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Zeroing neural dynamic (ZND) model is widely deployed for time‐variant non‐linear equations (TVNE). Various element‐wise non‐linear activation functions and integration operations are investigated to enhance the convergence performance and robustness in most proposed ZND models for solving TVNE, leading to a huge cost of hardware implementation and model complexity. To overcome these problems, the authors develop a new norm‐based ZND (NBZND) model with strong robustness for solving TVNE, not applying element‐wise non‐linear activated functions but introducing a two‐norm operation to achieve finite‐time convergence. Moreover, the authors develop a discrete‐time NBZND model for the potential deployment of the model on digital computers. Rigorous theoretical analysis for the NBZND is provided. Simulation results substantiate the advantages of the NBZND model for solving TVNE.

Dynamic Tensor Inversion (DTI) is an emerging issue in recent research, prevalent in artificial intelligence development frameworks such as TensorFlow and PyTorch. Traditional numerical methods suffer significant lagging error when addressing this issue. To address this, Zeroing-type Neural Dynamics (ZND) and Gradient-type Neural Dynamics (GND) are employed to tackle the DTI. However, these two methods exhibit inherent limitations in the resolution process, i.e. high computational complexity and low solution accuracy, respectively. Motivated by this technology gap, this paper proposes an Adaptive Coefficient Gradient Neural Dynamics (ACGND) for dynamically solving the DTI with an efficient and precise manner. Through a series of simulation experiments and validations in engineering applications, the ACGND demonstrates advantages in resolving DTI. The ACGND enhances computational efficiency by circumventing matrix inversion, thereby reducing computational complexity. Moreover, its incorporation of adaptive coefficients and activation functions enables real-time adjustments of the computational solution, facilitating rapid convergence to theoretical solutions and adaptation to non-statinary scenarios. Code is available at https://github.com/Maia2333/ACGND-Code-Implementation .

Generalisation is a crucial aspect of deep learning, enabling models to perform well on unseen data. Currently, most optimisers that improve generalisation typically suffer from efficiency bottlenecks. This paper proposes a double‐integration‐enhanced stochastic gradient descent (DIESGD) optimiser, which treats the negative gradient as an error term and the parameter's rate of change as a noise term. The generalisation superiority of DIESGD originates from its parameter update mechanism, which inherently favours flat minima. The convergence of DIESGD is proven, and extensive experiments are conducted on a variety of datasets and models, demonstrating the superior performance of DIESGD compared to existing optimisers. Furthermore, DIESGD exhibits reduced sensitivity to the initial learning rate, which enhances its robustness and ease of use in practical applications. The proposed DIESGD optimiser connects the distinct fields of optimisers in deep learning and neural dynamics, which is a typical form of dynamic neural networks. The source code is available at https://github.com/LongJin‐lab/DIESGD .

Sea ice plays a pivotal role in ocean-related research, necessitating the development of highly accurate and robust techniques for its extraction from diverse satellite remote sensing imagery. However, conventional learning methods face limitations due to the soaring cost and time associated with manually collecting sufficient sea ice data for model training. This paper introduces an innovative approach where Neural Dynamics (ND) algorithms are seamlessly integrated with a recurrent neural network, resulting in a Transfer-Learning-Like Neural Dynamics (TLLND) algorithm specifically tailored for sea ice extraction. Firstly, given the susceptibility of the image extraction process to noise in practical scenarios, an ND algorithm with noise tolerance and high extraction accuracy is proposed to address this challenge. Secondly, The internal coefficients of the ND algorithm are determined using a parametric method. Subsequently, the ND algorithm is formulated as a decoupled dynamical system. This enables the coefficients trained on a linear equation problem dataset to be directly generalized to solve the sea ice extraction challenges. Theoretical analysis ensures that the effectiveness of the proposed TLLND algorithm remains unaffected by the specific characteristics of various dataset. To validate its efficacy, robustness, and generalization performance, several comparative experiments are conducted using diverse Arctic sea ice satellite imagery with varying levels of noise. The outcomes of these experiments affirm the competence of the proposed TLLND algorithm in addressing the complexities associated with sea ice extraction.

Dynamic Field Theory (DFT) is an established framework for modeling embodied cognition. In DFT, elementary cognitive functions such as memory formation, formation of grounded representations, attentional processes, decision making, adaptation, and learning emerge from neuronal dynamics. The basic computational element of this framework is a Dynamic Neural Field (DNF). Under constraints on the time-scale of the dynamics, the DNF is computationally equivalent to a soft winner-take-all (WTA) network, which is considered one of the basic computational units in neuronal processing. Recently, it has been shown how a WTA network may be implemented in neuromorphic hardware, such as analog Very Large Scale Integration (VLSI) device. This paper leverages the relationship between DFT and soft WTA networks to systematically revise and integrate established DFT mechanisms that have previously been spread among different architectures. In addition, I also identify some novel computational and architectural mechanisms of DFT which may be implemented in neuromorphic VLSI devices using WTA networks as an intermediate computational layer. These specific mechanisms include the stabilization of working memory, the coupling of sensory systems to motor dynamics, intentionality, and autonomous learning. I further demonstrate how all these elements may be integrated into a unified architecture to generate behavior and autonomous learning.

The architecture of the brain is characterized by a modular organization repeated across a hierarchy of spatial scales-neurons, minicolumns, cortical columns, functional brain regions, and so on. It is important to consider that the processes governing neural dynamics at any given scale are not only determined by the behaviour of other neural structures at that scale, but also by the emergent behaviour of smaller scales, and the constraining influence of activity at larger scales. In this paper, we introduce a theoretical framework for neural systems in which the dynamics are nested within a multiscale architecture. In essence, the dynamics at each scale are determined by a coupled ensemble of nonlinear oscillators, which embody the principle scale-specific neurobiological processes. The dynamics at larger scales are 'slaved' to the emergent behaviour of smaller scales through a coupling function that depends on a multiscale wavelet decomposition. The approach is first explicated mathematically. Numerical examples are then given to illustrate phenomena such as between-scale bifurcations, and how synchronization in small-scale structures influences the dynamics in larger structures in an intuitive manner that cannot be captured by existing modelling approaches. A framework for relating the dynamical behaviour of the system to measured observables is presented and further extensions to capture wave phenomena and mode coupling are suggested.

The ability of neural systems to turn transient inputs into persistent changes in activity is thought to be a fundamental requirement for higher cognitive functions. In continuous attractor networks frequently used to model working memory or decision making tasks, the persistent activity settles to a stable pattern with the stereotyped shape of a “bump” independent of integration time or input strength. Here, we investigate a new bump attractor model in which the bump width and amplitude not only reflect qualitative and quantitative characteristics of a preceding input but also the continuous integration of evidence over longer timescales. The model is formalized by two coupled dynamic field equations of Amari-type which combine recurrent interactions mediated by a Mexican-hat connectivity with local feedback mechanisms that balance excitation and inhibition. We analyze the existence, stability and bifurcation structure of single and multi-bump solutions and discuss the relevance of their input dependence to modeling cognitive functions. We then systematically compare the pattern formation process of the two-field model with the classical Amari model. The results reveal that the balanced local feedback mechanisms facilitate the encoding and maintenance of multi-item memories. The existence of stable subthreshold bumps suggests that different to the Amari model, the suppression effect of neighboring bumps in the range of lateral competition may not lead to a complete loss of information. Moreover, bumps with larger amplitude are less vulnerable to noise-induced drifts and distance-dependent interaction effects resulting in more faithful memory representations over time.

Our decisions often depend on multiple sensory experiences separated by time delays. The brain can remember these experiences and, simultaneously, estimate the timing between events. To understand the mechanisms underlying working memory and time encoding, we analyze neural activity recorded during delays in four experiments on nonhuman primates. To disambiguate potential mechanisms, we propose two analyses, namely, decoding the passage of time from neural data and computing the cumulative dimensionality of the neural trajectory over time. Time can be decoded with high precision in tasks where timing information is relevant and with lower precision when irrelevant for performing the task. Neural trajectories are always observed to be low-dimensional. In addition, our results further constrain the mechanisms underlying time encoding as we find that the linear “ramping” component of each neuron’s firing rate strongly contributes to the slow timescale variations that make decoding time possible. These constraints rule out working memory models that rely on constant, sustained activity and neural networks with high-dimensional trajectories, like reservoir networks. Instead, recurrent networks trained with backpropagation capture the time-encoding properties and the dimensionality observed in the data.

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators—trained using model simulations—to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin–Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics. Computational neuroscientists use mathematical models built on observational data to investigate what’s happening in the brain. Models can simulate brain activity from the behavior of a single neuron right through to the patterns of collective activity in whole neural networks. Collecting the experimental data is the first step, then the challenge becomes deciding which computer models best represent the data and can explain the underlying causes of how the brain behaves. Researchers usually find the right model for their data through trial and error. This involves tweaking a model’s parameters until the model can reproduce the data of interest. But this process is laborious and not systematic. Moreover, with the ever-increasing complexity of both data and computer models in neuroscience, the old-school approach of building models is starting to show its limitations. Now, Gonçalves, Lueckmann, Deistler et al. have designed an algorithm that makes it easier for researchers to fit mathematical models to experimental data. First, the algorithm trains an artificial neural network to predict which models are compatible with simulated data. After initial training, the method can rapidly be applied to either raw experimental data or selected data features. The algorithm then returns the models that generate the best match. This newly developed machine learning tool was able to automatically identify models which can replicate the observed data from a diverse set of neuroscience problems. Importantly, further experiments showed that this new approach can be scaled up to complex mechanisms, such as how a neural network in crabs maintains its rhythm of activity. This tool could be applied to a wide range of computational investigations in neuroscience and other fields of biology, which may help bridge the gap between ‘data-driven’ and ‘theory-driven’ approaches.

Mind wandering (MW) can be understood as a transient state in which attention drifts from an external task to internal self-generated thoughts. MW has been associated with the activation of the Default Mode Network (DMN). In addition, it has been shown that the activity of the DMN is anti-correlated with activation in brain networks related to the processing of external events (e.g., Salience network, SN). In this study, we present a mean field model based on weakly coupled Kuramoto oscillators. We simulated the oscillatory activity of the entire brain and explored the role of the interaction between the nodes from the DMN and SN in MW states. External stimulation was added to the network model in two opposite conditions. Stimuli could be presented when oscillators in the SN showed more internal coherence (synchrony) than in the DMN, or, on the contrary, when the coherence in the SN was lower than in the DMN. The resulting phases of the oscillators were analyzed and used to simulate EEG signals. Our results showed that the structural complexity from both simulated and real data was higher when the model was stimulated during periods in which DMN was more coherent than the SN. Overall, our results provided a plausible mechanistic explanation to MW as a state in which high coherence in the DMN partially suppresses the capacity of the system to process external stimuli.