skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Friday, September 29 until 11:59 PM ET on Saturday, September 30 due to maintenance. We apologize for the inconvenience.

Title: Extended Variational Inference for Propagating Uncertainty in Convolutional Neural Networks
Model confidence or uncertainty is critical in autonomous systems as they directly tie to the safety and trustworthiness of the system. The quantification of uncertainty in the output decisions of deep neural networks (DNNs) is a challenging problem. The Bayesian framework enables the estimation of the predictive uncertainty by introducing probability distributions over the (unknown) network weights; however, the propagation of these high-dimensional distributions through multiple layers and non-linear transformations is mathematically intractable. In this work, we propose an extended variational inference (eVI) framework for convolutional neural network (CNN) based on tensor Normal distributions (TNDs) defined over convolutional kernels. Our proposed eVI framework propagates the first two moments (mean and covariance) of these TNDs through all layers of the CNN. We employ first-order Taylor series linearization to approximate the mean and covariances passing through the non-linear activations. The uncertainty in the output decision is given by the propagated covariance of the predictive distribution. Furthermore, we show, through extensive simulations on the MNIST and CIFAR-10 datasets, that the CNN becomes more robust to Gaussian noise and adversarial attacks.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
IEEE 29th International Workshop on Machine Learning for Signal Processing
Page Range / eLocation ID:
1 to 6
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. 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. 
    more » « less
  2. 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). 
    more » « less
  3. 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. 
    more » « less
  4. Abstract

    Machine learning (ML) tools are able to learn relationships between the inputs and outputs of large complex systems directly from data. However, for time-varying systems, the predictive capabilities of ML tools degrade if the systems are no longer accurately represented by the data with which the ML models were trained. For complex systems, re-training is only possible if the changes are slow relative to the rate at which large numbers of new input-output training data can be non-invasively recorded. In this work, we present an approach to deep learning for time-varying systems that does not require re-training, but uses instead an adaptive feedback in the architecture of deep convolutional neural networks (CNN). The feedback is based only on available system output measurements and is applied in the encoded low-dimensional dense layers of the encoder-decoder CNNs. First, we develop an inverse model of a complex accelerator system to map output beam measurements to input beam distributions, while both the accelerator components and the unknown input beam distribution vary rapidly with time. We then demonstrate our method on experimental measurements of the input and output beam distributions of the HiRES ultra-fast electron diffraction (UED) beam line at Lawrence Berkeley National Laboratory, and showcase its ability for automatic tracking of the time varying photocathode quantum efficiency map. Our method can be successfully used to aid both physics and ML-based surrogate online models to provide non-invasive beam diagnostics.

    more » « less
  5. Better understanding of the dose-toxicity relationship is critical for safe dose escalation to improve local control in late-stage cervical cancer radiotherapy. In this study, we introduced a convolutional neural network (CNN) model to analyze rectum dose distribution and predict rectum toxicity. Forty-two cervical cancer patients treated with combined external beam radiotherapy (EBRT) and brachytherapy (BT) were retrospectively collected, including twelve toxicity patients and thirty non-toxicity patients. We adopted a transfer learning strategy to overcome the limited patient data issue. A 16-layers CNN developed by the visual geometry group (VGG-16) of the University of Oxford was pre-trained on a large-scale natural image database, ImageNet, and fine-tuned with patient rectum surface dose maps (RSDMs), which were accumulated EBRT + BT doses on the unfolded rectum surface. We used the adaptive synthetic sampling approach and the data augmentation method to address the two challenges, data imbalance and data scarcity. The gradient-weighted class activation maps (Grad-CAM) were also generated to highlight the discriminative regions on the RSDM along with the prediction model. We compare different CNN coefficients fine-tuning strategies, and compare the predictive performance using the traditional dose volume parameters, e.g. D 0.1/1/2cc, and the texture features extracted from the RSDM. Satisfactory prediction performance was achieved with the proposed scheme, and we found that the mean Grad-CAM over the toxicity patient group has geometric consistence of distribution with the statistical analysis result, which indicates possible rectum toxicity location. The evaluation results have demonstrated the feasibility of building a CNN-based rectum dose-toxicity prediction model with transfer learning for cervical cancer radiotherapy. 
    more » « less