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1. PremiUm-CNN: Propagating Uncertainty Towards Robust Convolutional Neural Networks

   Dimah Dera, Nidhal C. (July 2021, IEEE transactions on signal processing)

   Deep neural networks (DNNs) have surpassed human-level accuracy in various learning tasks. However, unlike humans who have a natural cognitive intuition for probabilities, DNNs cannot express their uncertainty in the output decisions. This limits the deployment of DNNs in mission critical domains, such as warfighter decision-making or medical diagnosis. Bayesian inference provides a principled approach to reason about model’s uncertainty by estimating the posterior distribution of the unknown parameters. The challenge in DNNs remains the multi-layer stages of non-linearities, which make the propagation of high-dimensional distributions mathematically intractable. This paper establishes the theoretical and algorithmic foundations of uncertainty or belief propagation by developing new deep learning models named PremiUm-CNNs (Propagating Uncertainty in Convolutional Neural Networks). We introduce a tensor normal distribution as a prior over convolutional kernels and estimate the variational posterior by maximizing the evidence lower bound (ELBO). We start by deriving the first-order mean-covariance propagation framework. Later, we develop a framework based on the unscented transformation (correct at least up to the second-order) that propagates sigma points of the variational distribution through layers of a CNN. The propagated covariance of the predictive distribution captures uncertainty in the output decision. Comprehensive experiments conducted on diverse benchmark datasets demonstrate: 1) superior robustness against noise and adversarial attacks, 2) self-assessment through predictive uncertainty that increases quickly with increasing levels of noise or attacks, and 3) an ability to detect a targeted attack from ambient noise. 

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2. Bayes-SAR Net: Robust SAR Image Classification with Uncertainty Estimation Using Bayesian Convolutional Neural Network

   Dera, D; Rasool, G; Bouaynaya, N; Eicheny, A; Shankoy, S; Cammeratay, J; Arnold, S (July 2020, IEEE International Radar Conference)

   Synthetic aperture radar (SAR) image classification is a challenging problem due to the complex imaging mechanism as well as the random speckle noise, which affects radar image interpretation. Recently, convolutional neural networks (CNNs) have been shown to outperform previous state-of-the-art techniques in computer vision tasks owing to their ability to learn relevant features from the data. However, CNNs in particular and neural networks, in general, lack uncertainty quantification and can be easily deceived by adversarial attacks. This paper proposes Bayes-SAR Net, a Bayesian CNN that can perform robust SAR image classification while quantifying the uncertainty or confidence of the network in its decision. Bayes-SAR Net propagates the first two moments (mean and covariance) of the approximate posterior distribution of the network parameters given the data and obtains a predictive mean and covariance of the classification output. Experiments, using the benchmark datasets Flevoland and Oberpfaffenhofen, show superior performance and robustness to Gaussian noise and adversarial attacks, as compared to the SAR-Net homologue. Bayes-SAR Net achieves a test accuracy that is around 10% higher in the case of adversarial perturbation (levels > 0.05). 

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3. Robust Transformer Neural Network for Computer Vision Applications

   Karim, Fazlur R; Dera, D (September 2023, Texas Advanced Computing Center Symposium (TACCSTER))

   The remarkable success of the Transformer model in Natural Language Processing (NLP) is increasingly capturing the attention of vision researchers in contemporary times. The Vision Transformer (ViT) model effectively models long-range dependencies while utilizing a self-attention mechanism by converting image information into meaningful representations. Moreover, the parallelism property of ViT ensures better scalability and model generalization compared to Recurrent Neural Networks (RNN). However, developing robust ViT models for high-risk vision applications, such as self-driving cars, is critical. Deterministic ViT models are susceptible to noise and adversarial attacks and incapable of yielding a level of confidence in output predictions. Quantifying the confidence (or uncertainty) level in the decision is highly important in such real-world applications. In this work, we introduce a probabilistic framework for ViT to quantify the level of uncertainty in the model's decision. We approximate the posterior distribution of network parameters using variational inference. While progressing through non-linear layers, the first-order Taylor approximation was deployed. The developed framework propagates the mean and covariance of the posterior distribution through layers of the probabilistic ViT model and quantifies uncertainty at the output predictions. Quantifying uncertainty aids in providing warning signals to real-world applications in case of noisy situations. Experimental results from extensive simulation conducted on numerous benchmark datasets (e.g., MNIST and Fashion-MNIST) for image classification tasks exhibit 1) higher accuracy of proposed probabilistic ViT under noise or adversarial attacks compared to the deterministic ViT. 2) Self-evaluation through uncertainty becomes notably pronounced as noise levels escalate. Simulations were conducted at the Texas Advanced Computing Center (TACC) on the Lonestar6 supercomputer node. With the help of this vital resource, we completed all the experiments within a reasonable period. 

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4. Robust Torque Predictions From Electromyography Across Multiple Levels of Active Exoskeleton Assistance Despite Non-linear Reorganization of Locomotor Output

   https://doi.org/10.3389/fnbot.2021.700823  

   George, Jacob A.; Gunnell, Andrew J.; Archangeli, Dante; Hunt, Grace; Ishmael, Marshall; Foreman, K. Bo; Lenzi, Tommaso (November 2021, Frontiers in Neurorobotics)

   Robotic exoskeletons can assist humans with walking by providing supplemental torque in proportion to the user's joint torque. Electromyographic (EMG) control algorithms can estimate a user's joint torque directly using real-time EMG recordings from the muscles that generate the torque. However, EMG signals change as a result of supplemental torque from an exoskeleton, resulting in unreliable estimates of the user's joint torque during active exoskeleton assistance. Here, we present an EMG control framework for robotic exoskeletons that provides consistent joint torque predictions across varying levels of assistance. Experiments with three healthy human participants showed that using diverse training data (from different levels of assistance) enables robust torque predictions, and that a convolutional neural network (CNN), but not a Kalman filter (KF), can capture the non-linear transformations in EMG due to exoskeleton assistance. With diverse training, the CNN could reliably predict joint torque from EMG during zero, low, medium, and high levels of exoskeleton assistance [root mean squared error (RMSE) below 0.096 N-m/kg]. In contrast, without diverse training, RMSE of the CNN ranged from 0.106 to 0.144 N-m/kg. RMSE of the KF ranged from 0.137 to 0.182 N-m/kg without diverse training, and did not improve with diverse training. When participant time is limited, training data should emphasize the highest levels of assistance first and utilize at least 35 full gait cycles for the CNN. The results presented here constitute an important step toward adaptive and robust human augmentation via robotic exoskeletons. This work also highlights the non-linear reorganization of locomotor output when using assistive exoskeletons; significant reductions in EMG activity were observed for the soleus and gastrocnemius, and a significant increase in EMG activity was observed for the erector spinae. Control algorithms that can accommodate spatiotemporal changes in muscle activity have broad implications for exoskeleton-based assistance and rehabilitation following neuromuscular injury. 

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5. Reconstructing cosmological initial conditions from late-time structure with convolutional neural networks

   https://doi.org/10.1093/mnras/stad528  

   Shallue, Christopher J.; Eisenstein, Daniel J. (February 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We present a method to reconstruct the initial linear-regime matter density field from the late-time non-linearly evolved density field in which we channel the output of standard first-order reconstruction to a convolutional neural network (CNN). Our method shows dramatic improvement over the reconstruction of either component alone. We show why CNNs are not well-suited for reconstructing the initial density directly from the late-time density: CNNs are local models, but the relationship between initial and late-time density is not local. Our method leverages standard reconstruction as a preprocessing step, which inverts bulk gravitational flows sourced over very large scales, transforming the residual reconstruction problem from long-range to local and making it ideally suited for a CNN. We develop additional techniques to account for redshift distortions, which warp the density fields measured by galaxy surveys. Our method improves the range of scales of high-fidelity reconstruction by a factor of 2 in wavenumber above standard reconstruction, corresponding to a factor of 8 increase in the number of well-reconstructed modes. In addition, our method almost completely eliminates the anisotropy caused by redshift distortions. As galaxy surveys continue to map the Universe in increasingly greater detail, our results demonstrate the opportunity offered by CNNs to untangle the non-linear clustering at intermediate scales more accurately than ever before. 

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