Integrated Gradients

The Completeness axiom dictates that the sum of all feature attributions must exactly equal the difference between the model's output for the actual input and the baseline input. For a genomic model predicting binding affinity, this means the sum of all nucleotide importance scores perfectly accounts for the total change in the prediction from a neutral reference sequence. This property guarantees no attribution is unaccounted for, providing a full and auditable decomposition of the prediction, which is critical for regulatory compliance in clinical genomics.

The Sensitivity axiom states that if a single feature differs between the baseline and the input, and changing that feature alters the model's prediction, it must receive a non-zero attribution. Conversely, a feature that has no effect on the output must receive zero attribution. In a genomic context, if mutating a single nucleotide from the reference allele to an alternate allele changes a variant effect prediction, Integrated Gradients is guaranteed to assign a non-zero importance score to that specific position, ensuring no influential variant is overlooked.

Two functionally equivalent neural networks—meaning they produce identical outputs for all inputs—will yield identical attributions under Integrated Gradients, regardless of their internal architectural differences. This Implementation Invariance is crucial for genomic models where the same predictive function might be learned by a convolutional network or a transformer. It ensures that the explanation is a property of the model's mathematical function, not an artifact of a specific training run or weight configuration, enabling consistent interpretation across different model versions.

Integrated Gradients is fundamentally a path integral of gradients along a straight line from a baseline input to the actual input. This linear path ensures that the attribution is computed symmetrically and avoids the saturation problem common in simple gradient methods. For a genomic sequence, the method interpolates between a reference sequence (e.g., all zeros or expected dinucleotide frequencies) and the observed sequence, accumulating the gradient of the prediction at each infinitesimal step. This path integral approach is what mathematically guarantees the Completeness axiom.

If two input features are symmetric with respect to the model's function—meaning swapping their values leaves the output unchanged—they must receive identical attributions. In a genomic model, two perfectly palindromic binding sites for a transcription factor would be assigned equal importance scores. This Symmetry Preservation property ensures that Integrated Gradients respects the inherent symmetries of the biological sequence and the model's learned function, preventing spurious asymmetries in the explanation that could mislead a researcher about the relative importance of identical motifs.

The choice of baseline is a critical hyperparameter that encodes the definition of 'absence' in a genomic context. Common baselines include a sequence of all zeros, a uniform dinucleotide-shuffled sequence, or a set of random sequences averaged together. The baseline represents a neutral or uninformative input. For variant effect prediction, the reference allele often serves as the baseline, and the alternate allele is the input, allowing the attribution to directly quantify the functional impact of the mutation. The explanation is always relative to this chosen reference point.