Source-linked AI summary
What is the Effect of Importance Weighting in Deep Learning?
Jonathon Byrd, Zachary C. Lipton
TL;DR
The paper asks how importance weighting affects over-parameterized deep neural networks, a setting where prior evidence is limited despite widespread use. It investigates weighted training across architectures, tasks, datasets, and regularization choices, finding that weighting effects generally fade with training but can be partly restored by L2 regularization or batch normalization.
Problem
The effect of importance weighting is poorly understood for over-parameterized deep networks, which can fit separable training data and continue training beyond zero error.
Method
The authors evaluate class-conditioned importance weighting across synthetic, image, and text classification tasks, testing multiple architectures and combinations with L2 regularization, dropout, and batch normalization.
Results
Across tasks, architectures, and datasets, weighting affects models early but usually becomes indistinguishable from unweighted training after sufficient epochs; L2 regularization and batch normalization restore some impact, unlike dropout.
Takeaways & Limitations
Importance weighting in deep networks may be useful mainly with early stopping or selected regularization, raising concerns about its standard application.
Takeaways & Limitations
The paper leaves open how to choose stopping times or weight-decay coefficients when importance weighting is intended to matter.
Abstract
from arXiv · showhide
Importance-weighted risk minimization is a key ingredient in many machine learning algorithms for causal inference, domain adaptation, class imbalance, and off-policy reinforcement learning. While the effect of importance weighting is well-characterized for low-capacity misspecified models, little is known about how it impacts over-parameterized, deep neural networks. This work is inspired by recent theoretical results showing that on (linearly) separable data, deep linear networks optimized by SGD learn weight-agnostic solutions, prompting us to ask, for realistic deep networks, for which many practical datasets are separable, what is the effect of importance weighting? We present the surprising finding that while importance weighting impacts models early in training, its effect diminishes over successive epochs. Moreover, while L2 regularization and batch normalization (but not dropout), restore some of the impact of importance weighting, they express the effect via (seemingly) the wrong abstraction: why should practitioners tweak the L2 regularization, and by how much, to produce the correct weighting effect? Our experiments confirm these findings across a range of architectures and datasets.
1. Introduction
Importance weighting is widely used to correct distributional discrepancies, but its effect on over-parameterized deep networks is unclear. This paper investigates when weighting changes learned decision boundaries and finds that its influence depends on training and regularization choices.
- Importance weighting: Importance sampling estimates quantities under a target distribution using samples from a different source distribution.Practitioners implement it by resampling or weighting examples by likelihood ratios.
- Applications: Weighted risk minimization is used in domain adaptation, active learning, causal inference, crowdsourcing, and deep reinforcement learning.Applications include covariate or label shift correction, treatment-effect estimation, logged bandit feedback, and replay-buffer sampling.
- Open question: Importance weighting has established benefits for low-capacity misspecified models because changing error weights typically produces a different fitted model.This motivates asking whether the same effect persists when deep networks can fit training data perfectly.
- Open question: Over-parameterized neural networks can separate training data and continue improving generalization after reaching zero training error, making weighting effects theoretically uncertain.If all training points can be classified correctly, the need to trade off errors across examples is unclear.
- Study design: The experiments examine class-conditioned weighting across architectures, classification tasks, and datasets, including CIFAR-10, MRPC, and synthetic two-dimensional data.They evaluate training and test classifications, decision boundaries, and off-manifold points.
- Salient findings: Weighting significantly affects standard neural networks early in training, but its effect generally dissipates after sufficient epochs.L2 regularization and batch normalization restore some impact, whereas dropout does not; the findings are replicated across networks, tasks, and datasets.
2. Theoretical Motivation
The paper draws on linear-network theory suggesting that separable-data solutions can be invariant to reweighting, then tests whether this intuition extends to practical nonlinear networks. It also asks how regularization changes the interaction between importance weights and learned solutions.
- Theoretical Motivation: The paper investigates whether importance weighting changes solutions in realistic deep networks, where many practical datasets are separable.The experiments use the linear-network results as intuition rather than as a direct theoretical guarantee for nonlinear models.
- Theoretical Motivation: Prior theory studies separable data, cross-entropy, linear separators, and SGD, where weights may diverge while their direction converges.The resulting decision boundary depends on weight direction rather than magnitude.
- Theoretical Motivation: The hard-margin solution depends only on data-point locations, so oversampling and reweighting do not affect it in the linear setting.This motivates testing whether weight invariance also appears in modern deep nonlinear networks.
- Regularization: L2 regularization penalizes large-norm solutions, whereas dropout does not, suggesting that these methods may interact differently with importance weighting.This motivates examining regularization as a possible determinant of weighting effects.
3. Experiments
The experiments test importance weighting across synthetic, image, and text settings, including different architectures, regularization choices, class-imbalance scenarios, and training regimes. They compare how weighting affects learned boundaries, classification ratios, and test behavior.
- Datasets and tasks: Experiments span separable and non-separable synthetic datasets, CIFAR-10 image classification, and MRPC paraphrase classification.The synthetic study includes a two-dimensional linearly separable dataset plus moons and overlapping Gaussian data; CIFAR-10 experiments include binary, imbalanced, and multiclass settings.
- Synthetic experiments: The synthetic separable-data experiment compares unregularized logistic regression and a 64-unit ReLU MLP trained with minibatch SGD for 10,000 epochs.Both models use batch size 8 and a learning rate of approximately 0.045 determined from the data matrix's maximum singular value.
- CIFAR-10 experiments: The CIFAR-10 binary classifier uses cats and dogs for training, evaluates on all ten test classes and random noise, and is implemented as a convolutional network.The architecture contains five convolutional layers, two pooling layers, two dense layers, and a binary output layer; models are trained for 1000 epochs with minibatch SGD.
- CIFAR-10 results: Across differently weighted CIFAR-10 models, 82% of test-example labels agree on average, including 74% agreement for out-of-sample images from the other eight classes.Predictions for each weighting are formed by majority vote across nine random seeds before agreement is measured.
4. Discussion
Importance weighting affects deep-network decision boundaries early, but its influence generally fades with training, even under label noise. Regularization and batch normalization can preserve some effect, whereas subsampling changes predictions more clearly.
- Training dynamics: Importance-weighted models converge toward similar classification ratios and separators after sufficient training, including under label noise.The reported convergence extends across in-domain, out-of-domain, and random-vector evaluations.
- Sampling versus weighting: Subsampling the training set changes classification ratios, unlike loss weighting, which does not balance predictions across classes.The reported effect appears for in-domain, out-of-domain, and random-noise images.
- Training dynamics: Extreme importance weights slow convergence, with classification-ratio stabilization occurring long after perfect training accuracy.BERT models required over 100 epochs for extreme-weight ratios to stabilize, compared with typical fine-tuning of 3–4 epochs.
- Normalization: Batch normalization preserves an importance-weighting effect in ResNet models after 1000 epochs, but removing it makes behavior resemble ordinary convolutional networks.The passage reports a persistent effect with batch normalization and its disappearance without it.
- Regularization: L2 regularization affects importance-weighted classifiers and slows classification-ratio convergence, while replacing it with dropout yields behavior similar to unregularized models.On synthetic data, L2 causes models to partition less sample space to the down-weighted class.
5. Related Work
The paper builds on prior theoretical work about weight-agnostic solutions in separable deep linear networks and situates importance weighting within diverse deep-learning applications. It addresses a gap in explicit studies of importance weighting’s effects on modern deep-network decision boundaries.
- Research gap: No previous paper explicitly studied how importance weighting affects decision boundaries learned by modern deep neural networks.The related-work discussion distinguishes many applications from direct analysis of learned boundaries.
- Theoretical inspiration: The experiments draw on theories that deep linear networks optimized by SGD become importance-weight agnostic on separable data.This theoretical motivation is paired with earlier work motivating importance weighting under model misspecification.
- Applications: Prior work applies importance-weighted or weighted training to contextual bandits, imitation learning, and replay-buffer temporal-difference updates.The replay-buffer weights cited here are heuristic Bellman-error weights rather than likelihood ratios.
6. Conclusions
Across architectures and domains, importance-weighting effects appear mainly with early stopping and can disappear asymptotically, while L2 regularization and batch normalization preserve some influence. The findings question standard deep-learning applications of importance weighting and identify subsampling as a possible alternative for class imbalance.
- Main conclusion: Importance-weighting effects may require early stopping and disappear asymptotically in over-parameterized deep networks.The authors suggest learned solutions may depend on training-example locations rather than density.
- Main conclusion: Different weightings can produce similar separators and high agreement even on out-of-domain images, while label-shift correction may lose test accuracy over training.The reported concern is that classifier improvement can coincide with diminishing weighting effects.
- Scope and mechanisms: The same patterns occur across MLPs, convolutional networks, attention-based transformers, synthetic data, images, and natural language.Residual networks retain some effect, but it vanishes when batch normalization is removed.
- Scope and mechanisms: L2 regularization can preserve some weighting effect by preventing convergence to large-norm, support-vector-dominated solutions, unlike dropout.This is presented as the authors’ explanation for the differing regularization behavior.
- Practical implications: Loss weighting fails to correct deep-network training-set class imbalance, whereas subsampling clearly changes predictions and may be an alternative on sufficiently large datasets.The alternative is stated cautiously as a possibility rather than a universal replacement.
- Practical implications: The findings support rethinking standard deep-learning uses of importance weighting and leave the choice of stopping times or weight-decay coefficients unresolved.The authors specifically call for a principled way to choose these settings when weighting is desired.
A. Supplemental Materials
The supplemental materials report results across nonlinearly separable and overlapping synthetic datasets, CIFAR-10 image subsets, regularization settings, and optimization variants.
- Results include experiments on a nonlinearly separable moons dataset and an overlapping Gaussians dataset.
- Supplemental figures examine early stopping for L2-regularized models and models with dropout.
- Additional CIFAR-10 analyses cover class imbalance, label-flipped training data, automobile-versus-truck classification, and models with batch normalization.
- The supplemental experiments also include convolutional networks trained with Adam and ResNet models.