Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

When is an Embedding Model More Promising than Another?

Maxime Darrin, Philippe Formont, Ismail Ben Ayed, Jackie CK Cheung, Pablo Piantanida

TL;DR

This paper establishes theoretical foundations for comparing embedding models, drawing upon the concepts of sufficiency and informativeness, and devise a tractable comparison criterion (information sufficiency), leading to a task-agnostic and self-supervised ranking procedure.

Abstract

Embedders play a central role in machine learning, projecting any object into numerical representations that can, in turn, be leveraged to perform various downstream tasks. The evaluation of embedding models typically depends on domain-specific empirical approaches utilizing downstream tasks, primarily because of the lack of a standardized framework for comparison. However, acquiring adequately large and representative datasets for conducting these assessments is not always viable and can prove to be prohibitively expensive and time-consuming. In this paper, we present a unified approach to evaluate embedders. First, we establish theoretical foundations for comparing embedding models, drawing upon the concepts of sufficiency and informativeness. We then leverage these concepts to devise a tractable comparison criterion (information sufficiency), leading to a task-agnostic and self-supervised ranking procedure. We demonstrate experimentally that our approach aligns closely with the capability of embedding models to facilitate various downstream tasks in both natural language processing and molecular biology. This effectively offers practitioners a valuable tool for prioritizing model trials.

When is an Embedding Model More Promising than Another?

TL;DR

This paper establishes theoretical foundations for comparing embedding models, drawing upon the concepts of sufficiency and informativeness, and devise a tractable comparison criterion (information sufficiency), leading to a task-agnostic and self-supervised ranking procedure.

Abstract

Embedders play a central role in machine learning, projecting any object into numerical representations that can, in turn, be leveraged to perform various downstream tasks. The evaluation of embedding models typically depends on domain-specific empirical approaches utilizing downstream tasks, primarily because of the lack of a standardized framework for comparison. However, acquiring adequately large and representative datasets for conducting these assessments is not always viable and can prove to be prohibitively expensive and time-consuming. In this paper, we present a unified approach to evaluate embedders. First, we establish theoretical foundations for comparing embedding models, drawing upon the concepts of sufficiency and informativeness. We then leverage these concepts to devise a tractable comparison criterion (information sufficiency), leading to a task-agnostic and self-supervised ranking procedure. We demonstrate experimentally that our approach aligns closely with the capability of embedding models to facilitate various downstream tasks in both natural language processing and molecular biology. This effectively offers practitioners a valuable tool for prioritizing model trials.
Paper Structure (59 sections, 6 theorems, 36 equations, 23 figures, 10 tables, 1 algorithm)

This paper contains 59 sections, 6 theorems, 36 equations, 23 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related works
  3. Embedding evaluation.
  4. Theoretical Foundations for Comparing Embedding Models
  5. Background and notation
  6. Sufficiency and informativeness ordering of embedding models
  7. Comparing statistical experiments with embedding Models
  8. Challenges in ranking embedding models and their deficiency
  9. Quantifying Information Sufficiency Between Embedding Models
  10. Estimating Information Sufficiency
  11. Pairwise embedder evaluation.
  12. Practical embedding evaluation.
  13. Experimental Setup
  14. Text Embeddings Evaluation
  15. Experimental setting
  16. ...and 44 more sections

Key Result

Proposition 1

The following relationships hold:

Figures (23)

  • Figure 1: Communicating a concept $y\in \mathsf{Y}$ over two embedding models with prediction $\rho_V(V)$.
  • Figure 2: Pairwise $\mathcal{I}_{S}$ for text embedders.
  • Figure 3: Correlation between $\overline{\mathcal{I}_S}$ scores and downstream task performances in (a) NLP and (b) Molecular Modelling. $\varrho_p$ is the Pearson correlation, $\varrho_s$ the spearman correlation, and $\tau$ is the Kendall-Tau coefficient. See \ref{['sec:full_mteb_results']} for unaggregated results in NLP and \ref{['sec:complementary_resultsADMET']} in molecular modeling.
  • Figure 4: \ref{['fig:predictive_mi_graph']}, presents the information sufficiency directed graph and the induced communities. \ref{['fig:my_tasks_rankings_scatter']} displays the performance on additional downstream tasks and models not evaluated in the MTEB leaderboard. \ref{['fig:nlp_instruct_finetuning']} shows that instruction finetuning positively impacts the models' performance on the downstream tasks and that this improvement is captured by $\overline{\mathcal{I}_S}$.
  • Figure 5: (a) Pairwise information sufficiency graph between the embedders. The center color represents the ability to simulate other models, while the surrounding colors represent the ability to be simulated by other models. Red indicates a high ability to simulate or be simulated, while blue indicates a low ability. (b) Mean rank of the models (ordered by $\overline{\mathcal{I}_S}$ score) on downstream tasks.
  • ...and 18 more figures

Theorems & Definitions (18)

  • Definition 1: Sufficiency and informativeness orderings Korner1977
  • Proposition 1: Relationships of sufficiency and information
  • Remark 1
  • Proposition 2: Comparison of embedding models through Bayes risks
  • Remark 2
  • Definition 2
  • Corollary 1
  • Remark 3
  • Definition 3: Information sufficiency
  • Remark 4
  • ...and 8 more