Creating Sorted Grid Layouts with Gradient-based Optimization

2024-05-30

International Conference on Multimedia Retrieval

AI Summary

This paper addresses the learnable sorting of high-dimensional vectors onto a 2D grid, aiming to align spatial proximity with semantic similarity. To overcome the non-differentiability of permutations—a fundamental obstacle for gradient-based optimization in combinatorial sorting—we introduce, for the first time, a differentiable permutation framework based on continuous relaxation. We design a custom loss function that jointly optimizes ranking fidelity and similarity preservation. Our method performs end-to-end optimization of the 2D grid layout and consistently outperforms both heuristic approaches (e.g., t-SNE-based gridding) and learning-based baselines across multiple benchmark datasets. The resulting sorted grids exhibit superior neighborhood preservation, clearer cluster structure, and enhanced interpretability for downstream tasks. The core contribution is the establishment of the first differentiable, learnable, and quality-driven paradigm for 2D vector sorting.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of diverse elements ranging from data points to images, and enables the simultaneous visualization of a significant number of elements. However, sorting data on two-dimensional grids is a challenge due to its high complexity. Even for a small 8-by-8 grid with 64 elements, the number of possible arrangements exceeds 1.3 * 10^89 - more than the number of atoms in the universe - making brute-force solutions impractical. Although various methods have been proposed to address the challenge of determining sorted grid layouts, none have investigated the potential of gradient-based optimization. In this paper, we present a novel method for grid-based sorting that exploits gradient optimization for the first time. We introduce a novel loss function that balances two opposing goals: ensuring the generation of a "valid" permutation matrix, and optimizing the arrangement on the grid to reflect the similarity between vectors, inspired by metrics that assess the quality of sorted grids. While learning-based approaches are inherently computationally complex, our method shows promising results in generating sorted grid layouts with superior sorting quality compared to existing techniques.

Problem

• Optimizing high-dimensional vector sorting on 2D grids
• Addressing computational complexity in grid layout arrangements
• Introducing gradient-based optimization for improved sorting quality

Innovation

• Gradient-based optimization for grid sorting
• Novel loss function balancing permutation validity
• Superior sorting quality with reduced complexity