Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training. The F-Principle has been very useful in providing both qualitative and quantitative understandings of DNNs. In this paper, we rigorously investigate the F-Principle for the training dynamics of a general DNN at three stages: initial stage, intermediate stage, and final stage. For each stage, a theorem is provided in terms of proper quantities characterizing the F-Principle. Our results are general in the sense that they work for multilayer networks with general activation functions, population densities of data, and a large class of loss functions. Our work lays a theoretical foundation of the F-Principle for a better understanding of the training process of DNNs.

Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a nonlinear system identification method for gray-box modeling. It consists of two interlaced parts of modeling that are computer-aided. The first performs computer-aided identification of a model structure composed of elements selected from user-specified domain-specific modeling knowledge, while the second part performs parameter estimation. In this paper, recent developments of the equation discovery method called process-based modeling, suited for nonlinear system identification, are elaborated and illustrated on two continuous-time case studies. The first case study illustrates the use of the process-based modeling on synthetic data while the second case-study evaluates on measured data for a standard system-identification benchmark. The experimental results clearly demonstrate the ability of process-based modeling to reconstruct both model structure and parameters from measured data.

Fuzzy Rule Interpolation (FRI) reasoning methods have been introduced to address sparse fuzzy rule bases and reduce complexity. The first FRI method was the Koczy and Hirota (KH) proposed "Linear Interpolation". Besides, several conditions and criteria have been suggested for unifying the common requirements FRI methods have to satisfy. One of the most conditions is restricted the fuzzy set of the conclusion must preserve a Piece-Wise Linearity (PWL) if all antecedents and consequents of the fuzzy rules are preserving on PWL sets at {\alpha}-cut levels. The KH FRI is one of FRI methods which cannot satisfy this condition. Therefore, the goal of this paper is to investigate equations and notations related to PWL property, which is aimed to highlight the problematic properties of the KH FRI method to prove its efficiency with PWL condition. In addition, this paper is focusing on constructing benchmark examples to be a baseline for testing other FRI methods against situations that are not satisfied with the linearity condition for KH FRI.

We discuss the objectives of any endeavor in creating artificial intelligence, AI, and provide a possible alternative. Intelligence might be an unintended consequence of curiosity left to roam free, best exemplified by a frolicking infant. This suggests that our attempts at AI could have been misguided; what we actually need to strive for can be termed artificial curiosity, AC, and intelligence happens as a consequence of those efforts. For this unintentional yet welcome aftereffect to set in a foundational list of guiding principles needs to be present. We discuss what these essential doctrines might be and why their establishment is required to form connections, possibly growing, between a knowledge store that has been built up and new pieces of information that curiosity will bring back. As more findings are acquired and more bonds are fermented, we need a way to, periodically, reduce the amount of data; in the sense, it is important to capture the critical characteristics of what has been accumulated or produce a summary of what has been gathered. We start with the intuition for this line of reasoning and formalize it with a series of models (and iterative improvements) that will be necessary to make the incubation of intelligence a reality. Our discussion provides conceptual modifications to the Turing Test and to Searle's Chinese room argument. We discuss the future implications for society as AI becomes an integral part of life.

Deep reinforcement learning (RL) algorithms can use high-capacity deep networks to learn directly from image observations. However, these kinds of observation spaces present a number of challenges in practice, since the policy must now solve two problems: a representation learning problem, and a task learning problem. In this paper, we aim to explicitly learn representations that can accelerate reinforcement learning from images. We propose the stochastic latent actor-critic (SLAC) algorithm: a sample-efficient and high-performing RL algorithm for learning policies for complex continuous control tasks directly from high-dimensional image inputs. SLAC learns a compact latent representation space using a stochastic sequential latent variable model, and then learns a critic model within this latent space. By learning a critic within a compact state space, SLAC can learn much more efficiently than standard RL methods. The proposed model improves performance substantially over alternative representations as well, such as variational autoencoders. In fact, our experimental evaluation demonstrates that the sample efficiency of our resulting method is comparable to that of model-based RL methods that directly use a similar type of model for control. Furthermore, our method outperforms both model-free and model-based alternatives in terms of final performance and sample efficiency, on a range of difficult image-based control tasks.

Recent works on end-to-end trainable neural network based approaches have demonstrated state-of-the-art results on dialogue state tracking. The best performing approaches estimate a probability distribution over all possible slot values. However, these approaches do not scale for large value sets commonly present in real-life applications and are not ideal for tracking slot values that were not observed in the training set. To tackle these issues, candidate-generation-based approaches have been proposed. These approaches estimate a set of values that are possible at each turn based on the conversation history and/or language understanding outputs, and hence enable state tracking over unseen values and large value sets however, they fall short in terms of performance in comparison to the first group. In this work, we analyze the performance of these two alternative dialogue state tracking methods, and present a hybrid approach (HyST) which learns the appropriate method for each slot type. To demonstrate the effectiveness of HyST on a rich-set of slot types, we experiment with the recently released MultiWOZ-2.0 multi-domain, task-oriented dialogue-dataset. Our experiments show that HyST scales to multi-domain applications. Our best performing model results in a relative improvement of 24% and 10% over the previous SOTA and our best baseline respectively.

Transfer learning across different reinforcement learning (RL) tasks is becoming an increasingly valuable area of research. We consider a goal-based multi-task RL framework and mechanisms by which previously solved tasks can reduce sample complexity and regret when the agent is faced with a new task. Specifically, we introduce two metrics on the state space that encode notions of traversibility of the state space for an agent. Using these metrics a topological covering is constructed by way of a set of landmark states in a fully self-supervised manner. We show that these landmark coverings confer theoretical advantages for transfer learning within the goal-based multi-task RL setting. Specifically, we demonstrate three mechanisms by which landmark coverings can be used for successful transfer learning. First, we extend the Landmark Options Via Reflection (LOVR) framework to this new topological covering; second, we use the landmark-centric value functions themselves as features and define a greedy zombie policy that achieves near oracle performance on a sequence of zero-shot transfer tasks; finally, motivated by the second transfer mechanism, we introduce a learned reward function that provides a more dense reward signal for goal-based RL. Our novel topological landmark covering confers beneficial theoretical results, bounding the Q values at each state-action pair. In doing so, we introduce a mechanism that performs action-pruning at infeasible actions which cannot possibly be part of an optimal policy for the current goal.

Modern data sets that arise in various branches of science and engineering are characterized by their ever increasing scale and richness. This is spurred in part by easier access to computer, internet and various sensor-based technologies that enable the collection of such varied datasets. But on the flip side, these large and rich data-sets are no longer carefully curated, are often collected in a decentralized, distributed fashion, and consequently are plagued with the complexities of heterogeneity, adversarial manipulations, and outliers. The analysis of these huge datasets is thus fraught with methodological challenges. To understand the fundamental challenges and tradeoffs in handling such "dirty data" is precisely the premise of the field of robust statistics. Here, the aforementioned complexities are largely formalized under two different models of robustness: (1) The heavy-tailed model: Here the sampling distribution can have thick tails, for instance, only low-order moments of the distribution are assumed to be finite; and (2) The ǫ-contamination model: Here the sampling distribution is modeled as a well-behaved distribution contaminated by an ǫ fraction of arbitrary outliers. In each case, classical estimators of the distribution (based for instance on the maximum likelihood estimator) can behave considerably worse (potentially arbitrarily worse) than under standard settings where the data is better behaved, satisfying various regularity properties. In particular, these classical estimators can be extremely sensitive to the tails of the distribution or to the outliers, so that the broad goal in robust statistics is to construct estimators that improve on these classical estimators by reducing their sensitivity to outliers.

In recent years, an active field of research has developed around automated machine learning (AutoML). Unfortunately, comparing different AutoML systems is hard and often done incorrectly. We introduce an open, ongoing, and extensible benchmark framework which follows best practices and avoids common mistakes. The framework is open-source, uses public datasets and has a website with up-to-date results. We use the framework to conduct a thorough comparison of 4 AutoML systems across 39 datasets and analyze the results.

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.