Multimodal Integrated Gradients

The defining property of Integrated Gradients is that the sum of all feature attributions across all modalities exactly equals the difference between the model's output at the actual input and its output at a neutral baseline. This guarantees no attribution is unaccounted for, providing a mathematically rigorous audit trail for multimodal predictions. Unlike perturbation-based methods that can miss synergistic cross-modal effects, the path integral inherently captures how features from text and image modalities jointly build the final logit.

The choice of baseline is critical and modality-specific. For visual inputs, a black image or Gaussian blur serves as the absence of information. For textual inputs, a sequence of zero-embedding tokens or padding tokens represents a null sentence. The path from baseline to input must be traversed simultaneously for both modalities, ensuring the accumulated gradients reflect the joint emergence of cross-modal interactions rather than treating each modality independently.

Attributions are computed by accumulating gradients along a straight-line path from the baseline to the actual input in the joint multimodal embedding space:

• Sample interpolation points: ( x_i(\alpha) = x_i^{\text{baseline}} + \alpha \times (x_i^{\text{input}} - x_i^{\text{baseline}}) ) for ( \alpha \in [0,1] )
• Compute the gradient of the target logit with respect to each interpolated input
• Approximate the integral using the Riemann sum over ( m ) steps
• The result is a separate attribution map for each modality that sums to the total prediction delta

The output of Multimodal Integrated Gradients is a set of attribution tensors with the exact same shape as each input modality:

• Image attribution: A heatmap with pixel-level granularity showing which visual regions contributed positively or negatively to the text-conditioned prediction
• Text attribution: Token-level importance scores revealing which words in the prompt drove the model's visual grounding
• These maps can be overlaid directly on the original inputs, enabling engineers to visually debug vision-language grounding failures

A known limitation in deep networks is gradient saturation, where large input values push activation functions into flat regions, causing near-zero gradients and misleadingly low attribution scores. Multimodal Integrated Gradients mitigates this by averaging gradients along the entire path, but practitioners should still monitor for noisy attributions. Techniques like SmoothGrad can be combined with Integrated Gradients by adding Gaussian noise to interpolated inputs and averaging the resulting attributions, producing cleaner visual explanations.

A class of methods that assign importance scores to input features in one modality based on their interaction with and influence on features from another modality. Unlike unimodal attribution, cross-modal attribution quantifies how a specific word directs attention to an image region, or how a visual patch influences the interpretation of a text token. This is essential for debugging vision-language grounding failures.

An explainability method that systematically removes or zeroes out one input modality to measure its causal contribution to the model's final output. By comparing the prediction with and without the visual stream, engineers can assess cross-modal reliance. A significant drop in confidence when ablating an image indicates strong visual dependence, while minimal change suggests the model is primarily relying on the text.

A metric that evaluates whether the features identified as important by a multimodal explanation truly influence the model's prediction when perturbed. Faithfulness is tested by removing or altering the attributed cross-modal features and measuring the resulting change in output. A faithful explanation accurately identifies the inputs that causally drive the decision, not just correlated artifacts.

A technique that backpropagates a model's prediction score through the network layers, decomposing the relevance and assigning it to the input features of all modalities while conserving the total relevance. MLRP extends the completeness axiom to multimodal settings, ensuring that the sum of relevance scores across text tokens and image pixels equals the model's output magnitude.

A method that linearly combines attention matrices across transformer layers to trace how information from one modality propagates to another, producing a single map of cross-modal information flow. By rolling out attention weights, engineers can visualize the cumulative path of visual information as it influences textual representations, revealing how the model fuses modalities over successive layers.

A diagnostic metric that measures the uncertainty or dispersion in how a model distributes its attention across different modalities at the fusion point. High entropy indicates a balanced, distributed integration strategy, while low entropy suggests the model is biased toward one modality. This metric helps identify brittle models that over-rely on a single data stream.