16 papers
Infinitesimal Causality
Sridhar Mahadevan
Interventions can be varied continuously in many causal models. Differentiating a specified smooth intervention protocol produces vector fields on a statistical model, and their Li…
Latent Confounded Causal Discovery via Lie Bracket Geometry
Sridhar Mahadevan
We study causal discovery from observational and interventional regimes when latent variables may affect the measured system. Our first algorithm, BRIDGE (Bracket Residuals for Int…
Causal Density Functions
Sridhar Mahadevan
We study the full density ratio between a specified intervention regime and an observational regime , , under the prerequisite . We call the r…
Learning in Infinitesimal Non-Compositional Sketches
Sridhar Mahadevan
This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor…
Agentic Skill Optimization over Lie Algebroids
Sridhar Mahadevan
Agentic systems increasingly improve themselves by editing skills: prompts, rubrics, plans, tool contracts, examples, validators, and traces. Skill edits are not independent coordi…
Odyssey: Constructing Verifiable Local Truth-Preserving Foundation Models
Sridhar Mahadevan
We introduce a categorical framework called ODYSSEY for constructing verifiable, local truth-preserving foundation models as compositions of foundries: building-block architectural…
PROMETHEUS: Automating Deep Causal Research Integrating Text, Data and Models
Sridhar Mahadevan
Large language models can extract local causal claims from text, but those claims become more useful when organized as persistent, navigable world models rather than as flat summar…
Universal Decision Learners
Sridhar Mahadevan
Many theories of decision making -- planning, reinforcement learning, causal intervention, online learning, and game-theoretic equilibrium -- turn local information into globally c…
Decentralized Causal Discovery using Judo Calculus
Sridhar Mahadevan
We describe a theory and implementation of an intuitionistic decentralized framework for causal discovery using judo calculus, which is formally defined as j-stable causal inferenc…
Intuitionistic -Do-Calculus in Topos Causal Models
Sridhar Mahadevan
In this paper, we generalize Pearl's do-calculus to an Intuitionistic setting called -stable causal inference inside a topos of sheaves. Our framework is an elaboration of the r…
Consciousness as a Functor
Sridhar Mahadevan
We propose a novel theory of consciousness as a functor (CF) that receives and transmits contents from unconscious memory into conscious memory. Our CF framework can be seen as a c…
A Rose by Any Other Name Would Smell as Sweet: Categorical Homotopy Theory for Large Language Models
Sridhar Mahadevan
Natural language is replete with superficially different statements, such as ``Charles Darwin wrote" and ``Charles Darwin is the author of", which carry the same meaning. Large lan…
Topos Causal Models
Sridhar Mahadevan
We propose topos causal models (TCMs), a novel class of causal models that exploit the key properties of a topos category: they are (co)complete, meaning all (co)limits exist, they…
Universal Imitation Games
Sridhar Mahadevan
Alan Turing proposed in 1950 a framework called an imitation game to decide if a machine could think. Using mathematics developed largely after Turing -- category theory -- we anal…
GAIA: Categorical Foundations of Generative AI
Sridhar Mahadevan
In this paper, we propose GAIA, a generative AI architecture based on category theory. GAIA is based on a hierarchical model where modules are organized as a simplicial complex. Ea…
Categoroids: Universal Conditional Independence
Sridhar Mahadevan
Conditional independence has been widely used in AI, causal inference, machine learning, and statistics. We introduce categoroids, an algebraic structure for characterizing univers…