aspg-21-4108-1791472394 20261008151314 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2026 27 1 Bassim A. Hassan College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq Issam A. R. Moghrabi Department of Information Systems and Technology, Kuwait Technical College, Kuwait City, Kuwait Talal M. Alharbi Department of Mathematics, College of Science, Buraydah, Qassim University, Saudi Arabia Alaa Luqman Ibrahim Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region, Iraq 16.00 Normal false false false TR X-NONE AR-SA DefSemiHidden="false" DefQFormat="false" DefPriority="99" LatentStyleCount="371"> UnhideWhenUsed="true" QFormat="true" Name="heading 2"/> UnhideWhenUsed="true" QFormat="true" Name="heading 3"/> UnhideWhenUsed="true" QFormat="true" Name="heading 4"/> UnhideWhenUsed="true" QFormat="true" Name="heading 5"/> UnhideWhenUsed="true" QFormat="true" Name="heading 6"/> UnhideWhenUsed="true" QFormat="true" Name="heading 7"/> UnhideWhenUsed="true" QFormat="true" Name="heading 8"/> UnhideWhenUsed="true" QFormat="true" Name="heading 9"/> Name="index 1"/> Name="index 2"/> Name="index 3"/> Name="index 4"/> Name="index 5"/> Name="index 6"/> Name="index 7"/> Name="index 8"/> Name="index 9"/> UnhideWhenUsed="true" Name="toc 1"/> UnhideWhenUsed="true" Name="toc 2"/> UnhideWhenUsed="true" Name="toc 3"/> UnhideWhenUsed="true" Name="toc 4"/> UnhideWhenUsed="true" Name="toc 5"/> UnhideWhenUsed="true" Name="toc 6"/> UnhideWhenUsed="true" Name="toc 7"/> UnhideWhenUsed="true" Name="toc 8"/> UnhideWhenUsed="true" Name="toc 9"/> Name="Normal Indent"/> Name="footnote text"/> Name="annotation text"/> Name="header"/> Name="footer"/> Name="index heading"/> UnhideWhenUsed="true" QFormat="true" Name="caption"/> Name="table of figures"/> Name="envelope address"/> Name="envelope return"/> Name="footnote reference"/> Name="annotation reference"/> Name="line number"/> Name="page number"/> Name="endnote reference"/> Name="endnote text"/> Name="table of authorities"/> Name="macro"/> Name="toa heading"/> Name="List"/> Name="List Bullet"/> Name="List Number"/> Name="List 2"/> Name="List 3"/> Name="List 4"/> Name="List 5"/> Name="List Bullet 2"/> Name="List Bullet 3"/> Name="List Bullet 4"/> Name="List Bullet 5"/> Name="List Number 2"/> Name="List Number 3"/> Name="List Number 4"/> Name="List Number 5"/> Name="Closing"/> Name="Signature"/> UnhideWhenUsed="true" Name="Default Paragraph Font"/> Name="Body Text"/> Name="Body Text Indent"/> Name="List Continue"/> Name="List Continue 2"/> Name="List Continue 3"/> Name="List Continue 4"/> Name="List Continue 5"/> Name="Message Header"/> Name="Salutation"/> Name="Date"/> Name="Body Text First Indent"/> Name="Body Text First Indent 2"/> Name="Note Heading"/> Name="Body Text 2"/> Name="Body Text 3"/> Name="Body Text Indent 2"/> Name="Body Text Indent 3"/> Name="Block Text"/> Name="Hyperlink"/> Name="FollowedHyperlink"/> Name="Document Map"/> Name="Plain Text"/> Name="E-mail Signature"/> Name="HTML Top of Form"/> Name="HTML Bottom of Form"/> Name="Normal (Web)"/> Name="HTML Acronym"/> Name="HTML Address"/> Name="HTML Cite"/> Name="HTML Code"/> Name="HTML Definition"/> Name="HTML Keyboard"/> Name="HTML Preformatted"/> Name="HTML Sample"/> Name="HTML Typewriter"/> Name="HTML Variable"/> Name="Normal Table"/> Name="annotation subject"/> Name="No List"/> Name="Outline List 1"/> Name="Outline List 2"/> Name="Outline List 3"/> Name="Table Simple 1"/> Name="Table Simple 2"/> Name="Table Simple 3"/> Name="Table Classic 1"/> Name="Table Classic 2"/> Name="Table Classic 3"/> Name="Table Classic 4"/> Name="Table Colorful 1"/> Name="Table Colorful 2"/> Name="Table Colorful 3"/> Name="Table Columns 1"/> Name="Table Columns 2"/> Name="Table Columns 3"/> Name="Table Columns 4"/> Name="Table Columns 5"/> Name="Table Grid 1"/> Name="Table Grid 2"/> Name="Table Grid 3"/> Name="Table Grid 4"/> Name="Table Grid 5"/> Name="Table Grid 6"/> Name="Table Grid 7"/> Name="Table Grid 8"/> Name="Table List 1"/> Name="Table List 2"/> Name="Table List 3"/> Name="Table List 4"/> Name="Table List 5"/> Name="Table List 6"/> Name="Table List 7"/> Name="Table List 8"/> Name="Table 3D effects 1"/> Name="Table 3D effects 2"/> Name="Table 3D effects 3"/> Name="Table Contemporary"/> Name="Table Elegant"/> Name="Table Professional"/> Name="Table Subtle 1"/> Name="Table Subtle 2"/> Name="Table Web 1"/> Name="Table Web 2"/> Name="Table Web 3"/> Name="Balloon Text"/> Name="Table Theme"/> Name="List Paragraph"/> Name="Intense Quote"/> Name="Subtle Emphasis"/> Name="Intense Emphasis"/> Name="Subtle Reference"/> Name="Intense Reference"/> UnhideWhenUsed="true" Name="Bibliography"/> UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/> Name="Grid Table 1 Light Accent 1"/> Name="Grid Table 6 Colorful Accent 1"/> Name="Grid Table 7 Colorful Accent 1"/> Name="Grid Table 1 Light Accent 2"/> Name="Grid Table 6 Colorful Accent 2"/> Name="Grid Table 7 Colorful Accent 2"/> Name="Grid Table 1 Light Accent 3"/> Name="Grid Table 6 Colorful Accent 3"/> Name="Grid Table 7 Colorful Accent 3"/> Name="Grid Table 1 Light Accent 4"/> Name="Grid Table 6 Colorful Accent 4"/> Name="Grid Table 7 Colorful Accent 4"/> Name="Grid Table 1 Light Accent 5"/> Name="Grid Table 6 Colorful Accent 5"/> Name="Grid Table 7 Colorful Accent 5"/> Name="Grid Table 1 Light Accent 6"/> Name="Grid Table 6 Colorful Accent 6"/> Name="Grid Table 7 Colorful Accent 6"/> Name="List Table 1 Light Accent 1"/> Name="List Table 6 Colorful Accent 1"/> Name="List Table 7 Colorful Accent 1"/> Name="List Table 1 Light Accent 2"/> Name="List Table 6 Colorful Accent 2"/> Name="List Table 7 Colorful Accent 2"/> Name="List Table 1 Light Accent 3"/> Name="List Table 6 Colorful Accent 3"/> Name="List Table 7 Colorful Accent 3"/> Name="List Table 1 Light Accent 4"/> Name="List Table 6 Colorful Accent 4"/> Name="List Table 7 Colorful Accent 4"/> Name="List Table 1 Light Accent 5"/> Name="List Table 6 Colorful Accent 5"/> Name="List Table 7 Colorful Accent 5"/> Name="List Table 1 Light Accent 6"/> Name="List Table 6 Colorful Accent 6"/> Name="List Table 7 Colorful Accent 6"/> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:8.0pt; mso-para-margin-left:0in; line-height:107%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri",sans-serif; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:Arial; mso-bidi-theme-font:minor-bidi; mso-ansi-language:TR;} Artificial neural networks have become a cornerstone of modern artificial intelligence, powering progress in a wide range of fields. Their effective training heavily depends on techniques from unconstrained optimization, with iterative methods based on gradients being especially common. This study presents a new variant of the conjugate gradient method tailored specifically for unconstrained optimization tasks. The method is carefully designed to meet the sufficient descent condition and ensures global convergence. Comprehensive numerical testing highlights its advantages over traditional conjugate gradient techniques, showing improved performance in terms of iteration counts, function evaluations, and overall computational time across a variety of problem sizes. Additionally, this new approach has been successfully used to improve neural network training. Experimental results show faster convergence and better accuracy, with fewer training iterations and reduced mean squared error compared to standard methods. Overall, this work offers a meaningful contribution to optimization strategies in neural network training, displaying the method is potential to tackle the complex optimization problems often encountered in machine learning. 2026 220 233 4108 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.270120 https://www.americaspg.com/journal/21/article/4108 https://www.americaspg.com/storage/61758236896.pdf