Large language models (LLMs) have revolutionized machine learning due to their ability to capture complex interactions between input features. Popular post-hoc explanation methods like SHAP provide marginal feature attributions, while their extensions to interaction importances only scale to small input lengths ($\approx 20$). We propose Spectral Explainer (SPEX), a model-agnostic interaction attribution algorithm that efficiently scales to large input lengths ($\approx 1000)$. SPEX exploits underlying natural sparsity among interactions -- common in real-world data -- and applies a sparse Fourier transform using a channel decoding algorithm to efficiently identify important interactions. We perform experiments across three difficult long-context datasets that require LLMs to utilize interactions between inputs to complete the task. For large inputs, SPEX outperforms marginal attribution methods by up to 20% in terms of faithfully reconstructing LLM outputs. Further, SPEX successfully identifies key features and interactions that strongly influence model output. For one of our datasets, HotpotQA, SPEX provides interactions that align with human annotations. Finally, we use our model-agnostic approach to generate explanations to demonstrate abstract reasoning in closed-source LLMs (GPT-4o mini) and compositional reasoning in vision-language models.

With the rapid growth of large-scale machine learning models in genomics, Shapley values have emerged as a popular method for model explanations due to their theoretical guarantees. While Shapley values explain model predictions locally for an individual input query sequence, extracting biological knowledge requires global explanation across thousands of input sequences. This demands exponential model evaluations per sequence, resulting in significant computational cost and carbon footprint. Herein, we develop SHAP zero, a method that estimates Shapley values and interactions with a near-zero marginal cost for future queried sequences after paying a one-time fee for model sketching. SHAP zero achieves this by establishing a surprisingly underexplored connection between the Shapley values and interactions and the Fourier transform of the model. Explaining two genomic models, one trained to predict guide RNA binding and the other to predict DNA repair outcome, we demonstrate that SHAP zero achieves orders of magnitude reduction in amortized computational cost compared to state-of-the-art algorithms, revealing almost all predictive motifs -- a finding previously inaccessible due to the combinatorial space of possible interactions.

Fourier transformations of pseudo-Boolean functions are popular tools for analyzing functions of binary sequences. Real-world functions often have structures that manifest in a sparse Fourier transform, and previous works have shown that under the assumption of sparsity the transform can be computed efficiently. But what if we want to compute the Fourier transform of functions defined over a $q$-ary alphabet? These types of functions arise naturally in many areas including biology. A typical workaround is to encode the $q$-ary sequence in binary, however, this approach is computationally inefficient and fundamentally incompatible with the existing sparse Fourier transform techniques. Herein, we develop a sparse Fourier transform algorithm specifically for $q$-ary functions of length $n$ sequences, dubbed $q$-SFT, which provably computes an $S$-sparse transform with vanishing error as $q^n \rightarrow \infty$ in $O(Sn)$ function evaluations and $O(S n^2 \log q)$ computations, where $S = q^{n\delta}$ for some $\delta < 1$. Under certain assumptions, we show that for fixed $q$, a robust version of $q$-SFT has a sample complexity of $O(Sn^2)$ and a computational complexity of $O(Sn^3)$ with the same asymptotic guarantees. We present numerical simulations on synthetic and real-world RNA data, demonstrating the scalability of $q$-SFT to massively high dimensional $q$-ary functions.