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Sprint projectAug 16, 2026Berlin

Dense Jacobian Transport Changes Model-Brain RSA in a Prompt- and Depth-Dependent Manner

Frank Peterlein · Team J-Lens Model-Brain Audit

Submitted to Digital Minds Research Sprint. Sprint projects are early-stage work by participants, not Apart Research publications.

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Report: Dense Jacobian Transport Changes Model-Brain RSA in a Prompt- and Depth-Dependent Manner

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Does emphasizing output-relevant directions in a language model make its representations more brain-like? We compare normalized dense J-Lens transport with ordinary residual states using representational similarity analysis against fMRI responses to 515 natural scenes from eight Natural Scenes Dataset participants. Dense transport reduced alignment in the preregistered aggregate and in 15 of 18 frozen extension contrasts; effects varied by prompt and transformer depth. Full-rank but anisotropic Jacobians indicate geometric reweighting rather than rank collapse. This bounds a tempting workspace analogy: dense transport is not a shortcut to neural alignment and is not the formal sparse J-space projection.

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How much would this matter for the field if it worked? How innovative is it? For scores of 4-5: is this actually new to the field, or replicating recent work?

Scoring guide
  1. 1Negligible. No clear problem addressed, or no meaningful novelty.
  2. 2Limited. Addresses a real problem but with a generic or well-trodden approach. Incremental at best.
  3. 3Moderate. Clear problem with a reasonable approach; some novelty in framing or method beyond routine application of existing tools.
  4. 4Significant. Important problem with an original approach, or identifies a neglected problem area. A valuable contribution others could build on.
  5. 5Exceptional. Tackles a critical problem with a genuinely novel approach, or opens a new research direction. Clear theory of change. You'd be excited to share this with researchers in the area.

How sound are methodology, implementation, and findings?

Scoring guide
  1. 1Seriously flawed. Methodology broken, results uninterpretable, or implementation doesn't work.
  2. 2Weak. Approach has significant gaps: missing validation, flawed experimental design, or incomplete implementation.
  3. 3Competent. Technically solid given the short duration. Methodology makes sense, results are interpretable, limitations acknowledged, work builds toward clear conclusions.
  4. 4Strong. Thorough methodology with convincing validation. Results clearly support conclusions. Immediately useful for future work.
  5. 5Exceptional. Ambitious scope executed rigorously. Surprising findings, novel methods, or unusually robust validation.

How clearly are work, findings, and impact potential communicated?

Scoring guide
  1. 1Incomprehensible. Cannot determine what the project is actually claiming or doing.
  2. 2Hard to follow. Key information buried, missing, or diluted by excessive length. Significant effort to extract main points.
  3. 3Clear enough. Can understand the problem, approach, and results without undue effort. Core content clearly present: problem, method, findings, limitations.
  4. 4Well presented. Easy to follow, well-structured, appropriate level of detail. Target audience would get it quickly.
  5. 5Exceptionally clear. A pleasure to read. Complex ideas made accessible. Could serve as a model for how to present this type of work.

  1. The strongest part is the separation between the preregistered result, the post-result frozen extension, and the claim boundary. Dense transport is consistently worse in the confirmatory analysis, and the spectral and normalization controls make that result more informative than a simple null. The main limit is scope: eight participants, one model and lens, caption-mediated fMRI alignment, no early-visual control, and dense J_l h_l rather than the formal sparse J-space projection. The decisive next test is the one the paper identifies: compare formal sparse J-space with variance-matched random and complementary subspaces, add early visual cortex, and report encoding models alongside RSA.

Cite this project

@misc{peterlein2026dense,
  title = {{Dense Jacobian Transport Changes Model-Brain RSA in a Prompt- and Depth-Dependent Manner}},
  author = {Frank Peterlein},
  year = {2026},
  month = aug,
  note = {Submitted to Digital Minds Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/dense-jacobian-transport-changes-modelbrain-rsa-in-a-prompt-and-depthdependent-manner-c5fk}},
  url = {https://apartresearch.com/sprints/projects/dense-jacobian-transport-changes-modelbrain-rsa-in-a-prompt-and-depthdependent-manner-c5fk}
}

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