SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism

TL;DR

This paper introduces a framework for efficiently computing SHAP explanations for Tensor Networks, especially Tensor Trains, using parallelism, and extends these results to various ML models, revealing width as a key complexity factor.

Contribution

It provides the first provably exact SHAP computation method for Tensor Networks and demonstrates poly-logarithmic time algorithms for Tensor Trains with parallelism, extending to other models.

Findings

SHAP computation for Tensor Trains is poly-logarithmic with parallelism.

Width of neural networks is the primary bottleneck for SHAP computation.

Efficient SHAP explanations are possible for fixed-width neural networks.

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.