SLIC and Semantic Shapley Value: Measuring Agent Contributions in LLM Systems With 93% Less Compute

In July 2026, a preprint appeared on arXiv describing SLIC, an algorithm that estimates each agent's contribution in a multi-agent LLM system in a single pass and cuts computational cost by 93.3% compared with the Monte Carlo Shapley baseline.

Why agent contributions are hard to measure

Classical attribution methods require rerunning the system many times: remove individual agents, then compare how the final result changes. In language workflows, every such run means new model calls. Exact Shapley attribution requires enumerating all 2^n subsets of agents, which produces high-variance estimates and quickly becomes intractable as the number of agents grows.

The authors point to a second problem: counterfactual methods cannot see intermediate semantic states, meaning how agents generate, retain, and transform task-relevant information as they exchange messages. They evaluate only the system's input and output, not the logic by which meaning passes between roles.

How Semantic Shapley Value works

SLIC builds a semantic hypergraph from a realized language flow and computes the Semantic Shapley Value (SSV) without rerunning subsets of agents. The algorithm recovers minimal semantic supports, applies Boolean absorption, and distributes contribution according to the logic of semantic support within a single execution trajectory. That is where the "single-trajectory" label in the method's description comes from.

The authors prove that SSV reduces to the classical Shapley value under standard conditions: set-based representation, full observability, and no order dependence. In other words, the new method is not a heuristic but a sound generalization of established cooperative game theory to language processes, where step order and intermediate meaning matter.

• Method: Semantic Cooperative Games (SCG) + Semantic Shapley Value (SSV)
• Algorithm: SLIC — single-pass computation, no counterfactual reruns
• Savings: −93.3% computational cost on a medical benchmark
• Consistency: results close to the Monte Carlo Shapley baseline
• Publication: arXiv:2607.18255 preprint, July 2026

What the tests showed

On a medical benchmark that satisfies the theorem's conditions, SLIC cut computational cost by 93.3% while remaining highly consistent with the Monte Carlo Shapley baseline. This is the paper's key result: practically the same contribution estimates at almost 15 times lower computational cost.

In more general multi-role workflows, SSV values match the score-drop profiles under perturbations and expose cases where an agent's semantic contribution and its influence on failures diverge. An agent can carry a lot of meaning without being a point of failure, and vice versa.

"SLIC is a fast, counterfactual-free, and interpretable attribution

method for complex multi-agent LLM systems," the paper's arXiv abstract states.

What this means

As products are assembled from several interacting LLM agents, the question of who actually added value and who broke the result becomes an engineering problem rather than a philosophical one. SLIC offers a way to answer it cheaply and without a black box. That matters for debugging, optimization, and fair evaluation of agents in multi-agent systems.

FAQ

What is contribution attribution in multi-agent LLM systems?

It is an estimate of which of several agents influenced the final result, and by how much, when the answer emerges through a chain of messages and workflow dependencies. SLIC tackles this task with a semantic hypergraph and the Semantic Shapley Value instead of expensive counterfactual runs.

How much faster is SLIC than earlier methods?

On a medical benchmark, SLIC cut computational cost by 93.3% relative to the Monte Carlo Shapley baseline, keeping results close to it without rerunning subsets of agents.