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Do Not Let the Beginning Trap You! On Inhibition, Associative Creative Chains, and Hopfield Neural Networks

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Title: Do Not Let the Beginning Trap You! On Inhibition, Associative Creative Chains, and Hopfield Neural Networks
Language: English
Authors: Ronald Mtenga, Mathias Bode, Radwa Khalil (ORCID 0000-0003-2632-8306)
Source: Journal of Creative Behavior. 2025 59(2).
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 19
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Descriptors: Inhibition, Creative Thinking, Cognitive Processes, Concept Formation, Problem Solving, Artificial Intelligence, Neurological Organization, Brain, Associative Learning
DOI: 10.1002/jocb.680
ISSN: 0022-0175
2162-6057
Abstract: Creative 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.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1474819
Database: ERIC
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  Value: <anid>AN0186049500;3u701jun.25;2025Jun23.03:08;v2.2.500</anid> <title id="AN0186049500-1">Do Not Let the Beginning Trap you! On Inhibition, Associative Creative Chains, and Hopfield Neural Networks </title> <p>Creative 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.</p> <p>Keywords: creative thinking; hopfield neural networks; patterns; memory; associative chains; inhibition; hyperparameters</p> <hd id="AN0186049500-2">INTRODUCTION</hd> <p>Individuals with creative thinking abilities can enhance their intellect by establishing connections between ideas and concepts (Finke, [<reflink idref="bib36" id="ref1">36</reflink>]). This cognitive process allows individuals to shift their attention away from familiar tools and instead focus on exploring the connections between various elements (Mednick, [<reflink idref="bib67" id="ref2">67</reflink>]; Mendelsohn, [<reflink idref="bib68" id="ref3">68</reflink>]). This approach facilitates the recognition of less obvious similarities, enabling the creation of ideas that would otherwise be challenging if one solely focused on the surface features of the task (Beaty, kenett, Hass, & Schacter, [<reflink idref="bib12" id="ref4">12</reflink>]; Kenett, [<reflink idref="bib50" id="ref5">50</reflink>]; Kenett & Beaty, [<reflink idref="bib51" id="ref6">51</reflink>]; Luchini et al., [<reflink idref="bib64" id="ref7">64</reflink>]).</p> <p>There is a consensus among scholars that creative products should effectively convey original, valuable, and potentially surprising concepts (Corazza, [<reflink idref="bib25" id="ref8">25</reflink>]; Han, Forbes, & Schaefer, [<reflink idref="bib42" id="ref9">42</reflink>]; Khalil & Moustafa, [<reflink idref="bib57" id="ref10">57</reflink>]; Mastria, Agnoli, Corazza, Grassi, & Franchin, [<reflink idref="bib65" id="ref11">65</reflink>]; Plucker, [<reflink idref="bib76" id="ref12">76</reflink>]; Runco & Jaeger, [<reflink idref="bib84" id="ref13">84</reflink>]; Torrance, [<reflink idref="bib94" id="ref14">94</reflink>]; Wilson, Guilford, Christensen, & Lewis, [<reflink idref="bib97" id="ref15">97</reflink>]). Creative thinkers can switch between analytical and associative modes to find solutions (Dietrich, [<reflink idref="bib28" id="ref16">28</reflink>],[<reflink idref="bib29" id="ref17">29</reflink>]; Finke, [<reflink idref="bib36" id="ref18">36</reflink>]; Xie et al., [<reflink idref="bib98" id="ref19">98</reflink>]), find hidden patterns, and make connections between events that do not seem to be associated, which can lead to extraordinary outcomes (Abraham, [<reflink idref="bib5" id="ref20">5</reflink>]; Herrmann, [<reflink idref="bib43" id="ref21">43</reflink>]; Khalil & Demarin, [<reflink idref="bib54" id="ref22">54</reflink>]; Khalil & Moustafa, [<reflink idref="bib57" id="ref23">57</reflink>]). However, creative thinking is a complex dynamical process that can manifest itself in a multitude of ways, making it difficult to precisely define its nature (Abraham, [<reflink idref="bib4" id="ref24">4</reflink>]; Agnoli, [<reflink idref="bib7" id="ref25">7</reflink>]; Gaut, [<reflink idref="bib39" id="ref26">39</reflink>]; Kaufman & Beghetto, [<reflink idref="bib49" id="ref27">49</reflink>]; Sawyer, [<reflink idref="bib85" id="ref28">85</reflink>], [<reflink idref="bib86" id="ref29">86</reflink>]; Squalli & Wilson, [<reflink idref="bib89" id="ref30">89</reflink>]; Tardif & Sternberg, [<reflink idref="bib90" id="ref31">90</reflink>]). Neural network models, such as connectionist (Doboli et al., [<reflink idref="bib32" id="ref32">32</reflink>]; Doboli & Brown, [<reflink idref="bib30" id="ref33">30</reflink>]; Doboli, Brown, & Minai, [<reflink idref="bib31" id="ref34">31</reflink>]; Iyer et al., [<reflink idref="bib45" id="ref35">45</reflink>]; Iyer, Minai, Doboli, Brown, & Paulus, [<reflink idref="bib46" id="ref36">46</reflink>]) and Hopfield neural networks (HNN) (Checiu, Bode, & Khalil, [<reflink idref="bib22" id="ref37">22</reflink>]), could serve as predictive tools in creative cognition, aiding in understanding the complex dynamics and redundancy of this creative process.</p> <p>We used HNN to establish a conceptual framework to understand the computationally creative process‐based semantic association. HNN was developed by John J. Hopfield in 1982 and is renowned for efficiently storing and retrieving information (McEliece, Posner, Rodemich, & Venkatesh, [<reflink idref="bib66" id="ref38">66</reflink>]), and its applications revealed significant achievement in neural computation and modeling (Abe, [<reflink idref="bib1" id="ref39">1</reflink>], [<reflink idref="bib2" id="ref40">2</reflink>]; Hopfield, [<reflink idref="bib44" id="ref41">44</reflink>]; Köksal & Sivasundaram, [<reflink idref="bib60" id="ref42">60</reflink>]; Ramsauer et al., [<reflink idref="bib78" id="ref43">78</reflink>]). HNN is a recurrent neural network model with the distinctive feature of receiving input from all neurons in the network. This unique feature enables the HNN to effectively retrieve memories even when presented with incomplete or noisy input (Hopfield, [<reflink idref="bib44" id="ref44">44</reflink>]).</p> <p>Through iterative updating, the HNN changes the states of neurons, either synchronously or asynchronously (Cheung, Atlas, & Marks, [<reflink idref="bib23" id="ref45">23</reflink>]). One of the ultimate applications is converging on one of the stored memories to reach a stable state that remembers the trained data (Krotov & Hopfield, [<reflink idref="bib61" id="ref46">61</reflink>]). HNN has been used for associative memory operations such as (a) linking input with its most similar stored pattern or (b) identifying unknown systems by calculating optimal coefficients through the learning mechanism to model the nonlinear system accurately (McEliece et al., [<reflink idref="bib66" id="ref47">66</reflink>]; Wang, Li, Wang, Su, & Wang, [<reflink idref="bib96" id="ref48">96</reflink>]; Wang, Tang, & Cao, [<reflink idref="bib95" id="ref49">95</reflink>]).</p> <p>Mendelsohn's [<reflink idref="bib68" id="ref50">68</reflink>] model used defocused and focused attention to explain the semantic hierarchy of creative associations. The concept of the creative process's associative foundation aligns with Mednick's earlier introduction of this term in [<reflink idref="bib67" id="ref51">67</reflink>]. In [<reflink idref="bib37" id="ref52">37</reflink>], Gabora called attention to this context, which may affect creative problem‐solving, and explained that each neuron saves several items and distributes them among neuron assemblies (Morris, [<reflink idref="bib69" id="ref53">69</reflink>]; Rumelhart, Hinton, & Williams, [<reflink idref="bib82" id="ref54">82</reflink>]). According to Gabora ([<reflink idref="bib37" id="ref55">37</reflink>]), the topology of HNN closely mirrors human memory, which encodes many neurons that fire together in response to microfeatures.</p> <p>Based on this notion, neural assemblies widely distribute concepts and ideas, with each neuron engaging in a process known as neural re‐entrance (Calvin, [<reflink idref="bib18" id="ref56">18</reflink>]). For instance, we can approximate neurons in clusters as patterns of zeros and ones; 0 represents low‐rate neurons, and 1 represents high‐rate neurons. This topology is explicable, as when the same neurons are excited repeatedly, the electrical signal resistance at the synapses decreases, increasing the likelihood that the neurons will excite one another in the presence of a signal (Abraham, Jones, & Glanzman, [<reflink idref="bib6" id="ref57">6</reflink>]). When internal or external stimuli stimulate some of these neurons, they activate the rest with the closest associative link, triggering an avalanche effect that recalls the stored concept.</p> <p>Building on our prior study by Checiu et al. ([<reflink idref="bib22" id="ref58">22</reflink>]), we used HNN to provide a credible mechanical account for the semantic connection between two associative links, thereby facilitating the exploration of alternative solutions.</p> <hd id="AN0186049500-3">METHODS</hd> <p></p> <hd id="AN0186049500-4">NEURAL NETWORK STRUCTURE</hd> <p>We chose the HNN model to establish a conceptual framework for semantic associations because it does not store patterns. Instead, it uses the weights matrix to remember patterns through neuron connections. John Hopfield implemented the Hebbian learning rule in [<reflink idref="bib44" id="ref59">44</reflink>], using the sum of the outer products of the stored patterns to create an auto‐correlation matrix, which he normalized by the number of stored patterns (Hopfield, [<reflink idref="bib44" id="ref60">44</reflink>]). The Hebb rule refers to increases in the synaptic weights between neurons when a pattern is introduced and they are firing together (Klein, [<reflink idref="bib58" id="ref61">58</reflink>]; Morris, [<reflink idref="bib69" id="ref62">69</reflink>]). When an input pattern includes misaligned information, it is analogous to applying excessive force to these weights. Once the system can update, the auto‐correlations of the closest stored pattern will dominate this distorted information, bringing it closer to its activation states. It is logical to use less‐correlated ideas to identify unexplored connections. Thus, patterns represent unrelated ideas, suggesting that a substantial proportion of neurons firing per pattern is unnecessary (Amari & Maginu, [<reflink idref="bib8" id="ref63">8</reflink>]; Anishchenko & Treves, [<reflink idref="bib10" id="ref64">10</reflink>]; Hopfield, [<reflink idref="bib44" id="ref65">44</reflink>]; McEliece et al., [<reflink idref="bib66" id="ref66">66</reflink>]).</p> <p>The original HNN was initially described as a simple auto‐associative memory. In this model, the bidirectional weights (<emph>w</emph><subs><emph>ij</emph></subs>) of a fully connected single‐layer neural network are computed by calculating the outer product of each of the discrete binary patterns (<emph>x</emph><subs><emph>k</emph></subs>, ..., <emph>x</emph><subs><emph>M</emph></subs>) for storage, then merging  the resulting matrices. <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0001" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>W</mi><mi mathvariant="italic">ij</mi></msub><mo linebreak="goodbreak">=</mo><munderover><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msubsup><mi>x</mi><mi>i</mi><mi>k</mi></msubsup><msubsup><mi>x</mi><mi>j</mi><mi>k</mi></msubsup></mrow><annotation encoding="application/x-tex">$$ {W}_{ij}=\sum \limits_{k=1}^M{x}_i^k{x}_j^k $$</annotation></semantics></math> </ephtml></p> <p>The network structure includes patterns and weights matrix updating (Figure 1).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/3U7/01jun25/jocb680-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="jocb680-fig-0001.jpg" title="1 bcstripbcstripDescription of the neural network structure of Hopfield neural networks (HNN). The mutual activation of neuron pairs determines system node weights. If two neurons are active simultaneously, their weights are ones; otherwise, they are zeros. The system strengthens the weights between activated nodes each time it adds a new pattern. Pattern, weights matrix, and updating indicate the fundamentals of how HNN processes information and generates output." /> </p> <p></p> <hd id="AN0186049500-6">SIMULATION AND IMPLEMENTATION</hd> <p>We simulated HNN with <emph>N</emph> = 1024 neurons with patterns chosen from the binomial distribution. Simulations were performed for varying probability parameters (<emph>P</emph>(<emph>σi</emph> = 1)). Accordingly, these weights are learned iteratively, with a weight's value only reinforced if the learned pattern activates the same pair of neurons. This process is analogous to computing cognitive learning, in which neurons perceive and analyze sensory and contextual information in realtime. Over time, the synaptic resistance reduces, allowing neurons connected to particular features to activate all other related neurons (Gage & Hickok, [<reflink idref="bib38" id="ref67">38</reflink>]).</p> <p>Given a pattern, <bold>X</bold><subs><emph>k</emph></subs> has been learned and is in a stable state in the system. <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0002" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold-italic">X</mi><mrow><mi>k</mi><mo>=</mo></mrow></msub><mi mathvariant="italic">sgn</mi><mfenced close=")" open="("><mrow><mi>W</mi><msub><mi mathvariant="bold-italic">x</mi><mi>k</mi></msub></mrow></mfenced></mrow><annotation encoding="application/x-tex">$$ {\boldsymbol{X}}_{k=}\mathit{\operatorname{sgn}}\left(W{\boldsymbol{x}}_k\right) $$</annotation></semantics></math> </ephtml> sgn()defines the state space of unipolar binary vectors, and <emph>W</emph> is the weights that also depends on previously learned patterns. We used asynchronous updating of the network to evaluate all the inputs that feed into the activation of a single neuron in the system.</p> <hd id="AN0186049500-7">PATTERN CHOICE</hd> <p>We extensively deliberated on patterns to represent neuron activation based on firing rate. We used binary activations to simulate the high and low neuron activations. According to research by Roxin, Hakim, and Brunel ([<reflink idref="bib81" id="ref68">81</reflink>]) and Šíma, Orponen, and Antti‐Poika ([<reflink idref="bib88" id="ref69">88</reflink>]), bipolar binary representations that map 0 to ‐1 and + 1 are advantageous. <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0003" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi><mo linebreak="goodbreak">=</mo><mfenced close=")" open="("><msub><mi>σ</mi><mi>i</mi></msub></mfenced><mo>∈</mo><msup><mfenced close=")" open=""><mfenced close="}" open="{" separators=","><mrow><mo linebreak="goodbreak">−</mo><mn>1</mn></mrow><mrow><mo linebreak="goodbreak">+</mo><mn>1</mn></mrow></mfenced></mfenced><mi>N</mi></msup></mrow><annotation encoding="application/x-tex">$$ \sigma =\left({\sigma}_i\right)\in {\left.\left\{-1,+1\right\}\right)}^N $$</annotation></semantics></math> </ephtml></p> <p>Bipolar activations facilitate the storage of patterns that include positive and negative values, enhancing the network's ability to represent information. This binary mode presents a simplified view of neuron functionality (Šíma, et al., [<reflink idref="bib88" id="ref70">88</reflink>]). Every neuron within the network is connected to other neurons, giving each connection a distinctive weights. These weights determine how neurons modify their states in response to this inter‐neuronal communication, and signals received from surrounding neurons should overcome a potential barrier to activating neurons (Ramsauer et al., [<reflink idref="bib78" id="ref71">78</reflink>]). A typical neuron has a negative potential relative to its surroundings, but its activation is a question of amplitude more than polarity. Therefore, we chose unipolar activations because bipolarity does not allow us to activate modestly, as the synaptic contact between neurons determines activation amplitude.</p> <hd id="AN0186049500-8">WEIGHTS MATRIX</hd> <p>We used a weights matrix <emph>W</emph> to compute the neurons' connections and memorize the n pattern based on the Hebbian learning rule for HNN pattern storage (Klein, [<reflink idref="bib58" id="ref72">58</reflink>]; Morris, [<reflink idref="bib69" id="ref73">69</reflink>]).</p> <p>The HNN has the benefit of training in one step by computing the weights matrix <emph>W</emph> in one operation (Abe, [<reflink idref="bib1" id="ref74">1</reflink>], [<reflink idref="bib2" id="ref75">2</reflink>]; Abe & Gee, [<reflink idref="bib3" id="ref76">3</reflink>]; Atencia, Joya, & Sandoval, [<reflink idref="bib11" id="ref77">11</reflink>]; Joya, Atencia, & Sandoval, [<reflink idref="bib47" id="ref78">47</reflink>]; Köksal & Sivasundaram, [<reflink idref="bib60" id="ref79">60</reflink>]; Ramsauer et al., [<reflink idref="bib78" id="ref80">78</reflink>]). Given their full connectivity, the neurons' symmetric and bidirectional connections generated <emph>W</emph> diagonal symmetry. As a result, the HNN iterates over the binary input × from N neurons to get a stable state. It is arbitrary whether to normalize the weights to limit their levels adequately. However, normalizing the weights does not affect the HNN's updating, as the relative magnitudes of the weights matter in this process rather than their absolute values. The weights matrix <emph>W</emph> facilitates convergence, and the network has been trained and contains all relevant information within <emph>W</emph> (Amit, [<reflink idref="bib9" id="ref81">9</reflink>]; Ramsauer et al., [<reflink idref="bib78" id="ref82">78</reflink>]; Šíma et al., [<reflink idref="bib88" id="ref83">88</reflink>]).</p> <hd id="AN0186049500-9">UPDATING</hd> <p>We considered that HNN only contains an associative memory of one pattern. Thus, the system receives input from distorted or perturbed patterns, allowing the system to update asynchronously for an entire iteration of the network, with each neuron being updated just once. The following equation illustrates the asynchronous update of the <emph>j</emph>‐<sups>th</sups> neuron: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0004" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>σ</mi><mi>j</mi><mfenced close=")" open="("><mrow><mi>n</mi><mo linebreak="goodbreak">+</mo><mn>1</mn></mrow></mfenced></msubsup><mo linebreak="goodbreak">=</mo><mi mathvariant="italic">sgn</mi><mfenced close=")" open="("><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><msubsup><mi>σ</mi><mi>i</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup><mspace width="0.25em" /><msub><mi>W</mi><mi mathvariant="italic">ij</mi></msub></mrow></mfenced></mrow><annotation encoding="application/x-tex">$$ {\sigma}_j^{\left(n+1\right)}=\mathit{\operatorname{sgn}}\left(\sum \limits_{i=1}^N{\sigma}_i^{(n)}\ {W}_{ij}\right) $$</annotation></semantics></math> </ephtml></p> <p>Since <emph>σ</emph> is a perturbation of the stored pattern, we expand the update equation to show that the proximity of the input to the stored pattern determines the overall input to the activation of the <emph>j</emph>‐<sups>th</sups> neuron. <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0005" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>σ</mi><mi>j</mi><mfenced close=")" open="("><mrow><mi>n</mi><mo linebreak="goodbreak">+</mo><mn>1</mn></mrow></mfenced></msubsup><mo linebreak="goodbreak">=</mo><mi mathvariant="italic">sgn</mi><mfenced close=")" open="("><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mfenced close=")" open="("><mrow><msubsup><mi>σ</mi><mi>i</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup><msubsup><mi>x</mi><mi>i</mi><mi>k</mi></msubsup></mrow></mfenced><msubsup><mi>x</mi><mi>j</mi><mi>k</mi></msubsup></mrow></mfenced></mrow><annotation encoding="application/x-tex">$$ {\sigma}_j^{\left(n+1\right)}=\mathit{\operatorname{sgn}}\left(\sum \limits_{i=1}^N\left({\sigma}_i^{(n)}{x}_i^k\right){x}_j^k\right) $$</annotation></semantics></math> </ephtml></p> <p>This rearrangement demonstrates that the <emph>closeness</emph> is the inner product of network input and stored state. Given the activation function: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0006" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="italic">gn</mi><mfenced close=")" open="("><mi>x</mi></mfenced><mo linebreak="goodbreak">=</mo><mfenced close="" open="{">1,x≥∅0,x<∅</mfenced></mrow><annotation encoding="application/x-tex">$$ gn(x)=\left\{\begin{array}{c}1,\kern0.5em x\ge \varnothing \\ {}0,\kern0.5em x<\varnothing \end{array}\right. $$</annotation></semantics></math> </ephtml></p> <p>The neuron will be switched on or off if the similarity with the stored pattern is larger or less than a threshold value <emph>φ</emph>. If <emph>M</emph> patterns are learned instead of one, we can detect the effect of the distribution of 1s in the training patterns. Given an input state derived from one of the training patterns, we can represent the asynchronous update of the system's <emph>j</emph>‐<sups>th</sups> neuron as follows: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0007" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>σ</mi><mi>j</mi><mfenced close=")" open="("><mrow><mi>n</mi><mo linebreak="goodbreak">+</mo><mn>1</mn></mrow></mfenced></msubsup><mo linebreak="goodbreak">=</mo><mi mathvariant="italic">sgn</mi><mfenced close=")" open="("><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><mo>⋅</mo><munderover><mo movablelimits="false">∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mfenced close=")" open="("><mrow><msubsup><mi>σ</mi><mi>i</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup><msubsup><mi>x</mi><mi>i</mi><mi>k</mi></msubsup></mrow></mfenced><msubsup><mi>x</mi><mi>j</mi><mi>k</mi></msubsup></mrow></mfenced></mrow><annotation encoding="application/x-tex">$$ {\sigma}_j^{\left(n+1\right)}=\mathit{\operatorname{sgn}}\left(\sum \limits_{k=1}^M\cdot \sum \limits_{i=1}^N\left({\sigma}_i^{(n)}{x}_i^k\right){x}_j^k\right) $$</annotation></semantics></math> </ephtml></p> <p>One pattern and all the learned patterns contribute to the update, demonstrating that their relationship significantly influences whether a neuron switches on or off during its asynchronous update. For instance, if the input to the system matches one of the learned patterns or closely resembles them, we can further expand the updated sum to: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0008" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>σ</mi><mi>j</mi><mfenced close=")" open="("><mrow><mi>n</mi><mo linebreak="goodbreak">+</mo><mn>1</mn></mrow></mfenced></msubsup><mo linebreak="goodbreak">=</mo><mi mathvariant="italic">sgn</mi><mfenced close=")" open="("><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mfenced close=")" open="("><mrow><msubsup><mi>σ</mi><mi>i</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup><msubsup><mi>x</mi><mi>i</mi><mi>l</mi></msubsup></mrow></mfenced><msubsup><mi>x</mi><mi>i</mi><mi>l</mi></msubsup><mo linebreak="goodbreak">+</mo><munderover><mo movablelimits="false">∑</mo>k=1k≠l<mi>M</mi></munderover><mo>⋅</mo><munderover><mo movablelimits="false">∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></munderover><mfenced close=")" open="("><mrow><msubsup><mi>σ</mi><mi>i</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup><msubsup><mi>x</mi><mi>i</mi><mi>k</mi></msubsup></mrow></mfenced><msubsup><mi>x</mi><mi>j</mi><mi>k</mi></msubsup></mrow></mfenced></mrow><annotation encoding="application/x-tex">$$ {\sigma}_j^{\left(n+1\right)}=\mathit{\operatorname{sgn}}\left(\sum \limits_{i=1}^N\left({\sigma}_i^{(n)}{x}_i^l\right){x}_i^l+\sum \limits_{\begin{array}{c}k=1\\ {}k\ne l\end{array}}^M\cdot \sum \limits_{i=1}^N\left({\sigma}_i^{(n)}{x}_i^k\right){x}_j^k\right) $$</annotation></semantics></math> </ephtml></p> <p>Since HNN convergence aims to recover the pattern best resembling the input, we denote it as the input for every <emph>j</emph>‐<sups>th</sups> neuron update. We derive this input from the outer sum, which signifies the <emph>1</emph>‐<sups>th</sups> pattern among the <emph>M</emph> patterns that has the highest correlation with the input pattern.</p> <p>Cross‐talk is one of the core aspects of HNN, which will have slight or no amplitude. Hence, it will not disrupt updating and converging to the closest pattern. Nevertheless, the correlation's significance becomes essential when the number of stored patterns increases. The <emph>j</emph>‐<sups>th</sups> neuron's value in the <emph>k</emph>‐<sups>th</sups> pattern and the dot product's magnitude between the input pattern and the <emph>k</emph>‐<sups>th</sups> stored pattern determines whether cross‐talk will impact the <emph>j</emph>‐<sups>th</sups> neuron. The correlation quantifies the dot product value, indicating that thresholding can effectively minimize cross‐talk using uncorrelated learning patterns.</p> <p>In a unipolar binary condition, the distribution of zeros and ones in each <emph>k</emph>‐<sups>th</sups> learning pattern affects the presence of cross‐talk. Cross‐talk occurs when an interfering pattern's <emph>j</emph>‐<sups>th</sups> neuron becomes active during updating. If the interfering neuron is off (inactive), there will be no communication between that pattern and other patterns. If the update coincides with the <emph>j</emph>‐<sups>th</sups> neuron of each training pattern, it may lead to cross‐talk and convergence problems, which is the most likely outcome. Under optimal conditions, all interfering patterns will cause the <emph>j</emph>‐<sups>th</sups> neuron to deactivate zeros, leaving only the <emph>1</emph>‐<sups>th</sups> pattern for detection.</p> <p>To further analyze the cross‐talk effect, we simulated different HNNs trained on random patterns with varying <emph>p</emph> and numbers of training patterns to determine how <emph>p</emph> affects convergence and capacity. We considered and related these simulations as three network scenarios. For the first scenario, we created a matrix, as <emph>M</emph> = 2 patterns were chosen with the length of <emph>N</emph> = 1024 and <emph>p</emph> = <emph>P</emph> (<emph>σi</emph> = 1) = 0.4.</p> <p>As a measure of the patterns correlation, the patterns were arranged as the row vectors of a single training matrix, <emph>V</emph> ∈ 0, 1<sups>(<emph>M</emph> × <emph>N</emph>)</sups>, whose squared norm was calculated, resulting in the following symmetric <emph>M</emph> × <emph>M</emph> matrix. <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0009" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="italic">VV</mi><mi>T</mi></msup><mo linebreak="goodbreak">=</mo><mfenced close=")" open="(">390160160415</mfenced></mrow><annotation encoding="application/x-tex">$$ {VV}^T=\left(\begin{array}{cc}390& 160\\ {}160& 415\end{array}\right) $$</annotation></semantics></math> </ephtml></p> <p>For the second scenario, we simulated <emph>M</emph> = 4 patterns with the norm square matrix: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0010" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="italic">VV</mi><mi>T</mi></msup><mo linebreak="goodbreak">=</mo><mfenced close=")" open="(">397172148139172410152170148152378161139170161403</mfenced></mrow><annotation encoding="application/x-tex">$$ {VV}^T=\left(\begin{array}{cccc}397& 172& 148& 139\\ {}172& 410& 152& 170\\ {}148& 152& 378& 161\\ {}139& 170& 161& 403\end{array}\right) $$</annotation></semantics></math> </ephtml></p> <p>As in the first scenario, we simulated the cross‐talk over 1024 iterations and selected a threshold slightly below the squared norm of the input's initial training pattern.</p> <p>When the input pattern is one of the training patterns, the cross‐talk weights from each pattern refer to the asynchronous update of the <emph>j</emph>‐<sups>th</sups> neuron in the system. Taking into account the off‐diagonal values in the matrix: we have reduced updating and converging the network to a competitive structure at the hidden layer. In this layer, the winner should always be closest to the network's present state.</p> <p>For the third scenario, we simulated <emph>M</emph> = 4 patterns with the norm square matrix: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0011" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="italic">VV</mi><mi>T</mi></msup><mo linebreak="goodbreak">=</mo><mfenced close=")" open="(">204364545361984054454021954455454224</mfenced></mrow><annotation encoding="application/x-tex">$$ {VV}^T=\left(\begin{array}{cccc}204& 36& 45& 45\\ {}36& 198& 40& 54\\ {}45& 40& 219& 54\\ {}45& 54& 54& 224\end{array}\right) $$</annotation></semantics></math> </ephtml></p> <p>We biased for the first pattern and picked a threshold slightly less than the norm squared to detect the most robust pattern while muting all others. The stability range for this simulation was (126 < <emph>φ</emph> < 204), as the threshold mutes cross‐talk and biases for the most robust pattern, the first pattern. By selecting training patterns with more sparsity in activation, we improved stability. We performed additional simulations using a probability parameter = <emph>P</emph> (<emph>σi</emph> = 1) = 0.1, starting from <emph>M</emph> = 5. This step was necessary to establish that HNN possesses adequate capacity for the subsequent phase of modeling creativity‐based associations.</p> <p>We determined the square norm matrix for the training patterns as follows: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0012" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="italic">VV</mi><mi>T</mi></msup><mo linebreak="goodbreak">=</mo><mfenced close=")" open="(">9771579794109415101091210791294894108110</mfenced></mrow><annotation encoding="application/x-tex">$$ {VV}^T=\left(\begin{array}{ccccc}97& 7& 15& 7& 9\\ {}7& 94& 10& 9& 4\\ {}15& 10& 109& 12& 10\\ {}7& 9& 12& 94& 8\\ {}9& 4& 10& 8& 110\end{array}\right) $$</annotation></semantics></math> </ephtml></p> <p>To determine the mechanisms for the associative chains, we used training patterns as weights instead of a weights matrix in a two‐layer network. The first layer represents the network state, while the second layer stores the ck<sups>(<emph>n</emph>)</sups> values, representing the network state's inner product and each training pattern. Each iteration transfers information from the input layer to the hidden layer and down from the hidden layer to the output layer.</p> <p>Content‐addressed memory operates effectively with sparse, distributed memory. To gain meaningful memory capacity for our HNN model, we implemented certain modifications, as suggested by Hopfield ([<reflink idref="bib44" id="ref84">44</reflink>]), Krotov and Hopfield ([<reflink idref="bib61" id="ref85">61</reflink>]), and Ramsauer et al. ([<reflink idref="bib78" id="ref86">78</reflink>]).</p> <p>After determining the cross‐talk effect and returning to the updated rule description, the next step was to improve pattern recollection.</p> <p>We used the middle sum as weights for the <emph>k‐</emph><sups>th</sups> pattern and its contribution to the <emph>j‐</emph><sups>th</sups> neuron update in the network. We updated these weights component as follows: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0013" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>σ</mi><mi>j</mi><mfenced close=")" open="("><mrow><mi>n</mi><mo linebreak="goodbreak">+</mo><mn>1</mn></mrow></mfenced></msubsup><mo linebreak="goodbreak">=</mo><mi mathvariant="italic">sgn</mi><mfenced close=")" open="("><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>K</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msup><mi>C</mi><mrow><mi>k</mi><mfenced close=")" open="("><mi>n</mi></mfenced></mrow></msup><msubsup><mi>x</mi><mi>j</mi><mi>k</mi></msubsup></mrow></mfenced></mrow><annotation encoding="application/x-tex">$$ {\sigma}_j^{\left(n+1\right)}=\mathit{\operatorname{sgn}}\left(\sum \limits_{K=1}^M{C}^{k(n)}{x}_j^k\right) $$</annotation></semantics></math> </ephtml></p> <p>After managing the <emph>influence</emph> values, we employed an activation function on this hidden layer. These <emph>Influence</emph> values are analogous to <emph>hyperparameters</emph> values. Initially, we used the p‐norm with a probability parameter value of 1, which only normalized the weights matrix within the range of 0 to 1. Normalization is formulated as follows: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0014" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>C</mi><mi>k</mi><mo>~</mo></msubsup><mo linebreak="goodbreak">=</mo><mi>F</mi><mfenced close=")" open="("><msubsup><mi>C</mi><mi>k</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup></mfenced><mo linebreak="goodbreak">=</mo><mfrac><msubsup><mi mathvariant="normal">C</mi><mi>k</mi><mi>p</mi></msubsup><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></msubsup><msubsup><mi>C</mi><mi>k</mi><mi>p</mi></msubsup></mrow></mfrac></mrow><annotation encoding="application/x-tex">$$ {C}_k^{\sim }=F\left({C}_k^{(n)}\right)=\frac{{\mathrm{C}}_k^p}{\sum_{k=1}^M{C}_k^p} $$</annotation></semantics></math> </ephtml></p> <p>We got nearly flawless recall by setting the sigmoid activation to 0.5 from a <emph>p</emph>‐norm of ≥5.</p> <p>The new update has the following form: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0015" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>σ</mi><mi>j</mi><mfenced close=")" open="("><mrow><mi>n</mi><mo linebreak="goodbreak">+</mo><mn>1</mn></mrow></mfenced></msubsup><mo linebreak="goodbreak">=</mo><mi mathvariant="italic">sgn</mi><mfenced close=")" open="("><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><mi>F</mi><mfenced close=")" open="("><msubsup><mi>C</mi><mi>k</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup></mfenced><msubsup><mi>x</mi><mi>j</mi><mi>k</mi></msubsup></mrow></mfenced></mrow><annotation encoding="application/x-tex">$$ {\sigma}_j^{\left(n+1\right)}=\mathit{\operatorname{sgn}}\left(\sum \limits_{k=1}^MF\left({C}_k^{(n)}\right){x}_j^k\right) $$</annotation></semantics></math> </ephtml></p> <p> <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0016" display="inline" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mfenced close=")" open="("><msubsup><mi>C</mi><mi>k</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup></mfenced></mrow><annotation encoding="application/x-tex">$$ F\left({C}_k^{(n)}\right) $$</annotation></semantics></math> </ephtml> represents the activation of the hidden layer, including the <emph>influence</emph> values (i.e., <emph>Hyperparameters</emph>), such as the <emph>p</emph>‐norm or another suitable alternative.</p> <p>Our algorithm treats inhibitor biases as system hyperparameters. After adding the inhibiting stimulus, we have the modified equation: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0017" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>σ</mi><mi>j</mi><mfenced close=")" open="("><mrow><mi>n</mi><mo linebreak="goodbreak">+</mo><mn>1</mn></mrow></mfenced></msubsup><mo linebreak="goodbreak">=</mo><mi mathvariant="italic">sgn</mi><mfenced close=")" open="("><mrow><munderover><mo movablelimits="false">∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><mi>F</mi><mfenced close=")" open="("><mrow><msubsup><mi>C</mi><mi>k</mi><mfenced close=")" open="("><mi>n</mi></mfenced></msubsup><mo>⋅</mo><msub><mi>b</mi><mi>k</mi></msub></mrow></mfenced><msubsup><mi>x</mi><mi>j</mi><mi>k</mi></msubsup></mrow></mfenced></mrow><annotation encoding="application/x-tex">$$ {\sigma}_j^{\left(n+1\right)}=\mathit{\operatorname{sgn}}\left(\sum \limits_{k=1}^MF\left({C}_k^{(n)}\cdot {b}_k\right){x}_j^k\right) $$</annotation></semantics></math> </ephtml></p> <p>The hyperparameters can have values of 0 ≤ <emph>b</emph> ≤ 1. We define the influence inhibition as a percentage value, where 0% represents full inhibition and 100% means lack of inhibition.</p> <p>The algorithm for iterating these hyperparameters defines each whole network update as one set of inhibitors, which are set while updating the first neuron. This algorithm determines which hidden layer node has the most significant value, the concept closest to the input state, or an unknown pattern stimulating the system. The system recalls the first link in our associative chain in the initial iteration, corresponding to the closest association.</p> <p>This algorithm initiates the operation when it updates the first neuron, specifying that each complete network update corresponds to a specific set of inhibitors. The algorithm identifies the node in the hidden layers with the highest value, signifying the concept or idea with the most robust connection to the input state. This unidentified pattern stimulates the system. For this first complete iteration, we allow our system to recall the closest association, which will be the first link in our associative chain. We initiate another loop of iterations to identify the following link, using the concept that converged in the previous system update as our initial state. Once the system locates the largest hidden layer node, it stores information about the closest associative concept, which, in this case, is the previously recalled concept. Therefore, the system fully inhibits that hidden node, muting it before activation on the third layer. The activation selects the closest associative option when the influence of concept  diminishes. Subsequent neuron updates will focus on this choice until the following link is fully created. In the next update, the inhibitors mute the previous two influences, allowing the closest concept to link to the chain. This process continues until the links between associations reach an appropriate length, completing the divergence from prominent to more obscure associations.</p> <p></p> <ulist> <item> <bold> All _I</bold>i_<subs><emph>k</emph></subs> starts with value 1.</item> <p></p> <item> The network gets updated with the initial state = input.</item> <p></p> <item> <bold> In the hidden layer, we identify the most significant response (largest _I_c_i__SB__I_k_i__sb_) and set the corresponding _I</bold>i_ ‐value to zero to suppress that pattern in the next round.</item> <p></p> <item> The initial input layer state for the network's next updating round is the result of the previous round, corresponding to the previously associated state.</item> </ulist> <p>Therefore, we can repeatedly execute this process, eliminating the need to establish a correlatation between subsequent chain components and the initial one, or even the input. The network identifies associations, suppresses them, then identifies the next connection, suppresses it, and repeats this cycle until a specific termination criterion is satisfied.</p> <p>We implemented the model using the Python programming language. The network's functionality was built from scratch, combining several libraries, such as numpy, matplotlib, etc (Davison et al., [<reflink idref="bib27" id="ref87">27</reflink>]). We generated the n patterns by randomly combining zeros and ones, resulting in a total length of N neurons. The code is available upon request.</p> <hd id="AN0186049500-10">RESULTS</hd> <p></p> <hd id="AN0186049500-11">CROSS‐TALK EFFECT</hd> <p>For simplicity, we have categorized our simulations into three distinct scenarios:</p> <hd id="AN0186049500-12">Scenario 1</hd> <p>We identified the optimal threshold range for the first training as between 160 and 390; however, we observed stability within the threshold values ranging from 160 to 415 for the second. When the threshold was less than the squared norm of the input training pattern and more than the dot product with the remaining pattern, it blocked cross‐talk. Therefore, the correct pattern influences the <emph>j</emph>‐<sups>th</sups> neuron. If the threshold value is above 390, it will deactivate all neurons. Conversely, if the threshold value falls below 160, excessive cross‐talk will occur, leading to instability in the training patterns. Hence, in this first scenario, the amount of cross‐talk each neuron experiences at each update shows how 1 s and 0 s affect it. In this first scenario, cross‐talk is often absent, but it is at a threshold of 160 when it does occur (Figure 2).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/3U7/01jun25/jocb680-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="jocb680-fig-0002.jpg" title="2 bcstripbcstripCross‐talk encountered by neurons at each update to the matrix's first scenario (M = 2). The graph on the right represents this simulation's M matrix [VVT] related to the indicated results in panels (a) and (b). If the training patterns were orthogonal (as shown by black arrows), they would fall within the range of optimal thresholds. Panel (a) displays the threshold (y‐axis) for 23 iterations, marked with numbers ranging from 0 to 22 on the x‐axis. The expected threshold for cross‐talk is 160, as indicated by a red line. Panel (b) shows the threshold activity heatmap for the two patterns in the first simulated scenario." /> </p> <p></p> <hd id="AN0186049500-14">Scenario 2</hd> <p>We categorized the cross‐talk into four levels (Figure 3).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/3U7/01jun25/jocb680-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="jocb680-fig-0003.jpg" title="3 bcstripbcstripCross‐talk encountered by neurons at each update of the second scenario of the matrix (M = 4). The graph on the right represents the simulation's M matrix [VVT] related to the indicated results in panels (a) and (b). If the training patterns were orthogonal (as shown by black arrows), they would fall within the range of optimal thresholds. Panel (a) displays the threshold (y‐axis) for 23 iterations, marked with numbers from 0 to 22 on the x‐axis. The expected threshold for cross‐talk is 400, as indicated by a red line. Panel (b) shows the threshold activity heatmap in the eight patterns for this second simulated scenario. The cross‐talk is categorized into four levels, each exhibiting a unique distribution pattern. The four levels correspond to increasing interference: no cross‐talk, one‐pattern interference, two‐pattern interaction, and concurrent intersection of all patterns. The first level refers to the j‐th neuron, which does not encounter any form of cross‐talk. The second level represents the interference of only one pattern with the asynchronous update. The third level shows the interaction between two distinct patterns. The fourth level signifies the most unfavorable condition, where all patterns intersect concurrently." /> </p> <p></p> <p>The first level relates to situations where the <emph>j</emph>‐<sups>th</sups> neuron does not engage in cross‐talk. The second level occurs when only one of the patterns interferes with the asynchronous update. The third level implicates the interference of any two patterns. Finally, the fourth level represents the worst‐case simulation situation, in which all patterns interfere simultaneously.</p> <p>The changing network state leads to a higher average cross‐talk for the second scenario, a clear sign of the instability of the training pattern we fed into the system. In a stable scenario, we would expect a constant average cross‐talk; however, certain levels are more prevalent. Notably, more iterations resulted in zero cross‐talk than any other number, and all patterns contributed to cross‐talk the least often.</p> <p>The pattern distribution of ones and zeros interferes with asynchronous updates. Therefore, we have reduced the probability parameter for our training patterns to <emph>P</emph>(<emph>σi</emph> = 1) = 0.2. This resulted in half the average number of ones compared to the previous simulation. On average, the sparser distribution should reduce interference at all four levels except 0.</p> <hd id="AN0186049500-16">Scenario 3</hd> <p>We first conducted the simulation for the third scenario using <emph>M</emph> = 4 patterns, followed by <emph>M</emph> = 5. We used a probability parameter of <emph>P</emph>(<emph>σi</emph> = 1) = 0.1, starting from <emph>M</emph> = 5. This step was necessary to establish that HNN possesses adequate capacity for the subsequent phase of modeling creativity‐based semantic associations.</p> <p>We determined the square norm matrix for the training patterns as follows: <ephtml> <math altimg="urn:x-wiley:00220175:media:jocb680:jocb680-math-0018" display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="italic">VV</mi><mi>T</mi></msup><mo linebreak="goodbreak">=</mo><mfenced close=")" open="(">9771579794109415101091210791294894108110</mfenced></mrow><annotation encoding="application/x-tex">$$ {VV}^T=\left(\begin{array}{ccccc}97& 7& 15& 7& 9\\ {}7& 94& 10& 9& 4\\ {}15& 10& 109& 12& 10\\ {}7& 9& 12& 94& 8\\ {}9& 4& 10& 8& 110\end{array}\right) $$</annotation></semantics></math> </ephtml></p> <p>This matrix was stable, with a threshold in the range (92 < <emph>φ</emph> < 60), which is still consistent with the threshold ranges (Figure 4).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/3U7/01jun25/jocb680-fig-0004.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="jocb680-fig-0004.jpg" title="4 bcstripbcstripCross‐talk encountered by neurons at each update of the third scenario of the matrix (M = 5). The graph outlined in bold black on the right side represents the simulation's M matrix [VVT] related to the indicated results in panels (a) and (b). If the training patterns were orthogonal (as shown by the black arrows), they would fall within the range of optimal thresholds. Panel (a) displays the threshold (y‐axis) for 23 iterations, marked with numbers from 0 to 22 on the x‐axis. The expected threshold for cross‐talk is 50, as indicated by a red line. Panel (b) shows the threshold activity heatmap in the six patterns for this third simulated scenario. The cross‐talk demonstrates bias toward the first pattern, selecting a threshold slightly below the square of the average value to identify the most resilient pattern while suppressing all others." /> </p> <p></p> <p>For the second and third scenarios, we measured the Pearson correlation of the threshold between 23 iterations of the training patterns (Figure 5).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/3U7/01jun25/jocb680-fig-0005.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="jocb680-fig-0005.jpg" title="5 bcstripbcstripPearson correlation matrices from the 23 iterations of previous simulated scenarios (Panel (a) for the second scenario and Panel (b) for the third). Each of the 23 rows and columns corresponds to an iteration of 1024 neurons. Black boxes highlight significant coefficients, and the heat map bar on the right indicates their significance level." /> </p> <p></p> <p>The significant correlation was more orthogonal and pseudo‐orthogonal in the third simulated scenario compared with the second scenario.</p> <hd id="AN0186049500-19">RECONSTRUCTING ASSOCIATIVE CHAINS</hd> <p>We initiate a new iteration loop to locate the second link based on the most stable simulated scenario (Figures 6 and 7 and Figures S1 andS2).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/3U7/01jun25/jocb680-fig-0006.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="jocb680-fig-0006.jpg" title="6 bcstripbcstripIllustration of the hyperparameters effect on convergent patterns in the third scenario by passing the value to the hidden layer and completing the update loop. Pattern 4 initiates a new iteration loop to locate the second link through pattern 6, which then displays the Pearson correlation matrix of these patterns. The black boxes in the Pearson correlation matrix indicate the significant coefficients related to patterns 3, 4, and 6." /> </p> <p></p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/3U7/01jun25/jocb680-fig-0007.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="jocb680-fig-0007.jpg" title="7 bcstripbcstripIllustration of the selected iterations across the patterns in the three simulated scenarios (Figures 2‐4). These graphs are selected based on the significant iterations across patterns in the third simulated scenario. The selected iterations and patterns, depicted in different panels (a–f), correspond to the significantly related iteration, as shown in Figures 5b and 6. In the third simulated scenario, the black boxes on the panels indicate and mark trends in the effects of the hyperparameters on the network's convergence. In contrast to the first and second scenarios, the third simulated scenario is represented in less transparent color to visualize the trend of these effects." /> </p> <p></p> <hd id="AN0186049500-22">DISCUSSION AND CONCLUDING REMARKS</hd> <p>Our study has revealed that altering specific state parameters can guide the HNN to converge on unrelated ideas, thereby enabling effective control over the network's overall activity (Figures 2–5). For instance, the network's convergence capability is diminished when the second nearest stored pattern significantly differs from the input pattern, thus fostering the connection between the input and patterns. Our model's ability to recall more than one pattern aligns with associative links, corresponding to focusing on context in finding the best optimal solutions (Gabora, [<reflink idref="bib37" id="ref88">37</reflink>]).</p> <p>To facilitate convergence, we implemented hyperparameters in our network. As a result, we detected a plausible mechanism for creating associative chains by inhibiting the influence of previously learned concepts, such as <emph>associative links</emph>. These new parameters, which we call hyperparameters, alter convergence by distributing zeros and ones as weighted parameters over each learning pattern in the unipolar binary layer. The hidden layer then receives the value, completing a specific update loop. We allowed the network to identify the first associative link from the most stable simulated scenarios (i.e., the third scenario) that best correlated with the input (Figures 6, 7 and Figures S1 andS2). After completing a single update, we established the subsequent link by suppressing the initial outcome and all prior recollections (Figures 6, 7 and Figures S1 andS2). Our model suggests that we do not have to search the whole network and compare the input with all the patterns to find a solution; instead, it retrieves the memorized items seamlessly using inhibition as an analog to the hyperparameters. Accordingly, inhibition could function as an additive inhibitory mechanism alongside the state layer's activation function, with its threshold serving as an additional on/off switch that controls the system's convergence to an association. These findings align with previous research on creativity, highlighting the critical role of inhibition in facilitating creative thinking (Benedek, Franz, Heene, & Neubauer, [<reflink idref="bib14" id="ref89">14</reflink>]; Carson, Peterson, & Higgins, [<reflink idref="bib20" id="ref90">20</reflink>]; Cassotti, Agogué, Camarda, Houdé, & Borst, [<reflink idref="bib21" id="ref91">21</reflink>]; Green & Williams, [<reflink idref="bib41" id="ref92">41</reflink>]; Khalil et al., [<reflink idref="bib53" id="ref93">53</reflink>]; Khalil, Karim, Kondinska, & Godde, [<reflink idref="bib55" id="ref94">55</reflink>]; Khalil, Lin, Karim, & Godde, [<reflink idref="bib56" id="ref95">56</reflink>]; Radel, Davranche, Fournier, & Dietrich, [<reflink idref="bib77" id="ref96">77</reflink>]; Scibinetti, Tocci, & Pesce, [<reflink idref="bib87" id="ref97">87</reflink>]).</p> <p>Creative thinking based on semantic associations allows us to search the lower levels of memories to find which concepts relate to our circumstances, even on a micro‐level (Beaty et al., [<reflink idref="bib12" id="ref98">12</reflink>]; Benedek et al., [<reflink idref="bib15" id="ref99">15</reflink>]; Kenett & Beaty, [<reflink idref="bib51" id="ref100">51</reflink>]; Kenett, Ovando‐Tellez, Benedek, & Volle, [<reflink idref="bib52" id="ref101">52</reflink>]; Li, Kenett, Hu, & Beaty, [<reflink idref="bib63" id="ref102">63</reflink>]; Luchini et al., [<reflink idref="bib64" id="ref103">64</reflink>]). Pattern storage and reconstruction align with human memory's biological processes (Abraham, Jones, and Glanzman, [<reflink idref="bib6" id="ref104">6</reflink>]; Gabora, [<reflink idref="bib37" id="ref105">37</reflink>]; Gerver, Griffin, Dennis, and Beaty, [<reflink idref="bib40" id="ref106">40</reflink>]; Krotov & Hopfield, [<reflink idref="bib61" id="ref107">61</reflink>]). The distribution of neurons involved in storage within neuron assembly significantly influences the brain's ability to store accessible memories and promote associative thinking (Beaty et al., [<reflink idref="bib12" id="ref108">12</reflink>]; Benedek, Beaty, Schacter, & Kenett, [<reflink idref="bib13" id="ref109">13</reflink>]; Gabora, [<reflink idref="bib37" id="ref110">37</reflink>]; Gerver, Griffin, Dennis, & Beaty, [<reflink idref="bib40" id="ref111">40</reflink>]; McEliece et al., [<reflink idref="bib66" id="ref112">66</reflink>]).</p> <p>In previous studies, Iyer, et al. ([<reflink idref="bib45" id="ref113">45</reflink>]), Iyer, Minai, et al. ([<reflink idref="bib46" id="ref114">46</reflink>]) used the connectionist model to converge the modulation of inhibition in the semantic representation system during the evaluation process (referred to as the <emph>critic</emph>) to a mechanism that can influence the search process. The 'critic' in this context is a component of the model that evaluates the current state and guides the search process based on its assessment. Researchers (Doboli et al., [<reflink idref="bib31" id="ref115">31</reflink>]; Iyer, et al., [<reflink idref="bib45" id="ref116">45</reflink>]; Iyer, Minai, et al., [<reflink idref="bib46" id="ref117">46</reflink>]) have utilized this model to examine how external cues can prime the concept network and the dynamic selector network of the connectionist system by projecting a temporary selective bias onto them. This bias can have diverse effects, from completely changing the search direction to having a minimal impact. Various factors influence these effects, including the relevance of the cue to the situation, its ability to trigger an associative response, familiarity with the situation, and the level of inhibition in the dynamic selector network upon receiving the cue. Our HNN results are compatible with neural network theories incorporating a broader spectrum of cognitive processes using connectionist models, validating the likelihood of its general framework. The dynamic formulation of the connectionist model, which comprises excitation and inhibition balancing, modulation, and modularity leveraging, is a key aspect of its operation. This model is part of a broader category of computational models that have successfully simulated extensive data on cognition (Bressler & Kelso, [<reflink idref="bib16" id="ref118">16</reflink>]; Carpenter & Grossberg, [<reflink idref="bib19" id="ref119">19</reflink>]; Tononi, Edelman, & Sporns, [<reflink idref="bib93" id="ref120">93</reflink>]), decision‐making (Levine, [<reflink idref="bib62" id="ref121">62</reflink>]; Roe, Busemeyer, & Townsend, [<reflink idref="bib80" id="ref122">80</reflink>]), attention (Tipper, Howard, & Houghton, [<reflink idref="bib91" id="ref123">91</reflink>]; Tipper, Lortie, & Baylis, [<reflink idref="bib92" id="ref124">92</reflink>]), and action selection (Brown, Bullock, & Grossberg, [<reflink idref="bib17" id="ref125">17</reflink>]; Cisek, [<reflink idref="bib24" id="ref126">24</reflink>]).</p> <p>In summary, we identified two mechanisms controlling the context focus, shifting 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 is the inhibition of stored concepts, similar to an on/off switch that guides the system to search for associative links and when to stop. In Figure 8, we graphically depict these two mechanisms and metaphorically demonstrate the links between various concepts or ideas by establishing associative chains.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/3U7/01jun25/jocb680-fig-0008.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="jocb680-fig-0008.jpg" title="8 bcstripbcstripSummary of a hypothetical model of the simulation of modern HNN (Panel a) along with a metaphorical illustration of the connection between concepts (Panel b). Panel (a) refers to modern HNN as a two‐layer model we have implemented. The input neurons comprise the first layer, and the patterns' neurons learn the connections between the two layers. The core of the updating process, known as the 'new weights,' resides in the top layer. The 'new weights' reflect how adding new parameters (i.e., hyperparameters) influences convergence. They function as weighted parameter distributions of 0s and 1s across each unipolar binary layer learning pattern, delivering the value to the hidden layer and completing one update loop. This resembles the first and second links, symbolized as a semantic association. Panel (b) illustrates a metaphorical example of a man in the forest attempting to build a house. The man has learned to build a house with hammers, nails, walls, and rocks. A nail and a wall symbolize driving a nail into the wall; the man might initially associate the hammer with it. However, if the man is in the forest and has left his hammer at home, he may think of something else that is more directly associated with the hammer, such as a rock. Because he could deviate from the hammer, he allowed himself to form an association that led to a solution. The inhibition functions as a crucial mechanical switch, guiding the neural system to engage in creative thinking‐based semantic association. This process involves shifting from evident to obscure (i.e., novel or unexplored) associations, allowing the man to solve his problem creatively." /> </p> <p></p> <hd id="AN0186049500-24">FUTURE DIRECTIONS</hd> <p>Our study unveils several intriguing possibilities for further investigation, which could spark a new wave of research in the field. Establishing a more comprehensive creative framework is fascinating and can significantly advance our understanding of creative thinking. While many questions remain unanswered, we will briefly discuss some unresolved questions, paving the way for future investigations and inspiring further research.</p> <p></p> <ulist> <item> Krotov and Hopfield ([<reflink idref="bib61" id="ref127">61</reflink>]) emphasized the remarkable duality of their discrete modern HNN and the feedforward structures of deep neural networks. This has led to the emergence of striking associative chains within extensive HNN systems capable of linking hundreds of thousands of ideas/concepts. The more complex the chain, the greater the potential for unexpected (i.e., surprising) and insightful outcomes. These chains play a crucial role in providing the HNN system with creative ideas and surprising insights based on existing information. A crucial avenue for future model development involves shifting from discrete to continuous neuron activations, which will broaden the ideas derived from activation variations and facilitate the application of inhibition to drive even more surprising and context-specific associative links.</item> <p></p> <item> Despite the current empirical challenges, developing an algorithm to process a given idea as input is feasible and achievable. Given that the word "bell" is composed of memory representations of visual, tactile, and auditory perceptions, these images illustrate the essential features of the "bell". Therefore, testing the framework on patterns that represent real‐life concepts would be beneficial. The next step would involve creating a dataset and defining multiple features for each pattern, such as human, animal, object, height, color, etc. (Richards, [<reflink idref="bib79" id="ref128">79</reflink>] ; Runco & Bahleda, [<reflink idref="bib83" id="ref129">83</reflink>]). We can collect data and transform it into an identifiable pattern by asking the individual about the concept's features. We can conceptualize a feature as a cluster of neurons, specifically the first 10 neurons in each pattern; its definition depends on the activated neurons' arrangement. For instance, when a neuron fires in the second position within a height feature, it indicates the presence of a light object; conversely, a value of 0 indicates the absence of height relevance. Expanding this network into large‐scale neural networks and testing this theoretical framework on real‐life ideas will make it easier to detect how the network's creativity‐based semantic associations operate. By fine‐tuning the creation of associative links, we can further refine the process and achieve substantial progress. This potential for refinement through iterative selection, while simultaneously suppressing certain features, offers a promising path for future research and development in this field.</item> <p></p> <item> The brainstorming context is another avenue to explore. Behavioral experiments in brainstorming have extensively studied the ability to generate relevant ideas in familiar and unfamiliar contexts (Osborn, [<reflink idref="bib73" id="ref130">73</reflink>]). Previous experiments have uncovered various social and cognitive factors that influence idea generation (Coskun, Paulus, Brown, & Sherwood, [<reflink idref="bib26" id="ref131">26</reflink>] ; Dugosh & Paulus, [<reflink idref="bib33" id="ref132">33</reflink>] ; Nijstad & Stroebe, [<reflink idref="bib71" id="ref133">71</reflink>] ; Paulus & Brown, [<reflink idref="bib74" id="ref134">74</reflink>] ; Paulus & Dzindolet, [<reflink idref="bib75" id="ref135">75</reflink>]). Research has indicated that guiding brainstorming can improve the quantity and quality of the generated ideas (Coskun et al., [<reflink idref="bib26" id="ref136">26</reflink>] ; Dugosh, Paulus, Roland, & Yang, [<reflink idref="bib34" id="ref137">34</reflink>] ; Karim, Cataltepe, Usman, Khedr, & Khalil, [<reflink idref="bib48" id="ref138">48</reflink>] ; Nijstad, Stroebe, & Lodewijkx, [<reflink idref="bib72" id="ref139">72</reflink>]). It is critical to comprehensively capture these components using neural network models to enhance brainstorming procedures and elucidate the cognitive aspects of the idea‐generation process. Established research firmly grounds these models, making them more than just theoretical constructs. Developing a detailed computational model of the group creative process will provide more precise predictions for experimental testing. Mapping this model onto brain regions based on their learning rules would be incredibly useful (Khalil & Moustafa, [<reflink idref="bib57" id="ref140">57</reflink>]).</item> </ulist> <p>Examining various perspectives can remarkably improve our comprehension of the dynamics involved in the creative process. We can evaluate predictions about the mechanisms that underlying these experimental findings by comparing the outcomes obtained from the computational model and assessing brain correlates. Therefore, collaboration across multiple disciplines will significantly benefit progress in this area. This cross‐disciplinary approach is essential for heightening our understanding of the social and cognitive dimensions of the creative process through a neural‐computational framework (Iyer, et al., [<reflink idref="bib45" id="ref141">45</reflink>]; Iyer, Minai, et al., [<reflink idref="bib46" id="ref142">46</reflink>]).</p> <hd id="AN0186049500-25">CONFLICT OF INTEREST STATEMENT</hd> <p>The authors declare that they do not have competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.</p> <hd id="AN0186049500-26">Acknowledgment</hd> <p>Open Access funding enabled and organized by Projekt DEAL.</p> <hd id="AN0186049500-27">AUTHOR CONTRIBUTIONS</hd> <p>Ronald Mtenga: Data curation, Methodology, Writing – original draft. Bode Mathias: Conceptualization, Investigation, Methodology, Supervision, Validation. Khalil Radwa: Conceptualization, Data curation, Methodology, Supervision, Visualization, Revision, Writing – review & editing.</p> <hd id="AN0186049500-28">DATA AVAILABILITY STATEMENT</hd> <p>Data will be made available on request.</p> <p>GRAPH: Figure S1. The hyperparameters' effect on convergent patterns in the second scenario is illustrated by passing the value down to the hidden layer and completing the update loop. Patterns 3 and 4, as the initiators of a new iteration loop, plays a key role in the process. They locate the second link through patterns 5 and 6, displaying the Pearson correlation matrix of these patterns. The black boxes in the Pearson correlation matrix indicate the significant coefficients related to patterns 3, 4, 7, and 8.</p> <p>GRAPH: Figure S2. Illustration of the selected iterations across the patterns in the three simulated scenarios. These graphs are selected based on the significant iterations across patterns in the second simulated scenario. The selected iterations and patterns, depicted in different panels (A–L), correspond to the significantly related iteration, as shown in Figure 5a and Figure S1. In the second simulated scenario, the black boxes on the panels indicate and mark trends in the effects of the hyperparameters on the network's convergence. In contrast to the first and third scenarios, the second simulated scenario is represented in less transparent color to visualize the trend of these effects.</p> <ref id="AN0186049500-29"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref39" type="bt">1</bibl> <bibtext> Open Access funding enabled and organized by Projekt DEAL.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref40" type="bt">2</bibl> <bibtext> Asynchronous updating provides several advantages over synchronous updating; it allows for faster convergence to stable states and better recall of stored patterns with noise, thus helping avoid oscillations and limit cycles (El Boustani & Destexhe, [35]; Kobayashi, [59]; Moyer, Halterman, Finkel, & Wolf, [70]).</bibtext> </blist> <blist> <bibl id="bib3" idref="ref76" type="bt">3</bibl> <bibtext> Nevertheless, bipolar activations offer additional benefits, such as a wide dynamic range, which makes convergence less sensitive to noise disturbances and facilitates pattern orthogonality.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref24" type="bt">4</bibl> <bibtext> When two neurons fire simultaneously, their connection value—the unique weights connecting them—increases, leading to a higher correlation in their activity over time (Morris, [69]).</bibtext> </blist> <blist> <bibl id="bib5" idref="ref20" type="bt">5</bibl> <bibtext> We do not name them as weights to avoid confusion with the recurrent network's training patterns.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref57" type="bt">6</bibl> <bibtext> Hyperparameters refer to the vector b (that is, to its components b<subs>1</subs>, b<subs>2</subs>, ... b<subs>M</subs>) used as coefficients. 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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Do Not Let the Beginning Trap You! On Inhibition, Associative Creative Chains, and Hopfield Neural Networks
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Ronald+Mtenga%22">Ronald Mtenga</searchLink><br /><searchLink fieldCode="AR" term="%22Mathias+Bode%22">Mathias Bode</searchLink><br /><searchLink fieldCode="AR" term="%22Radwa+Khalil%22">Radwa Khalil</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-2632-8306">0000-0003-2632-8306</externalLink>)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Journal+of+Creative+Behavior%22"><i>Journal of Creative Behavior</i></searchLink>. 2025 59(2).
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 19
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Inhibition%22">Inhibition</searchLink><br /><searchLink fieldCode="DE" term="%22Creative+Thinking%22">Creative Thinking</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Processes%22">Cognitive Processes</searchLink><br /><searchLink fieldCode="DE" term="%22Concept+Formation%22">Concept Formation</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+Solving%22">Problem Solving</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+Intelligence%22">Artificial Intelligence</searchLink><br /><searchLink fieldCode="DE" term="%22Neurological+Organization%22">Neurological Organization</searchLink><br /><searchLink fieldCode="DE" term="%22Brain%22">Brain</searchLink><br /><searchLink fieldCode="DE" term="%22Associative+Learning%22">Associative Learning</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1002/jocb.680
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0022-0175<br />2162-6057
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Creative 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.
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  Data: As Provided
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  Data: 2025
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  Data: EJ1474819
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        Value: 10.1002/jocb.680
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      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 19
    Subjects:
      – SubjectFull: Inhibition
        Type: general
      – SubjectFull: Creative Thinking
        Type: general
      – SubjectFull: Cognitive Processes
        Type: general
      – SubjectFull: Concept Formation
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Artificial Intelligence
        Type: general
      – SubjectFull: Neurological Organization
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      – SubjectFull: Brain
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      – SubjectFull: Associative Learning
        Type: general
    Titles:
      – TitleFull: Do Not Let the Beginning Trap You! On Inhibition, Associative Creative Chains, and Hopfield Neural Networks
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            NameFull: Ronald Mtenga
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            NameFull: Mathias Bode
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            NameFull: Radwa Khalil
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            – D: 01
              M: 06
              Type: published
              Y: 2025
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            – TitleFull: Journal of Creative Behavior
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