Large Science Models:

Foundation Models for
Generalizable Insights Into Complex Systems

with Psycho-social Application 

PI: Ishanu Chattopadhyay, PhD

Assistant Professor of Biomedical Informatics & Computer Science

University of Kentucky

DARPA-EA-25-02-05-MAGICS-PA-025

HR0011-26-3-E016

October 2026
Authorized for Public Release

LSMs for complex systems arising in non-sequential multivariate measurements

 

LSM Forest

1. How will proposer form and maintain a computationally tractable LSM tree structure given, as proposed, hundreds to thousands of observable variables?

\(\checkmark\)

Recursive LSM forest: hyperlinked nodes capturing emergent macro-structures

GSS 2018 dataset

  • Set of conditional inference trees (CIT)
    • Strict statistical guarantees: quantifies inference uncertainty
  • Each tree models exactly one variable as a function of potentially all other variables
  • Non-leaf nodes are "hyperlinked" to other trees

Large Science Models

Computationally tractable LSM tree structure given, as proposed, hundreds to thousands of observable variables.

GSS 2018 dataset

  • Each predictor is inferred independently
  • Can scale up to thousands of variables in Python implementation
  • Further scale-up \(10^6 - 10^8\) needs C/C++ implementation

https://34.66.189.202/data/trees2018/

Full Example  of Hyperlinked Trees

252 surveys "digitized"

Goal: Global Coverage                           

World Value Survey (WVS) is global

\(\checkmark\) Overlapping survey datasets

Large Science Models: Mathematical Framework

\begin{aligned} \text{Observables:} \quad & \color{yellow}X = \{x^1, \ldots, x^N\}, \overbrace{x^i \in \Sigma^i}^{\text{finite alphabet}} \\ {\color{gray}\text{Notation:} }\quad & \color{gray} x^{-i} = \{x^j : j \ne i\}\\ \text{Crosstalk:} \quad & \forall i \ P(x^i) = \color{red} f_i(x^{-i}) \\ \text{System state:} \quad & \color{Cyan} \psi = \bigotimes_{i=1}^N \psi^i, \quad \psi^i \in \mathscr{D}(\Sigma^i) \cup \varnothing \\ %\textbf{Degenerate case:} \quad & \psi^i \text{ is a delta distribution (fully observed)} \\ {\color{gray}\text{Notation:} }\quad & \color{gray}\psi^{-i} = \bigotimes_{j \ne i} \psi^j \end{aligned}

reliten

 gunlaw

abany

---

grass

Person 1

Person 2

---

Person m

observables

samples

Distributions over alphabet \(\Sigma^i\)

\phi = \bigotimes_{i=1}^N \phi^i, \quad \phi^i(\psi^{-i}) \in \mathscr{D}(\Sigma^i) \\

Individual Predictor (CIT)

cross-talk

\phi(\psi) \vert \vert \psi

Tension between predicted and observed distribution drives change

Example

GSS topic: There should be more gun-control

\(\psi^i\)

strongly agree

agree

neutral

disagree

strongly disagree
\Sigma^i

Digital Twin

\phi^i(\psi^{-i}) \sim \widetilde{\psi}^i

\(\phi\) estimates \(\psi\)

Examples: GSS, ANES, WVS, ESS, Eurobarometer, Afrobarometer, Asian Barometer etc

group

individual

estimate is always a non-empty non-degenerate distribution

missing observation

Large Science Models: Properties

LSM-Distance Metric*

\theta(\psi,\psi') \triangleq \frac{1}{N}\sum_{i=1}^{N} \sqrt{D_{JS}\Bigl(\phi^i(\psi^{-i}) \vert \vert \phi^i(\psi'^{-i})\Bigr)}

 where \(D_{JS}(P\vert \vert Q)\) is the Jensen-Shannon divergence.

g_{ij}(\psi) \;=\; \frac{1}{2}\,\frac{\partial^2}{\partial \psi^i\,\partial \psi^j}\,\theta^2(\psi,\psi')\Biggr|_{\psi'=\psi}
\left \lvert \ln \frac{\Pr(\psi\to \psi')}{\Pr(\psi' \rightarrow \psi')}\right \rvert \le \beta\,\theta(\psi,\psi')

Large Deviation Bound*

 Induced  Riemannian metric tensor

This bound connects ``closeness'' of samples to the odds of perturbing from one to the other, bridging geometry to dynamics

Ergodic Projection

\psi_\star \triangleq \bigotimes_{i=1}^N\phi^i\left (\prod_{1}^{N-1}\varnothing\right )

(Sanov's Theorem, Pinkser's Inequality)

\(\psi\)

\(\psi'\)

\(\theta\)

"spatial average":  average of all plausible worldviews or states

* Sizemore, Nicholas, Kaitlyn Oliphant, Ruolin Zheng, Camilia R. Martin, Erika C. Claud, and Ishanu Chattopadhyay. "A digital twin of the infant microbiome to predict neurodevelopmental deficits." Science Advances 10, no. 15 (2024): eadj0400.  https://www.science.org/doi/full/10.1126/sciadv.adj0400

persistence probability

Ergodic dispersion

\Psi_\star = \theta(\psi,\psi_\star)

Central to Model Drift Quantification

Start with opinion vector with all entries missing

This is a standard Physics construct, quantifying curvature of the underlying latent geometry

Pr(\psi \rightarrow \psi')

Easily computable in LSM framework!

Apply \(\phi^i\)

Random variable quantifying dispersion around the spatial average of worlviews

const. scaling as \(N^2\) 

Old Validation Strategy: Compare with LLMs

Validation?

Sample Persistence:

\omega(x)=\frac1n\sum_{i=1}^n \log_2\phi^i(x^i\mid x^{-i})

\(x^i\)

\(\phi^i(x^i | x^{-i})\)

How well does sample \(x\) fit the model, or doesnot tend to perturb?

Multi-scale LSM vi Progressive Persistence Peeling

Fit an LSM to the current population:

M_0=\mathrm{LSM}(R_0)

Score each observation by its conditional persistence:

\omega_d(x)=\frac1n\sum_{i=1}^n \log_2\phi_i^{(d)}(x_i\mid x_{-i})

Peel the low-persistence tail:

R_{d+1} = \left\{ x\in R_d: \frac{\omega_d(x)-\mu_d}{\sigma_d} < -z_* \right\}
R_0\supset R_1\supset R_2\supset\cdots

Repeatedly isolate progressively less-persistent observations and relearn LSM

M_{d+1}=\mathrm{LSM}(R_{d+1})

Refit LSM

MAP error \(\rightarrow\)

\upsilon_{M_d}(x,i) = \frac{\phi_i^{(d)}(x_i\mid x_{-i})} {\max_a\phi_i^{(d)}(a\mid x_{-i})}

Conditional displacement:

\Delta C(d) = \mathbb E_x \left[ \frac1n\sum_i \left| \upsilon_{M_d}(x,i) - \upsilon_{M_{d+1}}(x,i) \right| \right]

Description length \(\rightarrow \)

\ell_d(x) = -\frac1n\sum_i \log_2\phi_i^{(d)}(x_i\mid x_{-i})

Information displacement:

\Delta K^{\mathrm{pseudo}}(d) = \mathbb E_{R_{d+1}}[\ell_d] - \mathbb E_{R_d}[\ell_d]

Fingerprinting LSMs

How likely was the actual outcome?

How many bits needed to describe the distributions?

Multiscale spectrum \(\rightarrow\)

\mathcal S_X = \left\{ \left( \Delta C_X(d), \Delta K_X^{\mathrm{pseudo}}(d)\right) \right\}_{d}

The trajectory across depth fingerprints how organization is distributed from persistent to progressively less-persistent structure.

Fingerprinting LSMs

2018

Multiscale spectrum \(\rightarrow\)

\mathcal S_X = \left\{ \left( \Delta C_X(d), \Delta K_X^{\mathrm{pseudo}}(d)\right) \right\}_{d}

The trajectory across depth fingerprints how organization is distributed from persistent to progressively less-persistent structure.

Fingerprinting LSMs

2008

SECOND SURVEY PROGRAM

Eurobarometer: ten waves, 2018–2021

Characteristic Drift Spectra of Complex Systems

15 / 18

Eurobarometer polar rendering of the raw information drift versus structural drift plane for ten waves, 2018 to 2021

a

Eurobarometer structural drift versus exp of Kolmogorov drift, with error bars, for ten waves, 2018 to 2021

b

DIRECTION

All ten arrows point within ≈30–43° in the (information drift, structural drift) plane.

MAGNITUDE

Arrow lengths range from ≈0.045 to ≈0.12; the 2021 wave, ZA7780, lies within the 2018–19 range.

KOLMOGOROV DRIFT

Within ≈ ±0.006 for every wave except one ZA7561 transition at ≈ +0.009.

Validation

  • Multiscale Spectral fingerprinting

  • Corruption Recognition

  • Synthetic Data Generation

Multiscale spectrum \(\rightarrow\)

\mathcal S_X = \left\{ \left( \Delta C_X(d), \Delta K_X^{\mathrm{pseudo}}(d)\right) \right\}_{d}

Validating LSMs via Spectral Fingerprinting

| \Delta S_X |
\displaystyle u_{X,i}^{(d)}=\frac{\phi_{X,i}^{(d)}(x_i\mid x_{-i})}{\max_{a\in\mathcal A_i}\phi_{X,i}^{(d)}(a\mid x_{-i})}\\ \displaystyle \Delta C_X(d)=\frac{1}{n}\sum_{i=1}^{n}\left|u_{X,i}^{(d+1)}-u_{X,i}^{(d)}\right|

Validating LSMs via Spectral Fingerprinting

\(| \Delta C_X|\)

MAP alignment score

Multi-scale Measure of conditional organization

Validating via Corruption Recognition

VeRITAS: Vetting Response Integrity from cross-Talk in Adversarial Surveys

CorruptionAUC
>25%~100%
~10%80-90%
~5%60-80%

If using LSM to corrupt (LSM-imputation)

AUC < 60%

2.

1.

Validating LSMs Corruption Recognition

Comparing Against SOTA  for Synthetic Data Generation

Easy to match conditionals if we just shuffle the data! LSM keeps that error low while having high novelty

\(\Delta \) MAP score

Novelty

Conditional Kolmogorov complexity

Reflexivity

Making observations changes the system

x^{-i} \rightarrow y^{-i} \Rightarrow \phi^i(x^i \vert x^{-i}) \rightarrow \phi^i(x^i \vert y^{-i})

https://github.com/zeroknowledgediscovery/psisim

Towards a Functional TOM (theory of mind)

Opinion Control via Reflexivity

x^{-i} \rightarrow y^{-i} \Rightarrow \phi^i(x^i \vert x^{-i}) \rightarrow \phi^i(x^i \vert y^{-i})
\boxed{ y^{-i*} = \arg\max_{y^{-i}\in\mathcal F} \left[ \phi^i(x_\star^i\mid y^{-i}) - \lambda\,C(x^{-i},y^{-i}) \right] }

https://github.com/zeroknowledgediscovery/DTAG

Future Goal: Show Fixed Question Sets Exist That Move Different Persona Towards Polarization/Depolarization

Goal2: Show We can optimize question sequences to move the same persona in a chosen direction

  • Note: It is relatively easy to polarize than to depolarize

Progress & Dissemination

  • Publications: 1 published (Emergenet), 1 under review, 2 in preparation
  • Conference: CSS 2026 poster
  • Personnel: Hari Dahal, PhD — Postdoctoral Scholar

Request: No-Cost Extension

  • Postdoctoral start was delayed by ~5–6 months, compressing the planned research period
  • If administratively feasible, request a 3–6 month no-cost extension
  • Would allow completion of planned validation, analysis, and dissemination

Potential Follow-on Alignment

  • Next steps? Future Programs at IPTO?
  • LSMs for trust, influence, and population-level belief dynamics
  • Potential alignment with AFOSR Trust & Influence (Dr. Laura Steckman)  https://www.afrl.af.mil/