pith. machine review for the scientific record. sign in

arxiv: 2605.06920 · v1 · submitted 2026-05-07 · 💻 cs.GT · cs.AI· cs.LG

Recognition: 2 theorem links

· Lean Theorem

In-Context Credit Assignment via the Core

Asher Trockman, Keegan Harris, Siddharth Prasad

Authors on Pith no claims yet

Pith reviewed 2026-05-11 00:48 UTC · model grok-4.3

classification 💻 cs.GT cs.AIcs.LG
keywords credit assignmentleast corecooperative game theoryin-context learningLLMconstraint optimizationgame theory
0
0 comments X

The pith

The least core from cooperative game theory enables stable in-context credit assignment for AI-generated content using far fewer LLM calls.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes using the least core to distribute credit among creators whose intellectual property is used in an AI's context window. This ensures stability by preventing any group of creators from being underpaid compared to what they could achieve independently. Novel algorithms for seeding and separating constraints make it possible to approximate this distribution efficiently. These methods require orders of magnitude fewer calls to large language models than existing approaches on tasks like web retrieval credit assignment. A reader would care if they want AI systems to fairly compensate content creators without excessive computational cost.

Core claim

We develop algorithms for approximating the least core that leverage novel routines for constraint seeding and constraint separation. On a web retrieval credit assignment task, these approaches approximate the least core using orders of magnitude fewer LLM calls compared to alternative methods.

What carries the argument

The least core solution concept, which minimizes the maximum dissatisfaction of any coalition by distributing value such that no subset is significantly under-compensated relative to their independent generation value.

Load-bearing premise

That queries to large language models can accurately estimate the value any coalition of creators could produce on their own.

What would settle it

A direct comparison on the web retrieval task showing that the proposed algorithms do not use significantly fewer LLM calls than the alternative methods.

Figures

Figures reproduced from arXiv: 2605.06920 by Asher Trockman, Keegan Harris, Siddharth Prasad.

Figure 1
Figure 1. Figure 1: Convergence at tractable scale: Synthetic, n=10 (egal.). CG matches εbH in ∼30 calls. We compare three families of algorithms: random sampling (YP; Algorithm 5), our constraint generation approach (CG; Algo￾rithm 1), and a zero-shot (ZS) method in which we ask the LLM to directly output a least core utility vector in a single query. We assign binary rewards vb(S) ∈ {0, 1} to each coalition S by prompting t… view at source ↗
Figure 3
Figure 3. Figure 3: Credit assignment results on BrowseComp-Plus ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Calls-to-target of εbH ± .01. More in App. D.6. We set a maximum budget of B = 212 checked coalitions per method. YP exhausts its full budget, then solves the LP; CG methods terminate early when no violated constraint is found. All experiments use batches of 64 coalitions per CG round. We repeat across 32 problem instances per dataset. Aggregate results are summarized in [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
Figure 4
Figure 4. Figure 4: Convergence traces for representative n=32 instances. Top panels: holdout εbH (solid) and reported ε (dashed), with τb below. Bottom: credit heatmaps at the first, second, and last iterates. straint generation can approximate least-core allocations with orders of magnitude fewer value function queries compared to other approaches. More broadly, our work highlights the impor￾tance of integrating economic in… view at source ↗
Figure 5
Figure 5. Figure 5: Credit assignment results on Synthetic ( [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: ZS failure cases: ZS overshoots YP’s holdout ˆεH by +0.23, while CG(R,R) matches the baseline with 3–4× fewer calls. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: ZS success cases: ZS matches YP’s holdout ˆεH = 0.50 in a single call, with high τb. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Egalitarian effects on Synthetic n=32: non-egalitarian (left) vs. egalitarian (right). The QP objective redistributes credit more broadly, as visible in the heatmaps, with only minor impact on ˆεH relative to YP’s baseline. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Egalitarian effects on Synthetic n=32 (continued): non-egalitarian (left) vs. egalitarian (right). Credit heatmaps are visibly less sparse under the egalitarian objective. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Additional BrowseComp n=32 convergence traces. CG(R,R) consistently matches YP’s holdout ˆεH with 8–9× fewer calls; in Row 31 the LLM-oracle variants undershoot YP by 0.08. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Credit assignment results on Synthetic ( [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Synthetic n=10, non-egalitarian convergence traces. CG methods match or under￾shoot YP’s holdout ˆεH within ∼50–300 calls. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_12.png] view at source ↗
Figure 12
Figure 12. Figure 12: Synthetic n=10, non-egalitarian convergence traces (cont.). Selected egalitarian traces. The egalitarian objective redistributes credit without substan￾tially degrading ˆεH. In Row 10 (egal.), all CG variants still match YP’s ˆεH = 0.50, with visibly less sparse heatmaps. Row 15 shows CG(R,R) matching YP’s baseline within 0.01, with broader credit distribution. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Synthetic n=10, egalitarian convergence traces. Heatmaps show broader credit distribution with minimal ˆεH degradation relative to YP. D.5.2 BrowseComp n=10 31 [PITH_FULL_IMAGE:figures/full_fig_p031_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Credit assignment results on BrowseComp-Plus ( [PITH_FULL_IMAGE:figures/full_fig_p032_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: BrowseComp n=10, non-egalitarian convergence traces. CG methods match or undershoot YP’s holdout ˆεH in 80–420 calls. Selected egalitarian traces. The egalitarian traces show broader credit redistribution with minimal ˆεH degradation. In Row 26, CG(R,R) undershoots YP’s ˆεH = 0.80 by 0.13 (ˆεH = 0.67 at ∼144 calls). Row 25 shows CG(R,R) slightly undershooting YP (−0.03). In Row 28, CG(R,ZS) matches YP’s ˆ… view at source ↗
Figure 15
Figure 15. Figure 15: BrowseComp n=10, non-egalitarian convergence traces (cont.). D.6 Calls-to-Target CDF Plots The following plots show the fraction of n=10 instances for which each method’s holdout ˆεH falls within a given tolerance of the holdout-optimal ˆε ∗ H, as a function of LLM calls consumed. Since n=10 admits exhaustive evaluation (all 210 − 2 non-trivial coalitions), ˆεH is exact (Q1.0, i.e., the true maximum viola… view at source ↗
Figure 16
Figure 16. Figure 16: BrowseComp n=10, egalitarian convergence traces. Heatmaps show broader credit redistribution; CG(R,·) methods match or undershoot YP’s baseline. 35 [PITH_FULL_IMAGE:figures/full_fig_p035_16.png] view at source ↗
Figure 16
Figure 16. Figure 16: BrowseComp n=10, egalitarian convergence traces (cont.). 10 0 10 1 10 2 10 3 LLM Calls 0.0 0.2 0.4 0.6 0.8 1.0 Frac. within 0.01 of Synth n=10 YP YP S CG R R CG S R CG L R CG R L CG L L CG S L ZS (a) Synth (non-egal.) 10 0 10 1 10 2 10 3 LLM Calls 0.0 0.2 0.4 0.6 0.8 1.0 Frac. within 0.01 of Synth n=10 (egal.) YP YP S CG R R CG S R CG L R CG R L CG L L CG S L ZS (b) Synth (egal.) 10 0 10 1 10 2 10 3 LLM C… view at source ↗
Figure 17
Figure 17. Figure 17: Calls-to-target CDF at tolerance 0.01: fraction of [PITH_FULL_IMAGE:figures/full_fig_p036_17.png] view at source ↗
read the original abstract

We propose incentive-aligned mechanisms for in-context credit assignment: the task of assigning credit for AI-generated content (e.g. code, news articles, short-form videos) among creators whose intellectual property appears in the context window. Our approach is based on the least core solution concept from cooperative game theory, which distributes value in a way that is as stable as possible by ensuring that no subset of creators is significantly under-compensated relative to the value they could generate on their own. We develop algorithms for approximating the least core, which leverage novel routines for constraint seeding and constraint separation. On a web retrieval credit assignment task, we find that our approaches are capable of approximating the least core using orders of magnitude fewer LLM calls compared to alternative methods.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper proposes incentive-aligned mechanisms for in-context credit assignment among creators whose intellectual property appears in an LLM context window. It applies the least core solution concept from cooperative game theory and develops algorithms based on novel constraint seeding and separation routines to approximate the least core. On a web retrieval credit assignment task, the methods are reported to approximate the least core using orders of magnitude fewer LLM calls than alternative approaches.

Significance. If the empirical results hold with proper validation, the work offers a theoretically grounded approach to a timely problem in generative AI by importing an established cooperative game theory concept without introducing free parameters. The reported efficiency gains in LLM calls could make stable credit assignment practical at scale, and the internal consistency of the LP formulation once the value oracle is granted is a positive feature.

major comments (1)
  1. Abstract and experimental section: the central claim that the proposed methods approximate the least core using orders of magnitude fewer LLM calls is load-bearing, yet the manuscript provides no details on the experimental setup, the precise definition of the value function, how coalition values are estimated via LLM queries, the specific baselines, number of trials, or statistical significance testing. This prevents verification of the performance claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and for highlighting the need for greater experimental transparency. We address the single major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: Abstract and experimental section: the central claim that the proposed methods approximate the least core using orders of magnitude fewer LLM calls is load-bearing, yet the manuscript provides no details on the experimental setup, the precise definition of the value function, how coalition values are estimated via LLM queries, the specific baselines, number of trials, or statistical significance testing. This prevents verification of the performance claim.

    Authors: We agree that the current manuscript does not provide sufficient detail on the experimental protocol to allow independent verification of the reported efficiency gains. In the revised version we will expand the experimental section (and update the abstract if needed) to include: (i) the exact definition of the value function for the web-retrieval credit-assignment task, (ii) the procedure for estimating coalition values via LLM queries, (iii) the full list of baseline algorithms, (iv) the number of independent trials, and (v) the statistical tests used to support the “orders of magnitude” claim. These additions will make the central empirical result verifiable without altering the underlying algorithms or theoretical results. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies the established least core solution concept from cooperative game theory to the new domain of in-context credit assignment. The central contribution consists of algorithmic routines (constraint seeding and separation) for approximating the least core in an LP formulation, with empirical evaluation on LLM-based value oracles. No derivation step reduces by construction to the paper's own inputs, fitted parameters, or self-citations; the mathematical definition of the least core is imported as an external fact, and the performance claims concern computational efficiency rather than re-deriving the core itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; the central claim rests on standard cooperative game theory definitions of the least core and the ability to model credit assignment as a cooperative game with LLM-estimated values. No specific free parameters or invented entities are identifiable from the abstract.

axioms (1)
  • domain assumption The credit assignment problem can be modeled as a cooperative game with a well-defined value function for coalitions.
    Invoked implicitly in the proposal to use the least core solution concept.

pith-pipeline@v0.9.0 · 5421 in / 1267 out tokens · 85515 ms · 2026-05-11T00:48:52.133284+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Reference graph

Works this paper leans on

45 extracted references · 8 canonical work pages · 1 internal anchor

  1. [1]

    Making AI-enhanced videos: Analyzing generative AI use cases in YouTube content creation

    Torin Anderson and Shuo Niu. Making AI-enhanced videos: Analyzing generative AI use cases in YouTube content creation. InProceedings of the Extended Abstracts of the CHI Conference on Human Factors in Computing Systems, pages 1–7, 2025

    2025

  2. [2]

    Learning cooperative games

    Maria-Florina Balcan, Ariel D Procaccia, and Yair Zick. Learning cooperative games. InProceedings of the 24th International Joint Conference on Artificial Intelligence, pages 475–481, 2015. 11

    2015

  3. [3]

    Statistical cost sharing.Advances in Neural Information Processing Systems, 30, 2017

    Eric Balkanski, Umar Syed, and Sergei Vassilvitskii. Statistical cost sharing.Advances in Neural Information Processing Systems, 30, 2017

    2017

  4. [4]

    Jopa: Explaining large language model’s generation via joint prompt attribution

    Yurui Chang, Bochuan Cao, Yujia Wang, Jinghui Chen, and Lu Lin. Jopa: Explaining large language model’s generation via joint prompt attribution. InProceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 22106–22122, 2025

    2025

  5. [5]

    Mingxuan Du, Benfeng Xu, Chiwei Zhu, Xiaorui Wang, and Zhendong Mao

    Zijian Chen, Xueguang Ma, Shengyao Zhuang, Ping Nie, Kai Zou, Andrew Liu, Joshua Green, Kshama Patel, Ruoxi Meng, Mingyi Su, et al. BrowseComp-Plus: A more fair and transparent evaluation benchmark of deep-research agent.arXiv preprint arXiv:2508.06600, 2025

    work page arXiv 2025

  6. [6]

    Con- textcite: Attributing model generation to context.Advances in Neural Information Pro- cessing Systems, 37:95764–95807, 2024

    Benjamin Cohen-Wang, Harshay Shah, Kristian Georgiev, and Aleksander Madry. Con- textcite: Attributing model generation to context.Advances in Neural Information Pro- cessing Systems, 37:95764–95807, 2024

    2024

  7. [7]

    Quadratic core-selecting payment rules for combina- torial auctions.Operations Research, 60(3):588–603, 2012

    Robert W Day and Peter Cramton. Quadratic core-selecting payment rules for combina- torial auctions.Operations Research, 60(3):588–603, 2012

    2012

  8. [8]

    Fair payments for efficient allocations in public sector combinatorial auctions.Management science, 53(9):1389–1406, 2007

    Robert W Day and Subramanian Raghavan. Fair payments for efficient allocations in public sector combinatorial auctions.Management science, 53(9):1389–1406, 2007

    2007

  9. [9]

    Improving context-attribution with semi-supervised cross-encoders.Euro- pean Conference on Artificial Intelligence (ECAI), 2025

    Luca De Grandisa, Francesco Maria Granataa, Davide Costaa, Antonio Lanzaa, and Er- melinda Oroa. Improving context-attribution with semi-supervised cross-encoders.Euro- pean Conference on Artificial Intelligence (ECAI), 2025

    2025

  10. [10]

    Springer Science & Business Media, 2006

    Guy Desaulniers, Jacques Desrosiers, and Marius M Solomon.Column Generation, vol- ume 5. Springer Science & Business Media, 2006

    2006

  11. [11]

    Approximating the core via iterative coalition sampling

    Ian Gemp, Marc Lanctot, Luke Marris, Yiran Mao, Edgar Du´ e˜ nez-Guzm´ an, Sarah Perrin, Andras Gyorgy, Romuald Elie, Georgios Piliouras, Michael Kaisers, et al. Approximating the core via iterative coalition sampling. InProceedings of the 23rd International Confer- ence on Autonomous Agents and Multiagent Systems, pages 669–678, 2024

    2024

  12. [12]

    Data Shapley: Equitable valuation of data for machine learning

    Amirata Ghorbani and James Zou. Data Shapley: Equitable valuation of data for machine learning. InInternational Conference on Machine Learning, pages 2242–2251. PMLR, 2019

    2019

  13. [13]

    Solutions to general non-zero-sum games.Contributions to the Theory of Games, 4(40):47–85, 1959

    Donald B Gillies. Solutions to general non-zero-sum games.Contributions to the Theory of Games, 4(40):47–85, 1959

    1959

  14. [14]

    Gemini 3 flash model card

    Google DeepMind. Gemini 3 flash model card. Technical report, Google DeepMind, De- cember 2025. URLhttps://storage.googleapis.com/deepmind-media/Model-Cards/ Gemini-3-Flash-Model-Card.pdf. Model card

    2025

  15. [15]

    Gemini 3 pro model card

    Google DeepMind. Gemini 3 pro model card. Technical report, Google DeepMind, Novem- ber 2025. URLhttps://storage.googleapis.com/deepmind-media/Model-Cards/ Gemini-3-Pro-Model-Card.pdf. Model card

    2025

  16. [16]

    The ellipsoid method and its consequences in combinatorial optimization.Combinatorica, 1(2):169–197, 1981

    Martin Gr¨ otschel, L´ aszl´ o Lov´ asz, and Alexander Schrijver. The ellipsoid method and its consequences in combinatorial optimization.Combinatorica, 1(2):169–197, 1981

    1981

  17. [17]

    Springer, 1988

    Martin Gr¨ otschel, L´ aszl´ o Lov´ asz, and Alexander Schrijver.Geometric algorithms and com- binatorial optimization. Springer, 1988. 12

    1988

  18. [18]

    Laquer: Localized attribution queries in content-grounded generation

    Eran Hirsch, Aviv Slobodkin, David Wan, Elias Stengel-Eskin, Mohit Bansal, and Ido Da- gan. Laquer: Localized attribution queries in content-grounded generation. InProceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 15355–15370, 2025

    2025

  19. [19]

    Towards efficient data valuation based on the Shapley value

    Ruoxi Jia, David Dao, Boxin Wang, Frances Ann Hubis, Nick Hynes, Nezihe Merve G¨ urel, Bo Li, Ce Zhang, Dawn Song, and Costas J Spanos. Towards efficient data valuation based on the Shapley value. InThe 22nd International Conference on Artificial Intelligence and Statistics, pages 1167–1176. PMLR, 2019

    2019

  20. [20]

    How much research is being written by large language models.Human-Centered Artificial Intelligence

    P Kanna. How much research is being written by large language models.Human-Centered Artificial Intelligence. Stanford University. Retrieved August, 16, 2024

    2024

  21. [21]

    The cutting-plane method for solving convex programs.Journal of the society for Industrial and Applied Mathematics, 8(4):703–712, 1960

    James E Kelley, Jr. The cutting-plane method for solving convex programs.Journal of the society for Industrial and Applied Mathematics, 8(4):703–712, 1960

    1960

  22. [22]

    An exact bound on epsilon for nonempti- ness of epsilon cores of games.Mathematics of Operations Research, 26(4):654–678, 2001

    Alexander Kovalenkov and Myrna Holtz Wooders. An exact bound on epsilon for nonempti- ness of epsilon cores of games.Mathematics of Operations Research, 26(4):654–678, 2001

    2001

  23. [23]

    Attributing response to context: A jensen-shannon divergence driven mechanistic study of context attribution in retrieval-augmented generation.arXiv preprint arXiv:2505.16415, 2025

    Ruizhe Li, Chen Chen, Yuchen Hu, Yanjun Gao, Xi Wang, and Emine Yilmaz. Attributing response to context: A jensen-shannon divergence driven mechanistic study of context attribution in retrieval-augmented generation.arXiv preprint arXiv:2505.16415, 2025

    work page arXiv 2025

  24. [24]

    Attribot: A bag of tricks for efficiently approximating leave-one-out context attribution.arXiv preprint arXiv:2411.15102, 2024

    Fengyuan Liu, Nikhil Kandpal, and Colin Raffel. Attribot: A bag of tricks for efficiently approximating leave-one-out context attribution.arXiv preprint arXiv:2411.15102, 2024

    work page arXiv 2024

  25. [25]

    A unified approach to interpreting model predictions

    Scott M Lundberg and Su-In Lee. A unified approach to interpreting model predictions. Advances in neural information processing systems, 30, 2017

    2017

  26. [26]

    arXiv preprint arXiv:2507.04480 , year=

    Ikhtiyor Nematov, Tarik Kalai, Elizaveta Kuzmenko, Gabriele Fugagnoli, Dimitris Sacharidis, Katja Hose, and Tomer Sagi. Source attribution in retrieval-augmented gener- ation.arXiv preprint arXiv:2507.04480, 2025

    work page arXiv 2025

  27. [27]

    The fairest core in cooperative games with transferable utilities.Oper- ations Research Letters, 43(1):34–39, 2015

    Tri-Dung Nguyen. The fairest core in cooperative games with transferable utilities.Oper- ations Research Letters, 43(1):34–39, 2015

    2015

  28. [28]

    Finding the nucleoli of large cooperative games

    Tri-Dung Nguyen and Lyn Thomas. Finding the nucleoli of large cooperative games. European Journal of Operational Research, 248(3):1078–1092, 2016

    2016

  29. [29]

    Context Attribution with Multi-Armed Bandit Optimization

    Deng Pan, Keerthiram Murugesan, Nuno Moniz, and Nitesh Chawla. Context attribution with multi-armed bandit optimization.arXiv preprint arXiv:2506.19977, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  30. [30]

    Maxshapley: Towards incentive-compatible generative search with fair context attribution.arXiv preprint arXiv:2512.05958, 2025

    Sara Patel, Mingxun Zhou, and Giulia Fanti. Maxshapley: Towards incentive-compatible generative search with fair context attribution.arXiv preprint arXiv:2512.05958, 2025

    work page arXiv 2025

  31. [31]

    Weakest bidder types and new core-selecting combinatorial auctions

    Siddharth Prasad, Maria-Florina Balcan, and Tuomas Sandholm. Weakest bidder types and new core-selecting combinatorial auctions. InProceedings of the AAAI Conference on Artificial Intelligence, volume 40, pages 17206–17214, 2026

    2026

  32. [32]

    Model internals-based answer attribution for trustworthy retrieval-augmented generation

    Jirui Qi, Gabriele Sarti, Raquel Fern´ andez, and Arianna Bisazza. Model internals-based answer attribution for trustworthy retrieval-augmented generation. InProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 6037–6053, 2024

    2024

  33. [33]

    A value for n-person games.Contributions to the Theory of Games II, 1953

    Lloyd S Shapley. A value for n-person games.Contributions to the Theory of Games II, 1953. 13

    1953

  34. [34]

    On balanced sets and cores.Naval Research Logistics Quarterly, 14(4): 453–460, 1967

    Lloyd S Shapley. On balanced sets and cores.Naval Research Logistics Quarterly, 14(4): 453–460, 1967

    1967

  35. [35]

    Cores of convex games.International Journal of Game Theory, 1(1): 11–26, 1971

    Lloyd S Shapley. Cores of convex games.International Journal of Game Theory, 1(1): 11–26, 1971

    1971

  36. [36]

    Transparentize the internal and external knowledge utilization in llms with trustworthy citation

    Jiajun Shen, Tong Zhou, Yubo Chen, Delai Qiu, Shengping Liu, Kang Liu, and Jun Zhao. Transparentize the internal and external knowledge utilization in llms with trustworthy citation. InFindings of the Association for Computational Linguistics: ACL 2025, pages 17858–17877, 2025

    2025

  37. [37]

    pyDVL: The python library for data valuation, Mar 2025

    TransferLab Team. pyDVL: The python library for data valuation, Mar 2025. URLhttps: //pydvl.org/stable/

    2025

  38. [38]

    Data Shapley in one training run.arXiv preprint arXiv:2406.11011, 2024

    Jiachen T Wang, Prateek Mittal, Dawn Song, and Ruoxi Jia. Data Shapley in one training run.arXiv preprint arXiv:2406.11011, 2024

    work page arXiv 2024

  39. [39]

    In34th USENIX Security Symposium (USENIX Security 25), pages 3845–3864, 2025

    Yanting Wang, Wei Zou, Runpeng Geng, and Jinyuan Jia.{TracLLM}: A generic frame- work for attributing long context{LLMs}. In34th USENIX Security Symposium (USENIX Security 25), pages 3845–3864, 2025

    2025

  40. [40]

    The nucleolus and kernel for simple games or special valid inequalities for 0–1 linear integer programs.International Journal of Game Theory, 5(4):227–238, 1976

    LA Wolsey. The nucleolus and kernel for simple games or special valid inequalities for 0–1 linear integer programs.International Journal of Game Theory, 5(4):227–238, 1976

    1976

  41. [41]

    Tokenshapley: Token level context attribution with shapley value

    Yingtai Xiao, Yuqing Zhu, Sirat Samyoun, Wanrong Zhang, Jiachen T Wang, and Jian Du. Tokenshapley: Token level context attribution with shapley value. InFindings of the Association for Computational Linguistics: ACL 2025, pages 3882–3894, 2025

    2025

  42. [42]

    If you like Shapley then you’ll love the core

    Tom Yan and Ariel D Procaccia. If you like Shapley then you’ll love the core. InProceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 5751–5759, 2021

    2021

  43. [43]

    arXiv preprint arXiv:2509.13772 (2025)

    Baolei Zhang, Haoran Xin, Yuxi Chen, Zhuqing Liu, Biao Yi, Tong Li, Lihai Nie, Zheli Liu, and Minghong Fang. Who taught the lie? responsibility attribution for poisoned knowledge in retrieval-augmented generation.arXiv preprint arXiv:2509.13772, 2025

    work page arXiv 2025

  44. [44]

    X i∈S u(alg) i +ε (alg) <bv(S) # < δ, because otherwise the final oracle call would have returned a violated coalition instead of al- lowing termination. Sinceε≤bε, PS∼D

    Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li, Dacheng Li, Eric Xing, et al. Judging llm-as-a-judge with mt-bench and chatbot arena.Advances in neural information processing systems, 36:46595– 46623, 2023. 14 A Discussion: Cooperative solution concepts The Shapley value and the core are two of th...

    2023

  45. [45]

    Her mother was 21

    Since (u 0, t0) violates t0 ≥ 1 2 ∥u0∥2 2, we have u⊤ 0 u0 −t 0 > 1 2 ∥u0∥2 2, so (u 0, t0) lies strictly outside the halfspace, which therefore separates it from the epigraph. Hence the quadratic epigraph admits an exact deterministic separation oracle. The remaining constraints are the coalition constraints X i∈S ui ≥bv(S)−ε (alg) ∀S⊆N. 18 For these, us...