DeepLIFT SHAP: Bridging DeepLIFT and SHAP

• DeepLIFT SHAP is a method that uses DeepLIFT-style backpropagation and SHAP's axiomatic framework to approximate Shapley-value attributions in deep neural networks.
• It reinterprets reference-based explanations by applying feature independence and model linearization assumptions, enabling efficient layer-wise propagation of additive attributions.
• Deep SHAP improves consistency by averaging single-reference attributions over a background distribution, enhancing interpretability in mixed model stacks.

DeepLIFT SHAP denotes the relationship between DeepLIFT and SHAP and, in common usage, especially the Deep SHAP or DeepSHAP family: methods that use DeepLIFT-style propagation of reference-relative activation differences to approximate Shapley-value feature attributions in deep models. The decisive step was the SHAP framework of Lundberg and Lee, which placed DeepLIFT inside a class of additive feature attribution methods, proved that exact SHAP values are the unique members of that class satisfying local accuracy, missingness, and consistency, and reinterpreted DeepLIFT as an approximation under feature independence and model linearization assumptions before proposing “Deep SHAP (DeepLIFT + Shapley values)” (Lundberg et al., 2017). Later work made the connection more explicit by propagating Shapley values of local components, averaging single-reference attributions over a background distribution, and extending the method from neural networks to mixed model stacks and series of models (Chen et al., 2019, Chen et al., 2021).

1. DeepLIFT as the reference-based precursor

DeepLIFT was introduced as a method for decomposing the output prediction of a neural network on a specific input by backpropagating the contributions of all neurons in the network to every feature of the input. Its central objects are differences from a reference input. For any neuron $t$, DeepLIFT defines $\Delta t = t - t^0$, and for inputs or hidden units $x_i$, $\Delta x_i = x_i - x_i^0$. Contribution scores $C_{\Delta x_i \Delta t}$ are required to satisfy the summation-to-delta property,

$\sum_{i=1}^n C_{\Delta x_i \Delta t} = \Delta t,$

so the output difference from reference is exactly decomposed across inputs or intermediate neurons (Shrikumar et al., 2017).

This additive conservation law is implemented with multipliers,

$$m_{\Delta x \Delta t} = \frac{C_{\Delta x \Delta t}}{\Delta x},$$

and a chain rule,

$$m_{\Delta x_i \Delta t} = \sum_j m_{\Delta x_i \Delta y_j} m_{\Delta y_j \Delta t}.$$

For affine layers, DeepLIFT uses a linear rule. For single-input nonlinearities such as ReLU, tanh, and sigmoid, the Rescale rule uses the finite-difference ratio $\Delta y / \Delta x$ rather than the local derivative. The RevealCancel rule separately handles positive and negative components and is presented as an improved approximation of the Shapley values in cases where positive and negative terms interact and cancel inside a nonlinearity (Shrikumar et al., 2017).

These design choices explain why DeepLIFT later became a natural substrate for SHAP-style methods. It is already reference-based, explicitly additive, and computable in a single backward pass. This suggests a close affinity with Shapley-style decomposition, but not yet a full Shapley-value theory.

2. The SHAP additive attribution framework

SHAP formalizes local explanation as an explanation model $g$ that approximates the original model $\Delta t = t - t^0$0 around a single input $\Delta t = t - t^0$1, possibly through a simplified representation $\Delta t = t - t^0$2 and a mapping $\Delta t = t - t^0$3. The class of additive feature attribution methods is defined by

$\Delta t = t - t^0$4

where $\Delta t = t - t^0$5, $\Delta t = t - t^0$6 indicates whether simplified feature $\Delta t = t - t^0$7 is present, $\Delta t = t - t^0$8 is its attribution, and $\Delta t = t - t^0$9 is a baseline term (Lundberg et al., 2017).

Within this class, SHAP isolates three properties. Local accuracy requires

$x_i$0

Missingness requires

$x_i$1

Consistency requires that if the marginal contribution of feature $x_i$2 never decreases across all simplified coalitions, then its attribution should not decrease either. The main theorem states that there is only one additive feature attribution method satisfying local accuracy, missingness, and consistency, and that solution is given by the Shapley values,

$x_i$3

SHAP therefore does not treat DeepLIFT as merely similar in spirit; it places it in a common formal class and then distinguishes exact Shapley values as the unique theoretically justified member of that class (Lundberg et al., 2017).

The same framework also clarifies the semantics of missing features. SHAP defines $x_i$4 through a conditional expectation function of the original model, and then introduces practical approximations such as feature independence and model linearity. Those approximations become central in the interpretation of DeepLIFT.

3. DeepLIFT inside the SHAP framework

The original SHAP paper shows explicitly that DeepLIFT belongs to the additive feature attribution class. DeepLIFT assigns values $x_i$5 representing the effect of changing input $x_i$6 from a reference value $x_i$7 to its actual value, with the simplified mapping interpreted binarily: $x_i$8 means the feature takes its original value and $x_i$9 means it takes the reference value. Because DeepLIFT satisfies

$\Delta x_i = x_i - x_i^0$0

one can set

$\Delta x_i = x_i - x_i^0$1

so that DeepLIFT’s explanation model matches the additive form $\Delta x_i = x_i - x_i^0$2 exactly (Lundberg et al., 2017).

The critical distinction is not membership in the additive class but the status of the resulting attributions. Since DeepLIFT is additive and already satisfies local accuracy and missingness, the SHAP uniqueness theorem implies that whenever DeepLIFT does not equal Shapley values, it must fail consistency. The paper states this directly in the Deep SHAP discussion: “Since DeepLIFT is an additive feature attribution method that satisfies local accuracy and missingness, we know that Shapley values represent the only attribution values that satisfy consistency” (Lundberg et al., 2017).

The paper then gives the canonical SHAP interpretation of DeepLIFT: if the reference value is interpreted as representing $\Delta x_i = x_i - x_i^0$3, then DeepLIFT approximates SHAP values assuming that the input features are independent of one another and the deep model is linear. It immediately adds that DeepLIFT uses a linear composition rule, equivalent to linearizing the non-linear components of a neural network, and that its back-propagation rules are intuitive but heuristically chosen. This is the core meaning of “DeepLIFT SHAP”: DeepLIFT is not exact SHAP in general, but it can be reinterpreted as a reference-based approximation to SHAP under explicit assumptions (Lundberg et al., 2017).

4. Deep SHAP and the propagation of local Shapley values

The constructive response to these limitations was Deep SHAP, described explicitly as “DeepLIFT + Shapley values.” In the original SHAP paper, the method computes or approximates component-level SHAP values for simple network components—linear units, max pooling, or one-input activation functions—and composes them through the network with DeepLIFT-style multipliers. The paper emphasizes that this avoids heuristically choosing ways to linearize components and instead derives an effective linearization from the SHAP values computed for each component; the $\Delta x_i = x_i - x_i^0$4 function is presented as a case where this improves attributions and addresses “the open problem of max pooling functions in DeepLIFT” (Lundberg et al., 2017).

This local-to-global view was developed further in “Explaining Models by Propagating Shapley Values of Local Components,” which presents DeepSHAP for mixed model types as a framework for layer wise propagation of Shapley values that builds upon DeepLIFT. In that formulation, the Rescale rule is interpreted as computing exact SHAP values for a local one-input nonlinearity and then backpropagating those attributions linearly through the preceding linear component, while RevealCancel is interpreted as exact SHAP for a two-group nonlinear decomposition followed by linear propagation. The same paper argues that to explain relative to a background distribution one should compute single-reference SHAP values against many background samples and average them: $\Delta x_i = x_i - x_i^0$5 It also extends the framework to stacks of mixed models and to attribution of the loss (Chen et al., 2019).

A subsequent generalization, “Explaining a Series of Models by Propagating Shapley Values,” treats DeepSHAP as a tractable method for propagating local feature attributions through a composed model $\Delta x_i = x_i - x_i^0$6. It formalizes many-baseline averaging as the correct interventional Shapley object rather than using the average input as a single baseline, interprets DeepLIFT’s Rescale rule as a $\Delta x_i = x_i - x_i^0$7-partition approximation to interventional Shapley values and RevealCancel as a $\Delta x_i = x_i - x_i^0$8-partition approximation, and proves exactness in linear compositions. The same work also states that DeepSHAP is not guaranteed to satisfy all desirable axioms, such as implementation invariance (Chen et al., 2021).

5. Related specializations and neighboring SHAP computations

DeepLIFT-based SHAP approximation has been specialized beyond input-feature attribution. “Towards Better Explanations of Class Activation Mapping” reformulates CAM as an additive feature attribution problem in which the features are activation maps and the explanation model is linear in binary variables denoting whether each activation map is present. It argues that the appropriate CAM coefficients are SHAP values of activation maps and introduces LIFT-CAM, which approximates those SHAP values using DeepLIFT contribution scores propagated to the activation-map layer. In this setting, if the downstream subnetwork $\Delta x_i = x_i - x_i^0$9 is linear, the paper states that the LIFT-CAM coefficients are the exact SHAP coefficients (Jung et al., 2021).

By contrast, some later SHAP work addresses efficient exact computation without using DeepLIFT-style propagation. “Computing SHAP Efficiently Using Model Structure Information” studies SHAP definitions satisfying additivity and dummy assumptions, explicitly including kernel SHAP and Baseline-SHAP, and shows that exact SHAP can be computed from low-order functional decomposition or known interaction order in polynomial time for fixed low order. Its relevance to DeepLIFT SHAP is therefore indirect: it concerns exact structure-aware SHAP computation rather than neural-network-specific backpropagation rules (Hu et al., 2023).

This distinction is conceptually important. DeepLIFT SHAP is a propagation-based approximation family for deep or compositional models; it is not the only route to SHAP, and it should not be conflated with general SHAP algorithms that derive exact values from known model structure.

6. Applications, caveats, and recurrent misconceptions

In applied work, DeepLIFT SHAP has been used as a post hoc attribution method alongside Integrated Gradients, DeepLIFT, and Gradient SHAP. An automotive fault detection and diagnosis study on a hybrid $C_{\Delta x_i \Delta t}$0dCNN-GRU model reports that DeepLIFT SHAP provided “more balanced and consistent scores,” “smoother, more interpretable results with consistent feature rankings across baselines,” and supported reducing the feature set from $C_{\Delta x_i \Delta t}$1 to $C_{\Delta x_i \Delta t}$2, with accuracy changing from $C_{\Delta x_i \Delta t}$3 to $C_{\Delta x_i \Delta t}$4 and training time from $C_{\Delta x_i \Delta t}$5 to $C_{\Delta x_i \Delta t}$6. The same study also reports a runtime tradeoff: on the original FLM, DeepLIFT SHAP took $C_{\Delta x_i \Delta t}$7, compared with $C_{\Delta x_i \Delta t}$8 for DeepLIFT and $C_{\Delta x_i \Delta t}$9 for Gradient SHAP (Abboush et al., 9 Mar 2026).

Several misconceptions recur in the literature. First, original DeepLIFT is not exact SHAP in general; the original SHAP paper is explicit that DeepLIFT approximates SHAP only under feature independence and model linearization assumptions, and that the move from DeepLIFT to Deep SHAP is a substantive algorithmic revision rather than a renaming (Lundberg et al., 2017). Second, a single mean baseline is not the same object as a background-distribution explanation; later DeepSHAP work argues that many-background averaging is the correct interventional Shapley construction for nonlinear models (Chen et al., 2019). Third, SHAP-family methods do not automatically solve robustness or auditing problems. “Fooling SHAP with Output Shuffling Attacks” proves that exact Shapley values cannot detect shuffling attacks because the coalition value function is based on averages preserved by permutation, while practical SHAP implementations may detect those attacks “with varying degrees of effectiveness.” A plausible implication is that DeepLIFT SHAP should not be assumed robust merely because it approximates SHAP, since the paper directly targets exact Shapley reasoning and practical SHAP estimators rather than DeepSHAP specifically (Yuan et al., 2024).

Taken together, these results define DeepLIFT SHAP as a technically specific family of methods rather than a generic label. Its essential content is the combination of DeepLIFT’s reference-relative additive backpropagation with SHAP’s axiomatic target of Shapley-value attribution. The conceptual gain is a precise reinterpretation of DeepLIFT inside the additive attribution class; the methodological gain is Deep SHAP or DeepSHAP, which replaces heuristic local rules with component-level Shapley reasoning and many-baseline background averaging while retaining the computational advantages of propagation-based explanation.