Controlling Neural Networks with Rule Representations

ArXiv, 2022

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a ser...

Proceedings of the Northern Lights Deep Learning Workshop

Numerous applications rely on the efficiency of Deep Learning models to address complex classification tasks for critical decisions-making. However, we may not know how each feature in these models contributes towards the prediction. In contrast, Rule Induction algorithms provide an interpretable way to extract patterns from data, but traditional approaches suffer in terms of scalability. In this work, we bridge Deep Learning and Rule Induction and define the RIDDLE (Rule Induction with Deep Learning) architecture. We show that RIDDLE has state-of-the-art performance in Rule Induction via an empirical evaluation.

Southeast SAS Users Group, 2019

Neural network models are typically described as "black boxes" because their inner workings are not easy to understand. We propose that, since a neural network model that accurately predicts its target variable is a good representation of the training data, the output of the model may be recast as a target variable and subjected to standard regression algorithms to "explain" it as a response variable. Thus, the "black box" of the internal mechanism is transformed into a "glass box" that facilitates understanding of the underlying model. Deriving a regression model from a set of training data analogous to a neural network is an effective means to understand a neural network model because regression algorithms are commonly-used tools and the interpretation of a regression model is straightforward and well-understood .

2019

Deep Neural Networks (DNNs) have limited ability to explain their acquired knowledge or decision rationale. As a result, end-users perceive DNNs as black-boxes and are hesitant to fully adopt them in safety-critical applications. Therefore, developing explainable DNNs has become a prime interest in neural network research. This paper presents a methodology for linguistically explaining the knowledge a DNN classifier has acquired in training. The main objective is to help users understand what the DNN has learned about each class. The presented methodology is fuzzy logic based and involves end-users of the system in the explanation process, enabling users to customize the explanations to match their requirements. This paper presents the explanation methodology, metrics of explanation quality, validation steps, and a discussion of advantages and limitations. The explanation methodology was implemented on a benchmark classification problem. Experimental results demonstrated the method’...

Journal of Chemical Education, 1994

Acta Universitatis Sapientiae, Informatica, 2020

A common assumption about neural networks is that they can learn an appropriate internal representation on their own, see e.g. end-to-end learning. In this work we challenge this assumption. We consider two simple tasks and show that the state-of-the-art training algorithm fails, although the model itself is able to represent an appropriate solution. We will demonstrate that encouraging an appropriate internal representation allows the same model to solve these tasks. While we do not claim that it is impossible to solve these tasks by other means (such as neural networks with more layers), our results illustrate that integration of domain knowledge in form of a desired internal representation may improve the generalization ability of neural networks.

Studies in Computational Intelligence, 2017

Proceedings of the 24th Symposium on Principles and Practice of Parallel Programming, 2019

Deep learning (DL) research yields accuracy and product improvements from both model architecture changes and scale: larger data sets and models, and more computation. For hardware design, it is di cult to predict DL model changes. However, recent prior work shows that as dataset sizes grow, DL model accuracy and model size grow predictably. This paper leverages the prior work to project the dataset and model size growth required to advance DL accuracy beyond human-level, to frontier targets de ned by machine learning experts. Datasets will need to grow 33-971×, while models will need to grow 6.6-456× to achieve target accuracies. We further characterize and project the computational requirements to train these applications at scale. Our characterization reveals an important segmentation of DL training challenges for recurrent neural networks (RNNs) that contrasts with prior studies of deep convolutional networks. RNNs will have comparatively moderate operational intensities and very large memory footprint requirements. In contrast to emerging accelerator designs, largescale RNN training characteristics suggest designs with signicantly larger memory capacity and on-chip caches.

The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Abstract—Developments in deep learning have seen the use of layer-wise unsupervised learning combined with supervised learning for fine-tuning. With this layer-wise approach, a deep network can be seen as a more modular system which lends itself well to learning representations. In this paper we investigate whether such modularity can be useful to the insertion of background knowledge into deep networks, and whether it can improve learning performance when it is available, and to the extraction of knowledge from trained deep networks, and whether it can offer a better understanding of the representations learned by such networks. To this end we use a simple symbolic language-a set of logical rules which we call confidence rules-and show that it is suitable for the representation of quantitative reasoning in deep networks. We show by knowledge extraction that confidence rules can offer a low-cost representation for layer-wise networks (or restricted Boltzmann machines). We also show that layer-wise extraction can produce an improvement in the accuracy of Deep Belief Networks. Furthermore, the proposed symbolic characterisation of deep networks provides a novel method for the insertion of prior knowledge and training of deep networks. With the use of this method, a deep neural-symbolic system is proposed and evaluated, with experimental results indicating that modularity through the use of confidence rules and knowledge insertion can be beneficial to network performance.

1991

Scientific induction involves an iterative process of hypothesis formulation, testing, and refinement. People in ordinary life appear to undertake a similar process in explaining their world. We believe that it is instructive to study rule induction in connectionist systems from a similar perspective. We propose an approach, called the Connectionist Scientist Game, in which symbolic condition-action rules are extracted from the learned connection strengths in a network, thereby forming explicit hypotheses about a domain. The hypotheses are tested by injecting the rules back into the network and continuing the training process. This extraction-injection process continues until the resulting rule base adequately characterizes the domain. By exploiting constraints inherent in the domain of symbolic string-to-string mappings, we show how a connectionist architecture called RuleNet can induce explicit, symbolic condition-action rules from examples. RuleNet's performance is far superior to that of a variety of alternative architectures we've examined. RuleNet is capable of handling domains having both symbolic and subsymbolic components, and thus shows greater potential than purely symbolic learning algorithms. The formal string manipulation task performed by RuleNet can be viewed as an abstraction of several interesting cognitive models in the connectionist literature, including case role assignment and the mapping of orthography to phonology.

2020

We connect the widespread idea of interpreting classifier decisions to probabilistic prime implicants. A set of input features is deemed relevant for a classification decision if the classifier score remains nearly constant when randomising the remaining features. This introduces a rate-distortion trade-off between the set size and the deviation of the score. We explain how relevance maps can be interpreted as a greedy strategy to calculate the rate-distortion function. For neural networks we show that approximating this function even in a single point up to any non-trivial approximation factor is NP-hard. Thus, no algorithm will provably find small relevant sets of input features even if they exist. Finally, as a numerical comparison we express a Boolean function, for which the prime implicant sets are known, as a neural network and investigate which relevance mapping methods are able to highlight them.

Deep Learning and Edge Computing Solutions for High Performance Computing, 2021

ArXiv, 2020

Deep neural networks (DNNs) is demonstrated to be vulnerable to the adversarial example, which is generated by adding small adversarial perturbation into the original legitimate example to cause the wrong outputs of DNNs. Nowadays, most works focus on the robustness of the deep model, while few works pay attention to the robustness of the learning task itself defined on DNNs. So we redefine this issue as the robustness of deep neural learning system. A deep neural learning system consists of the deep model and the learning task defined on the deep model. Moreover, the deep model is usually a deep neural network, involving the model architecture, data, training loss and training algorithm. We speculate that the vulnerability of the deep learning system also roots in the learning task itself. This paper defines the interval-label classification task for the deep classification system, whose labels are predefined non-overlapping intervals, instead of a fixed value (hard label) or proba...

Electronics, 2020

The explanation of the decisions provided by a model are crucial in a domain such as medical diagnosis. With the advent of deep learning, it is very important to explain why a classification is reached by a model. This work tackles the transparency problem of convolutional neural networks(CNNs). We propose to generate propositional rules from CNNs, because they are intuitive to the way humans reason. Our method considers that a CNN is the union of two subnetworks: a multi-layer erceptron (MLP) in the fully connected layers; and a subnetwork including several 2D convolutional layers and max-pooling layers. Rule extraction exhibits two main steps, with each step generating rules from each subnetwork of the CNN. In practice, we approximate the two subnetworks by two particular MLP models that makes it possible to generate propositional rules. We performed the experiments with two datasets involving images: MNISTdigit recognition; and skin-cancer diagnosis. With high fidelity, the extra...