IConv: Hybrid MLP–CNN for Time-Series

• IConv is a hybrid MLP–CNN architecture that separates forecasting into an MLP-based trend predictor and a channel-independent CNN for local variation modeling.
• Its design efficiently captures long-term dependencies and fine-grained temporal patterns while reducing computational cost in non-stationary, high-dimensional settings.
• Empirical evaluations demonstrate that IConv outperforms traditional MLPs, CNNs, and transformers on benchmark MTSF datasets with lower error metrics.

IConv is a hybrid MLP–CNN architecture for multivariate time-series forecasting (MTSF) that is designed for real-world time-series data exhibiting non-stationarity, including changing trends, irregular seasonality, and residuals. The model combines an MLP-based trend predictor with a specialized convolutional module that focuses on fine-grained local variation. Its defining architectural idea is channel independent convolution: temporal dependency is processed channel independently, while inter-channel relationship is handled through distinct layers. This separation is intended to preserve the MLP’s strength on long-term dependency while allowing CNN-based modeling of diverse local temporal patterns that would otherwise be ignored (Lee et al., 25 Sep 2025).

1. Problem setting and modeling rationale

The motivating problem is that existing MLP-based models for MTSF are computationally efficient and capture long-term dependencies, but their linear nature poses limitations when applied to channels with diverse distributions. In the formulation motivating IConv, these limitations cause local variations such as seasonal patterns and residual components to be ignored. CNNs, by contrast, can effectively incorporate these variations, but standard convolutional designs become computationally expensive when large kernels or high channel counts are required.

IConv addresses this tension by explicitly decomposing forecasting into two functions. The overall trend is modeled using an MLP to consider long-term dependencies. A CNN module then uses diverse kernels to model fine-grained local patterns in conjunction with MLP trend predictions. The architecture is therefore neither a pure temporal MLP nor a conventional multichannel CNN. Instead, it separates long-range global dependency from local variation modeling and further separates channel-specific temporal processing from inter-channel mixing (Lee et al., 25 Sep 2025).

This design is targeted at non-stationary, high-dimensional MTSF settings in which different variables exhibit distinct local behaviors. Channel independence in the temporal convolutions is used to model diverse local temporal dependencies and to enable large kernel sizes, while distinct inter-channel consideration is used to reduce computational cost.

2. End-to-end architecture

Given an input sequence $X_{in} \in \mathbb{R}^{C\times T}$, the model first produces a preliminary forecast representing the global trend through an MLP encoder-regressor stack: $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$ Here, $\tilde{Y} \in \mathbb{R}^{C \times L}$ is the trend prediction.

The IConv block then refines $\tilde{Y}$ by modeling local, channel-specific temporal variations. The final prediction is formed by adding a reconstructed local variation term, scaled by the trend variance: $\hat{Y} = \tilde{Y} + V \times Var(\tilde{Y})$

Instance normalization is used for stability, and denormalization is applied after prediction. Training uses mean absolute error (L1 loss), which is described as robust to outliers.

Component	Function	Output
Trend prediction via MLP	Capture global dependency and long-term trend	$\tilde{Y} \in \mathbb{R}^{C \times L}$
Channel Independent Patch Compressor	Extract local temporal features independently per channel	$H$
Inter-Channel Mixer	Model inter-channel dependencies efficiently	$\hat{H}$
Channel Independent Patcher Expander	Reconstruct local variations to original sequence length	$V \in \mathbb{R}^{C \times L}$
Prediction fusion	Add scaled local variation to trend prediction	$\hat{Y}$

The architectural significance of this pipeline is that trend estimation does not depend on convolutional receptive field growth, while local fluctuation modeling is explicitly delegated to the IConv block.

3. Channel-independent convolution and local variation

The core of IConv is the Channel Independent Patch Compressor (CIP). It applies 1D convolution independently to each channel, with no inter-channel mixing at this stage: $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$0 where $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$1 is the kernel for the $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$2-th filter on channel $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$3. Strides are used to reduce sequence length for efficiency.

This component is intended to make the model sensitive to the unique local structure and distributional characteristics of each variable. In the paper’s framing, channel independence enables the modeling of diverse local temporal dependencies and the adoption of a large kernel size. It also reduces parameter growth: parameter size is reduced from $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$4 for full convolution to $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$5 for $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$6 filters per channel and patch size $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$7.

The design is explicitly hierarchical. The IConv block can be stacked with varying kernel sizes, enabling a hierarchy of local pattern extraction ranging from coarse to fine temporal scales. The accompanying interpretation is that progressively smaller kernels and strides allow decomposition of local patterns from broad to fine scales. This suggests a multiscale treatment of seasonal or residual structure rather than a single-scale local filter bank.

4. Inter-channel mixing and sequence reconstruction

After channel-independent temporal feature extraction, IConv introduces the Inter-Channel Mixer (ICM) to model inter-variable dependencies while maintaining computational efficiency. The ICM uses a $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$8 convolution, implemented as a linear layer for speed: $$\begin{align*} Enc(X_{in}) &= ReLU(X_{in}W_p + b_p)W_r + b_r \ X_{enc} &= X_{in} + Enc(X_{in}) \ \tilde{Y} &= X_{enc} W_{reg} + b_{reg} \end{align*}$$9 The first stage reduces to $\tilde{Y} \in \mathbb{R}^{C \times L}$0 features, then expands back to $\tilde{Y} \in \mathbb{R}^{C \times L}$1, and a residual connection reinforces stability.

This module operationalizes the paper’s broader separation principle: local pattern extraction remains lightweight and channel-specific, while channel correlation is handled in a modular layer. Distinct inter-channel considerations are therefore not merged into the temporal convolution itself. Instead, they are introduced after local extraction, which is the mechanism by which computational cost is reduced.

Reconstruction is handled by the Channel Independent Patcher Expander (CIPE), which applies transposed convolution independently to each channel: $\tilde{Y} \in \mathbb{R}^{C \times L}$2 This produces $\tilde{Y} \in \mathbb{R}^{C \times L}$3, a local variation signal aligned with the original prediction length. The final fusion step,

$\tilde{Y} \in \mathbb{R}^{C \times L}$4

restores scale lost by normalization by multiplying the local variation by the trend variance before adding it to the MLP trend prediction.

The architectural consequence is a strict decoupling: MLP layers model smooth, global trend structure; channel-independent convolutions model per-variable local variation; and a separate pointwise mixer captures inter-channel effects.

5. Empirical evaluation

The model is evaluated on large-scale, real-world MTSF datasets: ECL, ETT (multiple variants), Solar, Traffic, and Weather. The reported metrics are mean squared error (MSE) and mean absolute error (MAE). Baselines include advanced transformer, MLP, and CNN-based models such as TimeMixer++, PatchTST, Amplifier, DLinear, ModernTCN, and TimesNet (Lee et al., 25 Sep 2025).

The reported results state that IConv consistently outperformed these baselines on most datasets and prediction horizons. In Table 1, IConv ranked 1st in 45/64 settings and 2nd in 9. The paper also reports an ablation example on ECL with horizon 96, where MSE dropped from 0.200 for an MLP-only variant to 0.140 for the full IConv model.

Several qualitative and systems-level observations are also reported. Receptive field visualization indicates that IConv achieves wider, smoother receptive fields with periodic structure, which is interpreted as superior ability to capture local and periodic signals compared to ModernTCN or MLPs. In efficiency terms, IConv is reported to achieve lower memory usage and faster training time than standard CNNs, and to be competitive or faster than transformers and large MLPs, especially as channel count increases.

Hyperparameter sensitivity analysis indicates that increasing the multiplier, defined as the number of independent filters per channel, improves accuracy, while the benefits of large kernels depend on dataset periodicity. This supports the model’s central claim that local variation extraction is mediated by a flexible, channel-wise convolutional design rather than by a single fixed temporal operator.

6. Comparative significance, advantages, and limitations

The principal comparative claim is that IConv combines the strengths of MLPs and CNNs without collapsing them into a single undifferentiated temporal encoder. The MLP captures smooth, long-term global dependencies efficiently via dense layers and residual projections. The CNN module identifies segment-specific anomalies, periodicity, or abrupt changes overlooked by the MLP. In the paper’s formulation, the synergy is that the MLP prevents overfitting to local noise by robust trend estimation, while the CNN compensates for underfitting by modeling variations MLPs cannot capture.

Several advantages are reported. Accuracy is described as state-of-the-art or near-state-of-the-art on diverse MTSF datasets. Channel independence enables the use of more or larger kernels without exploding parameter counts. Computation and memory are significantly reduced compared to classic CNNs. The model is also described as more robust in non-stationary data with varying channel behavior, and visualizations are said to confirm improved usage of input context and more structured behavior in learned weights.

The paper also identifies limitations. The ICM assumes that inter-channel relationships can be effectively modeled using $\tilde{Y} \in \mathbb{R}^{C \times L}$5 convolutions or linear mixing; if inter-channel dependencies are highly complex and nonlinear, this may be limiting. The combined MLP plus multi-stage IConv design may require careful hyperparameter tuning, especially around kernel and stride settings. Aggressive local modeling could, in rare cases, risk overfitting to noise, although normalization and joint trend modeling are presented as mitigating factors.

Taken together, IConv is best understood as a structured hybrid forecaster for multivariate non-stationary sequences: the MLP handles the overall trend, while channel-independent convolution with explicit inter-channel mixing handles local variation. Within that formulation, its central technical contribution is the separation of temporal dependency and inter-channel relationship into distinct computational stages, allowing large-kernel local modeling at reduced cost while preserving competitive or superior forecasting accuracy (Lee et al., 25 Sep 2025).