DC-Mamber: Dual-Channel Forecasting Model

• DC-Mamber is a dual-channel multivariate forecasting model that combines a Mamba-based branch for intra-variable dynamics with a linear Transformer branch for global temporal dependencies.
• The model fuses distinct representations via dual embedding layers, separate encoders, and a learned fusion layer to align and integrate both local and global views.
• Empirical evaluations show that DC-Mamber achieves reduced MSE and MAE on various datasets, outperforming state-of-the-art baselines in efficiency and accuracy.

Searching arXiv for the exact paper and closely related naming variants to ground the article. DC-Mamber is a dual-channel prediction model for multivariate time series forecasting that combines a Mamba-based branch with a linear Transformer branch in order to couple channel-independent and channel-mixing views of the same sequence. In the formulation used by the model, the historical input is $$\mathbf{X}=\{\mathbf{x}_1,\ldots,\mathbf{x}_L\}\in\mathbb{R}^{L\times V}$$ and the objective is to forecast $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$. The Mamba-based channel is assigned to extract intra-variable features, while the Transformer-based channel models cross-timestep global dependencies; a learned fusion layer then integrates both streams for prediction (Fan et al., 6 Jul 2025).

1. Concept and problem setting

DC-Mamber is situated in multivariate time series forecasting (MTSF), where the central modeling problem is to preserve three kinds of structure simultaneously: global temporal dependencies, local intra-variable dynamics, and cross-variable correlations. The model is explicitly motivated by the observation that prevailing architectures usually privilege only one of these views. Channel-mixing strategies treat the multivariate vector at each time step as a token and therefore emphasize inter-variable relationships and global temporal modeling, whereas channel-independent strategies treat each variable history as a token and therefore emphasize per-variable temporal dynamics (Fan et al., 6 Jul 2025).

This bifurcation is also architectural. Transformer-based models are described as strong in global dependency modeling through self-attention, but constrained by quadratic complexity and limited sensitivity to local temporal patterns. Mamba, built on state space models (SSMs), is described as achieving linear complexity and efficient long-range modeling, while being less effective at aggregating global contextual information in parallel. DC-Mamber is designed as a direct response to this complementarity: one channel exploits Mamba where local, intra-variable temporal structure is central, and the other exploits linear attention where global temporal interactions across time steps are central (Fan et al., 6 Jul 2025).

The model therefore defines two tokenizations of the same normalized input $\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$. The time-token view is

$$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$

where the token at time $i$ is $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$. The variable-token view is

$$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$

where the token for variable $j$ is $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$. The architectural claim of DC-Mamber is that both views are necessary, and that assigning each view to the branch most compatible with it improves forecasting accuracy (Fan et al., 6 Jul 2025).

2. Architectural organization

DC-Mamber has four principal components: a dual-channel token embedding layer, dual-channel encoders stacked $N$ times, a feature-fusion module, and a prediction head. The processing flow is: normalize the input, construct two feature representations through separate embedding layers, process them in parallel through a temporal encoder and a variable encoder, align the resulting features to a common variable dimension, fuse them with an MLP and LayerNorm, and project to the forecast horizon (Fan et al., 6 Jul 2025).

Component	Representation	Function
T-Embedding + T-Encoder	$$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$0	Global temporal dependencies under channel-mixing
V-Embedding + V-Encoder	$$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$1	Local intra-variable dependencies under channel-independent processing
Fusion + Projector	$$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$2 to $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$3	Integrate both channels and predict future values

The temporal branch begins with T-Embedding. Positional encoding is added to the normalized input, after which a two-layer feed-forward projection maps the variable dimension $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$4 to the hidden dimension $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$5: $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$6 producing $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$7. This representation preserves the multivariate state at each time step and prepares it for linear attention (Fan et al., 6 Jul 2025).

The variable branch begins with V-Embedding. The normalized input is permuted to $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$8 and then projected from $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$9 to $\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$0 by a two-layer feed-forward mapping written in the paper as

$\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$1

The output is $\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$2, where each variable obtains a dedicated latent representation of its temporal evolution (Fan et al., 6 Jul 2025).

3. Variable encoder: Bi-Mamba and channel-independent modeling

The variable encoder is the Mamba-based branch. It operates on $\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$3 and is intended to capture local, intra-variable temporal structure through a channel-independent strategy. Its theoretical basis is the selective SSM formulation of Mamba. The continuous-time dynamics are written as

$\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$4

and after zero-order hold discretization with step $\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$5,

$\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$6

which yields

$\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$7

These equations provide the state-space substrate from which the Mamba block is constructed (Fan et al., 6 Jul 2025).

DC-Mamber uses a bidirectional variant, Bi-Mamba, to mitigate the unidirectional character of standard Mamba. The forward and backward passes are denoted

$\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$8

This design gives each variable access to information from both directions within its representation, which the paper positions as advantageous for temporal dependency capture (Fan et al., 6 Jul 2025).

The Mamba block itself is described procedurally. A linear projection first expands the input into $\mathbf{X}_{norm}\in\mathbb{R}^{B\times L\times V}$9. A Conv1D followed by SiLU produces $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$0. The model then learns a structured state matrix $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$1 and computes input-dependent $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$2 from $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$3. The dynamic step $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$4 is computed with a softplus transformation, after which the parameters are discretized to $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$5. A selective SSM computation produces $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$6, which is gated with $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$7 and projected back to $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$8 (Fan et al., 6 Jul 2025).

At the encoder level, the branch follows a Transformer-like residual layout: $$\mathbf{X}_{t\text{-token}}\in\mathbb{R}^{L\times V},$$9 The MLP-block is Conv1D-based. Stacking $i$0 such layers yields $i$1, the variable-centric representation passed to fusion (Fan et al., 6 Jul 2025).

4. Temporal encoder: linear Transformer and channel-mixing modeling

The temporal encoder operates on $i$2 and uses a channel-mixing strategy in which each time step is a token containing all variables. Its purpose is to model global temporal dependencies across the sequence while preserving computational efficiency. Rather than full self-attention, DC-Mamber adopts a Linformer-style linear attention, which reduces the dependence on sequence length from quadratic to linear in $i$3 when the projection dimension is fixed (Fan et al., 6 Jul 2025).

Given $i$4 and projection matrices $i$5 with $i$6, the branch defines

$i$7

and then computes

$i$8

The use of projected keys and values is the mechanism by which the temporal branch preserves efficiency on long contexts (Fan et al., 6 Jul 2025).

The T-Encoder layer is written as

$i$9

As in the variable encoder, the feed-forward stage is Conv1D-based. Stacking $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$0 layers yields $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$1 (Fan et al., 6 Jul 2025).

The conceptual asymmetry between the two branches is deliberate rather than incidental. Ablation results reported in the paper indicate that the best configuration is precisely the one adopted in DC-Mamber: the V-Encoder should be channel-independent and the T-Encoder should be channel-mixing. The swapped assignment, and the alternatives where both encoders use the same tokenization strategy, are reported as inferior. This suggests that the model’s gains do not derive simply from adding two branches, but from matching each architectural primitive to the data view for which it is best suited (Fan et al., 6 Jul 2025).

5. Fusion, prediction, and optimization

After the parallel encoder stacks, the two feature maps have incompatible token axes: $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$2 and $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$3. DC-Mamber therefore aligns the temporal features to the variable dimension. The temporal tensor is permuted to $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$4, projected along $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$5 to $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$6, and permuted back to obtain $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$7. It is then concatenated with $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$8 along the feature dimension to produce $$\boldsymbol{x}_{1:V}^{(i)}=(x_1^{(i)},\ldots,x_V^{(i)})$$9 (Fan et al., 6 Jul 2025).

Fusion is implemented by an MLP with LayerNorm: $$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$0 where $$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$1 and $$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$2. The result is a fused representation $$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$3. A linear projector then maps $$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$4 to the forecast horizon $$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$5, yielding $$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$6, which is permuted to the final prediction tensor $$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$7 (Fan et al., 6 Jul 2025).

Training uses mean squared error,

$$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$8

while evaluation also reports mean absolute error,

$$\mathbf{X}_{v\text{-token}}\in\mathbb{R}^{V\times L},$$9

Optimization is performed with Adam on MSE. LayerNorm is used in both encoder branches and in the fusion layer, and dropout with rate $j$0 is applied in attention, MLP-blocks, and Mamba modules. The implementation is in PyTorch and the experiments are run on an NVIDIA RTX 3090 with CUDA 11.4. The standard look-back window is $j$1, training lasts 10 epochs with early stopping, and the forecast horizons are dataset-specific: for ECL, Solar-Energy, Weather, and ETTm1, $j$2; for PEMS03, PEMS04, PEMS07, and PEMS08, $j$3 (Fan et al., 6 Jul 2025).

The computational argument of the model is equally central. Standard Transformer attention under channel-mixing has complexity $j$4, and under channel-independent tokenization has complexity $j$5. By contrast, the T-Encoder uses Linformer-style linear attention with complexity approximately $j$6, while the V-Encoder inherits Mamba’s linear dependence on the scanned dimension. This places both channels in a linear-time regime with respect to their primary sequence axes, which the paper identifies as essential for long-sequence forecasting (Fan et al., 6 Jul 2025).

6. Empirical results, ablations, and relation to similarly named models

DC-Mamber is evaluated on eight public datasets spanning traffic, electricity, energy, weather, and transformer temperature forecasting: PEMS03, PEMS04, PEMS07, PEMS08, ECL, Solar-Energy, Weather, and ETTm1. The baseline set includes S-Mamba, iTransformer, PatchTST, Crossformer, FEDformer, Stationary Transformer, TimesNet, RLinear, DLinear, TiDE, and SCINet. The paper reports that DC-Mamber achieves the best average performance in MSE and MAE on almost all datasets and horizons, with an average reduction of $j$7 in MSE and $j$8 in MAE compared to state-of-the-art baselines. It also records 30 first places in MSE and 30 in MAE across all dataset-horizon combinations (Fan et al., 6 Jul 2025).

The gains are especially visible relative to the nearest Mamba-family baseline, S-Mamba. In average MSE across horizons, the reported reductions are: PEMS03, $j$9; PEMS04, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$0; PEMS07, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$1; PEMS08, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$2; Electricity, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$3; Solar-Energy, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$4; Weather, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$5. In average MAE, the reported reductions include PEMS03, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$6; PEMS04, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$7; PEMS07, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$8; PEMS08, $$\boldsymbol{x}_{1:L}^{(j)}=(x_1^{(j)},\ldots,x_L^{(j)})$$9; Electricity, $N$0; Solar-Energy, $N$1 (Fan et al., 6 Jul 2025).

Ablation studies are structurally important. Removing the V-Encoder degrades performance, and removing the T-Encoder degrades it more severely; on PEMS08 averaged over horizons, the full model reports MSE $N$2 and MAE $N$3, compared with MSE $N$4 and MAE $N$5 without the V-Encoder, and MSE $N$6 and MAE $N$7 without the T-Encoder. Further ablations show that the adopted tokenization-to-encoder assignment is the best one: on PEMS04 average performance, the reported values are MSE $N$8, MAE $N$9 for the proposed design; MSE $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$00, MAE $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$01 for the swapped design; MSE $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$02, MAE $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$03 when both encoders are channel-independent; and MSE $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$04, MAE $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$05 when both are channel-mixing (Fan et al., 6 Jul 2025).

Parameter-sensitivity experiments indicate that the learning rate depends on the dataset, that $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$06 has a relatively minor effect, and that moderate increases in $$\mathbf{Y}=\{\mathbf{x}_{L+1},\ldots,\mathbf{x}_{L+W}\}\in\mathbb{R}^{W\times V}$$07 tend to help while overly small or overly large values can hurt. The paper also includes prediction-curve comparisons against S-Mamba and states that DC-Mamber’s predicted trajectories are closer to ground truth, with smaller deviations in amplitude and phase, especially on difficult horizons and high-dimensional traffic datasets (Fan et al., 6 Jul 2025).

The name “DC-Mamber” belongs specifically to the multivariate forecasting model described above. It should be distinguished from several similarly named Mamba-family systems in other domains, including “DCAMamba,” a framework for rapid DC arc fault detection (Wang et al., 3 Mar 2025), “DC-Mamba,” an “align-then-enhance” remote sensing change detection framework (Sun et al., 19 Sep 2025), and “DCMamba,” a semi-supervised medical image segmentation framework (Li et al., 19 Aug 2025). This suggests that the “DC” prefix is not semantically fixed across the literature; in the case of DC-Mamber, it denotes a dual-channel architecture in which Mamba and linear Transformer are combined within a single forecasting model (Fan et al., 6 Jul 2025).