Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

SimO Loss: Anchor-Free Contrastive Loss for Fine-Grained Supervised Contrastive Learning

Taha Bouhsine, Imad El Aaroussi, Atik Faysal, Wang Huaxia

TL;DR

A novel anchor-free contrastive learning method leveraging the proposed Similarity-Orthogonality (SimO) loss that minimizes a semi-metric discriminative loss function that simultaneously optimizes two key objectives: reducing the distance and orthogonality between embeddings of similar inputs while maximizing these metrics for dissimilar inputs, facilitating more fine-grained contrastive learning.

Abstract

We introduce a novel anchor-free contrastive learning (AFCL) method leveraging our proposed Similarity-Orthogonality (SimO) loss. Our approach minimizes a semi-metric discriminative loss function that simultaneously optimizes two key objectives: reducing the distance and orthogonality between embeddings of similar inputs while maximizing these metrics for dissimilar inputs, facilitating more fine-grained contrastive learning. The AFCL method, powered by SimO loss, creates a fiber bundle topological structure in the embedding space, forming class-specific, internally cohesive yet orthogonal neighborhoods. We validate the efficacy of our method on the CIFAR-10 dataset, providing visualizations that demonstrate the impact of SimO loss on the embedding space. Our results illustrate the formation of distinct, orthogonal class neighborhoods, showcasing the method's ability to create well-structured embeddings that balance class separation with intra-class variability. This work opens new avenues for understanding and leveraging the geometric properties of learned representations in various machine learning tasks.

SimO Loss: Anchor-Free Contrastive Loss for Fine-Grained Supervised Contrastive Learning

TL;DR

A novel anchor-free contrastive learning method leveraging the proposed Similarity-Orthogonality (SimO) loss that minimizes a semi-metric discriminative loss function that simultaneously optimizes two key objectives: reducing the distance and orthogonality between embeddings of similar inputs while maximizing these metrics for dissimilar inputs, facilitating more fine-grained contrastive learning.

Abstract

We introduce a novel anchor-free contrastive learning (AFCL) method leveraging our proposed Similarity-Orthogonality (SimO) loss. Our approach minimizes a semi-metric discriminative loss function that simultaneously optimizes two key objectives: reducing the distance and orthogonality between embeddings of similar inputs while maximizing these metrics for dissimilar inputs, facilitating more fine-grained contrastive learning. The AFCL method, powered by SimO loss, creates a fiber bundle topological structure in the embedding space, forming class-specific, internally cohesive yet orthogonal neighborhoods. We validate the efficacy of our method on the CIFAR-10 dataset, providing visualizations that demonstrate the impact of SimO loss on the embedding space. Our results illustrate the formation of distinct, orthogonal class neighborhoods, showcasing the method's ability to create well-structured embeddings that balance class separation with intra-class variability. This work opens new avenues for understanding and leveraging the geometric properties of learned representations in various machine learning tasks.
Paper Structure (18 sections, 6 theorems, 15 equations, 5 figures, 1 table, 2 algorithms)

This paper contains 18 sections, 6 theorems, 15 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Anchor-Based Contrastive Learning
  4. Dimensionality Collapse in Contrastive Learning Methods
  5. Explainability of Contrastive Learning
  6. Preliminaries
  7. Metric Space
  8. Semi-Metric Space
  9. Method
  10. Similarity-Orthogonality (SimO) Loss Function
  11. Anchor-Free Contrastive Learning
  12. Experimental Setup
  13. Results
  14. Ablation Study
  15. Discussion and Limitations
  16. ...and 3 more sections

Key Result

Theorem A.1

Let $([0, 1]^n, d')$ and $([0, 1]^n, d")$ be two spaces where $[0, 1]^n$ is the n-dimensional unit hypercube and $d'$ and $d"$ are defined as: where $e_i, e_j \in [0, 1]^n$, $d_{ij} = |e_i - e_j|^2$ is the squared Euclidean distance, and $o_{ij} = (e_i \cdot e_j)^2$ is the squared dot product. Then $([0, 1]^n, d')$ and $([0, 1]^n, d")$ are a semimetric space.

Figures (5)

  • Figure 1: 3D interpretation of Anchor-Free Contrastive Learning (AFCL) using Similarity-Orthogonality (SimO) loss: (a) On the left, all the samples are negatively contrasted with each other. The loss function aims to push them away from each other while maintaining the orthogonality between all the embedding vectors in our embedding Space. (b) On the right, all the data points belong to the same class. The loss function here decreases the orthogonality and the distance between embeddings of the same class.
  • Figure 2: Manifold visualization of the Embedding Space using T-SNE for both (a) trainset and (b) testset
  • Figure 3: Pairwise Manifold Visualization using TSNE (Lower-Triangular Plots
  • Figure 4: Normalized Similarity Matrix calculated using SimO (a) Pairwise embeddings (b) Class Means
  • Figure 5: Continual Learning Properties of SimO with AFCL Framework

Theorems & Definitions (10)

  • Theorem A.1: SimO semi-metric space
  • proof
  • Theorem A.2: SimO Dimentionality Collapse Prevention
  • proof
  • Theorem A.3: Curse of Orthogonality
  • proof
  • Lemma A.3.1: Johnson–Lindenstrauss Lemma
  • Theorem A.4: Johnson-Lindenstrauss Lemma Addressing the Curse of Orthogonality
  • proof
  • Corollary A.4.1