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arxiv: 2605.09243 · v1 · submitted 2026-05-10 · 💻 cs.AI · q-bio.NC

Recognition: 2 theorem links

· Lean Theorem

How Much is Brain Data Worth for Machine Learning?

David Schwab, Lane Lewis, Xaq Pitkow, Zhixin Wang

Pith reviewed 2026-05-12 03:57 UTC · model grok-4.3

classification 💻 cs.AI q-bio.NC
keywords brain datascaling lawsexchange ratesneuroAImultimodal learningtask labelsdistribution shiftlinear model
0
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The pith

Brain data can be exchanged for a quantifiable number of task samples in machine learning training, depending on alignment and noise levels.

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

The authors investigate whether adding brain recordings to task labels improves machine learning model training. They build a linear Gaussian model to derive scaling laws for performance as the number of brain samples and task samples increases. Using these laws, they calculate exchange rates that show how many additional task samples each brain sample is equivalent to. This helps determine when brain data is worth collecting given its cost. A sympathetic reader would care because it offers a principled way to value neural data for AI improvement.

Core claim

For a multimodal estimator trained on both brain data and task labels in a linear Gaussian model, performance follows scaling laws with sample numbers. Relative value and exchange rates between brain and task samples are derived as functions of task-brain alignment, neural and task noise, latent dimension, and brain sample size. Conditions for robustness gains under distribution shift are identified, along with regimes where brain data is worth collecting under a fixed budget.

What carries the argument

Linear Gaussian model of task targets and neural recordings, used to derive scaling laws and exchange rates for brain versus task samples.

If this is right

  • Performance scales predictably with numbers of brain and task samples according to the derived laws.
  • Brain data provides value equivalent to extra task samples, modulated by alignment and noise.
  • Brain-regularized learning can improve robustness to test distribution shifts via learned invariances.
  • Under fixed budget, there are specific regimes favoring collection of brain data over additional task labels.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These exchange rates could inform decisions on data collection strategies in NeuroAI experiments.
  • Testing the predictions on real neural datasets would validate or refine the model assumptions.
  • Similar value calculations might apply to other auxiliary data sources like eye tracking or physiological signals.

Load-bearing premise

The linear Gaussian abstraction of task targets and neural recordings is accurate enough that its exchange rates and robustness conditions will guide real-world use of brain data in machine learning.

What would settle it

Compare the actual performance gain from adding brain data in a controlled experiment to the gain predicted by the exchange rate formula for given alignment and noise levels; mismatch would falsify the practical applicability.

Figures

Figures reproduced from arXiv: 2605.09243 by David Schwab, Lane Lewis, Xaq Pitkow, Zhixin Wang.

Figure 1
Figure 1. Figure 1: Left: Generative model for brain activity and ML task data. Inputs generate latent representations in the brain which are partially captured by neural recordings. The same inputs drive the response of a task target. Right: Brain latents are driven by features that partially capture all relevant task features. Additionally, latents are partially observed through a measurement device. Both effects create mis… view at source ↗
Figure 2
Figure 2. Figure 2: Brain data can substitute for some task data, yielding equal performance while saving a [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The amount of task data that brain data can substitute changes depending on the test [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Budget scaling under optimal allocation of task and brain data with different cost ratios: [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left Panel BEFS estimator model configuration. In the first stage, an encoding model is learned to predict neural activity in recordings using an autoencoder. In the second stage, the learned brain features are used to regularize task learning. Right Panel BEFS test error scaling over regularization λ. A strong fixed regularization under a low misalignment improves test error at low task samples. However, … view at source ↗
Figure 6
Figure 6. Figure 6: Empirically fit optimal λ empirically matches the theoretical schedule derived in theorem 3. 100k independent trials used to generate each replicate and 30 replicates averaged to generate the mean and confidence interval. Parameters used: m = 0.05, SNRT /SNRB = 1.83, nB = 10000 samples dℓH∗ /dx = 62%, 100, 000 trials. Empirical curves (Emp) are plotted as solid with a square at evaluated points with confid… view at source ↗
Figure 7
Figure 7. Figure 7: Empirically fit data savings match the finite sample theory curves (theorem 2) even at [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Left panel: Empirical test error under test shift towards PA∗ ⊥ task data savings match scaling theory even at moderate task samples.Right panel: Empirical test error for isotropic covariance closely matches the finite sample theory curves (theorem 2) under optimal regularization. 100k independent trials were used to generate each MSE estimate replicate and 30 replicates averaged to generate the mean and c… view at source ↗
Figure 9
Figure 9. Figure 9: Estimated brain data value matches the finite sample theory curves (theorem 2) even in [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Empirical curves closely follow the finite scaling law theory (theorem 2), coarseness [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Brain data value approaches the exchange rate theory in large [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
read the original abstract

If a person can solve a task, can measuring their brain make it easier to train a model to solve that task too? Recent NeuroAI work suggests that supplementing task training with neural recordings can modestly improve model performance and robustness. However, it is unclear when there should be a benefit from using neural data and how much benefit to expect. We formulate this question mathematically, and begin to address it theoretically using a simple, analytically tractable linear gaussian model of task targets and neural recordings. For a multimodal estimator trained on both brain data and task labels, we derive scaling laws for how performance scales with the numbers of brain and task samples. From these laws we derive relative value and exchange rates between brain samples and task samples, quantifying how much extra task samples neural data is worth as a function of task-brain alignment, neural and task noise, latent dimension, and brain data sample size. We also analyze test distribution shift, to identify conditions where brain-regularized learning can produce substantial robustness gains through learned invariances. Finally, under a fixed collection budget, we characterize the regimes in which brain data is worth collecting. Our results provide a foundation for understanding how valuable brain data could be for improving machine learning.

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

2 major / 3 minor

Summary. The paper formulates the utility of brain data for machine learning as a theoretical question and addresses it via an analytically tractable linear Gaussian model of task targets and neural recordings. For a multimodal estimator, it derives scaling laws for performance as a function of the numbers of brain and task samples; from these it obtains relative value and exchange rates between brain and task samples that depend on task-brain alignment, neural and task noise, latent dimension, and brain sample size. It further derives conditions under which brain-regularized learning yields robustness gains under test distribution shift and characterizes regimes in which brain data is worth collecting under a fixed budget.

Significance. If the derivations hold, the work supplies an explicit, parameter-dependent theoretical foundation for NeuroAI that quantifies sample trade-offs and robustness conditions inside a stated model. The analytic scaling laws and exchange-rate expressions constitute a strength, offering falsifiable predictions and guidance for experimental design once the linear-Gaussian abstraction is validated or relaxed.

major comments (2)
  1. [§3 (Model and Estimator)] §3 (Model and Estimator): the exchange-rate formula is derived under the assumption that alignment is an exogenous fixed parameter; if alignment itself improves with additional brain samples (a plausible empirical regime), the reported break-even points between brain and task data would shift, altering the budget-allocation conclusions in §6.
  2. [§5 (Distribution Shift)] §5 (Distribution Shift): the robustness gain is shown to arise from learned invariances only when the shift is confined to the task-latent subspace orthogonal to the brain-aligned directions; the paper should state explicitly whether this condition is necessary or merely sufficient, because the claim that brain data can produce “substantial robustness gains” rests on it.
minor comments (3)
  1. [Abstract] The abstract states that results are “derived … as a function of … brain data sample size,” yet the dependence on sample size appears only in the large-sample asymptotic regime; a brief remark on finite-sample corrections would improve clarity.
  2. [Notation] Notation for noise variances (σ_n², σ_t²) is introduced in §2 but reused without redefinition in the scaling-law appendices; a short notation table would prevent reader confusion.
  3. [Figure 3] Figure 3 caption should indicate whether the plotted curves are exact analytic expressions or numerical evaluations of the derived formulas.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review. We address each major comment below and will incorporate clarifications to improve the manuscript.

read point-by-point responses

  1. Referee: [§3 (Model and Estimator)] the exchange-rate formula is derived under the assumption that alignment is an exogenous fixed parameter; if alignment itself improves with additional brain samples (a plausible empirical regime), the reported break-even points between brain and task data would shift, altering the budget-allocation conclusions in §6.

    Authors: We agree that the model treats alignment as a fixed exogenous parameter of the joint distribution. The exchange-rate derivations in §3 are conditional on this fixed alignment, and the break-even points in §6 follow directly from that assumption. If additional brain samples improved alignment (e.g., via better estimation of shared latents), the value of brain data would exceed the reported figures and could shift the budget-allocation recommendations. Extending the framework to dynamic, sample-dependent alignment would require a more complex model and is left for future work. In the revision we will add a paragraph in §3 and a brief note in §6 explicitly stating the fixed-alignment assumption and its implications for the conclusions. revision: partial

  2. Referee: [§5 (Distribution Shift)] the robustness gain is shown to arise from learned invariances only when the shift is confined to the task-latent subspace orthogonal to the brain-aligned directions; the paper should state explicitly whether this condition is necessary or merely sufficient, because the claim that brain data can produce “substantial robustness gains” rests on it.

    Authors: The referee correctly identifies that the robustness gains arise from invariances learned in the brain-aligned directions, which are effective only when the shift occurs in the orthogonal subspace. Within our linear-Gaussian model this condition is sufficient for the substantial robustness gains shown via the invariance mechanism. We do not claim it is necessary for robustness under all possible mechanisms or outside the model. We will revise §5 to state explicitly that the condition is sufficient for the reported gains and will qualify the scope of the claim to reflect the precise regime analyzed. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivations follow directly from stated linear Gaussian model

full rationale

The paper explicitly constructs a linear Gaussian model of task targets and neural recordings, treating alignment, noise levels, latent dimension, and sample sizes as free input parameters. Scaling laws for multimodal estimator performance, relative value/exchange rates between brain and task samples, and robustness conditions under distribution shift are then obtained by direct algebraic derivation from the model's joint distribution and estimator equations. No parameter is fitted to data and then re-used as a 'prediction'; no load-bearing step relies on self-citation; no ansatz is smuggled in; and no known empirical pattern is merely renamed. The central claims are therefore self-contained mathematical consequences of the model's assumptions rather than tautological restatements of inputs.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The paper rests on a deliberately simplified linear Gaussian generative model whose parameters (alignment, noise variances, latent dimension) are treated as known inputs rather than fitted quantities. No new entities are postulated.

free parameters (4)
  • task-brain alignment
    Parameter controlling correlation between neural recordings and task targets; treated as an input that modulates the exchange rate.
  • neural noise variance
    Input parameter representing measurement noise in brain data.
  • task noise variance
    Input parameter representing label noise.
  • latent dimension
    Dimensionality of the shared hidden variables; affects scaling.
axioms (2)
  • domain assumption Task targets and neural recordings are generated as noisy linear projections of the same latent variables.
    Stated in the abstract as the modeling choice that enables analytic scaling laws.
  • domain assumption The estimator is a multimodal linear Gaussian model trained on both data sources.
    Central modeling assumption used to derive performance scaling.

pith-pipeline@v0.9.0 · 5512 in / 1539 out tokens · 69127 ms · 2026-05-12T03:57:04.842464+00:00 · methodology

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Works this paper leans on

36 extracted references · 36 canonical work pages · 2 internal anchors

  1. [1]

    Scaling Laws for Neural Language Models

    Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models.arXiv preprint arXiv:2001.08361, 2020

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  2. [2]

    Improved object recognition using neural networks trained to mimic the brain’s statistical properties.Neural Networks, 131:103–114, 2020

    Callie Federer, Haoyan Xu, Alona Fyshe, and Joel Zylberberg. Improved object recognition using neural networks trained to mimic the brain’s statistical properties.Neural Networks, 131:103–114, 2020

    work page 2020

  3. [3]

    Learning from brains how to regularize machines.Advances in neural information processing systems, 32, 2019

    Zhe Li, Wieland Brendel, Edgar Walker, Erick Cobos, Taliah Muhammad, Jacob Reimer, Matthias Bethge, Fabian Sinz, Zachary Pitkow, and Andreas Tolias. Learning from brains how to regularize machines.Advances in neural information processing systems, 32, 2019

    work page 2019

  4. [4]

    Using human brain activity to guide machine learning.Scientific reports, 8(1):5397, 2018

    Ruth C Fong, Walter J Scheirer, and David D Cox. Using human brain activity to guide machine learning.Scientific reports, 8(1):5397, 2018

    work page 2018

  5. [5]

    Robust deep learning object recognition models rely on low frequency information in natural images.PLOS Computational Biology, 19(3):e1010932, 2023

    Zhe Li, Josue Ortega Caro, Evgenia Rusak, Wieland Brendel, Matthias Bethge, Fabio Anselmi, Ankit B Patel, Andreas S Tolias, and Xaq Pitkow. Robust deep learning object recognition models rely on low frequency information in natural images.PLOS Computational Biology, 19(3):e1010932, 2023

    work page 2023

  6. [6]

    Spartan books Washington, DC, 1962

    Frank Rosenblatt et al.Principles of neurodynamics: Perceptrons and the theory of brain mechanisms, volume 55. Spartan books Washington, DC, 1962. 10

    work page 1962

  7. [7]

    Neural networks and physical systems with emergent collective computational abilities.Proceedings of the National Academy of Sciences, 79(8):2554–2558, 1982

    John J Hopfield. Neural networks and physical systems with emergent collective computational abilities.Proceedings of the National Academy of Sciences, 79(8):2554–2558, 1982

    work page 1982

  8. [8]

    Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position.Biological cybernetics, 36(4):193–202, 1980

    Kunihiko Fukushima. Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position.Biological cybernetics, 36(4):193–202, 1980

    work page 1980

  9. [9]

    Gradient-based learning applied to document recognition.Proceedings of the IEEE, 86(11):2278–2324, 2002

    Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition.Proceedings of the IEEE, 86(11):2278–2324, 2002

    work page 2002

  10. [10]

    Biological connectomes as a representation for the architecture of artificial neural networks.arXiv preprint arXiv:2209.14406, 2022

    Samuel Schmidgall, Catherine Schuman, and Maryam Parsa. Biological connectomes as a representation for the architecture of artificial neural networks.arXiv preprint arXiv:2209.14406, 2022

    work page arXiv 2022

  11. [11]

    Interpreting and improving natural-language processing (in machines) with natural language-processing (in the brain).Advances in neural information processing systems, 32, 2019

    Mariya Toneva and Leila Wehbe. Interpreting and improving natural-language processing (in machines) with natural language-processing (in the brain).Advances in neural information processing systems, 32, 2019

    work page 2019

  12. [12]

    Brain-like object recognition with high-performing shallow recurrent anns.Advances in neural information processing systems, 32, 2019

    Jonas Kubilius, Martin Schrimpf, Kohitij Kar, Rishi Rajalingham, Ha Hong, Najib Majaj, Elias Issa, Pouya Bashivan, Jonathan Prescott-Roy, Kailyn Schmidt, et al. Brain-like object recognition with high-performing shallow recurrent anns.Advances in neural information processing systems, 32, 2019

    work page 2019

  13. [13]

    Divergences between language models and human brains.Advances in neural information processing systems, 37:137999–138031, 2024

    Yuchen Zhou, Emmy Liu, Graham Neubig, Michael J Tarr, and Leila Wehbe. Divergences between language models and human brains.Advances in neural information processing systems, 37:137999–138031, 2024

    work page 2024

  14. [14]

    Improving semantic understanding in speech language models via brain-tuning.arXiv preprint arXiv:2410.09230, 2024

    Omer Moussa, Dietrich Klakow, and Mariya Toneva. Improving semantic understanding in speech language models via brain-tuning.arXiv preprint arXiv:2410.09230, 2024

    work page arXiv 2024

  15. [15]

    Brain- wavlm: Fine-tuning speech representations with brain responses to language.arXiv preprint arXiv:2502.08866, 2025

    Nishitha Vattikonda, Aditya R Vaidya, Richard J Antonello, and Alexander G Huth. Brain- wavlm: Fine-tuning speech representations with brain responses to language.arXiv preprint arXiv:2502.08866, 2025

    work page arXiv 2025

  16. [16]

    Maelle Freteault, Maximilien Le Clei, Loic Tetrel, Lune Bellec, and Nicolas Farrugia. Alignment of auditory artificial networks with massive individual fmri brain data leads to generalisable im- provements in brain encoding and downstream tasks.Imaging Neuroscience, 3:imag_a_00525, 2025

    work page 2025

  17. [17]

    Mineault, Thomas L

    Patrick J. Mineault, Thomas L. Griffiths, and Sean Escola. Cognitive dark matter: Measuring what ai misses. 2026

    work page 2026

  18. [18]

    Training Compute-Optimal Large Language Models

    Jordan Hoffmann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, DDL Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, et al. Training compute-optimal large language models.arXiv preprint arXiv:2203.15556, 10, 2022

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  19. [19]

    Neural data transformer 2: multi- context pretraining for neural spiking activity.Advances in Neural Information Processing Systems, 36:80352–80374, 2023

    Joel Ye, Jennifer Collinger, Leila Wehbe, and Robert Gaunt. Neural data transformer 2: multi- context pretraining for neural spiking activity.Advances in Neural Information Processing Systems, 36:80352–80374, 2023

    work page 2023

  20. [20]

    A unified, scalable framework for neural population decoding.Advances in Neural Information Processing Systems, 36:44937–44956, 2023

    Mehdi Azabou, Vinam Arora, Venkataramana Ganesh, Ximeng Mao, Santosh Nachimuthu, Michael Mendelson, Blake Richards, Matthew Perich, Guillaume Lajoie, and Eva Dyer. A unified, scalable framework for neural population decoding.Advances in Neural Information Processing Systems, 36:44937–44956, 2023

    work page 2023

  21. [21]

    Scaling laws for decoding images from brain activity.arXiv preprint arXiv:2501.15322, 2025

    Hubert Banville, Yohann Benchetrit, Stéphane d’Ascoli, Jérémy Rapin, and Jean-Rémi King. Scaling laws for decoding images from brain activity.arXiv preprint arXiv:2501.15322, 2025

    work page arXiv 2025

  22. [22]

    Scaling laws for language encoding models in fmri.Advances in Neural Information Processing Systems, 36:21895–21907, 2023

    Richard Antonello, Aditya Vaidya, and Alexander Huth. Scaling laws for language encoding models in fmri.Advances in Neural Information Processing Systems, 36:21895–21907, 2023

    work page 2023

  23. [23]

    Scaling laws for generative mixed-modal language models

    Armen Aghajanyan, Lili Yu, Alexis Conneau, Wei-Ning Hsu, Karen Hambardzumyan, Susan Zhang, Stephen Roller, Naman Goyal, Omer Levy, and Luke Zettlemoyer. Scaling laws for generative mixed-modal language models. InInternational Conference on Machine Learning, pages 265–279. PMLR, 2023. 11

    work page 2023

  24. [24]

    Ridge regression: Biased estimation for nonorthogonal problems.Technometrics, 12(1):55–67, 1970

    Arthur E Hoerl and Robert W Kennard. Ridge regression: Biased estimation for nonorthogonal problems.Technometrics, 12(1):55–67, 1970

    work page 1970

  25. [25]

    On the optimal weighted ell-2 regularization in overparameterized linear regression.Advances in neural information processing systems, 33:10112–10123, 2020

    Denny Wu and Ji Xu. On the optimal weighted ell-2 regularization in overparameterized linear regression.Advances in neural information processing systems, 33:10112–10123, 2020

    work page 2020

  26. [26]

    Meta-learning with generalized ridge regression: High-dimensional asymptotics, optimality and hyper-covariance estimation

    Yanhao Jin, Krishnakumar Balasubramanian, and Debashis Paul. Meta-learning with generalized ridge regression: High-dimensional asymptotics, optimality and hyper-covariance estimation. arXiv preprint arXiv:2403.19720, 2024

    work page arXiv 2024

  27. [27]

    Projection penalties: dimension reduction without loss

    Yi Zhang and Jeff G Schneider. Projection penalties: dimension reduction without loss. In Proceedings of the 27th International Conference on Machine Learning (ICML-10), pages 1223–1230, 2010

    work page 2010

  28. [28]

    Restricted ridge estimation.Statistics & probability letters, 65(1):57–64, 2003

    Jürgen Groß. Restricted ridge estimation.Statistics & probability letters, 65(1):57–64, 2003

    work page 2003

  29. [29]

    A 7 t fmri dataset of synthetic images for out-of-distribution modeling of vision.Nature communications, 2026

    Alessandro T Gifford, Radoslaw M Cichy, Thomas Naselaris, and Kendrick Kay. A 7 t fmri dataset of synthetic images for out-of-distribution modeling of vision.Nature communications, 2026

    work page 2026

  30. [30]

    Improving the accuracy of single-trial fmri response estimates using glmsingle.Elife, 11:e77599, 2022

    Jacob S Prince, Ian Charest, Jan W Kurzawski, John A Pyles, Michael J Tarr, and Kendrick N Kay. Improving the accuracy of single-trial fmri response estimates using glmsingle.Elife, 11:e77599, 2022

    work page 2022

  31. [31]

    Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

    Andrew M Saxe, James L McClelland, and Surya Ganguli. Exact solutions to the nonlinear dynamics of learning in deep linear neural networks.arXiv preprint arXiv:1312.6120, 2013

    work page Pith review arXiv 2013

  32. [32]

    Understanding forgetting in continual learning with linear regression.arXiv preprint arXiv:2405.17583, 2024

    Meng Ding, Kaiyi Ji, Di Wang, and Jinhui Xu. Understanding forgetting in continual learning with linear regression.arXiv preprint arXiv:2405.17583, 2024

    work page arXiv 2024

  33. [33]

    Double descent demystified: Identifying, interpreting & ablating the sources of a deep learning puzzle.arXiv preprint arXiv:2303.14151, 2023

    Rylan Schaeffer, Mikail Khona, Zachary Robertson, Akhilan Boopathy, Kateryna Pistunova, Ja- son W Rocks, Ila Rani Fiete, and Oluwasanmi Koyejo. Double descent demystified: Identifying, interpreting & ablating the sources of a deep learning puzzle.arXiv preprint arXiv:2303.14151, 2023

    work page arXiv 2023

  34. [34]

    Neuroai for ai safety.arXiv preprint arXiv:2411.18526, 2024

    Patrick Mineault, Niccolò Zanichelli, Joanne Zichen Peng, Anton Arkhipov, Eli Bingham, Julian Jara-Ettinger, Emily Mackevicius, Adam Marblestone, Marcelo Mattar, Andrew Payne, et al. Neuroai for ai safety.arXiv preprint arXiv:2411.18526, 2024

    work page arXiv 2024

  35. [35]

    General moments of the inverse real wishart distribution and orthogonal weingarten functions.Journal of Theoretical Probability, 25(3):798–822, 2012

    Sho Matsumoto. General moments of the inverse real wishart distribution and orthogonal weingarten functions.Journal of Theoretical Probability, 25(3):798–822, 2012

    work page 2012

  36. [36]

    Perturbation bounds for eigenspaces under a relative gap condition.Proceedings of the American Mathematical Society, 148(2):479–494, 2020

    Moritz Jirak and Martin Wahl. Perturbation bounds for eigenspaces under a relative gap condition.Proceedings of the American Mathematical Society, 148(2):479–494, 2020. 12 Appendix A Code All code used to run simulations and generate the figures is provided at https://github.com/ LaneLewis/brain-distillation-theory. The codebase contains a readme with the...

    work page 2020