Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits | Paper Citation Record

Observation 1b6ad20a-543d-4b97-a2b7-6ab9004bcbb8 · outbound

This paper cites GPT-4 Technical Report.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits GPT-4 Technical Report

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Observation a3ae3b96-3888-4d31-8953-ca14d1e5f950 · outbound

This paper cites The statistical analysis of compositional data.Journal of the Royal Statistical Society: Series B (Methodological), 44(2):139–160, 1982.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits The statistical analysis of compositional data.Journal of the Royal Statistical Society: Series B (Methodological), 44(2):139–160, 1982

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Observation 0af79a6e-3b15-499c-8465-28e4b7c6cabf · outbound

This paper cites Understanding intermediate layers using linear classifier probes.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Understanding intermediate layers using linear classifier probes

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Observation f7319d65-375a-4f5c-8246-96dbfd9f1725 · outbound

This paper cites Self-RAG: Learning to retrieve, generate, and critique through self-reflection.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Self-RAG: Learning to retrieve, generate, and critique through self-reflection

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Observation db883630-d526-4241-b091-2f36bdfecc30 · outbound

This paper cites Plongements Lipschitziens dansR n.Bulletin de la Soci´ et´ e Math´ ematique de France, 111:429– 448, 1983.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Plongements Lipschitziens dansR n.Bulletin de la Soci´ et´ e Math´ ematique de France, 111:429– 448, 1983

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Observation e41442ad-2089-4fe2-8d1a-5211f4c68f3d · outbound

This paper cites Do we really need the Rademacher complexities?.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Do we really need the Rademacher complexities?

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Observation 3fc4fb83-e97f-4d10-9e70-2620f1c8efe0 · outbound

This paper cites Uniform mean estimation via generic chaining.arXiv preprint arXiv:2502.15116, 2025.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Uniform mean estimation via generic chaining.arXiv preprint arXiv:2502.15116, 2025

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Observation 3d07bbcc-118d-42f0-8141-d53b11543ac2 · outbound

This paper cites Local rademacher complexities.The Annals of Statistics, 33(4):1497–1537, 2005.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Local rademacher complexities.The Annals of Statistics, 33(4):1497–1537, 2005

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Observation 95d8249c-64e4-418f-a180-f73077074015 · outbound

This paper cites Rademacher and gaussian complexities: Risk bounds and structural results.Journal of machine learning research, 3(Nov):463–482, 2002.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Rademacher and gaussian complexities: Risk bounds and structural results.Journal of machine learning research, 3(Nov):463–482, 2002

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Observation 8730b3ed-4e0a-4b3d-b0d1-45fac8c54e83 · outbound

This paper cites Network dissection: Quantifying interpretability of deep visual representations.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Network dissection: Quantifying interpretability of deep visual representations

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Observation 13324ef2-a2c3-429c-9b33-8028b38c8e8f · outbound

This paper cites Minimalstellen von funktionen und extremalpunkte.Archiv der Mathematik, 9(4):389–393, 1958.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Minimalstellen von funktionen und extremalpunkte.Archiv der Mathematik, 9(4):389–393, 1958

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Observation dca76bf2-b502-4ac6-8f85-fb13a7b97d7f · outbound

This paper cites Square-root lasso: pivotal recovery of sparse signals via conic programming.Biometrika, 98(4):791–806, 2011.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Square-root lasso: pivotal recovery of sparse signals via conic programming.Biometrika, 98(4):791–806, 2011

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Observation ef47b9e0-b512-4289-8a5a-9e3957b255d9 · outbound

This paper cites Managing extreme AI risks amid rapid progress.Science, 384(6698):842–845, 2024.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Managing extreme AI risks amid rapid progress.Science, 384(6698):842–845, 2024

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Observation aa5c0a48-1a97-4846-b1c3-fd09bad1792a · outbound

This paper cites Neural algorithmic reasoning with causal regularisation.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Neural algorithmic reasoning with causal regularisation

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Observation 03865343-e669-46a8-bdd1-8ebeaa083de0 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Learnability and the Vapnik- Chervonenkis dimension.Journal of the ACM (JACM), 36(4):929–965, 1989

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Observation 37139608-cf7c-4adf-ba4c-e506adb76b1b · outbound

This paper cites Oxford University Press, 2014.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Oxford University Press, 2014

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Observation 28204388-d3d0-4d7d-b7f2-1b86147cf1bd · outbound

This paper cites A universal uniform approximation theorem for neural networks.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits A universal uniform approximation theorem for neural networks

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Observation 9abbd162-85ab-4dc4-90fd-3adda95c40b3 · outbound

This paper cites A metric on directed graphs and markov chains based on hitting probabilities.SIAM Journal on Mathematics of Data Science, 3(2):467–493, 2021.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits A metric on directed graphs and markov chains based on hitting probabilities.SIAM Journal on Mathematics of Data Science, 3(2):467–493, 2021

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Observation 24328d07-e36f-44df-9183-61e0ec9e5eb1 · outbound

This paper cites Pek¨ oz, and Sheldon M.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Pek¨ oz, and Sheldon M

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Observation eb27cd05-9757-4603-ab1f-ff02cf1c9575 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Language models are few-shot learners

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Observation ad5f6a60-38ef-438c-ada4-88adda52ce06 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Magicore: Multi-agent, iterative, coarse-to-fine refinement for reasoning

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Observation 73525e9d-e502-4e5f-a81e-71c36f8638b5 · outbound

This paper cites Transformers in uniform TC 0.arxiv, 2024.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Transformers in uniform TC 0.arxiv, 2024

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Observation ca05d65f-91a7-40be-a424-ad3465101614 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Laplacians and the cheeger inequality for directed graphs.Annals of Combinatorics, 9(1):1–19, 2005

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Observation 6e7da321-4049-43a7-ba0c-d2259349c801 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Turing completeness of bounded-precision recurrent neural networks

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Observation 11117bbe-f36e-4d7a-bfed-136244714d81 · outbound

This paper cites What you can cram into a single vector: Probing sentence embeddings for linguistic properties.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits What you can cram into a single vector: Probing sentence embeddings for linguistic properties

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Observation eea5d4db-dcba-4523-9ca0-40e34d223d0c · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits A dexire for extracting propositional rules from neural networks via binarization.Electronics, 11(24), 2022

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Extracting tree-structured representations of trained networks

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Observation fa4976fc-d24f-4350-8650-5ce46d39715c · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Knowledge neurons in pretrained transformers

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Gemini: A Family of Highly Capable Multimodal Models

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Observation b955126c-5e27-48ca-8741-b846807567f3 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Learning from one graph: transductive learning guarantees via the geometry of small random worlds

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Observation 58502942-2723-4b22-a794-6d0a54d7c4d3 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits The information-geometric perspective of compositional data analysis

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Birthday paradox, coupon collectors, caching algorithms and self-organizing search.Discrete Applied Mathematics, 39(3):207–229, 1992

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Neural algorithmic reasoning for combinatorial optimisation

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Compositional data analysis.Annual Review of Statistics and its Application, 8(1):271–299, 2021

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Fast construction of nets in low-dimensional metrics and their applications

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Instance-dependent generalization bounds via optimal transport.Journal of Machine Learning Research, 24(349):1–51, 2023

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Observation 0002751d-87f9-4dff-9e4b-d65a99354f22 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Polynomial bounds for vc dimension of sigmoidal and general pfaffian neural networks.Journal of Computer and System Sciences, 54(1):169–176, 1997

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Large Language Models are Zero-Shot Reasoners

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Retrieval-augmented generation for knowledge- intensive nlp tasks.Advances in neural information processing systems, 33:9459–9474, 2020

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Certifiable reasoning is universal: A differentiable reasoning AI.arXiv preprint, 2026

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Learning arithmetic circuits

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Is homophily a necessity for graph neural networks? In International Conference on Learning Representations, 2022

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Cambridge University Press, 2021

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Observation b78a3cf8-7b0a-4fcd-bace-060cc009499d · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Unresolved cited work

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Self-refine: Iterative refinement with self-feedback.Advances in Neural Information Processing Systems, 36:46534–46594, 2023

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits A neural state pushdown automata.IEEE Transactions on Artificial Intelligence, 1(3):193–205, 2021

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits John Wiley & Sons, 2009

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Polynomial-time solvable# csp problems via algebraic models and pfaffian circuits.Journal of Symbolic Computation, 74:152–180, 2016

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Observation c00e605e-c141-4977-b1a7-c3591423252b · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits The parallelism tradeoff: Limitations of log-precision transformers

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Observation 590a77f4-710c-4323-8858-0c0c0b21a27f · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Unresolved cited work

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Assouad’s theorem with dimension independent of the snowflaking.Revista Matematica Iberoamericana, 28(4):1123–1142, 2012

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Low dimensional embeddings of doubling metrics.Theory Comput

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Zoom in: An introduction to circuits.Distill, 5(3):e00024.001, 2020

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits The building blocks of interpretability.Distill, 3(3):e10, 2018

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Multiplicative schr¨ odinger problem and the dirichlet transport

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Compositional data and their analysis: an introduction

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Observation 6743a0cb-6e22-4eb2-af01-8aa386e41fe4 · outbound

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Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits On the turing completeness of modern neural network architectures

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Observation 12fff4ee-96dd-4ddb-8948-a7c3945702ed · outbound

This paper cites On a classical problem of probability theory.Magyar Tudom´ anyos Akad´ emia Matematikai Kutat´ o Int´ ezet´ enek K¨ ozlem´ enyei, 6:215–220, 1958.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits On a classical problem of probability theory.Magyar Tudom´ anyos Akad´ emia Matematikai Kutat´ o Int´ ezet´ enek K¨ ozlem´ enyei, 6:215–220, 1958

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Observation dcae6ed4-ad2a-4ec1-b476-9b84ac4079cd · outbound

This paper cites an unresolved cited work.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Unresolved cited work

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Observation 6e83d478-7fc2-4901-b95f-471ef264cdd1 · outbound

This paper cites Narasimhan.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Narasimhan

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Observation 793966da-2328-49a1-a4d2-3073e13dcc28 · outbound

This paper cites Springer Science & Business Media, 2012.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Springer Science & Business Media, 2012

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Observation 8b0fb987-7184-4c3a-98f4-ada404ed4d8f · outbound

This paper cites Depth efficient neural networks for division and related problems.IEEE Transactions on Information Theory, 39(3):946–956, 1993.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Depth efficient neural networks for division and related problems.IEEE Transactions on Information Theory, 39(3):946–956, 1993

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Observation 6a03402b-3130-43a5-a170-cee30900a1b7 · outbound

This paper cites Inference for empirical wasserstein distances on finite spaces.Journal of the Royal Statistical Society Series B: Statistical Methodology, 80(1):219–238, 2018.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Inference for empirical wasserstein distances on finite spaces.Journal of the Royal Statistical Society Series B: Statistical Methodology, 80(1):219–238, 2018

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Observation c44a978b-2587-4261-ade9-ccc2d20d6ca9 · outbound

This paper cites Thinking Isn't an Illusion: Overcoming the Limitations of Reasoning Models via Tool Augmentations.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Thinking Isn't an Illusion: Overcoming the Limitations of Reasoning Models via Tool Augmentations

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Observation acd03784-03f9-45ad-9392-db4966de302f · outbound

This paper cites Sharp oracle inequalities for square root regularization.Journal of Machine Learning Research, 18(67):1–29, 2017.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Sharp oracle inequalities for square root regularization.Journal of Machine Learning Research, 18(67):1–29, 2017

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Observation 267bf64d-71bd-4ca3-9731-5fc99192685e · outbound

This paper cites Springer, 2009.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Springer, 2009

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Observation 86ab0901-571f-48f0-b20f-c737de33ecb9 · outbound

This paper cites Voyager: An open-ended embodied agent with large language models.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Voyager: An open-ended embodied agent with large language models

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Observation 561017b8-81d6-47a7-a11a-94583069e2bb · outbound

This paper cites Le, Ed H.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Le, Ed H

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Observation c6363615-3ea8-4676-8ff1-9d93985f0aaa · outbound

This paper cites Le, Denny Zhou, et al.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Le, Denny Zhou, et al

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Observation 1c496b6f-0987-4d94-ad69-57835056fd27 · outbound

This paper cites Star: Self-taught reasoner.

Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits Star: Self-taught reasoner

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