Title: Similarity and Generalization: from Noise to Corruption. Abstract: Contrastive learning aims to extract distinctive features from data by finding an embedding representation where similar samples are close to each other, and different ones are far apart. We study how NNs generalize the concept of similarity in the presence of noise, investigating two phenomena: Double Descent (DD) behavior and online/offline correspondence.  While DD examines how the network adjusts to the dataset during a long training time or by increasing the number of parameters, online/offline correspondence compares the network performances varying the quality (diversity) of the dataset. We focus on the simplest contrastive learning representative: Siamese Neural Networks (SNNs). We point out that SNNs can be affected by two distinct sources of noise: Pair Label Noise (PLN) and Single Label Noise (SLN). The effect of SLN is asymmetric, but it preserves similarity relations, while PLN is symmetric but breaks transitivity. We find that DD also appears in SNNs and is exacerbated by noise. We show that the dataset topology crucially affects generalization. While sparse datasets show the same performances under SLN and PLN  for an equal amount of noise, SLN outperforms PLN in the overparametrized region in dense datasets. Indeed, in this regime, PLN similarity violation becomes macroscopical, corrupting the dataset to the point where complete overfitting cannot be achieved. We call this phenomenon Density-Induced Break of Similarity (DIBS). Probing the equivalence between online optimization and offline generalization in SNNs, we find that their correspondence breaks down in the presence of label noise for all the scenarios considered.