Sparse Mamba: Reinforcing Controllability In Structural State Space Models

In this article, we introduce the concept of controllability and observability to the M amba architecture in our Sparse-Mamba (S-Mamba) for natural language processing (NLP) applications. The structured state space model (SSM) development in recent studies, such as Mamba and Mamba2, outperformed and solved the computational inefficiency of transformers and large language models (LLMs) on longer sequences in small to medium NLP tasks. The Mamba SSMs architecture drops the need for attention layer or MLB blocks in transformers. However, the current Mamba models do not reinforce the controllability on state space equations in the calculation of A, B, C, and D matrices at each time step, which increase the complexity and the computational cost needed. In this article we show that the number of parameters can be significantly decreased by reinforcing controllability in the state space equations in the proposed Sparse-Mamba (S-Mamba), while maintaining the performance. The controllable n x n state matrix A is sparse and it has only n free parameters. Our novel approach will ensure a controllable system and could be the gate key for Mamba 3.

A Probabilistic Hadamard U-Net for MRI Bias Field Correction

Magnetic field inhomogeneity correction remains a challenging task in MRI analysis. Most established techniques are designed for brain MRI by supposing that image intensities in the identical tissue follow a uniform distribution. Such an assumption cannot be easily applied to other organs, especially those that are small in size and heterogeneous in texture (large variations in intensity), such as the prostate. To address this problem, this paper proposes a probabilistic Hadamard U-Net (PHU-Net) for prostate MRI bias field correction. First, a novel Hadamard U-Net (HU-Net) is introduced to extract the low-frequency scalar field, multiplied by the original input to obtain the prototypical corrected image. HU-Net converts the input image from the time domain into the frequency domain via Hadamard transform. In the frequency domain, high-frequency components are eliminated using the trainable filter (scaling layer), hard-thresholding layer, and sparsity penalty. Next, a conditional variational autoencoder is used to encode possible bias field-corrected variants into a low-dimensional latent space. Random samples drawn from latent space are then incorporated with a prototypical corrected image to generate multiple plausible images. Experimental results demonstrate the effectiveness of PHU-Net in correcting bias-field in prostate MRI with a fast inference speed. It has also been shown that prostate MRI segmentation accuracy improves with the high-quality corrected images from PHU-Net. The code will be available in the final version of this manuscript.

A novel asymmetrical autoencoder with a sparsifying discrete cosine Stockwell transform layer for gearbox sensor data compression

The lack of an efficient compression model remains a challenge for the wireless transmission of gearbox data in non-contact gear fault diagnosis problems. In this paper, we present a signal-adaptive asymmetrical autoencoder with a transform domain layer to compress sensor signals. First, a new discrete cosine Stockwell transform (DCST) layer is introduced to replace linear layers in a multi-layer autoencoder. A trainable filter is implemented in the DCST domain by utilizing the multiplication property of the convolution. A trainable hard-thresholding layer is applied to reduce redundant data in the DCST layer to make the feature map sparse. In comparison to the linear layer, the DCST layer reduces the number of trainable parameters and improves the accuracy of data reconstruction. Second, training the autoencoder with a sparsifying DCST layer only requires a small number of datasets. The proposed method is superior to other autoencoder-based methods on the University of Connecticut (UoC) and Southeast University (SEU) gearbox datasets, as the average quality score is improved by 2.00% at the lowest and 32.35% at the highest with a limited number of training samples

Domain Generalization with Fourier Transform and Soft Thresholding

Domain generalization aims to train models on multiple source domains so that they can generalize well to unseen target domains. Among many domain generalization methods, Fourier-transform-based domain generalization methods have gained popularity primarily because they exploit the power of Fourier transformation to capture essential patterns and regularities in the data, making the model more robust to domain shifts. The mainstream Fourier-transform-based domain generalization swaps the Fourier amplitude spectrum while preserving the phase spectrum between the source and the target images. However, it neglects background interference in the amplitude spectrum. To overcome this limitation, we introduce a soft-thresholding function in the Fourier domain. We apply this newly designed algorithm to retinal fundus image segmentation, which is important for diagnosing ocular diseases but the neural network's performance can degrade across different sources due to domain shifts. The proposed technique basically enhances fundus image augmentation by eliminating small values in the Fourier domain and providing better generalization. The innovative nature of the soft thresholding fused with Fourier-transform-based domain generalization improves neural network models' performance by reducing the target images' background interference significantly. Experiments on public data validate our approach's effectiveness over conventional and state-of-the-art methods with superior segmentation metrics.

Stein Variational Gradient Descent-based Detection For Random Access With Preambles In MTC

Traditional preamble detection algorithms have low accuracy in the grant-based random access scheme in massive machine-type communication (mMTC). We present a novel preamble detection algorithm based on Stein variational gradient descent (SVGD) at the second step of the random access procedure. It efficiently leverages deterministic updates of particles for continuous inference. To further enhance the performance of the SVGD detector, especially in a dense user scenario, we propose a normalized SVGD detector with momentum. It utilizes the momentum and a bias correction term to reduce the preamble estimation errors during the gradient descent process. Simulation results show that the proposed algorithm performs better than Markov Chain Monte Carlo-based approaches in terms of detection accuracy.

Electroencephalogram Sensor Data Compression Using An Asymmetrical Sparse Autoencoder With A Discrete Cosine Transform Layer

Electroencephalogram (EEG) data compression is necessary for wireless recording applications to reduce the amount of data that needs to be transmitted. In this paper, an asymmetrical sparse autoencoder with a discrete cosine transform (DCT) layer is proposed to compress EEG signals. The encoder module of the autoencoder has a combination of a fully connected linear layer and the DCT layer to reduce redundant data using hard-thresholding nonlinearity. Furthermore, the DCT layer includes trainable hard-thresholding parameters and scaling layers to give emphasis or de-emphasis on individual DCT coefficients. Finally, the one-by-one convolutional layer generates the latent space. The sparsity penalty-based cost function is employed to keep the feature map as sparse as possible in the latent space. The latent space data is transmitted to the receiver. The decoder module of the autoencoder is designed using the inverse DCT and two fully connected linear layers to improve the accuracy of data reconstruction. In comparison to other state-of-the-art methods, the proposed method significantly improves the average quality score in various data compression experiments.

A Hybrid Quantum-Classical Approach based on the Hadamard Transform for the Convolutional Layer

In this paper, we propose a novel Hadamard Transform (HT)-based neural network layer for hybrid quantum-classical computing. It implements the regular convolutional layers in the Hadamard transform domain. The idea is based on the HT convolution theorem which states that the dyadic convolution between two vectors is equivalent to the element-wise multiplication of their HT representation. Computing the HT is simply the application of a Hadamard gate to each qubit individually, so the HT computations of our proposed layer can be implemented on a quantum computer. Compared to the regular Conv2D layer, the proposed HT-perceptron layer is computationally more efficient. Compared to a CNN with the same number of trainable parameters and 99.26\% test accuracy, our HT network reaches 99.31\% test accuracy with 57.1\% MACs reduced in the MNIST dataset; and in our ImageNet-1K experiments, our HT-based ResNet-50 exceeds the accuracy of the baseline ResNet-50 by 0.59\% center-crop top-1 accuracy using 11.5\% fewer parameters with 12.6\% fewer MACs.

Orthogonal Transform Domain Approaches for the Convolutional Layer

In this paper, we propose a set of transform-based neural network layers as an alternative to the $3\times3$ Conv2D layers in Convolutional Neural Networks (CNNs). The proposed layers can be implemented based on orthogonal transforms such as Discrete Cosine Transform (DCT) and Hadamard transform (HT), and the biorthogonal Block Wavelet Transform (BWT). Convolutional filtering operations are performed in the transform domain using element-wise multiplications by taking advantage of the convolution theorems. Trainable soft-thresholding layers that remove noise in the transform domain bring nonlinearity to the transform domain layers. Compared to the Conv2D layer which is spatial-agnostic and channel-specific, the proposed layers are location-specific and channel-specific. The proposed layers reduce the number of parameters and multiplications significantly while improving the accuracy results of regular ResNets on the ImageNet-1K classification task. Furthermore, the proposed layers can be inserted with a batch normalization layer before the global average pooling layer in the conventional ResNets as an additional layer to improve classification accuracy with a negligible increase in the number of parameters and computational cost.

Normalized Stochastic Gradient Descent Training of Deep Neural Networks

In this paper, we introduce a novel optimization algorithm for machine learning model training called Normalized Stochastic Gradient Descent (NSGD) inspired by Normalized Least Mean Squares (NLMS) from adaptive filtering. When we train a high-complexity model on a large dataset, the learning rate is significantly important as a poor choice of optimizer parameters can lead to divergence. The algorithm updates the new set of network weights using the stochastic gradient but with $\ell_1$ and $\ell_2$-based normalizations on the learning rate parameter similar to the NLMS algorithm. Our main difference from the existing normalization methods is that we do not include the error term in the normalization process. We normalize the update term using the input vector to the neuron. Our experiments present that the model can be trained to a better accuracy level on different initial settings using our optimization algorithm. In this paper, we demonstrate the efficiency of our training algorithm using ResNet-20 and a toy neural network on different benchmark datasets with different initializations. The NSGD improves the accuracy of the ResNet-20 from 91.96\% to 92.20\% on the CIFAR-10 dataset.

Real-time Wireless ECG-derived Respiration Rate Estimation Using an Autoencoder with a DCT Layer

In this paper, we present a wireless ECG-derived Respiration Rate (RR) estimation using an autoencoder with a DCT Layer. The wireless wearable system records the ECG data of the subject and the respiration rate is determined from the variations in the baseline level of the ECG data. A straightforward Fourier analysis of the ECG data obtained using the wireless wearable system may lead to incorrect results due to uneven breathing. To improve the estimation precision, we propose a neural network that uses a novel Discrete Cosine Transform (DCT) layer to denoise and decorrelates the data. The DCT layer has trainable weights and soft-thresholds in the transform domain. In our dataset, we improve the Mean Squared Error (MSE) and Mean Absolute Error (MAE) of the Fourier analysis-based approach using our novel neural network with the DCT layer.