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Reactive Knowledge Representation and Asynchronous Reasoning

Simon Kohaut, Benedict Flade, Julian Eggert, Kristian Kersting, Devendra Singh Dhami

TL;DR

This work addresses the prohibitive cost of continual exact inference in dynamic, asynchronous environments by introducing Resin, a declarative asynchronous probabilistic programming language, and Reactive Circuits (RCs), an adaptive execution framework built on Algebraic Circuits. RCs track the Frequency of Change (FoC) of input signals and restructure computations online, memoizing stable sub-results and re-evaluating only the parts affected by new information. The approach yields orders-of-magnitude speedups in high-fidelity drone swarm simulations while preserving exact semantics, albeit with a memory-speed trade-off. By partitioning computation according to FoC and leveraging lift/drop restructurings, Resin+RC enables real-time, trustworthy autonomous reasoning in complex, dynamic settings, with open-source implementation available.

Abstract

Exact inference in complex probabilistic models often incurs prohibitive computational costs. This challenge is particularly acute for autonomous agents in dynamic environments that require frequent, real-time belief updates. Existing methods are often inefficient for ongoing reasoning, as they re-evaluate the entire model upon any change, failing to exploit that real-world information streams have heterogeneous update rates. To address this, we approach the problem from a reactive, asynchronous, probabilistic reasoning perspective. We first introduce Resin (Reactive Signal Inference), a probabilistic programming language that merges probabilistic logic with reactive programming. Furthermore, to provide efficient and exact semantics for Resin, we propose Reactive Circuits (RCs). Formulated as a meta-structure over Algebraic Circuits and asynchronous data streams, RCs are time-dynamic Directed Acyclic Graphs that autonomously adapt themselves based on the volatility of input signals. In high-fidelity drone swarm simulations, our approach achieves several orders of magnitude of speedup over frequency-agnostic inference. We demonstrate that RCs' structural adaptations successfully capture environmental dynamics, significantly reducing latency and facilitating reactive real-time reasoning. By partitioning computations based on the estimated Frequency of Change in the asynchronous inputs, large inference tasks can be decomposed into individually memoized sub-problems. This ensures that only the specific components of a model affected by new information are re-evaluated, drastically reducing redundant computation in streaming contexts.

Reactive Knowledge Representation and Asynchronous Reasoning

TL;DR

This work addresses the prohibitive cost of continual exact inference in dynamic, asynchronous environments by introducing Resin, a declarative asynchronous probabilistic programming language, and Reactive Circuits (RCs), an adaptive execution framework built on Algebraic Circuits. RCs track the Frequency of Change (FoC) of input signals and restructure computations online, memoizing stable sub-results and re-evaluating only the parts affected by new information. The approach yields orders-of-magnitude speedups in high-fidelity drone swarm simulations while preserving exact semantics, albeit with a memory-speed trade-off. By partitioning computation according to FoC and leveraging lift/drop restructurings, Resin+RC enables real-time, trustworthy autonomous reasoning in complex, dynamic settings, with open-source implementation available.

Abstract

Exact inference in complex probabilistic models often incurs prohibitive computational costs. This challenge is particularly acute for autonomous agents in dynamic environments that require frequent, real-time belief updates. Existing methods are often inefficient for ongoing reasoning, as they re-evaluate the entire model upon any change, failing to exploit that real-world information streams have heterogeneous update rates. To address this, we approach the problem from a reactive, asynchronous, probabilistic reasoning perspective. We first introduce Resin (Reactive Signal Inference), a probabilistic programming language that merges probabilistic logic with reactive programming. Furthermore, to provide efficient and exact semantics for Resin, we propose Reactive Circuits (RCs). Formulated as a meta-structure over Algebraic Circuits and asynchronous data streams, RCs are time-dynamic Directed Acyclic Graphs that autonomously adapt themselves based on the volatility of input signals. In high-fidelity drone swarm simulations, our approach achieves several orders of magnitude of speedup over frequency-agnostic inference. We demonstrate that RCs' structural adaptations successfully capture environmental dynamics, significantly reducing latency and facilitating reactive real-time reasoning. By partitioning computations based on the estimated Frequency of Change in the asynchronous inputs, large inference tasks can be decomposed into individually memoized sub-problems. This ensures that only the specific components of a model affected by new information are re-evaluated, drastically reducing redundant computation in streaming contexts.
Paper Structure (21 sections, 3 theorems, 8 equations, 9 figures, 2 algorithms)

This paper contains 21 sections, 3 theorems, 8 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. The Resin Programming Language
  3. Asynchronous Probabilistic Logic
  4. Data Model
  5. Compiling Resin
  6. Reactive Circuits
  7. Frequencies of Change
  8. Online Circuit Adaptation
  9. Reactive Circuit Evaluation
  10. Example
  11. Experiments
  12. Tracking Frequencies of Change
  13. Frequency Partitioning of Reactive Circuits
  14. Rapid and Reactive Safety Assertions in Advanced Air Mobility
  15. Related Work
  16. ...and 6 more sections

Key Result

lemma 1

Let $root(\mathcal{RC})(t)$ be the value of the root of the RC's DAG at time $t$. Then, the circuit adaptations lift and drop conserve its value, i.e., $\forall s \in \mathcal{S}: root(lift(\mathcal{RC}, \{s\}))(t) = root(drop(\mathcal{RC}, \{s\}))(t) = root(\mathcal{RC})(t)$.

Figures (9)

  • Figure 1: The Asynchronous Reasoning architecture: For each target of a Resin program, the compiler parses the program into a constrained Answer Set Program and generates the respective stable models. This causes an initial Reactive Circuit (RC) to be created and connected to datastreams, which is then, over time, adapted to reflect the volatility of its inputs.
  • Figure 2: Reactive Circuits enable Asynchronous Reasoning: After compiling a Resin program (a) into an initial Reactive Circuit, its structure is adapted over time to facilitate an optimized inference scheme (b) by dividing the original formula into memorized sub-formulas according to the volatility of the respective input signals (c). Here, the $speed$, $clearance$, and $rain$ signals are assumed to have a descending volatility, thereby being assigned to separate depths of the RC's DAG.
  • Figure 3: Asynchronous Inference in Resin via Reactive Circuits: For each inference target of a Resin program, a Reactive Circuit (RC) is initialized. Over time, the RC's structure is adapted to facilitate memorized intermediate results (green) and offload sub-formulas of the sum-product problem (yellow), enabling efficient updates based on a partitioning of the frequency of new values arriving through the source nodes (blue).
  • Figure 4: An example Resin program.
  • Figure 5: The result of compiling Listing \ref{['listing:example_resin_program']} for target $d$.
  • ...and 4 more figures

Theorems & Definitions (11)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • definition 5
  • definition 6
  • definition 7
  • definition 8
  • lemma 1
  • lemma 2
  • ...and 1 more