Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Statistical Framework for Data-dependent Retrieval-Augmented Models

Soumya Basu, Ankit Singh Rawat, Manzil Zaheer

TL;DR

The paper investigates data-dependent retrieval-augmented models (RAMs) by formalizing a joint training objective that couples a retriever with a predictor operating over a data-store. It provides a rigorous excess risk analysis decomposing errors into generalization, retriever, and predictor components, with Sobolev-space and Rademacher-based bounds to quantify approximation and generalization effects. The authors instantiate the framework with MLP-based retriever/predictor pairs and demonstrate benefits on open-domain QA benchmarks, including clear trade-offs between retriever and predictor capacity and data-store size. The work connects to existing end-to-end RAM training approaches and offers principled guidance for designing RAMs with provable generalization properties and scalable performance in real-world QA tasks.

Abstract

Modern ML systems increasingly augment input instances with additional relevant information to enhance final prediction. Despite growing interest in such retrieval-augmented models, their fundamental properties and training are not well understood. We propose a statistical framework to study such models with two components: 1) a {\em retriever} to identify the relevant information out of a large corpus via a data-dependent metric; and 2) a {\em predictor} that consumes the input instances along with the retrieved information to make the final predictions. We present a principled method for end-to-end training of both components and draw connections with various training approaches in the literature. Furthermore, we establish excess risk bounds for retrieval-augmented models while delineating the contributions of both retriever and predictor towards the model performance. We validate the utility of our proposed training methods along with the key takeaways from our statistical analysis on open domain question answering task where retrieval augmentation is important.

A Statistical Framework for Data-dependent Retrieval-Augmented Models

TL;DR

The paper investigates data-dependent retrieval-augmented models (RAMs) by formalizing a joint training objective that couples a retriever with a predictor operating over a data-store. It provides a rigorous excess risk analysis decomposing errors into generalization, retriever, and predictor components, with Sobolev-space and Rademacher-based bounds to quantify approximation and generalization effects. The authors instantiate the framework with MLP-based retriever/predictor pairs and demonstrate benefits on open-domain QA benchmarks, including clear trade-offs between retriever and predictor capacity and data-store size. The work connects to existing end-to-end RAM training approaches and offers principled guidance for designing RAMs with provable generalization properties and scalable performance in real-world QA tasks.

Abstract

Modern ML systems increasingly augment input instances with additional relevant information to enhance final prediction. Despite growing interest in such retrieval-augmented models, their fundamental properties and training are not well understood. We propose a statistical framework to study such models with two components: 1) a {\em retriever} to identify the relevant information out of a large corpus via a data-dependent metric; and 2) a {\em predictor} that consumes the input instances along with the retrieved information to make the final predictions. We present a principled method for end-to-end training of both components and draw connections with various training approaches in the literature. Furthermore, we establish excess risk bounds for retrieval-augmented models while delineating the contributions of both retriever and predictor towards the model performance. We validate the utility of our proposed training methods along with the key takeaways from our statistical analysis on open domain question answering task where retrieval augmentation is important.
Paper Structure (44 sections, 6 theorems, 96 equations, 1 figure, 6 tables)

This paper contains 44 sections, 6 theorems, 96 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Problem setup
  3. Joint training and excess risk
  4. Excess risk decomposition
  5. Generalization error
  6. Approximation error
  7. Retriever error
  8. Predictor error
  9. Usefulness of retrieval set:
  10. Final excess risk bound
  11. Illustrative example: MLPs
  12. Connections with prior end-to-end training
  13. Experiments
  14. Discussion and related work
  15. Conclusion
  16. ...and 29 more sections

Key Result

Theorem 3.3

Under Assumption a:gap-sobolev-main and a:true-sobolev-main, the excess risk for the retriever class $\Theta$ and predictor class $\Xi$ is bounded as where $f_{\mathcal{N}}(\nu; \mathcal{A}, \mathcal{B})\triangleq\sup_{b \in \mathcal{B}}\sqrt{\log(\mathcal{N}(\mathcal{A}, \nu, \|\cdot\|_{2, [n], b}))}$ and $\|\cdot\|_{2, [n], \theta}$ and $\|\cdot\|_{2, [n], \xi}$ are defined in eq:cov-norm.

Figures (1)

  • Figure 1: Left: Excess risk bound as we vary retriever and predictor size for a fixed $n$ and $\mathscr{I}$ based on Theorem \ref{['thm:main-mlp']}. Note that different size combination of predictor and retriever achieves same risk bound. Right: Excess risk bound of RAM as we increase data-store size in contrast to direct MLP predictor with no retrieval. We plot for various values of $n$, with each color corresponding to a fixed $n$.

Theorems & Definitions (16)

  • Theorem 3.3: Excess risk of joint training
  • Theorem 3.4: Excess risk for MLP
  • Definition A.1: Rademacher complexity
  • Definition A.2: Covering nsumber
  • Definition A.3: Multi-layer perceptron (MLP)
  • Definition A.4: Sobolev space
  • Theorem A.5: Restated siegel2023optimal Theorem 1
  • Definition A.6: VC dimension and growth of a binary function class
  • Definition A.7: Pseudo dimension of real valued function class
  • Theorem A.8: Adaptation of bartlett2019nearly Theorem 6
  • ...and 6 more