Colon cancer diagnosis method based on adaptive molecular LVQ neural network

Abstract

The application provides a colon cancer diagnosis method based on an adaptive molecular LVQ neural network, and comprises the following steps: determining the functions of an input layer, a competition layer and a linear output layer of the LVQ neural network; designing basic function modules of the molecular LVQ neural network according to DNA strand displacement reactions; adding a supervised learning module on the basis of the basic function modules; determining the DNA strand structures and small fulcrum structures of the auxiliary substances and reactants in the chemical reaction process; cascading the basic function modules and the supervised learning module into the adaptive molecular LVQ neural network; constructing a data set from TCGA and GTEx databases; inputting the data set into the adaptive molecular LVQ neural network, performing benign or malignant diagnosis, and triggering weight dynamic updating according to the diagnosis error, so as to complete adaptive optimization of the adaptive molecular LVQ neural network. The application realizes the supervised learning and adaptive optimization at the molecular level, and successfully classifies and identifies the benign and malignant colon cancer samples.

Description

Technical Field

[0001] This invention relates to the technical field of molecular neural networks and disease diagnosis, and in particular to a method for constructing a neural network circuit based on DNA strand substitution and a method for diagnosing colon cancer. Background Technology

[0002] Molecular LVQ neural networks use DNA strands as computational and information carriers, enabling pattern classification at the molecular level through strand substitution reactions. They offer advantages such as parallel computing, low energy consumption, and compatibility with biological systems. However, existing molecular LVQ neural networks only implement basic pattern classification and decision output functions, lacking dynamic weight updates and adaptive learning mechanisms. The initial weights and prototype vectors remain fixed, preventing iterative correction based on classification errors and lacking self-optimization and self-correction capabilities. When processing high-dimensional, highly perturbed molecular data, their classification accuracy and robustness are limited. Directly applying such static molecular LVQ neural networks lacking adaptability to colorectal cancer diagnosis is problematic. Due to the high dimensionality of colorectal cancer gene expression data, strong sample heterogeneity, and blurred feature distribution boundaries, fixed-weight models cannot dynamically adjust classification decision boundaries. Lacking error feedback and parameter optimization, they struggle to adapt to the differences in features and environmental fluctuations of different samples, leading to misdiagnosis and missed diagnosis. Their generalization ability and diagnostic stability are insufficient, failing to meet the requirements for accurate and stable clinical screening and early diagnosis of colorectal cancer.

[0003] In molecular LVQ neural networks, dynamically updating weight parameters using DNA strand substitution technology is a key method for optimizing system classification performance and accurately correcting model errors. Furthermore, the construction of the weight update module and its adaptation to the overall molecular LVQ neural network are crucial prerequisites for achieving a complete functional closed loop of "computation-classification-correction-recomputation." Molecular LVQ neural networks use DNA strands as the core computational and information carrier. All computational processes rely on molecular reactions such as hybridization, dissociation, and annihilation of DNA strands. This is fundamentally different from the numerical iterative update logic based on electrical signals in traditional electronic devices. Traditional weight update mechanisms cannot be directly transferred and adapted to molecular computing systems. Without a specifically designed weight update mechanism, the prototype vector of the molecular LVQ neural network cannot perform dynamic iterative optimization, and the model's inherent self-learning and self-correction capabilities cannot be realized. DNA strand substitution technology, based on the complementary base pairing principle of nucleic acid molecules, drives the DNA strand to undergo autonomous hybridization and dissociation reactions, providing a precise and controllable molecular-level operation carrier for weight updates. This technology transforms the error correction logic of weight updates in traditional LVQ neural networks into a process of quantitative regulation of DNA strand concentration and precise adjustment of molecular reaction dynamics. This transformation not only effectively resolves the compatibility contradiction between molecular computing carriers and traditional weight update mechanisms, but also provides a molecular basis for weight updates to be stably executed and flexibly regulated in a molecular reaction environment, thus providing technical support for the realization of weight update functions at the molecular level.

[0004] Conversely, without a weight update module in the molecular LVQ neural network, the DNA prototype vector obtained during initial training will remain fixed, making it difficult to cope with various problems in actual molecular computation. It cannot compensate for feature representation bias caused by insufficient training sample coverage, nor can it resolve molecular reaction dynamics imbalances caused by environmental interference. Furthermore, it cannot adapt to feature distribution changes brought about by new input patterns, ultimately resulting in significant deficiencies in the model's generalization ability and classification robustness. However, with the synergistic effect of the weight update module and DNA strand replacement technology, the molecular LVQ neural network can extract classification error signals after completing input pattern classification by comparing the classification results with the sample's true label. Using this signal as a trigger, it initiates a targeted DNA strand replacement reaction, achieving dynamic and precise correction of the prototype vector. This correction process reduces the model's classification error at its source, effectively improving the model's ability to cope with sample feature variations and environmental interference, significantly enhancing the robustness of the molecular LVQ neural network. Ultimately, it drives the model's upgrade from static pattern classification to dynamic intelligent classification, making the molecular LVQ neural network more suitable for complex molecular pattern recognition tasks in real-world scenarios. Summary of the Invention

[0005] To address the technical limitations of existing molecular LVQ neural networks, which cannot achieve autonomous learning and dynamic optimization and have limited flexibility in adapting to complex scenarios, this invention proposes a colorectal cancer diagnosis method based on an adaptive molecular LVQ neural network. The constructed molecular LVQ neural network with supervised learning function provides a novel technical solution for pattern recognition at the molecular level. Its excellent performance in colorectal cancer diagnosis also provides important technical support for primary healthcare institutions to carry out accurate and rapid tumor diagnosis.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: a method for diagnosing colon cancer based on an adaptive molecular LVQ neural network, comprising the following steps:

[0007] Step 1: Determine the functions of the input layer, competition layer, and linear output layer of the LVQ neural network;

[0008] Step 2: Design the basic functional modules of the molecular LVQ neural network based on the DNA strand substitution reaction; add a supervised learning module based on the basic functional modules.

[0009] Step 3: Determine the DNA chain structure and small pivot structure of the auxiliary substances and reactants in the chemical reaction process of the basic functional module and the supervised learning module;

[0010] Step 4: Based on the structure of the LVQ neural network, the basic functional module and the supervised learning module are cascaded into a complete adaptive molecular LVQ neural network based on DNA strand replacement, and the concentration setting and functional verification are completed in the Visual DSD platform.

[0011] Step 5: Obtain gene expression data of colorectal cancer cases and benign control samples from the TCGA and GTEx databases, and construct a dataset after data preprocessing and feature screening;

[0012] Step 6: Input the dataset into the constructed adaptive molecular LVQ neural network to diagnose whether the preprocessed colon cancer samples are benign or malignant, and dynamically update the weights based on the diagnostic error to complete the adaptive optimization of the adaptive molecular LVQ neural network.

[0013] Preferably, a fully connected layer is used between the input layer and the competition layer to realize information interaction and distance calculation between the input features and all neurons in the competition layer; the competition layer and the linear output layer are partially connected, the number of neurons in the competition layer is not less than the number of neurons in the linear output layer, and each neuron in the competition layer is connected to only one neuron in the linear output layer, with a connection weight of 1 between them, while a single neuron in the linear output layer is connected to multiple neurons in the competition layer; the output states of neurons in both the competition layer and the linear output layer are represented using binary representation; when the input features are input into the input layer in the form of feature vectors, the feature vectors are passed to the competition layer through a fully connected path, and all neurons in the competition layer perform similarity calculations with the feature vectors, selecting the neuron closest to the input features as the winning neuron, which is activated and its state is set to 1, while the other neurons in the competition layer remain inactive in the 0 state; based on the fixed connection relationship between the competition layer and the linear output layer, the linear output layer neurons connected to the winning neuron are activated and their states are simultaneously set to 1, while the other linear output layer neurons remain in the 0 state, thus completing the category determination of the input features;

[0014] If the actual category of the input feature matches the category corresponding to the linear output layer neuron, the weights of the corresponding competing layer neuron are adjusted in the direction of the input feature; otherwise, the weights of the corresponding competing layer neuron are adjusted in the opposite direction of the input vector.

[0015] Preferably, the supervised learning module includes a weighting activation module, a catalytic amplification module, a competition suppression module, an addition module, and a subtraction summation module. The output chain obtained from the basic functional module serves as the trigger signal for the weighting activation module, initiating weight updates. The weighting activation module is sequentially connected to the catalytic amplification module and the competition suppression module, which work together to complete the molecule multiplication operation. According to the weight update rules, the result of the molecule multiplication operation is connected to the addition module or the subtraction summation module to achieve dynamic calculation and updating of weights.

[0016] Preferably, the basic functional modules include a distance calculation module, a reversal summation module, an annihilation module, and a reporting module; the distance calculation module is connected to the reversal summation module, which is connected to both the annihilation module and the reporting module, and the output chain of the reporting module is the predicted label; the distance calculation module corresponds to the input layer, responsible for receiving and processing the input feature vector, and completing the similarity calculation between the feature vector and the weight; the reversal summation module corresponds to the competition layer, realizing signal normalization and competitive selection, and filtering out the neuron that best matches the input layer; the annihilation module and the reporting module together correspond to the linear output layer, completing the final signal output and category determination.

[0017] Preferably, the chemical reaction expression of the weighting activation module is:

[0018] When the output tag's output chain Yi When consistent with the original tag class,

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] When the output tag's output chain Y i When inconsistent with the original label,

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] Among them, BY i BY k Represents the original class tag chain; FG ii FG ik Represents the release gate, serving as the trigger switch for weight updates; IN X IN C Representing the activation chain, the activation chain INx is used to trigger a positive weight update when the classification is correct. The activation chain IN... C Used to trigger reverse weight updates when a classification error occurs; XF X XF C Represents the catalytic chain; GX 2j CX 2j Representative input substrate; GW 1j CW 1j Representing the weighted substrate, WG 2j NG 2j The WG gate represents a new input summation gate, which transforms a new input substrate into a new input chain that can participate in computation. 1j NG 1j The new weighted summation gate transforms the weighted substrate into a new weighted chain that can participate in computation; SX 2j LX 2j Represents a new input chain, LW 1j SW 1j Represents the new weighted chain; XP 2j WP 1j CP 2j NP 1j All are intermediate products;

[0029] The chemical reaction expression for the catalytic amplification module is as follows:

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] Wherein, chain K is represented. ij Characterizing the new input chain LX 2j SX 2j and the new weighted chain LW 1j SW 1j C i1 C i2 C i3 Represents auxiliary chain; SP i1 SP i2 SP i3 SP i4 SP i5 SP i6 B represents an intermediate product; ij Represents the amplification chain; Y ij Represents the output product;

[0035] The competitive inhibition module is responsible for regulating the reaction process and calibrating the concentration ratio. The chemical reaction expression for the competitive inhibition module is as follows:

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] Among them, D i1 D i2 D i3 Represents auxiliary chain; SP i7 SP i8 SP i9 SP i10 SP i11 SP i12 SP i13 B0 represents an intermediate product; ij Represents the inhibitory chain;

[0041] The chemical reaction expression for the addition module is:

[0042] ;

[0043] ;

[0044] ;

[0045] Among them, Y 1j Y 2j Represents the output product of the catalytic amplification module; USumW 1j USumX 2j Represents a summation gate chain; DP 1j and DP 2j Represents intermediate products; TSum j Represents a common summation gate chain; Z j Represents the output chain;

[0046] The chemical reaction expression for the subtraction summation module is:

[0047] ;

[0048] ;

[0049] ;

[0050] Among them, NUSumW 1j ,NTSumW 2j NTSum represents a summation gate chain. 1j ,NTSum 2j Represents a common summation gate chain; Z 1j Z 2j Represents the output chain, output chain Z 1j The concentration is the new positive weight value, and the output chain Z... 2j The concentration is then the new negative weight value; Indicates the product.

[0051] Preferably, the chemical reaction expression of the distance calculation module is:

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] Among them, K f1 K is the rate constant of the annihilation reaction. sK is the rate constant of the summation reaction. f1 ≫K s ;X ij The input chain represents the molecular signal of the i-th input layer neuron; W ij Anh represents the weight chain, storing the weight values ​​of the j-th competing layer neuron on the feature vector of the i-th input layer neuron; ij Represents the annihilation chain, implementing the input chain X. ij With weight chain W ij annihilation reaction, Indicates the product of an annihilation reaction; SumX ij The input summation gate annihilates the remaining input chain X. ij The concentration is converted into the input for the summation operation, summation chain XS ij SumW ij The weight summation gate represents the annihilation of the remaining weight chain W. ij The concentration is converted into the weight of the summation operation WS. ij Sum j Represents a common summation gate, completing the input summation chain XS. ij Weighted summation chain WS ij The concentration summation operation generates the distance factor D, representing the Manhattan distance. j "waste" represents the waste chain.

[0057] The chemical reaction expression for the inverse summation module is:

[0058] ;

[0059] Among them, SRG kj The RSG (Representative Signal Inversion Gate) is used to average the concentration of the distance factor of the j-th competing layer neuron to obtain the inverted signal corresponding to the k-th competing layer neuron; k This represents the inversion signal summation gate, which sums the concentrations of all inversion signals associated with the k-th competing layer neuron.

[0060] The chemical reaction expressions for the annihilation module and the reporting module are as follows:

[0061] ;

[0062] ;

[0063] Where Kf2 is the rate constant of the annihilation module, and LAnh jk Represents the annihilation chain; K s1 Let K be the rate constant of the reporting module, and K f2 ≫K s1 S jS represents the inverted signal of the j-th competing layer neuron. k Re represents the inverted signal of the k-th competing layer neuron; Re ji The representative report gate outputs the inverted signal remaining after annihilation as a report, Y. i This represents the output label.

[0064] Preferably, when the output class label matches the true class label of the sample, indicating that the sample has been correctly classified, the output chain Y in the system... i BY with the original class tag chain i Together they act on the release gate FG ii It releases the activating strand IN through a specific DNA strand displacement reaction. x When the output class label does not match the true class label of the sample, indicating that the sample has been misclassified, the output chain Y... i BY with the original class tag chain k Combined and acting on the release gate FG ik The activated chain IN is released through a chain displacement reaction. c ;

[0065] Inhibition chain B0 ij and auxiliary chain D i1 The intermediate product SP generated by the reaction i8 And representing chain K ij With auxiliary chain C i1 The intermediate product SP generated by the reaction i2 Simultaneously with amplification chain B ij Reacting at the same reaction rate, the intermediate product SP i2 Concentration and representative chain K ij Concentration-dependent, intermediate product SP i8 Concentration and inhibitory chain B0 ij The concentration is related to the final output product Y. ij Concentration and representative chain K ij and B ij Positively correlated with the inhibitory chain B0 ij Negative correlation;

[0066] When the output matches the true class label of the sample, the summation gate chain USumW is used. 1j Output product Y 1j The concentration of DP is converted into the intermediate product. 1j The concentration is obtained by summation gate USumX 2j Output product Y 2j The concentration of DP is converted into the intermediate product. 2j The concentration, and through the common summation gate chain TSum j intermediate product DP 1j and DP 2jThe concentration is summed to the output chain Z. j Above, output chain Z j The concentration is the new weight value;

[0067] When the output result is inconsistent with the true class label of the sample, w ij_new =Y 1j -Y 2j Output product Y 1j With output product Y 2j Participating in the annihilation reaction, when the output product Y 1j The concentration of the product Y is greater than that of the output product Y. 2j At a concentration of , the output product Y 1j Through the summation gate NUSumW 1j And the common summation gate NTSum 1j Generate output chain Z 1j Output chain Z 1j The concentration of the product Y is equal to that of the output product. 1j Concentration and output product Y 2j The difference in concentration, and when the output product Y 1j The concentration is less than that of the output product Y 2j At a concentration of , the output product Y 2j Through the summation gate NUSumW 2j And the common summation gate NTSum 2j Generate output chain Z 2j Output chain Z 2j The output represents a negative value;

[0068] The chemical reaction expression for negative weight processing in the distance calculation module is:

[0069] ;

[0070] ;

[0071] Among them, NW ij Represents a negative-weighted chain; the negative-weighted summation gate SumNW ij negative weight chain NW ij The concentration is converted into a negative weighted summation chain NXW for the summation operation. ij Through the common summation gate Sum j The negative weight summation chain NXW ij The concentration and input summation chain XS ij The concentration is summed to the distance factor D j At the concentration;

[0072] The inversion summation module transforms the neuron with the smallest distance factor concentration into the signal output with the largest inversion signal concentration, so that in the subsequent inversion signal annihilation process, the neuron with the smallest distance factor will eventually win and complete the output.

[0073] Preferably, RNA-seq data is obtained from the TCGA and GTEx databases. After data cleaning, eight key feature genes of colorectal cancer are selected as input features using the random forest algorithm. The structure of the adaptive molecular LVQ neural network is determined to be an 8-2-2 network structure through cross-validation, including 8 neurons in the input layer, 2 neurons in the competition layer, and 2 neurons in the output layer. All preprocessed samples are divided into a training set, a test set, and a weight update set using random stratified sampling. The training set is used for the network to learn the gene feature patterns and initialize molecular weights. The test set is used to test the classification effect of benign and malignant colorectal cancer. The weight update set is used to drive the adaptive molecular LVQ neural network to achieve dynamic weight updates under supervised learning.

[0074] Using eight key characteristic genes of colorectal cancer as input variables and clinical classification of benign and malignant samples as output categories, the cluster boundaries of benign and malignant samples were divided in the high-dimensional gene expression space by the feature clustering and competitive classification mechanism of the adaptive molecular LVQ neural network, and a nonlinear correlation mapping between gene expression patterns and benign and malignant status of colorectal cancer was constructed.

[0075] Preferably, the annihilation reaction involved in the partial distance calculation module, the annihilation module, and the partial subtraction summation module utilizes the base point G, which has 7 nucleotides; the base point V involved in the weighting activation module has 9 nucleotides; and the remaining base points all have 5 nucleotides.

[0076] The actual concentrations of the new weighted chain, new input chain, new input summation gate, and new weighted summation gate are exactly the same as the corresponding chains and gates in the basic module;

[0077] The generated new input chain LX 2j Concentration and input substrate GX ij Concentrations are completely identical, new weighted chain LW 1j Concentration and input substrate GW ij The concentrations are completely identical, and both concentrations are respectively related to the input chain X. ij Weighted chain W ij The initial concentrations remain matched;

[0078] New input chain SX 2j Concentration matching input substrate CX 2j Concentration, new weighted chain SW 1j Concentration matching input substrate CW 1jThe concentrations of both are consistent with the corresponding input parameters and weight parameters required in the weight reverse update process;

[0079] Auxiliary chain C i1 C i2 C i3 and auxiliary chain D i1 D i2 D i3 The theoretical initial concentration is considered to be infinite.

[0080] The beneficial effects of this invention are as follows: Based on the theory of LVQ neural networks, this invention integrates DNA strand substitution technology to complete the construction of a molecular LVQ neural network. First, it designs and implements four core functional modules: distance calculation, inversion summation, annihilation, and reporting. This resolves the inherent contradiction between negative weights and the non-negative DNA strand concentration, ensuring the efficiency and stability of molecular-level classification operations. Then, a supervised learning module is specifically built, consisting of sub-modules such as weighting activation, multiplication, addition, and subtraction annihilation, to achieve weight updates. This successfully transforms the weight iteration logic of the LVQ neural network into a molecular-level DNA strand substitution reaction, realizing dynamic weight correction. The construction of the supervised learning module allows the molecular LVQ neural network to overcome the limitations of fixed weights, possessing the learning ability to adapt to molecular data distribution and optimize classification decision boundaries. It can effectively adapt to the high-dimensionality and significant individual differences of molecular data, fundamentally reducing classification errors and improving the model's generalization ability and diagnostic stability. This is a key design for achieving high-precision intelligent classification at the molecular level. The constructed molecular LVQ neural network was applied to the diagnosis of colorectal cancer. Based on RNA-seq data from the TCGA and GTEx databases, the model was trained and validated using random forest algorithm feature selection and hierarchical dataset partitioning. The final model achieved an overall diagnostic accuracy of 95.56% on the test set, with a 100% accuracy rate for identifying benign samples. Confusion matrix analysis confirmed the model's excellent classification accuracy and generalization ability. Specific validation experiments on the weight update module further demonstrated that the model can accurately iteratively adjust the weight vectors W1 and W2 according to the correctness of the diagnostic results, maintaining a low iteration error for the weight components, effectively validating the module's practical application value. This invention completes the full validation of the molecular LVQ neural network from theoretical design and module construction to practical disease diagnosis applications, demonstrating the feasibility of DNA strand substitution technology in realizing the molecularization of artificial neural networks. It provides important theoretical and experimental support for intelligent classification at the molecular level and accurate diagnosis of complex diseases.

[0081] The introduction of a weight update mechanism in this invention enables the molecular LVQ neural network to dynamically optimize the classification decision boundary, effectively adapting to the high dimensionality and significant individual differences of molecular data, and significantly improving the model's generalization ability and classification stability. This invention introduces an adaptive optimization mechanism onto the basic molecular LVQ neural network, solving the problem of traditional molecular LVQ models being unable to dynamically update weights. It achieves supervised learning and adaptive optimization at the molecular level, showing great potential in early diagnosis of colorectal cancer and personalized precision medicine, and successfully identifying the benign and malignant nature of colorectal cancer samples. Attached Figure Description

[0082] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0083] Figure 1 This is a flowchart of the present invention.

[0084] Figure 2 This is a schematic diagram of the negative weight processing in the distance calculation module of the present invention.

[0085] Figure 3 This is a schematic diagram of the DNA strand replacement reaction process of the activation strand release in the patent activation module of the present invention.

[0086] Figure 4 The activation chain IN of this invention x A schematic diagram of the DNA strand replacement reaction process that mediates the generation of a new input strand and a new weight strand.

[0087] Figure 5 The activation chain IN of this invention c A schematic diagram of the DNA strand replacement reaction process that mediates the generation of a new input strand and a new weight strand.

[0088] Figure 6 This is a schematic diagram of the DNA strand replacement reaction process in the catalytic amplification module of the present invention.

[0089] Figure 7 This is a schematic diagram of the DNA strand replacement reaction process of the competitive inhibition module of the present invention.

[0090] Figure 8 This is a schematic diagram of the DNA strand replacement process of the addition module when the tags match in this invention.

[0091] Figure 9 This is a schematic diagram of the DNA strand replacement process in the subtraction summation reaction when the labels are inconsistent, as described in this invention.

[0092] Figure 10 This is a diagram showing the diagnostic results of the colon cancer experiment of the present invention on the test set. Detailed Implementation

[0093] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0094] like Figure 1 As shown, a colorectal cancer diagnosis method based on an adaptive molecular LVQ neural network includes: determining the functions of the input layer, competition layer, and linear output layer of the LVQ neural network; designing basic functional modules corresponding to the input layer, competition layer, and linear output layer of the molecular LVQ neural network according to the DNA strand substitution reaction; adding a supervised learning module to determine the DNA strand structure and small pivot structure of the auxiliary substances and reactants in each module's reaction process; cascading the basic functional modules and the newly added supervised learning module into a complete adaptive LVQ neural network based on DNA strand substitution according to the structure of the LVQ neural network, and completing the initial concentration setting; obtaining gene expression data of colorectal cancer cases and benign control samples from the TCGA and GTEx databases, constructing a dataset after feature screening and standardization preprocessing; and using the constructed adaptive molecular LVQ neural network on the Visual DSD platform to diagnose benign or malignant colorectal cancer cases. This invention includes the following steps:

[0095] Step 1: Determine the functions of the input layer, competition layer, and linear output layer of the LVQ neural network.

[0096] The LVQ neural network architecture consists of three layers: an input layer, a competition layer, and a linear output layer. The connections between these layers and the mechanisms of neuron operation exhibit distinct structural characteristics. In terms of layer connections, the input layer and the competition layer are fully connected, enabling information exchange and distance calculation between the input feature vector and all neurons in the competition layer. The competition layer and the linear output layer are partially connected, with explicit numerical constraints and weight settings. The number of neurons in the competition layer is always no less than the number of neurons in the linear output layer. Each neuron in the competition layer is connected to only one neuron in the linear output layer, and the connection weight between them is fixed at 1. A single neuron in the linear output layer can connect to multiple neurons in the competition layer. This connection design provides a flexible mapping space for classifying the network. Regarding neuron state representation, the output states of neurons in both the competition layer and the linear output layer are represented in a binary format, taking only two states: 0 or 1, clearly representing the activation and inactivation states of neurons. When an external input pattern is passed into the network input layer in the form of a feature vector, the feature information is transmitted to the competition layer through a fully connected path. All neurons in the competition layer perform similarity calculations with the input feature vector, and finally select the neuron closest to the input pattern as the winning neuron. The winning neuron is activated and its state is set to 1, while the other neurons in the competition layer remain inactive and in a 0 state. Based on the fixed connection relationship between the competition layer and the linear output layer, the linear output layer neurons connected to the winning neuron are activated and their states are synchronously set to 1, while the other linear output layer neurons remain in a 0 state. The network completes the category determination of the input pattern through this binary state output, which is also the core decision-making process of the LVQ neural network to achieve pattern classification.

[0097] The core idea of ​​the LVQ neural network is as follows: First, determine the competing layer neuron that is closest to the input vector through calculation. Then, find the corresponding linear output layer neuron based on the connection relationship of this neuron. If the actual class of the input vector matches the class corresponding to the linear output layer neuron, adjust the weights of this competing layer neuron in the direction of the input vector; otherwise, adjust its weights in the opposite direction of the input vector. The specific execution steps of this algorithm are as follows: First, adjust the connection weights w between the input layer and the competing layer. ij The learning rate η (η>0) is initialized; then the input vector is imported into the network input layer, the distance between each competing layer neuron and the input vector is calculated, the competing layer neuron with the smallest distance is selected, and the class label corresponding to the linear output layer neuron connected to it is used as the model output result, denoted as label Y. i Let BY denote the true class label of the input vector. i If the model outputs class label Y i BY with real category tags i Consistency, i.e., Yi =BY i Then according to the formula Adjust the connection weights; if the two categories do not match, then follow the formula. Complete the weight update operation. Among other things, This represents the new weight value after the weight update. represents the weight values ​​before the weight update, and x represents the input feature value.

[0098] Step 2: Design basic functional modules of molecular LVQ neural networks based on DNA strand displacement reactions; add a supervised learning module based on the basic functional modules.

[0099] The DNA strand replacement reaction is achieved based on the principle of complementary base pairing. It involves the binding of recognition sites on single-stranded DNA molecules with exposed sites on double-stranded DNA molecules, triggering the strand replacement process and generating new single-stranded and double-stranded products. When the product strands still retain matching recognition sites and branch migration domains, the reaction can proceed in reverse, forming a reversible reaction. The DNA strand replacement reaction is characterized by spontaneous occurrence, dynamic regulation, and multi-level cascade.

[0100] The basic functional modules include a distance calculation module, a reversal summation module, an annihilation module, and a reporting module. The distance calculation module is connected to the reversal summation module, which in turn is connected to both the annihilation and reporting modules. The reporting module outputs the predicted label. These basic functional modules implement the decision-making process of the molecular LVQ neural network. The distance calculation module corresponds to the input layer, responsible for receiving and processing the input feature vector and calculating the similarity between the input and weights. The reversal summation module corresponds to the competition layer, implementing signal normalization and competitive selection to filter out the neurons that best match the input. The annihilation and reporting modules together correspond to the linear output layer, completing the final signal output and category determination, thus realizing the complete process from feature input to classification decision.

[0101] The supervised learning module includes a weighting activation module, a catalytic amplification module, a competition inhibition module, an addition module, and a subtraction summation module. The output chain of the report module in the basic functional module serves as the trigger signal for the weighting activation module, initiating the weight update process. The weighting activation module is sequentially connected to the catalytic amplification module and the competition inhibition module; these two modules work together to complete molecular multiplication operations. Subsequently, according to the weight update rules, the calculation results are fed into the addition module or the subtraction summation module, ultimately achieving dynamic calculation and updating of the weights. The supervised learning module implements the dynamic updating of weights in the molecular LVQ neural network, enabling supervised learning and adaptive optimization at the molecular level. The addition of the weighting activation module accurately determines the direction of weight updates. Combined with the catalytic amplification module and the competition inhibition module, and the addition or subtraction summation module, it achieves forward and reverse iterative correction of the weights in the LVQ neural network, completing the functional closed loop of the molecular LVQ neural network.

[0102] The chemical reaction expression for the distance calculation module is:

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] K f1 ≫K s ;

[0108] Among them, K f1 K is the rate constant of the annihilation reaction. s X is the rate constant of the summation reaction; ij The input chain represents the molecular signal carrying the i-th input feature, whose concentration is proportional to the input feature value, and serves as the original input for distance calculation; W ij Anh represents the weight chain, storing the weight values ​​of the j-th competing layer neuron for the i-th input feature; its concentration is proportional to the weight value. ij Represents the annihilation chain, implementing the input chain X. ij With weight chain W ij The annihilation reaction, in which This indicates that the product of the annihilation reaction is a waste chain and does not participate in the next step of the calculation; SumX ij The input summation gate annihilates the remaining input chain X. ij The concentration is converted into an input summation chain XS that can participate in subsequent summation operations. ij SumW ij The weight summation gate represents the annihilation of the remaining weight chain W. ijThe concentration is converted into a weighted summation chain WS that can participate in subsequent summation operations. ij Sum j Represents a common summation gate, completing the input summation chain XS. ij Weighted summation chain WS ij The concentration summation operation generates the distance factor D, representing the Manhattan distance. j ;waste represents a waste chain, an inactive byproduct chain that no longer participates in any subsequent reactions, and there is no need to distinguish between the waste chains in this invention; where i represents the i-th input layer neuron and j represents the j-th competing layer neuron.

[0109] The distance calculation module is used to implement the input chain X ij and weight chain W ij The Manhattan distance between chains is calculated using annihilation and summation reactions to solve for distances at the molecular level. First, input chain X. ij and weight chain W ij Through the annihilation chain Anh ij Perform a subtraction operation, and then process the remaining input chain X after the annihilation reaction ends. ij Or weighted chain W ij Concentration is calculated using the weighted summation gate SumW ij Input summation gate SumX ij Sum gate j The input chain X with the same subscript "j" ij and weight chain W ij The concentration is summed to the distance factor D j The concentration is used to realize Manhattan distance calculation;

[0110] The chemical reaction expression for negative weight processing in the distance calculation module is:

[0111] ;

[0112] ;

[0113] Among them, NW ij Represents a negative-weighted chain, where the concentration is a negative weight value; the negative-weighted summation gate SumNW ij negative weight chain NW ij The concentration is converted into a negative-weighted summation chain NXW that can participate in subsequent summation operations. ij Then, through the common summation gate Sum j The negative weight summation chain NXW ij The concentration and input summation chain XS ij The concentration is summed to the distance factor D j At the concentration.

[0114] However, for cases with negative weights, annihilation reactions are not feasible. Therefore, a numerical transformation scheme was designed based on the kinetic mechanism of DNA strand substitution reactions, introducing a negative-weighted strand (NW). ij And construct the corresponding DNA strand replacement reaction system, using input strand X ij With negative weighted chain NW ij The summation method achieves the equivalent transformation of negative weights into positive chain concentrations, allowing the originally negative weight parameters to participate in subsequent distance calculations as DNA chains with positive concentrations. This not only aligns with the inherent positive property of DNA chain concentrations but also ensures the numerical accuracy of distance calculations.

[0115] like Figure 2 As shown, the numerical transformation and calculation process of negative weights in the distance calculation module can be achieved through a specially designed DNA strand substitution reaction system. Assuming the input vector has an input value of A1 in a certain dimension, and the corresponding weight parameter is −A2 (where A1 and A2 are both positive values ​​greater than 0), under this condition, the annihilation reaction designed for positive weights in the distance calculation module will not occur. The input strand X in the reaction system... ij Without consumption, its remaining concentration remains at the initial A1, while the negative weight chain NW, specifically constructed for negative weights, remains unchanged. ij It exists in the reaction system at a concentration of A2. Then, it enters the stage of chain concentration conversion and summation. After a specific transformation reaction involving DNA strand substitution, strand X is introduced. ij The concentration A1 is completely transferred to the input summation chain XS ij Make the input summation chain XS ij The final concentration is A1; negative weighted chain NW ij The concentration A2 is then mapped entirely to the negative-weighted summation chain NXW. ij NXW, making the negative weighted summation chain ij The final concentration is A2. The concentrations of the two summing chains will further participate in the synthesis reaction of the distance factor, ultimately making the distance factor D, which characterizes the distance in this dimension,... j The concentration is the sum of the concentrations of the input summing chain and the negative weight summing chain, i.e., D. j =A1+A2, thus completing the distance calculation for this dimension under negative weights, which satisfies the inherent property of constant positive DNA chain concentration and ensures the numerical accuracy of distance calculation.

[0116] The chemical reaction expression for the inverse summation module is:

[0117] ;

[0118] Where k represents the k-th competing layer neuron, and j and k represent neurons in different competing layers; SRG kjThe RSG (Representative Signal Inversion Gate) is used to average the concentration of the distance factor of the j-th competing layer neuron to generate an inverted signal corresponding to the other k-th competing layer neuron; k The inversion signal summation gate sums the concentrations of all inversion signals associated with neuron k in the k-th competing layer; S k This represents a reversal signal;

[0119] The mathematical essence of the inverse summation module is to obtain a numerical value representing the degree of similarity between the input feature vector and each prototype vector by quantifying the spatial difference between them. A smaller distance indicates a higher degree of overlap in the feature dimensions, while a larger distance signifies significant feature differences. First, the distance factor D... j The concentration is determined by the signal inversion gate SRG. kj Average distribution to signal factor SF kj Then, the signal factor SF with the same subscript "k" kj Using the inverted signal summation gate RSG k Summing yields the inverted signal S k The concentration of the inversion summation module is such that j ≠ k. The inversion summation module can transform the neuron with the smallest distance factor concentration into a signal output with the largest inversion signal concentration. Through signal inversion and concentration summation, a mechanism of "the smaller the distance, the stronger the inversion signal" is established, so that in the subsequent inversion signal competitive annihilation process, the neuron with the smallest distance factor will eventually win and complete the output, thus completing the winner selection of the competitive layer.

[0120] The chemical reaction expressions for the annihilation module and the reporting module are as follows:

[0121] ;

[0122] ;

[0123] Where Kf2 is the rate constant of the annihilation module, and LAnh jk Represents the annihilation chain; K s Let K be the rate constant of the reporting module, and K f2 ≫K s S j S represents the inverted signal of the j-th competing layer neuron. k Re represents the inverted signal of the k-th competing layer neuron; ji The representative report gate outputs the inverted signal remaining after annihilation as a report, Y. i This represents the output label.

[0124] When the output label Y i When it matches the original label, i.e., Y i =BY i New weights Perform iterations; for equation (1-η)w ij_old Treating the coefficient (1-η) as a whole, it can be implemented by the multiplication module. Similarly, ηx can also be implemented by the multiplication module. Then, the summation module can be used to implement (1-η)w. ij_old Summation with ηx. When the output label differs from the original label, i.e., Y... i ≠BY i New weights Perform iterations for equation (1+η)w ij_old Treating the coefficient (1+η) as a whole, it can also be implemented by the multiplication module, and then (1+η)w is implemented by the annihilation module. ij_old Subtraction with ηx. In summary, the new weight w ij _ new Solving this problem, at the DNA level, weight updates can be achieved using only a multiplication module, an annihilation module, and a summation module. However, to align with the iterative update logic of the overall LVQ neural network, after the molecular LVQ neural network outputs its results, it's necessary to first determine the formula followed by the weight updates; therefore, an additional weight activation module is required.

[0125] The annihilation and reporting modules work by mutually annihilating the inverted signals pairwise and selecting the inverted signal with the highest concentration for reporting. In the annihilation module, the inverted signal S... j Separately and different inversion signals are transmitted through the annihilation chain LAnh jk The process involves pairwise mutual annihilation until the reaction stabilizes, identifying the "winner" with remaining concentration. The reporting module then transmits the inversion signal S. j Through the Report Gate Re ji The output is the label Y. i The fluorophore and quencher-labeled chain in the report gate cause fluorescence enhancement. The reaction result is obtained by detecting the fluorescence level of the residual DNA species. This design ensures that the highest concentration of the inversion signal is uniquely retained, enabling precise selection of the winning single neuron in the competitive layer. The classification result is output intuitively through the fluorescence signal, ensuring that the classification judgment is unique, stable, and detectable, effectively improving the accuracy and reliability of molecular neural network classification.

[0126] The chemical reaction expression for the weighting activation module is:

[0127] When the output label Y i When it matches the original label, i.e., Y i =BY i

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] When the output label is inconsistent with the original label, i.e., Y i ≠BY i

[0133] ;

[0134] ;

[0135] ;

[0136] ;

[0137] Among them, BY i BY k Represents the original class label chain, storing the pre-defined true class signal of the sample, used to compare it with the predicted label to determine whether the classification is correct; FG ii FG ik The IN gate represents the release gate, acting as a trigger switch for weight updates. It selectively releases the corresponding activation chain based on whether the predicted label matches the true label. X IN C Representing the activation chain, activation chain INx triggers a positive weight update when the classification is correct, and activation chain INc triggers a negative weight update when the classification is incorrect. XF X XF C Representing the catalytic chain, the activating chain provides the reaction motive force, accelerates the generation of new input chains and new weight chains, and improves update efficiency. GX 2j CX 2j The representative input substrate provides the molecular structure and concentration basis required to generate the new input chain, ensuring that the new input signal is consistent with the original input; GW 1j CW 1j The WG represents the weighted substrate, providing the molecular structure and concentration basis required to generate new weighted chains, ensuring the accuracy of weight updates. 2j NG 2j The WG gate represents a new input summation gate, which transforms the new input substrate into a new input chain that can participate in the computation, thus reconstructing the input signal; 1j NG 1j Represents a new weighted summation gate, which transforms the weighted substrate into a new weight chain that can participate in the computation, thus reconstructing the weighted signal; SX 2j LX 2j Represents a new input chain, generated from the corresponding substrate and a summation gate, with concentrations equal to those in the basic module's input chain, used for a new round of weight calculations; LW 1j SW 1jRepresents the new weight chain; generated from the corresponding substrate and a summation gate, with concentrations equal to the weight chain of the basic module, used to complete weight iteration updates; XP 2j WP 1j CP 2j NP 1j As intermediate products, they react with the new input summation gate and the new weight summation gate to obtain the new weight chain and the new input chain, making the concentrations of the new weight chain and the new input chain equal to the concentrations of the input substrate and the weight substrate. From this module onwards, the weight update process begins. The new weight chain, new input chain, new input summation gate, and new weight summation gate are only distinguished from the basic functional modules in name; their actual concentrations are exactly the same as the corresponding chains and gates in the basic modules, ensuring consistent computational parameters and an accurate and stable update process.

[0138] The weight update activation module is the core trigger of the molecular LVQ neural network weight update system. Its key function is to release the corresponding activation chain after the network outputs the sample classification result, precisely determining the match between the classification result and the sample's true class. This drives the targeted generation of subsequent new input chains and weight chains, providing suitable molecular reaction substrates for subsequent weight update operations. When the network outputs class label Y... i BY with the sample's true class label i Consistency, i.e., Y i =BY i This indicates that when the samples are correctly classified, the output chain Y in the system... i BY with the original class tag chain i They will work together to release gate FG ii It releases the activating strand IN through a specific DNA strand displacement reaction. x When the network output class label Y i BY with the sample's true class label k Inconsistent, i.e., Y i ≠BY k This indicates that when a sample is misclassified, the molecular regulatory logic of the reaction system changes accordingly: the output chain Y... i BY with the original class tag chain k Combined and acting on the release gate FG ik The activation chain IN is released through a chain displacement reaction. c Its chain substitution reaction process is as follows: Figure 3 As shown.

[0139] Activation Chain IN x It will act as a reaction trigger signal to initiate the catalytic reaction. With summation reaction , A new input chain LX is generated through the synergistic effect of the dual reactions. 2j With the new weighted chain LW1j Under the regulation of catalytic reaction, the new input chain LX ultimately generated in the reaction system... 2j Concentration and substrate GX ij Concentrations are completely identical, new weighted chain LW 1j Concentration and substrate GW ij The concentrations are completely identical, and both concentrations are different from the original input chain X. ij Original weight chain W ij The initial concentrations are kept matched to ensure the accuracy of the numerical basis for positive weight updates, and the chain substitution reaction process is as follows: Figure 4 As shown.

[0140] With activation chain IN x The mechanisms of action are similar, activating the IN chain. c It will act as a dedicated trigger signal, sequentially initiating the corresponding catalytic and summation reactions, thereby generating a new input chain SX. 2j With the new weighted chain SW 1j During this process, the new input chain SX 2j Concentration strictly matched to substrate CX 2j Concentration, new weighted chain SW 1j Concentration strictly matched to substrate CW 1j The concentrations of both molecules are consistent with the corresponding input parameters and weight parameters required in the weight inverse update process, providing an accurate molecular concentration characterization for subsequent weight correction calculations under misclassification. The chain substitution reaction process is as follows: Figure 5 As shown.

[0141] The catalytic amplification module is responsible for amplifying the reaction signal and initially generating the product. The chemical reaction expression for the catalytic amplification module is as follows:

[0142] ;

[0143] ;

[0144] ;

[0145] ;

[0146] Among them, the representative chain K is used. ij Unified representation of the new input chain LX 2j SX 2j and the new weighted chain LW 1j SW 1j These chains have similar structures, differing only in their structural domains, while maintaining a consistent identification domain; C i1 C i2 C i3 Represents auxiliary chain; SPi1 SP i2 SP i3 SP i4 SP i5 SP i6 B represents an intermediate product; ij Represents an amplification chain; Y ij This represents the output product.

[0147] A catalytic amplification module refers to a module where the final product concentration is theoretically infinite, such as... Figure 6 As shown, this represents chain K. ij With auxiliary chain C i1 A reversible reaction occurs, producing the intermediate product SP. i1 With SP i2 Among them, the intermediate product SP i1 With auxiliary chain C i2 An irreversible forward reaction occurs, which can drive the representative chain K. ij With auxiliary chain C i1 The equilibrium of the reversible reaction shifts to the right. Simultaneously, the intermediate product SP... i2 With amplification chain B ij The intermediate product SP is generated through a reversible reaction. i3 With SP i6 Intermediate product SP i6 Then with auxiliary chain C i3 An irreversible reaction occurs, regenerating the original representative chain K. ij and amplification chain B ij And generate an output product Y. ij In this catalytic amplification module, the output product Y ij The theoretical final concentration is equal to the initial concentration of the auxiliary chain.

[0148] The competitive inhibition module is responsible for regulating the reaction process and calibrating the concentration ratio. The chemical reaction expression for the competitive inhibition module is as follows:

[0149] ;

[0150] ;

[0151] ;

[0152] ;

[0153] Among them, D i1 D i2 D i3 Represents auxiliary chain; SP i7 SP i8 SP i9 SPi10 SP i11 SP i12 SP i13 B0 represents an intermediate product; ij Represents the inhibitory chain.

[0154] The competition suppression module refers to the suppression chain B0. ij Suppressing the formation of final products in the catalytic amplification module, such as Figure 7 As shown, the inhibition chain B0 ij With auxiliary chain D i1 The intermediate product SP is generated reversibly through the reaction. i7 and SP i8 intermediate product SP i7 With auxiliary chain D i2 Irreversible formation of intermediate product SP i10 and SP i11 Amplifying chain B ij With intermediate product SP i8 Reversible generation of intermediate product SP i9 and SP i12 Then, from the intermediate product SP i12 With auxiliary chain D i3 The irreversible reaction regenerates the inhibitory chain B0 ij and a waste chain i2 The catalytic amplification module and the competitive inhibition module together constitute the multiplicative module, the core of which lies in the inhibition chain B0. ij and auxiliary chain D i1 The intermediate product SP generated by the reaction i8 And representing chain K ij With auxiliary chain C i1 The intermediate product SP generated by the reaction i2 Simultaneously with amplification chain B ij Reacting at the same reaction rate, while the intermediate product SP... i2 Concentration and chain K ij Concentration-dependent, intermediate product SP i8 Concentration and inhibitory chain B0 ij The concentration is related to the final output product Y. ij Concentration and chain K ij and B ij It is positively correlated with the inhibitory chain B0. ij It is negatively correlated, that is, Y ij =K ij *B ij / B0 ij It should be noted that the auxiliary chain C i1 C i2 C i3 and auxiliary chain D i1 Di2 D i3 Its theoretical initial concentration is considered to be infinite; and the higher the auxiliary chain concentration, the higher the output product Y. ij The higher the accuracy of concentration measurement, the better.

[0155] The catalytic amplification module and the competitive inhibition module work together synergistically to complete the molecular-level operations of the multiplication module. After a series of chain substitution reactions by this module, the final output product Y is generated in the system. ij Its concentration value can be obtained through the formula Y=(K ij *B ij ) / B0 ij Quantitative calculations are performed to achieve multiplication at the molecular level, providing accurate concentration characterization for subsequent numerical iterations of weight updates.

[0156] For the weight update formula ( or The value of x in the new input chain LX is equal to the value of x in the new input chain LX. 2j or SX 2j concentration, w ij_old The value is equal to the new weight chain LW. 1j or SW 1j The concentration, i.e., the representative chain K of the multiplication module. ij The concentration, and the values ​​of coefficients 1-η, η, and 1+η are equal to those of amplification chain B. ij With inhibitory chain B0 ij The concentration ratio, i.e., B ij / B0 ij This achieves the multiplication part in the weight update formula. For a specific input pattern, the weight update method is as follows: , will (1-η)w ij_old Consider as output product Y 1j Treating ηx as the output product Y 2j Then, the summation module is used to output product Y. 1j and Y 2j Summing yields the new weight w ij_new If the weight update method is as follows: Then (1+η)w ij_old View as Y 1j Treating ηx as Y 2j Then, the subtraction module will be used to subtract Y. 1j and Y 2j Subtracting the two values ​​yields the new weight w. ij_new .

[0157] The chemical reaction expression for the addition module is:

[0158] ;

[0159] ;

[0160] ;

[0161] Among them, Y 1j Y 2j This represents the output product of the multiplication module, which participates in the subsequent addition or subtraction summation module; USumW 1j USumX 2j Represents a summation gate chain; DP 1j and DP 2j Represents intermediate products; TSum j Represents a common summation gate chain; Z j The output chain represents the new weight value, and its concentration is the new weight value.

[0162] The addition module refers to the module that, when the output result matches the original label, w ij_new =Y 1j +Y 2j Chain Y 1j Using the summation gate chain USumW 1j Y 1j The concentration of DP is converted into the intermediate product. 1j The concentration of chain Y 2j Using the summation gate chain USumX 2j Y 2j The concentration of DP is converted into the intermediate product. 2j The concentration of the intermediate product DP 1j and DP 2j Through the common summation gate chain TSum j Sum the concentrations of the two to chain Z. j Above, therefore chain Z j The concentration is the new weight value obtained from equation (4-3).

[0163] The chemical reaction expression for the subtraction summation module is:

[0164] ;

[0165] ;

[0166] ;

[0167] Among them, NUSumW 1j ,NTSumW 2j NTSum represents a summation gate chain. 1j ,NTSum 2j Represents a common summation gate chain; Z 1j Z 2jRepresents the output chain, output chain Z 1j The concentration is the new positive weight value, and the output chain Z... 2j The concentration is then the new negative weight value.

[0168] The subtraction summation module refers to the module that performs subtraction summation when the output result is inconsistent with the original label. ij_new =Y 1j -Y 2j Chain Y 1j With chain Y 2j Participating in the annihilation reaction, when Y 1j >Y 2j At that time, Y 1j There will be a residual concentration, and the value of the residual concentration is equal to Y. 1j -Y 2j It uses the summation gate NUSumW 1j And the common summation gate NTSum 1j Generate chain Z 1j Chain Z 1j The concentration of Y is equal to 1j -Y 2j And when Y 2j >Y 1j At that time, Y 2j There will be residual concentration, Y 1j When the concentration of Y drops to 0, the remaining concentration is equal to the value of Y. 2j -Y 1j Then it passes through the summation gate NUSumW 2j And the common summation gate NTSum 2j Generate chain Z 2j Then Z 2j The concentration of Y is equal to 2j -Y 1j Here, chain Z 2j The output represents a negative value.

[0169] When the output result is consistent with the original label, the weight update is equivalent to w. ij_new =Y 1j +Y 2j ,like Figure 8 As shown, the output product Y 1j Using the summation gate chain USumW 1j Output product Y 1j The concentration of DP is converted into the intermediate product. 1j The concentration of the output product Y 2j Using the summation gate chain USumX 2j Output product Y 2j The concentration of DP is converted into the intermediate product. 2j The concentration of the intermediate product DP 1j and DP 2jThrough the common summation gate chain TSum j Sum the concentrations of the two into the output chain Z. j Therefore, the output chain Z is as follows. j The concentration is the new weight value obtained by weight update.

[0170] Similarly, when the output result is inconsistent with the original label, the weight update is equivalent to w ij_new =Y 1j -Y 2j ,like Figure 9 As shown, the output product Y 1j With output product Y 2j Participating in the annihilation reaction, when the output product Y 1j >Y 2j At that time, the output product Y 1j There will be a residual concentration, and the value of the residual concentration is equal to Y. 1j -Y 2j It uses the summation gate NUSumW 1j And the common summation gate NTSum 1j Generate chain Z 1j Output chain Z 1j The concentration of Y is equal to 1j -Y 2j And when Y 2j >Y 1j At that time, Y 2j There will be residual concentration, Y 1j When the concentration of Y drops to 0, the remaining concentration is equal to the value of Y. 2j -Y 1j Then it passes through the summation gate NUSumW 2j And the common summation gate NTSum 2j Generate output chain Z 2j Then Z 2j The concentration of Y is equal to 2j -Y 1j Output chain Z here 2j The output represents a negative value.

[0171] The annihilation reactions involved in some distance calculation modules, annihilation modules, and some subtraction summation modules utilize the base point G, which has 7 nucleotides. The base point V involved in the weighting activation module has 9 nucleotides, and the remaining base points have 5 nucleotides. By setting base point nucleotides of different lengths, the reaction rate and specificity of each module can be precisely controlled, so that the overall circuit operates in a coordinated manner and outputs accurately.

[0172] Step 3: Determine the DNA chain structure and small pivot structure of the auxiliary substances and reactants in the chemical reaction process of the basic functional module and the supervised learning module.

[0173] The number of DNA strands and the input values ​​are determined by the structure of the constructed molecular LVQ neural network, while the base sequence is generated using Visual DSD.

[0174] The input chain X ij There are two groups, one with 8 lines, for a total of 16 lines, which are the input chains X. 11 X 12 X 13 X 14 X 15 X 16 X 17 X 18 X 21 X 22 X 23 X 24 X 25 X 26 X 27 X 28 In the same input mode, the input chain X 11 -X 18 With X 21 -X 28 The representative features and eigenvalues ​​are all equal, and their structures are as follows:<G^ X11 H^> ,<G^ X12 H^> ,<G^ X13 H^> ,<G^ X14 H^> ,<G^ X15 H^> ,<G^ X16 H^> ,<G^ X17 H^> ,<G^ X18 H^> ,<G^ X21 H^> ,<G^X22 H^> ,<G^ X23 H^> ,<G^ X24 H^> ,<G^ X25 H^> ,<G^ X26 H^> ,<G^ X27 H^> ,<G^ X28 H^> Where X11-X28 represent the names of the branch transition structure domains of the 16 input chains, G and H represent the names of the small pivot domains, ^ represents a small pivot domain, and <> represents a single chain. Similarly, the weight chain W... ij There are two groups, one group with 8 items, for a total of 16 items, namely W 11 W 12 W 13 W 14 W 15 W 16 W 17 W 18 W 21 W 22 W 23 W 24 W 25 W 26 W 27 W 28Their structures are respectively<G^ W11 H^> ,<G^W12 H^> ,<G^ W13 H^> ,<G^ W14 H^> ,<G^ W15 H^> ,<G^ W16 H^> ,<G^ W17 H^> ,<G^ W18 H^> ,<G^ W21 H^> ,<G^ W22 H^> ,<G^ W23 H^> ,<G^ W24 H^> ,<G^ W25 H^> ,<G^ W26 H^> ,<G^ W27 H^> ,<G^ W28 H^> Among them, W11-W28 represent the names of the branch migration structure domains of the 16 weight chains; annihilation chain Anh ij The number of entries is 16, namely Anh 11 Anh 12 Anh 13 Anh 14 Anh 15 Anh 16 Anh 17 Anh 18 Anh 21 Anh 22 Anh 23 Anh 24 Anh 25 Anh 26 Anh 27 Anh 28 Their structures are {G^*}[X11 W11*] and {G^*}[X11 W11*], respectively.<G^*> {G^*}[X12 W12*]<G^*> {G^*}[X13 W13*]<G^*> {G^*}[X14 W14*]<G^*> {G^*}[X15 W15*]<G^*> {G^*}[X16 W16*]<G^*> {G^*}[X17 W17*]<G^*> {G^*}[X18 W18*]<G^*> {G^*}[X21W21*]<G^*> {G^*}[X22 W22*]<G^*> {G^*}[X23 W23*]<G^*> {G^*}[X24 W24*]<G^*> {G^*}[X25 W25*]<G^*> {G^*}[X26 W26*]<G^*> {G^*}[X27 W27*]<G^*> {G^*}[X28 W28*]<G^*> Where * represents complementarity, {} represents a single chain, and [] represents a double chain; input summation gate SumX ij There are 16 in total, namely SumX 11 SumX 12 SumX 13 SumX 14SumX 15 SumX 16 SumX 17 SumX 18 SumX 21 SumX 22 SumX 23 SumX 24 SumX 25 SumX 26 SumX 27 SumX 28 Their structures are respectively <d1>[T^ X11]{H^*}、 <d1>[T^ X12]{H^*}、 <d1>[T^ X13]{H^*}、 <d1>[T^ X14]{H^*}、 <d1>[T^ X15]{H^*}、 <d1>[T^ X16]{H^*}、 <d1>[T^X17]{H^*}、 <d1>[T^ X18]{H^*}、 <d2>[T^ X21]{H^*}、 <d2>[T^ X22]{H^*}、 <d2>[T^ X23]{H^*}、 <d2>[T^ X24]{H^*}、 <d2>[T^ X25]{H^*}、 <d2>[T^ X26]{H^*}、 <d2>[T^ X27]{H^*}、 <d2>[T^ X28]{H^*}; where D1 and D2 represent the names of the branch-transfer structure domains of the 16 input summation gates, and T represents the name of the small pivot domain; the weighted summation gate SumW ij There are 16 in total, namely SumW 11 SumW 12 SumW 13 SumW 14 SumW 15 SumW 16 SumW 17 SumW 18 SumW 21 SumW 22 SumW 23 SumW 24 SumW 25 SumW 26 SumW 27 SumW 28 Their structures are respectively <d1>[T^ W11]{H^*}、 <d1>[T^ W12]{H^*}、 <d1>[T^ W13]{H^*}、 <d1>[T^W14]{H^*}、 <d1>[T^ W15]{H^*}、 <d1>[T^ W16]{H^*}、 <d1>[T^ W17]{H^*}、 <d1>[T^ W18]{H^*}、 <d2>[T^ W21]{H^*}、 <d2>[T^ W22]{H^*}、 <d2>[T^ W23]{H^*}、 <d2>[T^ W24]{H^*}、 <d2>[T^ W25]{H^*}、 <d2>[T^ W26]{H^*}、 <d2>[T^ W27]{H^*}、 <d2>[T^ W28]{H^*};where D1 and D2 represent distance factors D j The branch migration structure name, T represents the name of the minor pivot field; the common summation gate Sum j There are two lines, Sum1 and Sum2, with the following structures:<N^> [D1]<N^> {T^*} and<N^> [D2]<N^> {T^*}, where N represents the name of the minor pivot field.

[0175] Signal Reversal Gate (SRG) kj The number is 2, namely SRG 12 and SRG 21 Their structures are respectively<V^ L1> [N^D2]{N^*} and<V^ L2> [N^D1]{N^*}, where L1 and L2 represent the names of the branch transition structure domains of the inverted signal; the inverted signal summing gate RSG k The number of elements is 2, namely RSG1 and RSG2, and their structures are respectively<H^ S1^> [V^ L1]{N^*} and<H^S2^> [V^ L2]{N^*}, where S1, S2 and V are the names of the small pivot domains.

[0176] Annihilation Chain LAnh jk The number is 1, which is LAnh 12 Its structure is<V^*> [S1^* S2^]{V^*};Report gate Re ji The number of elements is 2, and their structures are {H^*}[S1^V^] .<B1^> and {H^*}[S2^ V^]<B2^> Where B1 and B2 are the names of the small pivot fields.

[0177] Primitive class tag chain BY i There are two of them, BY1 and BY2, and their structures are as follows:<BS1^ V^ BB1^> and<BS2^ V^ BB2^> BS1, BS2, BB1, and BB2 are the names of the small pivot domains; release gate FG ik The number of elements is 4, namely FG11, FG12, FG21 and FG22, and their structures are {S1^*} respectively. <x>[V^ B1^ BS1^ V^]{BB1^*}、{S1^*} <c>[V^ B1^ BS2^ V^]{BB2^*}、{S2^*} <c>[V^ B2^ BS1^ V^]{BB1^*}、{S2^*} <x>[V^ B2^ BS2^V^]{BB2^*}.

[0178] Input catalytic substrate GX 2j and CX 2j The number of each is 8, namely GX 21 GX 22 GX 23 GX 24 GX 25 GX 26 GX 27 GX 28 and CX 21 CX 22 CX 23 CX 24 CX 25 CX 26 CX 27 CX 28 Their structures are {V^*}[XV^] and {V^], respectively.<BB21 G^> {V^*}[XV^]<BB22 G^> {V^*}[XV^]<BB23 G^> {V^*}[XV^]<BB24 G^> {V^*}[XV^]<BB25 G^> {V^*}[XV^]<BB26 G^> {V^*}[XV^]<BB27 G^> {V^*}[XV^]<BB28 G^> and {V^*}[CV^]<CB21 G^> {V^*}[CV^]<CB22 G^> {V^*}[CV^]<CB23 G^> {V^*}[CV^]<CB24G^> {V^*}[CV^]<CB25 G^> {V^*}[CV^]<CB26 G^> {V^*}[CV^]<CB27 G^> {V^*}[CV^]<CB28 G^> ; weighted catalytic substrate GW 2j and CW 2j The number of each is 8, namely GW 11 GW 12 GW 13 GW 14 GW 15 GW 16 GW 17 GW 18 and CW 11 CW 12 CW 13 CW 14 CW 15 CW 16 CW 17 CW 18 Their structures are {V^*}[XV^] and {V^], respectively.<BB11G^> {V^*}[XV^]<BB12 G^> {V^*}[XV^]<BB13 G^> {V^*}[XV^]<BB14 G^> {V^*}[XV^]<BB15 G^> {V^*}[XV^]<BB16 G^> {V^*}[XV^]<BB17 G^> {V^*}[XV^]<BB18 G^> and {V^*}[CV^]<CB11 G^> {V^*}[CV^]<CB12 G^> {V^*}[CV^]<CB13 G^> {V^*}[CV^]<CB14 G^> {V^*}[CV^]<CB15 G^> {V^*}[CV^]<CB16 G^> {V^*}[CV^]<CB17 G^> {V^*}[CV^]<CB18 G^> ;

[0179] New Input Summation Gate WG 2j and NG 2j The number of each is 8, namely WG 21 WG 22 WG 23 WG 24 WG 25 WG 26 WG 27 WG 28 and NG 21 NG 22 NG 23 NG 24 NG 25 NG 26 NG 27 NG 28 Their structures are {V^*}[BB21 G^] and {V^*}, respectively. <c21>、{V^*}[BB22 G^] <c22>、{V^*}[BB23 G^] <c23>、{V^*}[BB24 G^] <c24>、{V^*}[BB25 G^] <c25>、{V^*}[BB26 G^] <c26>、{V^*}[BB27 G^] <c27>、{V^*}[BB28 G^] <c28>and {V^*}[CB21G^] <c21>、{V^*}[CB22 G^] <c22>、{V^*}[CB23 G^] <c23>、{V^*}[CB24 G^] <c24>、{V^*}[CB25G^] <c25>,{V^*}[CB26 G^] <c26>,{V^*}[CB27 G^] <c27>、{V^*}[CB28 G^] <c28>New weighted summation gate WG 1j and NG 1j The number of each is 8, namely WG 11 WG 12 WG 13 WG 14 WG 15 WG 16 WG 17 WG 18 and NG 11 NG 12 NG 13 NG 14 NG 15 NG 16 NG 17 NG 18 Their structures are {V^*}[BB11 G^] and {V^*}, respectively. <w11>,{V^*}[BB12G^] <w12>,{V^*}[BB13 G^] <w13>、{V^*}[BB14 G^] <w14>、{V^*}[BB15 G^] <w15>、{V^*}[BB16 G^] <w16>、{V^*}[BB17 G^] <w17>,{V^*}[BB18 G^] <w18>and {V^*}[CB11 G^] <w11>,{V^*}[CB12 G^] <w12>、{V^*}[CB13 G^] <w13>、{V^*}[CB14 G^] <w14>,{V^*}[CB15 G^] <w15>、{V^*}[CB16 G^] <w16>,{V^*}[CB17 G^] <w17>,{V^*}[CB18 G^] <w18>.

[0180] Auxiliary chain C i1 There are 16 elements, namely C111, C121, C131, C141, C151, C161, C171, C181, C211, C221, C231, C241, C251, C261, C271, and C281, with the structure {G^*}[C11 G^]:[XR11 Q^]<BB11 G^ XL11 G^ YL11 G^> {G^*}[C12 G^]:[XR12 Q^]<BB11 G^ XL12 G^ YL12 G^> {G^*}[C13 G^]:[XR13 Q^]<BB13 G^ XL13 G^ YL13 G^> {G^*}[C14 G^]:[XR14 Q^]<BB14 G^ XL14 G^ YL14 G^> {G^*}[C15 G^]:[XR15 Q^]<BB15 G^ XL15 G^ YL15 G^> {G^*}[C16G^]:[XR16 Q^]<BB26 G^ XL16 G^ YL16 G^> {G^*}[C17 G^]:[XR17 Q^]<BB17 G^ XL17 G^ YL17 G^> {G^*}[C18 G^]:[XR18 Q^]<BB18 G^ XL18 G^ YL18 G^> ;{G^*}[C21 G^]:[XR21 Q^]<BB21 G^ XL21 G^ YL21 G^> {G^*}[C22 G^]:[XR22 Q^]<BB21 G^ XL22 G^YL22 G^> {G^*}[C23 G^]:[XR23 Q^]<BB23 G^ XL23 G^ YL23 G^> {G^*}[C24 G^]:[XR24Q^]<BB24 G^ XL24 G^ YL24 G^> {G^*}[C25 G^]:[XR25 Q^]<BB25 G^ XL25 G^ YL25 G^> {G^*}[C26 G^]:[XR26 Q^]<BB26 G^ XL26 G^ YL26 G^> {G^*}[C27 G^]:[XR27 Q^]<BB27 G^ XL27 G^ YL27 G^> {G^*}[C28 G^]:[XR28 Q^]<BB28 G^ XL28 G^ YL28 G^> .

[0181] Auxiliary chain C i2 There are 16 of them, namely C112, C122, C132, C142, C152, C162, C172, C182, C212, C222, C232, C242, C252, C262, C272, and C282, with structures of [C11]{G^*}, [C12]{G^*}, [C13]{G^*}, and [C14]{ G^*}、[C15]{G^*}、[C16]{G^*}、[C17]{G^*}、[C18]{G^*}、[C21]{G^*}、[C22]{G^ *}, [C23]{G^*}, [C24]{G^*}, [C25]{G^*}, [C26]{G^*}, [C27]{G^*}, [C28]{G^*}

[0182] Auxiliary chain C i3 There are 16 elements, namely C113, C123, C133, C143, C153, C163, C173, C183, C213, C223, C233, C243, C253, C263, C273, and C283, with the structure {Q^*}[B11 G^] respectively. <c11>:[XL11G^] <xr11>:[YL11 G^]<YR11 H^>、{Q^*}[B12 G^] <c12>:[XL12 G^] <xr12>:[YL12 G^]<YR12 H^>、{Q^*}[B13 G^] <c13>:[XL13 G^] <xr13>:[YL13 G^]<YR13 H^> ,{Q^*}[B14 G^] <c14>:[XL14 G^] <xr14>:[YL14 G^]<YR14 H^> ,{Q^*}[B15 G^] <c15>:[XL15 G^] <xr15>:[YL15 G^]<YR15 H^>、{Q^*}[B16 G^] <c16>:[XL16 G^] <xr16>:[YL16 G^]<YR16 H^>、{Q^*}[B17 G^] <c17>:[XL17 G^] <xr17>:[YL17 G^]<YR17 H^>、{Q^*}[B18 G^] <c18>:[XL18G^] <xr18>:[YL18 G^]<YR18 H^>、{Q^*}[B21 G^] <c21>:[XL21 G^] <xr21>:[YL21 G^]<YR21 H^> ,{Q^*}[B22 G^] <c22>:[XL22 G^] <xr22>:[YL22 G^]<YR22 H^>、{Q^*}[B23 G^] <c23>:[XL23 G^] <xr23>:[YL23 G^]<YR23 H^>、{Q^*}[B24 G^] <c24>:[XL24 G^] <xr24>:[YL24 G^]<YR24 H^>、{Q^*}[B25 G^] <c25>:[XL25 G^] <xr25>:[YL25 G^]<YR25 H^> ,{Q^*}[B26 G^] <c26>:[XL26 G^] <xr26>:[YL26 G^]<YR26 H^>、{Q^*}[B27 G^] <c27>:[XL27G^] <xr27>:[YL27 G^]<YR27 H^>、{Q^*}[B28 G^] <c28>:[XL28 G^] <xr28>[YL28 G^]<YR28 H^> .

[0183] Amplification chain B ij There are 16 of them, namely C11, C12, C13, C14, C15, C16, C17, C18, C21, C22, C23, C24, C25, C26, C27, and C28, and their structures are as follows:<XL11 G^ XR11> ,<XL12 G^ XR12> ,<XL13 G^XR13> ,<XL14 G^ XR14> ,<XL15 G^ XR15> ,<XL16 G^ XR16> ,<XL17 G^ XR17> ,<XL18 G^XR18> ,<XL21 G^ XR21> ,<XL22 G^ XR22> ,<XL23 G^ XR23> ,<XL24 G^ XR24> ,<XL25 G^XR25> ,<XL26 G^ XR26> ,<XL27 G^ XR27> ,<XL28 G^ XR28> .

[0184] Auxiliary chain D i1 There are 16 elements, namely D111, D121, D131, D141, D151, D161, D171, D181, D211, D221, D231, D241, D251, D261, D271, and D281, with the structure {G^*}[B0R G^]:[XR11 Q^] respectively.<B0L11 G^> {G^*}[B0R G^]:[XR12 Q^]<B0L12 G^> {G^*}[B0R G^]:[XR13 Q^]<B0L13 G^> {G^*}[B0R G^]:[XR14 Q^]<B0L14 G^> {G^*}[B0R G^]:[XR15 Q^]<B0L15 G^> {G^*}[B0R G^]:[XR16 Q^]<B0L16 G^> {G^*}[B0R G^]:[XR17 Q^]<B0L17 G^> {G^*}[B0R G^]:[XR18 Q^]<B0L18 G^> {G^*}[B0R G^]:[XR21 Q^]<B0L21 G^> {G^*}[B0R G^]:[XR22 Q^]<B0L22 G^> {G^*}[B0R G^]:[XR23 Q^]<B0L23 G^> {G^*}[B0R G^]:[XR24 Q^]<B0L24 G^> {G^*}[B0R G^]:[XR25 Q^]<B0L25 G^> {G^*}[B0R G^]:[XR26 Q^]<B0L26 G^> {G^*}[B0R G^]:[XR27 Q^]<B0L27 G^> {G^*}[B0R G^]:[XR28 Q^]<B0L28 G^> .

[0185] Auxiliary chain D i2 There are 16 numbers, namely D112, D122, D132, D142, D152, D162, D172, D182, D212, D222, D232, D242, D252, D262, D272, and D282, with structures of [B0R11]{G^*}, [B0R12]{G^*}, [B0R13]{G^*}, [B0R14]{G^*}, and [B0 R15]{G^*}、[B0R16]{G^*}、[B0R17]{G^*}、[B0R18]{G^*}、[B0R21]{G^*}、[B0R22]{G^*}、[ B0R23]{G^*}, [B0R24]{G^*}, [B0R25]{G^*}, [B0R26]{G^*}, [B0R27]{G^*}, [B0R28]{G^*}.

[0186] Auxiliary chain D i3 There are 16 elements, namely D113, D123, D133, D143, D153, D163, D173, D183, D213, D223, D233, D243, D253, D263, D273, and D283, with the structure {Q^*}[B0L11 G^] respectively. <b0r11>,{Q^*}[B0L12 G^] <b0r12>,{Q^*}[B0L13 G^] <b0r13>,{Q^*}[B0L14 G^] <b0r14>,{Q^*}[B0L15 G^] <b0r15>,{Q^*}[B0L16 G^] <b0r16>,{Q^*}[B0L17 G^] <b0r17>,{Q^*}[B0L18 G^] <b0r18>,{Q^*}[B0L21 G^] <b0r21>,{Q^*}[B0L22 G^] <b0r22>、{Q^*}[B0L23 G^] <b0r23>,{Q^*}[B0L24 G^] <b0r24>,{Q^*}[B0L25 G^] <b0r25>,{Q^*}[B0L26 G^] <b0r26>、{Q^*}[B0L27 G^] <b0r27>,{Q^*}[B0L28 G^] <b0r28>.

[0187] Summation gate chain USumW 1j USumX 2j The number of each is 8, namely USumW 11 USumW 12 USumW 13 USumW 14 USumW 15 USumW 16 USumW 17 USumW 18 USumX 21 USumX 22 USumX 23 USumX 24 USumX 25 USumX 26 USumX 27 USumX 28 Their structures are respectively <a1>[T^ YR21]{H^*}、 <a2>[T^ YR22]{H^*}、 <a3>[T^ YR23]{H^*}、 <a4>[T^ YR24]{H^*}、 <a5>[T^ YR25]{H^*}、 <a6>[T^ YR26]{H^*}、 <a7>[T^ YR27]{H^*}、 <a8>[T^ YR28]{H^*}、 <a1>[T^ YR11]{H^*}、 <a2>[T^ YR12]{H^*}、 <a3>[T^ YR13]{H^*}、 <a4>[T^ YR14]{H^*}、 <a5>[T^ YR15]{H^*}、 <a6>[T^ YR16]{H^*}、 <a7>[T^ YR17]{H^*}、 <a8>[T^ YR18]{H^*}, a common summation gate chain TSum j There are 8 Tsums, namely Tsum1, Tsum2, Tsum3, Tsum4, Tsum5, Tsum6, Tsum7, and Tsum8, with structures of [A1]{T^*}, [A2]{T^*}, [A3]{T^*}, [A4]{T^*}, [A5]{T^*}, [A6]{T^*}, [A7]{T^*}, and [A8]{T^*}, respectively.

[0188] Annihilation Chain UANH j There are 8 elements, namely UANh1, UANh2, UANh3, UANh4, UANh5, UANh6, UANh7, and UANh8, with structures {G^*}[YR11 YR21*] respectively.<G^*> {G^*}[YR12 YR22*]<G^*> {G^*}[YR13YR23*]<G^*> {G^*}[YR14 YR24*]<G^*> {G^*}[YR15 YR25*]<G^*> {G^*}[YR16 YR26*]<G^*> {G^*}[YR17 YR27*]<G^*> {G^*}[YR18 YR28*]<G^*> Summation gate chain NUSumW 1j 、NTSumW 2j The number of each is 8, namely NUSumW 11 、NUSumW 12 、NUSumW 13 、NUSumW 14 、NUSumW 15 、NUSumW 16 、NUSumW 17 、NUSumW 18 NUSumW21, NUSumW22, NUSumW23, NUSumW24, NUSumW25, NUSumW26, NUSumW27, and NUSumW28 have the following structures: <a11>[T^ YR11]{H^*}、 <a12>[T^ YR12]{H^*}、 <a13>[T^ YR13]{H^*}、 <a14>[T^ YR14]{H^*}、 <a15>[T^ YR15]{H^*}、 <a16>[T^ YR16]{H^*}、 <a17>[T^YR17]{H^*}、 <a18>[T^ YR18]{H^*}、 <a21>[T^ YR21]{H^*}、 <a22>[T^ YR22]{H^*}、 <a23>[T^ YR23]{H^*}、 <a24>[T^ YR24]{H^*}、 <a25>[T^ YR25]{H^*}、 <a26>[T^ YR26]{H^*}、 <a27>[T^ YR27]{H^*}、 <a28>[T^ YR28]{H^*};Common Summation Gate NTSum 1j ,NTSum 2j The number of each is 8, namely NTSum 11 ,NTSum 12 ,NTSum 13 ,NTSum 14 ,NTSum 15 ,NTSum 16 ,NTSum 17 ,NTSum 18 ,NTSum 21 ,NTSum 22 ,NTSum 23 ,NTSum 24 ,NTSum 25 ,NTSum 26 ,NTSum 27 ,NTSum 28 The structures are [A11]{T^*}, [A12]{T^*}, [A13]{T^*}, [A14]{T^*}, [A15]{T^*}, [A16]{T^*}, [A17]{T^*}, [A18]{T^*}, [A21]{T^*}, [A22]{T^*}, [A23]{T^*}, [A24]{T^*}, [A25]{T^*}, [A26]{T^*}, [A27]{T^*}, and [A28]{T^*}.

[0189] Step four: Based on the structure of the LVQ neural network, the basic functional module and the supervised learning module are cascaded into a complete adaptive molecular LVQ neural network based on DNA strand replacement, and the concentration setting and functional verification are completed in the Visual DSD platform.

[0190] Following the signal flow of the LVQ neural network, the basic functional modules are cascaded in the following order: distance operation module → inversion summation module → annihilation module → report module. The output label signal of the report module is then connected to the weighting activation module of the supervised learning module. Subsequently, the catalytic amplification module and the competition suppression module are connected in sequence for multiplication operations. Then, the addition module or the subtraction summation module is connected. Finally, the updated new input chain and the new weight chain are fed back to the input of the basic functional module, forming a complete closed-loop adaptive molecular LVQ neural network of classification operation—competition winning—result discrimination—weight update—iterative operation.

[0191] When conducting simulation and verification in the Visual DSD platform, the following steps are taken: First, all DNA input strands, weight strands, various gate structure strands, and auxiliary strands in the molecular LVQ neural network are input, and the strand substitution chemical reaction equations corresponding to each module are constructed one by one. Second, based on the nucleotide lengths at different starting points, the corresponding hybridization rate, branch migration rate, and leakage reaction kinetic parameters are calibrated. In accordance with the initialization rules of the molecular LVQ network, the initial concentrations of each feature input strand, weight strand, gate strand, and auxiliary strand are uniformly set. Then, a phased simulation approach is adopted. First, the distance calculation module, inversion summation module, annihilation module, report module, and weight update sub-module are independently simulated and debugged to verify whether the concentration change logic and reaction timing of a single module conform to the design mechanism. Then, all cascaded modules are integrated into a complete network circuit, the simulation duration and data sampling interval are set, and the dynamic change curves of the distance factor, inversion signal, output tag strand, and updated weight strand concentration are monitored in real time. The theoretical classification results are compared with the simulation output results to complete the effectiveness verification of the overall circuit logic function and adaptive weight update performance.

[0192] Experimental results show that the relative errors of the four sets of experiments in the addition module are all below 0.5%, proving that the DNA strand substitution reaction can perform linear algebraic operations with high precision and stability, providing a solid experimental foundation for the weight update module. The relative errors of the constructed subtraction summation module are all below 0.7%, confirming that linear algebraic operations based on the DNA strand substitution reaction can be performed with high precision and stability, laying a reliable experimental foundation for the subsequent weight update module.

[0193] This invention uses Visual DSD software to conduct simulation experiments, sets the simulation environment to random simulation mode, and uses 1M -1 s -1 The default leakage rate allows for polymer formation. The binding rate of the small pivot V is defined as 1 × 10⁻⁶. 9 M -1 s -1 The unbinding speed is 0.1s. -1 The binding rate of the small pivot G is defined as 9 × 10⁻⁶. 7 M -1 s -1 The unbinding speed is 0.1s. -1 The binding rate of the small fulcrum H is defined as 3 × 10⁻⁶. 5 M -1 s -1 The unbinding speed is 26 seconds. -1 The binding rate of the small fulcrum T is defined as 3 × 10⁻⁶. 5 M -1 s -1 The unbinding speed is 26 seconds. -1 The binding rate of the small pivot N is defined as 3 × 10⁻⁶. 5 M -1 s -1 The unbinding speed is 26 seconds. -1 The binding rate of the small fulcrum Q is defined as 3 × 10⁻⁶. 5 M -1 s -1 The unbinding speed is 26 seconds. -1 Small Pivot BS i The binding rate is defined as 3 × 10 5 M -1 s -1 The unbinding speed is 26 seconds. -1 Small Pivot BS k The binding rate is defined as 3 × 10 5 M -1 s -1 The unbinding speed is 26 seconds. -1 Small fulcrum BB i The binding rate is defined as 3 × 10 5 M -1 s -1 The unbinding speed is 26 seconds. -1 Small fulcrum BB k The binding rate is defined as 3 × 10 5 M -1 s -1 The unbinding speed is 26 seconds. -1 Small fulcrum S j The binding rate is defined as 3 × 10 5 M -1 s -1 The unbinding speed is 26 seconds. -1 Small fulcrum B i The binding rate is defined as 3 × 10 5 M -1 s -1 The unbinding speed is 26 seconds. -1 By setting reasonable simulation parameters in Visual DSD software, the binding and unbinding rates of each support point can be differentially controlled. At the same time, the leakage rate and polymer formation conditions can be standardized, which can accurately match the reaction sequence of each module, suppress non-specific interference, improve the realism and reliability of simulation results, and ensure that the network function fits the design logic.

[0194] Step 5: Obtain gene expression data of colorectal cancer cases and benign control samples from the TCGA and GTEx databases, and construct a dataset after data preprocessing and feature screening.

[0195] Medical research has confirmed that the occurrence and development of colorectal cancer are closely related to abnormal gene expression. RNA-seq technology can comprehensively capture the expression profile of the entire transcriptome, accurately identify the specific gene expression characteristics of colorectal cancer, and provide direct molecular-level evidence for disease diagnosis. A total of 534 RNA-seq datasets from 333 colorectal cancer patients and 201 benign control individuals were obtained from the TCGA and GTEx databases, covering research subjects of different ages and backgrounds. After data cleaning, eight key colorectal cancer characteristic genes were selected as input features using the random forest algorithm. Cross-validation confirmed that the adaptive molecular LVQ neural network has an 8-2-2 structure: 8 neurons in the input layer, 2 neurons in the competition layer, and 2 neurons in the output layer. All preprocessed samples were randomly stratified and divided into training, testing, and weight update sets. The training set was used for the network to learn gene feature patterns and initialize molecular weights; the testing set was used to test the classification effect of benign and malignant colorectal cancer; and the weight update set was used to drive the adaptive molecular LVQ neural network to achieve dynamic weight updates under supervised learning, thus enabling a complete system simulation experiment. From 534 sets of colorectal cancer-related data, 481 sets were randomly selected as the training set for model training, 45 sets were selected as the test set to verify the basic predictive performance of the model, and the remaining 8 sets were selected as the weight update set to verify the effectiveness of the weight update module and support the dynamic update of the colorectal cancer prediction model, thereby stabilizing and enhancing the model's anti-interference ability.

[0196] The initial weights of the network were set using the training set. The feature center vectors of the two classes of samples were obtained by clustering using the classic LVQ algorithm based on the expression features of 8 key genes from 481 training samples. The numerical values ​​of each dimension of the feature centers were then linearly mapped to the initial concentration of the DNA weight chains. According to the 8-2-2 network topology, the concentration values ​​of each dimension of the weight chains corresponding to the neurons of the two competing layers were assigned to complete the initial weight configuration of the adaptive molecular LVQ neural network, providing initial parameters for the subsequent classification and adaptive weight iteration of the DNA molecular circuit.

[0197] By mining the differential patterns of gene expression profiles to establish diagnostic associations, this method first uses the expression levels of eight key characteristic genes selected through screening as quantitative indicators. Gene expression features are used as input variables, and the clinical classification of benign or malignant samples is used as the output category. Utilizing the feature clustering and competitive classification mechanisms of an LVQ neural network, cluster boundaries for benign and malignant samples are delineated in a high-dimensional gene expression space, constructing a nonlinear correlation mapping between gene expression patterns and the benign or malignant status of colorectal cancer. The network is trained using dataset samples to continuously fit the disease attributes corresponding to different gene expression combinations. Based on the established feature-classification association, feature matching and category determination are performed on the gene expression features of unknown test samples, thereby achieving auxiliary diagnosis of colorectal cancer based on gene expression features.

[0198] Step six: Input the dataset into the constructed adaptive molecular LVQ neural network, run the circuit through the Visual DSD platform to diagnose whether the preprocessed colon cancer sample is benign or malignant, and dynamically update the weights based on the diagnostic error to complete the adaptive optimization of the model.

[0199] The input features consist of eight key colorectal cancer characteristic genes selected from the TCGA and GTEx databases. The expression levels of these eight genes are used as the input signals for an adaptive molecular LVQ neural network. The output layer includes output products Y1 and Y2, representing the colorectal cancer diagnosis categories. Y1 represents a benign diagnosis, and Y2 represents a malignant colorectal cancer diagnosis. Y1=1 indicates a benign colorectal cancer sample, and Y2=0 indicates a malignant colorectal cancer sample.

[0200] like Figure 10 As shown, output categories Y1 and Y2 correspond to benign and malignant diagnoses of colon cancer samples, respectively. The pathological type of the sample can be intuitively determined through the differentiated responses of the two output signals. In this colon cancer diagnostic test experiment, to fully verify the diagnostic performance of the constructed molecular LVQ neural network, the test set was strictly divided according to the distribution pattern of clinical samples, including 13 benign control samples (healthy individuals and non-tumor benign lesion samples) and 32 malignant colon cancer samples (colon cancer patients diagnosed by clinical pathological biopsy). The sample selection took into account individual differences of different ages and clinical stages to ensure the objectivity and reliability of the test results. The experimental results show that for the diagnosis of benign individuals, the model exhibits perfect recognition ability, with all 13 samples correctly identified, achieving an accuracy rate of 100%. In the diagnosis of malignant colon cancer cases, the model successfully identified 30 malignant samples, but 2 cases were misdiagnosed, with an accuracy rate of 93.75%. Based on the above data, the molecular LVQ neural network constructed in this invention achieved an overall accuracy of 95.56% in the colorectal cancer diagnosis task. This result fully demonstrates that the molecular model has efficient and accurate classification and recognition capabilities, can effectively distinguish the gene expression differences between benign and malignant colorectal cancer samples, and also shows good clinical application potential, providing a reliable molecular computing tool for the subsequent early screening and accurate diagnosis of colorectal cancer.

[0201] Further verification of the adaptive weight update mechanism was conducted using eight pre-set weight update sets. Due to the small size of the weight update sets, they were only used for local fine-tuning and parameter correction of the network weights, without significantly altering the overall diagnostic accuracy of the test set. Experimental verification showed that, by relying on DNA strand replacement to achieve adaptive iteration of network weights, the initial weight distribution of the molecular LVQ neural network can be reasonably optimized, feature mapping matching bias can be corrected, and the model's classification decision boundary can be improved. This demonstrates that the weight update module designed in this invention possesses autonomous parameter adjustment and adaptive optimization capabilities, can adapt to individual heterogeneity in gene expression, and provides a mechanism to support the long-term stable operation of the model, subsequent incremental sample learning, and clinical screening applications.

[0202] Test results show that the model achieves an overall accuracy of 95.56% in diagnosing colorectal cancer, with an F1 score of 0.929, demonstrating excellent performance in identifying benign and malignant samples. The introduction of a weight update mechanism allows the model to dynamically optimize the classification decision boundary, effectively adapting to the high dimensionality and significant individual differences of molecular data, significantly improving the model's generalization ability and classification stability. The molecular LVQ neural network with supervised learning functionality constructed in this study provides a novel technical solution for pattern recognition at the molecular level. Its excellent performance in colorectal cancer diagnosis also provides important technical support for primary healthcare institutions to conduct accurate and rapid tumor diagnosis.

[0203] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention. < / x> < / c> < / c> < / x>

Claims

1. A method for diagnosing colon cancer based on an adaptive molecular LVQ neural network, characterized in that, The steps are as follows: Step 1: Determine the functions of the input layer, competition layer, and linear output layer of the LVQ neural network; Step 2: Design the basic functional modules of the molecular LVQ neural network based on the DNA strand substitution reaction; A supervised learning module has been added to the basic functional modules; Step 3: Determine the DNA chain structure and small pivot structure of the auxiliary substances and reactants in the chemical reaction process of the basic functional module and the supervised learning module; Step 4: Based on the structure of the LVQ neural network, the basic functional module and the supervised learning module are cascaded into a complete adaptive molecular LVQ neural network based on DNA strand replacement, and the concentration setting and functional verification are completed in the Visual DSD platform. Step 5: Obtain gene expression data of colorectal cancer cases and benign control samples from the TCGA and GTEx databases, and construct a dataset after data preprocessing and feature screening; Step 6: Input the dataset into the constructed adaptive molecular LVQ neural network to diagnose whether the preprocessed colon cancer samples are benign or malignant, and dynamically update the weights based on the diagnostic error to complete the adaptive optimization of the adaptive molecular LVQ neural network.

2. The colorectal cancer diagnosis method based on adaptive molecular LVQ neural network according to claim 1, characterized in that, The input layer and the competition layer are fully connected to enable information exchange and distance calculation between the input features and all neurons in the competition layer. The competition layer and the linear output layer are partially connected. The number of neurons in the competition layer is no less than the number of neurons in the linear output layer. Each neuron in the competition layer is connected to only one neuron in the linear output layer, and the connection weight between them is 1. A single neuron in the linear output layer is connected to multiple neurons in the competition layer. The output states of neurons in both the competition layer and the linear output layer are represented using binary representation. When the input features are passed to the input layer in the form of feature vectors, the feature vectors are passed to the competition layer through the fully connected path. All neurons in the competition layer perform similarity calculations with the feature vectors, and the neuron closest to the input feature is selected as the winning neuron. The winning neuron is activated and its state is set to 1, while the other neurons in the competition layer remain inactive and in a 0 state. Based on the fixed connection relationship between the competition layer and the linear output layer, the linear output layer neurons connected to the winning neuron are activated and their states are simultaneously set to 1, while the other linear output layer neurons remain in a 0 state, thus completing the category determination of the input features. If the actual category of the input feature matches the category corresponding to the linear output layer neuron, the weights of the corresponding competing layer neuron are adjusted in the direction of the input feature; otherwise, the weights of the corresponding competing layer neuron are adjusted in the opposite direction of the input vector.

3. The colorectal cancer diagnosis method based on an adaptive molecular LVQ neural network according to claim 1 or 2, characterized in that, The supervised learning module includes a weighting activation module, a catalytic amplification module, a competition suppression module, an addition module, and a subtraction summation module. The output chain obtained from the basic functional module serves as the trigger signal for the weighting activation module, initiating weight updates. The weighting activation module is sequentially connected to the catalytic amplification module and the competition suppression module, which work together to complete molecule multiplication. According to the weight update rules, the results of the molecule multiplication are fed into the addition module or the subtraction summation module to achieve dynamic calculation and updating of weights.

4. The colorectal cancer diagnosis method based on adaptive molecular LVQ neural network according to claim 3, characterized in that, The basic functional modules include a distance calculation module, a reversal summation module, an annihilation module, and a reporting module. The distance calculation module is connected to the reversal summation module, which in turn is connected to both the annihilation and reporting modules. The output chain of the reporting module is the predicted label. The distance calculation module corresponds to the input layer, responsible for receiving and processing the input feature vector and calculating the similarity between the feature vector and the weights. The reversal summation module corresponds to the competition layer, implementing signal normalization and competitive selection to filter out the neurons that best match the input layer. The annihilation module and the reporting module together correspond to the linear output layer, completing the final signal output and category determination.

5. The colorectal cancer diagnostic method based on adaptive molecular LVQ neural network according to claim 3, characterized in that, The chemical reaction expression for the weighting activation module is: When the output tag's output chain Y i When consistent with the original tag class, ； ； ； ； When the output tag's output chain Y i When inconsistent with the original label, ； ； ； ； Among them, BY i BY k Represents the original class tag chain; FG ii FG ik Represents the release gate, serving as the trigger switch for weight updates; IN X IN C Representing the activation chain, the activation chain INx is used to trigger a positive weight update when the classification is correct. The activation chain IN... C Used to trigger reverse weight updates when a classification error occurs; XF X XF C Represents the catalytic chain; GX 2j CX 2j Representative input substrate; GW 1j CW 1j Represents the weighted substrate, WG 2j NG 2j The WG gate represents a new input summation gate, which transforms a new input substrate into a new input chain that can participate in computation. 1j NG 1j The new weighted summation gate transforms the weighted substrate into a new weighted chain that can participate in computation; SX 2j LX 2j Represents a new input chain, LW 1j SW 1j Represents the new weighted chain; XP 2j WP 1j CP 2j NP 1j All are intermediate products; The chemical reaction expression for the catalytic amplification module is as follows: ； ； ； ； Wherein, chain K is represented. ij Characterizing the new input chain LX 2j SX 2j and the new weighted chain LW 1j SW 1j C i1 C i2 C i3 Represents auxiliary chain; SP i1 SP i2 SP i3 SP i4 SP i5 SP i6 B represents an intermediate product; ij Represents the amplification chain; Y ij Represents the output product; The competitive inhibition module is responsible for regulating the reaction process and calibrating the concentration ratio. The chemical reaction expression for the competitive inhibition module is as follows: ； ； ； ； Among them, D i1 D i2 D i3 Represents auxiliary chain; SP i7 SP i8 SP i9 SP i10 SP i11 SP i12 SP i13 B0 represents an intermediate product; ij Represents the inhibitory chain; The chemical reaction expression for the addition module is: ； ； ； Among them, Y 1j Y 2j Represents the output product of the catalytic amplification module; USumW 1j USumX 2j Represents a summation gate chain; DP 1j and DP 2j Represents intermediate products; TSum j Represents a common summation gate chain; Z j Represents the output chain; The chemical reaction expression for the subtraction summation module is: ； ； ； Among them, NUSumW 1j 、NTSumW 2j NTSum represents a summation gate chain. 1j ,NTSum 2j Represents a common summation gate chain; Z 1j Z 2j Represents the output chain, output chain Z 1j The concentration is the new positive weight value, and the output chain Z... 2j The concentration is then the new negative weight value; Indicates the product.

6. The colorectal cancer diagnosis method based on an adaptive molecular LVQ neural network according to claim 4 or 5, characterized in that, The chemical reaction expression for the distance calculation module is: ； ； ； ； Among them, K f1 K is the rate constant of the annihilation reaction. s K is the rate constant of the summation reaction. f1 ≫K s ;X ij W represents the input chain, carrying the molecular signal of the i-th input layer neuron; ij Anh represents the weight chain, storing the weight values ​​of the j-th competing layer neuron on the feature vector of the i-th input layer neuron; ij Represents the annihilation chain, implementing the input chain X. ij With weight chain W ij annihilation reaction, Indicates the product of an annihilation reaction; SumX ij The input summation gate annihilates the remaining input chain X. ij The concentration is converted into the input for the summation operation, summation chain XS ij SumW ij The weight summation gate represents the annihilation of the remaining weight chain W. ij The concentration is converted into the weight of the summation operation WS. ij Sum j Represents a common summation gate, completing the input summation chain XS. ij Weighted summation chain WS ij The concentration summation operation generates the distance factor D, representing the Manhattan distance. j "waste" represents the waste chain. The chemical reaction expression for the inverse summation module is: ； Among them, SRG kj The RSG (Representative Signal Inversion Gate) is used to average the concentration of the distance factor of the j-th competing layer neuron to obtain the inverted signal corresponding to the k-th competing layer neuron; k This represents the inversion signal summation gate, which sums the concentrations of all inversion signals associated with the k-th competing layer neuron. The chemical reaction expressions for the annihilation module and the reporting module are as follows: ； ； Where Kf2 is the rate constant of the annihilation module, and LAnh jk Represents the annihilation chain; K s1 Let K be the rate constant of the reporting module, and K f2 ≫K s1 S j S represents the inverted signal of the j-th competing layer neuron. k Re represents the inverted signal of the k-th competing layer neuron; Re ji The representative report gate outputs the inverted signal remaining after annihilation as a report, Y. i This represents the output label.

7. The colorectal cancer diagnosis method based on adaptive molecular LVQ neural network according to claim 6, characterized in that, When the output class label matches the true class label of the sample, indicating that the sample has been correctly classified, the output chain Y in the system... i BY with the original class tag chain i Together they act on the release gate FG ii It releases the activating strand IN through a specific DNA strand displacement reaction. x When the output class label does not match the true class label of the sample, indicating that the sample has been misclassified, the output chain Y... i BY with the original class tag chain k Combined and acting on the release gate FG ik The activation chain IN is released through a chain displacement reaction. c ; Inhibition chain B0 ij and auxiliary chain D i1 The intermediate product SP generated by the reaction i8 And representing chain K ij With auxiliary chain C i1 The intermediate product SP generated by the reaction i2 Simultaneously with amplification chain B ij Reacting at the same reaction rate, the intermediate product SP i2 Concentration and representative chain K ij Concentration-dependent, intermediate product SP i8 Concentration and inhibitory chain B0 ij The concentration is related to the final output product Y. ij Concentration and representative chain K ij and B ij Positively correlated with the inhibitory chain B0 ij Negative correlation; When the output matches the true class label of the sample, the summation gate chain USumW is used. 1j Output product Y 1j The concentration of DP is converted into the intermediate product. 1j The concentration is obtained by summation gate USumX 2j Output product Y 2j The concentration of DP is converted into the intermediate product. 2j The concentration, and through the common summation gate chain TSum j intermediate product DP 1j and DP 2j The concentration is summed to the output chain Z. j Above, output chain Z j The concentration is used as the new weight value; When the output result is inconsistent with the true class label of the sample, w ij_new =Y 1j -Y 2j Output product Y 1j With output product Y 2j Participating in the annihilation reaction, when the output product Y 1j The concentration of the product Y is greater than that of the output product Y. 2j At a concentration of , the output product Y 1j Through the summation gate NUSumW 1j And the common summation gate NTSum 1j Generate output chain Z 1j Output chain Z 1j The concentration of the product Y is equal to that of the output product. 1j Concentration and output product Y 2j The difference in concentration, and when the output product Y 1j The concentration is less than that of the output product Y 2j At a concentration of , the output product Y 2j Through the summation gate NUSumW 2j And the common summation gate NTSum 2j Generate output chain Z 2j Output chain Z 2j The output represents a negative value; The chemical reaction expression for negative weight processing in the distance calculation module is: ； ； Among them, NW ij Represents a negative weighted chain; the negative weighted summation gate SumNW ij negative weight chain NW ij The concentration is converted into a negative weighted summation chain NXW for the summation operation. ij Through the common summation gate Sum j The negative weight summation chain NXW ij The concentration and input summation chain XS ij The concentration is summed to the distance factor D j At the concentration; The inversion summation module transforms the neuron with the smallest distance factor concentration into the signal output with the largest inversion signal concentration, so that in the subsequent inversion signal annihilation process, the neuron with the smallest distance factor will eventually win and complete the output.

8. The colorectal cancer diagnosis method based on adaptive molecular LVQ neural network according to claim 7, characterized in that, The input chain X ij There are two groups, one with 8 lines, for a total of 16 lines, which are the input chains X. 11 X 12 X 13 X 14 X 15 X 16 X 17 X 18 X 21 X 22 X 23 X 24 X 25 X 26 X 27 X 28 The structures are respectively<G^ X11 H^> ,<G^ X12 H^> ,<G^ X13 H^> ,<G^ X14 H^> ,<G^ X15 H^> ,<G^ X16 H^> ,<G^ X17 H^> ,<G^ X18 H^> ,<G^ X21 H^> ,<G^X22 H^> ,<G^ X23 H^> ,<G^ X24 H^> ,<G^ X25 H^> ,<G^ X26 H^> ,<G^ X27 H^> ,<G^ X28 H^> Where X11-X28 represent the names of the branch-transition structure domains of the 16 input chains, G and H represent the names of the small pivot domains, ^ represents a small pivot domain, and <> represents a single chain; the weight chain W ij There are two groups, one group with 8 items, for a total of 16 items, namely W 11 W 12 W 13 W 14 W 15 W 16 W 17 W 18 W 21 W 22 W 23 W 24 W 25 W 26 W 27 W 28 Their structures are respectively<G^ W11 H^> ,<G^ W12 H^> ,<G^ W13 H^> ,<G^ W14 H^> ,<G^ W15 H^> ,<G^ W16 H^> ,<G^ W17 H^> ,<G^ W18 H^> ,<G^W21 H^> ,<G^ W22 H^> ,<G^ W23 H^> ,<G^ W24 H^> ,<G^ W25 H^> ,<G^ W26 H^> ,<G^ W27 H^> ,<G^ W28 H^> Among them, W11-W28 represent the names of the branch migration structure domains of the 16 weight chains; annihilation chain Anh ij The number of entries is 16, namely Anh 11 Anh 12 Anh 13 Anh 14 Anh 15 Anh 16 Anh 17 Anh 18 Anh 21 Anh 22 Anh 23 Anh 24 Anh 25 Anh 26 Anh 27 Anh 28 The structures are {G^*}[X11 W11*] and {G^*}[X11 W11*].<G^*> {G^*}[X12W12*]<G^*> {G^*}[X13 W13*]<G^*> {G^*}[X14 W14*]<G^*> {G^*}[X15 W15*]<G^*> {G^*}[X16 W16*]<G^*> {G^*}[X17 W17*]<G^*> {G^*}[X18 W18*]<G^*> {G^*}[X21 W21*]<G^*> {G^*}[X22 W22*]<G^*> {G^*}[X23 W23*]<G^*> {G^*}[X24 W24*]<G^*> {G^*}[X25W25*]<G^*> {G^*}[X26 W26*]<G^*> {G^*}[X27 W27*]<G^*> {G^*}[X28 W28*]<G^*> Where * represents complementarity, {} represents a single chain, and [] represents a double chain; input summation gate SumX ij There are 16 in total, namely SumX 11 SumX 12 SumX 13 SumX 14 SumX 15 SumX 16 SumX 17 SumX 18 SumX 21 SumX 22 SumX 23 SumX 24 SumX 25 SumX 26 SumX 27 SumX 28 The structures are respectively <d1>[T^ X11]{H^*}、 <d1>[T^ X12]{H^*}、 <d1>[T^ X13]{H^*}、 <d1>[T^ X14]{H^*}、 <d1>[T^ X15]{H^*}、 <d1>[T^ X16]{H^*}、 <d1>[T^ X17]{H^*}、 <d1>[T^ X18]{H^*}、 <d2>[T^ X21]{H^*}、 <d2>[T^ X22]{H^*}、 <d2>[T^ X23]{H^*}、 <d2>[T^ X24]{H^*}、 <d2>[T^ X25]{H^*}、 <d2>[T^ X26]{H^*}、 <d2>[T^ X27]{H^*}、 <d2>[T^ X28]{H^*}; where D1 and D2 represent the names of the branch-transfer structure domains of the 16 input summation gates; the weighted summation gate SumW ij There are 16 in total, namely SumW 11 SumW 12 SumW 13 SumW 14 SumW 15 SumW 16 SumW 17 SumW 18 SumW 21 SumW 22 SumW 23 SumW 24 SumW 25 SumW 26 SumW 27 SumW 28 The structures are respectively <d1>[T^ W11]{H^*}、 <d1>[T^ W12]{H^*}、 <d1>[T^ W13]{H^*}、 <d1>[T^ W14]{H^*}、 <d1>[T^ W15]{H^*}、 <d1>[T^W16]{H^*}、 <d1>[T^ W17]{H^*}、 <d1>[T^ W18]{H^*}、 <d2>[T^ W21]{H^*}、 <d2>[T^ W22]{H^*}、 <d2>[T^ W23]{H^*}、 <d2>[T^ W24]{H^*}、 <d2>[T^ W25]{H^*}、 <d2>[T^ W26]{H^*}、 <d2>[T^ W27]{H^*}、 <d2>[T^ W28]{H^*};where D1 and D2 represent distance factors D j The branch migration structure name, T represents the name of the minor pivot field; the common summation gate Sum j There are two lines, Sum1 and Sum2, with the following structures:<N^> [D1]<N^> {T^*} and<N^> [D2]<N^> {T^*}, where N represents the name of the minor pivot field; Signal Reversal Gate (SRG) kj The number is 2, namely SRG 12 and SRG 21 The structures are respectively<V^ L1> [N^D2]{N^*} and<V^ L2> [N^D1]{N^*}, where L1 and L2 represent the names of the branch transition structure domains of the inverted signal; the inverted signal summing gate RSG k There are two of them, RSG1 and RSG2, and their structures are respectively<H^ S1^> [V^ L1]{N^*} and<H^ S2^> [V^L2]{N^*}, where S1, S2, and V are the names of the minor pivot fields; annihilation chain LAnh jk The number is 1, which is LAnh 12 Its structure is<V^*> [S1^* S2^]{V^*};Report gate Re ji The number of elements is 2, and their structures are {H^*}[S1^V^] .<B1^> and {H^*}[S2^ V^]<B2^> Where B1 and B2 are the names of the minor pivot domains; Primitive class tag chain BY i The number of elements is 2, namely BY1 and BY2, and their structures are respectively<BS1^ V^ BB1^> and<BS2^ V^BB2^> BS1, BS2, BB1, and BB2 are the names of the small pivot domains; release gate FG ik The number of elements is 4, namely FG11, FG12, FG21 and FG22, with structures {S1^*} respectively. <x>[V^ B1^ BS1^ V^]{BB1^*}、{S1^*} <c>[V^ B1^ BS2^ V^]{BB2^*}、{S2^*} <c>[V^ B2^ BS1^ V^]{BB1^*}、{S2^*} <x> [V^ B2^ BS2^ V^]{BB2^*};< / x> < / c> < / c> < / x> Input catalytic substrate GX 2j and CX 2j The number of each is 8, namely GX 21 GX 22 GX 23 GX 24 GX 25 GX 26 GX 27 GX 28 and CX 21 CX 22 CX 23 CX 24 CX 25 CX 26 CX 27 CX 28 The structures are {V^*}[XV^] and , respectively.<BB21 G^> {V^*}[XV^]<BB22 G^> {V^*}[XV^]<BB23 G^> {V^*}[XV^]<BB24 G^> {V^*}[XV^]<BB25 G^> {V^*}[XV^]<BB26 G^> {V^*}[XV^]<BB27 G^> {V^*}[XV^]<BB28 G^> and {V^*}[CV^]<CB21 G^> {V^*}[CV^]<CB22 G^> {V^*}[CV^]<CB23 G^> {V^*}[CV^]<CB24 G^> {V^*}[CV^]<CB25 G^> {V^*}[CV^]<CB26 G^> {V^*}[CV^]<CB27 G^> {V^*}[CV^]<CB28G^> ; weighted catalytic substrate GW 2j and CW 2j The number of each is 8, namely GW 11 GW 12 GW 13 GW 14 GW 15 GW 16 GW 17 GW 18 and CW 11 CW 12 CW 13 CW 14 CW 15 CW 16 CW 17 CW 18 ,jiégòufēnbiéwèi{V^*}[XV^]<BB11 G^> ,{V^*}[XV^]<BB12 G^> ,{V^*}[XV^]<BB13 G^> ,{V^*}[XV^]<BB14 G^> ,{V^*}[XV^]<BB15 G^> ,{V^*}[XV^]<BB16 G^> ,{V^*}[XV^]<BB17 G^> ,{V^*}[XV^]<BB18 G^> hé{V^*}[CV^]<CB11 G^> ,{V^*}[CV^]<CB12 G^> ,{V^*}[CV^]<CB13 G^> ,{V^*}[CV^]<CB14 G^> ,{V^*}[CV^]<CB15 G^> ,{V^*}[CV^]<CB16 G^> ,{V^*}[CV^]<CB17 G^> ,{V^*}[CV^]<CB18G^> ; New Input Summation Gate WG 2j and NG 2j The number of each is 8, namely WG 21 WG 22 WG 23 WG 24 WG 25 WG 26 WG 27 WG 28 and NG 21 NG 22 NG 23 NG 24 NG 25 NG 26 NG 27 NG 28 The structures are {V^*}[BB21 G^] and {V^*}, respectively. <c21>、{V^*}[BB22 G^] <c22>、{V^*}[BB23 G^] <c23>、{V^*}[BB24 G^] <c24>、{V^*}[BB25 G^] <c25>、{V^*}[BB26 G^] <c26>、{V^*}[BB27 G^] <c27>、{V^*}[BB28 G^] <c28>and {V^*}[CB21 G^] <c21>、{V^*}[CB22 G^] <c22>、{V^*}[CB23 G^] <c23>、{V^*}[CB24 G^] <c24>、{V^*}[CB25G^] <c25>,{V^*}[CB26 G^] <c26>,{V^*}[CB27 G^] <c27>、{V^*}[CB28 G^] <c28>New weighted summation gate WG 1j and NG 1j The number of each is 8, namely WG 11 WG 12 WG 13 WG 14 WG 15 WG 16 WG 17 WG 18 and NG 11 NG 12 NG 13 NG 14 NG 15 NG 16 NG 17 NG 18 The structures are {V^*}[BB11 G^] and {V^*}, respectively. <w11>、{V^*}[BB12 G^] <w12>,{V^*}[BB13 G^] <w13>、{V^*}[BB14 G^] <w14>、{V^*}[BB15 G^] <w15>、{V^*}[BB16 G^] <w16>、{V^*}[BB17 G^] <w17>,{V^*}[BB18 G^] <w18>and {V^*}[CB11 G^] <w11>,{V^*}[CB12 G^] <w12>、{V^*}[CB13 G^] <w13>、{V^*}[CB14 G^] <w14>,{V^*}[CB15 G^] <w15>、{V^*}[CB16 G^] <w16>,{V^*}[CB17 G^] <w17>,{V^*}[CB18 G^] <w18> ；< / w18> Auxiliary chain C i1 There are 16 elements, namely C111, C121, C131, C141, C151, C161, C171, C181, C211, C221, C231, C241, C251, C261, C271, and C281, with the structure {G^*}[C11 G^]:[XR11 Q^]<BB11 G^XL11 G^ YL11 G^> {G^*}[C12 G^]:[XR12 Q^]<BB11 G^ XL12 G^ YL12 G^> {G^*}[C13 G^]:[XR13 Q^]<BB13 G^ XL13 G^ YL13 G^> {G^*}[C14 G^]:[XR14 Q^]<BB14 G^ XL14 G^YL14 G^> {G^*}[C15 G^]:[XR15 Q^]<BB15 G^ XL15 G^ YL15 G^> {G^*}[C16 G^]:[XR16Q^]<BB26 G^ XL16 G^ YL16 G^> {G^*}[C17 G^]:[XR17 Q^]<BB17 G^ XL17 G^ YL17 G^> {G^*}[C18 G^]:[XR18 Q^]<BB18 G^ XL18 G^ YL18 G^> ;{G^*}[C21 G^]:[XR21 Q^]<BB21 G^ XL21 G^ YL21 G^> {G^*}[C22 G^]:[XR22 Q^]<BB21 G^ XL22 G^ YL22 G^> {G^*}[C23 G^]:[XR23 Q^]<BB23 G^ XL23 G^ YL23 G^> {G^*}[C24 G^]:[XR24 Q^]<BB24 G^ XL24 G^ YL24 G^> {G^*}[C25 G^]:[XR25 Q^]<BB25 G^ XL25 G^ YL25 G^> {G^*}[C26G^]:[XR26 Q^]<BB26 G^ XL26 G^ YL26 G^> {G^*}[C27 G^]:[XR27 Q^]<BB27 G^ XL27 G^ YL27 G^> {G^*}[C28 G^]:[XR28 Q^]<BB28 G^ XL28 G^ YL28 G^> ; Auxiliary chain C i2 There are 16 of them, namely C112, C122, C132, C142, C152, C162, C172, C182, C212, C222, C232, C242, C252, C262, C272, and C282, with structures of [C11]{G^*}, [C12]{G^*}, [C13]{G^*}, and [C14]{ G^*}、[C15]{G^*}、[C16]{G^*}、[C17]{G^*}、[C18]{G^*}、[C21]{G^*}、[C22]{G^ *}, [C23]{G^*}, [C24]{G^*}, [C25]{G^*}, [C26]{G^*}, [C27]{G^*}, [C28]{G^*} Auxiliary chain C i3 There are 16 elements, namely C113, C123, C133, C143, C153, C163, C173, C183, C213, C223, C233, C243, C253, C263, C273, and C283, with the structure {Q^*}[B11 G^] <c11>:[XL11 G^] <xr11>:[YL11 G^]<YR11 H^>、{Q^*}[B12 G^] <c12>:[XL12 G^] <xr12>:[YL12 G^]<YR12 H^>、{Q^*}[B13 G^] <c13>:[XL13 G^] <xr13>:[YL13 G^]<YR13 H^> ,{Q^*}[B14 G^] <c14>:[XL14 G^] <xr14>:[YL14 G^]<YR14 H^> ,{Q^*}[B15 G^] <c15>:[XL15 G^] <xr15>:[YL15 G^]<YR15 H^>、{Q^*}[B16 G^] <c16>:[XL16 G^] <xr16>:[YL16 G^]<YR16 H^>、{Q^*}[B17 G^] <c17>:[XL17 G^] <xr17>:[YL17 G^]<YR17 H^>、{Q^*}[B18 G^] <c18>:[XL18 G^] <xr18>:[YL18 G^]<YR18 H^>、{Q^*}[B21 G^] <c21>:[XL21 G^] <xr21>:[YL21 G^]<YR21 H^> ,{Q^*}[B22 G^] <c22>:[XL22 G^] <xr22>:[YL22 G^]<YR22 H^>、{Q^*}[B23 G^] <c23>:[XL23G^] <xr23>:[YL23 G^]<YR23 H^>、{Q^*}[B24 G^] <c24>:[XL24 G^] <xr24>:[YL24 G^]<YR24 H^>、{Q^*}[B25 G^] <c25>:[XL25 G^] <xr25>:[YL25 G^]<YR25 H^> ,{Q^*}[B26 G^] <c26>:[XL26 G^] <xr26>:[YL26 G^]<YR26 H^>、{Q^*}[B27 G^] <c27>:[XL27 G^] <xr27>:[YL27 G^]<YR27 H^>、{Q^*}[B28 G^] <c28>:[XL28 G^] <xr28> [YL28 G^]<YR28 H^> ; Amplification chain B ij There are 16 numbers, namely C11, C12, C13, C14, C15, C16, C17, C18, C21, C22, C23, C24, C25, C26, C27, and C28, with the following structures:<XL11 G^ XR11> ,<XL12 G^ XR12> ,<XL13 G^ XR13> ,<XL14 G^ XR14> ,<XL15 G^ XR15> ,<XL16 G^ XR16> ,<XL17 G^ XR17> ,<XL18 G^ XR18> ,<XL21 G^ XR21> ,<XL22 G^ XR22> ,<XL23 G^ XR23> ,<XL24 G^ XR24> ,<XL25 G^ XR25> ,<XL26 G^ XR26> ,<XL27 G^ XR27> ,<XL28 G^ XR28> ; Auxiliary chain D i1 There are 16 elements, namely D111, D121, D131, D141, D151, D161, D171, D181, D211, D221, D231, D241, D251, D261, D271, and D281, with the structure {G^*}[B0R G^]:[XR11 Q^]<B0L11 G^> {G^*}[B0R G^]:[XR12 Q^]<B0L12 G^> {G^*}[B0R G^]:[XR13 Q^]<B0L13 G^> {G^*}[B0R G^]:[XR14 Q^]<B0L14 G^> {G^*}[B0R G^]:[XR15 Q^]<B0L15 G^> {G^*}[B0R G^]:[XR16 Q^]<B0L16 G^> {G^*}[B0R G^]:[XR17 Q^]<B0L17 G^> {G^*}[B0R G^]:[XR18 Q^]<B0L18 G^> {G^*}[B0R G^]:[XR21 Q^]<B0L21 G^> {G^*}[B0R G^]:[XR22 Q^]<B0L22 G^> {G^*}[B0R G^]:[XR23 Q^]<B0L23 G^> {G^*}[B0R G^]:[XR24 Q^]<B0L24 G^> {G^*}[B0R G^]:[XR25 Q^]<B0L25 G^> {G^*}[B0R G^]:[XR26 Q^]<B0L26 G^> {G^*}[B0R G^]:[XR27 Q^]<B0L27 G^> {G^*}[B0R G^]:[XR28 Q^]<B0L28 G^> ; Auxiliary chain D i2 There are 16 numbers, namely D112, D122, D132, D142, D152, D162, D172, D182, D212, D222, D232, D242, D252, D262, D272, and D282, with structures of [B0R11]{G^*}, [B0R12]{G^*}, [B0R13]{G^*}, [B0R14]{G^*}, and [B0R] respectively. 15]{G^*}、[B0R16]{G^*}、[B0R17]{G^*}、[B0R18]{G^*}、[B0R21]{G^*}、[B0R22]{G^*}、[B 0R23]{G^*}, [B0R24]{G^*}, [B0R25]{G^*}, [B0R26]{G^*}, [B0R27]{G^*}, [B0R28]{G^*}; Auxiliary chain D i3 There are 16 elements, namely D113, D123, D133, D143, D153, D163, D173, D183, D213, D223, D233, D243, D253, D263, D273, and D283, with the structure {Q^*}[B0L11 G^] <b0r11>,{Q^*}[B0L12 G^] <b0r12>,{Q^*}[B0L13 G^] <b0r13>,{Q^*}[B0L14 G^] <b0r14>,{Q^*}[B0L15 G^] <b0r15>,{Q^*}[B0L16 G^] <b0r16>,{Q^*}[B0L17 G^] <b0r17>,{Q^*}[B0L18 G^] <b0r18>,{Q^*}[B0L21 G^] <b0r21>,{Q^*}[B0L22 G^] <b0r22>、{Q^*}[B0L23 G^] <b0r23>,{Q^*}[B0L24 G^] <b0r24>,{Q^*}[B0L25 G^] <b0r25>,{Q^*}[B0L26 G^] <b0r26>、{Q^*}[B0L27 G^] <b0r27>,{Q^*}[B0L28 G^] <b0r28> ；< / b0r28> Summation gate chain USumW 1j USumX 2j The number of each is 8, namely USumW 11 USumW 12 USumW 13 USumW 14 USumW 15 USumW 16 USumW 17 USumW 18 USumX 21 USumX 22 USumX 23 USumX 24 USumX 25 USumX 26 USumX 27 USumX 28 The structures are respectively <a1>[T^ YR21]{H^*}、 <a2>[T^ YR22]{H^*}、 <a3>[T^ YR23]{H^*}、 <a4>[T^ YR24]{H^*}、 <a5>[T^ YR25]{H^*}、 <a6>[T^ YR26]{H^*}、 <a7>[T^ YR27]{H^*}、 <a8>[T^ YR28]{H^*}、 <a1>[T^ YR11]{H^*}、 <a2>[T^ YR12]{H^*}、 <a3>[T^ YR13]{H^*}、 <a4>[T^ YR14]{H^*}、 <a5>[T^ YR15]{H^*}、 <a6>[T^ YR16]{H^*}、 <a7>[T^ YR17]{H^*}、 <a8>[T^ YR18]{H^*}, a common summation gate chain TSum j There are 8 Tsums, namely Tsum1, Tsum2, Tsum3, Tsum4, Tsum5, Tsum6, Tsum7, and Tsum8, with structures of [A1]{T^*}, [A2]{T^*}, [A3]{T^*}, [A4]{T^*}, [A5]{T^*}, [A6]{T^*}, [A7]{T^*}, and [A8]{T^*}, respectively. Annihilation Chain UANH j There are 8 elements, namely UANh1, UANh2, UANh3, UANh4, UANh5, UANh6, UANh7, and UANh8, with structures {G^*}[YR11 YR21*] respectively.<G^*> {G^*}[YR12 YR22*]<G^*> {G^*}[YR13YR23*]<G^*> {G^*}[YR14 YR24*]<G^*> {G^*}[YR15 YR25*]<G^*> {G^*}[YR16 YR26*]<G^*> {G^*}[YR17 YR27*]<G^*> {G^*}[YR18 YR28*]<G^*> Summation gate chain NUSumW 1j 、NTSumW 2j The number of each is 8, namely NUSumW 11 、NUSumW 12 、NUSumW 13 、NUSumW 14 、NUSumW 15 、NUSumW 16 、NUSumW 17 、NUSumW 18 NUSumW21, NUSumW22, NUSumW23, NUSumW24, NUSumW25, NUSumW26, NUSumW27, and NUSumW28 have the following structures: <a11>[T^ YR11]{H^*}、 <a12>[T^ YR12]{H^*}、 <a13>[T^ YR13]{H^*}、 <a14>[T^ YR14]{H^*}、 <a15>[T^ YR15]{H^*}、 <a16>[T^ YR16]{H^*}、 <a17>[T^YR17]{H^*}、 <a18>[T^ YR18]{H^*}、 <a21>[T^ YR21]{H^*}、 <a22>[T^ YR22]{H^*}、 <a23>[T^ YR23]{H^*}、 <a24>[T^ YR24]{H^*}、 <a25>[T^ YR25]{H^*}、 <a26>[T^ YR26]{H^*}、 <a27>[T^ YR27]{H^*}、 <a28>[T^ YR28]{H^*};Common Summation Gate NTSum 1j ,NTSum 2j The number of each is 8, namely NTSum 11 ,NTSum 12 ,NTSum 13 ,NTSum 14 ,NTSum 15 ,NTSum 16 ,NTSum 17 ,NTSum 18 ,NTSum 21 ,NTSum 22 ,NTSum 23 ,NTSum 24 ,NTSum 25 ,NTSum 26 ,NTSum 27 ,NTSum 28 The structures are [A11]{T^*}, [A12]{T^*}, [A13]{T^*}, [A14]{T^*}, [A15]{T^*}, [A16]{T^*}, [A17]{T^*}, [A18]{T^*}, [A21]{T^*}, [A22]{T^*}, [A23]{T^*}, [A24]{T^*}, [A25]{T^*}, [A26]{T^*}, [A27]{T^*}, and [A28]{T^*}.

9. The colorectal cancer diagnosis method based on an adaptive molecular LVQ neural network according to claim 7 or 8, characterized in that, RNA-seq data were obtained from the TCGA and GTEx databases. After data cleaning, eight key colorectal cancer genes were selected as input features using the random forest algorithm. Cross-validation determined the structure of the adaptive molecular LVQ neural network to be an 8-2-2 network structure, including an input layer of 8 neurons, a competition layer of 2 neurons, and an output layer of 2 neurons. All preprocessed samples were randomly stratified and divided into a training set, a test set, and a weight update set. The training set was used for the network to learn gene feature patterns and initialize molecular weights. The test set was used to test the classification effect of benign and malignant colorectal cancer. The weight update set was used to drive the adaptive molecular LVQ neural network to achieve dynamic weight updates under supervised learning. Using eight key characteristic genes of colorectal cancer as input variables and clinical classification of benign and malignant samples as output categories, the cluster boundaries of benign and malignant samples were divided in the high-dimensional gene expression space by the feature clustering and competitive classification mechanism of the adaptive molecular LVQ neural network, and a nonlinear correlation mapping between gene expression patterns and benign and malignant status of colorectal cancer was constructed.

10. The colorectal cancer diagnosis method based on adaptive molecular LVQ neural network according to claim 9, characterized in that, The annihilation reactions involved in some distance calculation modules, annihilation modules, and some subtraction summation modules utilize the base point G, which has 7 nucleotides; the base point V involved in the weighting activation module has 9 nucleotides; and the remaining base points all have 5 nucleotides. The actual concentrations of the new weighted chain, new input chain, new input summation gate, and new weighted summation gate are exactly the same as the corresponding chains and gates in the basic module; The generated new input chain LX 2j Concentration and input substrate GX ij Concentrations are completely identical, new weighted chain LW 1j Concentration and input substrate GW ij The concentrations are completely identical, and both concentrations are respectively related to the input chain X. ij Weighted chain W ij The initial concentrations remain matched; New input chain SX 2j Concentration matching input substrate CX 2j Concentration, new weighted chain SW 1j Concentration matching of input substrate CW 1j The concentrations of both are consistent with the corresponding input parameters and weight parameters required in the weight reverse update process; Auxiliary chain C i1 C i2 C i3 and auxiliary chain D i1 D i2 D i3 The theoretical initial concentration is considered to be infinite.

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