[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84809-en":3,"doc-seo-84809-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84809,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","How Far is Too Far? Defining the Distance Threshold for Verification Siamese Networks","Siamese verification networks compare objects by learning an embedding space where similar instances map closer and dissimilar instances map further apart. Verification assigns two inputs to the same class when their embedding distance is below a predefined threshold t. Selecting t is difficult and typically relies on labeled data. This work proposes an unsupervised approach that models the distance distribution as bimodal and sets t at the minimum between modes, enabling threshold updates in deployment without annotation while reaching about 94% average accuracy on MNIST, CIFAR-10, LFW, and PKLot.","How Far is Too Far? Defining the Distance Threshold for Verification Siamese Networks.  \nHelo´ısa Dias Viotto∗ , Cau Samonek∗ , Lucas Garcia Pedroso†, Marcos Sunye∗ , Andr Abed Grgio∗ , Paulo Lisboa de Almeida∗  \n∗ Departamento de Informtica (DInf), Universidade Federal do Paran, Curitiba, PR -Brazil {heloisa.viotto,cauesamonek,sunye,gregio,[paulorla](paulorla}@ufpr.br)[}](paulorla}@ufpr.br)[@ufpr.br](paulorla}@ufpr.br)  \n† Departamento de Matemtica (DMAT), Universidade Federal do Paran Curitiba, PR -Brazil  \n[lucaspedroso@ufpr.br](lucaspedroso@ufpr.br)  \narXiv :2607 .05329v 1 [ cs .LG] 6 Jul 2026  \nAbstract—Siamese verification networks are widely used to compare items such as faces, cars, or signatures. In these scenarios, the network is trained to learn an embedding space in which similar objects are mapped closer together, while dissimilar objects are mapped further apart. Two objects are considered to belong to the same class (e.g., the same person in two different images) when the distance between their embeddings falls below a predefined threshold. Defining this threshold, however, is a nontrivial task and typically requires labeled data. In this work, we assume that the distribution of distances produced by a siamese verification network can be approximated by a bimodal function. Based on this assumption, we propose an unsupervised method to determine the verification threshold by identifying the minimum point between the two modes. The proposed approach does not require annotated samples, enabling the verification threshold tobe updated directly in the deployment environment without the cost of manual labeling. We evaluate our method on four datasets: MNIST, CIFAR-10, LFW, and PKLot. The results indicate that the proposed approach achieves an average verification accuracy of 94%, comparable to the Equal Error Rate method, while eliminating the need for labeled data.  \nIndex Terms—Deep Learning, Embedding, Verification Siamese Network, Bimodal Function.  \nI. INTRODUCTION  \nSiamese networks have become ubiquitous due to their effectiveness in tasks such as object tracking, matching, andreidentification [1]–[3] . This paper focuses on defining the distance threshold t for verification-by-distance tasks, in which two objects are projected into an embedding space RE and compared using a distance metric [1], [3] .  \nIn verification problems [3], [4], siamese networks are typically composed of two identical branches that share the same weights. Each branch implements a function f(x) : RI → RE , responsible for mapping the input space RI into the embedding space RE , where often I > E. During training, the network parameters are optimized to project similar inputs close to eachother in the embedding space, while mapping dissimilar inputs further apart [1], [2] . A general scheme of such networks is shown in Figure 1a, and an example of a 2D embedding for digit comparison is shown in Figure 1b.  \nThis work was funded by the Ministry of Health’s R&D project between SAPS/MS and C3SL/UFPR, by the Brazilian National Council for Scientific and Technological Development (CNPq)– Grant 444192/2024-7, and by a CNPq Research Productivity grant.  \ninput A  \ninput B  \nembedding  \n....  \n....  \n....  \n\n|  |\n| --- |\n|  |\n|  |\n| .... |\n|  |\n\ndistance out  \n(a) General scheme.  \nDimension  \n1  \n0.5  \n0  \n−1 −0 .5 0 0.5 1 First Dimension  \n(b) 2D embedding example.  \nFig. 1. (a) General scheme of a verification siamese network. (b) Example of a 2D embedding generated by a verification siamese network for the MNIST [5] dataset for the digits 0 to 3 . Solid lines represent distances between objects of the same class and dashed lines indicate distances between different classes.  \nAfter training, two inputs A and B can be compared by feeding them to the network to generate their embeddings. These embeddings are then compared using a distance function d (f(A), f (B)), where a common choice is the L2 distance. 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