arxiv: 2602.11398 · v4 · submitted 2026-02-11 · 💻 cs.NE

Evolution With Purpose: Hierarchy-Informed Optimization of Whole-Brain Models

Hormoz Shahrzad , Niharika Gajawelli , Kaitlin Maile , Manish Saggar , Risto Miikkulainen This is my paper

Pith reviewed 2026-05-16 01:56 UTC · model grok-4.3

classification 💻 cs.NE

keywords braincurricularparametersapproachevolutionheterogeneoushicoknowledge

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The pith

Hierarchy-informed curricular optimization of heterogeneous whole-brain models enables generalization to new subjects and prediction of behavioral abilities from parameters.

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

Brain models with many parameters are hard to tune because interactions are nonlinear. Researchers used evolutionary search to fit a model where each of seven brain regions gets its own set of 20 parameters. They tested four ways to run the search: all parameters together, a step-by-step order that follows the known hierarchy of brain networks, the reverse order, and random order. All versions fit the MRI data, but only the hierarchy-guided order produced parameters that worked on new people and could forecast how well those people performed on behavioral tests. This shows that telling the optimizer the real-world order of brain regions helps it find solutions that capture something meaningful rather than just memorizing one dataset.

Core claim

only HICO made it possible to use the parameter sets to predict the subjects' behavioral abilities as well.

Load-bearing premise

That the curricular ordering based on the hierarchy of brain networks is the causal factor enabling behavioral prediction rather than other unstated details of the optimization or data processing.

Figures

Figures reproduced from arXiv: 2602.11398 by Hormoz Shahrzad, Kaitlin Maile, Manish Saggar, Niharika Gajawelli, Risto Miikkulainen.

**Figure 1.** Figure 1: Large-scale cortical organization used to define RSN-specific parameter blocks. (a) Surface renderings of a 400-region cortical parcellation mapped to the seven canonical RSNs of Yeo et al. [36], shown for lateral and medial views of both hemispheres. Colors denote Visual, Somatomotor, Dorsal Attention, Ventral Attention, Limbic, Frontoparietal Control, and Default Mode RSNs. (b) Distribution of parcels … view at source ↗

**Figure 2.** Figure 2: Distribution of fitness scores across optimization strategies when models were optimized separately for each individual subject. The points represent subjects and the boxes show the interquartile range (IQR) with median (solid line) and mean (dashed line). Unpaired statistical tests against the homogeneous baseline indicate that the heterogeneous, HICO, and reverse curricula achieve significantly higher fi… view at source ↗

**Figure 3.** Figure 3: Leave-one-out (LOO) fitness distributions across optimization strategies. Violin plots show the distribution of LOO fitness scores across subjects, with embedded boxplots indicating median and interquartile range; triangles denote means. Homogeneous and flat heterogeneous strategies collapse to zero LOO fitness across the board, reflecting dynamical instability LOO fitness calculation. In contrast, curric… view at source ↗

**Figure 4.** Figure 4: UMAP embedding of subject-level parameter vectors (averaged by parameter type). Each point is a subject, colored according to the approach used. Curriculum-based methods (HICO, Reverse, Shuffled) occupy a large overlapping region of parameter space, whereas homogeneous and heterogeneous approaches form distinct, focused clusters shifted away from this region. As seen in [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗

**Figure 5.** Figure 5: Predicting behavior based on solutions obtained by the different optimization strategies. Each subplot reports ridge regression 𝑅 2 values (across RSNs) for a different behavioral target: (A) fluid reasoning ability (PMAT24_A_CR), (B) inwardly directed affective and somatic symptoms (ASR_Intn_Raw), and (C) outwardly directed behavioral tendencies (ASR_Extn_Raw). For each optimization strategy, colored poin… view at source ↗

**Figure 6.** Figure 6: Localization of permutation-calibrated parameter–behavior associations across the different RSNs. Top: fluid reasoning ability (PMAT24_A_CR). Middle: inwardly directed behavioral problems (ASR_Intn_Raw). Bottom: outwardly directed behavioral problems (ASR_Extn_Raw). For each RSN and optimization approach, histograms show the null distribution of ridge regression 𝑅 2 obtained from 10,000 permutations of beh… view at source ↗

read the original abstract

Evolutionary search is well suited for large-scale biophysical brain modeling, where many parameters with nonlinear interactions and no tractable gradients need to be optimized. Standard evolutionary approaches achieve an excellent fit to MRI data; however, among many possible such solutions, it finds ones that overfit to individual subjects and provide limited predictive power. This paper investigates whether guiding evolution with biological knowledge can help. Focusing on whole-brain Dynamic Mean Field (DMF) models, a baseline where 20 parameters were shared across the brain was compared against a heterogeneous formulation where different sets of 20 parameters were used for the seven canonical brain regions. The heterogeneous model was optimized using four strategies: optimizing all parameters at once, a curricular approach following the hierarchy of brain networks (HICO), a reversed curricular approach, and a randomly shuffled curricular approach. While all heterogeneous strategies fit the data well, only curricular approaches generalized to new subjects. Most importantly, only HICO made it possible to use the parameter sets to predict the subjects' behavioral abilities as well. Thus, by guiding evolution with biological knowledge about the hierarchy of brain regions, HICO demonstrated how domain knowledge can be harnessed to serve the purpose of optimization in real-world domains.

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.

Desk Editor's Note private letter to a colleague

HICO shows hierarchy-guided evolution can make heterogeneous DMF models generalize and predict behavior, but the abstract gives almost no numbers to check if it actually works.

read the letter

The core result is that only the hierarchy-informed curricular optimization (HICO) turned heterogeneous 20-parameter-per-region DMF models into something that generalized to held-out subjects and predicted behavioral scores, while fitting all at once or using reversed or random order did not. The paper compares a shared-parameter baseline against four heterogeneous strategies and reports that curricular ordering based on brain-network hierarchy is what made the difference for out-of-sample use and behavioral linkage. That is the concrete new piece: a specific way to inject known hierarchy into evolutionary search so the resulting parameters carry functional meaning rather than just fitting noise. It is a clean demonstration that domain knowledge can steer the search away from subject-specific overfitting. The execution looks straightforward on paper—evolutionary search on DMF parameters, four curricular variants, held-out evaluation, and a behavioral regression step. The claim is narrow and falsifiable in principle. The main weakness is the complete absence of quantitative support in the abstract: no sample sizes, no error bars, no p-values, no effect sizes, and no description of how behavioral prediction was measured or cross-validated. Without those, it is impossible to judge whether HICO produced a real improvement or whether the result is sensitive to unstated choices in data processing or fitness function. The comparisons between strategies are at least non-circular, but the lack of detail leaves the central claim unverified. This paper is aimed at computational neuroscientists who already work with large-scale biophysical models and want them to generalize beyond fitting. It is worth a serious referee if the full text supplies the missing statistics and controls; otherwise the contribution stays provisional. I would send it to review rather than desk-reject, mainly to get the numbers and methods checked.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that brain networks have a meaningful hierarchy that can be used to order optimization steps, plus the choice of seven canonical regions and 20 parameters per region.

free parameters (1)

20 parameters per brain region
Heterogeneous model assigns independent sets of 20 parameters to each of the seven regions; these are fitted by evolution.

axioms (1)

domain assumption Brain networks follow a canonical hierarchy that can guide curricular optimization order
Invoked to define the HICO strategy versus reversed and shuffled controls.

pith-pipeline@v0.9.0 · 5530 in / 1212 out tokens · 131359 ms · 2026-05-16T01:56:58.834896+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Hierarchy-Informed Curriculum Optimization (HICO)... phases: Phase II — Transmodal core (Default Mode and Limbic RSNs)... Phase VI — Somatomotor RSN
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

only HICO made it possible to use the parameter sets to predict the subjects' behavioral abilities

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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