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Hardware-Friendly Token-Group Activation Quantization for Low-Bit Mamba Super-Resolution
Jinwoo Chung, Jangho Kim
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Abstract
Abstract:Mamba-based super-resolution models are efficient alternatives to Transformer-based restoration backbones, but their low-bit post-training quantization remains challenging because selective scan, Mamba's input-dependent state-space operator, induces different activation ranges across spatial tokens. Thus, a single layer-wise clipping range poorly matches all tokens. We propose Token-Group Quantization, a hardware-friendly activation PTQ framework that statically approximates a hardware-unfriendly post-scan grouping oracle, where tokens with similar preferred clipping ranges are assigned to the same group. To avoid runtime post-scan grouping in static low-bit inference, a lightweight predictor infers the groups from pre-scan features available before the quantized scan path. During calibration, we form pseudo-labels by clustering post-scan activation descriptors that capture similar rounding--clipping behavior. At inference, the frozen predictor maps pre-scan features to groups and selects entries from offline-calibrated group-wise clipping-bound tables, without runtime statistics collection, dynamic clipping updates, or post-scan group assignment. To address low-bit restoration degradation, we further introduce a Frequency-Preserving Refinement (FPR) objective for clipping-bound calibration. FPR aligns Fourier amplitude and phase between full-precision teacher and quantized student outputs to preserve high-frequency structures. Across PTQ protocols, bit-widths, backbones, and tasks, our method consistently outperforms prior Mamba and SR PTQ baselines, transfers to Transformer SR and Vision Mamba classification, composes with rotation-based quantization, and achieves 2.23x speedup on Jetson Orin Nano over FP16. Code is available here.
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- Source: https://arxiv.org/abs/2610.16261v1
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Hardware-Friendly Token-Group Activation Quantization for Low-Bit Mamba Super-Resolution Jinwoo Chung Affiliation: Kookmin University Affiliation: Seoul, Republic of Korea Email: imaboybut@kookmin.ac.kr Jangho Kim â thanks: Corresponding author. Affiliation: Kookmin University Affiliation: Seoul, Republic of Korea Email: jangho.kim@kookmin.ac.kr Abstract Mamba-based super-resolution models are efficient alternatives to Transformer-based restoration backbones, but their low-bit post-training quantization remains challenging because selective scan, Mambaâs input-dependent state-space operator, induces different activation ranges across spatial tokens. Thus, a single layer-wise clipping range poorly matches all tokens. We propose Token-Group Quantization, a hardware-friendly activation PTQ framework that statically approximates a hardware-unfriendly post-scan grouping oracle, where tokens with similar preferred clipping ranges are assigned to the same group. To avoid runtime post-scan grouping in static low-bit inference, a lightweight predictor infers the groups from pre-scan features available before the quantized scan path. During calibration, we form pseudo-labels by clustering post-scan activation descriptors that capture similar roundingâclipping behavior. At inference, the frozen predictor maps pre-scan features to groups and selects entries from offline-calibrated group-wise clipping-bound tables, without runtime statistics collection, dynamic clipping updates, or post-scan group assignment. To address low-bit restoration degradation, we further introduce a Frequency-Preserving Refinement (FPR) objective for clipping-bound calibration. FPR aligns Fourier amplitude and phase between full-precision teacher and quantized student outputs to preserve high-frequency structures. Across PTQ protocols, bit-widths, backbones, and tasks, our method consistently outperforms prior Mamba and SR PTQ baselines, transfers to Transformer SR and Vision Mamba classification, composes with rotation-based quantization, and achieves 2.23Ă2.23Ă speedup on Jetson Orin Nano over FP16. Code is available here. 1 Introduction Single image super-resolution (SR) reconstructs high-resolution images from low-resolution inputs. Recent SR backbones have progressed from CNNs to Transformers, where long-range dependency modeling improves reconstruction fidelity [27, 46, 26, 4]. More recently, Mamba-based SR models have emerged as efficient alternatives by replacing quadratic self-attention with selective state-space modeling, capturing long-range spatial dependencies with linear complexity [15, 17, 16]. Selective scan is the core input-dependent state-space operator in this family, propagating information across flattened spatial tokens; in MambaIRv2, our primary backbone, it is implemented inside Attentive State-Space Modules (ASSMs). While this improves architectural efficiency, edge deployment still requires reducing activation memory traffic and enabling low-bit fixed-point execution, motivating the study of post-training quantization (PTQ) for Mamba-based SR. Although PTQ compresses pretrained models without updating the backbone weights [34, 25], conventional PTQ severely degrades low-bit Mamba SR. We identify a key cause. Selective scan substantially amplifies token-wise activation heterogeneity. As shown in Sec. 4, in MambaIRv2-Light, 18 out of 20 ASSM blocks show increased per-token range variation after selective scan, with an average 1.80Ă1.80Ă increase over pre-scan activations. Thus, the bottleneck is not a few rare outliers, but broad token-wise range heterogeneity: a loose range wastes precision on typical tokens, while a tight range clips high-response tokens critical for restoration. This mismatch suggests that different token groups should be quantized under different clipping ranges. The most direct way to obtain such groups is to inspect post-scan activations at the target quantization sites and assign each token to a group accordingly, since these activations reveal the clipping range preferred at those sites. However, this post-scan group assignment is hardware-unfriendly for static low-bit deployment. It requires runtime statistics collection inside the quantized path and complicates ahead-of-time compilation with low-bit fixed-point kernels. We call this hardware-unfriendly upper-bound grouping rule the downstream oracle, a post-scan grouping oracle instantiated by K-means over post-scan activation descriptors that encode roundingâclipping regimes. The challenge is therefore to recover the oracleâs grouping behavior under a static deployment constraint, where clipping-bound tables and quantization parameters remain fixed after calibration. Building on this observation, we propose Token-Group Quantization, which distills the downstream oracleâs grouping behavior into a static pre-scan prediction problem. This approximation is feasible because selective scan generates token-dependent recurrence parameters from pre-scan features, which therefore already encode signals predictive of downstream activation regimes. During offline calibration, quantization-aware pseudo-labels capture token groups that should share clipping ranges, and a lightweight shared predictor learns to assign tokens to these groups from pre-scan features. At inference, the frozen predictor selects entries from clipping-bound tables indexed by layer, quantization site, and group, avoiding runtime statistics collection, dynamic clipping updates, and post-scan group assignment. Beyond activation range mismatch, low-bit SR quantization also degrades high-frequency edges and textures, which pixel-space losses can under-supervise. To address this restoration-specific degradation, we introduce a teacher-supervised Frequency-Preserving Refinement (FPR) objective for clipping-bound calibration, which aligns Fourier amplitude and phase between full-precision teacher and quantized student outputs. Our main contributions are summarized as follows: ⢠We identify selective-scan-induced token-wise activation heterogeneity as a key failure mode of low-bit PTQ for Mamba-based SR, showing through pre- and post-scan analysis that selective scan consistently amplifies token-range variation across most ASSM blocks. ⢠We propose Token-Group Quantization, which frames token-adaptive low-bit quantization as a static approximation to a hardware-unfriendly post-scan grouping oracle. During calibration, we instantiate this oracle by K-means over downstream activation descriptors and train a lightweight pre-scan predictor to recover oracle-aligned groups before the quantized sites. ⢠We introduce a teacher-supervised Frequency-Preserving Refinement (FPR) objective for low-bit SR PTQ, which refines clipping bounds by aligning Fourier amplitude and phase between full-precision teacher and quantized student outputs. Experiments show consistent gains over prior Mamba and SR PTQ baselines with 2.23Ă2.23Ă speedup on Jetson Orin Nano. ⢠The gains hold across MambaIR v1 and v2 at Light and Base scales and across denoising and JPEG artifact removal, transfer to SwinIR-light and to ImageNet on Vision Mamba, and compose with channel-axis transforms such as SpinQuant, as shown in Appendices A and B. 2 Related work 2.1 Image Super-Resolution Single image super-resolution recovers high-resolution images from low-resolution inputs. Early SR models were dominated by CNNs such as SRCNN [12], VDSR [22], EDSR [27], and RCAN [46], while Transformer-based models such as SwinIR [26] and HAT [4] improve restoration quality by modeling long-range dependencies at higher compute and memory cost. State-space models with selective scan [15] have been introduced to vision [49, 29] as efficient long-range backbones, and MambaIR [17] and MambaIRv2 [16] adapt them to image restoration by combining attention, state-space blocks, and convolution. Despite their efficiency, edge deployment of Mamba-based SR remains challenging due to activation memory traffic and low-bit quantization sensitivity. 2.2 Post-Training Quantization Neural network quantization reduces deployment cost and is commonly divided into quantization-aware training (QAT) and post-training quantization (PTQ). QAT simulates quantization during training and can achieve high accuracy, but requires costly retraining and careful tuning [13, 23, 48, 9], including recent SSM restoration work such as Q-MambaIR [5]. PTQ instead keeps the backbone weights fixed and calibrates quantization parameters from a small dataset [2, 34, 25, 20], but low-bit PTQ is vulnerable to activation outliers and input-dependent distribution shifts. Recent studies further go beyond simulated (fake) quantization and demonstrate actual low-bit acceleration on hardware [47, 1, 11, 10]. For SR, where activation statistics vary across spatial locations and tokens, prior methods use clipping-bound calibration and outlier-aware designs [37, 28, 38]. Mamba-specific PTQ methods such as PTQ4VM [8], Quamba [6], and MambaQuant [44] target selective state-space architectures, but are mainly validated outside SR restoration and still degrade substantially on Mamba-based SR. Weight-training PTQ methods such as AIQViT [21] and SPR2Q [43] compensate quantization error with LoRA-style adapters [18] fused before deployment. Rotation, affine, and scaling transforms from LLM and diffusion quantization [1, 30, 31, 35, 42, 24] remove channel-wise outliers, and Quamba and MambaQuant apply the same idea to Mamba. All of these assign the quantization range independently of token identity, which is sound when token distributions are homogeneous but is exactly the assumption that selective scan breaks in Sec. 4. Atom [47] acts on the token axis but relies on runtime statistics. Token-Group Quantization instead assigns ranges per token group statically through offline-calibrated clipping-bound tables and a lightweight pre-scan predictor, and it is complementary to channel-axis transforms, as combining it with rotation-based methods such as SpinQuant yields further gains in Appendix B.4. 3 Preliminaries 3.1 Selective Scan in Mamba-based SR A discretized state-space model updates a hidden state hth_t and produces an output yty_t as ht=AÂŻtâhtâ1+BÂŻtâxt,yt=Ctâht+Dâxt.h_t= A_th_t-1+ B_tx_t, y_t=C_th_t+Dx_t. (1) Unlike linear time-invariant SSMs, Mamba makes recurrence input-dependent by generating token-specific parameters from xtx_t. Thus, different tokens can induce different recurrence dynamics. In Mamba-based SR, selective scan is applied to flattened spatial tokens inside restoration blocks, where an image feature map is represented as a sequence of length L=HâWL=HW. Since the recurrence parameters are token-dependent, selective scan can produce different post-scan activation regimes across spatial locations. This property motivates our analysis of token-wise post-scan activation heterogeneity in Section 4. 3.2 Uniform Quantization for PTQ Post-training quantization (PTQ) converts a pretrained full-precision model into a low-bit model by calibrating quantization parameters while keeping the backbone weights fixed. For an activation tensor x, we use a b-bit uniform quantizer with lower and upper clipping bounds l and u: QâĄ(x,l,u,b)=sâ clipâĄ(âxâlsâ,0,2bâ1)+l,s=uâl2bâ1.Q(x;l,u,b)=s¡clip ( x-ls ,0,2^b-1 )+l, s= u-l2^b-1. (2) In conventional layer-wise activation PTQ, a single set of clipping bounds is shared by all tokens at each layer and quantization site: x^i(â,m)=QâĄ(xi(â,m),lâ,m,uâ,m,b), x^( ,m)_i=Q (x^( ,m)_i;l_ ,m,u_ ,m,b ), (3) where â denotes the layer, m denotes the activation quantization site, and i denotes the spatial token. The bounds (lâ,m,uâ,m)(l_ ,m,u_ ,m) are calibrated offline and fixed during inference. Therefore, layer-wise activation PTQ is effective only when one set of bounds can represent the activation distributions of all tokens at the same quantization site. 4 Observations This section analyzes how selective scan affects token-wise activation distributions in Mamba-based restoration backbones. We study 20 ASSM blocks of MambaIRv2-Light and collect pre-scan and post-scan activations from FP32 ASSM modules using low-resolution DIV2K [36] validation patches. (a) Activation distribution. (b) Layer-wise token-range CoV. Figure 1: Selective scan induces token-wise activation heterogeneity. (a) Post-scan activations exhibit a broader distribution than pre-scan activations in a representative ASSM layer (layer 18). (b) Per-token range CoV increases after selective scan in most ASSM layers. 4.1 Selective Scan Induces Token-wise Activation Heterogeneity The central question for low-bit activation quantization is whether a single set of layer-wise clipping bounds can represent all tokens at the same quantization site. In Mamba-based restoration backbones, selective scan undermines this assumption by producing token-dependent activation regimes. Distributional expansion. Fig. 1(a) shows that post-scan activations spread over a broader range than pre-scan activations after median-|x||x| normalization. This indicates that selective scan disperses tokens into different magnitude regimes, making one clipping range poorly matched to all tokens. Per-token range variation. For each token i, we define its activation range as ri=maxjâĄxi,jâminjâĄxi,jr_i= _jx_i,j- _jx_i,j and measure token-wise dispersion by CoVâĄ(r)=stdiâ(ri)meaniâ(ri).CoV(r)= std_i(r_i)mean_i(r_i). (4) As shown in Fig. 1(b), post-scan CoV exceeds pre-scan CoV in 18 out of 20 ASSM layers, with an average amplification of about 1.80Ă1.80Ă. Thus, token-wise range variation is a consistent effect of selective scan rather than a layer-specific artifact. Conflict with low-bit quantization. With a single layer-wise clipping bound, fitting high-response tokens enlarges the step size and wastes resolution for typical tokens, whereas fitting typical tokens severely clips high-response tokens. This trade-off becomes more severe as the bit-width decreases. The issue is therefore not isolated outliers, but token populations with distinct activation ranges. This motivates considering group-wise clipping bounds for low-bit Mamba SR. Figure 2: Clipping-scale regimes. Violin plots show token-level preferred clipping scales ciâc_i under random, post-scan descriptor K-means (oracle), and predicted groups. 4.2 From Observation to Design Section 4.1 shows that selective scan makes a single layer-wise clipping range poorly matched to all tokens. However, larger token-wise variation alone does not guarantee useful groups. For low-bit PTQ, groups should be defined by quantization compatibility: tokens should share a clipping range only when they prefer similar downstream roundingâclipping trade-offs. Fig. 2 visualizes this criterion using the token-level preferred clipping scale ciâ=argâĄmincâĄâxiâQâĄ(xi,âc,c,b)â22c_i = _c\|x_i-Q(x_i;-c,c,b)\|_2^2, a symmetric proxy for the clipping range preferred by token i. Random grouping yields similar clipping-scale distributions across groups, whereas post-scan descriptor K-means separates tokens into distinct clipping-scale regimes. The pre-scan predicted groups recover part of this hardware-unfriendly oracle structure without observing downstream activations. The most direct realization is a downstream oracle that assigns groups from post-scan activations, but this is hardware-unfriendly for static low-bit deployment because it requires runtime statistics inside the quantized path. A static approximation must therefore satisfy two constraints: C1, group indices must be produced by a frozen function without runtime statistics; and C2, group indices must be predicted before the target grouped quantization sites while being supervised by labels derived from their post-scan activation behavior. These constraints rule out simpler alternatives. Layer-wise PTQ ignores token heterogeneity; runtime post-scan grouping violates C1; per-token dynamic clipping requires irregular scale metadata; and pre-scan clustering is deployable but not aligned with the downstream roundingâclipping trade-off, violating C2. Thus, we use pre-scan group prediction, downstream-aware targets, and fixed clipping-bound tables. This is feasible because pre-scan features generate token-dependent selective-scan parameters and therefore provide the earliest deployable signal for approximating the oracle. 5 Method: Token-Group Quantization Section 4.2 motivates a static approximation to the post-scan grouping oracle. Token-Group Quantization implements this design with three components: a group-conditional activation quantizer, downstream-aware pseudo-labels, and a lightweight pre-scan predictor. At inference, the frozen predictor selects entries from fixed clipping-bound tables without runtime statistics or post-scan group assignment. Fig. 3 illustrates the pipeline. 5.1 Group-Conditional Activation Quantizer We apply group-wise clipping bounds to the activation sites where token-dependent distributions are most pronounced. In each block, this includes eight group-conditional sites: three downstream linear sites and five scan-internal per-token operands. The remaining quantized sites use layer-wise PTQ. Given the predicted group assignment g^i(â) g_i^( ), token i at layer â and quantization site m is quantized as x^i(â,m)=QâĄ(xi(â,m),lâ,m,g^i(â),uâ,m,g^i(â),b). x_i^( ,m)=Q (x_i^( ,m);l_ ,m, g_i^( ),u_ ,m, g_i^( ),b ). (5) The bounds (lâ,m,g,uâ,m,g)(l_ ,m,g,u_ ,m,g) form a layer-, site-, and group-specific clipping-bound table. 5.2 Quantization-Aware Pseudo-Labels A pre-scan predictor requires supervision, but the labels should encode quantization-error regimes rather than semantics. We therefore construct pseudo-labels offline from downstream activation descriptors, so that tokens in the same group prefer similar clipping bounds at the quantization sites. For each token and group-conditional site mââłm , where âłM denotes the eight sites above, we use a descriptor summarizing the roundingâclipping trade-off: Ďmâ(xi(â,m))=[q0.99â(|xi(â,m)|),q0.999â(|xi(â,m)|),RMSâĄ(xi(â,m)),maxâĄ|xi(â,m)|]. _m (x_i^( ,m) )= [q_0.99(|x_i^( ,m)|),\;q_0.999(|x_i^( ,m)|),\;RMS(x_i^( ,m)),\; |x_i^( ,m)| ]. (6) Here, qpq_p is the empirical p-quantile over channel entries. For each tokenâlayer pair (i,â)(i, ), we concatenate descriptors over mââłm . We then run a single K-means over the pooled tokenâlayer samples from the calibration set to obtain pseudo-labels giâ(â)g_i ( ). Descriptor construction and clustering are used only offline. See Appendix C. 5.3 Pre-scan Group Prediction Following C1 and C2, group indices must be predicted from pre-scan inputs without runtime activation statistics. Let x~i(â) x_i^( ) be the pre-scan feature of token i at layer â . Since selective scan generates token-dependent recurrence parameters from these features, we implement the predictor as a shared two-layer FFN: g^i(â)=argâĄmaxkâ1,âŚ,KâĄ[fθâ(x~i(â))]k. g_i^( )= _kâ\1,âŚ,K\ [f_θ( x_i^( )) ]_k. (7) Although fθf_θ is shared, x~i(â) x_i^( ) is layer-dependent, so the assignment remains layer-adaptive. We refer to this as structureâmagnitude decoupling: the shared FFN captures recurring token-structure cues for grouping, whereas the layer- and site-specific bound tables absorb the actual magnitude drift induced by selective scan. See Appendix D. The predictor is trained from pre-scan inputs by âpred=(i,â)â[CEâĄ(fθâ(x~i(â)),giâ(â))].L_pred=E_(i, ) [CE (f_θ( x_i^( )),g_i ( ) ) ]. (8) Figure 3: Overview of Token-Group Quantization. A frozen pre-scan predictor predicts token groups, and grouped INT sites use offline-calibrated clipping-bound tables without runtime statistics. 5.4 Bound Initialization and Teacher Distillation After training and freezing the pre-scan predictor, we replay the calibration set and collect activations according to the predicted group assignment g^i(â) g_i^( ). For each (â,m,g)( ,m,g), we form the activation pool assigned to group g: â,mâ(g)=xi(â,m):g^i(â)=g.X_ ,m(g)= \x_i^( ,m): g_i^( )=g \. (9) Then we initialize the clipping bounds by minimizing empirical quantization error: (lâ,m,g,uâ,m,g)=argâĄminl,uâxâźâ,mâ(g)â[âxâQâĄ(x,l,u,b)â22].(l_ ,m,g,u_ ,m,g)= _l,uE_x _ ,m(g) [ \|x-Q(x;l,u,b) \|_2^2 ]. (10) Starting from these bounds, we refine only the clipping-bound tensors using a full-precision teacher. Given teacher/student outputs y, y and features Fh,F^hF_h, F_h at distillation layers hââh , we use âpix=â^ââ1,âfeat=1|â|ââhâââF^hâF^hâ2âFhâFhâ2â22.L_pix=\| y-y\|_1, _feat= 1|H| _h \| F_h\| F_h\|_2- F_h\|F_h\|_2 \|_2^2. (11) 5.5 Frequency-Preserving Refinement for Bound Calibration Low-bit activation quantization can attenuate textures and shift edges, while pixel-space distillation is often dominated by low-frequency energy. Motivated by the effectiveness of frequency-domain objectives in image restoration [14, 7], we formulate Frequency-Preserving Refinement (FPR) as a teacher-supervised objective for SR PTQ. FPR calibrates clipping bounds by aligning Fourier amplitude and phase between full-precision teacher and quantized student outputs. We apply a 2D Hann window w and compute 2D Fourier transforms =âąâĄ(âw)Y=F(y w) and ^=âąâĄ(^âw) Y=F( y w), then decompose coefficients into amplitude |||Y| and phase â ââ[âĎ,Ď] â[-Ď,Ď]: âFPR=12ââ||â|^|â1âamplitude+12ââwrapâĄ(â âââ â^)â1âphase,L_FPR= 12 \|\,|Y|-| Y|\, \|_1_amplitude+ 12 \|\,wrap( - Y)\, \|_1_phase, (12) where wrapâĄ(â )wrap(¡) maps the phase difference to (âĎ,Ď](-Ď,Ď]. Amplitude matching preserves high-frequency energy, while phase matching penalizes structural shifts in edges and textures. Combining the three distillation terms gives the final objective: â=âpix+Îťfeatââfeat+ÎťFPRââFPR.L=L_pix+ _feat\,L_feat+ _FPR\,L_FPR. (13) Only clipping-bound tensors are optimized, while backbone weights, pseudo-labels, predictor parameters, and bit-widths remain fixed. Table 1: Quantitative comparison under the Weight-freeze PTQ protocol on MambaIRv2-Light. Scale Method W / A Set5 Set14 BSD100 Urban100 Manga109 PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ Ă4 MambaIRv2-Light 32 / 32 32.51 0.8992 28.84 0.7878 27.75 0.7426 26.82 0.8079 31.24 0.9182 PTQ4VM [8] (WACVâ25) 4 / 4 30.82 0.8670 27.69 0.7546 26.95 0.7115 24.76 0.7321 28.19 0.8660 Quamba [6] (ICLRâ25) 4 / 4 31.01 0.8715 27.77 0.7585 26.99 0.7149 25.01 0.7470 28.57 0.8752 MambaQuant [44] (ICLRâ25) 4 / 4 30.74 0.8650 27.17 0.7413 26.37 0.6920 23.28 0.6694 26.73 0.8186 OAQ-SR [38] (ICCVâ25) 4 / 4 30.40 0.8577 27.41 0.7470 26.75 0.7045 24.31 0.7136 27.39 0.8485 Ours 4 / 4 31.46 0.8811 28.14 0.7683 27.24 0.7231 25.39 0.7600 29.21 0.8884 PTQ4VM [8] (WACVâ25) 2 / 2 28.77 0.8162 26.36 0.7167 26.16 0.6802 23.37 0.6704 25.26 0.7943 Quamba [6] (ICLRâ25) 2 / 2 28.88 0.8080 26.45 0.7131 26.20 0.6752 23.48 0.6651 25.43 0.7818 MambaQuant [44] (ICLRâ25) 2 / 2 28.84 0.8079 26.41 0.7114 26.18 0.6739 23.45 0.6648 25.38 0.7829 OAQ-SR [38] (ICCVâ25) 2 / 2 28.78 0.8122 26.37 0.7143 26.17 0.6780 23.40 0.6681 25.33 0.7892 Ours 2 / 2 29.12 0.8260 26.57 0.7259 26.32 0.6891 23.57 0.6805 25.58 0.8031 Ă2 MambaIRv2-Light 32 / 32 38.26 0.9615 34.09 0.9221 32.36 0.9019 33.26 0.9378 39.35 0.9785 PTQ4VM [8] (WACVâ25) 4 / 4 37.17 0.9549 32.86 0.9099 31.57 0.8900 30.47 0.9084 37.22 0.9706 Quamba [6] (ICLRâ25) 4 / 4 37.07 0.9544 32.77 0.9092 31.47 0.8896 30.54 0.9107 36.94 0.9699 MambaQuant [44] (ICLRâ25) 4 / 4 36.67 0.9495 31.76 0.8899 30.85 0.8756 28.08 0.8407 33.47 0.9186 OAQ-SR [38] (ICCVâ25) 4 / 4 37.22 0.9551 32.60 0.9071 31.51 0.8897 30.49 0.9122 36.91 0.9717 Ours 4 / 4 37.56 0.9578 33.24 0.9149 31.86 0.8950 31.34 0.9204 37.85 0.9742 PTQ4VM [8] (WACVâ25) 2 / 2 34.38 0.9328 31.05 0.8886 30.21 0.8660 27.61 0.8603 32.04 0.9399 Quamba [6] (ICLRâ25) 2 / 2 34.66 0.9339 31.26 0.8899 30.38 0.8687 27.80 0.8613 32.50 0.9407 MambaQuant [44] (ICLRâ25) 2 / 2 34.65 0.9337 31.22 0.8885 30.36 0.8685 27.78 0.8610 32.43 0.9395 OAQ-SR [38] (ICCVâ25) 2 / 2 34.54 0.9332 31.19 0.8907 30.33 0.8705 27.71 0.8613 32.29 0.9408 Ours 2 / 2 35.02 0.9436 31.41 0.8966 30.51 0.8766 27.90 0.8708 32.67 0.9508 6 Experiments 6.1 Experimental Setup Datasets. We follow the standard SR PTQ protocol in prior work [37, 28]. Calibration is performed using only low-resolution images without high-resolution targets. We construct the calibration set from 96 low-resolution patches sampled from the DF2K training split [36, 27]. Evaluation is conducted on Set5 [3], Set14 [45], BSD100 [32], Urban100 [19], and Manga109 [33]. Metrics and protocol. We report PSNR and SSIM [39] on the Y channel in YCbCr. Following common SR practice, image boundaries are cropped by the upscaling factor before evaluation. Backbone. We use MambaIRv2-Light [16] as the primary backbone. We additionally evaluate MambaIRv1 [17] to verify the token-group quantization generalizes across selective-scan SR architectures. Implementation details. Calibration images are cropped and augmented following prior SR PTQ work [43, 28]. We initialize clipping bounds by empirical quantization-error minimization (Eq. 10) and refine the clipping bounds using Eq. 13 with Îťfeat=5 _feat=5 and ÎťFPR=0.01 _FPR=0.01. Unless otherwise specified, we use K=8K=8 token groups. We use a shared two-layer FFN predictor detailed in Appendix E.1. Bound refinement is performed for 3,000 iterations with a batch size of 8. All experiments are conducted on three NVIDIA RTX A6000 GPUs. Reported numbers use seed 0, and repeating the full pipeline under five seeds gives std below 0.03 dB at W4A4 and 0.05 dB at W2A2 (Appendix F.1). Table 2: FLOPs and W/A quantization scope. Module FLOPs Ratio Quant. (G) (%) Linear + Conv 8.49 85.9 Yes Scan operands 0.49 4.9 Yes Other Conv 0.90 9.1 No Total 9.88 100.0 â Baselines. For the Weight-freeze PTQ protocol, we compare with PTQ4VM [8], Quamba [6], MambaQuant [44], and OAQ-SR [38]. PTQ4VM, Quamba, and MambaQuant results are taken from SPR2Q [43], while OAQ-SR and ours are evaluated by us. For the Weight-training PTQ with LoRA protocol, we compare with AIQViT [21] and SPR2Q [43]. Our Ours+LoRA follows the SPR2Q rectifier training-and-fusion protocol, while applying token-group activation quantization. All methods use the same W/A low-bit scope. Table 2 shows that this low-bit path covers 90.8% of FLOPs, where Quant. for scan operands denotes activation-operand quantization. Table 3: Quantitative comparison under the Weight-training PTQ with LoRA protocol on MambaIRv2-Light. Scale Method W / A Set5 Set14 BSD100 Urban100 Manga109 PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ Ă4 MambaIRv2-Light 32 / 32 32.51 0.8992 28.84 0.7878 27.75 0.7426 26.82 0.8079 31.24 0.9182 AIQViT [21] (AAAIâ25) 4 / 4 31.51 0.8856 28.10 0.7707 27.26 0.7268 25.18 0.7546 28.76 0.8854 SPR2Q [43] (ICLRâ26) 4 / 4 32.04 0.8929 28.59 0.7812 27.52 0.7359 26.07 0.7864 30.12 0.9048 Ours + LoRA 4 / 4 32.25 0.8953 28.67 0.7830 27.61 0.7377 26.24 0.7906 30.49 0.9095 AIQViT [21] (AAAIâ25) 2 / 2 30.52 0.8667 27.44 0.7541 26.79 0.7102 24.35 0.7210 27.27 0.8515 SPR2Q [43] (ICLRâ26) 2 / 2 30.43 0.8635 27.45 0.7531 26.86 0.7110 24.37 0.7215 27.30 0.8529 Ours + LoRA 2 / 2 30.93 0.8749 27.80 0.7626 27.06 0.7190 24.72 0.7365 28.11 0.8709 Ă2 MambaIRv2-Light 32 / 32 38.26 0.9615 34.09 0.9221 32.36 0.9019 33.26 0.9378 39.35 0.9785 AIQViT [21] (AAAIâ25) 4 / 4 37.73 0.9598 33.19 0.9148 31.92 0.8968 30.97 0.9167 37.59 0.9750 SPR2Q [43] (ICLRâ26) 4 / 4 37.84 0.9601 33.42 0.9171 31.99 0.8972 32.09 0.9286 38.60 0.9772 Ours + LoRA 4 / 4 38.02 0.9608 33.77 0.9200 32.24 0.9005 32.41 0.9314 38.76 0.9777 AIQViT [21] (AAAIâ25) 2 / 2 36.99 0.9552 32.35 0.9092 31.42 0.8907 29.70 0.9007 36.01 0.9700 SPR2Q [43] (ICLRâ26) 2 / 2 36.92 0.9527 32.38 0.9105 31.46 0.8910 30.12 0.9058 36.98 0.9707 Ours + LoRA 2 / 2 37.27 0.9580 32.93 0.9121 31.72 0.8939 30.34 0.9090 37.02 0.9729 Figure 4: Visual comparison for image SR (Ă2Ă 2 and Ă4Ă 4) on Urban100 under 4-bit PTQ. 6.2 Results Quantitative results. Table 1 shows that our Weight-freeze PTQ consistently outperforms Mamba-specific and SR-oriented PTQ baselines across both scales and bit-widths. Table 3 evaluates the LoRA-style Weight-training protocol. Our Ours+LoRA variant follows the rectifier training-and-fusion protocol of SPR2Q while using our token-group activation quantization. It achieves the best results in all settings and nearly recovers full precision at 4-bit; on BSD100, the PSNR drop is only 0.120.12 dB for Ă2Ă 2 and 0.140.14 dB for Ă4Ă 4. Qualitative results. Figure 4 shows that our method better preserves structural details under low-bit quantization. In the Ă2Ă 2 example, Ours maintains the straight canopy edges closer to the FP result, while in the Ă4Ă 4 example, Ours reconstructs sharper text contours with less blur than the baselines. Offline calibration cost. Table 4 compares the calibration cost on MambaIRv2-Light (Ă2Ă 2, 4-bit). In the Weight-freeze PTQ setting, our method adds only a small overhead over OAQ-SR, increasing the wall-clock time from 1.29 h to 1.42 h. Under the LoRA-style Weight-training protocol, Ours+LoRA also remains close to SPR2Q, with 6.57 h vs. 6.12 h. These results show that the proposed group-wise activation quantization introduces only modest additional calibration cost. Inference speed. Table 5 reports end-to-end latency of the W4A4 static low-bit inference path with byte-aligned integer kernels and fixed quantization codes. Our method achieves 1.70Ă speedup on A6000 and 2.23Ă on Jetson Orin Nano over FP16, nearly matching the base 4-bit path, whereas the runtime post-scan oracle loses the speedup entirely since it needs an extra observation pass before quantization. Appendix G explains the overhead of both paths. Weight-freeze PTQ Method Wall-clock Iter Params OAQ-SR 1.29 h 3,000 1.9 k Ours 1.42 h 3,000 4.1 k Weight-training PTQ with LoRA SPR2Q 6.12 h 12,500 617.2 k Ours + LoRA 6.57 h 12,500 619.4 k Table 4: Calibration cost on MambaIRv2-Light (Ă2, W4A4). NVIDIA RTX A6000 Method Latency (ms) Speedup FP16 180.7 1.00Ă 4-bit Oracle 254.5 0.71Ă 4-bit Base 102.7 1.76Ă 4-bit Ours 106.2 1.70Ă Jetson Orin Nano FP16 3149.6 1.00Ă 4-bit Oracle 3213.9 0.98Ă 4-bit Base 1380.1 2.28Ă 4-bit Ours 1410.7 2.23Ă Table 5: Latency on Set5, MambaIRv2-Light (Ă2, W4A4). K Set14 Urban100 PSNR / SSIM PSNR / SSIM 1 32.62 / 0.9073 30.59 / 0.9127 4 33.07 / 0.9117 31.03 / 0.9175 6 33.19 / 0.9142 31.28 / 0.9199 8 33.24 / 0.9149 31.34 / 0.9204 Table 6: Number of token groups K (MambaIRv2-Light, Ă2, W4A4). Refinement objective TG Set14 Urban100 PSNR / SSIM PSNR / SSIM None (Eq. 10 init. only) â 32.15 / 0.8931 29.84 / 0.8915 âpix+âfeatL_pix+L_feat (layer-wise PTQ) â 32.45 / 0.9056 30.34 / 0.9107 None (Eq. 10 init. only) â 32.38 / 0.9015 30.56 / 0.9115 âpixL_pix only â 32.53 / 0.9018 30.72 / 0.9123 âpix+L_pix+ feat. MSE (conventional KD) â 33.01 / 0.9091 30.89 / 0.9136 âpix+âfeatL_pix+L_feat â 33.06 / 0.9107 30.99 / 0.9172 ++ amplitude term only â 33.15 / 0.9122 31.14 / 0.9190 ++ phase term only â 33.10 / 0.9128 31.10 / 0.9183 +âFPR+\,L_FPR (amp. + phase, Ours) â 33.24 / 0.9149 31.34 / 0.9204 Table 7: Supervision ablation on MambaIRv2-Light at Ă2 and W4A4. TG marks token-group quantization. Rows differ only in the refinement objective. Rule Static Set14 Urban100 PSNR / SSIM PSNR / SSIM Layer-wise PTQ â 32.45 / 0.9056 30.34 / 0.9107 Random groups â 31.76 / 0.8904 29.91 / 0.9070 Pre-scan K-means â 32.84 / 0.9092 30.77 / 0.9161 Post-scan oracle â 33.41 / 0.9176 31.57 / 0.9253 Predicted (Ours) â 33.24 / 0.9149 31.34 / 0.9204 Table 8: Grouping rule ablation (MambaIRv2-Light, Ă2, W4A4). Static: no runtime statistics (C1). The post-scan oracle (gray) is a hardware-unfriendly upper bound; bold marks the best static rule. 6.3 Ablation Study Number of token groups. Table 6 shows that performance improves as the number of token groups increases, while the gain from K=6K=6 to K=8K=8 nearly saturates. We therefore use K=8K=8 as the default setting. On MambaIRv2-Base the optimum shifts mildly to K=16K=16, but K=8K=8 already recovers 89% of the range (Appendix F.3). Component analysis. Table 7 separates the two sources of gain. Token grouping alone accounts for 77% of the improvement over layer-wise PTQ on Set14 and 65% on Urban100, and it helps even without refinement. On top of the strongest conventional objective, the amplitude and phase terms each help alone and their combination adds a further 0.35 dB on Urban100, showing that the two are complementary. Appendix H shows that this gain comes from the high-frequency band that pixel and feature matching under-supervise. Grouping rule. Table 8 shows that the gain is not from having more ranges: random groups fall below layer-wise PTQ, and our predicted groups outperform pre-scan K-means and recover 82.3% and 81.3% of the oracle gain on Set14 and Urban100 without runtime statistics. FPR objective weight. A sensitivity analysis on ÎťFPR _FPR is provided in Appendix I. Generalization. Appendices A and B extend the evaluation to MambaIRv1-Light, MambaIRv1-Base, MambaIRv2-Base, denoising, and JPEG artifact removal, to the Transformer backbone SwinIR-light against 2DQuant, FIMA-Q, APHQ-ViT, and SPR2Q, and to ImageNet classification on Vision Mamba, where the token-range amplification of Sec. 4 is even larger. Ours is best in every setting. Ported Hadamard, SpinQuant, and Affine transforms trail ours by up to 2.12 dB, and SpinQuant combined with ours is best everywhere, so the token axis and the channel axis compose. Appendix F.2 further shows robustness to input resolution up to 16 times the calibration length. 7 Conclusion We presented Token-Group Quantization, a static yet token-adaptive PTQ framework for low-bit Mamba-based super-resolution. By analyzing MambaIRv2-Light, we showed that selective scan amplifies token-wise activation heterogeneity, making conventional layer-wise clipping ranges poorly matched to all tokens. Our method addresses this mismatch with a lightweight pre-scan predictor, quantization-aware pseudo-labels, and offline-calibrated group-wise clipping bounds. We further introduced a teacher-supervised FPR objective for frequency-preserving clipping-bound refinement. Experiments demonstrate consistent gains over prior Mamba and SR PTQ baselines under Weight-freeze and LoRA-based protocols, transfer to Transformer SR and Vision Mamba, and compose with channel-axis transforms, while preserving practical acceleration on Jetson Orin Nano. Limitation and Future Work. While Token-Group Quantization improves low-bit Mamba SR accuracy and preserves practical acceleration, its pre-scan prediction and group-wise bound lookup introduce a small inference overhead relative to the base quantized path. Future work may explore deployment on other on-device accelerators, such as NPUs, DSPs, mobile GPUs, or vendor-specific low-bit runtimes, under the same token-adaptive quantization framework. 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Wang (2024) Vision mamba: efficient visual representation learning with bidirectional state space model. arXiv preprint arXiv:2401.09417. Cited by: §B.2, §2.1. Appendix A Generalization Protocol We evaluate generalization on MambaIRv1-Light, JPEG artifact removal, and color image denoising. For these appendix experiments, we include two complementary baselines. Layer-wise PTQ uses the same Weight-freeze protocol and quantization scope as ours, but uses one clipping range per layer/site instead of group-wise ranges; thus, it directly isolates the benefit of token grouping. OAQ-SR is included as a recent SR-oriented outlier-aware PTQ baseline. Since the goal of these experiments is to test transferability rather than to establish a new benchmark suite for every restoration task, this combination provides a controlled baseline and a strong task-relevant PTQ baseline. These experiments also test the robustness of pre-scan group prediction under degraded restoration inputs. JPEG artifact removal contains spatially non-uniform compression artifacts, while color denoising uses noisy inputs; thus, the predictor must infer useful token groups from corrupted features rather than clean or single-degradation inputs. The consistent gains on these tasks indicate that the proposed grouping rule remains effective under input degradation. Table 9: Generalization results on MambaIRv1-Light under the Weight-freeze PTQ protocol. Scale Method W / A Set5 Set14 BSD100 Urban100 Manga109 PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ Ă4 MambaIRv1-Light 32 / 32 32.42 0.8977 28.74 0.7847 27.68 0.7400 26.52 0.7983 30.94 0.9135 Layer-wise PTQ 4 / 4 30.39 0.8257 27.45 0.7249 26.71 0.6811 24.99 0.7185 28.62 0.8372 OAQ-SR [38] (ICCVâ25) 4 / 4 30.85 0.8507 27.80 0.7446 26.93 0.7019 25.03 0.7392 28.59 0.8611 Ours 4 / 4 31.10 0.8627 27.91 0.7534 27.09 0.7097 25.23 0.7444 28.90 0.8682 Layer-wise PTQ 2 / 2 23.10 0.4199 22.29 0.3725 22.25 0.3453 20.92 0.3736 21.99 0.4017 OAQ-SR [38] (ICCVâ25) 2 / 2 27.98 0.7367 25.68 0.6477 25.55 0.6133 23.07 0.6080 25.02 0.7135 Ours 2 / 2 28.33 0.7611 26.09 0.6713 25.89 0.6365 23.29 0.6278 25.19 0.7390 Ă2 MambaIRv1-Light 32 / 32 38.13 0.9610 33.95 0.9208 32.31 0.9013 32.85 0.9349 39.20 0.9782 Layer-wise PTQ 4 / 4 35.07 0.9178 31.83 0.8774 30.67 0.8581 30.05 0.8835 35.06 0.9325 OAQ-SR [38] (ICCVâ25) 4 / 4 36.55 0.9445 32.67 0.9013 31.46 0.8821 30.58 0.9042 36.53 0.9593 Ours 4 / 4 37.12 0.9527 33.06 0.9105 31.73 0.8910 31.06 0.9160 37.25 0.9686 Layer-wise PTQ 2 / 2 22.57 0.4159 21.95 0.4086 21.80 0.3942 21.33 0.4402 22.47 0.4216 OAQ-SR [38] (ICCVâ25) 2 / 2 34.03 0.9303 30.76 0.8809 29.22 0.8471 27.01 0.8537 31.78 0.9354 Ours 2 / 2 34.40 0.9371 31.05 0.8896 30.20 0.8685 27.60 0.8624 32.07 0.9436 Table 10: Generalization results on color image denoising with noise level Ď=15Ď=15 under the Weight-freeze PTQ protocol. Method W / A CBSD68 Kodak24 McMaster Urban100 PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ MambaIRv2-Base 32 / 32 34.15 0.9388 35.15 0.9363 35.07 0.9421 34.72 0.9484 Layer-wise PTQ 4 / 4 32.84 0.9161 33.49 0.9098 33.06 0.9169 32.62 0.9229 OAQ-SR [38] (ICCVâ25) 4 / 4 33.52 0.9290 34.33 0.9243 34.04 0.9305 33.59 0.9371 Ours 4 / 4 33.78 0.9335 34.69 0.9299 34.51 0.9356 34.04 0.9419 Layer-wise PTQ 2 / 2 27.20 0.7871 27.00 0.7667 24.31 0.7564 25.44 0.7860 OAQ-SR [38] (ICCVâ25) 2 / 2 31.63 0.8960 32.06 0.8838 31.16 0.8857 30.25 0.8944 Ours 2 / 2 32.41 0.9142 32.89 0.9060 31.94 0.9081 31.38 0.9174 Table 11: Generalization results on JPEG artifact removal under the Weight-freeze PTQ protocol. Quality Method W / A Classic5 LIVE1 PSNRâ SSIMâ PSNRâ SSIMâ q=10q=10 MambaIRv2-Base 32 / 32 30.37 0.8269 29.91 0.8301 Layer-wise PTQ 4 / 4 28.95 0.7834 28.74 0.7928 OAQ-SR [38] (ICCVâ25) 4 / 4 29.59 0.8064 29.26 0.8125 Ours 4 / 4 29.93 0.8183 29.57 0.8230 Layer-wise PTQ 2 / 2 27.57 0.7324 27.48 0.7474 OAQ-SR [38] (ICCVâ25) 2 / 2 28.06 0.7511 28.06 0.7686 Ours 2 / 2 28.30 0.7698 28.22 0.7851 q=30q=30 MambaIRv2-Base 32 / 32 33.81 0.8970 33.73 0.9179 Layer-wise PTQ 4 / 4 32.47 0.8752 32.37 0.8940 OAQ-SR [38] (ICCVâ25) 4 / 4 33.05 0.8871 33.05 0.9084 Ours 4 / 4 33.39 0.8927 33.34 0.9133 Layer-wise PTQ 2 / 2 22.78 0.4427 22.70 0.4525 OAQ-SR [38] (ICCVâ25) 2 / 2 31.60 0.8617 31.45 0.8822 Ours 2 / 2 31.90 0.8719 31.90 0.8934 q=40q=40 MambaIRv2-Base 32 / 32 34.64 0.9093 34.73 0.9323 Layer-wise PTQ 4 / 4 33.34 0.8909 33.28 0.9110 OAQ-SR [38] (ICCVâ25) 4 / 4 34.02 0.9033 34.14 0.9262 Ours 4 / 4 34.31 0.9068 34.38 0.9292 Layer-wise PTQ 2 / 2 30.79 0.8153 31.17 0.8413 OAQ-SR [38] (ICCVâ25) 2 / 2 32.83 0.8895 32.86 0.9110 Ours 2 / 2 33.11 0.8925 33.22 0.9147 Tables 9â11 show that our method consistently outperforms both baselines across backbones, tasks, and bit-widths. This suggests that the proposed static token-group activation ranges address a general activation-heterogeneity issue in Mamba restoration models, rather than overfitting to the main MambaIRv2-Light SR setting. Notably, the same pre-scan prediction principle remains effective even when the input features are degraded by noise or JPEG artifacts, suggesting that the predictor does not rely on clean-image-specific cues but captures quantization regimes that persist across restoration tasks. For generalization experiments, we prioritize controlled isolation over exhaustive benchmarking. Appendix B Generalization Beyond Mamba-Based SR The main paper evaluates MambaIRv2-Light as the primary backbone, and Appendix A adds MambaIRv1-Light and MambaIRv2-Base on further restoration tasks. This section tests whether the observation of Sec. 4 and the proposed grouping principle extend to a Transformer SR backbone, to Mamba outside restoration, to larger MambaIR backbones, and to channel-axis quantization transforms from the LLM and diffusion literature. B.1 Transformer SR Backbone We apply the same framework to SwinIR-light [26] with the identical quantization scope as 2DQuant [28] and SPR2Q [43], replacing the post-attention MLP activation quantizers with our group-conditional quantizers at K=8K=8. Since SwinIR has no scan stage, the predictor becomes a pre-site predictor trained from pre-block features. Group indices are still produced before the target quantization sites without runtime statistics, so the deployment constraint C1 is unchanged. All distillation settings follow the main paper. Table 12 compares against 2DQuant and the ViT PTQ methods FIMA-Q [40] and APHQ-ViT [41] under the Weight-freeze protocol, and Table 13 compares against SPR2Q under the LoRA protocol. Ours is best in every cell. On SwinIR-light we measured token-range CoV before and after attention and did not observe the amplification induced by selective scan. Token ranges still vary with image content, so tokens can be clustered into distinct range regimes and both the descriptor K-means and the pre-site predictor operate as designed. Since the inter-group range gap is smaller without scan amplification, the clipping error recoverable by grouping is also smaller, which is consistent with the more modest margins than on MambaIRv2-Light. The gain magnitude thus tracks the degree of token heterogeneity across backbones. The method is generally applicable and particularly beneficial for Mamba. Table 12: Ă2Ă 2 SR on SwinIR-light under the Weight-freeze PTQ protocol. Method W / A Set5 Set14 BSD100 Urban100 Manga109 PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ SwinIR-light 32 / 32 38.14 0.9611 33.86 0.9206 32.31 0.9012 32.76 0.9340 39.12 0.9783 2DQuant (NeurIPSâ24) 4 / 4 37.87 0.9594 33.41 0.9161 32.02 0.8971 31.84 0.9251 38.31 0.9761 FIMA-Q (CVPRâ25) 4 / 4 37.71 0.9598 33.38 0.9160 32.01 0.8964 31.95 0.9283 38.44 0.9764 APHQ-ViT (CVPRâ25) 4 / 4 37.76 0.9591 33.41 0.9165 31.94 0.8965 31.98 0.9280 38.34 0.9759 Ours 4 / 4 37.91 0.9600 33.47 0.9171 32.09 0.8978 32.06 0.9287 38.51 0.9773 2DQuant (NeurIPSâ24) 2 / 2 36.00 0.9497 31.98 0.9012 30.91 0.8810 28.62 0.8819 34.40 0.9602 FIMA-Q (CVPRâ25) 2 / 2 36.06 0.9515 32.10 0.9048 31.01 0.8848 28.77 0.8873 34.75 0.9638 APHQ-ViT (CVPRâ25) 2 / 2 36.14 0.9517 32.14 0.9049 31.04 0.8850 28.86 0.8885 34.99 0.9644 Ours 2 / 2 36.58 0.9530 32.36 0.9056 31.17 0.8853 29.18 0.8908 35.47 0.9657 Table 13: Ă2Ă 2 SR on SwinIR-light under the Weight-training PTQ with LoRA protocol. Method W / A Set5 Set14 BSD100 Urban100 Manga109 PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ SwinIR-light 32 / 32 38.14 0.9611 33.86 0.9206 32.31 0.9012 32.76 0.9340 39.12 0.9783 SPR2Q (ICLRâ26) 4 / 4 37.95 0.9602 33.55 0.9178 32.14 0.8989 32.04 0.9275 38.59 0.9769 Ours + LoRA 4 / 4 38.04 0.9608 33.65 0.9193 32.22 0.9003 32.28 0.9302 38.75 0.9776 SPR2Q (ICLRâ26) 2 / 2 37.28 0.9572 32.83 0.9113 31.63 0.8921 30.20 0.9077 37.08 0.9726 Ours + LoRA 2 / 2 37.69 0.9596 33.22 0.9157 31.96 0.8971 31.16 0.9193 37.74 0.9753 B.2 Vision Mamba on ImageNet To test the observation outside restoration, we evaluate Vision Mamba [49] on ImageNet classification. The observation of Sec. 4 transfers. Token-range CoV increases after the Mamba block in all 24 blocks of both models, with an average amplification of 4.94Ă4.94Ă on Vim-Tiny and 3.11Ă3.11Ă on Vim-Small, which is larger than the 1.80Ă1.80Ă measured on MambaIRv2-Light. For quantization we follow the scope and the 256-image calibration protocol of PTQ4VM [8] and apply our group-conditional quantizers with K=8K=8. The predictor runs once per block from the pre-scan block input, and the same group indices are reused across all six per-token linear sites in the block. Since classification outputs logits, we replace the pixel loss with a logit KD loss and drop the FPR term while keeping feature distillation. Only the activation clipping bounds are trained. Table 14 shows that ours is best in every setting. Table 14: ImageNet Top-1 accuracy in percent on Vision Mamba under PTQ. Calibration and quantization scope follow PTQ4VM. Method W / A Vim-Tiny Vim-Small FP 32 / 32 76.07 80.48 Layer-wise PTQ 6 / 6 71.92 76.66 PTQ4VM (WACVâ25) 6 / 6 74.42 79.62 Ours 6 / 6 75.88 79.95 Layer-wise PTQ 4 / 4 53.61 67.06 PTQ4VM (WACVâ25) 4 / 4 56.62 70.41 Ours 4 / 4 57.98 72.50 Although the token-range dispersion is even larger on Vim than in restoration, its impact is task-dependent. Classification aggregates token features into a single prediction, whereas restoration is dense per-pixel regression under static deployment, where every token is on the critical path with all ranges fixed ahead of time. The dispersion therefore becomes the first-order bottleneck in restoration. At aggressive bit-widths it resurfaces in classification as well, where ours again improves over PTQ4VM. B.3 Larger MambaIR Backbones Table 15 evaluates MambaIRv1-Base and MambaIRv2-Base at Ă2Ă 2 under the Weight-freeze protocol with the same quantization scope, calibration setup, and baselines as Appendix A. Ours is best in every setting, so the failure mode identified in Sec. 4 and its remedy are not confined to lightweight models. Table 15: Ă2Ă 2 SR on MambaIRv1-Base and MambaIRv2-Base under the Weight-freeze PTQ protocol. Backbone Method W / A Set14 Urban100 PSNRâ SSIMâ PSNRâ SSIMâ MambaIRv2-Base FP 32 / 32 34.89 0.9275 34.49 0.9468 Layer-wise PTQ 4 / 4 32.39 0.9060 29.25 0.8930 OAQ-SR (ICCVâ25) 4 / 4 33.04 0.9132 31.25 0.9195 Ours 4 / 4 33.28 0.9157 31.60 0.9236 Layer-wise PTQ 2 / 2 30.54 0.8556 27.53 0.8398 OAQ-SR (ICCVâ25) 2 / 2 31.33 0.8958 27.81 0.8699 Ours 2 / 2 31.47 0.8974 28.13 0.8756 MambaIRv1-Base FP 32 / 32 34.67 0.9261 34.15 0.9446 Layer-wise PTQ 4 / 4 31.72 0.8808 29.07 0.8719 OAQ-SR (ICCVâ25) 4 / 4 32.19 0.8952 29.53 0.8874 Ours 4 / 4 33.07 0.9094 31.17 0.9153 Layer-wise PTQ 2 / 2 29.13 0.7846 25.47 0.6770 OAQ-SR (ICCVâ25) 2 / 2 30.84 0.8830 27.43 0.8561 Ours 2 / 2 31.23 0.8940 27.71 0.8672 B.4 Relation to Channel-Axis Quantization Transforms Rotation, affine, and scaling quantizers from the LLM and diffusion literature [1, 30, 31, 35, 42, 24] share one property with prior SR and Mamba PTQ methods. The quantization range is assigned independently of token identity, through a channel-axis transform shared by every token. This is sound when token distributions are homogeneous, which is exactly the assumption that selective scan breaks in Sec. 4. To verify this empirically, we ported the core transforms onto MambaIRv2-Light under the identical protocol, sites, calibration set, and budget. Hadamard covers QuaRot [1], SpinQuant [30] covers learned rotation, and Affine covers AffineQuant [31] and FlatQuant [35], with SmoothQuant-style scale migration [42] as its diagonal case. Atom [47] alone acts on the token axis but through runtime statistics, which C1 rules out, so ours is its static counterpart. Table 16 shows two findings. First, even the best channel-axis transform on each benchmark trails ours by up to 2.12 dB at W4A4. Second, the two axes compose. SpinQuant combined with our method is best in every setting, with the largest gains at W2A2. The two remove different error sources, so Token-Group Quantization occupies a design axis these literatures do not cover while remaining compatible with them. Table 16: Ă2Ă 2 SR on MambaIRv2-Light with channel-axis transforms ported onto the identical Weight-freeze PTQ protocol. Affine covers AffineQuant and FlatQuant, and Hadamard covers QuaRot. Method W / A Set5 Set14 BSD100 Urban100 Manga109 PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ PSNRâ SSIMâ MambaIRv2-Light 32 / 32 38.26 0.9615 34.09 0.9221 32.36 0.9019 33.26 0.9378 39.35 0.9785 Affine 4 / 4 35.80 0.9452 32.81 0.9091 30.89 0.8789 30.57 0.9163 34.67 0.9550 Hadamard 4 / 4 36.33 0.9492 32.61 0.9085 31.04 0.8823 30.36 0.9123 35.73 0.9655 SpinQuant 4 / 4 36.42 0.9500 32.50 0.9063 31.08 0.8828 30.74 0.9188 35.54 0.9622 Ours 4 / 4 37.56 0.9578 33.24 0.9149 31.86 0.8950 31.34 0.9204 37.85 0.9742 SpinQuant + Ours 4 / 4 37.69 0.9588 33.40 0.9163 31.96 0.8965 31.61 0.9228 37.94 0.9750 Affine 2 / 2 34.59 0.9365 31.18 0.8904 30.32 0.8703 27.71 0.8643 32.31 0.9438 Hadamard 2 / 2 34.72 0.9389 31.23 0.8923 30.37 0.8722 27.75 0.8656 32.35 0.9456 SpinQuant 2 / 2 34.84 0.9400 31.29 0.8935 30.42 0.8734 27.79 0.8668 32.46 0.9467 Ours 2 / 2 35.02 0.9436 31.41 0.8966 30.51 0.8766 27.90 0.8708 32.67 0.9508 SpinQuant + Ours 2 / 2 36.23 0.9513 32.17 0.9037 31.06 0.8841 28.77 0.8850 34.72 0.9614 Appendix C Rationale for Quantization-Aware Descriptors C.1 Why These Descriptor Statistics? We motivate the descriptor in Eq. 6 from the error decomposition of a uniform quantizer. For clarity, consider symmetric clipping [âc,c][-c,c] for a token-level random variable XiX_i drawn from the channel entries of xi(â,m)x_i^( ,m). The quantization step size is ÎâĄ(c)=2âc/(2bâ1) (c)=2c/(2^b-1). Under the standard high-resolution approximation, the per-token quantization error can be written as Eiâ(c)âÎâ(c)212âPrâĄ(|Xi|â¤c)+âĄ[(|Xi|âc)+2].E_i(c)â (c)^212 (|X_i|⤠c)+E [(|X_i|-c)^2_+ ]. (14) Here, (z)+=maxâĄ(z,0)(z)_+= (z,0). The first term is the rounding error within the clipping range and increases with the step size, while the second term is the clipping error from tail activations. Therefore, tokens should share a clipping bound only when their bulk scale and tail behavior are similar. The descriptor in Eq. 6 provides a compact proxy for this precisionâclipping trade-off. RMSâĄ(xi(â,m))RMS(x_i^( ,m)) captures the bulk activation energy that influences rounding sensitivity, q0.99q_0.99 and q0.999q_0.999 capture near-tail and extreme-tail scales, and maxâĄ|xi(â,m)| |x_i^( ,m)| captures the worst-case tail extent. Although these statistics are not sufficient statistics for the full activation distribution, they characterize the dominant factors that shape the quantization-error curve over clipping bounds. Clustering tokens in this descriptor space therefore groups tokens that are likely to have similar MSE-preferred clipping ranges. Appendix D Pre-scan Predictor Details and Robustness D.1 Prediction Accuracy and Error Structure The pre-scan predictor is trained to reproduce pseudo-labels obtained by K-means clustering in the downstream activation-descriptor space. For K=8K=8, the predictor achieves approximately 84% top-1 accuracy on held-out tokens. This accuracy should not be interpreted as classification accuracy against semantic ground truth. The pseudo-labels are calibration artifacts that compress quantization-error regimes, so the accuracy measures how well pre-scan features recover the descriptor-space partition used for grouping. More importantly, prediction errors are structured. We further observe that many misclassified tokens are assigned to nearby clusters in the descriptor space rather than to distant regimes. Since the descriptor is constructed from statistics that dominate the roundingâclipping trade-off, nearby clusters tend to have similar MSE-preferred clipping bounds. Therefore, such errors still often select bounds that are close to the oracle-preferred range. This supports the robustness of using a lightweight pre-scan predictor instead of runtime post-scan group assignment. The pseudo-labels should therefore be understood not as semantic labels, but as a compact representation of quantization-error regimes. What matters is not perfect label stability, but whether tokens assigned to the same group exhibit similar clipping-error and rounding-error behavior. D.2 Robustness to Inference-Time Predictor Errors While Table 8 compares different grouping rulesâeach requiring its own calibrationâwe now ask a complementary question: how much does the framework tolerate runtime errors in the predictor output? In Table 17, we keep the calibrated bound tables and the trained predictor exactly as in our default deployment, and only at evaluation time randomly reassign a fraction Ď of the predicted group ids to a uniformly random group in 1,âŚ,K\1,âŚ,K\. No re-calibration, no bound re-refinement, and no predictor re-training is performed. The Ď=0%Ď=0\% row therefore matches our default result, while Ď=100%Ď=100\% corresponds to fully random group ids on top of the bound tables calibrated for our predictor, and is conceptually distinct from the âRandom groupsâ row of Table 8, where bounds are calibrated jointly with random grouping. Table 17: Robustness to inference-time predictor perturbation on MambaIRv2-Light (Ă2Ă 2, W4A4) under the Weight-freeze PTQ protocol. We use the calibrated bound tables and the trained predictor from our default setting and, only at evaluation time, randomly reassign a fraction Ď of predicted group ids to a uniformly random group in 1,âŚ,K\1,âŚ,K\. Calibration, bound refinement, and the predictor are unchanged across rows. The Ď=0%Ď=0\% row matches our default deployment. Perturbation rate Ď Set14 Urban100 PSNRâ SSIMâ PSNRâ SSIMâ Ď=0%Ď=0\% (ours, no perturbation) 33.24 0.9149 31.34 0.9204 Ď=5%Ď=5\% 33.21 0.9145 31.34 0.9204 Ď=10%Ď=10\% 33.18 0.9143 31.33 0.9202 Ď=20%Ď=20\% 33.09 0.9137 31.25 0.9193 Ď=30%Ď=30\% 33.01 0.9127 31.13 0.9178 Ď=50%Ď=50\% 32.72 0.9108 31.02 0.9165 Ď=100%Ď=100\% (uniform random ids) 32.56 0.9084 30.45 0.9121 The empirical predictor error rate is approximately 16%16\% (K=8K=8, top-1 accuracy 84%84\%). Around this regime, perturbation has only a marginal effect: at Ď=10%Ď=10\% and Ď=20%Ď=20\%, the Set14 PSNR drops by only 0.060.06 dB and 0.150.15 dB from the unperturbed default, with similarly small drops on Urban100. Even at Ď=50%Ď=50\%âwhere half of all predicted group ids are randomly corruptedâPSNR degrades by only 0.520.52 dB on Set14 and 0.320.32 dB on Urban100, well below the gap between layer-wise PTQ and our method (Table 8). A particularly informative comparison is the Ď=100%Ď=100\% row, in which predicted group ids are entirely replaced by uniformly random ids while the bound tables remain those calibrated for our predictor. This setting still attains 32.5632.56 / 30.4530.45 dB on Set14 / Urban100, clearly above the âRandom groupsâ row of Table 8 (31.7631.76 / 29.9129.91 dB), where the bound tables themselves were calibrated under random grouping. The 0.800.80 / 0.540.54 dB gap indicates that a substantial portion of the benefit comes from the calibrated bound tables themselves, with the predictor providing additional gains on top. Together with the structured-error analysis in Appendix D, this confirms that the framework does not rely on the predictor being near-perfect. Small fluctuations in predicted group ids are absorbed by the bound tables, and the method degrades gracefully rather than catastrophically as prediction quality decreases. Appendix E Additional Implementation Details E.1 Pre-scan Predictor Training Details The pre-scan predictor is a shared two-layer FFN (Câ64âKCâ64âK with GELU, where C=48C=48 for MambaIRv2-Light and K=8K=8 by default). It is trained only during calibration to reproduce the descriptor-K-means pseudo-labels using cross-entropy. We use Adam with learning rate 10â310^-3, batch size 1024, 20 epochs, an 80/20 train/validation split, and random seed 0. The input is the pre-ASSM feature at each tokenâlayer pair, and the target is the K-means label obtained from descriptors concatenated over all eight group-conditional sites: three downstream linear sites and five scan-internal per-token operands. After training, the FFN is frozen and used only to assign group indices for fixed clipping-bound table lookup. E.2 Quantization Scope We apply low-bit quantization to two functional groups of activations. First, we quantize the inputs to the linear and pointwise convolution modules in the backbone, including the post-scan projection out_proj and the two convffn2 linear layers in each ASSM block. This part accounts for 85.9%85.9\% of the FLOPs. Second, inside selective scan, we quantize five token-adaptive operands: xs, dts, delta, Bs, and Cs. These scan operands account for an additional 4.9%4.9\% of the FLOPs. Together, the low-bit path covers 90.8%90.8\% of the total FLOPs, matching the quantization scope reported in Table 2. Among these quantized activations, group-wise clipping is applied to the eight token-indexed sites used for pseudo-label construction: out_proj, convffn2.fc1, convffn2.fc2, and the five scan operands xs, dts, delta, Bs, and Cs. The remaining modules are kept in full precision due to sensitivity or limited benefit from low-bit quantization. For feature distillation, âH contains the outputs of all ASSM blocks. In MambaIRv2-Light, |â|=20|H|=20, and Fh,F^hF_h, F_h denote the corresponding full-precision teacher and quantized student features after the residual output of block h. E.3 Reproducibility The source code is publicly available at https://github.com/imaboybut/TGQ-MambaSR. Appendix F Robustness Analyses F.1 Sensitivity to Calibration Sampling and Random Seeds The calibration pipeline involves patch sampling, K-means initialization, predictor training, and bound refinement. We repeat the full pipeline from scratch under five random seeds on MambaIRv2-Light at Ă2Ă 2. Each seed jointly re-samples the 96 patches from DF2K, re-initializes the K-means, and re-seeds predictor training. Bound initialization and refinement are re-run per seed, so nothing is shared except the pretrained backbone. The results are highly stable. The standard deviation across seeds stays below 0.03 dB PSNR and 0.005 SSIM on all five benchmarks at W4A4, and below 0.05 dB and 0.01 at W2A2. These deviations are far smaller than the margins over the strongest baseline, such as the 0.85 dB gain over OAQ-SR on Urban100 at W4A4, so the improvements are not a favorable calibration draw. The predictor reaches 85Âą1.3%85Âą 1.3\% top-1 accuracy across runs, close to the 84% reported in Appendix D, which indicates that the pseudo-labels remain similarly learnable across seeds. This stability is consistent with the design, since the bound tables absorb group-assignment fluctuations and such small swings are well within the tolerance shown in Table 17. F.2 Robustness to Input Resolution Calibration uses 64Ă6464Ă 64 LR crops of about 4k tokens, while selective scan runs unwindowed over L=HâWL=HW, so Urban100 evaluation already reaches about 308k tokens, which is 75 times the calibration length. To isolate resolution from content, Table 18 freezes the predictor and bound tables and crops the same Urban100 images across a 64 times token range. We report the gap between FP and Ours, since crop size shifts content statistics for both models identically and the gap isolates what the frozen grouping rule loses. The gap remains nearly flat across the whole range, and at 16 times the calibration length it is no larger than at the calibration length itself. The method is therefore insensitive to input resolution, and this flatness under fixed K=8K=8 suggests that per-resolution retuning of K is unnecessary. Table 18: Resolution robustness on Urban100 at Ă2Ă 2 and W4A4 over 20 images. Predictor and bound tables are frozen and only the LR input crop size varies. Gap is FP minus Ours. LR crop Tokens Ratio to calib. FP Ours Gap PSNR SSIM PSNR SSIM PSNR SSIM 32Ă3232Ă 32 1,024 0.25Ă 33.77 0.9127 31.88 0.8929 1.89 0.0198 64Ă6464Ă 64 4,096 1Ă 32.60 0.9084 30.48 0.8825 2.12 0.0259 128Ă128128Ă 128 16,384 4Ă 31.89 0.9105 29.78 0.8873 2.11 0.0232 256Ă256256Ă 256 65,536 16Ă 32.13 0.9217 30.07 0.9003 2.06 0.0214 F.3 Number of Token Groups on a Larger Backbone Table 19 repeats the K sweep of Table 6 on MambaIRv2-Base, extended to K=12K=12 and K=16K=16. The optimum shifts mildly upward with model size, since a wider channel dimension supports more distinguishable activation regimes, but the returns diminish quickly. Moving from K=1K=1 to K=8K=8 already recovers 89% of the total range on Set14. K=8K=8 therefore remains a robust default without per-model tuning, and larger backbones can raise K for a small further gain. The identical two-layer FFN transfers without architectural change, and only its input width follows the backbone channel dimension. Table 19: Effect of the number of token groups K on MambaIRv2-Base at Ă2Ă 2 and W4A4. K Set14 Urban100 PSNRâ SSIMâ PSNRâ SSIMâ 1 32.55 0.9099 30.98 0.9084 4 33.20 0.9141 31.37 0.9193 8, default 33.28 0.9157 31.60 0.9236 12 33.34 0.9163 31.68 0.9244 16 33.37 0.9168 31.71 0.9249 Appendix G Deployment Details We implement a CUDA deployment path for the W4A4 quantized model to evaluate practical 4-bit acceleration. After calibration, all clipping-bound tables, quantization scales, weight quantization parameters, and pre-scan predictor parameters are frozen. Runtime execution predicts token groups from pre-scan features and selects the corresponding fixed clipping bounds, without runtime statistics collection, dynamic clipping updates, or post-scan group assignment. For grouped activation sites, calibration-time fake-quantization modules are replaced with static CUDA kernels that fuse group-wise bound lookup, clamping, rounding, and dequantization. The activation and weight quantization codes are constrained to the 4-bit range, while byte-aligned integer buffers are used for efficient CUDA execution. Quantized linear layers use pre-quantized weights, integer CUDA kernels, and dequantization with fixed activation and weight quantization parameters. We also apply CUDA graph capture after static conversion to reduce CPU dispatch overhead. As reported in Table 5, the W4A4 deployment achieves 1.70Ă speedup on A6000 and 2.23Ă speedup on Jetson Orin Nano over FP16, demonstrating practical 4-bit acceleration for Token-Group Quantization. We measure end-to-end latency on Set5 with batch size 1 using the same evaluation script, backend, graph mode, and timing protocol for FP16, the 4-bit base path, and our grouped 4-bit path. For each image, we run 5 warm-up iterations, synchronize the device, run 10 timed repetitions, synchronize again, and report the average latency per image. Since Set5 contains images with different resolutions, CUDA graph capture is performed once for each encountered input shape and then reused for that shape. The reported latency excludes graph construction time but includes pre-scan predictor execution, group-wise bound lookup, quantization/dequantization, and low-bit linear execution. Overhead breakdown. The measured latency in Table 5 includes every component of the grouped path. Predictor execution is inside the timed path, and group-wise bound lookup, clamping, rounding, and dequantization are fused into the static CUDA kernels described above. The resulting overhead over the base 4-bit path is 3.4% on A6000 and 2.2% on Jetson Orin Nano, and the added memory is about 5 KB of bound tables plus a two-layer FFN, so the two paths are nearly identical in cost. By hardware-friendly we mean the property that matters for static deployment. There are no runtime statistics and no dynamic clipping updates, and all parameters are fixed after calibration, so the path stays compatible with ahead-of-time compilation and CUDA graph capture. Runtime post-scan oracle. The 4-bit Oracle rows of Table 5 measure the most favorable dynamic implementation of the post-scan oracle of Table 8. Descriptor statistics of Eq. 6 are computed by dedicated kernels and groups are assigned by nearest-centroid lookup against the offline K-means centroids, with no K-means re-run and with the same CUDA graph capture and timing protocol. Its cost has three sources. First, and dominant, the block must run twice. The group id of a token is determined by statistics of its post-scan activations at the eight grouped sites, but those activations exist only after the block has executed, and the quantizers of the same block already need the id. The only resolution is to run the block once to observe, assign groups, and run it again quantized. Our predictor breaks this dependency by reading pre-scan features, so one pass suffices. Second, the descriptors themselves are costly. At 160 sites, eight per block over 20 blocks, the activation tensor is read once more to obtain per-token q0.99q_0.99, q0.999q_0.999, RMS, and max. The two quantiles are order statistics that cannot be fused into the quantization kernel, so this step adds separate memory-bound kernels and a synchronization point between the two passes. Third, nearest-centroid assignment over the 32-dimensional descriptor is cheap but adds one more launch per block. As a result, the oracle takes 254.5 ms on A6000 and 3213.9 ms on Jetson Orin Nano, a 0.71Ă and 0.98Ă speedup over FP16, so 4-bit execution brings no acceleration at all, whereas the base path and ours reach 1.76Ă and 1.70Ă on A6000 and 2.28Ă and 2.23Ă on Orin Nano. The oracleâs 0.17 dB advantage in Table 8 therefore comes at a cost that static low-bit deployment cannot pay, whereas ours retains most of that gain with a single pass and fixed bound tables. Appendix H Frequency-Domain Evidence for FPR Table 7 in the main paper shows that the amplitude and phase terms each help alone and are complementary in combination. Here we show where in the spectrum the gain arises. Table 20 decomposes the error of the quantized output against the FP output on Urban100 at Ă2Ă 2 and W4A4 into low, mid, and high radial frequency bands and reports the mean amplitude and phase error per band. Set14 shows the same pattern. The variants correspond to the last four rows of Table 7, and the row labeled none is âpix+âfeatL_pix+L_feat with token groups. Table 20: Band-wise Fourier errors of the quantized output against the FP output on Urban100 at Ă2Ă 2 and W4A4. Lower is better. All variants use token groups, and none denotes âpix+âfeatL_pix+L_feat without any frequency term. Frequency term Amplitude error Phase error Low Mid High Low Mid High none 0.0208 0.2853 0.536 0.0213 0.3211 0.673 + amplitude only 0.0206 0.2784 0.512 0.0212 0.3191 0.668 + phase only 0.0213 0.2830 0.531 0.0216 0.3181 0.635 + âFPRL_FPR, Ours 0.0214 0.2850 0.518 0.0219 0.3213 0.643 Three observations follow. First, the error concentrates in the high band, while low-band errors are an order of magnitude smaller and flat across variants, so pixel and feature matching already cover low frequencies and under-supervise high ones. Second, in the high band the amplitude term primarily reduces amplitude error and the phase term primarily reduces phase error, so the two emphasize complementary error axes. Third, each single term concentrates its supervision on one axis, whereas FPR reduces both high-band errors jointly. Since restoration quality depends on the joint error, only FPR reaches the best PSNR and SSIM in Table 7. Existing frequency-domain losses [14, 7] train network weights and are supervised by ground-truth HR images or a larger teacher. FPR differs on both sides. Only the clipping bounds are trained while all weights stay frozen, and the teacher is the FP model supervising its own quantized counterpart. The objective is thus not to learn a representation but to correct the spectral error that quantization itself introduces. Appendix I FPR Objective Weight Sensitivity Table 21 studies the sensitivity to ÎťFPR _FPR in Eq. 13 under the Weight-freeze PTQ protocol at Ă2Ă 2, W4A4. All other settings, including the pre-scan predictor, bound initialization, Îťfeat=5 _feat=5, and the bound-refinement schedule, are kept at their default values. A small weight (0.0050.005) provides too weak a frequency-domain signal, while a large weight (0.10.1) competes with âpixL_pix and âfeatL_feat and degrades high-frequency textures, as reflected by the larger drop on Urban100. The performance is stable in a broad neighborhood around the default ÎťFPR=0.01 _FPR=0.01. Table 21: Sensitivity to FPR objective weight ÎťFPR _FPR on MambaIRv2-Light (Ă2Ă 2, W4A4) under the Weight-freeze PTQ protocol. All other settings are kept at their default values. ÎťFPR=0.01 _FPR=0.01 corresponds to our default setting. ÎťFPR _FPR Set14 Urban100 PSNRâ SSIMâ PSNRâ SSIMâ 0.0050.005 33.11 0.9124 31.19 0.9184 0.010.01 (ours) 33.24 0.9149 31.34 0.9204 0.050.05 33.22 0.9140 31.31 0.9197 0.10.1 33.09 0.9116 31.04 0.9175 Appendix J Clipping-Scale Regimes Across Layers To complement Fig. 2, we visualize token-level preferred clipping scales ciâc_i across additional ASSM layers and post-scan sites. These plots show that downstream descriptor groups often reveal stronger clipping-scale structure than random groups, while predicted groups provide a deployable but less sharply separated approximation. Figure 5: Clipping-scale regimes in early/middle layers. Token-level preferred clipping scales ciâc_i for layers 1 and 6 under random, post-scan descriptor K-means (oracle), and predicted groups. Figure 6: Clipping-scale regimes in later layers. Token-level preferred clipping scales ciâc_i for layers 11 and 16 under random, post-scan descriptor K-means (oracle), and predicted groups. NeurIPS Paper Checklist 1. Claims Question: Do the main claims made in the abstract and introduction accurately reflect the paperâs contributions and scope? Answer: [Yes] Justification: The abstract and introduction summarize the main contributions and scope, which are supported by our analysis, ablations, experiments, and latency results. 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