[Paper Review] Estimating Training Data Influence by Tracing Gradient Descent

Garima Pruthi, Frederick Liu+2 more|arXiv (Cornell University)|Feb 19, 2020

AI and HR Technologies121 citations

TL;DR

TracIn traces how training data influence a test prediction by aggregating first-order gradient contributions across training iterations, offering a scalable, checkpoint-based influence metric usable across models and tasks.

ABSTRACT

We introduce a method called TracIn that computes the influence of a training example on a prediction made by the model. The idea is to trace how the loss on the test point changes during the training process whenever the training example of interest was utilized. We provide a scalable implementation of TracIn via: (a) a first-order gradient approximation to the exact computation, (b) saved checkpoints of standard training procedures, and (c) cherry-picking layers of a deep neural network. In contrast with previously proposed methods, TracIn is simple to implement; all it needs is the ability to work with gradients, checkpoints, and loss functions. The method is general. It applies to any machine learning model trained using stochastic gradient descent or a variant of it, agnostic of architecture, domain and task. We expect the method to be widely useful within processes that study and improve training data.

Motivation & Objective

• Motivate the need to quantify how individual training examples affect a specific test prediction.
• Introduce TracIn as a practical, gradient-based influence measure.
• Provide a scalable implementation using first-order approximations, checkpoints, and selective layers.
• Show that TracIn generalizes across architectures, domains, and SGD-based training.
• Suggest applications in data cleaning and mislabelling detection.

Proposed method

• Define TracIn as the sum of first-order gradient dot products across iterations where a training example is used: TracIn(z, z') = sum_t or minibatch t of eta_t * grad l(w_t, z') · grad l(w_t, z).
• Extend to minibatches with a 1/b scaling: TracIn(z, z') = (1/b) sum_t: z in B_t eta_t grad l(w_t, z') · grad l(w_t, z).
• Approximate the idealized influence with a first-order Taylor expansion of the test loss change per update.
• Introduce TracInCP which uses checkpoints to replay training steps and sums gradients at selected checkpoints: TracInCP(z, z') = sum_i eta_i grad l(w_{t_i}, z) · grad l(w_{t_i}, z').
• Offer practical guidance on layer selection and using checkpoints to reduce computation while preserving informative signals.

Experimental results

Research questions

• RQ1 Can we quantify how individual training examples influence a specific test prediction using gradients from training iterations?
• RQ2 Does a checkpoint-based, first-order approximation provide a scalable and accurate measure of training-data influence across models and tasks?
• RQ3 How does TracIn compare to existing influence methods (e.g., influence functions, representer point selection) in identifying mislabelled data or data points that most affect a test prediction?
• RQ4 What practical considerations (minibatch handling, layer selection, learning rate schedules) affect the accuracy and utility of TracIn in real training pipelines?

Key findings

• TracIn outperforms influence functions and representer points in identifying mislabelled training data in CIFAR-10 and MNIST experiments.
• Using TracInCP with checkpoints, a large fraction of mislabelled data can be recovered early in the ranking (e.g., more than 80% recovered in the first 20% of the ranking on CIFAR-10).
• The first-order approximation correlates highly with actual loss changes, with Pearson correlation around 0.978 in MNIST experiments.
• Different checkpoints contribute complementary information, and sampling checkpoints with high loss reduction improves the signal.
• TracIn scales to large models such as ResNet-50 on ImageNet and can operate by projecting gradients to lower-dimensional representations (rank-1 gradient structure for FC layers).
• TracIn provides interpretable insights into proponents (positive influence) and opponents (negative influence) for test predictions and can aid data-centric improvements like correcting mislabeled data.