{"id":"70ff1501-0cac-474d-9f85-1ab5e977708b","arxiv_id":"2501.16738","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A post-training quantization recipe using k-scaled token-wise scaling and SSM reparameterization keeps Vision Mamba 8-bit ImageNet accuracy within 0.8-1.2% of FP32.","lead":"This paper introduces a post-training quantization method for Vision Mamba that keeps 8-bit accuracy within 1.2% of the full-precision model on ImageNet-1k. It combines token-wise scaling for linear layers with a reparameterization trick that smooths the SSM hidden state before quantization.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim depends on an unquantified rank-1 approximation of the SSM hidden state; if that approximation is weak, the reparameterization smoothing may not reduce quantization error.","rationale":"The reader's weakest_assumption correctly identifies the rank-1 approximation in Eq. (10) as the load-bearing element. The reparameterization is algebraically exact, so the only way the method can fail is if the chosen factors do not actually flatten the hidden-state distribution. My stress-test agrees and adds a more precise reproducibility risk: the factor-determining step, Eqs. (29)–(31), uses pow(x,a) with fractional exponents, which is undefined for negative x. Since SSM hidden states can plausibly take negative values, this is not a purely theoretical edge case; it should be checked empirically. The reader's verdict of CONDITIONAL is appropriate: the method is plausible and the reported numbers are encouraging, but the core mechanism is asserted rather than demonstrated. No change to the verdict is needed; the concrete test would either confirm the smoothing assumption or reveal that the reported results rely on an undocumented modification of the factor formula. I find no reason to move toward acceptance or rejection without this additional evidence.","tokens_in":9728,"tokens_out":10239,"duration_ms":105393,"concrete_test":"Reconstruct or obtain the ViM-T checkpoint and the 256-image calibration set; for each SSM layer, compute rC, rL, rD exactly as in Eqs. (26)–(31) using mean and standard deviation, then record: (a) the fraction of negative or zero entries in rC0/rL0/rD0 and whether pow returns NaN; (b) the relative rank-1 residual ||h - rC⊗rL⊗rD||_F / ||h||_F; and (c) the 8-bit MinMax quantization MSE of h versus h* over all recurrent steps. If (a) produces NaN, or if (b) is large (e.g., >0.5) for any layer, or if (c) shows h* is not quantized more accurately than h, then the smoothing mechanism described in the paper does not explain the reported accuracy, and the central claim is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The accuracy claim (0.8–1.2% drop on ImageNet-1k) rests on Section IV-B's reparameterization actually making the SSM hidden state h easier to quantize. The algebra in Eqs. (15)–(21) is exact for arbitrary nonzero factors, so the make-or-break assumption is the rank-1 structure h ≈ rC⊗rL⊗rD in Eq. (10), which the paper itself says is 'not strictly correct.' No quantitative evidence is given that this approximation is good: the paper does not report the rank-1 residual, the reduction in dynamic range from h to h*, or the 8-bit quantization error of h* versus h. If the residual is large in some layers, Eq. (16) can propagate or amplify error; moreover, the factor formula in Eqs. (29)–(31) uses a fractional power of values that may be negative or zero, which is undefined as written and would make the method non-reproducible. Since Table III's 74.9% and 79.7% results depend on these factors, the central claim is not yet supported without a direct test of the smoothing assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a post-training quantization (PTQ) pipeline for Vision Mamba (ViM) at 8-bit weights/activations. Three components are introduced: similarity-based scale search combined with k-scaled token-wise quantization for linear and convolutional layers, a reparameterization of the SSM hidden state that divides h by a rank-1 outer-product approximation before quantization, and a factor-determination rule based on representative and dispersion statistics. Experiments on ImageNet-1k report 74.9% for ViM-T (FP 76.1%) and 79.7% for ViM-S (FP 80.5%), against MinMax baselines of 12.2% and 51.6%, respectively. The central claim is that the proposed method limits PTQ degradation to 0.8–1.2% while quantizing all linear, convolutional, and SSM layers.","tokens_in":9987,"tokens_out":6579,"duration_ms":68104,"significance":"If the reported results are reproducible, the paper would be a useful first demonstration of PTQ for ViM, with a clean and exact reparameterization algebra (Eqs. 15–21), a hardware-motivated scale design, and an explicit focus on SSM hidden-state quantization that prior Mamba PTQ works did not address. The ablation in Table I for the linear/convolutional components is informative, and the paper is honest about the approximate nature of the rank-1 assumption. However, the empirical evidence is narrow: two model sizes on one dataset, no variance reporting, no code, and no comparison with existing Mamba-specific PTQ methods adapted to ViM. The load-bearing SSM smoothing assumption is not directly quantified, and two equations (Eqs. 8 and 29–31) are problematic as written. These issues prevent acceptance in the current form but are addressable within the manuscript's scope.","major_comments":[{"comment":"The reparameterization algebra in Eqs. (15)-(21) is exact for arbitrary nonzero factors, so the real question is whether h* is smoother and easier to quantize than h. The paper itself states that Eq. (9) is \"not strictly correct,\" but it provides no quantitative evidence for the rank-1 approximation: no relative residual norm of h - rC⊗rL⊗rD, no comparison of the dynamic range or 8-bit quantization error of h versus h*, and no plot of h*'s distribution over recurrent steps. Table II ablates different Rep/Disp choices but does not include a no-reparameterization row with the same linear-layer methods, so Table III's improvement cannot be attributed to the SSM reparameterization alone. Please add a direct evaluation of the smoothing assumption, e.g., per-layer rank-1 residual and quantization SNR of h* versus h.","section":"Section IV-B, Eq. (10)-(12), Fig. 7"},{"comment":"The factor formula rC = pow(rC0, Disp(rC0)/Dispsum) is undefined when rC0 contains negative or zero entries, because a fractional power of a negative real number is not real. Since rC0 is a mean/median of hidden-state values over dimensions, negative entries are expected in practice. As written, the method is not reproducible without a rule for handling negative or zero representatives. Please specify a sign-preserving or clamped variant and verify that the chosen rule is what produced Table III.","section":"Section IV-C, Eqs. (29)-(31)"},{"comment":"The hardware-friendly scale redefinition s*_i = s1 >> floor(log(s_i/s1)) uses a negative shift amount whenever s_i < s1, because log(s_i/s1) is negative. Right-shifting by a negative value is undefined in standard integer arithmetic (and the logarithm base is not specified). If the intent is to approximate smaller scales by powers of two, the formula should be s1 >> floor(log2(s1/s_i)) or an equivalent left-shift/rounding scheme. Please correct the equation and clarify the base of the logarithm.","section":"Section III-C, Eq. (8)"},{"comment":"The central accuracy claim rests on single runs on ImageNet-1k with no standard deviations or repeated calibration draws, and the experiments do not compare against existing Mamba-specific PTQ methods (Mamba-PTQ [13], Quamba [14]) adapted to ViM, nor against general ViT PTQ methods such as SmoothQuant or RepQ-ViT applied to the same layers. Because the reported degradation is only 0.8–1.2%, the claim of effectiveness needs at least one strong adapted baseline and some indication of run-to-run variability to be convincing.","section":"Section V, Table III and Experimental Setups"},{"comment":"The manuscript says it quantizes \"the SSM block\" and reports 8/8 W/A in Table III, but the method description only specifies quantization of the hidden state h* and reparameterization of A, B, and C. It is not stated which of A*, B*, C*, x, y, and D are quantized, with which quantizers, and which values remain floating-point. Without this information, Table III is not reproducible even if the rank-1 and factor issues are resolved.","section":"Section IV-B and Section V-A"}],"minor_comments":[{"comment":"The sentence preceding Eq. (26) contains a missing expression: \"compute the representative of h along each corresponding dimension as , where Rep is...\" The formula or definition is absent. Please fill in the missing text.","section":"Section IV-C, Eq. (26)"},{"comment":"The tensor shapes are inconsistent: Eq. (13) states h ∈ R^{C×L×D}, but the recurrence h_t = A_t h_{t-1} + B_t x_t treats h_t as a slice over one token with dimension C×D. Please define all dimensions (C, L, D) and the per-token shapes of A_t, B_t, C_t, x_t, and y_t explicitly.","section":"Section II-A and Section IV-B"},{"comment":"The k-scaled token-wise method is underspecified: the k-means clustering is applied to the token dimension, but the paper does not state the number of clusters (other than the global k=4), the number of calibration iterations, or how a token is assigned to a scale during inference (fixed token-index groups or per-input clustering).","section":"Section III-C and Figure 3"},{"comment":"Figure 7 shows \"error propagation in SSM recurrent process\" but lacks labeled axes and numeric units, so the reader cannot assess the magnitude of the effect being claimed. Please add axis labels and report the quantitative difference at selected steps.","section":"Section IV-B, Fig. 7"},{"comment":"Reference [10] is listed as \"Yu-Shan Tai et al.\" without a complete author list or venue information; please provide the full citation for MPTQ-ViT.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable engineering contribution, and the exact reparameterization algebra is a real strength. My main reservation is the gap between the claimed 0.8–1.2% degradation and the evidence supporting the SSM smoothing assumption; the missing no-reparameterization ablation and the problematic Eqs. (8) and (29)–(31) need to be addressed before the results can be trusted. I would also encourage the editor to require the authors to state code/model availability, since no code is currently provided and the method has several underspecified implementation details."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thing to know: this is the first PTQ recipe for Vision Mamba that includes quantizing the SSM hidden state, and the trick is a clean reparameterization. They absorb outer-product scale factors r_C, r_L, r_D into A, B, C, so the smoothing costs nothing at inference. The ImageNet numbers are good: ViM-T drops 1.2%, ViM-S 0.8%, against MinMax collapsing to 12.2%. If those hold, it's a useful result.\n\nThe reparameterization algebra in Eqs. (15)–(21) is exact for any nonzero factors. The k-scaled token-wise quantization is a sensible adaptation of FQ-ViT/TSPTQ to the token grid of images. They also honestly say the rank-1 approximation is 'not strictly correct.'\n\nThe soft spots are real. Single runs, one dataset, no error bars. No comparison to Mamba-PTQ or Quamba adapted to ViM. Hyperparameters (k, Rep/Disp) are chosen on the validation set. No code. And the stress-test note is right: Eqs. (29)–(31) raise the representative values to a fractional power; if a representative is negative, pow is undefined. That is a concrete reproducibility gap. The paper doesn't say to take absolute values.\n\nThe rank-1 smoothing assumption itself is unquantified. They don't report the residual, the dynamic-range reduction, or the 8-bit error of h* vs h. The algebra is exact, but the make-or-break claim is that h* is easier to quantize. That is asserted, not shown.\n\nWho this is for: researchers working on PTQ for Mamba-based vision models or SSM deployment. It deserves a serious referee, with requests for comparisons, error bars, code, and a fix for the pow issue. I wouldn't cite it yet, but I'd keep it in view.","headline":"First PTQ for Vision Mamba that quantizes the SSM hidden state via exact reparameterization; good ImageNet numbers, but thin empirical support and an undefined factor formula for negative representatives.","tokens_in":10561,"tokens_out":4070,"would_cite":false,"duration_ms":38160,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that Vision Mamba's SSM hidden state can be smoothed by a rank-1 reparameterization so that full 8-bit post-training quantization of all linear, convolutional, and SSM layers loses at most 1.2% top-1 accuracy on…","keywords":["post-training quantization","Vision Mamba","state-space model","SSM hidden-state quantization","k-scaled quantization","rank-1 reparameterization","model compression","ImageNet-1k classification"],"falsifier":"Quantize a second SSM-based vision backbone with a larger state dimension $D$ and a different scan order, and check whether the accuracy gap stays within the reported 0.8–1.2% range; if it grows, the rank-1 smoothing is the fragile piece. More directly, measure the relative reconstruction error $\\|h - r_C \\otimes r_L \\otimes r_D\\| / \\|h\\|$ across layers and tokens, and check whether the difference between quantized and floating-point $h^*$ stays flat over the recurrent steps — if the error grows linearly with $t$ even after reparameterization, the smoothing has failed.","tokens_in":9530,"feed_emoji":"⚡","tokens_out":6890,"duration_ms":60830,"temperature":0.7,"pith_summary":"This paper claims that Vision Mamba models can be post-training quantized to 8-bit weights and activations with almost no accuracy loss, provided the SSM's hidden state is handled separately from the linear and convolutional layers. The method rests on three techniques: a similarity-based scale search combined with k-scaled token-wise quantization for outlier-heavy projection layers, and a rank-1 reparameterization that smooths the hidden state so recurrent quantization error does not compound. On ImageNet-1k, the authors report 74.9% accuracy for ViM-T versus 76.1% at full precision, and 79.7% for ViM-S versus 80.5%, while naive MinMax quantization drops ViM-T to 12.2%. If correct, this would make Mamba-based vision backbones practical for low-bit edge inference without retraining.","feed_headline":"8-bit Vision Mamba loses only 1.2% top-1 accuracy","feed_subtitle":"Direct SSM quantization drops ViM-T to 12.2%; rank-1 reparameterization keeps 74.9%.","key_machinery":"The load-bearing identity is the rank-1 factorization of the hidden state, $h \\approx r_C \\otimes r_L \\otimes r_D$, where $r_C \\in \\mathbb{R}^C$, $r_L \\in \\mathbb{R}^L$, and $r_D \\in \\mathbb{R}^D$. This defines a smoothed hidden state $h^* = h/(r_C \\otimes r_L \\otimes r_D)$, and the paper reparameterizes $\\bar{A}$, $\\bar{B}$, and $C$ so that the quantized recurrence runs on $h^*$ without extra per-step multiplications; the final output is recovered by one multiplication by $r_C$ (Eqs. 18–21). The second piece is k-scaled token-wise quantization, which clusters the token dimension into $k$ groups and gives each group a power-of-two-related scale so that token outliers do not dominate the quantization range.","core_discovery":"The paper's central discovery is that the error that destroys accuracy under naive 8-bit PTQ of ViM comes from two separable sources: extreme token outliers in linear projection layers, and the compounding quantization of the recurrent hidden state of the SSM. The authors show the hidden-state tensor $h \\in \\mathbb{R}^{C \\times L \\times D}$ is approximately rank-one with respect to scale variation along each dimension, $h \\approx r_C \\otimes r_L \\otimes r_D$, which lets them divide it into a smoother version $h^*$ before quantizing. Because the smoothing factors can be absorbed into $\\bar{A}$, $\\bar{B}$, and $C$ and then fused into the preceding linear projections, the reparameterization adds almost no recurrent computation. They further select the factors by weighting per-dimension representatives with normalized dispersion. The result is that all linear, convolutional, and SSM layers run at 8 bits with only a 0.8–1.2% top-1 accuracy degradation on ImageNet-1k.","pith_inferences":["The rank-1 regularity of $h$ is likely testable on other Mamba-based vision backbones, such as VMamba or MambaVision; if the reconstruction error stays low, this reparameterization recipe would transfer without retraining.","The token-wise scale assignment relies on the fixed token length of image inputs, so applying the same method to variable-length inputs, such as video or high-resolution images, would require a new clustering or scale assignment.","The factor-selection rule (a representative weighted by dispersion) is heuristic; an alternative would be to choose $r_C, r_L, r_D$ to directly minimize expected quantization error over calibration data, potentially improving results further.","The paper only reports 8-bit results; testing 4-bit would reveal how much of the gain comes from the smoothing itself versus the relatively generous bit width."],"forward_implications":["8-bit PTQ of all linear, convolutional, and SSM layers keeps 74.9% top-1 accuracy on ViM-T and 79.7% on ViM-S, versus 76.1% and 80.5% at full precision.","The SSM reparameterization removes the need for extra per-step divisions and multiplications during recurrent inference, so the quantization gain does not come with a runtime penalty.","The combination of similarity-based scale search and k-scaled token-wise scales recovers most of the accuracy lost by MinMax quantization of the conv1d and out_proj layers.","A calibration set of 256 ImageNet training samples is enough to determine the scales and factors, preserving PTQ's low-overhead promise."],"supporting_citations":[{"why":"Supplies the Vision Mamba architecture, bidirectional SSM, and pretrained ViM-T/ViM-S checkpoints that are the quantization targets.","marker":"[1]"},{"why":"Defines the Mamba SSM recurrence and selectivity that the reparameterization operates on.","marker":"[2]"},{"why":"Defines symmetric MinMax quantization, which serves as the baseline quantizer and the starting point for the proposed methods.","marker":"[19]"},{"why":"Prior Mamba PTQ work identifying activation outliers as the main challenge, which the paper builds on and extends to vision tasks.","marker":"[13]"},{"why":"Prior Mamba PTQ recipe handling SSM inputs and outputs; the paper contrasts its own SSM-interior hidden-state quantization with this approach.","marker":"[14]"},{"why":"Introduces per-channel smoothing factors for activations, the conceptual ancestor of the scale-splitting idea used here.","marker":"[7]"},{"why":"Scale reparameterization for vision transformers, whose idea of transferring variation into linear layers the SSM reparameterization adapts.","marker":"[9]"},{"why":"Multi-scale and power-of-two factor quantization for vision transformers, which the k-scaled method generalizes to tokens.","marker":"[5]"}],"fun_headline_variants":["8-bit Vision Mamba loses only 1.2% top-1 accuracy","Vision Mamba quantized to 8-bit with 0.8-1.2% loss","K-scaled quantization and reparameterization tame Vision Mamba","Vision Mamba PTQ: 8-bit, just 1.2% accuracy drop","Reparameterization keeps Vision Mamba accurate at 8-bit"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim stands on the assumption that the SSM hidden state's value pattern is well approximated by a rank-1 outer product of three vectors, an approximation the paper itself calls \"not strictly correct\" — if that regularity fails, the smoothing that keeps recurrent quantization error small disappears.","fun_headline_variants_meta":{"raw":{"variants":["8-bit Vision Mamba loses only 1.2% top-1 accuracy","Vision Mamba quantized to 8-bit with 0.8-1.2% loss","K-scaled quantization and reparameterization tame Vision Mamba","Vision Mamba PTQ: 8-bit, just 1.2% accuracy drop","Reparameterization keeps Vision Mamba accurate at 8-bit"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000381,"raw_usage":{"total_tokens":2039,"prompt_tokens":982,"completion_tokens":1057,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":598,"completion_tokens_details":{"reasoning_tokens":951}},"tokens_in":598,"tokens_out":1057,"duration_ms":9086,"temperature":1.0,"reasoning_tokens":951,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T11:03:38.319807+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Quantize a second SSM-based vision backbone with a larger state dimension $D$ and a different scan order, and check whether the accuracy gap stays within the reported 0.8–1.2% range; if it grows, the rank-1 smoothing is the fragile piece. More directly, measure the relative reconstruction error $\\|h - r_C \\otimes r_L \\otimes r_D\\| / \\|h\\|$ across layers and tokens, and check whether the difference between quantized and floating-point $h^*$ stays flat over the recurrent steps — if the error grows linearly with $t$ even after reparameterization, the smoothing has failed.","supporting_citations":[{"cited_title":"Smoothquant: Accurate and efficient post-training quantization for large language models,","cited_arxiv_id":null,"evidence_quote":"Introduces per-channel smoothing factors for activations, the conceptual ancestor of the scale-splitting idea used here."},{"cited_title":"Repq-vit: Scale reparameterization for post-training quantization of vision transformers,","cited_arxiv_id":null,"evidence_quote":"Scale reparameterization for vision transformers, whose idea of transferring variation into linear layers the SSM reparameterization adapts."}],"review_version":1}