We propose an approach that connects recurrent networks with different orders of hidden interaction with regular grammars of different levels of complexity. We argue that the correspondence between recurrent networks and formal computational models gives understanding to the analysis of the complicated behaviors of recurrent networks. We introduce an entropy value that categorizes all regular grammars into three classes with different levels of complexity, and show that several existing recurrent networks match grammars from either all or partial classes. As such, the differences between regular grammars reveal the different properties of these models. We also provide a unification of all investigated recurrent networks. Our evaluation shows that the unified recurrent network has improved performance in learning grammars, and demonstrates comparable performance on a real-world dataset with more complicated models.
National Institute of Informatics（国立信息学研究所）；The Graduate University for Advanced Studies（综合研究大学院大学）
We present a method to extract a weighted finite automaton (WFA) from a recurrent neural network (RNN). Our algorithm is based on the WFA learning algorithm by Balle and Mohri, which is in turn an extension of Angluin's classic \lstar algorithm. Our technical novelty is in the use of \emph{regression} methods for the so-called equivalence queries, thus exploiting the internal state space of an RNN to prioritize counterexample candidates. This way we achieve a quantitative/weighted extension of the recent work by Weiss, Goldberg and Yahav that extracts DFAs. We experimentally evaluate the accur…
Mila；Université de Montréal（蒙特利尔大学）；McGill University（麦吉尔大学）
In this paper, we unravel a fundamental connection between weighted finite automata~(WFAs) and second-order recurrent neural networks~(2-RNNs): in the case of sequences of discrete symbols, WFAs and 2-RNNs with linear activation functions are expressively equivalent. Motivated by this result, we build upon a recent extension of the spectral learning algorithm to vector-valued WFAs and propose the first provable learning algorithm for linear 2-RNNs defined over sequences of continuous input vectors. This algorithm relies on estimating low rank sub-blocks of the so-called Hankel tensor, from whi…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both shortcomings with a class of recurrent networks that use a stochastic state transition mechanism between cell applications. This mechanism, which we term state-regularization, makes RNNs transition between a finite set of learnable states. We evaluate state-regularized RNNs on (…
We present a novel algorithm that uses exact learning and abstraction to extract a deterministic finite automaton describing the state dynamics of a given trained RNN. We do this using Angluin's L* algorithm as a learner and the trained RNN as an oracle. Our technique efficiently extracts accurate automata from trained RNNs, even when the state vectors are large and require fine differentiation.
Univ Lyon（里昂大学）；UJM-Saint-Etienne（圣艾蒂安大学）；CNRS（法国国家科学研究中心）；Laboratoire Hubert Curien（休伯特·居里安实验室）；Aix Marseille Univ（艾克斯-马赛大学）；Universite de Toulon（土伦大学）；LIS（信息科学实验室）
This paper is an attempt to bridge the gap between deep learning and grammatical inference. Indeed, it provides an algorithm to extract a (stochastic) formal language from any recurrent neural network trained for language modelling. In detail, the algorithm uses the already trained network as an oracle -- and thus does not require the access to the inner representation of the black-box -- and applies a spectral approach to infer a weighted automaton. As weighted automata compute linear functions, they are computationally more efficient than neural networks and thus the nature of the approach i…
Amazon（亚马逊）；NEC Laboratories Europe（NEC欧洲实验室）；University of Stuttgart（斯图加特大学）
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as how they arrive at a particular prediction. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both shortcomings with a class of recurrent networks that use a stochastic state transition mechanism between cell applications. This mechanism, which we term state-regulariza…
Rice University（莱斯大学）；Baylor College of Medicine（贝勒医学院）
We investigate the internal representations that a recurrent neural network (RNN) uses while learning to recognize a regular formal language. Specifically, we train a RNN on positive and negative examples from a regular language, and ask if there is a simple decoding function that maps states of this RNN to states of the minimal deterministic finite automaton (MDFA) for the language. Our experiments show that such a decoding function indeed exists, and that it maps states of the RNN not to MDFA states, but to states of an {\em abstraction} obtained by clustering small sets of MDFA states into …
In this paper, we present connections between three models used in different research fields: weighted finite automata~(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks which encompasses a set of optimization techniques for high-order tensors used in quantum physics and numerical analysis. We first present an intrinsic relation between WFA and the tensor train decomposition, a particular form of tensor network. This relation allows us to exhibit a novel low rank structure of the Hankel matrix of a function computed by a WFA and…
Recurrent Neural Networks (RNNs) have achieved tremendous success in sequential data processing. However, it is quite challenging to interpret and verify RNNs' behaviors directly. To this end, many efforts have been made to extract finite automata from RNNs. Existing approaches such as exact learning are effective in extracting finite-state models to characterize the state dynamics of RNNs for formal languages, but are limited in the scalability to process natural languages. Compositional approaches that are scablable to natural languages fall short in extraction precision. In this paper, we i…
W. M. Keck Science Department, Claremont McKenna, Scripps, and Pitzer College（克莱蒙特·麦肯纳学院、斯克里普斯学院和皮策学院 W. M. 凯克科学系）；University of California, Davis（加州大学戴维斯分校）
Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA). PDFAs provide an excellent performance benchmark in that they can be systematically enumerated, the randomness and correlation structure of their generated processes are exactly known, and thei…
We present an algorithm for extracting a subclass of the context free grammars (CFGs) from a trained recurrent neural network (RNN). We develop a new framework, pattern rule sets (PRSs), which describe sequences of deterministic finite automata (DFAs) that approximate a non-regular language. We present an algorithm for recovering the PRS behind a sequence of such automata, and apply it to the sequences of automata extracted from trained RNNs using the L* algorithm. We then show how the PRS may converted into a CFG, enabling a familiar and useful presentation of the learned language. Extracting…
Recent neural network architectures such as the basic recurrent neural network (RNN) and Gated Recurrent Unit (GRU) have gained prominence as end-to-end learning architectures for natural language processing tasks. But what is the computational power of such systems? We prove that finite precision RNNs with one hidden layer and ReLU activation and finite precision GRUs are exactly as computationally powerful as deterministic finite automata. Allowing arbitrary precision, we prove that RNNs with one hidden layer and ReLU activation are at least as computationally powerful as pushdown automata. …
Escuela Politécnica Superior, Universidad Autónoma de Madrid（马德里自治大学高等理工学院）
We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. When a small amount of noise is introduced into the activation function, the neurons in the recurrent layer tend to saturate in order to compensate the variability. In this saturated regime, analysis of the network activation shows a set of clusters that resemble discrete states in a finite state machine. We show that transitions between these states in response to input symbols are deterministic and stable. The networks display a stable behavior for arbitrarily long strings, and…
MILA, Université de Montréal（蒙特利尔大学 MILA）；University of Toronto（多伦多大学）；Institut des Hautes Études Scientifiques, France（法国高等科学研究所）；Carnegie Mellon University（卡内基梅隆大学）
In this paper, we systematically analyze the connecting architectures of recurrent neural networks (RNNs). Our main contribution is twofold: first, we present a rigorous graph-theoretic framework describing the connecting architectures of RNNs in general. Second, we propose three architecture complexity measures of RNNs: (a) the recurrent depth, which captures the RNN's over-time nonlinear complexity, (b) the feedforward depth, which captures the local input-output nonlinearity (similar to the "depth" in feedforward neural networks (FNNs)), and (c) the recurrent skip coefficient which captures…
Technion（以色列理工学院）；Bar Ilan University（巴伊兰大学）；Allen Institute for AI（艾伦人工智能研究所）
We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*, adapted to a probabilistic setting with noise. The key insight is the use of conditional probabilities for observations, and the introduction of a local tolerance when comparing them. When applied to RNNs, our algorithm often achieves better word error rate (WER) and normalised distributed cumulative gain (NDCG) than that achieved by spectral extraction of w…
Escuela Politécnica Superior, Universidad Autónoma de Madrid（马德里自治大学高等理工学院）
We explore a neural network architecture that stacks a recurrent layer and a feedforward layer that is also connected to the input, and compare it to standard Elman and LSTM architectures in terms of accuracy and interpretability. When noise is introduced into the activation function of the recurrent units, these neurons are forced into a binary activation regime that makes the networks behave much as finite automata. The resulting models are simpler, easier to interpret and get higher accuracy on different sample problems, including the recognition of regular languages, the computation of add…
McGill University（麦吉尔大学）；Pennsylvania State University（宾夕法尼亚州立大学）
The verification problem for neural networks is verifying whether a neural network will suffer from adversarial samples, or approximating the maximal allowed scale of adversarial perturbation that can be endured. While most prior work contributes to verifying feed-forward networks, little has been explored for verifying recurrent networks. This is due to the existence of a more rigorous constraint on the perturbation space for sequential data, and the lack of a proper metric for measuring the perturbation. In this work, we address these challenges by proposing a metric which measures the dista…
One way to interpret the behavior of a blackbox recurrent neural network (RNN) is to extract from it a more interpretable discrete computational model, like a finite state machine, that captures its behavior. In this work, we propose a new method for extracting finite automata from RNNs inspired by the state merging paradigm from grammatical inference. We demonstrate the effectiveness of our method on the Tomita languages benchmark, where we find that it is able to extract faithful automata from RNNs trained on all languages in the benchmark. We find that extraction performance is aided by the…
Yale University（耶鲁大学）；Allen Institute for Artificial Intelligence（艾伦人工智能研究所）
This work attempts to explain the types of computation that neural networks can perform by relating them to automata. We first define what it means for a real-time network with bounded precision to accept a language. A measure of network memory follows from this definition. We then characterize the classes of languages acceptable by various recurrent networks, attention, and convolutional networks. We find that LSTMs function like counter machines and relate convolutional networks to the subregular hierarchy. Overall, this work attempts to increase our understanding and ability to interpret ne…
Department of Computer Science Özyeğin University（奥泽因大学计算机科学系）
The purpose of this paper is to use reinforcement learning to model learning agents which can recognize formal languages. Agents are modeled as simple multi-head automaton, a new model of finite automaton that uses multiple heads, and six different languages are formulated as reinforcement learning problems. Two different algorithms are used for optimization. First algorithm is Q-learning which trains gated recurrent units to learn optimal policies. The second one is genetic algorithm which searches for the optimal solution by using evolution inspired operations. The results show that genetic …
University of British Columbia（不列颠哥伦比亚大学）；Stewart Blusson Quantum Matter Institute（斯图尔特·布鲁森量子物质研究所）；University of Cambridge（剑桥大学）
Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent neural networks, based on dissipative quantum neural networks, capable of learning general causal quantum automata. A quantum training algorithm is proposed and classical simulations for the case of product outputs with the fidelity as cost function are carried out. We thereby demonstrate the potential of these algorithms to learn complex quantum processes with …
LSV, CNRS, ENS Paris-Saclay, Université Paris-Saclay（巴黎萨克雷高等师范学院、巴黎萨克雷大学、法国国家科学研究中心、验证与安全实验室）；Inria（法国国家信息与自动化研究所）；Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）；Université Paris-Est Créteil（巴黎东大克雷泰伊校区）；Universität zu Lübeck（吕贝克大学）；CentraleSupélec（中央理工-高等电力学院）；Institut Universitaire de France（法国大学研究院）
This paper presents a property-directed approach to verifying recurrent neural networks (RNNs). To this end, we learn a deterministic finite automaton as a surrogate model from a given RNN using active automata learning. This model may then be analyzed using model checking as verification technique. The term property-directed reflects the idea that our procedure is guided and controlled by the given property rather than performing the two steps separately. We show that this not only allows us to discover small counterexamples fast, but also to generalize them by pumping towards faulty flows hi…
Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps. The uncertainty of the model can be quantified by running a prediction several times, each time sampling from the recurrent state transition distribution, leading to potentially different results if the model is uncertain. Alongside uncertainty quantification, our proposed method offers several advantages in different settings. The proposed method can (1) lea…
Zhejiang University（浙江大学）；Singapore Management University（新加坡管理大学）；Huawei International Pte Ltd（华为国际私人有限公司）；National University of Singapore（新加坡国立大学）
Neural networks are becoming a popular tool for solving many real-world problems such as object recognition and machine translation, thanks to its exceptional performance as an end-to-end solution. However, neural networks are complex black-box models, which hinders humans from interpreting and consequently trusting them in making critical decisions. Towards interpreting neural networks, several approaches have been proposed to extract simple deterministic models from neural networks. The results are not encouraging (e.g., low accuracy and limited scalability), fundamentally due to the limited…
Harvard John A. Paulson School of Engineering and Applied Sciences（哈佛大学约翰·A·保尔森工程与应用科学学院）；MIT Computer Science and Artificial Intelligence Laboratory（麻省理工学院计算机科学与人工智能实验室）
We introduce three memory-augmented Recurrent Neural Networks (MARNNs) and explore their capabilities on a series of simple language modeling tasks whose solutions require stack-based mechanisms. We provide the first demonstration of neural networks recognizing the generalized Dyck languages, which express the core of what it means to be a language with hierarchical structure. Our memory-augmented architectures are easy to train in an end-to-end fashion and can learn the Dyck languages over as many as six parenthesis-pairs, in addition to two deterministic palindrome languages and the string-r…
Penn State University（宾夕法尼亚州立大学）；Rochester Institute of Technology（罗切斯特理工学院）
In order to learn complex grammars, recurrent neural networks (RNNs) require sufficient computational resources to ensure correct grammar recognition. A widely-used approach to expand model capacity would be to couple an RNN to an external memory stack. Here, we introduce a "neural state" pushdown automaton (NSPDA), which consists of a digital stack, instead of an analog one, that is coupled to a neural network state machine. We empirically show its effectiveness in recognizing various context-free grammars (CFGs). First, we develop the underlying mechanics of the proposed higher order recurre…
McGill University（麦吉尔大学）；Pennsylvania State University（宾夕法尼亚州立大学）
Understanding recurrent networks through rule extraction has a long history. This has taken on new interests due to the need for interpreting or verifying neural networks. One basic form for representing stateful rules is deterministic finite automata (DFA). Previous research shows that extracting DFAs from trained second-order recurrent networks is not only possible but also relatively stable. Recently, several new types of recurrent networks with more complicated architectures have been introduced. These handle challenging learning tasks usually involving sequential data. However, it remains…
Recurrent neural networks are powerful models for sequential data, able to represent complex dependencies in the sequence that simpler models such as hidden Markov models cannot handle. Yet they are notoriously hard to train. Here we introduce a training procedure using a gradient ascent in a Riemannian metric: this produces an algorithm independent from design choices such as the encoding of parameters and unit activities. This metric gradient ascent is designed to have an algorithmic cost close to backpropagation through time for sparsely connected networks. We use this procedure on gated le…
PES University（PES大学）；Microspin Machine Works Pvt. Ltd.（Microspin机械工程私人有限公司）
In this paper, we introduce a novel architecture to connecting adaptive learning and neural networks into an arbitrary machine's control system paradigm. Two consecutive Recurrent Neural Networks (RNNs) are used together to accurately model the dynamic characteristics of electromechanical systems that include controllers, actuators and motors. The age-old method of achieving control with the use of the- Proportional, Integral and Derivative constants is well understood as a simplified method that does not capture the complexities of the inherent nonlinearities of complex control systems. In th…
University of Glasgow（格拉斯哥大学）；The University of British Columbia（不列颠哥伦比亚大学）
It is challenging to construct generalized physical models of wave propagation in nature owing to their complex physics as well as widely varying environmental parameters and dynamical scales. In this article, we present the convolutional autoencoder recurrent network (CRAN) as a data-driven model for learning wave propagation phenomena. The CRAN consists of a convolutional autoencoder for learning low-dimensional system representation and a long short-term memory recurrent neural network for the system evolution in low dimension. We show that the convolutional autoencoder significantly outper…
Connecting different text attributes associated with the same entity (conflation) is important in business data analytics since it could help merge two different tables in a database to provide a more comprehensive profile of an entity. However, the conflation task is challenging because two text strings that describe the same entity could be quite different from each other for reasons such as misspelling. It is therefore critical to develop a conflation model that is able to truly understand the semantic meaning of the strings and match them at the semantic level. To this end, we develop a ch…
