Integrated Gradients

The axiom of Sensitivity states that if an input feature differs from the baseline and causes a change in the prediction, it must receive a non-zero attribution. Completeness is a stronger corollary: the sum of all feature attributions must exactly equal the difference between the model's output for the actual input and the baseline input.

• Guarantees no attribution is 'lost' during the calculation
• For a genomic sequence model, the sum of nucleotide importance scores equals the total predicted expression change
• Violated by simple gradient methods that can miss saturated features

Two functionally equivalent neural networks—networks that produce identical outputs for all inputs despite having different architectures or parameters—must yield identical attributions under Integrated Gradients.

• Prevents attribution manipulation by architectural choices
• A ResNet and a Transformer predicting the same expression levels from a promoter sequence will assign identical importance to a key TATA box motif
• This property fails for methods like DeepLIFT or LIME, which depend on model internals or local sampling

If a model is a linear combination of two sub-models, the Integrated Gradients attribution for the combined model is the same linear combination of the attributions from the sub-models.

• Enables compositional debugging of ensemble models
• If an expression predictor averages outputs from a CNN branch and an attention branch, the final attribution is the average of each branch's attribution map
• Critical for verifying that multi-task learning models fairly weight shared genomic features

Two input variables that are symmetric with respect to the model—meaning swapping their values leaves the output unchanged—must receive identical attributions.

• Ensures fair treatment of functionally equivalent features
• In a homodimer binding prediction, two identical half-sites in a palindromic sequence receive equal importance scores
• Prevents spurious asymmetry that could mislead biologists about which motif copy is the 'driver' of binding

The baseline input represents the 'absence' of signal and is a critical hyperparameter. The attribution explains the transition from this baseline to the actual input.

• For genomic sequences, common baselines include a dinucleotide-shuffled sequence preserving local composition or a uniform 0.25 probability vector for each nucleotide
• A poor baseline (e.g., all zeros) can create artifacts where the model extrapolates from non-biological inputs
• The path integral accumulates gradients along a straight line from baseline to input in the embedding space

A computational perturbation method where every nucleotide in an input DNA sequence is systematically mutated to measure the predicted change in a model's output. While Integrated Gradients attributes importance to existing features, in silico mutagenesis reveals causal regulatory logic by asking 'what if this base were different?' The technique is foundational for identifying transcription factor binding motifs and interpreting the sequence determinants of gene expression.

The choice of baseline is the most critical hyperparameter in Integrated Gradients. For genomic models, common baselines include:

• Dinucleotide-shuffled sequences: Preserves local composition while destroying functional motifs
• Uniform nucleotide distributions: All positions set to 0.25 probability for each base
• Reference genome segments: A biologically neutral region with no known regulatory activity A poor baseline produces misleading attributions that violate the completeness axiom.

Deep Learning Important FeaTures (DeepLIFT) is a precursor to Integrated Gradients that computes feature importance by comparing neuron activation to a reference state. It uses rescale and reveal-cancel rules to backpropagate contribution scores. While faster than Integrated Gradients, it can violate implementation invariance—two functionally identical networks may produce different attributions. Integrated Gradients was designed to satisfy this axiom.

An extension of Integrated Gradients that removes the dependency on a single baseline by averaging attributions over multiple baselines drawn from a background distribution. This is particularly valuable in genomics where no single 'neutral' sequence exists. By sampling from shuffled genomic backgrounds, Expected Gradients produces more robust and less noisy saliency maps for regulatory DNA models.

An exhaustive experimental or computational technique where every position in a regulatory sequence is mutated to all three alternative nucleotides, and the effect on expression is measured. When compared with Integrated Gradients attributions, saturation mutagenesis provides ground-truth validation. High correlation between predicted importance scores and empirical mutational effects confirms that the model has learned genuine cis-regulatory grammar.

A technique that reduces visual noise in saliency maps by averaging the gradients of multiple noisy copies of the input. When combined with Integrated Gradients, SmoothGrad produces cleaner nucleotide-resolution importance tracks for genomic sequences. This is especially useful for visualizing attributions in genome browsers where pixel-level clarity is required for publication-quality figures.