to backward-compatible training. However, the significance is tempered by two factors: the experimental evidence comes from two small image datasets with no large-scale validation, and the central uncertainty mechanism, which is the paper’s main conceptual novelty, has only weak empirical support. The method’s gains appear to come substantially from the hyperbolic geometry/entailment constraint rather than from the uncertainty-aware weighting, and the comparison against Euclidean baselines is confounded by the use of different (and often better) hyperbolic old models. The core idea is promising and worth developing, but the current evidence falls short of establishing that the uncertainty-driven mechanism is the source of the benefits.","major_comments":[{"comment":"The uncertainty measure q(ho)=1-(1/sqrt(K))tanh(sqrt(K)||z||) is used per-sample to set the RINCE exponent in Eq. (12) and to widen entailment cones via Eq. (11), but the only evidence that this quantity tracks old-model reliability is the aggregate, class-conditional histogram in Fig. 2. Old-model error is per-example: an embedding can have low norm because it is out-of-distribution, because it is a hard example, or because it lies near a classification boundary, and these cases do not necessarily coincide with the errors that actually hurt new-to-old retrieval. The authors should validate the calibration directly, for example by correlating Uncertainty(ho) with per-sample retrieval errors of the old model, or with the distance between same-class old and new embeddings. Without such evidence, the central mechanism of the paper—adaptive downweighting of unreliable old embeddings—remains an unsupported assumption.","section":"§4.1, Eq. (10), Fig. 2"},{"comment":"The headline claim that HBCT improves CMC@1 compatibility by 21.4% over the strongest Euclidean baseline is not clearly reproducible from Table 1. In the Both/TinyImageNet scenario the HBCT Pcom (0.348) is actually lower than the best Euclidean baseline Hot-Refresh (0.365), and across all eight cells the relative improvements vary from -4.7% to +53%. Moreover, Pcom as defined in Eq. (14) is not invariant to the choice of old model: its denominator M(phi*, phi*_G) - M(phi_o, phi_o_G) shrinks when the old model improves, so the stronger hyperbolic old models (e.g., 0.425 vs 0.376 on Ext-class CIFAR CMC@1) inflate Pcom even for identical absolute compatibility gains. The paper acknowledges that old models differ but claims Pcom is ‘calibrated’; it is not fully calibrated. The authors should either use the same old model across geometries (e.g., lift a Euclidean old model’s embeddings into hyperbolic space) or report raw cross-retrieval metrics with a careful sensitivity analysis.","section":"§5.1, Eq. (14), Table 1"},{"comment":"The experimental protocol has no validation split: for each Euclidean baseline, 10 hyperparameter combinations are evaluated and the run that best performs on the test metrics (subject to not degrading the new model) is selected, while HBCT’s hyperparameters are fixed based on an ablation. No error bars, standard deviations, or multiple seeds are reported. This makes it impossible to assess whether the reported margins are statistically meaningful or whether the baseline tuning procedure overfits the test set. The authors should select hyperparameters on a hold-out validation set and report mean ± std over at least three independent runs for all methods.","section":"§5.1, Implementation Details"},{"comment":"The ablation in Table 2 shows that replacing the uncertainty-weighted RINCE loss with a standard InfoNCE loss changes CMC@1 Pcom only from 0.495 to 0.475, while removing the entailment loss reduces it to 0.435. The difference attributable to the uncertainty-aware weighting (0.02) is small relative to the overall improvement over Euclidean baselines (e.g., 0.495 vs 0.360 for the best Euclidean baseline in the same setting). This suggests that the paper’s central narrative—that dynamically adjusting alignment weights based on uncertainty is the key to the gains—is not supported by the ablation. The authors should either provide additional experiments that isolate the effect of q(ho) (e.g., random or reverse uncertainty weighting) or temper the claims about the uncertainty mechanism.","section":"§5.4, Table 2"}],"minor_comments":[{"comment":"The 21.4% and 44.8% improvements are stated without a precise definition of how the average is computed across settings and datasets. Specify the aggregation rule and report the per-setting numbers.","section":"Abstract and §5.2"},{"comment":"The displayed formula for Uncertainty(h) is garbled in the manuscript, with several alignment artifacts. Please rewrite it clearly, and also clarify the relationship between the Lorentz-model expression and the Poincaré-ball uncertainty used in prior work (the factor 1/sqrt(K) appears inconsistent with the stated equivalence for K ≠ 1).","section":"§4.1, Eq. (10)"},{"comment":"The aperture constant ε is fixed to 0.1 without discussion. A one-sentence sensitivity analysis or a reference to the original derivation would help.","section":"§4.2, Eq. (11)"},{"comment":"The sequential-update experiment reports that HBCT ‘demonstrates superior compatibility maintenance’ but gives no quantitative summary of the compatibility matrices. Include the average or diagonal-to-off-diagonal decay metrics.","section":"§5.3"}],"recommendation":"major_revision","confidential_remarks":"The paper has a promising idea and the code is a strength, but the experimental validation needs substantial work: the uncertainty mechanism is not calibrated, the Pcom comparison is confounded by different old models, and the lack of error bars/test-set tuning makes the reported margins unreliable. I would push the authors to address the first two issues head-on before considering acceptance. The claim of being the first to use embedding geometry for model-update consistency is slightly overstated given prior geometric compatibility work, but that is not a blocker."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"HBCT is a sensible combination of existing ingredients—Lorentz embeddings, entailment cones, and RINCE—with a new twist: the norm of the old hyperbolic embedding is used as a per-sample uncertainty to widen the cone and downweight the contrastive alignment. The method is simple, has few hyperparameters, and reports large compatibility gains over strong Euclidean baselines across most settings. To my knowledge the specific combination is new, and the idea of treating the old embedding's norm as a quality signal in backward-compatible training is worth exploring.\n\nWhat the paper does well: the geometry is mostly careful, the entailment cone loss is borrowed from Desai et al. and applied sensibly, the RINCE-based adaptive weighting is clearly motivated, and the experiments cover four realistic scenarios including architecture change and new classes. The ablation in Table 2 shows that both the cone and the robust loss add something, though the robust loss's contribution is modest (RINCE w/ entail vs InfoNCE w/ entail: 0.495 vs 0.475 CMC@1 Pcom). The code is promised on GitHub, which is good practice.\n\nThe soft spots are real. First, the uncertainty assumption is not validated at the per-example level. Eq (10) defines a deterministic function of the norm, and Figure 2 only shows that unseen classes have lower norms on average. That doesn't establish that low norm correlates with the old-model errors that actually hurt new-to-old retrieval. If the ranking is wrong, the adaptive weighting and cone widening downweight the wrong pairs. The small RINCE-vs-InfoNCE gap in the ablation makes this more, not less, urgent. Second, the experimental protocol is weaker than the claims: baselines are tuned over 10 hyperparameter combinations with the best run on the test metrics, no validation split is mentioned, and no error bars or multi-seed results are given. That can easily inflate gaps, especially the 21.4% and 44.8% headline numbers. Third, there's a minor algebraic slip in Eq (10): the factor 1/sqrt(K) appears misplaced for K != 1 (the time coordinate already carries a 1/sqrt(K)), and the uncertainty formula should be 1 - tanh(sqrt(K)||z||) rather than 1 - (1/sqrt(K)) tanh(...). The experiments use K=1, so it's cosmetic, but it should be fixed. Finally, HBCT is not uniformly best: in the Both/TinyImageNet row, Hot-Refresh has higher CMC@1 Pcom (0.365 vs 0.348).\n\nI think the core idea is sound and the gains may be real, but the paper doesn't yet prove that the uncertainty mechanism is the source of the gains. It's a good candidate for serious peer review, not a desk reject. A referee should ask for per-example calibration analysis, multi-seed runs with a validation split for hyperparameter selection, and a corrected Eq (10).","headline":"A promising but under-validated hyperbolic approach to backward-compatible retrieval; the uncertainty mechanism is the main risk.","tokens_in":19500,"tokens_out":6800,"would_cite":false,"duration_ms":59813,"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":"By lifting embeddings into hyperbolic space and constraining new ones inside old entailment cones, this paper claims to keep upgraded models compatible with existing galleries while letting uncertain old embeddings be downweighted.","keywords":["backward-compatible representation learning","hyperbolic geometry","entailment cone","uncertainty estimation","contrastive alignment","model evolution","image retrieval","Lorentz model"],"falsifier":"Measure, on a held-out set, the correlation between the old model's norm-based hyperbolic uncertainty and its actual retrieval errors for each gallery item; if low-uncertainty (high-norm) embeddings are equally or more error-prone, or if downweighting low-norm embeddings does not improve new-to-old retrieval, the central mechanism is falsified. A direct experiment would inject label noise into high-norm training samples so that old-model errors concentrate there, and check whether HBCT's gains invert.","tokens_in":18459,"feed_emoji":"📐","tokens_out":8038,"duration_ms":78313,"temperature":0.7,"pith_summary":"Backward-compatible representation learning aims to let an upgraded embedding model query a gallery built by its predecessor, so stored data never needs to be re-embedded. The paper claims this compatibility is more naturally achieved in hyperbolic space: embeddings are lifted onto a hyperboloid, each new embedding is constrained to lie inside the entailment cone of its old counterpart, and the alignment loss weights each old–new pair by a norm-derived uncertainty of the old embedding. Uncertain old embeddings get wider cones and lower alignment weight, so the new model is free to improve rather than being forced to reproduce outdated representations. The reported gains are a 21.4% improvement in CMC@1 compatibility and a 44.8% improvement in mAP compatibility over the strongest Euclidean baseline, with little loss in new-model performance. The paper frames this as treating model evolution as movement along a time-like dimension of hyperbolic space.","feed_headline":"Hyperbolic cones boost model-upgrade compatibility by 21.4%","feed_subtitle":"New embeddings stay inside old cones, and uncertain old embeddings get wider cones, so no re-embedding is needed after updates.","key_machinery":"The load-bearing object is the hyperbolic entailment cone in the Lorentz model of hyperbolic space. For an old embedding $h_o$, the cone has half-aperture $\\mathrm{aper}(h_o)=\\sin^{-1}(2\\epsilon\\sqrt K/\\|h_{o,\\mathrm{space}}\\|)$, which narrows as the embedding moves away from the origin; the loss $\\mathcal L_{\\mathrm{entail}}=\\max(0,\\mathrm{ext}(h_o,h_n)-\\mathrm{aper}(h_o))$ penalizes new embeddings that fall outside it. Uncertainty is measured by $\\mathrm{Uncertainty}(h)=1-\\frac{1}{\\sqrt K}\\tanh(\\sqrt K\\|z\\|)$, which equals the norm shrinkage caused by the exponential map and is bounded in $[0,1]$ for $K=1$. A robust contrastive alignment loss (RINCE) with $q(h_o)=\\mathrm{Uncertainty}(h_o)$ downweights positive pairs whose old embedding is uncertain. The full objective is $\\mathcal L=\\mathcal L_{\\mathrm{base}}+\\lambda(\\mathcal L_{\\mathrm{entail}}+\\mathcal L_{\\mathrm{contrast}})$, applied after exponential-map lifting of any Euclidean encoder's output.","core_discovery":"The central claim is that the radial structure of hyperbolic embeddings provides a usable signal for model evolution: the same coordinate that encodes an old embedding's uncertainty also controls how much the new embedding may deviate from it. Concretely, HBCT defines uncertainty as $1-\\frac{1}{\\sqrt K}\\tanh(\\sqrt K\\|z\\|)$ for the pre-exponential Euclidean vector $z$, and sets the entailment-cone aperture inversely to the old embedding's norm, so unreliable old embeddings produce wider permissible cones. The contrastive term uses RINCE with $q(h_o)=\\mathrm{Uncertainty}(h_o)$, dynamically lowering the pull toward uncertain old embeddings. The paper demonstrates across extended-data, extended-class, new-architecture, and combined scenarios that this yields stronger new-to-old retrieval compatibility than Euclidean baselines such as BCT, Hot-Refresh, AdvBCT, and HOC, and that the advantage persists through five consecutive model updates.","pith_inferences":["One natural test is to replace the norm-based uncertainty with a calibrated measure, such as the old model's own softmax entropy on a probe set, and check whether compatibility improves further; the geometry would stay intact while the weight $q(h_o)$ becomes task-grounded.","Because the objective is agnostic to the base loss, HBCT could be applied to self-supervised and multimodal foundation-model updates; a concrete extension would be fine-tuning a CLIP-style model with the hyperbolic alignment and measuring zero-shot retrieval compatibility.","The paper's own limitation about growing clipping thresholds implies a stress test: run fifty or more sequential updates and observe whether norm growth destabilizes training, or whether periodic rescaling of the time coordinate restores stability.","The exponential volume growth of hyperbolic space suggests the approach may scale naturally to continual learning with many emerging classes, a regime where Euclidean compatibility methods degrade, though the paper only demonstrates five update steps."],"forward_implications":["An upgraded model can query the existing gallery immediately, so backfilling the vector database becomes optional rather than mandatory.","Old embeddings are no longer treated as ground truth: high-uncertainty old embeddings are downweighted and allowed to drift more, so the new model can learn better representations without sacrificing compatibility.","The compatibility advantage is reported to survive multiple consecutive updates, where Euclidean alignment methods' compatibility declines rapidly.","The method is described as applicable to any base loss, meaning the same hyperbolic alignment could wrap supervised, self-supervised, or foundation-model training.","Even the hyperbolic method without the entailment loss outperforms Euclidean baselines in several settings, suggesting the geometry itself, not just the cone constraint, drives part of the gain."],"supporting_citations":[{"why":"Defines the backward-compatible training problem, the compatibility metrics $P_{\\mathrm{com}}$ and $P_{\\mathrm{up}}$, and supplies the BCT baseline that HBCT must beat.","marker":"(Shen et al., 2020)"},{"why":"Introduces hyperbolic entailment cones, the partial-order constraint HBCT adapts to relate old and new embeddings.","marker":"(Ganea et al., 2018)"},{"why":"Provides the Lorentz model notation, the entailment-cone loss derivation, and the norm-clipping recipe HBCT relies on.","marker":"(Desai et al., 2023)"},{"why":"Shows hyperbolic encoders capture representation uncertainty and supplies the hybrid Euclidean–hyperbolic encoder used for lifting.","marker":"(Khrulkov et al., 2020)"},{"why":"Source of the norm-based hyperbolic uncertainty measure that Eq. (10) adapts to the Lorentz model.","marker":"(Atigh et al., 2022)"},{"why":"Also uses the $\\ell^2$-norm uncertainty in hyperbolic space, and is cited for the same uncertainty-as-norm assumption.","marker":"(Franco et al., 2023)"},{"why":"Introduces RINCE, the robust contrastive loss that HBCT converts into an uncertainty-aware alignment by setting $q(h_o)=\\mathrm{Uncertainty}(h_o)$.","marker":"(Chuang et al., 2022)"},{"why":"Supplies the HOC high-order alignment baseline and the contrastive-alignment approach HBCT is compared against.","marker":"(Biondi et al., 2024)"},{"why":"Supplies the Hot-Refresh baseline and the regression-alleviating compatible-training framework that HBCT extends to hyperbolic space.","marker":"(Zhang et al., 2022)"}],"fun_headline_variants":["Hyperbolic cones make model upgrades backward-compatible","Uncertainty-aware cones let old embeddings guide new models","Time as a natural axis for backward-compatible learning","Wider cones for uncertain old embeddings boost compatibility","New models stay inside old cones via hyperbolic geometry"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that an old embedding's norm in hyperbolic space reliably measures how uncertain or unreliable that embedding is; if low-norm embeddings are not the ones causing retrieval failures, the adaptive weighting and cone-widening would be miscalibrated and the compatibility gains could vanish.","fun_headline_variants_meta":{"raw":{"variants":["Hyperbolic cones make model upgrades backward-compatible","Uncertainty-aware cones let old embeddings guide new models","Time as a natural axis for backward-compatible learning","Wider cones for uncertain old embeddings boost compatibility","New models stay inside old cones via hyperbolic geometry"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000734,"raw_usage":{"total_tokens":3257,"prompt_tokens":897,"completion_tokens":2360,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":513,"completion_tokens_details":{"reasoning_tokens":2286}},"tokens_in":513,"tokens_out":2360,"duration_ms":21677,"temperature":1.0,"reasoning_tokens":2286,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:13:19.127365+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure, on a held-out set, the correlation between the old model's norm-based hyperbolic uncertainty and its actual retrieval errors for each gallery item; if low-uncertainty (high-norm) embeddings are equally or more error-prone, or if downweighting low-norm embeddings does not improve new-to-old retrieval, the central mechanism is falsified. A direct experiment would inject label noise into high-norm training samples so that old-model errors concentrate there, and check whether HBCT's gains invert.","supporting_citations":[{"cited_title":"Towards backward-compatible representation learning","cited_arxiv_id":null,"evidence_quote":"Defines the backward-compatible training problem, the compatibility metrics $P_{\\mathrm{com}}$ and $P_{\\mathrm{up}}$, and supplies the BCT baseline that HBCT must beat."},{"cited_title":"Hyperbolic entailment cones for learning hierarchical embeddings","cited_arxiv_id":null,"evidence_quote":"Introduces hyperbolic entailment cones, the partial-order constraint HBCT adapts to relate old and new embeddings."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Lorentz model notation, the entailment-cone loss derivation, and the norm-clipping recipe HBCT relies on."},{"cited_title":"Hyperbolic image embeddings","cited_arxiv_id":null,"evidence_quote":"Shows hyperbolic encoders capture representation uncertainty and supplies the hybrid Euclidean–hyperbolic encoder used for lifting."},{"cited_title":"G., Schoep, J., Acar, E., Van Noord, N., and Mettes, P","cited_arxiv_id":null,"evidence_quote":"Source of the norm-based hyperbolic uncertainty measure that Eq. (10) adapts to the Lorentz model."},{"cited_title":"D., Wang, X., Vineet, V., Joshi, N., Torralba, A., Jegelka, S., and Song, Y","cited_arxiv_id":null,"evidence_quote":"Introduces RINCE, the robust contrastive loss that HBCT converts into an uncertainty-aware alignment by setting $q(h_o)=\\mathrm{Uncertainty}(h_o)$."},{"cited_title":"Stationary representations: Optimally approximating compatibility and implications for improved model replacements","cited_arxiv_id":null,"evidence_quote":"Supplies the HOC high-order alignment baseline and the contrastive-alignment approach HBCT is compared against."},{"cited_title":"Hot-Refresh Model Upgrades with Regression-Alleviating Compatible Training in Image Retrieval","cited_arxiv_id":"2201.09724","evidence_quote":"Supplies the Hot-Refresh baseline and the regression-alleviating compatible-training framework that HBCT extends to hyperbolic space."}],"review_version":1}