Bart Kosko

Akash Kumar Panda, Olaoluwa Adigun, Bart Kosko

We automatically generate feedback causal fuzzy cognitive maps (FCMs) from text by teaching large-language-model agents to break the text into overlapping chunks of text. Convex mixing of these chunk FCMs gives a representative cyclic FCM knowledge graph. The text chunks can have different levels of overlap. The chunk FCMs still mix to form a new FCM causal knowledge graph. The mixing technique scales because it uses light computation with sparse causal chunk matrices. The mixing structure allows an operator-level type of Bayesian inference that produces "de-chunked" or posterior-like FCMs from the mixed FCM. These de-chunked FCMs are useful in their own right and allow further iterations of Bayesian updating. We demonstrate these mixing techniques on the essay text of Allison's "Thucydides Trap" model of conflict between a dominant power such as the United States and a rising power such as China. The FCM dynamical systems predict outcomes as they equilibrate to fixed-point or limit-cycle attractors. Seven out of 8 FCM knowledge graphs predicted a type of war when we stimulated them by turning on and keeping on the concept node that stands for the rising power's ambition and entitlement. Gemini 3.1 LLMs served as the chunking AI agents.

Akash Kumar Panda, Olaoluwa Adigun, Bart Kosko

We design a large-language-model (LLM) agent system that extracts causal feedback fuzzy cognitive maps (FCMs) from raw text. The causal learning or extraction process is agentic both because of the LLM's semi-autonomy and because ultimately the FCM dynamical system's equilibria drive the LLM agents to fetch and process causal text. The fetched text can in principle modify the adaptive FCM causal structure and so modify the source of its quasi-autonomy$-$its equilibrium limit cycles and fixed-point attractors. This bidirectional process endows the evolving FCM dynamical system with a degree of autonomy while the system still stays on its agentic leash. We show in particular that a sequence of three system-instruction sets guide an LLM agent as it systematically extracts key nouns and noun phrases from text, as it extracts FCM concept nodes from among those nouns and noun phrases, and then as it extracts or infers partial or fuzzy causal edges between those FCM nodes. We test this FCM generation on a recent essay about the promise of AI from the late diplomat and political theorist Henry Kissinger and his colleagues. This three-step process produced FCM dynamical systems that converged to the same equilibrium limit cycles as did the human-generated FCMs even though the human-generated FCM differed in the number of nodes and edges. A final FCM mixed generated FCMs from separate Gemini and ChatGPT LLM agents. The mixed FCM absorbed the equilibria of its dominant mixture component but also created new equilibria of its own to better approximate the underlying causal dynamical system.

Akash Kumar Panda, Olaoluwa Adigun, Bart Kosko

A large language model (LLM) can map a feedback causal fuzzy cognitive map (FCM) into text and then reconstruct the FCM from the text. This explainable AI system approximates an identity map from the FCM to itself and resembles the operation of an autoencoder (AE). Both the encoder and the decoder explain their decisions in contrast to black-box AEs. Humans can read and interpret the encoded text in contrast to the hidden variables and synaptic webs in AEs. The LLM agent approximates the identity map through a sequence of system instructions that does not compare the output to the input. The reconstruction is lossy because it removes weak causal edges or rules while it preserves strong causal edges. The encoder preserves the strong causal edges even when it trades off some details about the FCM to make the text sound more natural.

Bart Kosko, Olaoluwa Adigun

We present the new bidirectional variational autoencoder (BVAE) network architecture. The BVAE uses a single neural network both to encode and decode instead of an encoder-decoder network pair. The network encodes in the forward direction and decodes in the backward direction through the same synaptic web. Simulations compared BVAEs and ordinary VAEs on the four image tasks of image reconstruction, classification, interpolation, and generation. The image datasets included MNIST handwritten digits, Fashion-MNIST, CIFAR-10, and CelebA-64 face images. The bidirectional structure of BVAEs cut the parameter count by almost 50% and still slightly outperformed the unidirectional VAEs.

Akash Kumar Panda, Bart Kosko

An adaptive multiexpert mixture of feedback causal models can approximate missing or phantom nodes in large-scale causal models. The result gives a scalable form of \emph{big knowledge}. The mixed model approximates a sampled dynamical system by approximating its main limit-cycle equilibria. Each expert first draws a fuzzy cognitive map (FCM) with at least one missing causal node or variable. FCMs are directed signed partial-causality cyclic graphs. They mix naturally through convex combination to produce a new causal feedback FCM. Supervised learning helps each expert FCM estimate its phantom node by comparing the FCM's partial equilibrium with the complete multi-node equilibrium. Such phantom-node estimation allows partial control over these causal hallucinations and helps approximate the future trajectory of the dynamical system. But the approximation can be computationally heavy. Mixing the tuned expert FCMs gives a practical way to find several phantom nodes and thereby better approximate the feedback system's true equilibrium behavior.

Olaoluwa Adigun, Bart Kosko

This chapter presents the new family of soft diamond synaptic regularizers based on thick-tailed symmetric alpha stable $SαS$ probability bell curves. These new parametrized weight priors improved deep-learning performance on image and language-translation test sets and increased the sparsity of the trained weights. They outperformed the state-of-the-art hard-diamond Laplacian regularizer of sparse lasso regression and classification. The $SαS$ synaptic weight priors have power-law bell-curve tails that are thicker than the thin exponential tails of Gaussian bell curves that underly ridge regularizers. Their tails get thicker as the $α$ parameter decreases. These thicker tails model more impulsive behavior and allow for occasional distant search in synaptic weight spaces of extremely high dimension. The geometry of their constraint sets has a diamond shape. The shape varies from a circle to a star or diamond that depends on the $α$ tail thickness and dispersion of the $SαS$ weight prior. These $SαS$ bell curves lack a closed form in general and this makes direct training computationally intensive. We removed this computational bottleneck by using a precomputed look-up table. We tested the soft diamond regularizers with deep neural classifiers on both image test sets and German-to-English language translation. The image simulations used the three datasets CIFAR-10, CIFAR-100, and Caltech-256. The regularizers improved the accuracy and sparsity of the classifiers. We also tested with deep neural machine-translation models on the IWSLT-2016 Evaluation dataset for German-to-English text translation. They also outperformed ridge regularizers and lasso regularizers. These findings recommend the sub-Cauchy $α= 0.5$ soft diamond regularizer as a competitive and sparse regularizer for large-scale machine learning.

Osonde Osoba, Bart Kosko

Fuzzy cognitive maps (FCMs) model feedback causal relations in interwoven webs of causality and policy variables. FCMs are fuzzy signed directed graphs that allow degrees of causal influence and event occurrence. Such causal models can simulate a wide range of policy scenarios and decision processes. Their directed loops or cycles directly model causal feedback. Their nonlinear dynamics permit forward-chaining inference from input causes and policy options to output effects. Users can add detailed dynamics and feedback links directly to the causal model or infer them with statistical learning laws. Users can fuse or combine FCMs from multiple experts by weighting and adding the underlying fuzzy edge matrices and do so recursively if needed. The combined FCM tends to better represent domain knowledge as the expert sample size increases if the expert sample approximates a random sample. Many causal models use more restrictive directed acyclic graphs (DAGs) and Bayesian probabilities. DAGs do not model causal feedback because they do not contain closed loops. Combining DAGs also tends to produce cycles and thus tends not to produce a new DAG. Combining DAGs tends to produce a FCM. FCM causal influence is also transitive whereas probabilistic causal influence is not transitive in general. Overall: FCMs trade the numerical precision of probabilistic DAGs for pattern prediction, faster and scalable computation, ease of combination, and richer feedback representation. We show how FCMs can apply to problems of public support for insurgency and terrorism and to US-China conflict relations in Graham Allison's Thucydides-trap framework. The appendix gives the textual justification of the Thucydides-trap FCM. It also extends our earlier theorem [Osoba-Kosko2017] to a more general result that shows the transitive and total causal influence that upstream concept nodes exert on downstream nodes.

Osonde Osoba, Bart Kosko

We present a noise-injected version of the Expectation-Maximization (EM) algorithm: the Noisy Expectation Maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that injected noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. The generalized form of the noisy expectation-maximization (NEM) algorithm allow for arbitrary modes of noise injection including adding and multiplying noise to the data. We demonstrate these noise benefits on EM algorithms for the Gaussian mixture model (GMM) with both additive and multiplicative NEM noise injection. A separate theorem (not presented here) shows that the noise benefit for independent identically distributed additive noise decreases with sample size in mixture models. This theorem implies that the noise benefit is most pronounced if the data is sparse. Injecting blind noise only slowed convergence.