Along with the great success of deep neural networks, there is also growing concern about their black-box nature. The interpretability issue affects people's trust on deep learning systems. It is also related to many ethical problems, e.g., algorithmic discrimination. Moreover, interpretability is a desired property for deep networks to become powerful tools in other research fields, e.g., drug discovery and genomics. In this survey, we conduct a comprehensive review of the neural network interpretability research. We first clarify the definition of interpretability as it has been used in many different contexts. Then we elaborate on the importance of interpretability and propose a novel taxonomy organized along three dimensions: type of engagement (passive vs. active interpretation approaches), the type of explanation, and the focus (from local to global interpretability). This taxonomy provides a meaningful 3D view of distribution of papers from the relevant literature as two of the dimensions are not simply categorical but allow ordinal subcategories. Finally, we summarize the existing interpretability evaluation methods and suggest possible research directions inspired by our new taxonomy.

Reservoir computing (RC) refers to a new class of state-space models with a fixed state transition structure (the reservoir) and an adaptable readout form the state space. The reservoir is supposed to be sufficiently complex so as to capture a large number of features of the input stream that can be exploited by the reservoir-to-output readout mapping. The field of RC has been growing rapidly with many successful applications. However, RC has been criticized for not being principled enough. Reservoir construction is largely driven by a series of randomized model-building stages, with both researchers and practitioners having to rely on a series of trials and errors. To initialize a systematic study of the field, we concentrate on one of the most popular classes of RC methods, namely echo state network, and ask: What is the minimal complexity of reservoir construction for obtaining competitive models and what is the memory capacity (MC) of such simplified reservoirs? On a number of widely used time series benchmarks of different origin and characteristics, as well as by conducting a theoretical analysis we show that a simple deterministically constructed cycle reservoir is comparable to the standard echo state network methodology. The (short-term) of linear cyclic reservoirs can be made arbitrarily close to the proved optimal value.

It has previously been shown that gradient-descent learning algorithms for recurrent neural networks can perform poorly on tasks that involve long-term dependencies, i.e. those problems for which the desired output depends on inputs presented at times far in the past. We show that the long-term dependencies problem is lessened for a class of architectures called nonlinear autoregressive models with exogenous (NARX) recurrent neural networks, which have powerful representational capabilities. We have previously reported that gradient descent learning can be more effective in NARX networks than in recurrent neural network architectures that have "hidden states" on problems including grammatical inference and nonlinear system identification. Typically, the network converges much faster and generalizes better than other networks. The results in this paper are consistent with this phenomenon. We present some experimental results which show that NARX networks can often retain information for two to three times as long as conventional recurrent neural networks. We show that although NARX networks do not circumvent the problem of long-term dependencies, they can greatly improve performance on long-term dependency problems. We also describe in detail some of the assumptions regarding what it means to latch information robustly and suggest possible ways to loosen these assumptions.

The recent advanced LIGO detections of gravitational waves from merging binary black holes enhance the prospect of exploring binary evolution via gravitational-wave observations of a population of compact-object binaries. In the face of uncertainty about binary formation models, model-independent inference provides an appealing alternative to comparisons between observed and modelled populations. We describe a procedure for clustering in the multidimensional parameter space of observations that are subject to significant measurement errors. We apply this procedure to a mock data set of population-synthesis predictions for the masses of merging compact binaries convolved with realistic measurement uncertainties, and demonstrate that we can accurately distinguish subpopulations of binary neutron stars, binary black holes, and mixed neutron star–black hole binaries with tens of observations.

The emergence of large sensor networks has facilitated the collection of large amounts of real-time data to monitor and control complex engineering systems. However, in many cases the collected data may be incomplete or inconsistent, while the underlying environment may be time-varying or unformulated. In this paper, we develop an innovative cognitive fault diagnosis framework that tackles the above challenges. This framework investigates fault diagnosis in the model space instead of the signal space. Learning in the model space is implemented by fitting a series of models using a series of signal segments selected with a sliding window. By investigating the learning techniques in the fitted model space, faulty models can be discriminated from healthy models using a one-class learning algorithm. The framework enables us to construct a fault library when unknown faults occur, which can be regarded as cognitive fault isolation. This paper also theoretically investigates how to measure the pairwise distance between two models in the model space and incorporates the model distance into the learning algorithm in the model space. The results on three benchmark applications and one simulated model for the Barcelona water distribution network confirm the effectiveness of the proposed framework.

A new class of state-space models, reservoir models, with a fixed state transition structure (the “reservoir”) and an adaptable readout from the state space, has recently emerged as a way for time series processing and modeling. Echo state network (ESN) is one of the simplest, yet powerful, reservoir models. ESN models are generally constructed in a randomized manner. In our previous study (Rodan & Tiňo, 2011 ), we showed that a very simple, cyclic, deterministically generated reservoir can yield performance competitive with standard ESN. In this contribution, we extend our previous study in three aspects. First, we introduce a novel simple deterministic reservoir model, cycle reservoir with jumps (CRJ), with highly constrained weight values, that has superior performance to standard ESN on a variety of temporal tasks of different origin and characteristics. Second, we elaborate on the possible link between reservoir characterizations, such as eigenvalue distribution of the reservoir matrix or pseudo-Lyapunov exponent of the input-driven reservoir dynamics, and the model performance. It has been suggested that a uniform coverage of the unit disk by such eigenvalues can lead to superior model performance. We show that despite highly constrained eigenvalue distribution, CRJ consistently outperforms ESN (which has much more uniform eigenvalue coverage of the unit disk). Also, unlike in the case of ESN, pseudo-Lyapunov exponents of the selected optimal CRJ models are consistently negative. Third, we present a new framework for determining the short-term memory capacity of linear reservoir models to a high degree of precision. Using the framework, we study the effect of shortcut connections in the CRJ reservoir topology on its memory capacity.