6 Essential Insights for Scaling Interaction Discovery in LLMs

Understanding how large language models (LLMs) make decisions is a central challenge in modern AI. As these models grow in complexity, their behavior often hinges not on single features or training examples, but on intricate interactions between them. Identifying these interactions at scale is like finding needles in a haystack—except the haystack expands exponentially with model size. In this article, we explore six key insights to tackle this challenge, drawing on the cutting-edge algorithms SPEX and ProxySPEX. We'll break down why interactions matter, how different interpretability lenses view them, the foundational idea of ablation, and how SPEX and ProxySPEX make the process tractable. By the end, you'll have a clear roadmap for scaling interaction discovery in LLMs.

1. The Exponential Complexity of Interactions

Large language models achieve state-of-the-art performance by synthesizing complex dependencies across features, training data, and internal components. But this very strength creates a scalability problem: the number of potential interactions grows exponentially as the system scales. For example, with just 100 input features, the pairwise interactions number nearly 5,000, and higher-order combinations explode factorially. Traditional interpretability methods—like checking feature importance individually—miss these synergistic effects. To truly explain an LLM's prediction, we must capture how features, data points, and mechanisms combine. This exponential growth makes exhaustive analysis computationally infeasible. SPEX (Scalable Pattern Extraction) and ProxySPEX are designed to cut through this complexity by focusing only on the most influential interactions, using clever sampling and approximation techniques.

2. Three Lenses to Analyze Interactions

Interpretability research approaches LLM behavior from three complementary perspectives, each exposed to interaction challenges. Feature attribution (Lundberg & Lee, 2017; Ribeiro et al., 2022) isolates which input words or tokens drive a prediction—but interactions between tokens matter, e.g., negation patterns or phrase conjunctions. Data attribution (Koh & Liang, 2017; Ilyas et al., 2022) links model behaviors to influential training examples—here interactions arise from mixed data sources that together shape a response. Mechanistic interpretability (Conmy et al., 2023; Sharkey et al., 2025) dissects internal components like attention heads and MLP layers—interactions between these parts create emergent circuits. Across all three, the core hurdle is the same: interactions, not isolated units, define behavior. Algorithms like SPEX must integrate insights from all lenses to provide a holistic view. Each lens also highlights different ablation strategies, as we'll see next.

3. Attribution Through Ablation: The Guiding Principle

At the heart of SPEX and ProxySPEX lies the concept of ablation: measuring influence by observing what changes when a component is removed. This principle applies across all three interpretability lenses:

• Feature ablation: Mask or remove specific segments of the input prompt and measure the shift in predictions.
• Data ablation: Train models on different subsets of the training set and assess how outputs change without particular data points.
• Mechanistic ablation: Intervene on the model's forward pass to remove the influence of specific internal components (e.g., zero out a neuron).

The goal is always the same: isolate the drivers of a decision by systematically perturbing the system. However, each ablation carries a significant cost—whether expensive inference calls or retrainings. The challenge becomes: can we compute attributions with the fewest possible ablations? SPEX and ProxySPEX answer yes by strategically selecting which ablations to perform and then inferring the missing ones.

4. SPEX: Efficient Interaction Search via Sparse Masking

SPEX (Scalable Pattern Exchange) is an algorithm designed to discover influential interactions with a tractable number of ablations. It works by constructing a sparse set of masks that cover different subsets of features, data points, or components. Instead of testing all possible interaction combinations, SPEX uses a combinatorial design (like covering arrays) to sample a small but representative set. After performing ablations on these masks, it applies regression or sparse recovery techniques to infer which interactions are most influential. This approach reduces the computational burden from exponential to polynomial or even linear in practice. For instance, if you have 1,000 input features, SPEX might require only a few hundred ablations to estimate all pairwise interactions. The output is a ranked list of interaction strengths, allowing researchers to focus on the most impactful patterns. This method works for feature, data, and mechanistic attributions alike.

5. ProxySPEX: Scaling Further with Proxy Models

While SPEX already makes interaction discovery tractable, some scenarios still demand too many ablations—for example, very large models or datasets where each inference is costly. ProxySPEX extends SPEX by introducing a lightweight proxy model that approximates the LLM's behavior. The proxy is trained on a small set of full ablations, then used to predict outcomes for many more mask configurations cheaply. This hybrid approach combines the accuracy of real ablation with the speed of approximation. The proxy could be a smaller transformer, a linear model, or even a neural network trained on the LLM's outputs. ProxySPEX effectively amortizes the cost of expensive inference: after an initial investment, it can explore interactions at a fraction of the original expense. Early results show that ProxySPEX maintains high fidelity while reducing the required ablations by an order of magnitude. This makes it feasible to analyze models with billions of parameters or datasets with millions of examples.

6. The Path to Trustworthy AI Through Scalable Interaction Discovery

Identifying interactions at scale is not just a technical feat—it's a stepping stone to safer and more trustworthy AI. When we understand how features, data, and mechanisms combine, we can better predict model failures, detect biases, and ensure alignment. SPEX and ProxySPEX provide practical tools for researchers to perform this analysis without exponential resource demands. The algorithms are model-agnostic and can be integrated into existing interpretability pipelines. As LLMs continue to grow, the ability to discern influential interactions will become even more critical. The next frontier includes extending these methods to continuous interactions, dynamic behaviors, and multi-task settings. By investing in scalable interaction discovery today, we build the foundation for AI systems that are not only powerful but also transparent and accountable.

In summary, understanding interactions is essential for LLM interpretability, and SPEX/ProxySPEX offer practical solutions to the exponential complexity problem. From the basic principle of ablation to the use of proxy models, these methods empower researchers to uncover the hidden synergies driving model behavior. With the insights above, you're now equipped to explore your own LLMs at scale.