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HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks

Yuanyuan Chen, Boyang Li, Han Yu, Pengcheng Wu, Chunyan Miao

TL;DR

HYDRA (Hypergradient Data Relevance Analysis) reframes DNN predictions as outcomes of training data by unrolling the test-loss hypergradient with respect to per-sample weights along the full optimization trajectory. It introduces a Hessian-free approximation for efficient data-credit computation and provides theoretical bounds on the approximation error, demonstrated to be accurate and more stable than influence functions. Empirically, HyDRA identifies influential or mislabeled data with higher fidelity, delivers substantial speedups (up to ~971×) over Hessian-based approaches, and aids debugging by effectively removing mislabeled examples. The work offers a scalable, data-centric interpretability tool with practical impact on data debugging, bias assessment, and transparency in DNN predictions.

Abstract

The behaviors of deep neural networks (DNNs) are notoriously resistant to human interpretations. In this paper, we propose Hypergradient Data Relevance Analysis, or HYDRA, which interprets the predictions made by DNNs as effects of their training data. Existing approaches generally estimate data contributions around the final model parameters and ignore how the training data shape the optimization trajectory. By unrolling the hypergradient of test loss w.r.t. the weights of training data, HYDRA assesses the contribution of training data toward test data points throughout the training trajectory. In order to accelerate computation, we remove the Hessian from the calculation and prove that, under moderate conditions, the approximation error is bounded. Corroborating this theoretical claim, empirical results indicate the error is indeed small. In addition, we quantitatively demonstrate that HYDRA outperforms influence functions in accurately estimating data contribution and detecting noisy data labels. The source code is available at https://github.com/cyyever/aaai_hydra_8686.

HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks

TL;DR

HYDRA (Hypergradient Data Relevance Analysis) reframes DNN predictions as outcomes of training data by unrolling the test-loss hypergradient with respect to per-sample weights along the full optimization trajectory. It introduces a Hessian-free approximation for efficient data-credit computation and provides theoretical bounds on the approximation error, demonstrated to be accurate and more stable than influence functions. Empirically, HyDRA identifies influential or mislabeled data with higher fidelity, delivers substantial speedups (up to ~971×) over Hessian-based approaches, and aids debugging by effectively removing mislabeled examples. The work offers a scalable, data-centric interpretability tool with practical impact on data debugging, bias assessment, and transparency in DNN predictions.

Abstract

The behaviors of deep neural networks (DNNs) are notoriously resistant to human interpretations. In this paper, we propose Hypergradient Data Relevance Analysis, or HYDRA, which interprets the predictions made by DNNs as effects of their training data. Existing approaches generally estimate data contributions around the final model parameters and ignore how the training data shape the optimization trajectory. By unrolling the hypergradient of test loss w.r.t. the weights of training data, HYDRA assesses the contribution of training data toward test data points throughout the training trajectory. In order to accelerate computation, we remove the Hessian from the calculation and prove that, under moderate conditions, the approximation error is bounded. Corroborating this theoretical claim, empirical results indicate the error is indeed small. In addition, we quantitatively demonstrate that HYDRA outperforms influence functions in accurately estimating data contribution and detecting noisy data labels. The source code is available at https://github.com/cyyever/aaai_hydra_8686.

Paper Structure

This paper contains 28 sections, 7 theorems, 47 equations, 6 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. HyDRA: Hypergradient for Data Relevance Analysis
  3. Measuring Data Contribution
  4. Fast Approximation
  5. Time and Space Complexity
  6. Related Work
  7. Influence function.
  8. Interpreting DNNs.
  9. Hypergradient-based optimization.
  10. Experimental Evaluation
  11. Datasets and Networks
  12. Manual Inspection
  13. Influential examples.
  14. Inter-class contribution.
  15. Approximation Error
  16. ...and 13 more sections

Key Result

theorem 1

Under the above conditions and vanilla GD, the norm of the approximation error is bounded by

Figures (6)

  • Figure 1: An illustration of HyDRA and influence functions (IF). After the removal of some training data points, the training loss shifts from the blue curve to the red curve. IF estimates the contribution within the convex region near the old $\boldsymbol{\theta}$. HyDRA tracks the influence of data removal along the entire optimization process, possibly leading to a different local optimum.
  • Figure 2: Inter-class contribution shown as heatmaps. Rows represent classes of training data and columns represent classes of test data.
  • Figure 3: HyDRA's hypergradient approximation error averaged over 500.0 Fashion-MNIST data points.
  • Figure 4: Sign error rates of HyDRA's approximation and influence functions on Fashion-MNIST
  • Figure 5: Spearman's rank correlation with the ground truth for HyDRA's approximation technique and influence functions on Fashion-MNIST
  • ...and 1 more figures

Theorems & Definitions (8)

  • theorem 1
  • theorem 2
  • definition 1
  • theorem 1
  • theorem 2
  • corollary 1
  • theorem 3
  • theorem 4