Post-hoc attribution is widely used to identify important model inputs, but evaluating whether these attributions identify truly informative features is difficult because real datasets rarely provide reliable ground truth. We introduce a multimodal benchmark containing symbolic tabular, vision, and audio tasks with known informative feature sets. In the main benchmark conditions, informative variables, spatial regions, or channels occupy fixed input coordinates while the remaining inputs provide irrelevant or distracting information. We use the benchmark to study how attribution quality depends on predictive performance, irrelevant-feature burden and structure, model configuration, and attribution mechanism, while separately measuring identification, stability, and computational cost. In most symbolic-data sweeps, informative-set identification co-varies with predictive performance, while the relative ordering of attribution methods remains largely stable. Across modalities, no method dominates all architectures and conditions, and greater attribution complexity does not consistently improve identification. Simple gradient attribution is often competitive at lower computational cost, while the vision and audio results show that architecture and the form of irrelevant content materially affect attribution quality.
Figures & tables
Figure 1 : Benchmark motivation. Attribution scores are evaluated against a known informative feature set while irrelevant inputs and model conditions are varied.
Table 1 : Captum implementations and attribution parameters.
Figure 2 : Vision benchmark conditions. A class-bearing CIFAR-10 foreground is placed at a fixed (FP) or random (RP) position over a Gaussian random background (RB) or a structured but task-irrelevant Flower102 background (SB).
Figure 3 : Audio sources: (a) the predictive speech command, (b) Gaussian input, and (c) a structured but task-irrelevant environmental recording.
Data
Task
Predictive performance
Informative-set identification
Ground-truth informative set
Task-irrelevant inputs
Symbolic
Regression
NPS
RRA
Variables in the generating formula
Additional independent variables
Vision
Classification
Accuracy
IoU
CIFAR-10 foreground region
Gaussian noise or Flower102 background
Audio
Classification
Accuracy
RMA
Speech Commands channel
Gaussian noise or rainforest-audio channels
Table 2 : Benchmark design, evaluation, and ground-truth annotation.
Figure 4 : Symbolic one-factor sweeps. Colors and markers identify the six methods: ∙ DL, ▲ FA, ■ IG, ⧫ KS, × LIME, and ⊕ SA. The ▼ denotes prediction NPS. NPS and RRA are normalized to [0,1] , with larger values indicating better performance.
Figure 5 : Complementary symbolic-data evaluation. Convergence is the area under the RRA curve over 300 training epochs; consistency compares each sample’s top-ranked features with the dataset-average attribution. Both are normalized to SA. Memory and runtime are measured at test time. KS and LIME runtime values are scaled by (1/100) for visualization.
Panel A: Random background, fixed position (RBFP)
Architecture
Acc. (%)
SA
DL
IG
FA
KS
DLS
GB
LIME
ConvNeXt-Tiny ( Liu et al., 2022 )
85.11
0.829
0.666
0.554
0.860
0.021
0.666
0.656
0.021
DenseNet-121 ( Huang et al., 2017 )
83.38
0.738
0.566
0.601
0.748
0.022
0.674
0.639
0.022
EfficientNet-V2 ( Tan and Le, 2021 )
85.07
0.791
0.611
0.636
0.866
0.021
0.611
0.549
0.021
ResNet-18 ( He et al., 2016 )
77.44
0.678
0.530
0.551
0.677
0.020
0.532
0.450
0.020
ResNet-50 ( He et al., 2016 )
83.23
0.656
0.326
0.457
0.682
0.022
0.513
0.585
0.022
Table 3 : Vision accuracy and IoU under fixed-position random-background (RBFP) and structured-background (SBFP) conditions.
Panel A: Random background, fixed channel (RBFP)
Architecture
Acc. (%)
SA
DL
IG
FA
KS
DLS
GB
LIME
Conformer ( Gulati et al., 2020 )
20.97
0.310
0.015
0.025
0.225
0.277
0.025
0.100
0.320
LSTM ( Sak et al., 2014 )
73.77
0.684
0.590
0.260
0.515
0.431
0.248
0.697
0.564
RNN ( Medsker and Jain, 2001 )
67.00
0.653
0.585
0.275
0.447
0.427
0.440
0.814
0.548
TCN ( Kalchbrenner et al., 2016 )
80.96
0.641
0.297
0.258
0.539
0.139
0.185
0.663
0.325
Transformer ( Vaswani et al., 2017 )
23.25
0.460
0.236
0.138
0.335
0.170
0.110
0.440
0.305
Table 4 : Audio accuracy and RMA under fixed-channel Gaussian (RBFP) and structured task-irrelevant (SBFP) backgrounds.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
ID
∣S⋆∣
Generating function fj
1
1
a
2
1
a2
3
1
a2+12−1
4
1
sin(a)
5
1
exp(a)−1.5
6
1
2log(a2+1)−1
Appendix
Table 5 : Symbolic generating functions and informative-set sizes. Variables appearing in a formula are informative; all additional coordinates are task-irrelevant.
Feature attribution methods explain predictions by assigning importance scores to input features. Path-based methods such as Integrated Gradients are especially appealing because they satisfy \textit{completeness}: attributions sum to the change in model output between a reference state and the input. Yet most path methods define this trajectory in input space, explaining a model through pointwise perturbed inputs along a chosen path. An input-space path integrates the model's raw response at each point it passes through, with no control over the resolution at which a feature is queried; the early, baseline-adjacent part of the trajectory contributes to the explanation on equal footing with the input itself. Here, we lift path attribution from input space to a space of structured probe distributions around the example of interest, and call our method Reveal-IG. Rather than traversing raw input values, Reveal-IG progressively reveals information about the input and attributes changes in the model's expected output along this distributional path. The result is a path-attribution framework that retains completeness with respect to the expected model response, and naturally accommodates multiscale image probes and feature-wise uncertainty in tabular data. Synthetic diagnostics show that Reveal-IG avoids path artifacts that affect input-space methods, and across ImageNet classification and tabular regression it produces stable, signed attributions -- leading on metrics that use attribution sign while remaining competitive on the rest.
Data attribution seeks to quantify how individual training examples shape a model's predictions and underpins problems including data valuation, machine unlearning, and model interpretability. Despite having a long line of work, computationally scalable methods often struggle to predict the effect of removing training data in neural networks due to their non-convex nature. To overcome this challenge, metagradient-based methods such as MAGIC (Ilyas and Engstrom, 2025) differentiate each prediction through the entire training run and compute its exact influence with respect to the training data, but require a separate run for every prediction. To reduce this cost, we cast budgeted attribution as estimating a large influence matrix from a small number of measurements. We show that the measurements most appropriate for recovering this matrix differ from those best suited for attribution itself. We then present two algorithms, MAGE and SPELL, suited for reconstruction and attribution respectively, that run on existing metagradient machinery at no extra cost. Empirical studies demonstrate strong performance over existing baselines across training scales and measurement budgets.
Yuxi Chen, Hamza Golubovic, Han Tong +2
Carnegie Mellon University 1Department of Statistics & Data Science · Columbia University 2Department of Statistics · Columbia University 3Electrical Engineering Department +2
Feature-attribution methods are central to explainable artificial intelligence. Their assumptions are expressed in several mathematical languages: cooperative-game values, path integrals, gradient operators, perturbation distributions, and backpropagation rules. This survey proposes a common framework for local additive feature attribution. It organizes Shapley, path-based, gradient/backpropagation, perturbation, and CAM-style methods around five specification choices: value function, reference, path, perturbation distribution, and conservation rule. It then compares these methods through an axiom-by-method matrix and links common failure modes, including baseline sensitivity, off-manifold perturbations, sanity-check failures, adversarial manipulation, and method disagreement, to the assumptions that produce them. Finally, the survey proposes a ten-item reporting checklist for studies that use local additive attributions. The central message is that attribution results are meaningful only relative to the mathematical assumptions under which they are defined, and that those assumptions should be reported.