SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism
Reda Marzouk, Shahaf Bassan, Guy Katz
TL;DR
This work analyzes the computational complexity of exact SHAP explanations for Tensor Networks (TNs), introducing a general tensorized framework that yields provably exact SHAP values for TNs. For Tensor Trains (TTs), SHAP computation is shown to be in NC, enabling poly-logarithmic-time parallel evaluation via TT contractions. By reductions, these TT-based tractability results extend to other models such as decision trees, tree ensembles, linear models, and linear RNNs, tightening prior complexity bounds. A fine-grained, parameterized analysis of SHAP for BNNs reveals width and sparsity as the critical bottlenecks: SHAP is para-NP-hard with fixed depth, XP with fixed width, and FPT when both width and reified cardinality are bounded. Overall, the paper advances the theoretical understanding of when and how exact SHAP explanations can be computed efficiently in parallel across expressive model families, guiding practical algorithm design and architectural choices.
Abstract
Although Shapley additive explanations (SHAP) can be computed in polynomial time for simple models like decision trees, they unfortunately become NP-hard to compute for more expressive black-box models like neural networks - where generating explanations is often most critical. In this work, we analyze the problem of computing SHAP explanations for *Tensor Networks (TNs)*, a broader and more expressive class of models than those for which current exact SHAP algorithms are known to hold, and which is widely used for neural network abstraction and compression. First, we introduce a general framework for computing provably exact SHAP explanations for general TNs with arbitrary structures. Interestingly, we show that, when TNs are restricted to a *Tensor Train (TT)* structure, SHAP computation can be performed in *poly-logarithmic* time using *parallel* computation. Thanks to the expressiveness power of TTs, this complexity result can be generalized to many other popular ML models such as decision trees, tree ensembles, linear models, and linear RNNs, therefore tightening previously reported complexity results for these families of models. Finally, by leveraging reductions of binarized neural networks to Tensor Network representations, we demonstrate that SHAP computation can become *efficiently tractable* when the network's *width* is fixed, while it remains computationally hard even with constant *depth*. This highlights an important insight: for this class of models, width - rather than depth - emerges as the primary computational bottleneck in SHAP computation.