Reactive Inference Composition

• Reactive Inference Composition is a framework that performs continual online Bayesian inference over structured latent variables to synthesize behavior and control without test-time parameter updates.
• It leverages modular components, hypothesis tracking, and compositional operators to rapidly recombine learned skills and adjust to dynamic, partially observable settings.
• The approach underpins advances in meta-learning, robot control, and task planning by integrating probabilistic models with recursive inference techniques.

Reactive Inference Composition is a unifying framework for the data-efficient, modular, and adaptive synthesis of behavior and control in systems that operate over time in dynamic, partially observable, or compositional environments. It generalizes classical approaches to synthesis, control, and meta-learning by emphasizing continual, online inference over structured latent representations—whether sub-tasks, skills, modules, entity-role bindings, or symbolic plans—while integrating new evidence in a streaming, feedback-driven manner. This mechanism enables a system to compose previously learned components, recombine them under learned transition rules or dependencies, and replan in response to contingencies or unexpected stimuli, all without extensive parameter adaptation at test time. Theoretical instantiations are found across meta-learning (Bakermans et al., 2 Oct 2025), task and motion planning (Zhang et al., 2023), compositional synthesis (Finkbeiner et al., 2020), probabilistic programming (Baudart et al., 2019), sequential decision making (Ren et al., 2020), and hierarchical robot control (Hansel et al., 2022).

1. Core Principles and Formalizations

At the heart of Reactive Inference Composition lies the correspondence between compositional structure in a domain and the probabilistic inference of latent variables that capture this structure. Systems are typically modeled with explicit latent variables that represent modular components or context identities (such as task segments, sub-tasks, modular neural computations, or skill indices), and whose transitions or activations are governed by learned or inferred rules.

• Probabilistic Generative Models: Formalizations represent a sequence of system states, observations, and actions with latent variables for compositional structure (e.g., sequence of modules $z_{1:T}$ (Bakermans et al., 2 Oct 2025), local/global context variables $c^l_{1:T}, c_g$ (Ren et al., 2020), policy weights $\beta_{t:t+h}$ (Hansel et al., 2022)).
• Inference as Filtering: Solving a new task amounts to conducting online Bayesian filtering or variational inference over latent structure, conditioned on streaming observations or feedback.
• No Test-Time Parameter Update: Post-training, system behavior adapts through hypothesis management and probabilistic selection, not gradient-based weight changes.
• Compositionality: Structure is defined compositionally—by recombining modules, sub-goals, policies, or entity-role pairs—enabling radical generalization to new tasks (Kurth-Nelson et al., 2022).

A generic schematic for compositional inference is: $$p(\text{Latents},\,\text{Obs} \mid \text{Input}; \Lambda) = p(\text{Latents}_1) \prod_{t=2}^{T} p(\text{Latents}_t \mid \cdot)\; \prod_{t=1}^{T} p(\text{Obs}_t \mid \text{Latents}_t, \cdot)$$ where the nature of the latent variables and transition dynamics depends on the system domain.

2. Algorithms and Inference Mechanisms

The methods for reactive inference composition are unified by their explicit hypothesis tracking and online adaptation, but differ in their realizations:

• Particle Filtering: For modular meta-learning, latent module sequences are filtered via bootstrap or particle filtering with likelihood weighting, resampling, and MAP decoding, enabling one-shot adaptation to compositional tasks (Bakermans et al., 2 Oct 2025).
• Recursive Variational Inference: In online compositional RL, e.g., OCEAN, the global context is inferred across episodes or task windows, while a local latent (sub-task identity) is recursively inferred at every time step by filtering through an RNN and updating posterior beliefs (Ren et al., 2020).
• Policy Blending via Inference: In hierarchical control, such as HiPBI, multiple reactive expert policies are blended into a weighted product of experts (PoE) policy, with weights inferred online by optimizing a variational posterior over weight sequences via improved cross-entropy method (iCEM) sampling, biasing toward likely goal achievement (Hansel et al., 2022).
• Hybrid Symbolic-Probabilistic Planning: For robust robotic task and motion planning, Active Inference planners generate symbolic plans and alternative actions via free energy minimization, while low-level Model Predictive Path Integral controllers blend task-specific cost functions, dynamically fusing and re-weighting strategies in real time (Zhang et al., 2023).

Conceptually, the system maintains a set of hypotheses over latent structure (e.g., module sequences, policy blends, or plan alternatives), propagates and updates them as new evidence arrives, and prunes inconsistent ones, all in a streaming manner.

3. Structural Models and Compositional Operators

Reactive Inference Composition is rooted in explicit structural models:

• Mixture-of-Experts with Structured Gating: Modular neural architectures employ multiple RNN modules (skills), with a separate gating network encoding allowed transitions. The system executes by selecting, via inference, which module is active at each time and combining their outputs appropriately (Bakermans et al., 2 Oct 2025).
• Context Hierarchies: Global-local latent architectures factor context into a slowly evolving global task identity and rapidly switching local sub-task, realized as a hierarchically coupled process (global-episodic, local-timestep) (Ren et al., 2020).
• Entity-Role Binding: Neural and symbolic representations of replay, or "compositional computation," sequence sampled bindings of roles to entities, generating new relational hypotheses online (for instance, transitive inferences) (Kurth-Nelson et al., 2022).
• Choice Operators: In the semantics of reactive systems, operators such as sequential composition, demonic (greatest lower bound) and angelic (least upper bound) choice, and refinement orderings allow the formal composition and verification of reactive probabilistic stream functions (Preoteasa et al., 2014, Baudart et al., 2019).

These structural models enable the tracking of complex, history-dependent dependencies and facilitate reasoning and synthesis at multiple levels of granularity.

4. Applications, Domains, and Evaluation Metrics

Reactive Inference Composition is validated across diverse domains:

Domain	Structural Latents	Inference Strategy	Notable Metrics	Reference
Meta-learning	Module sequences	Particle filtering	NLL, MSE, module alignment	(Bakermans et al., 2 Oct 2025)
Reinforcement Learning	Global/local context	Recursive variational	Adaptation speed, final return	(Ren et al., 2020)
Robot Control	PoE policy weights	CEM/ELBO optim.	Collision avoidance, trajectory cost	(Hansel et al., 2022)
Task/Motion Planning	Symbolic plan hypotheses	Active Inference + MPPI	Position/orientation error, time	(Zhang et al., 2023)
Program Synthesis	Dependency graphs	Incremental synthesis	Synthesis time, scalability	(Finkbeiner et al., 2020)
Probabilistic Programming	Stream transformers	Streaming/delayed infer	Memory usage, exactness	(Baudart et al., 2019)
Compositional Replay	Role-entity sequences	Sampling/sequencing	N/A (theoretical, neuro-cognitive)	(Kurth-Nelson et al., 2022)

Performance is systematically assessed using log-marginals, output MSE, transition alignment, task adaptation speed, control accuracy, and scalability to complex or multi-stage tasks. Notably, fully modular, inference-driven approaches achieve one-shot adaptation, dramatic reductions in required planning code, and robustness to environmental change (e.g., 88% reduction in behavior tree nodes, robust recovery to perturbations, evidence-efficient task identification) (Bakermans et al., 2 Oct 2025, Pezzato et al., 2020, Zhang et al., 2023).

5. Connections to Synthesis and Denotational Semantics

Reactive Inference Composition draws from and extends compositional synthesis frameworks:

• Dependency-based Compositional Synthesis: System decomposition via semantic and syntactic dependency analysis enables the construction of dominant strategies incrementally and compositionally. Each component's strategy is synthesized assuming already-constructed strategies for dependencies, following the partial order induced by a dependency graph (Finkbeiner et al., 2020).
• Denotational Models: Monotonic property transformers (MPTs) facilitate formal reasoning about the composition, refinement, and correctness of reactive systems. Operators for sequential composition, demonic/angelic choice, and hiding enable the algebraic assembly of complex behaviors from primitive components (Preoteasa et al., 2014).
• Probabilistic Programming Semantics: Streaming probabilistic programming with synchronous semantics (e.g., ProbZelus) defines co-iterative, measure-theoretic composition of probabilistic stream functions, supporting real-time inference and control in bounded memory (Baudart et al., 2019).

These approaches guarantee that inference-based composition preserves desired properties (correctness, safety, responsiveness) by leveraging monotonicity, soundness, and compositionality of the underlying operators.

6. Theoretical Implications, Neuroscientific Connections, and AI Relevance

The principle of reactive inference composition provides both a theoretical lens and an algorithmic prescription applicable to artificial and biological systems:

• Neural Basis of Compositional Computation: The hippocampal replay mechanism is hypothesized to execute compositional inference by dynamically binding entities to roles and sequentially assembling new knowledge structures—enabling radical one-shot generalization hallmarking human cognition (Kurth-Nelson et al., 2022).
• AI System Design: Such architectures motivate the construction of AI agents capable of radical generalization and efficient reuse via modular, inference-based composition rather than monolithic adaptation. “Replay engines” can be implemented offline to drive search over role bindings, prune candidate hypotheses, and drive generative consolidation—a positive-feedback mechanism for compositional learning (Kurth-Nelson et al., 2022, Bakermans et al., 2 Oct 2025).
• Bridging Symbolic and Subsymbolic Reasoning: Hybrid planners combine symbolic (BT, task plans) with probabilistic inference (active inference leaves, policy blending), yielding systems that maintain explicable structure yet respond fluidly to uncertainty and contingency (Zhang et al., 2023, Pezzato et al., 2020, Hansel et al., 2022).

In summary, Reactive Inference Composition establishes a foundational paradigm for constructing systems that effectively exploit modular structure and dynamically adapt to ongoing experience through principled, online, hypothesis-driven inference. The breadth of formal, algorithmic, and practical realizations attests to its significance across machine learning, control, synthesis, neuroscience, and beyond.