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1Scan for outdated or missing drivers - takes under a minute2Repair Windows errors before they cause bigger problems3Fix the driver behind crashes, sound loss and screen glitchesIntegrated Gradients (IG) estimates how much each input feature contributes to the difference between a model’s output for a specific example and its output for a chosen reference baseline. It is a local, gradient-based diagnostic—not proof that a model is fair, correct, causal, or fully understood. The baseline, selected output, and numerical approximation all shape what the attribution means.
How does Integrated Gradients work?
For a differentiable model function F, an input x, and a baseline x′, IG follows the straight-line path from the baseline to the input. It evaluates the model’s gradients along that path, integrates them, then scales each feature’s result by the difference between that feature in the input and baseline. In plain terms, IG allocates the output change between the two cases across the input features.
The path integral is generally approximated numerically. The attribution is therefore tied to the specific input, baseline, model output, and approximation settings; it is not a universal importance score for a feature.
The axioms behind the method
The method was introduced in Mukund Sundararajan, Ankur Taly, and Qiqi Yan’s 2017 paper, “Axiomatic Attribution for Deep Networks”. The authors write: “We identify two fundamental axioms—Sensitivity and Implementation Invariance that attribution methods ought to satisfy.” These are design criteria for attribution methods. Satisfying them does not make an attribution a causal explanation or an exhaustive account of model behavior.
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What baseline should you use?
The baseline is the reference case against which the input’s output difference is attributed. Changing it can change the meaning and values of the resulting attributions. Choose a reference that makes sense for the data and question, and state what it represents when reporting results.
- For images: Consider what a meaningful reference image represents for the task; an all-zero input is not automatically a meaningful absence of content.
- For text: Select a reference representation that is valid for the model’s input format and makes sense as a comparison case.
- For structured data: Explain what the reference values mean in the context of the example and model.
These are considerations, not universal baseline prescriptions. Captum uses zero internally when no baseline is supplied, but that software default should not be assumed meaningful for every task or modality. Check whether reasonable alternative baselines materially change the interpretation.
How do you calculate IG in practice?
An implementation needs a differentiable forward computation, an input, a baseline, and a target output when the model returns multiple outputs. It samples gradients at interpolated points between the baseline and input, approximates the integral, and scales the result by the input–baseline difference.
Choose an implementation that fits your framework
| Route | What it provides | What to check |
|---|---|---|
| PyTorch with Captum Integrated Gradients | A generic implementation with options for baselines, target, approximation method, number of steps, batching, and convergence delta. | Confirm that the model and input are compatible with the API and that the selected target identifies the output you intend to explain. |
| TensorFlow | The official TensorFlow tutorial walks through a gradient-based implementation and an image example. | Use the implementation with a compatible TensorFlow model and input representation; it is not interchangeable with a PyTorch implementation by default. |
Set and check the numerical approximation
Captum documents Riemann variants and Gauss-Legendre quadrature. Its API documentation specifies 50 steps and Gauss-Legendre as defaults when those options are not supplied. These are implementation defaults, not guarantees that the approximation is adequate for every model and input. More steps may improve an approximation in a particular case, but check convergence rather than assuming it.
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Captum can return a convergence delta based on the completeness relationship: the sum of attributions should correspond to F(input) − F(baseline). Treat the delta as a numerical diagnostic, not a measure of fairness, causal validity, or overall explanation quality.
What can Integrated Gradients help you investigate?
IG can help examine which input features influence an individual prediction, investigate surprising model behavior, and build intuition about what a model may have learned. It can be applied to image, text, and structured inputs when the model and implementation support them. Captum describes troubleshooting and feature or rule extraction as uses; TensorFlow describes inspecting feature importance, debugging, and possible data-skew signals.
These are starting points for investigation. An attribution may suggest a question to test, but does not prove that a suspected bias exists or that the model is behaving correctly.
What are Integrated Gradients’ limits?
It explains an individual example, not global behavior
TensorFlow’s tutorial describes IG as providing feature importances for individual examples, not global feature importances across a dataset. Aggregating attributions over examples is a separate analysis choice; its result depends on the examples selected, how attributions are combined, and which output is being explained.
It does not explain feature interactions
The TensorFlow tutorial also notes that IG does not explain feature interactions and combinations. A feature attribution should not be read as a complete account of how combinations of inputs affect a prediction.
Results depend on analysis choices
The baseline defines the reference comparison. The target output determines which model result is explained; the input representation determines what counts as a feature; and the approximation settings affect the numerical estimate. Visualizations can also influence how a result is perceived. Report the baseline, target, representation, and approximation settings, and interpret an attribution within those choices.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How should you compare IG implementations or analyses?
Before comparing results, check that the analyses use comparable conditions. Differences in setup can change the question being answered, even when both use Integrated Gradients.
- Framework and model compatibility: PyTorch with Captum or a TensorFlow-compatible implementation.
- Baseline: What reference state each analysis uses and why it is meaningful.
- Target and input representation: Which output is explained and how the model’s input is represented as features.
- Approximation and compute: Which numerical method and step count are used, and whether the approximation is checked.
- Scope: Whether the question concerns a particular prediction or a separate dataset-level analysis.
Captum’s Integrated Gradients tutorial discusses applications to different input types, while its introduction describes the library’s scope. The implementation choice should follow the model and task, not an assumption that the frameworks or their inputs are interchangeable.
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