Integrated Gradients

The attribution process requires a baseline input representing the absence of signal. For genomic sequences, this is typically an all-zero vector (representing no nucleotide at each position) or a dinucleotide-shuffled sequence that preserves local composition while destroying functional motifs. The choice of baseline critically affects which features are highlighted—a biologically informed baseline yields more interpretable attributions for regulatory genomics.

Integrated Gradients computes attributions by accumulating the gradients of the model's output with respect to the input along a straight-line path from the baseline to the actual input. Mathematically, this is the path integral of the gradient field. For each feature i, the attribution is:

• The integral of ∂F(x)/∂xᵢ along the linear interpolation path
• Approximated in practice using Riemann summation with m steps (typically 50–200)
• Equivalent to the difference between the input and baseline multiplied by the average gradient

Unlike gradient-based saliency maps or Guided Backpropagation, Integrated Gradients satisfies the Completeness axiom: the sum of all feature attributions exactly equals the difference between the model's output at the input and at the baseline. This guarantees that every bit of the prediction is accounted for. Additionally, Sensitivity ensures that if a single feature change alters the prediction, that feature receives non-zero attribution—a property violated by simple gradient methods when operating near saturation regions.

In genomic binding prediction models like DeepBind or BPNet, Integrated Gradients produces per-nucleotide hypothetical importance scores that quantify each base's contribution to the predicted binding affinity. These scores can be visualized as sequence logos where letter height corresponds to attribution magnitude, revealing:

• The precise nucleotides driving binding predictions
• Subtle motif variations that distinguish high-affinity from low-affinity sites
• Cooperative effects between adjacent transcription factor binding positions

Integrated Gradients attributions serve as the primary input to TF-MoDISco (Transcription Factor Motif Discovery from Importance Scores), which clusters high-attribution genomic subsequences to extract consolidated, non-redundant sequence motifs. This pipeline:

• Identifies multiple distinct binding modes captured by a single model
• Separates direct binding motifs from dinucleotide repeat artifacts
• Recovers known motifs and discovers novel co-factor binding patterns
• Produces position weight matrices suitable for downstream scanning tools

A critical advantage of Integrated Gradients over simple input × gradient methods is its ability to detect features operating in saturated activation regimes. When a transcription factor binding site is so strong that small perturbations do not change the prediction, raw gradients approach zero—falsely suggesting no importance. Integrated Gradients accumulates gradients along the entire path from baseline, capturing the feature's contribution even when the model's output has plateaued at the actual input.

A computational perturbation method that systematically introduces virtual nucleotide substitutions into a DNA sequence and measures the resulting change in a neural network's binding prediction. Unlike Integrated Gradients, which provides per-base attribution, ISM directly quantifies the causal effect of each variant.

• Computationally expensive: requires forward pass for every possible mutation
• Produces mutation effect maps for every position
• Identifies causal regulatory variants driving binding changes
• Complements gradient-based methods with direct perturbation evidence

The choice of baseline input critically shapes Integrated Gradients attributions. For genomic models, common baselines include:

• Zero embedding: All-zero vector, representing absence of information
• Dinucleotide-shuffled sequences: Preserves dinucleotide composition while disrupting functional motifs
• Uniform background: Equal probability (0.25) for each nucleotide at every position
• Empirical genomic background: Sampled from intergenic or inactive regions

The Saturation of Completeness axiom requires that attributions sum to the prediction difference between input and baseline.

An extension of Integrated Gradients that averages attributions over multiple baselines drawn from a background distribution rather than using a single reference point. This removes the sensitivity to baseline choice that can affect standard Integrated Gradients.

• Samples baselines from a background dataset (e.g., shuffled sequences)
• Reduces noise in attributions for genomic models
• Maintains the completeness axiom in expectation
• Computationally more expensive due to multiple integration paths
• Particularly useful when no single 'neutral' baseline is biologically meaningful

The simplest attribution method: the gradient of the prediction with respect to the input. Unlike Integrated Gradients, which accumulates gradients along a path, saliency maps use only the gradient at the actual input point.

• Computationally trivial: single backward pass
• Suffers from gradient saturation: flat regions yield near-zero attributions
• Does not satisfy Sensitivity axiom (can miss features that flip predictions)
• Integrated Gradients was specifically designed to address these limitations
• Still widely used as a fast baseline comparison for more rigorous methods