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1. Predicting Software Defect Discovery Incorporating Covariates with Recurrent Neural Networks

   https://doi.org/10.1002/qre.70063  

   Salboukh, Fatemeh; Silva, Priscila; Nagaraju, Vidhyashree; Fiondella, Lance (September 2025, Quality and Reliability Engineering International)

   ABSTRACT Traditional software reliability growth models (SRGM) characterize defect discovery with the Non‐Homogeneous Poisson Process (NHPP) as a function of testing time or effort. More recently, covariate NHPP SRGM models have substantially improved tracking and prediction of the defect discovery process by explicitly incorporating discrete multivariate time series on the amount of each underlying testing activity performed in successive intervals. Both classes of NHPP models with and without covariates are parametric in nature, imposing assumptions on the defect discovery process, and, while neural networks have been applied to SRGM models without covariates, no such studies have been applied in the context of covariate SRGM models. Therefore, this paper assesses the effectiveness of neural networks in predicting the software defect discovery process, incorporating covariates. Three types of neural networks are considered, including (i) recurrent neural networks (RNNs), (ii) long short‐term memory (LSTM), and (iii) gated recurrent unit (GRU), which are then compared with covariate models to validate tracking and predictive accuracy. Our results suggest that GRU achieved better overall goodness‐of‐fit, such as approximately 3.22 and 1.10 times smaller predictive mean square error, and 5.33 and 1.22 times smaller predictive ratio risk in DS1G and DS2G data sets, respectively, compared to covariate models when of the data is used for training. Moreover, to provide an objective comparison, three different proportions for training data splits were employed to illustrate the advancements between the top‐performing covariate NHPP model and the neural network, in which GRU illustrated a better performance over most of the scenarios. Thus, the neural network model with gated recurrent units may be a suitable alternative to track and predict the number of defects based on covariates associated with the software testing process. 

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2. Tiny Eats: Eating Detection on a Microcontroller

   https://doi.org/10.1109/SenSysML50931.2020.00011  

   Nyamukuru, Maria T.; Odame, Kofi M. (April 2020, IEEE Workshop on Machine Learning on Edge in Sensor Systems (SenSys-ML))

   There is a growing interest in low power highly efficient wearable devices for automatic dietary monitoring (ADM) [1]. The success of deep neural networks in audio event classification problems makes them ideal for this task. Deep neural networks are, however, not only computationally intensive and energy inefficient but also require a large amount of memory. To address these challenges, we propose a shallow gated recurrent unit (GRU) architecture suitable for resource-constrained applications. This paper describes the implementation of the Tiny Eats GRU, a shallow GRU neural network, on a low power microcontroller, Arm Cortex M0+, to classify eating episodes. Tiny Eats GRU is a hybrid of the traditional GRU [2] and eGRU [3] which makes it small and fast enough to fit on the Arm Cortex M0+ with comparable accuracy to the traditional GRU. The Tiny Eats GRU utilizes only 4% of the Arm Cortex M0+ memory and identifies eating or non-eating episodes with 6 ms latency and accuracy of 95.15%. 

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3. Adjoint dynamics of stable limit cycle neural networks

   Sokol, P.; Jordan, I.; Kadile, E.; Park, I. M. (October 2019, Asilomar Conference on Signals, Systems and Computers)

   Exploding and vanishing gradient are both major problems often faced when an artificial neural network is trained with gradient descent. Inspired by the ubiquity and robustness of nonlinear oscillations in biological neural systems, we investigate the properties of their artificial counterpart, the stable limit cycle neural networks. Using a continuous time dynamical system interpretation of neural networks and backpropagation, we show that stable limit cycle neural networks have non-exploding gradients, and at least one effective non-vanishing gradient dimension. We conjecture that limit cycles can support the learning of long temporal dependence in both biological and artificial neural networks. 

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4. Slow manifolds within network dynamics encode working memory efficiently and robustly

   https://doi.org/10.1371/journal.pcbi.1009366  

   Ghazizadeh, Elham; Ching, ShiNung (September 2021, PLOS Computational Biology)

   Cai, Ming Bo (Ed.)

   Working memory is a cognitive function involving the storage and manipulation of latent information over brief intervals of time, thus making it crucial for context-dependent computation. Here, we use a top-down modeling approach to examine network-level mechanisms of working memory, an enigmatic issue and central topic of study in neuroscience. We optimize thousands of recurrent rate-based neural networks on a working memory task and then perform dynamical systems analysis on the ensuing optimized networks, wherein we find that four distinct dynamical mechanisms can emerge. In particular, we show the prevalence of a mechanism in which memories are encoded along slow stable manifolds in the network state space, leading to a phasic neuronal activation profile during memory periods. In contrast to mechanisms in which memories are directly encoded at stable attractors, these networks naturally forget stimuli over time. Despite this seeming functional disadvantage, they are more efficient in terms of how they leverage their attractor landscape and paradoxically, are considerably more robust to noise. Our results provide new hypotheses regarding how working memory function may be encoded within the dynamics of neural circuits. 

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5. Orthogonal Gated Recurrent Unit With Neumann-Cayley Transformation

   https://doi.org/10.1162/neco_a_01710  

   Zadorozhnyy, Vasily; Mucllari, Edison; Pospisil, Cole; Nguyen, Duc; Ye, Qiang (November 2024, Neural Computation)

   In recent years, using orthogonal matrices has been shown to be a promising approach to improving recurrent neural networks (RNNs) with training, stability, and convergence, particularly to control gradients. While gated recurrent unit (GRU) and long short-term memory (LSTM) architectures address the vanishing gradient problem by using a variety of gates and memory cells, they are still prone to the exploding gradient problem. In this work, we analyze the gradients in GRU and propose the use of orthogonal matrices to prevent exploding gradient problems and enhance long-term memory. We study where to use orthogonal matrices and propose a Neumann series–based scaled Cayley transformation for training orthogonal matrices in GRU, which we call Neumann-Cayley orthogonal GRU (NC-GRU). We present detailed experiments of our model on several synthetic and real-world tasks, which show that NC-GRU significantly outperforms GRU and several other RNNs. 

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