Channel-Split Quantization

• Channel-split quantization is a technique that treats the channel dimension as the primary axis, enabling exponential coding capacity and task-specific precision.
• It employs methods such as channel grouping, duplication, and mixed-precision calibration to reduce quantization error and manage outliers without extensive retraining.
• The approach offers practical trade-offs by balancing increased representation power with minor memory overhead, improved rate–distortion performance, and robustness in multimodal settings.

Searching arXiv for recent and foundational papers on channel-split quantization and closely related channel-wise quantization methods. Channel-split quantization denotes a family of quantization strategies that treat the channel dimension as the primary axis for nonuniform discretization, rather than quantizing an activation tensor, latent tensor, or weight tensor as a single homogeneous object. In the literature, this family includes several distinct mechanisms: decomposition of a feature tensor into channel groups with independent codebooks; splitting an expanded latent into multiple channel blocks quantized by a look-up-free base quantizer; duplicating outlier channels and halving their contributions to reduce extreme values under post-training quantization; splitting high-sensitivity channels before fixed-point deployment of learned codecs; and assigning channel-dependent quantization levels or bit-widths according to channel importance, modality-specific outliers, or downstream action sensitivity (Fostiropoulos et al., 2022, Argaw et al., 6 Jul 2025, Sun et al., 2022, Zhao et al., 2019).

1. Definitions and terminological scope

The term is used for related but non-identical operations. In capacity-oriented discrete latent models, the channel axis is partitioned into multiple groups that are quantized independently, so the effective number of joint codes grows combinatorially. In fixed-point compression and post-training quantization, the channel axis is split or duplicated to reduce dynamic range or isolate outliers. In variable-precision schemes, channels are sorted, grouped, or calibrated separately, with different quantization levels, scales, or bit-widths assigned to different channel subsets.

Paradigm	Core channel operation	Primary objective
Depthwise Quantization	Partition $C$ channels into $M$ slices and learn separate codebooks	Exponential increase in representation capacity with linear memory growth
Video channel-split quantization	Expand channels from $c$ to $c\!\cdot\!K$, split into $K$ groups, quantize each independently	Increase effective codebook size while preserving token count
Channel splitting for fixed-point compression	Split selected channels, reduce range, then prune	Reduce quantization error under 8-bit deployment
Outlier channel splitting	Duplicate channels with outliers and halve contributions	Reduce outlier magnitude without retraining
Channel-wise variable or mixed precision	Sort or rank channels and assign different quantizers or bit-widths	Match precision to channel importance

A common source of confusion is that “channel-split quantization” does not identify one canonical operator. The shared premise is that channels are statistically, functionally, or distributionally non-equivalent. What differs across papers is the reason for exploiting that non-equivalence: representational capacity in vector-quantized latents, rate–distortion control in learned compression, outlier handling in post-training quantization, or robustness to modality and control errors in multimodal systems.

2. Capacity-oriented formulations in discrete latent models

In Depthwise Quantization (DQ), the encoder output $X\in\mathbb R^{C\times H\times W}$ is decomposed along the channel axis, motivated by the empirical observation that spatial locations are heavily correlated whereas different channels exhibit weak statistical dependence, expressed as

$I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$

The tensor is partitioned as

$$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$

and each slice receives its own codebook $C_i=\{c_i^1,\dots,c_i^K\}$ with $c_i^k\in\mathbb R^D$. Quantization is then

$M$0

with nearest-neighbor assignment

$M$1

Training uses a straight-through estimator and the loss

$M$2

with $M$3. Its central claim is a capacity–memory asymmetry: stored code vectors scale linearly as $M$4, whereas the number of representable joint codes is $M$5, so capacity grows exponentially in $M$6 for fixed $M$7 (Fostiropoulos et al., 2022).

This same combinatorial argument reappears in channel-split quantization for discrete video tokenization, but with look-up-free base quantizers rather than learned VQ codebooks. The encoder output is expanded from $M$8 channels to $M$9, split into $c$0 groups of size $c$1, and each group is quantized independently with LFQ or FSQ:

$c$2

To preserve the total number of tokens, the spatio-temporal compression ratio is increased by a factor of $c$3, so the smaller grid exactly offsets the $c$4-fold increase in channel count. The paper states that, given a codebook budget $c$5, a $c$6-tuple of tokens $c$7 can be mapped to a single integer

$c$8

so the construction operates “as if using a single codebook of size $c$9” while maintaining token count. In this setting, channel splitting is used to recover representational power lost by binary or finite-scalar look-up-free quantizers, not to reduce sequence length or search cost further (Argaw et al., 6 Jul 2025).

3. Dynamic-range reduction, rate–distortion control, and outlier management

A different line of work uses channel splitting to reduce quantization error rather than to enlarge a discrete code space. In Q-LIC, the starting point is that quantization error affects different channels unequally. For a channel $c\!\cdot\!K$0 with dynamic range $c\!\cdot\!K$1 and quantization step $c\!\cdot\!K$2, the mean-squared quantization error is approximated as

$c\!\cdot\!K$3

Propagation to reconstruction error is modeled as

$c\!\cdot\!K$4

where $c\!\cdot\!K$5 measures sensitivity of final MSE to quantization in channel $c\!\cdot\!K$6. Splitting a channel into $c\!\cdot\!K$7 sub-channels reduces its dynamic range by $c\!\cdot\!K$8 and its quantization-error term by $c\!\cdot\!K$9, yielding gain

$K$0

In practice the paper ranks channels by

$K$1

and splits the top-$K$2 channels with $K$3, then prunes the lowest-energy channels to restore the original width. Under 8-bit quantization for weight and activation of both main and hyper path, this reduces the BD-rate by $K$4 compared with the previous QLIC, and the method can be combined with EWGS for further gains (Sun et al., 2022).

Outlier Channel Splitting (OCS) uses duplication rather than subgroup VQ. The objective is post-training quantization without retraining, in settings where a symmetric linear quantizer

$K$5

is dominated by rare large outliers. OCS selects channels containing outliers, duplicates each selected channel, and applies the quantization-aware split

$K$6

This guarantees

$K$7

under round-to-nearest, so the network remains functionally identical while affected outliers move toward the center of the distribution. The reported overhead is minor; for ResNet-50 with $K$8, weights increase by $K$9 and activations by $X\in\mathbb R^{C\times H\times W}$0. Empirically, OCS outperforms state-of-the-art clipping techniques on ImageNet classification and language modeling at low precision, with no additional training and no specialized hardware (Zhao et al., 2019).

A frequent misconception is that channel splitting necessarily changes the represented function. That is true for many learned capacity-expansion schemes, but not for OCS: its explicit design goal is functional equivalence. Conversely, Q-LIC intentionally changes the parametrization and then prunes channels to keep the total number of channels as origin, so it is a rate–distortion optimization method rather than a function-preserving transform.

4. Channel importance, static scaling, and mixed-precision allocation

The broader channel-wise quantization literature applies the same nonuniform-channel premise even when the operation is not an explicit split-then-concatenate block. In the Channel-Level Variable Quantization Network for deep image compression, latent channels are sorted by a learned importance score $X\in\mathbb R^{C\times H\times W}$1, split into $X\in\mathbb R^{C\times H\times W}$2 contiguous groups, and quantized with different quantization levels $X\in\mathbb R^{C\times H\times W}$3. The controller combines a channel importance module with a splitting–merging module:

$X\in\mathbb R^{C\times H\times W}$4

Its scalar quantizer is formulated as a Gaussian mixture model, with hard forward assignment to a centroid $X\in\mathbb R^{C\times H\times W}$5 and soft backward relaxation through mixture responsibilities. On Kodak, compared with a single-group quantizer at level $X\in\mathbb R^{C\times H\times W}$6 giving MS-SSIM $X\in\mathbb R^{C\times H\times W}$7 and BPP $X\in\mathbb R^{C\times H\times W}$8, the 3-group controller with levels $X\in\mathbb R^{C\times H\times W}$9 and predefined importance achieves MS-SSIM $I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$0 and BPP $I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$1 (Zhong et al., 2020).

Static per-channel calibration makes a similar point from a deployment perspective. SPIQ derives a fixed activation scale for each input channel from BatchNorm statistics,

$I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$2

then folds those input-channel scales into the next weight tensor,

$I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$3

This preserves static inference speed while more finely modeling cross-channel range differences. The paper reports that SPIQ matches or exceeds dynamic input quantization accuracy on ImageNet, Pascal VOC, and CityScapes while running about $I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$4 faster than dynamic quantization (Yvinec et al., 2022).

MergeQuant extends the static-calibration idea to 4-bit LLM quantization through per-channel static quantization and Quantization Step Migration (QSM), which merges per-channel quantization steps into adjacent RMSNorm and linear layers. It further proposes dimensional reconstruction, which splits scales $I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$5 that exceed a threshold

$I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$6

replicates the corresponding rows, and then prunes the least important channels to restore the original dimension. Under static W4A4, it reduces the accuracy gap on zero-shot tasks compared to FP16 baseline to $I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$7 points on Llama-2-70B, and on Llama-2-7B reports up to $I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$8 decoding speedup and up to $I(X_c;X_{c'}) \ll I(X_{(h,w)};X_{(h',w')}) .$9 end-to-end speedup compared to FP16 baseline (Wang et al., 7 Mar 2025).

CMPQ pursues channel-wise mixed precision rather than explicit channel splitting. It assigns each channel a bit-width $$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$0, protects activation-based outliers in the top $$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$1 of channels and residual outliers in the top $$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$2 of entries in FP16, and uses K-means centroids per channel for non-uniform quantization. This suggests a broader design principle: many practical gains associated with channel-split quantization arise from acknowledging that channels differ in range, entropy, and sensitivity, even when the implementation uses mixed precision or per-channel calibration rather than literal channel duplication (Chen et al., 2024).

5. Multimodal and action-centric extensions

In large vision-LLMs, channel splitting is used to decouple modality-specific outliers. SplitQ observes that text and vision activations exhibit heterogeneous distributions and that the outlier channels for the two modalities are typically different. It partitions the input-channel index set of a linear layer into three disjoint subsets,

$$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$3

corresponding to modality-compatible channels, text outliers, and vision outliers. Vision-specific outliers are selected by maximum absolute activation over sampled vision tokens; text-specific outliers are selected by an instability score derived from percentile-rank clustering over text tokens. Each group then receives its own diagonal transform $$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$4 through the objective

$$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$5

For the main group, SplitQ adds Adaptive Cross-Modal Calibration, consisting of Cross-Modal Weight Smoothing and Modality-Aware Activation Compensation via low-rank branches anchored in the SVD subspace of the weights. On Qwen2.5-VL, the method reports averages of $$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$6 at W4A8, $$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$7 at W4A4, and $$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$8 at W3A3 for the $$X = \mathrm{concat}[X^1, X^2, \dots, X^M],\qquad X^i\in\mathbb R^{D\times H\times W},\quad D=C/M,$$9B/$C_i=\{c_i^1,\dots,c_i^K\}$0B models; for the $C_i=\{c_i^1,\dots,c_i^K\}$1B model, $C_i=\{c_i^1,\dots,c_i^K\}$2 under W3A3 preserves $C_i=\{c_i^1,\dots,c_i^K\}$3 of the FP16 average $C_i=\{c_i^1,\dots,c_i^K\}$4 (Zhong et al., 19 May 2026).

QVLA, developed for Vision-Language-Action models, does not use the label “channel-split quantization,” but it advances the same channel-granular logic into embodied control. For each layer $C_i=\{c_i^1,\dots,c_i^K\}$5, output channel $C_i=\{c_i^1,\dots,c_i^K\}$6, and bit-width $C_i=\{c_i^1,\dots,c_i^K\}$7, it defines a single-step action-space sensitivity

$C_i=\{c_i^1,\dots,c_i^K\}$8

and a cumulative rollout sensitivity $C_i=\{c_i^1,\dots,c_i^K\}$9. Bit-width assignment is then cast as

$c_i^k\in\mathbb R^D$0

with $c_i^k\in\mathbb R^D$1 bits denoting pruning. A greedy demotion algorithm lowers precision on the least sensitive channels first. On LIBERO, the quantized OpenVLA-OFT requires only $c_i^k\in\mathbb R^D$2 of the original model's VRAM while maintaining $c_i^k\in\mathbb R^D$3 of its original performance and achieving a $c_i^k\in\mathbb R^D$4 speedup, improving performance by $c_i^k\in\mathbb R^D$5 over SmoothQuant at the same average bit budget (Xu et al., 3 Feb 2026).

These multimodal results shift the emphasis from codebook capacity or reconstruction loss to heterogeneous semantics. Channel granularity becomes a way to separate causal sources of quantization error: modality-specific outliers in VLMs and action-critical channels in robotics.

6. Empirical behavior, design trade-offs, and persistent distinctions

Across domains, the empirical gains are substantial but method-dependent. In DQ, single-tensor VQ on CIFAR-10 gives NLL $c_i^k\in\mathbb R^D$6 bits/dim, whereas DQ with $c_i^k\in\mathbb R^D$7 gives $c_i^k\in\mathbb R^D$8 bits/dim; the hierarchical DQ-AE reports $c_i^k\in\mathbb R^D$9 bits/dim on CIFAR-10, $M$00 on ImageNet-32, and $M$01 on ImageNet-64, while using about $M$02M parameters versus $M$03M in VD-VAE (Fostiropoulos et al., 2022). In video tokenization, Magvit-v2 + LFQ averages PSNR $M$04 dB, Magvit-v2 + CS-LFQ reaches $M$05 dB, and the Mamba-based tokenizer with CS-FSQ reaches $M$06 dB; for unconditional generation, the reported FVD improves from $M$07 for Magvit-v2 (LFQ)+VideoGPT to $M$08 for the proposed tokenizer with CS-FSQ on SkyTimelapse/UCF-101 (Argaw et al., 6 Jul 2025).

The trade-offs are equally clear. Capacity-oriented channel splitting increases expressivity at linear memory cost, but only under assumptions of weak channel dependence or factorable latent structure. DQ states this explicitly through feature decomposition along the channel axis of weak statistical dependence, and CS-Q for video preserves token count only by increasing upstream compression by a factor of $M$09. By contrast, Q-LIC reduces quantization error by halving channel range and then pruning channels to restore width, while OCS increases channels by approximately $M$10 and accepts minor overhead in exchange for train-free functional equivalence (Sun et al., 2022, Zhao et al., 2019).

Several distinctions recur and are often blurred. First, channel-split quantization is not synonymous with per-channel quantization: SPIQ, CMPQ, and MergeQuant are channel-wise calibration or mixed-precision methods, whereas DQ, video CS-Q, Q-LIC, and OCS explicitly split or duplicate channels (Yvinec et al., 2022, Chen et al., 2024, Wang et al., 7 Mar 2025). Second, not all channel-based methods rely on learned codebooks. DQ uses separate learned codebooks, video CS-Q deliberately avoids learned lookup with LFQ or FSQ, and OCS keeps the original linear quantizer unchanged (Fostiropoulos et al., 2022, Argaw et al., 6 Jul 2025, Zhao et al., 2019). Third, “more channels” does not imply “more tokens” or “more compute” in the same way across papers: video CS-Q preserves sequence length; Q-LIC prunes to keep the number of overall channels as origin; OCS adds a small but real width overhead; MergeQuant compensates scale non-uniformity by split-and-prune dimensional reconstruction (Argaw et al., 6 Jul 2025, Sun et al., 2022, Zhao et al., 2019, Wang et al., 7 Mar 2025).

Taken together, the literature supports a precise characterization: channel-split quantization is best understood not as one algorithm but as a structural quantization principle. It exploits the fact that channels often differ in dependence structure, dynamic range, outlier profile, semantic role, or downstream sensitivity. Depending on the task, this principle yields exponential latent capacity, lower fixed-point distortion, train-free outlier suppression, more accurate static quantization, or robustness to multimodal heterogeneity and action-space error.