[Paper Review] HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks

Yuanyuan Chen, Boyang Li+3 more|arXiv (Cornell University)|Feb 4, 2021

Adversarial Robustness in Machine Learning3 references4 citations

TL;DR

HYDRA proposes a hypergradient-based method to interpret deep neural network predictions by tracing the influence of training data across the entire optimization trajectory, avoiding reliance on the Hessian while maintaining bounded approximation error. It outperforms influence functions in data contribution estimation and noisy label detection, with a 971× speedup on GPU hardware.

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.

Motivation & Objective

• To address the black-box nature of deep neural networks by attributing model predictions to training data.
• To overcome the limitations of influence functions, which only analyze data influence near final model parameters and rely on computationally expensive Hessian matrices.
• To develop a scalable, Hessian-free method that tracks data influence throughout the full training trajectory.
• To theoretically bound the approximation error when removing the Hessian from hypergradient computation.
• To empirically validate that the Hessian-free HYDRA method achieves higher accuracy and efficiency than influence functions in data contribution estimation and noisy label detection.

Proposed method

• HYDRA computes the hypergradient of the test loss with respect to training data weights by unrolling the entire optimization trajectory.
• It uses a recursive formulation to propagate the gradient of test loss through all training steps, capturing how changes in data weights affect the model’s convergence path.
• The method replaces the Hessian with a Lipschitz-based approximation, proving that the approximation error is bounded under mild conditions.
• A theoretical upper bound on the error is derived using assumptions on learning rate decay and Hessian convergence.
• The algorithm is adapted to mini-batch training by incorporating batch indicators and modifying gradient updates accordingly.
• The Hessian is omitted in practice, and the method is shown to maintain high correlation with Hessian-aware measurements.

Experimental results

Research questions

• RQ1 Can hypergradient-based data relevance analysis that tracks the full training trajectory outperform local influence functions in estimating training data contribution?
• RQ2 What is the theoretical impact of removing the Hessian from hypergradient computation, and can the resulting error be bounded?
• RQ3 Does the Hessian-free approximation in HYDRA maintain high accuracy while achieving significant speedups compared to Hessian-based methods?
• RQ4 How does HYDRA compare to influence functions in detecting data points with noisy labels?
• RQ5 Can the Hessian-free HYDRA method scale efficiently with model size and number of tracked samples?

Key findings

• HYDRA reduces wall-clock running time by a factor of 971 compared to Hessian-aware methods on 2 Titan X Pascal GPUs.
• The Hessian-free approximation introduces only 11% to 16% more error than Hessian-aware measurements, while influence functions add 11% to 16% more error than the Hessian-aware baseline.
• HYDRA achieves higher correlation with Hessian-aware data influence estimates than influence functions do.
• The method demonstrates superior performance in detecting data points with erroneous labels compared to influence functions.
• Theoretical analysis shows that the approximation error is bounded, and under exponential learning rate decay, the error diminishes to zero as training progresses.
• HYDRA maintains strong performance even when the Hessian is omitted, with error bounds provably controlled under standard optimization conditions.