Decentralized Digital Twins

Shared, verifiable, networked local models of real-world systems

Understand costs and benefits of strategies/projects

Better decisions: recommendations, negotiations, valuations...

Initial application: agroecology

Distributed non-iid data
- Sparse
- Heterogeneous
- Private
- Potentially unreliable
Localized, collaborative forecasting and planning
- Personalized
- Privacy preserving
Recommendations, not direct control

Desiderata

A practical implementation tackling real-world challenges:

Federated active inference agents

Fangorn: engine used by each Ent to inquire, learn, plan, and allocate resources

Gaia Protocol: language used by Ents to independently interact with their environments and each other

Gaia Network: mesh of AI agents called Natural Entities (Ents) that act as proxies for real-world systems

If we do this right, the Gaia Network approximates a single composite agent (more on this later)

Fangorn Overview

Highlights

Automatic Model Selection

Match on:

Configurations
Available observable modalities

Hierarchical generative models

Hyperprior

$p\left( \pmb{\phi}\right)$

Prior

$\prod_{n=1}^Np\left( \pmb{\theta}_n | \pmb{\phi}\right)$

Agent 2

Agent N

Agent 1

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$\pmb{C}^1_t = \left(\pmb{c}^1_1, \ldots, \pmb{c}^1_t \right)$

$p\left( \pi^1 \right)$

$p_{\pmb{\theta}_1}\left( \pmb{s}^1_t|\pmb{c}^1_{t}, \pmb{s}^1_{t-1}, \pi \right)$

$p_{\pmb{\theta}_1}\left( \pmb{o}^1_t| \pmb{s}^1_t \right)$

Structured Variational inference

Ambrogioni, Luca, et al. "Automatic structured variational inference." International Conference on Artificial Intelligence and Statistics. PMLR, 2021.

$x_1$

$x_2$

$x_3$

$x_4$

$x_5$

$x_6$

$x_7$

$p(\pmb{x})=\prod_{j=1}^kp_j\left( x_j|\pmb{\theta}_j(\pi_j) \right)$

parent variables

$\pi_j \subseteq \{ x_i\}_{i\neq j}$

$x_1$

$x_2$

$x_3$

$x_4$

$x_5$

$x_6$

$x_7$

$q(\pmb{x}|\Lambda, \pmb{\Alpha})=\prod_{j=1}^k q_j\left( x_j|\Omega^{\pmb{\alpha}_j}_{\pmb{\lambda_j}} \left[ \pmb{\theta}_j\right] \right)$

$\Omega^{\pmb{\alpha}}_{\pmb{\lambda}} \left[ \pmb{\theta}\right] = \pmb{\lambda} \odot \pmb{\theta} + \left( 1 - \pmb{\lambda} \right) \odot \pmb{\alpha}$

P2P Federated inference

local data

$\pmb{D}_n$

local prior

$p \left( \pmb{\theta_n|\pmb{\phi}}\right)$

global posterior $q\left(\pmb{\phi} \right)$

local posterior

$q\left(\pmb{\theta}_n \right)$

local data

$\pmb{D}_n$

local prior

$p \left( \pmb{\theta_n|\pmb{\phi}}\right)$

global posterior $q^{(i)}\left(\pmb{\phi} \right)$

local posterior

$q^{(i)}\left(\pmb{\theta}_n|\pmb{\phi} \right)$

local data

$\pmb{D}_n$

local prior

$p \left( \pmb{\theta_n|\pmb{\phi}}\right)$

global posterior $q\left(\pmb{\phi} \right)$

local posterior

$q\left(\pmb{\theta}_n \right)$

local data

$\pmb{D}_{n^\prime}$

local prior

$p \left( \pmb{\theta_{n^\prime}|\pmb{\phi}}\right)$

global posterior $q^{(i+1)}\left(\pmb{\phi} \right)$

local posterior

$q^{(i+1)}\left(\pmb{\theta}_{n^\prime}|\pmb{\phi} \right)$

Node $n$

Node $n^\prime$

Gong, Jinu, Osvaldo Simeone, and Joonhyuk Kang. "Bayesian variational federated learning and unlearning in decentralized networks." 2021 IEEE 22nd International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). IEEE, 2021.

Hyper-prior ConstrainTs

Academic studies

Expert

knowledge

Entmoot

Meta-analysis Model

Entmoot DB

Federated Parameter Store

Fangorn

Project-level

Agent Models

Project context and data

Project assessment and decision support

Project-level results

Global constrains on regression

Regression results

Global constrains on agents

Data Source reliability

Williams, Donald R., Stephen R. Martin, and Philippe Rast. "Putting the individual into reliability: Bayesian testing of homogeneous within-person variance in hierarchical models." Behavior research methods 54.3 (2022): 1272-1290.

$p(y_{mj}|x) = \mathcal{N} \left(x, \sigma_{mj}^2 \right)$

Source reliability

$\rho_{mj} = \frac{\sigma_x^2}{\sigma_x^2 + \sigma^2_{mj}}$

Simplified generative model

$p(x) = \mathcal{N} \left( \mu, \sigma_x^2 \right)$

Modality reliability

$\rho_{m} = \frac{\sigma_x^2}{\sigma_x^2 + \frac{1}{M^2}\sum_j \sigma^2_{mj}}$

$m \in \{1, \ldots, M \}$ and $j \in \{1, \ldots, K \}$

Coming soon

Category-theoretic model composition (Smithe, 2023)
Category-theoretic model discovery (Sennesh et al, 2023)
Machine-verifiable inference and planning (Kaufmann et al, unpublished)
Automatic lit review (Kaufmann et al, unpublished)
Integrating goals via constraints and satisficing (Simon, 1996)
Knowledge economics (Hubbard, 2007)
Multiscale ActInf agents via Theory of Mind and goal alignment (Kaufmann et al, 2021)
ActInf over models of arbitrary HW+SW systems (Coy and Kaufmann, unpublished)
Internalizing externalities with ActInf (Hesp and Kaufmann, unpublished)