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Faithful and Efficient Explanations for Neural Networks via Neural Tangent Kernel Surrogate Models
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Proposes trace NTK (trNTK) and random-projection variants of approximate empirical NTK as kernels for kernel-GLM surrogate models, evaluating faithfulness via Kendall-tau rank correlation and data attribution on CIFAR10, MNIST variants, COLA, and poisoned data.
Problem
Approximate empirical neural tangent kernels are expensive to compute, and prior evaluations of kernel surrogate models for neural networks relied on test accuracy or label similarity, which do not measure how faithfully the surrogate reproduces the network's output for explanation and data attribut
Approach
Defines the trace NTK, a cosine-normalized block-trace of the eNTK that drops the C^2 memory scaling, plus random-projection versions (proj-trNTK, proj-pNTK), and measures surrogate faithfulness by Kendall-tau correlation between kGLM and NN correct-class softmax probabilities.
Key results
- trNTK achieves Kendall-tau of 0.776 on ResNet18 (CIFAR10) and 0.809 on BERT-base (COLA), with TAD near zero.
- Across all experiments the kGLM tau_K has a lower bound of 0.7, with the trNTK the most consistent kernel across ResNet18 and BERT-base.
- Projection trNTK takes 1.12h versus 389h for full trNTK on ResNet18, while staying close in faithfulness (0.737 vs 0.776).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use cosine-normalized trace NTK instead of unnormalized trNTK⁰ (ablation) | kGLM surrogate for a 21-layer CNN · CIFAR10 poisoned-data experiment, clean test | Kendall-τ: 0.344 -> 0.643 | Helped |
| use cosine-normalized trace NTK instead of unnormalized trNTK⁰ (ablation) | kGLM surrogate for a 21-layer CNN · CIFAR10 poisoned-data experiment, poisoned test | Kendall-τ: 0.125 -> 0.569 | Helped |
| use random projection for trace NTK (ablation) | kGLM surrogate for a 21-layer CNN · CIFAR10 poisoned-data experiment, clean test | Kendall-τ: 0.643 -> 0.565 | Hurt |
| use random projection for trace NTK (ablation) | kGLM surrogate for a 21-layer CNN · CIFAR10 poisoned-data experiment, poisoned test | Kendall-τ: 0.569 -> 0.418 | Hurt |
| replace trace aggregation with projected pseudo-NTK aggregation (ablation) | kGLM surrogate for a 21-layer CNN · CIFAR10 poisoned-data experiment | Kendall-τ: 0.643 -> 0.554; 0.569 -> 0.665 | Mixed |
| use trNTK rather than the embedding kernel (ablation) | kGLM surrogate for ResNet18 · CIFAR10 | Kendall-τ: 0.768 -> 0.776 | Helped |
| use trNTK rather than proj-trNTK (ablation) | kGLM surrogate for BERT-base · COLA | Kendall-τ: 0.800(9) -> 0.809(9) | Helped |
| train the kGLM using ground-truth labels rather than NN outputs (ablation) | kGLM surrogate · ResNet18 and BERT-base experiments | Kendall-τ | Helped |
Surprising findings
- The projection pNTK has much lower faithfulness on ResNet18 (tau 0.407) than projected trNTK, despite being cheaper.
- The conjugate kernel gives near-random precision (1.65%) as a poisoned-data forensic model despite reasonable tau_K.
Limitations
- Kendall-tau requires reducing the vector output to a scalar (correct-class logit), losing information from the full softmax.
- Faithfulness of the kGLM surrogate does not guarantee the same reasoning as the underlying network.
- trNTK computation scales linearly with the number of output classes, and evaluations are restricted to kGLM surrogates.
Experimental setup
Datasets: MNIST FMNIST CIFAR10 COLA BadNet poisoned CIFAR10
Benchmarks: MNIST FMNIST CIFAR10 COLA BadNet poisoned CIFAR10
Metrics: Kendall-tau rank correlation test accuracy differential misclassification coincidence rate precision recall computation time
Baselines: unnormalized trNTK proj-pNTK embedding kernel conjugate kernel Representer Points
Builds on: neural tangent kernel TRAK Representer Points pseudo neural tangent kernel
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