ResNet-Based Convolutional Autoencoder

• ResNet-based convolutional autoencoders are neural networks that use symmetric encoder-decoder architectures with residual blocks and attention modules to enhance training stability and reconstruction quality.
• They are applied in fields like weather data compression and image steganography, achieving significant dimensionality reduction and robust signal preservation compared to traditional methods.
• Key performance metrics, such as LW-RMSE for weather prediction and PSNR/SSIM for steganography, demonstrate the practical benefits of these models in scientific and digital security applications.

A ResNet-based convolutional autoencoder (CAE) is a neural architecture for efficient nonlinear dimensionality reduction, reconstruction, and, in some cases, information hiding, built around the principles of convolutional autoencoding and deep residual learning. Distinguished from canonical CAEs by the integration of residual (ResNet) blocks and—when applicable—attention modules, these models enable more stable optimization and improved representational capacity for high-dimensional structured data. Two prominent instantiations of this paradigm—one targeting high-fidelity weather data compression and short-range prediction (Hedayat et al., 16 Nov 2025), and another for color image steganography (Hashemi et al., 2022)—exemplify the architectural and methodological choices underlying state-of-the-art ResNet-based CAEs.

1. Architectural Principles

ResNet-based CAEs employ a symmetric encoder-decoder structure constructed from convolutional layers interleaved with residual connections. The encoder ingests high-dimensional spatial inputs (e.g., $X\in\mathbb R^{4\times240\times121}$ for ERA5 weather fields or $256\times256\times3$ images for steganography), applies downsampling via strided convolutions or pooling, and projects the resultant feature maps to a lower-dimensional latent vector $z$. The decoder inverts this mapping, using upsampling and convolution to reconstruct the original spatial format.

A defining feature is the use of residual blocks. Each block consists of two or more convolutions with skip connections—either identity or $1\times1$ convolutions when dimensions change—to facilitate backpropagation and reduce gradient vanishing, especially in deep architectures. In weather modeling, each ResNet block performs a sequence:

• $3\times3$ Conv $\rightarrow$ BatchNorm $\rightarrow$ ReLU (possibly with stride 2)
• $3\times3$ Conv $\rightarrow$ BatchNorm
• Skip connection, summed before final ReLU.

Block attention modules—specifically convolutional block attention modules (CBAM)—may be inserted after each residual block for feature recalibration. The decoder mirrors the encoder structure, using nearest-neighbor or transposed convolution upsampling with residual blocks for progressive spatial resolution restoration (Hedayat et al., 16 Nov 2025, Hashemi et al., 2022).

2. Encoder and Decoder Configurations

Specific architectural parameters are chosen to balance compression, accuracy, and computational load:

Weather Prediction CAE (Hedayat et al., 16 Nov 2025):

• Encoder: Four-stage downsampling with channel dimensions $[64, 128, 256, 512]$, each stage containing two ResNet blocks. An initial $7\times7$ convolution sets the input to $64\times120\times61$. After the last stage, a $1\times1$ convolution with 8 filters yields an $8\times15\times8$ latent tensor, flattened to $z\in\mathbb{R}^{960}$.
• Decoder: Mirrors the encoder, using nearest-neighbor upsampling and residual blocks. Final reconstruction is performed by a $7\times7$ convolution with 4 filters and a Tanh (or linear) output.
• Total Parameters: 31.72M.

Steganography CAE (Hashemi et al., 2022):

• Preprocess Network: A lightweight CNN with three $3\times3$ convolutions (strides 2, channels doubling per layer), reducing $256\times256\times3$ images to $32\times32\times64$ features.
• Operational Model: For both embedding (stego image generation) and extraction (secret recovery), a symmetric decoder composed of three residual blocks, each using paired transposed convolutions for upsampling and shortcut connections for dimension matching.

Both models leverage deep residual learning for improved training dynamics and high-fidelity reconstructions.

3. Attention Mechanisms

In weather prediction applications, CBAM is utilized to perform feature-wise recalibration after each ResNet block. For feature tensor $\mathbf F\in\mathbb R^{C\times H\times W}$:

• Channel Attention: Two pooled descriptors ($\mathrm{AvgPool}_{spatial}$ and $\mathrm{MaxPool}_{spatial}$) are each passed through a shared two-layer MLP, summed, and sigmoid-activated to compute channel-wise weights, producing $\mathbf M_c$:

$$\mathbf M_c = \sigma\!\bigl(\mathrm{MLP}(\mathrm{AvgPool}(\mathbf F)) + \mathrm{MLP}(\mathrm{MaxPool}(\mathbf F))\bigr)$$

The result refines $\mathbf F$ by channel-wise scaling.

• Spatial Attention: Averaged and max-pooled channel descriptors are concatenated and passed through a $7\times7$ convolution and sigmoid to yield spatial weights $\mathbf M_s$, which modulate the feature tensor spatially:

$$\mathbf M_s = \sigma\!\Bigl(f^{7\times7}\bigl[\mathrm{AvgPool}(\mathbf F');\,\mathrm{MaxPool}(\mathbf F')\bigr]\Bigr)$$

This dual mechanism enables the network to emphasize salient channels and spatial regions adaptively (Hedayat et al., 16 Nov 2025).

4. Dimensionality Reduction and Latent Space

The CAE compresses high-dimensional fields to compact latent codes:

• Weather Data: $z=\mathrm{vec}(\mathcal E(X))\in\mathbb R^{960}$, representing a 121:1 compression from the $4\times240\times121$ input. No additional $\ell_2$ or sparsity penalties are placed on $z$; regularization is enforced via batch normalization, weight decay, and early stopping (Hedayat et al., 16 Nov 2025).
• Steganography: Concealed color images are encoded as feature maps that, after processing by the symmetric operational model, retain high recoverability and visually imperceptible embedding (Hashemi et al., 2022).

This reduction allows linear or shallow models to capture temporal evolution (for dynamical systems), or enables high-capacity information hiding (for digital steganography).

5. Loss Functions, Training Procedures, and Metrics

Weather Prediction (Hedayat et al., 16 Nov 2025):

• Loss: Latitude-weighted RMSE (LW-RMSE), designed to account for the nonuniform grid area in the ERA5 dataset:

$$\mathcal L = \sqrt{\frac{1}{N}\sum_{i=1}^N w(\phi_i)\,[X_i - \hat X_i]^2},\quad w(\phi) = \frac{\cos\phi}{\frac{1}{M}\sum_{j=1}^M\cos\phi_j}$$

• Training: Adam optimizer, initial learning rate $10^{-3}$, batch size 32, 100 epochs, with only weight decay on convolution kernels.
• Performance: Out-of-distribution LW-RMSE for $u_{10}$, $v_{10}$, $T_{2m}$, $P_{msl}$ is $[1.25, 1.25, 1.90, 102]$ (units m/s, m/s, K, Pa, respectively) with 121:1 compression. CAE reconstructions better preserve fine-scale wind features compared to Proper Orthogonal Decomposition (POD) (Hedayat et al., 16 Nov 2025).

Steganography (Hashemi et al., 2022):

• Loss: Weighted sum of MSE for stego/cover and secret/recovery; $$L = \alpha\,\text{MSE}(c,h) + (1-\alpha)\,\text{MSE}(s,e)$$, $\alpha=0.5$. Metrics include PSNR and SSIM:
  • $$\text{PSNR}(X,Y) = 10\,\log_{10}\left(\frac{\text{MAX}_I^2}{\text{MSE}(X,Y)}\right)$$
  • $\text{SSIM}$ calculated by the standard formula with three components $l, c, s$.
• Training: Adam optimizer (fixed $10^{-3}$), batch size 100, 2000 epochs.
• Performance: PSNR > 39 dB, SSIM > 0.98; hiding capacity of 8 bpp (entire color image in another of the same size).

6. Application Contexts

Short-Range Weather Prediction: The ResNet-based CAE with CBAM is tailored to high-dimensional geophysical data reduction with an emphasis on computational efficiency. The latent codes feed into linear operators learned in a delay-embedded latent space for forecasting:

• Delay-embedding: $$z_k^{td} = [z_k^\top,\;z_{k-1}^\top,\;\dots,\;z_{k-d+1}^\top]^\top$$
• Linear prediction: $z_{k+1} = L z_k^{td}$, $X_{k+1} \approx \mathcal D(z_{k+1})$.

Accurate in-distribution weather pattern reconstructions are obtained, with inference per sample being $\mathcal O(10^9)$ FLOPs, corresponding to tens of ms on a GPU (Hedayat et al., 16 Nov 2025).

Color Image Steganography: The ResNet-based CAE structure enables robust, imperceptible embedding and extraction of color images. The concatenation of cover and secret feature maps followed by the operational model provides effective hiding of full-sized color images with high PSNR/SSIM and capacity (Hashemi et al., 2022).

7. Comparative Evaluation

The following table summarizes salient architectural parameters and core metrics for the principal ResNet-based CAE variants discussed:

Application	Latent Size	Key Metric(s)	Notable Feature
Weather (Hedayat et al., 16 Nov 2025)	960	LW-RMSE: $u_{10}$ 1.25, $T_{2m}$ 1.90	CBAM after every block, 31.72M params
Steganography (Hashemi et al., 2022)	-- (maps)	PSNR > 39 dB, SSIM > 0.98, 8 bpp capacity	Preprocess + operational model, transposed conv shortcuts

A plausible implication is that the design and hyperparameters of the encoder-decoder and the integration of attention and/or preprocessing modules are application-dependent, reflecting the structural properties of the input domain and end-task.

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ResNet-based convolutional autoencoders, across scientific and information security domains, provide a versatile framework for nonlinear compression, structured reconstruction, and latent representation learning, leveraging deep residual learning with or without modern attention mechanisms. Their empirical performance—contrasted against linear and non-residual baselines—demonstrates advantages in compactness, accuracy, and stability, particularly for high-dimensional, spatially structured inputs (Hedayat et al., 16 Nov 2025, Hashemi et al., 2022).