How Far is Too Far? Defining the Distance Threshold for Verification Siamese Networks

Jul 16, 2026

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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.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages6

Reading Time15 min

Abstract

Introduction

Siamese verification and distance threshold t

Challenges in defining t

Existing threshold estimation practices

Proposed bimodal modeling approach and contributions

How Far is Too Far? Defining the Distance Threshold for Verification Siamese Networks. Helo´ısa Dias Viotto∗ , Cau Samonek∗ , Lucas Garcia Pedroso†, Marcos Sunye∗ , Andr Abed Grgio∗ , Paulo Lisboa de Almeida∗ ∗ 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) † Departamento de Matemtica (DMAT), Universidade Federal do Paran Curitiba, PR -Brazil [lucaspedroso@ufpr.br](lucaspedroso@ufpr.br) arXiv :2607 .05329v 1 [ cs .LG] 6 Jul 2026 Abstract—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. Index Terms—Deep Learning, Embedding, Verification Siamese Network, Bimodal Function. I. INTRODUCTION Siamese 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] . In 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. This 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. input A input B embedding .... .... .... | | | --- | | | | | | .... | | | distance out (a) General scheme. Dimension 1 0.5 0 −1 −0 .5 0 0.5 1 First Dimension (b) 2D embedding example. Fig. 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. After 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. The inputs A and B are considered to b

FAQs

What is the role of the distance threshold t in verification Siamese networks?

It determines whether two inputs belong to the same class by checking whether their embedding distance d(f(A), f(B)) is below t.

Why is defining the threshold t nontrivial in practice?

Common strategies require labeled data and can bias the threshold toward training/validation distributions that may differ from deployment data.

How does the proposed method estimate t without labeled samples?

It models the distribution of distances produced by the network as a bimodal function and selects t as the minimum point between the two modes.

Jul 16, 2026

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