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Despite the tremendous success of convolutional neural networks (CNNs) in computer vision, the mechanism of CNNs still lacks clear interpretation. Currently, class activation mapping (CAM), a famous visualization technique to interpret CNN's decision, has drawn increasing attention. Gradient-based CAMs are efficient while the performance is heavily affected by gradient vanishing and exploding. In contrast, gradient-free CAMs can avoid computing gradients to produce more understandable results. However, existing gradient-free CAMs are quite time-consuming because hundreds of forward interference per image are required. In this paper, we proposed Cluster-CAM, an effective and efficient gradient-free CNN interpretation algorithm. Cluster-CAM can significantly reduce the times of forward propagation by splitting the feature maps into clusters in an unsupervised manner. Furthermore, we propose an artful strategy to forge a cognition-base map and cognition-scissors from clustered feature maps. The final salience heatmap will be computed by merging the above cognition maps. Qualitative results conspicuously show that Cluster-CAM can produce heatmaps where the highlighted regions match the human's cognition more precisely than existing CAMs. The quantitative evaluation further demonstrates the superiority of Cluster-CAM in both effectiveness and efficiency.

In machine learning, the selection of a promising model from a potentially large number of competing models and the assessment of its generalization performance are critical tasks that need careful consideration. Typically, model selection and evaluation are strictly separated endeavors, splitting the sample at hand into a training, validation, and evaluation set, and only compute a single confidence interval for the prediction performance of the final selected model. We however propose an algorithm how to compute valid lower confidence bounds for multiple models that have been selected based on their prediction performances in the evaluation set by interpreting the selection problem as a simultaneous inference problem. We use bootstrap tilting and a maxT-type multiplicity correction. The approach is universally applicable for any combination of prediction models, any model selection strategy, and any prediction performance measure that accepts weights. We conducted various simulation experiments which show that our proposed approach yields lower confidence bounds that are at least comparably good as bounds from standard approaches, and that reliably reach the nominal coverage probability. In addition, especially when sample size is small, our proposed approach yields better performing prediction models than the default selection of only one model for evaluation does.

Reliability is one of the major design criteria in Cyber-Physical Systems (CPSs). This is because of the existence of some critical applications in CPSs and their failure is catastrophic. Therefore, employing strong error detection and correction mechanisms in CPSs is inevitable. CPSs are composed of a variety of units, including sensors, networks, and microcontrollers. Each of these units is probable to be in a faulty state at any time and the occurred fault can result in erroneous output. The fault may cause the units of CPS to malfunction and eventually crash. Traditional fault-tolerant approaches include redundancy time, hardware, information, and/or software. However, these approaches impose significant overheads besides their low error coverage, which limits their applicability. In addition, the interval between error occurrence and detection is too long in these approaches. In this paper, based on Deep Reinforcement Learning (DRL), a new error detection approach is proposed that not only detects errors with high accuracy but also can perform error detection at the moment due to very low inference time. The proposed approach can categorize different types of errors from normal data and predict whether the system will fail. The evaluation results illustrate that the proposed approach has improved more than 2x in terms of accuracy and more than 5x in terms of inference time compared to other approaches.

Depth separation results propose a possible theoretical explanation for the benefits of deep neural networks over shallower architectures, establishing that the former possess superior approximation capabilities. However, there are no known results in which the deeper architecture leverages this advantage into a provable optimization guarantee. We prove that when the data are generated by a distribution with radial symmetry which satisfies some mild assumptions, gradient descent can efficiently learn ball indicator functions using a depth 2 neural network with two layers of sigmoidal activations, and where the hidden layer is held fixed throughout training. By building on and refining existing techniques for approximation lower bounds of neural networks with a single layer of non-linearities, we show that there are $d$-dimensional radial distributions on the data such that ball indicators cannot be learned efficiently by any algorithm to accuracy better than $\Omega(d^{-4})$, nor by a standard gradient descent implementation to accuracy better than a constant. These results establish what is to the best of our knowledge, the first optimization-based separations where the approximation benefits of the stronger architecture provably manifest in practice. Our proof technique introduces new tools and ideas that may be of independent interest in the theoretical study of both the approximation and optimization of neural networks.

Previous work has separately addressed different forms of action, state and action-state entropy regularization, pure exploration and space occupation. These problems have become extremely relevant for regularization, generalization, speeding up learning and providing robust solutions at unprecedented levels. However, solutions of those problems are hectic, ranging from convex and non-convex optimization, and unconstrained optimization to constrained optimization. Here we provide a general dual function formalism that transforms the constrained optimization problem into an unconstrained convex one for any mixture of action and state entropies. The cases with pure action entropy and pure state entropy are understood as limits of the mixture.

Many real-world systems can be described by mathematical formulas that are human-comprehensible, easy to analyze and can be helpful in explaining the system's behaviour. Symbolic regression is a method that generates nonlinear models from data in the form of analytic expressions. Historically, symbolic regression has been predominantly realized using genetic programming, a method that iteratively evolves a population of candidate solutions that are sampled by genetic operators crossover and mutation. This gradient-free evolutionary approach suffers from several deficiencies: it does not scale well with the number of variables and samples in the training data, models tend to grow in size and complexity without an adequate accuracy gain, and it is hard to fine-tune the inner model coefficients using just genetic operators. Recently, neural networks have been applied to learn the whole analytic formula, i.e., its structure as well as the coefficients, by means of gradient-based optimization algorithms. We propose a novel neural network-based symbolic regression method that constructs physically plausible models based on limited training data and prior knowledge about the system. The method employs an adaptive weighting scheme to effectively deal with multiple loss function terms and an epoch-wise learning process to reduce the chance of getting stuck in poor local optima. Furthermore, we propose a parameter-free method for choosing the model with the best interpolation and extrapolation performance out of all models generated through the whole learning process. We experimentally evaluate the approach on the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the anti-lock braking system. The results clearly show the potential of the method to find sparse and accurate models that comply with the prior knowledge provided.

Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it cannot explore the flat curvature of the loss function. To overcome that issue, we propose to exponentially increase the step-size of the GD algorithm. Under homogeneous assumptions on the loss function, we demonstrate that the iterates of the proposed \emph{exponential step size gradient descent} (EGD) algorithm converge linearly to the optimal solution. Leveraging that optimization insight, we then consider using the EGD algorithm for solving parameter estimation under both regular and non-regular statistical models whose loss function becomes locally convex when the sample size goes to infinity. We demonstrate that the EGD iterates reach the final statistical radius within the true parameter after a logarithmic number of iterations, which is in stark contrast to a \emph{polynomial} number of iterations of the GD algorithm in non-regular statistical models. Therefore, the total computational complexity of the EGD algorithm is \emph{optimal} and exponentially cheaper than that of the GD for solving parameter estimation in non-regular statistical models while being comparable to that of the GD in regular statistical settings. To the best of our knowledge, it resolves a long-standing gap between statistical and algorithmic computational complexities of parameter estimation in non-regular statistical models. Finally, we provide targeted applications of the general theory to several classes of statistical models, including generalized linear models with polynomial link functions and location Gaussian mixture models.

In the dominant paradigm for designing equitable machine learning systems, one works to ensure that model predictions satisfy various fairness criteria, such as parity in error rates across race, gender, and other legally protected traits. That approach, however, typically ignores the downstream decisions and outcomes that predictions affect, and, as a result, can induce unexpected harms. Here we present an alternative framework for fairness that directly anticipates the consequences of decisions. Stakeholders first specify preferences over the possible outcomes of an algorithmically informed decision-making process. For example, lenders may prefer extending credit to those most likely to repay a loan, while also preferring similar lending rates across neighborhoods. One then searches the space of decision policies to maximize the specified utility. We develop and describe a method for efficiently learning these optimal policies from data for a large family of expressive utility functions, facilitating a more holistic approach to equitable decision-making.

The Boolean Satisfiability (SAT) problem stands out as an attractive NP-complete problem in theoretic computer science and plays a central role in a broad spectrum of computing-related applications. Exploiting and tuning SAT solvers under numerous scenarios require massive high-quality industry-level SAT instances, which unfortunately are quite limited in the real world. To address the data insufficiency issue, in this paper, we propose W2SAT, a framework to generate SAT formulas by learning intrinsic structures and properties from given real-world/industrial instances in an implicit fashion. To this end, we introduce a novel SAT representation called Weighted Literal Incidence Graph (WLIG), which exhibits strong representation ability and generalizability against existing counterparts, and can be efficiently generated via a specialized learning-based graph generative model. Decoding from WLIGs into SAT problems is then modeled as finding overlapping cliques with a novel hill-climbing optimization method termed Optimal Weight Coverage (OWC). Experiments demonstrate the superiority of our WLIG-induced approach in terms of graph metrics, efficiency, and scalability in comparison to previous methods. Additionally, we discuss the limitations of graph-based SAT generation for real-world applications, especially when utilizing generated instances for SAT solver parameter-tuning, and pose some potential directions.

Most algorithms for representation learning and link prediction in relational data have been designed for static data. However, the data they are applied to usually evolves with time, such as friend graphs in social networks or user interactions with items in recommender systems. This is also the case for knowledge bases, which contain facts such as (US, has president, B. Obama, [2009-2017]) that are valid only at certain points in time. For the problem of link prediction under temporal constraints, i.e., answering queries such as (US, has president, ?, 2012), we propose a solution inspired by the canonical decomposition of tensors of order 4. We introduce new regularization schemes and present an extension of ComplEx (Trouillon et al., 2016) that achieves state-of-the-art performance. Additionally, we propose a new dataset for knowledge base completion constructed from Wikidata, larger than previous benchmarks by an order of magnitude, as a new reference for evaluating temporal and non-temporal link prediction methods.