Information Technology and Control

Image Enhancement Model for Open-Pit Mine Monitoring Based on Parallel Multi-Scale Feature Fusion

Xuewei Tao — 2025-04-01

The workspace in open-pit mining systems often suffers from insufficient or uneven illumination due to spatial constraints and obstructions caused by large equipment or geotechnical structures, leading to degraded surveillance imagery and consequently impacting safety monitoring efforts. This study designed an open-pit mine surveillance image enhancement model based on a parallel multi-scale feature fusion Transformer to address the degradation of surveillance video images and leverage the superior expressive power of Transformer networks in visual image processing compared to other networks. The network architecture mainly processes and integrates full-size feature maps and various levels of downsampled feature maps in parallel, preserving both the semantic relationships of image elements and their overall structure. The downsampling process of the network aims to maximize the extraction and restoration of the luminance features of small-sized objects from low-resolution images. By integrating features from downsampling, full-size image processing effectively restores illumination, thereby enhancing the accuracy of the images. To reduce the computational demands of the Transformer structure and facilitate its application in monitoring imagery, we employed an orthogonal self-attention mechanism along both the rows and columns of the image to be processed. This mechanism shifts the network's computational demand from exponential to linear growth. During the training phase, the network model was trained using a dataset collected on-site to enhance the model's adaptability to field conditions. SSIM and PSNR test results confirm that this model performs exceptionally well in open-pit mining production systems.

Multi-Dimensional Temporal Feature Fusion and Density Perception for Time Series Clustering

Jie Gao — 2025-04-01

In the field of data mining and knowledge discovery, clustering algorithms have emerged as a powerful tool for unsupervised learning. The adaptability and efficiency of these algorithms make them indispensable in a multitude of applications, including customer segmentation in marketing and anomaly detection in cybersecurity. However, when these clustering algorithms are applied to time series data, a number of distinctive challenges emerge. The representation of time series data, which is often vast and high-dimensional, requires the application of efficient techniques that reduce the dimensionality of the data while ensuring the preservation of vital information. Furthermore, existing clustering methods encounter difficulties when dealing with variable density distributions. In response to these challenges, we present the Density-based Clustering Model for Time Series (DCMD). This model seamlessly integrates temporal representation and clustering, ensuring efficiency and accuracy. Our Multi-dimensional Representation Fusion (MDR) method for time series retains critical features while reducing data dimensions. Furthermore, the K-Nearest Neighbor Weighted (NNW) clustering method enhances local density calculation. Rigorous benchmark evaluations validate the efficacy of our approach. Our contributions advance the field of time series clustering research and show promise for diverse applications.

Occluded Lane Line Detection with Deep Polynomial Regression in Global View

Shuman Ren — 2025-04-01

Occluded Lane line detection method based on depth polynomial regression in global field of view is proposed for the problem of lane lines being obscured on driving road. In order to obtain better lane line feature representation capability, a dual attention mechanism module that connects spatial attention and channel attention in series is introduced to improve the network's ability to obtain lane line features, and then its feature information is used to adopt the lane line detection method of line-direction position classification by adding a line-by-line detection branch after the VGG backbone network to search lane line pixel points through line-direction scanning; in order to distinguish the lane line In order to distinguish which lane line the pixel points belong to, a loss function is designed according to the idea of metric learning, and a vector block is introduced on the semantic segmentation network to record the vector distance of the lane line pixels; finally, the pixels on the current lane line are extracted by the OPTICS clustering model, and a depth polynomial approach is used to complete the fitting of the lane line. Experiments are conducted on the Tusimple dataset, and the results show that compared with the LaneNet network, the method in this paper improves 4.79% and 6.34% in accuracy and precision, respectively, and has a better detection effect on the obscured lane lines.

Optical-Flow Based Symmetric Feature Extraction for Facial Expression Recognition

Mohammad Zeraatkar — 2025-04-01

Facial expression analysis is one of the most essential tools for behavior interpretation and emotion modeling in Intelligent Human-Computer Interaction (HCI). Although humans can easily interpret facial emotions, computers have great difficulty doing so. Analyzing changes and deformations in the face is one of the methods through which machines can interpret facial expressions. However, maintaining great precision while being accurate, stable, and quick is still challenging in this field. To address this issue, this research presents an innovative and novel method to fully automatically extract critical features from a face during a facial expression. Various machine learning models are used on these features to analyze emotions. We used the optical flow algorithm to extract motion vectors divided into sections on the subject’s face. Finally, each section and its symmetric section were used to calculate a new vector. The final features produce a state-of-the-art accuracy of over 98% in emotion classification in the Extended Cohen-Kanade (CK+) facial expression dataset. Furthermore, we proposed an algorithm to filter the most important features with an SVM classifier and achieved an accuracy of over 97 % by only looking at 15% of the face area.

Personalized Intelligent Recommendation Model for Educational Games Based on Data Mining

Min Yang — 2025-04-01

In the era of Big data, how to filter massive information and push it to appropriate users is a subject that has been explored in computer information technology. In this context, in view of the poor effect of educational game recommendation affected by data sparsity, a collaborative filtering recommendation (CFR) algorithm integrating the covering rough granular layer clustering (CRGLC) and K-means clustering is proposed. On the basis of the K-means clustering CFR model, granular computing (GC) is introduced to build a covering rough granular space (CRGS) based on the user's comprehensive score and game type. By setting and adjusting coverage coefficients, local rough particle (LRP) sets of game users are searched under different particle layers to mitigate the impact of data sparsity. The improved algorithm is tested on the data sets with the sparsity of 0.937 and 0.901, and the mean absolute error (MAE) values of the two are 0.708 and 0.716. The results are relatively close, indicating that the model can effectively improve the accuracy of the model in the case of sparse data. Research is organized on the classification accuracy of the model, and the accuracy and F1 scores are 0.880 and 0.826, which are higher than the social spatial-temporal probabilistic matrix factorization and Slope One models in the literature. This indicates that the model is more accurate in identifying and classifying game types and is more conducive to educational game recommendations. In practical application performance testing, the model has small and large intra-cluster variations, resulting in good clustering performance. Compared with the known and better recommended algorithms of attributes clustering and score matrix filtering, dynamic evolutionary collaborative filtering, double trace normal minimization, and evolutionary heterogeneous clustering collaborative filtering, its MAE and root-mean-square error of scoring prediction are the lowest. By using this model to predict ratings for 500 user samples, the error is only 2.8%. It has been proved that this algorithm has higher accuracy in educational game recommendations. Overall, the innovation of the algorithm lies in the fusion of CRGLC and K-means clustering, and the introduction of grain computing to deal with the data sparsity problem and improve the recommendation accuracy. This research has some practical value in solving the problem of sparse data in educational game recommendations.

Application of Intelligent Obstacle Avoidance Algorithm Combined with Internet of Things Technology in Navigation

Yu Guo — 2025-04-01

With the prosperity and development of the Maritime Silk Road, China's maritime industry has reached a new height. While the maritime transport industry has been vigorously developed, it has also brought great challenges to safe navigation. To realize intelligent navigation, effectively prevent maritime collision accidents, and improve navigation safety, a structural model of intelligent navigation obstacle avoidance platform based on Internet of Things technology is first proposed. Then the research combines the analytic hierarchy process, artificial neural network and BP neural network algorithm, and introduces environmental factors to design an optimized intelligent navigation obstacle avoidance algorithm, so that the algorithm can make real-time intelligent adjustment strategies according to the changes of the actual environment. Finally, the collision risk at the location of the research ship is judged, and the priority list of obstacle avoidance is constructed by the risk value between different ships and the research ship, providing reference for the pilot. The research results show that the prediction accuracy of I-INOA algorithm is 97.83%. In the two obstacle avoidance experiments, the decision-making efficiency of the four ships based on I-IONA algorithm is the highest, which is 1. In practical application, the priority list of obstacle avoidance is P, O and S2. In conclusion, I-INOA algorithm has better performance and practicability, enabling the research ship to respond more intelligently and quickly.

FACENet: A Fusion Atrous and Channel Enhancement Network for Remote Sensing Image Instance Segmentation

Shenhua Zhao — 2025-04-01

The instance segmentation task has been widely used in remote sensing. However, existing remote sensing instance segmentation models may lead to incomplete mask segmentation in complex and diverse background environments. In addition, commonly used feature fusion methods struggle to handle instances of different sizes well and predominantly suffer from loss of semantic information, failing to segment the mask accurately. To solve these problems, we propose a fusion atrous and channel enhancement network (FACENet) for the remote sensing image (RSI) instance segmentation. Specifically, we first replace the FPN with the FACE-FPN, which produces a more detailed pyramid by increasing the receptive field at the feature level. Second, we propose a semantic enhancement module for mining the rich semantic information of the underlying features. Then, we enhance the model's adaptability to complex object deformations by introducing deformable convolution. Experiments on the iSAID, NWPU VHR-10, and HRSID datasets demonstrate that our proposed FACENet outperforms SOLOv2 in terms of average accuracy by 5.1%, 12.9%, and 7.6%, respectively, and beats other instance segmentation models.

Estimation and Recognition Methods of Human Gait Pose based on Computer Vision and Transformer

Yu Zou — 2025-04-01

Human gait pose estimation and recognition, as an emerging biometric technology, have advantages such as no need for target object cooperation, difficulty in forgery, and long-distance recognition. However, compared with traditional biometric special recognition, it is more susceptible to the influence of target object's arbitrary motion. In response to the above issues, the study introduces heterogeneous transfer learning to construct a human gait pose estimation and recognition method based on computer vision and Transformer, and improves it using the perspective gradually shift training method based on this. The research results indicated that the improved human gait pose estimation and recognition model had good recognition performance in 11 perspectives with intervals of 16° from 0° to 180°, and the corresponding change curve remained stable, with an average recognition rate of over 97%. The average initial validation rate of the improved model was 65.32% higher than before, and the maximum validation rate of the improved model achieved significant improvement from different angles. In comparison with other mainstream algorithms, the improved model proposed in the study had the highest average validation rate and average accuracy, which were 98.56% and 97.51%, respectively, and the corresponding average improvement index was greater than 20%. The above results confirm the performance and reliability of the research method, providing new solutions for the problem of human gait pose estimation and recognition in complex scenes.

Research on Real-time Detection of Pipeline Weld Defects Based on Lightweight Neural Networks

Zeyu Yu — 2025-04-01

In the field of pipeline weld defect detection, common object detection algorithms have high complexity and huge computational load, making it difficult to meet the real-time monitoring requirements of pipeline weld defects on pipeline production lines. To address this issue, this paper proposes a lightweight pipeline weld defect detection model YOLOv8-BVS based on the YOLOv8 object detection framework. The model introduces the BRA module to improve the recognition ability of small defects. To further improve the accuracy of model recognition, a lightweight upsampling algorithm CARAFE is used in the feature fusion network to improve the quality and richness of fused features. Finally, the experimental results showed that the model parameters were 1.56M, which was only 51.6% of the baseline, while the average accuracy reached 87.9%, an improvement of 3.4% compared to the baseline. This verified that the YOLOv8 BVS model met the requirements of online detection of pipeline weld defects while ensuring detection quality.

Driver Fatigue Detection Based on Multiple Physiological Signals and an Improved Deep Belief Network

Lin Wang — 2025-04-01

In order to accurately discriminate the driver fatigue, multiple physiological signals of 10 drivers were collected by a wireless body area network in actual driving, including neck electromyography (EMG) and electroencephalography (EEG). Then, the noises of signals were removed by several denoising methods, and 22 features were extracted, including energy entropy, multiscale entropy, and other relevant features. Subsequently, a deep belief network (DBN) was used to further extract multi-domain features. And then, a grey wolf optimization algorithm was used to optimize the performance of the DBN. The results showed that the accuracy of the model built in the present work was up to 96% in discriminating the fatigue states.

Improved YOLOv8n based lotus seedpod detection algorithm

Kun Zhang — 2025-04-01

These Aiming at the influence of the shape appearance, color and growth environment of lotus seedling, lotus seedling detection exists problems such as low efficiency, low precision, leakage and misdetection, etc., an improved lotus seedling detection algorithm FSM-YOLOv8 is proposed based on the YOLOv8n model. First, the C2f-Faster module reduces the number of model parameters while ensuring the structural feature extraction capability of the YOLOv8n network. Then, the SimAM attention mechanism is applied to the model feature extraction module, which enhances the multi-scale and spatial feature extraction capability of the model. Finally, MPDIoU is used as the boundary loss function to effectively solve the problem of low detection rate caused by the spatial overlap and occlusion of the lotus seed pods and lotus leaves.The results show that the improved FSM-YOLOv8 achieves 84.8%, 84.1%, and 87.9% of detection accuracy, 84.1%, and 87.9% of recall, respectively, compared with the YOLOv8n model, and reduces 13.4% of the parameter amount. 13.4%, which is a significant improvement in detection accuracy and model lightweighting, and can realize rapid identification of lotus seedpods in complex environments, and meet the demand of real-time identification of lotus seedpod picking robots in the process of picking.

Data-Fusion Based On Transfer Learning For Plant Disease Recognition

Jing Liu — 2025-04-01

In this paper, the research focused on wild and introduced cultivated flowers with multiple diseases such as Stephanitis, Sooty Mould, Xanthosis, and Leaf Blight, utilizing transfer learning and and data fusion technology to construct a plant disease detection model employing Faster R-CNN.The self-built data set collected during the flower growth cycle was trained and identified.To solve the problem of disease category imbalance in the actual collected data samples, the data of small category samples is enhanced from the perspective of category balance and label balance, and FocalLoss is used to improve the original classification loss function. Based on this self-built data set, the constructed IFRCNN disease detection model was compared with the SSD (Single Shot multibox Detector), ResNet18 and Yolov3 models. The results showed that for several common plant diseases in the dataset, the mAP of IFRCNN disease detection model was significantly higher than that of the other three models. It can effectively locate plant leaf disease areas, realize the detection of multiple diseases, and provide reference for accurate disease prevention and control.

YOLOv8-SS: A Method of Localizing Soldiers in Intricate Battlefield Environments

Yunlong Gao — 2025-04-01

As combat becomes more autonomous and intelligent in the future, and effective military target localization techniques are essential to understanding operational military deployment and target tracking. In this paper, we offer an instance segmentation technique for precise soldier localization in intricate battlefield environments, called YOLOv8-SS. First, in the YOLOv8 backbone network, the C2f module is replaced by the DualC2f module, which we created based on DualConv in order to minimize the amount of parameter computation while maintaining accuracy. Second, the feature extraction network is enhanced by import the global attention mechanism (GAM), which increases the cross-dimensional interaction between the channel and spatial information and boosts the model's feature extraction performance. Lastly, the reparameterization module DBB is used to redesign the segmentation head of YOLOv8. Convolutional branches of various sizes and shapes are added to the network's feature representation capacity during the training phase. In the inference phase, the convolutional branches are equivalently replaced with regular convolutional, which increases accuracy while maintaining inference efficiency. Additionally, a dataset for segmenting soldier instances include various battlefield situations is provided in this paper, and experimental validation is carried out using this dataset. The experimental results demonstrate that YOLOv8-SS improves the Box P, Box mAP50, and Box mAP50-95 measures by 2.7%, 2.9%, and 5.1%, respectively, in comparison to the baseline model YOLOv8n. As a result, the YOLOv8-SS model performs more accurately when it comes to segmenting soldiers in intricate battlefield environments.

An Efficient Point Cloud Correlation Enhancement RCNN for 3D Object Detection

Jialong Du — 2025-04-01

To meet the requirement of 3D object detection task , an efficient point clouds correlation enhancement RCNN(EPCE-RCNN) is proposed. The proposed method reduces the computational complexity and time consumption of the network through a lightweight proposal generation module, and accelerates the generation of the 3D proposal box. Meanwhile, during region of interest feature coding, the relevance among different grid points is enhanced through an efficient self-attention pooling module, so that the limitation that the pooling operation is influenced by the radius of a neighborhood query sphere is addressed. In addition, the combination of an attention mechanism and a feedforward network ensures the nonlinearity of the model, so that the model can perform feature expression better. Thus, the synchronous improvement of the network detection efficiency and the detection precision is realized. On the KITTI dataset, the detection accuracy of three difficulty levels reaches 89.99%, 81.69% and 77.17% respectively. Compared with the baseline Voxel-RCNN, the detection efficiency of EPCE-RCNN is improved by 12%. To verify the generalization and application value of the proposed method, a power equipment dataset with 3D label information is constructed, the 3D label frame information of the YCB dataset is also supplemented. Experiments are carried out on these datasets. In the experimental results of the verification set, the mAP of a mug, gelatin box, single clip, wedge clip and C clip can reach 37.67%, 40.06%, 35.63%, 30.01% and 37.31% respectively. Compared with the baseline, the proposed algorithm has a significant improvement and its generalization has been fully verified.

Optical Flow Estimation Method Based on Bidirectional Consistency Combined Occlusion

Haoxin Guo — 2025-04-01

In response to the failure of optical flow estimation to solve the tracking accuracy degradation caused by motion occlusion, this paper proposes an optical flow estimation method based on bidirectional consistency combined occlusion reasoning to improve the tracking accuracy degradation caused by motion occlusion. First, by utilizing the symmetry between forward and reverse optical flow mapping and occlusion mapping, the optical flow estimation value, luminance, contrast, and structure are simultaneously used as constraints for occlusion detection. Then, a new dynamic weight loss function module was designed to supervise the training of the optical flow estimation model. The endpoint error loss function is used and smooth L1 and gradient terms are introduced to obtain a continuous and smooth optical flow field, and binary cross entropy loss is used to solve the occlusion problem of consistency. Finally, experiments have shown that the proposed method outperforms FPCR Net, FlowNet3 and SCV algorithms in tracking accuracy on the MPI Sintel and Flying Chairs datasets, and has significant advantages in preserving resisting occlusion.

The Regularization and Deconvolution Algorithm Combining Salient Edges and Average Curvature in High-quality Visual Communication

Shuo Tan — 2025-04-01

The reconstruction of high-quality images is of great significance in fields such as medicine, visual communication, and satellite imaging. In order to avoid the interference of subjective and objective factors on image details and information quality, and reduce the damage of noise to video images, a deconvolution algorithm combining important edges and average curvature regularization is proposed to achieve image deblurring processing. By designing deconvolution models, alternating optimization of auxiliary variables, average curvature filter constraints, and mutual derivative image processing, image clarity can be improved. The proposed method was tested and the results showed that the success rate of deburring was higher than other comparative algorithms, and the repair results showed that the method can effectively achieve deblurring. This optimization method has good convergence during the iteration process, with peak signal-to-noise ratio, structural similarity index measurement value, and error ratio of 31.03, 0.96, and 1.61, respectively. The algorithm that considers edge information and curvature regularization processing can better preserve the quality and details of image information, which can effectively provide new technical means and tools for the field of visual communication.

Accelerated task learning using Q-learning with reduced state space and reward with bootstrapping effect

Varun Prakash Rajamohan — 2025-04-01

The influence of robots has been rapidly increasing in domestic scenarios. Robots learning in a self-supervised manner will be more efficient than programmed intelligence. In this paper, we present Q-learning-based task learning through interaction with the environment in a table-cleaning scenario. The environment consists of a table partitioned into two segments with a single object on it. The goal of the agent is to learn the sequence of tasks required to clean both segments of the table. Here, the state space is designed in such a way that its size is reduced to achieve better training time and success rate. Furthermore, four different rewards, denoted as r1, r2, r3 and r4, were allocated. The general reward allocation was based on the effect on the environment. The reward r4 is allocated in a novel way by relating two consecutive states to enhance the bootstrapping effect. Rewards r2 and r4 have improved the training time compared to r1 and r3. With reward allocation r2, the average reward starts converging around 290 iterations, and a success rate of approximately 84% is reached by 240 iterations. With reward allocation r4, the success rate reaches around 84% by 150 iterations.

Optimization of Speed Reducer Design based on an Enhanced Grey Wolf Optimizer

Mingshang Ma — 2025-04-01

Traditional swarm intelligence optimization methods perform erratically in engineering design due to difficulties in handling nonlinear data, local optimal errors and premature convergence. To address these problems, we developed an enhanced Gray Wolf Optimizer (OGWO) that employs Levy flight and elite adversarial-based learning methods. We evaluated its effectiveness using 20 benchmark functions and compared it with other GWO variants and popular algorithms. The results show that OGWO is superior in terms of convergence speed, accuracy, and freedom from stagnation, as confirmed by the Wilcoxon rank sum test. Furthermore, the effectiveness of OGWO in training Multilayer Perceptron (MLP) has been evaluated using the UCL datasets. Finally, OGWO has been applied to solve the gearbox design problem, proving its ability to provide optimal solutions in addressing real-life engineering issues.

YOLOv8-GRW:A YOLOv8-based Algorithm for Road Defect Detection

Ao Xu — 2025-04-01

Given the critical importance of road defect detection for ensuring vehicular safety and the inefficiencies and high costs associated with traditional detection methods, this paper introduces an enhanced road defect detection algorithm based on an improved YOLOv8-GRW model. This model incorporates a novel convolutional module, GSPConv, which utilizes GhostConv and space-to-depth (SPD) modifications to replace standard convolutional layers in the YOLOv8 backbone network, thereby significantly enhancing detection accuracy. Additionally, the feature fusion approach employs an optimized RepGFPN method, modified via GhostConv, which reduces the computational and operational load of RepGFPN while improving the model's feature fusion capabilities. Furthermore, the loss function has been designed around the WNIoU loss, which integrates the Normalized Wasserstein Distance (NWD) into the existing WIoU loss to balance the regression of bounding boxes between high and low-quality sample data, enhancing the detection performance for relatively small defects. Experimental results demonstrate a marked improvement in the performance of the modified algorithm over the original YOLOv8 model. Specifically, the detection accuracy rate of the revised algorithm increased by 3.6%, the F1 score increased by 2.2%, and the mAP@0.5 increased by 2.6% . These advancements substantiate the significant enhancements achieved by the proposed algorithm in the application of road defect detection.

Optimization of RED-PID controller using the chaotic-subpopulation strategy-based Aquila and Math algorithms

Junyong Tang — 2025-04-01

While the Transmission Control Protocol (TCP) is essential for congestion control by adjusting packet sending rates, it falls short of resolving the buffer bloat problem in critical routers. In response, Active Queue Management (AQM) mechanisms, notably Random Early Detection (RED), have been proposed to construct a feedback system, TCP/RED, for congestion control. However, existing AQM controllers like RED lack comprehensive optimization of control parameters for adapting to dynamic network conditions effectively. In this study, we propose a novel heuristic algorithm (AOMOA), which combines the global exploration of Aquila Optimizer (AO) with the local exploitation of Math Optimizer (MO), to optimize AQM controller parameters within the TCP/RED feedback system. AOMOA leverages chaotic-subpopulation and dynamic k-worst shift strategies to ensure a balance between exploration and exploitation, thereby mitigating premature convergence. Additionally, we analyze RED's intrinsic flaw and, therefore introduce a Proportional-Integral-Derivative (PID) adjuster into RED, RED-PID, to overcome the limitation according to theory analysis. To optimize RED-PID parameters, we present an optimization model ensuring stability and sensitivity in congestion control. Comprehensive simulations demonstrate that RED-PID, optimized by AOMOA, outperforms the standard RED controller, showcasing superior congestion control performance.

A Lightweight Multi-Party Key Authentication Management Protocol Based on Cyber-Physical Systems

Xiaoran Zhao — 2025-04-01

In the era of digital healthcare, secure information interaction among users, gateways, and multiple devices in a cyber-physical system (CPS) is very important, but also very challenging. However, existing authentication schemes can only accomplish authentication between gateways and smart devices, and do not consider the authentication needs of gateways, users and multiple devices. In addition, users need to initiate multiple key authentication requests to complete multi-device authentication, which greatly increases the communication overhead and security risks. In response, this paper proposes a lightweight multi-party key authentication protocol based on cyber-physical system. On the basis of meeting the user, gateway and multi-device authentication requirements, the key authentication process is effectively simplified by the CPS architecture, and the user only needs to initiate a request to complete the three-party multi-device authentication, which greatly reduces the communication overhead, reduces the security risks, and improves the scheme's adaptability and generalization ability in largescale device scenarios. Finally, the mathematical analysis confirms the reliability of the proposed scheme and points out that the scheme reduces the computational and communication requirements compared with similar methods, which is crucial for CPSs with limited resources.

Synthetic Data Enhances Mathematical Reasoning of Language Models Based on Artificial Intelligence

Zeyu Han — 2025-04-01

Current large language models (LLMs) training involves extensive training data and computing resources to handle multiple natural language processing (NLP) tasks. This paper endeavors to assist individuals to compose feasible mathematical question-answering (QA) language models in specific fields. We leveraged Gretel.ai, a feasible data generation platform, to generate high-quality mathematical QA data covering several areas, including definitions, theorems, and calculations related to linear algebra and abstract algebra. After fine- tuning through Open-AI infrastructure, GPT-3 performed significant improvements on accuracy, achieving a roughly 18.2% increase in abstract algebra benchmark, approximately 1.6x improvement on linear algebra theorems benchmark, and approximately 24.0% increase on linear algebra calculations benchmark. And small language models (SLMs) such as LLama-2-7B/13B and Mistral-7B have outstanding around 2x accuracy advancements in linear algebra calculations. This study demonstrates the potential for individuals to develop customized SLMs for specialized mathematical domains using synthetic data generation and fine-tuning techniques.