Technical Summary: In-Context Credit Assignment via the Core

Problem Statement

The paper addresses the challenge of in-context credit assignment for AI-generated content. As generative AI tools (e.g., LLMs for web search, text-to-video models) increasingly synthesize intellectual property (IP) from multiple creators within a model's context window, there is a need to economically distribute the value generated by the final output among the original creators.

The core question is: What is an economically principled and computationally tractable way to allocate credit for AI-generated content among a set of creators whose IP appears in the model's context window?

The authors model this as a cooperative game where creators form coalitions to generate value. The goal is to find a value-sharing scheme (allocation) that respects creator incentives. Specifically, the paper seeks to minimize the "deficit"—the amount by which any subset of creators is under-compensated relative to the value they could generate independently.

Methodology

1. Game-Theoretic Formulation

The problem is cast in the language of cooperative game theory with a set of creators $N$ and a value function $v: 2^N \to [0, 1]$.

• The Core: Ideally, an allocation lies in the "core," where no coalition receives less than its standalone value. However, the core is often empty.
• The Least Core: The authors propose the least core as the solution concept. This is the set of allocations that minimizes the maximum under-compensation ($\epsilon$) across all possible coalitions.
• Estimated Least Core: Since the ground-truth reward function $v$ is unobservable, the authors work with an estimated value function $\hat{v}$ (e.g., derived via LLM-as-a-Judge or human feedback). They compute the least estimated core based on $\hat{v}$.
• Egalitarian Least Core: To break ties among allocations in the least core set, the authors minimize the $\ell_2$ norm of the allocation vector, promoting a more equitable distribution.

2. Sensitivity Analysis

The paper establishes theoretical bounds on the difference between the true least core deficit ($\epsilon^*$) and the estimated least core deficit ($\hat{\epsilon}$).

• General Case: The sensitivity is bounded by the maximum weighted deviation between $v$ and $\hat{v}$, where weights are drawn from a balanced distribution (a distribution where every creator has an equal marginal probability of inclusion in a coalition). This result is presented as a quantitative analog of the Bondareva-Shapley theorem.
• Binary Rewards: In settings where rewards are binary (0 or 1), the authors show that a small fraction of misclassifications can lead to large deficits. However, the sensitivity is bounded by the worst-case probability of misclassification under a balanced distribution.

3. Algorithms for Approximation

Computing the least core involves solving a Linear Program (LP) with an exponential number of constraints ($2^N$), making direct solution infeasible for moderate $N$. The authors develop iterative Constraint Generation (CG) algorithms:

• Separation Oracles: Instead of enumerating all constraints, the algorithm iteratively identifies "unhappy" coalitions (those violating the core constraints) and adds them to the LP.
• Sampling-Based Oracle: Randomly samples coalitions to find violations. The authors provide probabilistic guarantees that this approach finds an approximate least-core allocation with polynomial sample complexity.
• LLM-Based Oracle: Leverages Large Language Models to act as "adversarial testers." Given a candidate allocation, the LLM proposes coalitions it believes are under-compensated. This heuristic guides the search toward informative constraints without requiring exhaustive sampling.
• Coalition Seeding: For binary value functions, the authors utilize Minimal Winning Coalitions (MWCs) as an initial constraint set. They prove that if the separation oracle identifies highly violated coalitions, the algorithm can efficiently recover missing MWCs.

Key Contributions

1. Conceptual Framework: Modeling in-context credit assignment as a cooperative game and selecting the least core as the solution concept to ensure incentive compatibility by minimizing the worst-case under-compensation.
2. Sensitivity Bounds: Providing theoretical bounds on how errors in the estimated reward function propagate to the least core allocation, utilizing balanced distributions over coalitions.
3. Scalable Algorithms: Developing practical Constraint Generation methods that approximate the least core using orders of magnitude fewer value function queries than baseline sampling methods. This includes both sampling-based and LLM-based separation oracles.
4. Empirical Validation: Demonstrating on semi-synthetic web retrieval tasks that the proposed CG methods achieve comparable or better stability ($\epsilon$) than baselines while reducing LLM calls by 3–17$\times$.

Experimental Results

The authors evaluated their methods on two datasets: BrowseComp-Plus (a multi-hop QA benchmark) and a Synthetic dataset designed to ensure genuine interaction effects between documents.

• Efficiency: The CG algorithms (particularly those using LLM oracles) converged to stable allocations using significantly fewer LLM calls (often <100 calls for $n=10$ and ~1,000 for $n=32$) compared to the baseline sampling method (YP), which required thousands of calls (up to 8,192).
• Accuracy: CG methods achieved holdout deficit ($\hat{\epsilon}_H$) scores comparable to or better than the baseline. In some instances, LLM-oracle variants even outperformed the baseline by finding allocations with lower deficits.
• Egalitarianism: The egalitarian variants (minimizing $\ell_2$ norm) successfully redistributed credit more broadly (reducing sparsity) with only minor degradation in the stability metric $\epsilon$.
• Zero-Shot Baseline: A zero-shot approach (asking the LLM to directly output an allocation) performed surprisingly well but lacked the iterative refinement and formal guarantees of the CG approach.

Significance and Claims

The paper claims to offer a computationally tractable and economically principled mechanism for credit assignment in generative AI.

• Economic Alignment: Unlike prior work focused on interpretability or attribution, this approach explicitly prioritizes creator incentives, ensuring no group of creators is systematically under-compensated.
• Practicality: By leveraging LLMs as separation oracles within a constraint generation framework, the authors demonstrate that complex cooperative game solutions (the least core) can be approximated efficiently in real-world scenarios where the value function is expensive to query.
• Future Directions: The authors note that while they assume black-box access to a value function estimate, improving the estimation of value functions themselves remains an important future direction. They also suggest exploring other core variants (e.g., closest to Shapley value) and integrating these methods into real-world platform designs.

The work positions the least core not just as a theoretical construct, but as a viable, scalable tool for managing the economics of the emerging creator economy in the age of generative AI.