Mixed Dimension Embeddings with Application to Memory-Efficient Recommendation Systems (1909.11810v3)

Abstract: Embedding representations power machine intelligence in many applications, including recommendation systems, but they are space intensive -- potentially occupying hundreds of gigabytes in large-scale settings. To help manage this outsized memory consumption, we explore mixed dimension embeddings, an embedding layer architecture in which a particular embedding vector's dimension scales with its query frequency. Through theoretical analysis and systematic experiments, we demonstrate that using mixed dimensions can drastically reduce the memory usage, while maintaining and even improving the ML performance. Empirically, we show that the proposed mixed dimension layers improve accuracy by 0.1% using half as many parameters or maintain it using 16X fewer parameters for click-through rate prediction task on the Criteo Kaggle dataset.

• The paper introduces a novel mixed-dimension embedding design that allocates vector sizes based on object popularity.
• It empirically demonstrates up to 16x parameter reduction or enhanced accuracy on datasets like Criteo.
• The work provides a theoretical framework distinguishing data-limited and memory-limited regimes for scalable recommendations.

An Analysis of Mixed Dimension Embeddings for Memory-Efficient Recommendation Systems

The paper explores the adoption of mixed dimension embeddings as a memory-efficient alternative for large-scale recommendation systems. Traditional embedding layers, which map categorical features to a vector space of fixed dimensions, can be hugely memory-intensive, accounting for the vast majority of the storage demands in large-scale recommendation systems. The authors propose an innovative embedding layer architecture where the dimension of each embedding vector adapts to the popularity of the object it represents. The objective is to manage memory usage effectively without compromising model performance, or even enhancing it.

Key Contributions and Findings

1. Mixed Dimension (MD) Embeddings Design: The paper introduces MD embedding layers, which adjust the dimension of embedding vectors based on anisotropic object frequencies in datasets. In many real-world datasets, like the Criteo Kaggle dataset, a small fraction of indices dominates the query distribution, necessitating a strategy that allocates resources where needed most.
2. Empirical Results: The paper reveals that using MD embeddings can simultaneously cut memory demands and bolster model performance. On the Criteo Kaggle dataset, the proposed method enhances accuracy by 0.1% with half the parameters or sustains it using 16 times fewer parameters. Furthermore, training times on GPUs are more than halved with MD embeddings compared to uniform dimension (UD) ones.
3. Theoretical Foundation: The authors put forth a mathematical framework segmenting recommendation systems into data-limited and memory-limited regimes. They establish mathematical assurances that MD embeddings outperform UD embeddings in terms of matrix recovery and reduced reconstruction distortion when dealing with popularity-skewed data distributions. Additionally, they provide specific criteria under which MD embeddings excel, such as when object popularity is significantly uneven.
4. Implementation and Generalization: The authors apply MD embeddings to well-documented collaborative filtering and neural collaborative filtering contexts, using datasets with pronounced popularity skews. Across these applications, MD embeddings demonstrate that capacity for frequently-accessed embeddings can be increased without affecting overall performance, leading to efficient generalization and better resource utilization.

Implications

The implications of this research offer potential advancements along multiple dimensions. Practically, recommendation systems across numerous domains—including e-commerce, streaming services, and social media—could benefit from reduced computational costs and enhanced scalability. Theoretically, the work links embedding dimensionality to data prominence metrics and spectral characteristics, presenting meaningful insights into data representation and feature learning.

Future Directions

Future exploration could focus on the simultaneous optimization of both data and memory constraints, looking into adaptive strategies that dynamically manage embedding dimensions as the query distribution evolves over time. Moreover, extending the benefits demonstrated in recommendation systems to other functional areas within AI, such as natural language processing and computer vision, offers promising opportunities, given that these domains could also exhibit similar data skew characteristics.

In conclusion, the proposed mixed dimension embedding strategy presents a compelling step forward in balancing memory efficiency with model performance, particularly in the memory-intensive landscape of modern recommendation systems. Through strong theoretical underpinnings and empirical validation, it serves as a solid foundation for future research and implementation in related spheres.