Untapped Potential in Self-Optimization of Hopfield Networks: The Creativity of Unsupervised Learning.

Logic programming is a superior language because it operates on a higher level of mathematical or logical reasoning. Logic programming is well-suited in building the artificial intelligence systems. In this paper, we reviewed the performance of the logic programming in Hopfield Neural Network (HNN) and Radial Basis Function Neural Network (RBFNN). Logic programming by using the Embedding method will improve the performance of RBFNN. In HNN, the logic programming can be implemented by finding the optimal synaptic weight via Wan Abdullah method. RBFNN is expected to do logic programming optimally compared to HNN. This study gives an overview of HNN and RBFNN regarding architectures, learning processing, and their application in 2 Satisfiability (2SAT) logic programming. Both networks will be assessed based on accuracy, sensitivity, and robustness. Pursuing that, RBFNN is expected to outperform HNN in doing 2 Satisfiability logic programming.Logic programming is a superior language because it operates on a higher level of mathematical or logical reasoning. Logic programming is well-suited in building the artificial intelligence systems. In this paper, we reviewed the performance of the logic programming in Hopfield Neural Network (HNN) and Radial Basis Function Neural Network (RBFNN). Logic programming by using the Embedding method will improve the performance of RBFNN. In HNN, the logic programming can be implemented by finding the optimal synaptic weight via Wan Abdullah method. RBFNN is expected to do logic programming optimally compared to HNN. This study gives an overview of HNN and RBFNN regarding architectures, learning processing, and their application in 2 Satisfiability (2SAT) logic programming. Both networks will be assessed based on accuracy, sensitivity, and robustness. Pursuing that, RBFNN is expected to outperform HNN in doing 2 Satisfiability logic programming.

The ideal Hopfield network would be able to remember information and recover the missing information based on what has been remembered. It is expected to have applications in areas such as associative memory, pattern recognition, optimisation computation, parallel implementation of VLSI and optical devices, but the lack of memory capacity and the tendency to generate pseudo-attractors make the network capable of handling only a very small amount of data. In order to make the network more widely used, we propose a scheme to optimise and improve its memory and resilience by introducing quantum perceptrons instead of Hebbian rules to complete its weight matrix design. Compared with the classical Hopfield network, our scheme increases the threshold of each node in the network while training the weights, and the memory space of the Hopfield network changes from being composed of the weight matrix only to being composed of the weight matrix and the threshold matrix together, resulting in a dimensional increase in the memory capacity of the network, which greatly solves the problem of the Hopfield network’s memory The problem of insufficient memory capacity and the tendency to generate pseudo-attractors was solved to a great extent. To verify the feasibility of the proposed scheme, we compare it with the classical Hopfield network in four different dimensions, namely, non-orthogonal simple matrix recovery, incomplete data recovery, memory capacity and model convergence speed. These experiments demonstrate that the improved Hopfield network with quantum perceptron has significant advantages over the classical Hopfield network in terms of memory capacity and recovery ability, which provides a possibility for practical application of the network.

Cooperation, the process through which individuals work together to achieve common goals, is fundamental to human and animal societies and increasingly critical in artificial intelligence. Here, we investigated cooperation in mice and artificial intelligence systems, examining how they learn to actively coordinate their actions to obtain shared rewards. We identified key social behavioral strategies and decision-making processes in mice that facilitate successful cooperation. These processes are represented in the anterior cingulate cortex (ACC) and ACC activity causally contributes to cooperative behavior. We extended our findings to artificial intelligence systems by training artificial agents in a similar cooperation task. The agents developed behavioral strategies and neural representations reminiscent of those observed in the biological brain, revealing parallels between cooperative behavior in biological and artificial systems.

<span>Despite the burgeoning rhetoric from political, social and educational commentators regarding creativity and learning and teaching, there is a paucity of scalable and measurable examples of creativity-centric pedagogical practice. This paper makes an argument for the application of social network visualisations to inform and support creativity-enabling pedagogical practice. This paper first describes social networks and how they relate to creative capacities and learning as a social process. It then provides an initial case study of how social network analysis may be meaningfully applied to evaluate students' learning networks and creative capacities, and elaborates on how such an evaluative resource can allow educators to design and implement creativity-enabling pedagogical practice. In so doing, this paper contributes conceptual, methodological and empirical advances that can take learning and teaching for creativity, particularly in higher education, beyond rhetoric towards more observable and measurable mainstream pedagogical practice.</span>

The present research discusses four ‘physical’ models of system and calculates thereliability function during system’s aging and maturity on the basis of the system structure.

Error-correcting coding is introduced in associative memories based on Hopfield networks in order to increase the learning diversity as well as the recall robustness in presence of erasures and errors. To achieve this, the graph associated with the classical Hopfield network is transformed into a bipartite graph in which incoming information is linked to orthogonal or quasi-orthogonal codes. Whereas learning is similar to that of classical (i.e. Hebbian) Hopfield networks, memory retrieval relies on error correction decoding which offers strong discrimination properties between the memorized patterns.

In cognitive psychology, creativity is an established and well-researched construct. Creativity is linked to openness to experience, and creating innovative solutions. It is this synthesis of prior knowledge and experience that reflects the core ideas of constructivist learning theory. Recently, the investigation and measurement of students’ creative capacities has gained traction in computing. Although being creative is important in the solution of programming problems, creativity is neither embedded in computing curricula as a learning objective, nor established in competency-based educational practice. Assuming that creativity is a malleable component of competency, the present paper aims at investigating constructivist theories to help foster creativity as part of programming competency in computing. Accordingly, learning theories from Piaget, Vygotskiy, Bruner and Dewey were reviewed with regard to their perspective on human learning and the creation of new knowledge through connections. Their review and alignment with the context of programming education results in recommendations for pedagogical interventions, such as collaborative project work, social interaction, scaffolding, active learning, multi-sensory experiences, gamification, and authentic tasks. As a next step, these pedagogical approaches will be investigated with regard to their effects on the creativity of novice learners of programming.

Hopfield Neural Networks (HNNs) are recurrent neural networks used to implement associative memory. They can be applied to pattern recognition, optimization, or image segmentation. However, sometimes it is not easy to provide the users with good explanations about the results obtained with them due to mainly the large number of changes in the state of neurons (and their weights) produced during a problem of machine learning. There are currently limited techniques to visualize, verbalize, or abstract HNNs. This paper outlines how we can construct automatic video-generation systems to explain its execution. This work constitutes a novel approach to obtain explainable artificial intelligence systems in general and HNNs in particular building on the theory of data-to-text systems and software visualization approaches. We present a complete methodology to build these kinds of systems. Software architecture is also designed, implemented, and tested. Technical details about the implementation are also detailed and explained. We apply our approach to creating a complete explainer video about the execution of HNNs on a small recognition problem. Finally, several aspects of the videos generated are evaluated (quality, content, motivation and design/presentation).

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

The TSP (travelling salesman problem) is about the combinatorial optimization, many practical applications such as the designing of safe and efficient transportation network, the planning of logistics line, can all be converted to TSP after simplification. The number of possible routes in TSP is growing exponentially with the number of the cities N and the optimum solution is difficult to calculate. So how to find the efficient solving algorithm is of great importance. The Hopfield network is designed to solve traveling salesman problem. Because of the poor convergence and invalid solution of Hopfield network in solving TSP, the energy function of Hopfield is improved and the genetic algorithm is applied in the Hopfield network. The results of simulation show that the improved Hopfield network can get better optimization than the classical Hopfield network to solve TSP.

In today’s postmodern world, change is the only thing for sure. As a result, creative capacity is the key. Learning creative thinking in fact is a useful vehicle for adult learners to polish their abilities and orientate the world around them. This article attempts to review creativity-related literature and to provide some salient considerations for adult educators with the desire to promote creativity in the classrooms. To begin, the definition of creativity was disclosed. Then the process of creativity was reviewed. Following this line, several factors, including personality traits, knowledge and expertise, motivation and self-efficacy, learning style and thinking style, teaching approaches, assessment and reward, and environment, that might facilitate or stifle creativity were discussed. Finally, some suggestions for adult educators were provided.

Crosstalk phenomena taking place between synapses can influence signal transmission and, in some cases, brain functions. It is thus important to discover the dynamic behaviors of the neural network infected by synaptic crosstalk. To achieve this, in this paper, a new circuit is structured to emulate the Coupled Hyperbolic Memristors, which is then utilized to simulate the synaptic crosstalk of a Hopfield Neural Network (HNN). Thereafter, the HNN's multi-stability, asymmetry attractors, and anti-monotonicity are observed with various crosstalk strengths. The dynamic behaviors of the HNN are presented using bifurcation diagrams, dynamic maps, and Lyapunov exponent spectrums, considering different levels of crosstalk strengths. Simulation results also reveal that different crosstalk strengths can lead to wide-ranging nonlinear behaviors in the HNN systems.

ABSTRACTCreative thinking stems from the cognitive process that fosters the creation of new ideas and problem‐solving solutions. Artificial intelligence systems and neural network models can reduce the intricacy of understanding creative cognition. For instance, the generation of ideas could be symbolized as patterns of binary code in which clusters of neurons synchronize their firing and store information inside a neural network, forming connections based on correlation. The Hopfield neural network (HNN) is a simple model known for its biological plausibility in storing and retrieving neuron patterns. We implemented certain modifications to HNN as a step toward the larger framework of creative thinking‐based association. These modifications included introducing pattern weights control, which provides a robust representation for content addressable memory and conceptual links in stored data. We identified two mechanisms controlling the transition from analytical to associative‐based thinking. The first mechanism refers to the activation threshold of neurons, which acts as an on/off switch for the network. The second was the inhibition of stored concepts, similar to an on/off switch that guides the network to search for associative links and when to stop. Our findings suggest that neurons step back from the contextual focus and find alternatives when analytical thinking is insufficient. These alternatives are linked to seemingly unrelated ideas, using inhibition as an analogy to the hyperparameters. Using hyperparameters to inhibit the stored patterns, we could control the creation of associative links.

Multi-scroll and coexisting attractors in a Hopfield neural network under electromagnetic induction and external stimuli

When we speak of "reimagining education," we refer to a fundamental reconsideration of educational purposes, practices, and possibilities that go beyond incremental reform or technological updates. Educational systems worldwide are at a critical juncture where traditional approaches to teaching and learning no longer adequately address the realities facing students, institutions, and communities. This reimagining becomes urgent when we consider that many educational frameworks were designed for contexts that have been dramatically transformed by technological advancement, changing social structures, and evolving economic demands. Yet we must ask ourselves: are we truly prepared to abandon the comfortable certainties of traditional education, or are we simply repackaging old approaches with new terminology? The need to reimagine education emerges from multiple pressures that challenge traditional educational models. In many contexts, educational institutions face resource constraints that limit their ability to serve diverse student populations. This is particularly evident in specialised educational settings where student numbers far exceed available instructional capacity, creating conditions that make meaningful learning difficult to achieve. Such circumstances force us to confront an uncomfortable truth: perhaps the problem is not a lack of resources but rather our persistent adherence to educational models that assume abundance and stability in contexts where neither exists. Language education provides a clear example of how educational challenges intersect with broader social and cultural dynamics. In multilingual societies, educational institutions must navigate complex decisions about which languages to prioritise, how to balance local and global communication needs, and what role education should play in preserving culture versus promoting economic advancement. These decisions carry significant implications that extend far beyond the classroom, affecting community identity, economic opportunity, and social cohesion. However, we might question whether our current approaches to language education are perpetuating linguistic hierarchies that privilege certain communities while marginalising others despite rhetoric about multilingual inclusion. The integration of technology in educational practice presents both opportunities and challenges that require careful consideration. While digital tools offer new possibilities for flexible and personalised learning experiences, their implementation raises questions about equity, accessibility, and educational purpose. The effectiveness of technological solutions depends not only on their technical capabilities but also on how well they align with pedagogical goals and local contexts. Moreover, the rapid development of artificial intelligence tools is forcing educators to reconsider fundamental questions about knowledge, authority, and authentic learning in ways that challenge established educational practices. We must confront the possibility that much of what we consider essential educational content may become obsolete, leaving us to question what unique value human educators and educational institutions actually provide. Educational reimagining also involves addressing the persistent gap between educational rhetoric and institutional reality. Many educational institutions face organisational and communication challenges that affect their ability to serve their communities effectively. These internal dynamics shape the educational environment in ways that extend far beyond classroom instruction, influencing how educational missions are understood, communicated, and implemented throughout institutional structures. Perhaps it is time to acknowledge that many educational institutions have become more concerned with their own survival and reputation than with genuine educational transformation. The relationship between education and broader social challenges requires particular attention in contexts where educational institutions serve communities facing significant socioeconomic pressures. In such settings, education cannot be separated from questions of social justice, economic development, and community resilience. Educational approaches that acknowledge and address these connections demonstrate how curriculum content and pedagogical methods can be designed to serve both individual learning needs and collective social goals. However, we must honestly assess whether our educational approaches are genuinely addressing social challenges or merely providing the illusion of progress while maintaining existing inequalities. Perhaps most importantly, educational reimagining must address questions about the relationship between human learning and technological capability. As artificial intelligence tools become more sophisticated and accessible, educational institutions must consider how to maintain focus on human development, critical thinking, and creative capacity while acknowledging the transformed landscape of information access and processing. This challenge requires moving beyond simple questions of whether to allow or restrict particular technologies toward more fundamental consideration of educational purposes and human values. Are we preparing students for a future where human intelligence is valued, or are we simply delaying their inevitable dependence on artificial systems? The research contributions in this issue emerge from diverse geographical and institutional contexts, offering multiple perspectives on these challenges and possibilities. They demonstrate that meaningful educational transformation requires both global awareness and a deep understanding of local contexts. They also reveal that reimagining education involves addressing complex relationships between individual learning needs, institutional capacities, and broader social purposes. However, we must consider whether academic research itself has become too removed from educational practice to drive meaningful change. We invite readers to engage with these contributions as part of ongoing conversations about the educational purpose, possibilities, and responsibilities. The future of education depends on our collective ability to create institutions and practices that serve human flourishing while addressing the complex realities facing contemporary societies. But this future also requires our willingness to question fundamental assumptions about education that we may be reluctant to abandon.