8 Search Results for "Navon, Inbal Livni"


Document
Sparser Abelian High Dimensional Expanders

Authors: Yotam Dikstein, Siqi Liu, and Avi Wigderson

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)


Abstract
The focus of this paper is the development of new elementary techniques for the construction and analysis of high dimensional expanders. Specifically, we present two new explicit constructions of Cayley high dimensional expanders (HDXs) over the abelian group 𝔽₂ⁿ. Our expansion proofs use only linear algebra and combinatorial arguments. The first construction gives local spectral HDXs of any constant dimension and subpolynomial degree exp(n^ε) for every ε > 0, improving on a construction by Golowich [Golowich, 2023] which achieves ε = 1/2. [Golowich, 2023] derives these HDXs by sparsifying the complete Grassmann poset of subspaces. The novelty in our construction is the ability to sparsify any expanding Grassmann posets, leading to iterated sparsification and much smaller degrees. The sparse Grassmannian (which is of independent interest in the theory of HDXs) serves as the generating set of the Cayley graph. Our second construction gives a 2-dimensional HDX of any polynomial degree exp(ε n) for any constant ε > 0, which is simultaneously a spectral expander and a coboundary expander. To the best of our knowledge, this is the first such non-trivial construction. We name it the Johnson complex, as it is derived from the classical Johnson scheme, whose vertices serve as the generating set of this Cayley graph. This construction may be viewed as a derandomization of the recent random geometric complexes of [Liu et al., 2023]. Establishing coboundary expansion through Gromov’s "cone method" and the associated isoperimetric inequalities is the most intricate aspect of this construction. While these two constructions are quite different, we show that they both share a common structure, resembling the intersection patterns of vectors in the Hadamard code. We propose a general framework of such "Hadamard-like" constructions in the hope that it will yield new HDXs.

Cite as

Yotam Dikstein, Siqi Liu, and Avi Wigderson. Sparser Abelian High Dimensional Expanders. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 7:1-7:98, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{dikstein_et_al:LIPIcs.CCC.2025.7,
  author =	{Dikstein, Yotam and Liu, Siqi and Wigderson, Avi},
  title =	{{Sparser Abelian High Dimensional Expanders}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{7:1--7:98},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.7},
  URN =		{urn:nbn:de:0030-drops-237013},
  doi =		{10.4230/LIPIcs.CCC.2025.7},
  annote =	{Keywords: Local spectral expander, coboundary expander, Grassmannian expander}
}
Document
Smooth Calibration and Decision Making

Authors: Jason Hartline, Yifan Wu, and Yunran Yang

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)


Abstract
Calibration requires predictor outputs to be consistent with their Bayesian posteriors. For machine learning predictors that do not distinguish between small perturbations, calibration errors are continuous in predictions, e.g. smooth calibration error [Foster and Hart, 2018], distance to calibration [Błasiok et al., 2023]. On the contrary, decision-makers who use predictions make optimal decisions discontinuously in probabilistic space, experiencing loss from miscalibration discontinuously. Calibration errors for decision-making are thus discontinuous, e.g., Expected Calibration Error [Foster and Vohra, 1997], and Calibration Decision Loss [Hu and Wu, 2024]. Thus, predictors with a low calibration error for machine learning may suffer a high calibration error for decision-making, i.e. they may not be trustworthy for decision-makers optimizing assuming their predictions are correct. It is natural to ask if post-processing a predictor with a low calibration error for machine learning is without loss to achieve a low calibration error for decision-making. In our paper, we show post-processing an online predictor with ε distance to calibration achieves O(√{ε}) ECE and CDL, which is asymptotically optimal. The post-processing algorithm adds noise to make predictions differentially private. The optimal bound from low distance to calibration predictors from post-processing is non-optimal compared with existing online calibration algorithms that directly optimize for ECE and CDL.

Cite as

Jason Hartline, Yifan Wu, and Yunran Yang. Smooth Calibration and Decision Making. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 16:1-16:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{hartline_et_al:LIPIcs.FORC.2025.16,
  author =	{Hartline, Jason and Wu, Yifan and Yang, Yunran},
  title =	{{Smooth Calibration and Decision Making}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{16:1--16:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.16},
  URN =		{urn:nbn:de:0030-drops-231438},
  doi =		{10.4230/LIPIcs.FORC.2025.16},
  annote =	{Keywords: Calibration, calibration errors, decision making, differential privacy}
}
Document
Model Ensembling for Constrained Optimization

Authors: Ira Globus Harris, Varun Gupta, Michael Kearns, and Aaron Roth

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)


Abstract
Many instances of decision making under objective uncertainty can be decomposed into two steps: predicting the objective function and then optimizing for the best feasible action under the estimate of the objective vector. We study the problem of ensembling models for optimization of uncertain linear objectives under arbitrary constraints. We imagine we are given a collection of predictive models mapping a feature space to multi-dimensional real-valued predictions, which form the coefficients of a linear objective that we would like to optimize. We give two ensembling methods that can provably result in transparent decisions that strictly improve on all initial policies. The first method operates in the "white box" setting in which we have access to the underlying prediction models and the second in the "black box" setting in which we only have access to the induced decisions (in the downstream optimization problem) of the constituent models, but not their underlying point predictions. They are transparent or trustworthy in the sense that the user can reliably predict long-term ensemble rewards even if the instance by instance predictions are imperfect.

Cite as

Ira Globus Harris, Varun Gupta, Michael Kearns, and Aaron Roth. Model Ensembling for Constrained Optimization. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{globusharris_et_al:LIPIcs.FORC.2025.14,
  author =	{Globus Harris, Ira and Gupta, Varun and Kearns, Michael and Roth, Aaron},
  title =	{{Model Ensembling for Constrained Optimization}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.14},
  URN =		{urn:nbn:de:0030-drops-231412},
  doi =		{10.4230/LIPIcs.FORC.2025.14},
  annote =	{Keywords: model ensembling, trustworthy AI, decision-making under uncertainty}
}
Document
On Average Baby PIH and Its Applications

Authors: Yuwei Liu, Yijia Chen, Shuangle Li, Bingkai Lin, and Xin Zheng

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)


Abstract
The Parameterized Inapproximability Hypothesis (PIH) asserts that no FPT algorithm can decide whether a given 2CSP instance parameterized by the number of variables is satisfiable, or at most a constant fraction of its constraints can be satisfied simultaneously. In a recent breakthrough, Guruswami, Lin, Ren, Sun, and Wu (STOC 2024) proved the PIH under the Exponential Time Hypothesis (ETH). However, it remains a major open problem whether the PIH can be established assuming only W[1]≠FPT. Towards this goal, Guruswami, Ren, and Sandeep (CCC 2024) showed a weaker version of the PIH called the Baby PIH under W[1]≠FPT. In addition, they proposed one more intermediate assumption known as the Average Baby PIH, which might lead to further progress on the PIH. As the main contribution of this paper, we prove that the Average Baby PIH holds assuming W[1]≠FPT. Given a 2CSP instance where the number of its variables is the parameter, the Average Baby PIH states that no FPT algorithm can decide whether (i) it is satisfiable or (ii) any multi-assignment that satisfies all constraints must assign each variable more than r values on average for any fixed constant r > 1. So there is a gap between (i) and (ii) on the average number of values that are assigned to a variable, i.e., 1 vs. r. If this gap occurs in each variable instead of on average, we get the original Baby PIH. So central to our paper is an FPT self-reduction for 2CSP instances that turns the above gap for each variable into a gap on average. By the known W[1]-hardness for the Baby PIH, this proves that the Average Baby PIH holds under W[1] ≠ FPT. As applications, we obtain (i) for the first time, the W[1]-hardness of constant approximating k-ExactCover, and (ii) a tight relationship between running time lower bounds in the Average Baby PIH and approximating the parameterized Nearest Codeword Problem (k-NCP).

Cite as

Yuwei Liu, Yijia Chen, Shuangle Li, Bingkai Lin, and Xin Zheng. On Average Baby PIH and Its Applications. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 65:1-65:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{liu_et_al:LIPIcs.STACS.2025.65,
  author =	{Liu, Yuwei and Chen, Yijia and Li, Shuangle and Lin, Bingkai and Zheng, Xin},
  title =	{{On Average Baby PIH and Its Applications}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{65:1--65:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.65},
  URN =		{urn:nbn:de:0030-drops-228900},
  doi =		{10.4230/LIPIcs.STACS.2025.65},
  annote =	{Keywords: Average Baby PIH, Parameterized Inapproximability, Constraint Satisfaction Problem, Exact Set Cover, W\lbrack1\rbrack-hardness}
}
Document
Generative Models of Huge Objects

Authors: Lunjia Hu, Inbal Rachel Livni Navon, and Omer Reingold

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)


Abstract
This work initiates the systematic study of explicit distributions that are indistinguishable from a single exponential-size combinatorial object. In this we extend the work of Goldreich, Goldwasser and Nussboim (SICOMP 2010) that focused on the implementation of huge objects that are indistinguishable from the uniform distribution, satisfying some global properties (which they coined truthfulness). Indistinguishability from a single object is motivated by the study of generative models in learning theory and regularity lemmas in graph theory. Problems that are well understood in the setting of pseudorandomness present significant challenges and at times are impossible when considering generative models of huge objects. We demonstrate the versatility of this study by providing a learning algorithm for huge indistinguishable objects in several natural settings including: dense functions and graphs with a truthfulness requirement on the number of ones in the function or edges in the graphs, and a version of the weak regularity lemma for sparse graphs that satisfy some global properties. These and other results generalize basic pseudorandom objects as well as notions introduced in algorithmic fairness. The results rely on notions and techniques from a variety of areas including learning theory, complexity theory, cryptography, and game theory.

Cite as

Lunjia Hu, Inbal Rachel Livni Navon, and Omer Reingold. Generative Models of Huge Objects. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{hu_et_al:LIPIcs.CCC.2023.5,
  author =	{Hu, Lunjia and Livni Navon, Inbal Rachel and Reingold, Omer},
  title =	{{Generative Models of Huge Objects}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.5},
  URN =		{urn:nbn:de:0030-drops-182758},
  doi =		{10.4230/LIPIcs.CCC.2023.5},
  annote =	{Keywords: pseudorandomness, generative models, regularity lemma}
}
Document
Bidding Strategies for Proportional Representation in Advertisement Campaigns

Authors: Inbal Livni Navon, Charlotte Peale, Omer Reingold, and Judy Hanwen Shen

Published in: LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)


Abstract
Many companies rely on advertising platforms such as Google, Facebook, or Instagram to recruit a large and diverse applicant pool for job openings. Prior works have shown that equitable bidding may not result in equitable outcomes due to heterogeneous levels of competition for different types of individuals. Suggestions have been made to address this problem via revisions to the advertising platform. However, it may be challenging to convince platforms to undergo a costly re-vamp of their system, and in addition it might not offer the flexibility necessary to capture the many types of fairness notions and other constraints that advertisers would like to ensure. Instead, we consider alterations that make no change to the platform mechanism and instead change the bidding strategies used by advertisers. We compare two natural fairness objectives: one in which the advertisers must treat groups equally when bidding in order to achieve a yield with group-parity guarantees, and another in which the bids are not constrained and only the yield must satisfy parity constraints. We show that requiring parity with respect to both bids and yield can result in an arbitrarily large decrease in efficiency compared to requiring equal yield proportions alone. We find that autobidding is a natural way to realize this latter objective and show how existing work in this area can be extended to provide efficient bidding strategies that provide high utility while satisfying group parity constraints as well as deterministic and randomized rounding techniques to uphold these guarantees. Finally, we demonstrate the effectiveness of our proposed solutions on data adapted from a real-world employment dataset.

Cite as

Inbal Livni Navon, Charlotte Peale, Omer Reingold, and Judy Hanwen Shen. Bidding Strategies for Proportional Representation in Advertisement Campaigns. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{navon_et_al:LIPIcs.FORC.2023.3,
  author =	{Navon, Inbal Livni and Peale, Charlotte and Reingold, Omer and Shen, Judy Hanwen},
  title =	{{Bidding Strategies for Proportional Representation in Advertisement Campaigns}},
  booktitle =	{4th Symposium on Foundations of Responsible Computing (FORC 2023)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-272-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{256},
  editor =	{Talwar, Kunal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.3},
  URN =		{urn:nbn:de:0030-drops-179245},
  doi =		{10.4230/LIPIcs.FORC.2023.3},
  annote =	{Keywords: Algorithmic fairness, diversity, advertisement auctions}
}
Document
Cube vs. Cube Low Degree Test

Authors: Amey Bhangale, Irit Dinur, and Inbal Livni Navon

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)


Abstract
We revisit the Raz-Safra plane-vs.-plane test and study the closely related cube vs. cube test. In this test the tester has access to a "cubes table" which assigns to every cube a low degree polynomial. The tester randomly selects two cubes (affine sub-spaces of dimension 3) that intersect on a point x in F^m, and checks that the assignments to the cubes agree with each other on the point x. Our main result is a new combinatorial proof for a low degree test that comes closer to the soundness limit, as it works for all epsilon >= poly(d)/{|F|}^{1/2}, where d is the degree. This should be compared to the previously best soundness value of epsilon >= poly(m, d)/|F|^{1/8}. Our soundness limit improves upon the dependence on the field size and does not depend on the dimension of the ambient space. Our proof is combinatorial and direct: unlike the Raz-Safra proof, it proceeds in one shot and does not require induction on the dimension of the ambient space. The ideas in our proof come from works on direct product testing which are even simpler in the current setting thanks to the low degree. Along the way we also prove a somewhat surprising fact about connection between different agreement tests: it does not matter if the tester chooses the cubes to intersect on points or on lines: for every given table, its success probability in either test is nearly the same.

Cite as

Amey Bhangale, Irit Dinur, and Inbal Livni Navon. Cube vs. Cube Low Degree Test. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 40:1-40:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{bhangale_et_al:LIPIcs.ITCS.2017.40,
  author =	{Bhangale, Amey and Dinur, Irit and Livni Navon, Inbal},
  title =	{{Cube vs. Cube Low Degree Test}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{40:1--40:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.40},
  URN =		{urn:nbn:de:0030-drops-81748},
  doi =		{10.4230/LIPIcs.ITCS.2017.40},
  annote =	{Keywords: Low Degree Test, Probabilistically Checkable Proofs, Locally Testable Codes}
}
Document
Exponentially Small Soundness for the Direct Product Z-Test

Authors: Irit Dinur and Inbal Livni Navon

Published in: LIPIcs, Volume 79, 32nd Computational Complexity Conference (CCC 2017)


Abstract
Given a function f:[N]^k->[M]^k, the Z-test is a three query test for checking if a function f is a direct product, namely if there are functions g_1,...g_k:[N]->[M] such that f(x_1,...,x_k)=(g_1(x_1),...,g_k(x_k)) for every input x in [N]^k. This test was introduced by Impagliazzo et. al. (SICOMP 2012), who showed that if the test passes with probability epsilon > exp(-sqrt k) then f is Omega(epsilon) close to a direct product function in some precise sense. It remained an open question whether the soundness of this test can be pushed all the way down to exp(-k) (which would be optimal). This is our main result: we show that whenever f passes the Z test with probability epsilon > exp(-k), there must be a global reason for this: namely, f must be close to a product function on some Omega(epsilon) fraction of its domain. Towards proving our result we analyze the related (two-query) V-test, and prove a "restricted global structure" theorem for it. Such theorems were also proven in previous works on direct product testing in the small soundness regime. The most recent work, by Dinur and Steurer (CCC 2014), analyzed the V test in the exponentially small soundness regime. We strengthen their conclusion of that theorem by moving from an "in expectation" statement to a stronger "concentration of measure" type of statement, which we prove using hyper-contractivity. This stronger statement allows us to proceed to analyze the Z test. We analyze two variants of direct product tests. One for functions on ordered tuples, as above, and another for functions on sets of size k. The work of Impagliazzo et al. was actually focused only on functions of the latter type, i.e. on sets. We prove exponentially small soundness for the Z-test for both variants. Although the two appear very similar, the analysis for tuples is more tricky and requires some additional ideas.

Cite as

Irit Dinur and Inbal Livni Navon. Exponentially Small Soundness for the Direct Product Z-Test. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 29:1-29:50, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{dinur_et_al:LIPIcs.CCC.2017.29,
  author =	{Dinur, Irit and Livni Navon, Inbal},
  title =	{{Exponentially Small Soundness for the Direct Product Z-Test}},
  booktitle =	{32nd Computational Complexity Conference (CCC 2017)},
  pages =	{29:1--29:50},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-040-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{79},
  editor =	{O'Donnell, Ryan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2017.29},
  URN =		{urn:nbn:de:0030-drops-75336},
  doi =		{10.4230/LIPIcs.CCC.2017.29},
  annote =	{Keywords: Direct Product Testing, Property Testing, Agreement}
}
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