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Cognitive Structure Generation: From Educational Priors to Policy Optimization

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper argues that ordering-based causal discovery under additive noise models can be substantially improved by replacing the MLP score model with a function-space neural-operator diffusion model that stably approximates the Hessian…

desk verdict The submission is a solid empirical causal-discovery paper wrapped in a confusing wrapper: the arXiv metadata advertises a different paper, the theory section overclaims a convergence guarantee it does not prove, and the empirical results are strong enough to deserve a serious referee. read the letter →

arxiv 2508.12647 v1 pith:IMRLJXXN submitted 2025-08-18 cs.AI cs.CYcs.LG

Hengnian Gu , Zhifu Chen , Yuxin Chen , Jin Peng Zhou , Dongdai Zhou This is my paper · ORCID
classification cs.AIcs.CYcs.LG
keywords causaldiscoveryordering-basedscorematchingHessiandiagonaldiffusionmodelsneuraloperatorsadditivenoiselargelanguage
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that ordering-based causal discovery under additive noise models can be made substantially more accurate by replacing the usual multilayer-perceptron score model with a score model that lives in a function space and is built from neural operators. This model, SciNO, is designed to approximate not just the score but its Jacobian diagonal—the Hessian diagonal of the log-density—which is the statistic the leaf-node criteria in SCORE, DiffAN, and CaPS rely on. Reported results show SciNO reduces order divergence by 42.7% on synthetic graphs and by 31.5% on real-world graphs relative to DiffAN, and that it stays within memory limits where kernel-based estimators fail. The paper also argues that the same evidence can be combined with autoregressive-model probabilities to guide LLM causal reasoning without fine-tuning or prompt engineering.

What carries the argument

The load-bearing object is SciNO, a functional diffusion model whose score network is a neural operator rather than an MLP: the score is treated as a map between function spaces, so derivatives can be learned as functions instead of being numerically differentiated from a pointwise network. Two design choices carry the argument: Fourier-layer outputs are split into real and imaginary parts in the spectral domain, and a Learnable Time Encoding is injected multiplicatively so the model can learn spatial and temporal derivatives jointly. The quantities that matter are the leaf-selection statistics—$\mathrm{Var}(H_{ii})$ under SCORE's criterion and $\mathbb{E}[H_{ii}]$ under CaPS's—where $H_{ii} = \partial_i^2 \log p(x)$ is the Hessian diagonal; SciNO approximates these through the deciduous-score formula (6) inherited from DiffAN. The paper justifies the approximation with a Sobolev-embedding argument showing neural operators can approximate the score in a norm that controls derivatives, together with pointwise approximation theorems for the target score function.

What would settle it

Take a 2D nonlinear Gaussian SEM whose log-density and Hessian diagonal are known analytically, train SciNO and an MLP score model on the same samples, and compare both the score error and the Hessian-diagonal error on a held-out grid. The central claim fails if SciNO's second-derivative error is not lower than the MLP's at comparable first-order score error, or if the reported order-divergence gains disappear once Hessian accuracy is matched. A second check: rerun the LLM control experiments with randomized variable-name masks and no descriptions; if the evidence term no longer improves on the uncontrolled LLM, the semantic-versus-statistical contribution is misattributed.

Watch

Extended reading notes

Core claim

The central claim is that stable second-derivative estimation is the unlock for ordering-based causal discovery, and that SciNO achieves it. Under the additive noise model, a leaf node is identifiable from the variance (SCORE) or expectation (CaPS) of the Hessian diagonal of the log-density; DiffAN avoids refitting by approximating these terms from a trained diffusion score model. SciNO replaces the MLP with a time-conditioned Fourier neural operator in a Hilbert space, adding a Learnable Time Encoding and a real/imaginary spectral decomposition so the model can track spatiotemporal derivatives. In experiments, DiffAN with SciNO cuts order divergence from 117.0 to 86.6 on 100-node random graphs, and CaPS with a probed SciNO scales to sample sizes where CaPS hits out-of-memory errors. The paper further claims that multiplying an autoregressive model's next-token probabilities by SciNO-based evidence—average-rank or confidence-interval statistics from deep ensembles—improves LLM causal ordering by up to 75% while reducing the number of LLM calls from quadratic to linear.

Load-bearing premise

The load-bearing premise is that training a score model with a first-order denoising score-matching objective also makes its second derivatives approximate the true Hessian diagonal; the Hilbert-space completeness argument in the paper says a good approximator exists in principle, not that the optimizer finds one.

Editorial extensions

If this is right

  • Swapping SciNO's score model into an existing ordering pipeline is enough to lower order divergence on graphs from 2 to 100 nodes, with the largest gains at high dimensionality.
  • Causal ordering stays usable when samples are large: the probing variant avoids CaPS's cubic kernel-matrix inversion and out-of-memory failures beyond 100,000 samples.
  • LLM-based causal reasoning can be controlled with data-derived evidence, reducing order divergence by up to 75% on a 107-node graph and needing only O(n) LLM calls per ordering.
  • The improvement is not just generative fit: order divergence tracks goodness-of-fit under SciNO, whereas the MLP baseline shows no such correlation.
  • Partial context is enough: when variable names are masked and only 10% of variables have descriptions, the combined control still reduces order divergence relative to the uncontrolled LLM.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension would be to use SciNO's Hessian-diagonal estimates for other score-derivative tasks, such as sensitivity analysis, marginal likelihood approximations, or second-order optimization diagnostics; the paper does not evaluate these.
  • The rank-based and confidence-interval evidence terms are one way to fuse LLM priors with data statistics; the same Bayesian multiplication could be applied to other autoregressive models or to non-LLM sequential predictors, although the paper only demonstrates LLMs.
  • Because the identifiability guarantee rests on the additive noise model, an obvious stress test is to run the same pipeline on non-additive or discrete data; the paper flags this as a limitation, so a neutral reader should treat the ordering claims as scoped to continuous ANMs.
  • The correlation between MMD and order divergence under SciNO suggests generated samples could serve as a cheap diagnostic for ordering reliability, but this connection is an inference from the paper's Figure 3 rather than a stated result.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. As submitted, the front matter (title and abstract) describes a different paper: 'Cognitive Structure Generation: From Educational Priors to Policy Optimization,' about pretraining a Cognitive Structure Diffusion Probabilistic Model and optimizing it with reinforcement learning. The body, however, is a causal discovery paper proposing SciNO (Score-informed Neural Operator), a functional diffusion model that aims to stably approximate the Hessian diagonal of log-densities and thereby improve ordering-based causal discovery under additive noise models. The body's central claim is that SciNO reduces order divergence by 42.7% on synthetic graphs and 31.5% on real-world datasets compared to DiffAN, and that a probabilistic control method combining SciNO evidence with autoregressive model priors improves LLM-based causal ordering without fine-tuning or prompt engineering. The main theoretical support is Theorem 3.1, which asserts that neural operators can approximate the target score function in a Sobolev/Hölder norm, and the main empirical support consists of synthetic and real-world experiments comparing SciNO with DiffAN, CaPS, and other baselines, supplemented by ablations of the proposed architectural components.

Significance. If the empirical results hold, the paper makes a useful contribution: stable estimation of second-order score derivatives is genuinely important for score-matching-based causal ordering, and the proposed neural-operator architecture with learnable time encoding shows consistent improvements on high-dimensional graphs while reducing memory footprint. The paper also benefits from a fairly complete set of ablations (PE vs. LTE, additive vs. multiplicative LTE, DiffAN with LTE), from a clear statement of the underlying ANM assumptions, and from explicit runtime and memory comparisons against kernel-based methods. The probabilistic control method is a reasonable and potentially practical way to combine data-driven statistics with LLM priors. However, the theoretical justification for the central claim contains a logical gap, and the mismatch between the submitted abstract/body is a substantial consistency problem that must be addressed before the paper can be considered publishable.

major comments (2)
  1. [Section 3.1 and Theorem 3.1] The theoretical support for the central claim is incomplete. The paper states that because neural operators can approximate the target score function in a Sobolev/Hölder norm, the trained score model's second-order derivatives approximate the Hessian diagonal, and it justifies training convergence by saying that 'the completeness of Hilbert space implies that the distance between ... will close to zero as we train score models accurately.' This is a non-sequitur: completeness guarantees that Cauchy sequences converge in the ambient space, but it does not imply that the stochastic optimizer's trajectory is Cauchy, nor that the limit has small Hessian error. Since the leaf-node criteria (3) and (4) and the residue approximation (6) use second derivatives of the trained model, this gap is load-bearing for the headline claim. The empirical evidence in Figure 2 and Table 2 may support the claim, but the theoretical statements in Section 3.1 and the proof of Theorem 3.1 should be revised to either provide a score-error-to-Hessian-error bound under the actual training objective or explicitly reframe the claim as empirical rather than theoretical.
  2. [Title and Abstract] The title and abstract submitted for review describe Cognitive Structure Generation (CSDPM with reinforcement learning), but the entire body is about SciNO for causal discovery. None of the abstract's claims—cognitive structure assessment, pretraining a diffusion model over student structures, or hierarchical reward optimization—appears anywhere in the full text, and none of the body's contributions (SciNO, Hessian diagonal approximation, LLM control) is mentioned in the abstract. This is a fundamental internal inconsistency in the manuscript as submitted and must be corrected before the paper can be evaluated as a coherent contribution.
minor comments (5)
  1. [Theorem 3.1] There is a typo in the theorem statement: 'compect subset' should be 'compact subset.'
  2. [Figure 3 caption] The caption says 'Comparion,' which should be 'Comparison.'
  3. [Section 3.2] The sentence beginning 'SciNO elaboratesCausal Relationship' appears garbled and should be rewritten, as it is not a readable English sentence.
  4. [Section 2, DiffAN paragraph] The term 'deciduous score' is unusual and likely a typo or mistranslation; I assume 'residual score' or 'residue score' is intended, but the term should be defined or corrected for clarity.
  5. [Section 4.3 and Table 4] The paper reports large percentage improvements but does not provide confidence intervals or significance tests for the order-divergence reductions across the 10 runs; adding such statistics would make the comparison more convincing.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: SciNO's Hessian estimates are trained on a first-order score-matching objective and evaluated against external ordering baselines, so the empirical claims do not reduce to their inputs; the HDM citation is independent prior work.

full rationale

The central derivation chain is: (i) leaf-node criteria (3) and (4) depend on the Hessian diagonal of the true log-density; (ii) SciNO approximates that Hessian diagonal by computing second derivatives of a score model trained with denoising score matching; (iii) those variance estimates are used as an evidence term in the probabilistic LLM control (10) and (12). At no point is the predicted quantity—order divergence, SHD, or SID—used as a training target, and no fitted parameter is renamed as a prediction. The Hessian diagonal is not defined in terms of the SciNO score model; rather, the score model is trained on a first-order objective and its second derivatives are then used. This is a coherence claim that can fail empirically, but it is not circular. The paper's approximation theorem (Theorem 3.1 / A.2) is existential, citing independent FNO approximation results [24] and Sobolev embedding [17]; it does not assume the target conclusion. The dependence on HDM [26], which shares a corresponding author, is a genuine reliance on prior work, but that work is a published NeurIPS paper with its own statements and results, so it counts as external support rather than a circular loop inside this manuscript. One passage deserves explicit flagging as a rigor gap rather than circularity: Section 3.1 says 'the completeness of Hilbert space implies that the distance between ... will close to zero as we train score models accurately.' Completeness does not guarantee convergence of a stochastic training trajectory, and the training loss controls first-order score error, not Hessian error. That is a missing transfer guarantee and a correctness risk, but it is not a case of the derivation reducing to its own inputs by construction. The empirical claims are benchmarked against DiffAN, CaPS, SCORE, CAM, PC, and GES, giving the paper self-contained external comparisons. I therefore find no significant circularity and assign score 0.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities or conserved quantities. Its free parameters are standard ML hyperparameters and two control-method constants (alpha, tau) that are chosen by hand. The axioms are dominated by the ANM assumption inherited from prior causal discovery work and the regularity assumptions needed for the neural-operator approximation theorem. The heaviest unstated burden is the assumption that first-order score-matching training yields accurate second-order derivatives.

free parameters (4)
  • LLM length-normalization exponent alpha = 1.2 (per A.6.1; value partially garbled in rendering)
    Chosen by hand to counteract token-length bias in LLM prior probabilities; affects the leaf-node selection in the control algorithm.
  • Control temperature tau = Set to a value used for main experiments (A.6.2; numeric value garbled in rendering)
    Trades off the LLM prior versus the SciNO evidence term in soft supervision; no sensitivity analysis is shown in the main text.
  • Deep ensemble size M = 5 (Section 4.3)
    Number of independently trained SciNO models used in the rank and confidence-interval estimators; no ablation justifies this choice.
  • Model hyperparameters (hidden dims, number of Fourier layers, LTE dimension) = Not fully recoverable from the rendered text
    Architectural choices that influence Hessian-diagonal accuracy; no hyperparameter sensitivity study is reported.
assumptions (5)
  • domain assumption Additive Noise Model with Gaussian noise and twice-differentiable nonlinear mechanisms (for DiffAN/SCORE) or variance conditions (for CaPS)
    Inherited from SCORE [33], DiffAN [35], and CaPS [45]; this restricts the method to continuous additive settings, acknowledged in the conclusion.
  • domain assumption The true score function lies in the Sobolev space W^{s,2} on a Lipschitz domain with s > d/2 + 2
    Invoked in Theorem 3.1 and A.2 to obtain Holder-norm convergence of derivatives via Sobolev embedding; stated as a natural assumption without verification for the datasets used.
  • standard math The map from smooth coefficients of the forward SDE to the score function is continuous, so FNO approximation theorems [24, Thm 8, 11] apply
    Used to prove the existence of a neural operator approximating the score and its derivatives; the continuity assumption is asserted, not established for the specific parameterization.
  • standard math HDM time-reversal and score-matching theory in Hilbert spaces from [26]
    Provides the functional diffusion framework underpinning SciNO; this is self-cited prior work by the corresponding author and is not independently verified in this paper.
  • standard math Central Limit Theorem for the across-ensemble variance estimates used in the confidence-interval estimator (12)
    Justifies treating the sample mean of variance estimates as approximately Gaussian; requires sufficiently many ensemble members and finite variance, which are plausible but unexamined.

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Cite this review

Pith. "Pith review of Cognitive Structure Generation: From Educational Priors to Policy Optimization." pith.science (2026). https://pith.science/paper/IMRLJXXN

@misc{pith2026250812647,
  author       = {Pith},
  title        = {Pith review of: Cognitive Structure Generation: From Educational Priors to Policy Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IMRLJXXN}},
  note         = {Machine review of arXiv:2508.12647}
}
read the original abstract

Cognitive structure is a student's subjective organization of an objective knowledge system, reflected in the psychological construction of concepts and their relations. However, cognitive structure assessment remains a long-standing challenge in student modeling and psychometrics, persisting as a foundational yet largely unassessable concept in educational practice. This paper introduces a novel framework, Cognitive Structure Generation (CSG), in which we first pretrain a Cognitive Structure Diffusion Probabilistic Model (CSDPM) to generate students' cognitive structures from educational priors, and then further optimize its generative process as a policy with hierarchical reward signals via reinforcement learning to align with genuine cognitive development levels during students' learning processes. Experimental results on four popular real-world education datasets show that cognitive structures generated by CSG offer more comprehensive and effective representations for student modeling, substantially improving performance on KT and CD tasks while enhancing interpretability.

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Reference graph

Works this paper leans on

47 extracted references · 33 canonical work pages

  1. [1]

    Zero-shot causal graph extrapola- tion from text via LLMs.arXiv preprint arXiv:2312.14670, 2023

    Alessandro Antonucci, Gregorio Piqué, and Marco Zaffalon. Zero-shot causal graph extrapola- tion from text via LLMs.arXiv preprint arXiv:2312.14670, 2023

    arXiv 2023

  2. [2]

    From query tools to causal architects: Harnessing large language models for advanced causal discovery from data.CoRR, 2023

    Taiyu Ban, Lyuzhou Chen, Xiangyu Wang, and Huanhuan Chen. From query tools to causal architects: Harnessing large language models for advanced causal discovery from data.CoRR, 2023

    work page 2023

  3. [3]

    Ordering-based causal structure learning in the presence of latent variables

    Daniel Bernstein, Basil Saeed, Chandler Squires, and Caroline Uhler. Ordering-based causal structure learning in the presence of latent variables. InInternational conference on artificial intelligence and statistics, pages 4098–4108. PMLR, 2020

    work page 2020

  4. [4]

    CAM: Causal additive models, high-dimensional order search and penalized regression.The Annals of Statistics, pages 2526–2556, 2014

    Peter Bühlmann, Jonas Peters, and Jan Ernest. CAM: Causal additive models, high-dimensional order search and penalized regression.The Annals of Statistics, pages 2526–2556, 2014

    work page 2014

  5. [5]

    Unveiling causal reasoning in large language models: Reality or mirage?Advances in Neural Information Processing Systems, 37:96640–96670, 2024

    Haoang Chi, He Li, Wenjing Yang, Feng Liu, Long Lan, Xiaoguang Ren, Tongliang Liu, and Bo Han. Unveiling causal reasoning in large language models: Reality or mirage?Advances in Neural Information Processing Systems, 37:96640–96670, 2024

    2024

  6. [6]

    Learning Bayesian networks is NP-complete.Learning from data: Artificial intelligence and statistics V, pages 121–130, 1996

    David Maxwell Chickering. Learning Bayesian networks is NP-complete.Learning from data: Artificial intelligence and statistics V, pages 121–130, 1996

    work page 1996

  7. [7]

    Optimal structure identification with greedy search.Journal of machine learning research, 3(Nov):507–554, 2002

    David Maxwell Chickering. Optimal structure identification with greedy search.Journal of machine learning research, 3(Nov):507–554, 2002

    work page 2002

  8. [8]

    Large Language Models are Effective Priors for Causal Graph Discovery.arXiv e-prints, 2024

    Victor-Alexandru Darvariu, Stephen Hailes, and Mirco Musolesi. Large Language Models are Effective Priors for Causal Graph Discovery.arXiv e-prints, 2024

    work page 2024

Show all 47 references
  1. [9]

    On the evolution of random graphs.Publ

    Paul Erdos and Alfred Renyi. On the evolution of random graphs.Publ. Math. Inst. Hung. Acad. Sci., 5(1):17–60, 1960

    1960

  2. [10]

    The llama 3 herd of models.arXiv preprint arXiv:2407.21783, 2024

    Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al. The llama 3 herd of models.arXiv preprint arXiv:2407.21783, 2024

    2024 arXiv

  3. [11]

    Borgwardt, Malte J

    Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, and Alexander Smola. A Kernel Two-Sample Test.Journal of Machine Learning Research, 13(25):723–773, 2012

    2012

  4. [12]

    Mamba: Linear-Time Sequence Modeling with Selective State Spaces

    Albert Gu and Tri Dao. Mamba: Linear-Time Sequence Modeling with Selective State Spaces. InFirst Conference on Language Modeling, 2024

    2024

  5. [13]

    Denoising diffusion probabilistic models.Advances in neural information processing systems, 33:6840–6851, 2020

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models.Advances in neural information processing systems, 33:6840–6851, 2020

    2020

  6. [14]

    Gpt-4o system card.arXiv preprint arXiv:2410.21276, 2024

    Aaron Hurst, Adam Lerer, Adam P Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, Alan Hayes, Alec Radford, et al. Gpt-4o system card.arXiv preprint arXiv:2410.21276, 2024

    2024 arXiv

  7. [15]

    Causal Reasoning and Large Language Models: Opening a New Frontier for Causality.Transactions on Machine Learning Research, 2024

    Emre Kiciman, Robert Ness, Amit Sharma, and Chenhao Tan. Causal Reasoning and Large Language Models: Opening a New Frontier for Causality.Transactions on Machine Learning Research, 2024. Featured Certification

    2024

  8. [16]

    Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, 24(89):1–97, 2023

    Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Neural operator: Learning maps between function spaces with applications to pdes.Journal of Machine Learning Research, 24(89):1–97, 2023

    2023

  9. [17]

    American Mathematical Soc., 2008

    Nicolai Vladimirovich Krylov.Lectures on Elliptic and Parabolic Equations in Sobolev Spaces, volume 96. American Mathematical Soc., 2008

    2008

  10. [18]

    Gradient- Based Neural DAG Learning

    Sébastien Lachapelle, Philippe Brouillard, Tristan Deleu, and Simon Lacoste-Julien. Gradient- Based Neural DAG Learning. InInternational Conference on Learning Representations, 2020. 11

    2020

  11. [19]

    Simple and scalable predictive uncertainty estimation using deep ensembles.Advances in neural information processing systems, 30, 2017

    Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles.Advances in neural information processing systems, 30, 2017

    2017

  12. [20]

    On Incorporating Prior Knowledge Extracted from Pre-trained Language Models into Causal Discovery

    Chanhui Lee, Juhyeon Kim, YongJun Jeong, Yoonseok Yeom, Juhyun Lyu, Jung-Hee Kim, Sangmin Lee, Sangjun Han, Hyeokjun Choe, Soyeon Park, Woohyung Lim, Kyunghoon Bae, Sungbin Lim, and Sanghack Lee. On Incorporating Prior Knowledge Extracted from Pre-trained Language Models into ...

    2024

  13. [21]

    RealTCD: temporal causal discovery from interventional data with large language model

    Peiwen Li, Xin Wang, Zeyang Zhang, Yuan Meng, Fang Shen, Yue Li, Jialong Wang, Yang Li, and Wenwu Zhu. RealTCD: temporal causal discovery from interventional data with large language model. InProceedings of the 33rd ACM International Conference on Information and Knowledge Man...

    2024

  14. [22]

    Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding.Advances in Neural Information Processing Systems, 34:15816–15829, 2021

    Yang Li, Si Si, Gang Li, Cho-Jui Hsieh, and Samy Bengio. Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding.Advances in Neural Information Processing Systems, 34:15816–15829, 2021

    2021

  15. [23]

    Gradient Estimators for Implicit Models

    Yingzhen Li and Richard E Turner. Gradient Estimators for Implicit Models. InInternational Conference on Learning Representations, 2018

    2018

  16. [24]

    Fourier Neural Operator for Parametric Partial Differential Equations

    Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar, et al. Fourier Neural Operator for Parametric Partial Differential Equations. InInternational Conference on Learning Representations, 2021

    2021

  17. [25]

    Score-based diffusion models in function space.arXiv preprint arXiv:2302.07400, 2023

    Jae Hyun Lim, Nikola B Kovachki, Ricardo Baptista, Christopher Beckham, Kamyar Azizzade- nesheli, Jean Kossaifi, Vikram V oleti, Jiaming Song, Karsten Kreis, Jan Kautz, et al. Score-based diffusion models in function space.arXiv preprint arXiv:2302.07400, 2023

    2023 arXiv

  18. [26]

    Score-based Generative Modeling through Stochastic Evolution Equations in Hilbert Spaces

    Sungbin Lim, Eunbi Yoon, Taehyun Byun, Taewon Kang, Seungwoo Kim, Kyungjae Lee, and Sungjoon Choi. Score-based Generative Modeling through Stochastic Evolution Equations in Hilbert Spaces. InThirty-seventh Conference on Neural Information Processing Systems, 2023

    2023

  19. [27]

    Causal Discovery with Language Models as Imperfect Experts

    Stephanie Long, Alexandre Piché, Valentina Zantedeschi, Tibor Schuster, and Alexandre Drouin. Causal Discovery with Language Models as Imperfect Experts. InICML 2023 Workshop on Structured Probabilistic Inference & Generative Modeling, 2023

    2023

  20. [28]

    From correlation to causation networks: a simple approximate learning algorithm and its application to high-dimensional plant gene expression data.BMC systems biology, 1:1–10, 2007

    Rainer Opgen-Rhein and Korbinian Strimmer. From correlation to causation networks: a simple approximate learning algorithm and its application to high-dimensional plant gene expression data.BMC systems biology, 1:1–10, 2007

    2007

  21. [29]

    Structural Intervention Distance for Evaluating Causal Graphs.Neural Computation, 27(3):771–799, 03 2015

    Jonas Peters and Peter Bühlmann. Structural Intervention Distance for Evaluating Causal Graphs.Neural Computation, 27(3):771–799, 03 2015

    2015

  22. [30]

    MIT Press, 2017

    Jonas Peters, Dominik Janzing, and Bernhard Schölkopf.Elements of Causal Inference: Foun- dations and Learning Algorithms. MIT Press, 2017

    2017

  23. [31]

    Causal discovery with continuous additive noise models.The Journal of Machine Learning Research, 15(1):2009– 2053, 2014

    Jonas Peters, Joris M Mooij, Dominik Janzing, and Bernhard Schölkopf. Causal discovery with continuous additive noise models.The Journal of Machine Learning Research, 15(1):2009– 2053, 2014

    2009

  24. [32]

    The analysis of permutations.Journal of the Royal Statistical Society Series C: Applied Statistics, 24(2):193–202, 1975

    Robin L Plackett. The analysis of permutations.Journal of the Royal Statistical Society Series C: Applied Statistics, 24(2):193–202, 1975

    1975

  25. [33]

    Score Matching Enables Causal Discovery of Nonlinear Additive Noise Models

    Paul Rolland, V olkan Cevher, Matthäus Kleindessner, Chris Russell, Dominik Janzing, Bernhard Schölkopf, and Francesco Locatello. Score Matching Enables Causal Discovery of Nonlinear Additive Noise Models. InInternational Conference on Machine Learning, pages 18741–18753. PMLR, 2022

    2022

  26. [34]

    Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data.Science, 308(5721):523–529, 2005

    Karen Sachs, Omar Perez, Dana Pe’er, Douglas A Lauffenburger, and Garry P Nolan. Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data.Science, 308(5721):523–529, 2005. 12

    2005

  27. [35]

    Diffusion Models for Causal Discovery via Topological Ordering

    Pedro Sanchez, Xiao Liu, Alison Q O’Neil, and Sotirios A Tsaftaris. Diffusion Models for Causal Discovery via Topological Ordering. InThe Eleventh International Conference on Learning Representations, 2023

    2023

  28. [36]

    A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics.Statistical applications in genetics and molecular biology, 4(1), 2005

    Juliane Schäfer and Korbinian Strimmer. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics.Statistical applications in genetics and molecular biology, 4(1), 2005

    2005

  29. [37]

    Bayesian networks, magic populations and multiple trait prediction

    M Scutari. Bayesian networks, magic populations and multiple trait prediction. InInvited Talk at the 5th International Conference on Quantitative Genetics (ICQG 2016), 2016

    2016

  30. [38]

    Multiple quantitative trait analysis using Bayesian networks.Genetics, 198(1):129–137, 2014

    Marco Scutari, Phil Howell, David J Balding, and Ian Mackay. Multiple quantitative trait analysis using Bayesian networks.Genetics, 198(1):129–137, 2014

    2014

  31. [39]

    Score-Based Generative Modeling through Stochastic Differential Equations

    Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-Based Generative Modeling through Stochastic Differential Equations. In International Conference on Learning Representations, 2021

    2021

  32. [40]

    MIT press, 2000

    Peter Spirtes, Clark N Glymour, and Richard Scheines.Causation, prediction, and search. MIT press, 2000

    2000

  33. [41]

    The Max-Min Hill-Climbing Bayesian Network Structure Learning Algorithm.Machine Learning, 65:31–78, 10 2006

    Ioannis Tsamardinos, Laura Brown, and Constantin Aliferis. The Max-Min Hill-Climbing Bayesian Network Structure Learning Algorithm.Machine Learning, 65:31–78, 10 2006

    2006

  34. [42]

    Balasubramanian, and Amit Sharma

    Aniket Vashishtha, Abbavaram Gowtham Reddy, Abhinav Kumar, Saketh Bachu, Vineeth N. Balasubramanian, and Amit Sharma. Causal Order: The Key to Leveraging Imperfect Experts in Causal Inference. InThe Thirteenth International Conference on Learning Representations, 2025

    2025

  35. [43]

    Attention is all you need.Advances in neural information processing systems, 30, 2017

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need.Advances in neural information processing systems, 30, 2017

    2017

  36. [44]

    Google’s neural machine translation system: Bridging the gap between human and machine translation.arXiv preprint arXiv:1609.08144, 2016

    Yonghui Wu, Mike Schuster, Zhifeng Chen, Quoc V Le, Mohammad Norouzi, Wolfgang Macherey, Maxim Krikun, Yuan Cao, Qin Gao, Klaus Macherey, et al. Google’s neural machine translation system: Bridging the gap between human and machine translation.arXiv preprint arXiv:1609.08144, 2016

    2016 arXiv

  37. [45]

    Ordering-Based Causal Discovery for Linear and Nonlinear Relations

    Zhuopeng Xu, Yujie Li, Cheng Liu, and Ning Gui. Ordering-Based Causal Discovery for Linear and Nonlinear Relations. InThe Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024

    2024

  38. [46]

    DAG-GNN: DAG structure learning with graph neural networks

    Yue Yu, Jie Chen, Tian Gao, and Mo Yu. DAG-GNN: DAG structure learning with graph neural networks. InInternational conference on machine learning, pages 7154–7163. PMLR, 2019. 13 A Supplementary Material In this supplementary material, we provide the information for understand...

    2019

  39. [47]

    partially addresses this by extracting pairwise edge-direction probabilities from the LLM and combining them with mutual information, but this approach remains limited, as it does not directly reflect causal relationships, limiting its explanatory power. A.2 Proof of Theorems ...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.