In particular, we conjecture and empirically illustrate that, the celebrated batch normalization (BN) technique actually adapts the "normalized" bias such that it approximates

Deep neural networks have been widely adopted in many vision and robotics applications with visual inputs. It is essential to verify its robustness against semantic transformation perturbations, such as brightness and contrast. However, current certified training and robustness certification methods face the challenge of over-parameterization, which hinders the tightness and scalability due to the over-complicated neural networks. To this end, we first analyze stability and variance of layers and neurons against input perturbation, showing that certifiable robustness can be indicated by a fundamental Unbiased and Smooth Neuron metric (USN). Based on USN, we introduce a novel neural network pruning method that removes neurons with low USN and retains those with high USN, thereby preserving model expressiveness without over-parameterization. To further enhance this pruning process, we propose a new Wasserstein distance loss to ensure that pruned neurons are more concentrated across layers. We validate our approach through extensive experiments on the challenging robust keypoint detection task, which involves realistic brightness and contrast perturbations, demonstrating that our method achieves superior robustness certification performance and efficiency compared to baselines.

Neural Information Processing Systems http://nips.cc/

Neural networks are often regarded as "black boxes" due to their complex functions and numerous parameters, which poses significant challenges for interpretability. This study addresses these challenges by introducing methods to enhance the understanding of neural networks, focusing specifically on models with a single hidden layer. We establish a theoretical framework by demonstrating that the neural network estimator can be interpreted as a nonparametric regression model. Building on this foundation, we propose statistical tests to assess the significance of input neurons and introduce algorithms for dimensionality reduction, including clustering and (PCA), to simplify the network and improve its interpretability and accuracy. The key contributions of this study include the development of a bootstrapping technique for evaluating artificial neural network (ANN) performance, applying statistical tests and logistic regression to analyze hidden neurons, and assessing neuron efficiency. We also investigate the behavior of individual hidden neurons in relation to out-put neurons and apply these methodologies to the IDC and Iris datasets to validate their practical utility. This research advances the field of Explainable Artificial Intelligence by presenting robust statistical frameworks for interpreting neural networks, thereby facilitating a clearer understanding of the relationships between inputs, outputs, and individual network components.

Various deep neural network (DNN) coverage criteria have been proposed to assess DNN test inputs and steer input mutations. The coverage is characterized via neurons having certain outputs, or the discrepancy between neuron outputs. Nevertheless, recent research indicates that neuron coverage criteria show little correlation with test suite quality. In general, DNNs approximate distributions, by incorporating hierarchical layers, to make predictions for inputs. Thus, we champion to deduce DNN behaviors based on its approximated distributions from a layer perspective. A test suite should be assessed using its induced layer output distributions. Accordingly, to fully examine DNN behaviors, input mutation should be directed toward diversifying the approximated distributions. This paper summarizes eight design requirements for DNN coverage criteria, taking into account distribution properties and practical concerns. We then propose a new criterion, NeuraL Coverage (NLC), that satisfies all design requirements. NLC treats a single DNN layer as the basic computational unit (rather than a single neuron) and captures four critical properties of neuron output distributions. Thus, NLC accurately describes how DNNs comprehend inputs via approximated distributions. We demonstrate that NLC is significantly correlated with the diversity of a test suite across a number of tasks (classification and generation) and data formats (image and text). Its capacity to discover DNN prediction errors is promising. Test input mutation guided by NLC results in a greater quality and diversity of exposed erroneous behaviors.

In this work, we characterize the outputs of individual neurons in a trained feed-forward neural network by entropy, mutual information with the class variable, and a class selectivity measure based on Kullback-Leibler divergence. By cumulatively ablating neurons in the network, we connect these information-theoretic measures to the impact their removal has on classification performance on the test set. We observe that, looking at the neural network as a whole, none of these measures is a good indicator for classification performance, thus confirming recent results by Morcos et al. However, looking at specific layers separately, both mutual information and class selectivity are positively correlated with classification performance. We thus conclude that it is ill-advised to compare these measures across layers, and that different layers may be most appropriately characterized by different measures. We then discuss pruning neurons from neural networks to reduce computational complexity of inference. Drawing from our results, we perform pruning based on information-theoretic measures on a fully connected feed-forward neural network with two hidden layers trained on MNIST dataset and compare the results to a recently proposed pruning method. We furthermore show that the common practice of re-training after pruning can partly be obviated by a surgery step called bias balancing, without incurring significant performance degradation.

We revisit fuzzy neural network with a cornerstone notion of generalized hamming distance, which provides a novel and theoretically justified framework to re-interpret many useful neural network techniques in terms of fuzzy logic. In particular, we conjecture and empirically illustrate that, the celebrated batch normalization (BN) technique actually adapts the “normalized” bias such that it approximates the rightful bias induced by the generalized hamming distance. Once the due bias is enforced analytically, neither the optimization of bias terms nor the sophisticated batch normalization is needed. Also in the light of generalized hamming distance, the popular rectified linear units (ReLU) can be treated as setting a minimal hamming distance threshold between network inputs and weights. This thresholding scheme, on the one hand, can be improved by introducing double-thresholding on both positive and negative extremes of neuron outputs. On the other hand, ReLUs turn out to be non-essential and can be removed from networks trained for simple tasks like MNIST classification. The proposed generalized hamming network (GHN) as such not only lends itself to rigorous analysis and interpretation within the fuzzy logic theory but also demonstrates fast learning speed, well-controlled behaviour and state-of-the-art performances on a variety of learning tasks.

ABSTRACT This report describes the design of a programmable general purpose analog neural computer and simulator. It is intended primarily for real-world real-time computations such as analysis of visual or acoustical patterns, robotics and the development of special purpose neural nets. The machine is scalable and composed of interconnected modules containing arrays of neurons, modifiable synapses and switches. It runs entirely in analog mode but connection architecture, synaptic gains and time constants as well as neuron parameters are set digitally. Each neuron has a limited number of inputs and can be connected to any but not all other neurons.

ABSTRACT This report describes the design of a programmable general purpose analog neural computer and simulator. It is intended primarily for real-world real-time computations such as analysis of visual or acoustical patterns, robotics and the development of special purpose neural nets. The machine is scalable and composed of interconnected modules containing arrays of neurons, modifiable synapses and switches. It runs entirely in analog mode but connection architecture, synaptic gains and time constants as well as neuron parameters are set digitally. Each neuron has a limited number of inputs and can be connected to any but not all other neurons.

ABSTRACT This report describes the design of a programmable general purpose analog neural computer and simulator. It is intended primarily for real-world real-time computations such as analysis of visual or acoustical patterns, robotics and the development of special purpose neural nets. The machine is scalable and composed of interconnected modules containing arrays ofneurons, modifiable synapses and switches. It runs entirely in analog mode but connection architecture, synaptic gains and time constants as well as neuron parameters are set digitally. Each neuron has a limited number of inputs and can be connected to any but not all other neurons.