Ishanu Chattopadhyay PRO
ML | Data Science Biomedical Informatics | Social Science | Assistant Professor
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
Proposed Concept
- Develop Foundation models of complex systems with
- hundreds to thousands of evolving variables with apriori unknown cross-talk
- no governing equations are know a priori
- reflexivity: system changes if observed
- Learn intrinsic system geometry from data
- Derive equations of motion with variational principles (stationary action on Lagrangian).
- Inference under data sparsity
- Detect data (in)sufficiency, adapt to model drift
- Support forward simulation and perturbation analysis
- Digital twins of individuals & groups wrt to opinion dynamics
Proposer Overview
PI: Ishanu Chattopadhyay, PhD
Assistant Professor of Biomedical Informatics & Computer Science
Associate Faculty Sanders-Brown Center of Aging
University of Kentucky
- PI on 4 past DARPA grants
- D3M (Data-driven Discovery of Models, I20, PM: Wade Shen)
- PAI (Physics of AI, DSO, PM: James Gimlett)
- PREEMPT (PREventing EMerging Pathogenic Threats, BTO, Site-PI, PM: James Gimlett)
- YFA 2020 (Topic: Cognitive Dissonance, PM: Bartlett Russell)
- High impact publications (https://scholar.google.com/citations?user=JpUbOmsAAAAJ&hl=en)
- Funding from Alzheimer's Association, NIA
- Advised 3 Postdocs, 2 PhD, over 30 graduate and undergraduate students
- >40 Invited lectures including at NIH, DoD Facilities, National Labs
Dmytro Onishchenko
Staff Scientist + PhD Student:
- ML/AI
- C++/Python
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
Full Example of Hyperlinked Trees
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 \(N^2\)
Datasets
DatasetAccess modelLicense / use constraints (typical for research use)
| General Social Survey (GSS) | Open public download | Free for research use; citation required; no redistribution of modified datasets |
| American National Election Studies (ANES) | Public-use + restricted-use tiers | Public-use data freely available; restricted-use data requires application and secure handling |
| Cooperative Election Study (CES) | Public download (common content) | Free for academic research; team modules may have additional citation or use constraints |
| Eurobarometer | Registration-based access (GESIS) | Free for non-commercial research; user registration required; citation and compliance with GESIS terms |
| World Values Survey (WVS) | Registration-based download | Free for non-commercial research; attribution required; redistribution restricted |
| European Social Survey (ESS) | Registration-based download | Free for non-commercial research; strict citation and documentation compliance |
| Latinobarómetro | Controlled public access | Use subject to project terms; citation required; redistribution limitations apply |
| Afrobarometer | Public download | Free for research and policy use; attribution required; redistribution limited |
| Arab Barometer | Form-based access | Free for non-commercial research; short request form; citation required |
| Asian Barometer | Application-based access | Explicit permission required; usage and redistribution restrictions apply |
Access Difficulty
least easy
less easy
easy
Datasets: Global Coverage
World Value Survey (WVS) is global
\(\checkmark\) Overlapping survey datasets
Digital Twin & Fidelity of Simulation
\mathcal{N}_\epsilon(\psi) \triangleq \big\{ \psi': {\color{red}\forall i \ \psi'_i \sim \phi^i\left ( \psi^{-i}\right )}
\wedge {\color{yellow} \theta(\psi,\psi') \leqq \epsilon }\big \}
Sample predicted distributions
perturbed state within \(\epsilon\) of \(\psi\)
| Variable | Masked | Reconstructed |
|---|---|---|
| spkcom | allowed | allowed |
| colcom | not fired | not fired |
| spkmil | allowed | allowed |
| colmil | allowed | not allowed |
| libmil | not remove | not remove |
| libhomo | not remove | not remove |
| reliten | strong | no religion |
| pray | once a day | once a day |
| bible | inspired word | word of god |
| abhlth | yes | yes |
| abpoor | no | no |
| pillok | agree | agree |
| intmil | very interested | very interested |
| abpoorw | always wrong | not wrong at all |
| godchnge | believe now, always have | believe now, always have |
| prayfreq | several times a week | several times a week |
| religcon | strong disagree | disagree |
| religint | disagree | disagree |
| Variable | Masked | Reconstructed |
|---|---|---|
| spkcom | allowed | allowed |
| colcom | not fired | not fired |
| libmil | not remove | not remove |
| libhomo | not remove | not remove |
| gunlaw | favor | favor |
| reliten | no religion | no religion |
| prayer | approve | approve |
| bible | book of fables | inspired word |
| abnomore | yes | yes |
| abhlth | yes | yes |
| abpoor | yes | yes |
| abany | yes | yes |
| owngun | no | no |
| intmil | moderately interested | moderately interested |
| abpoorw | not wrong at all | not wrong at all |
| godchnge | believe now, didn't used to | believe now, always have |
| prayfreq | several times a week | several times a week |
2018 GSS individual samples
Digital Twin
-Neighborhood of state \(\psi\)
\epsilon
Definition
Sample neighborhood to impute missing data
\psi
\epsilon
}
2018 GSS out-of-sample reconstruction
post-reconstruction error ratio (%)
LSM sampling: sampling the \(\epsilon\)-neighborhood of a state or worldview allows reconstruction of censored opinions
examples
Predictive ability of LSM quantified as ability to reconstruct censored out-of-sample opinions**
{\color{Tomato}\psi_\star }\rightarrow \psi \rightarrow \cdots \rightarrow \psi'
Null state (all missing observations)
Valid perturbations/ simulations
LSM sampling allows simulating opinion perturbations
Both Individuals and groups maybe modeled as digital twins\(\dag\)
Global Emergent Structure via Clusters & Poles
2018 GSS
\theta_t(\psi_+,\psi_-)
Polar separation over time
2016 Presidential Election Vote Prediction
2004
| abany | no | yes |
| abdefctw | always wrong | not wrong at all |
| abdefect | no | yes |
| abhlth | no | yes |
| abnomore | no | yes |
| abpoor | no | yes |
| abpoorw | always wrong | not wrong at all |
| abrape | no | yes |
| absingle | no | yes |
| bible | inspired word | book of fables |
| colcom | fired | not fired |
| colmil | not fired | not allowed |
| comfort | strongly agree | strongly disagree |
| conlabor | hardly any | a great deal |
| godchnge | believe now, always have | don't believe now, never have |
| grass | not legal | legal |
| gunlaw | oppose | favor |
| intmil | very interested | not at all interested |
| libcom | remove | not remove |
| libmil | not remove | remove |
| maboygrl | true | false |
| owngun | yes | no |
| pillok | agree | strongly agree |
| pilloky | strongly disagree | strongly agree |
| polabuse | no | yes |
| pray | several times a day | never |
| prayer | disapprove | approve |
| prayfreq | several times a day | never |
| religcon | strongly disagree | strongly agree |
| religint | strongly disagree | strongly agree |
| reliten | strong | no religion |
| rowngun | yes | no |
| shotgun | yes | no |
| spkcom | not allowed | allowed |
| spkmil | allowed | not allowed |
| taxrich | about right | much too low |
conservative pole
\psi_+
liberal pole
\psi_-
Clustering LSM distance \(\theta(x,y)\) between out-of-sample individuals
conservative
liberal
poles:
partial states aligning with extreme opposing worldviews
- Compare across time and different GSS surveys
- Derived features for individuals (ideology index)
I(x) = \frac{\theta(x,\psi_+) - \theta(x,\psi_-)}{\theta(\psi_+,\psi_-)}
Predict 2016 votes using ideology index
Emergent global structure
Reflexivity and State Collapse on Observation
Emergent Equations of Motion
L \triangleq \frac{1}{2} \sum_i g_{kl} P^k_p \dot{\psi}^p_i P^l_n \dot{\psi}^n_i - \theta(\psi, \phi)
Define Lagrangian*
\frac{d}{dt} \left( \frac{\partial L}{\partial \dot{\psi}^m_i} \right) - \frac{\partial L}{\partial \psi^m_i} = 0
Via the Euler-Lagrange Equations\(^\dag\):
\ddot{\psi}^m_i = -g^{km} P^k_m \frac{1}{2N} \sum_j \frac{1}{\sqrt{D_{JS}(\psi^m_j \| \phi^m_j)}} \left[ \ln\left( \frac{2e\psi^m_j}{\psi^m_j + \phi^m_j} \right) - \frac{1}{2(\psi^m_j + \phi^m_j)} \right]
Over-damped Gradient flow Equation*
where \(-g^{km}\) is the inverse metric tensor
kinetic energy
state collapse
strongly agree
agree
neutral
disagree
strongly disagree
strongly agree
agree
neutral
disagree
strongly disagree
Query/
Observation
\(X_i\)
Non-local Influence propagation on measurement/observation (QM-like)
\phi^i(\psi^{-i})
potential energy
* Einstein notation used
Goldstein, Herbert, et al. Classical Mechanics. 3rd ed., Pearson, 2002.
\(^\dag\)
Principle of stationary action
Dynamics
Local potential field eqn
Local Potential Fields
Stable
(captured by local extrema)
Free to move locally towards extrema
Why propaganda works so well
* “Exposure to opposing views on social media can increase political polarization”
by Christopher A. Bail et al., published in PNAS in September 2018 (Vol. 115, No. 37, pp. 9216–9221; DOI: 10.1073/pnas.1804840115)
GSS 2018 individuals and neighborhoods
Influenza C : strains and their neighborhoods
Even random perturbations will tend to move individuals towards local extrema increasing polarization
*
- Polarization is "easy", can occur via random perturbations (falling into the local well)
Hypotheses
Observation: This lineage (Mississippi lineage) is now extinct since 2022/23
stable lineage
Implications on Social Theory
The LSM tells the latent opinion "space-time" how to curve, the curved "space-time" tells opinions how to change.
Local potential fields can be computed given the LSM and dynamical considerations, which reveal future evolution
- De-polarization is "hard", needs specific communication (climbing up from the well)
Data Sufficiency via Conservation of Complexity
%K(x) = K(S) + K(x \vert S_\star) + O(1) = K(S') + K(x \vert S'_\star) +O(1)
K(x \vert S_\star) = O(1) = K(S \vert x_\star)
The No-cheating Thorem: Generative models cannot cheat on complexity
Kolmogorov Complexity
Optimal Generative Model
compressed data representation
compressed model representation
Theorem
K(\textrm{data}) = K(\textrm{LSM}) +O(1)
Conservation Law arising from the continuous symmetry of typicality*
\mu_0(X) \triangleq \frac{\delta(\vert \langle S(X) \rangle \vert)}{\delta(\vert \langle X \rangle \vert)} \leq 1
Saturation relation:
Data Sufficiency Statistic \(\mu_0\)
We need LSM-sampling to calculate this
*Noether's Theorem
For every continuous symmetry of a physical system, there exists a corresponding conserved quantity
\(\checkmark\) 6. Explain how you will measure the accuracy of predicted structure emergence and data sufficiency.
\vert \langle X' \rangle \vert \approx \max\{1,\mu_0(X)\} \vert \langle X \rangle \vert
How much more data do we need?
Data saturation
Data deficient
Needed
Current
Empirical Validation
Model Drift Quantification
Ergodic dispersion
\Delta_\star = \theta(\Psi,\psi_\star)
z(\Delta_\star) = \frac{\Delta_\star^{[t]} - \langle \Delta_\star^{[t]} \rangle}{\sigma(\Delta_\star^{[t]} )}
Z-value of dispersion
Do new samples (survey respondents) still conform to the model?
GSS Model drift
ergodic projection (all missing values)
A random belief state (with possibly missing entries)
random variable
normal variate
\zeta(M) = \vert z(\Delta_\star^0) - z(\Delta_\star^{[t]}) \vert
Model drift stochastic process (\(\zeta\))
\mathbf{E}(\zeta(M) )
assess if \(\zeta\) is stationary: if not then new samples are not conforming to model
Example for GSS LSM inferred for year 2000
Large Science Models & Ergodicity
No Convergence
(~50% belief mismatch between pairs)
2018 GSS survey belief vectors simulated via LSM sampling
- No ergodicity assumption: LSMs are built for non-ergodic systems
- Sampling and simuation "remembers" the start point (No convergence), demonstrating non-ergodic learned structure
- Local potential fields vary across the space
- Potential wells may arise, driven by the dynamics at hand, not via assumptions
- "change" is driven by non-equilibrium (dissonance)
Embedded Social Theories in LSM
How LSMs reflect and operationalize foundational social-scientific ideas
-
Belief about topic iii is expected to align with beliefs about other topics \(\displaystyle\psi^{-i}\).
Deviations are exponentially improbable \(\Rightarrow \) people/groups seek internal coherence. -
Theory Link:
-
Cognitive consistency theory – Abelson et al. (1968)
-
Constraint satisfaction in beliefs – Read & Marcus-Newhall (1993)
-
-
Beliefs evolve to minimize tension between actual state and “expected” state.
Reflexive gradient flow — system reduces internal contradiction. -
Theory Link:
-
Cognitive Dissonance Theory – Festinger (1957)
-
Homeostatic belief adjustment – Gawronski & Strack (2004)
-
-
Observing a belief changes it and affects all conditionals.
Direct encoding of feedback loops central to human systems. -
Theory Link:
-
Reflexivity in social systems – Giddens (1984), Soros (1994)
-
Theory of mind / mutual modeling – Premack & Woodruff (1978)
-
Validation of Social Theory Questions:
- Perception changes reality, which changes perception
- The Constitution of Society
- The Alchemy of Finance
- Does a chimpanzee have a theory of mind?
- Our system “wants” to reach a low-energy (low-dissonance) state — a direct computational analog of Festinger’s theory.
- People strive to align beliefs and attitudes across related domains. Inconsistencies create cognitive discomfort, prompting adjustments across belief clusters to restore harmony.
| Exploratory: Belief systems react measurably to exogenous events and shocks |
Exploratory: Cross-dependencies between beliefs have observable effects on societal resilience.
Is Polarization an Inevitable Attractor?
Social Identity Theory vs. Belief Proximity
Large Science Models: Broader Applications
A General Framework for modeling Complex Systems
Genomic database: Missing heritability problem
Personalized Clinical Digital Twin, Virtual Patients
Any structured interview, PTSD fabrication
Assess sysmptom data and co-pathologies
Predict future mutations; which animal strain is closest to jumping to humans
Mental health diagnosis
Microbiome Analysis**
Algorithmic lie detector
Viral emergence
Teomims
Opinion Dynamics
Darkome
Generative model of complex microbial ecosystems, and their impact on health and disease
Data requirements
- Tabular data
- Potentially large number of features/covariates (\(10^2 - 10^8 \))
- Sufficient number of samples (\(10^3 - 10^6\))
- Small number of longitudinal samples (currently, \( < 100\))
| Limitation | Mitigation / Response |
|---|---|
| Conventional time series is currently out-of-scope | Focus on cross-sectional interdependencies and belief geometry; time handled via drift |
| LSMs model statistical interdependence, not causal mechanisms | Use perturbation-based simulations to infer plausible influence pathways |
| Limited by observed belief variables | Integrate multiple surveys; use latent proxies and test sensitivity of digital twins |
| Social theory connections and interpretability may be challenging | Anchor dynamics with theory-driven constructs (e.g., ToM, cognitive dissonance) |
LSMs for complex systems
**preliminary study published (https://www.science.org/doi/10.1126/sciadv.adj0400)
DTAG: Global Digital Twin of Opinions
Recall Bail etal.
“Exposure to opposing views on social media can increase political polarization” by Christopher A. Bail et al., published in PNAS in September 2018 (Vol. 115, No. 37, pp. 9216–9221; DOI: 10.1073/pnas.1804840115)
We find more general possibilities: We can make world-views go more extreme or less extreme based on the line of questions and the persona
Perturbing with opposing views made conservatives more conservative (statistically significant), liberals more liberal (not statistically significant)
LSM
- Fixed Question Sets Exist That Move Different Persona Towards Polarization/Depolarization
- We can optimize question sequences to move the same persona in a chosen direction
- Note: It is relatively easy to polarize than to depolarize
Copy of kickoff_MAGICS
By Ishanu Chattopadhyay
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DARPA-EA-25-02-05-MAGICS-PA-025 University of Kentucky Kickoff
