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Formal Logic Enabled Personalized Federated Learning Through Property Inference

Ziyan An, Taylor T. Johnson, Meiyi Ma

TL;DR

FedSTL addresses the absence of symbolic temporal reasoning in federated learning by automatically inferring temporal logic properties for each client and dynamically clustering clients based on property alignment. It introduces a teacher-student mechanism to correct predictions toward the inferred STL properties and employs a hierarchical update scheme that preserves personalization while enabling cluster-level learning. Across real-world highway traffic and SUMO-based smart-city data, FedSTL achieves substantial improvements in predictive accuracy and property satisfaction, including up to a 54% reduction in MSE and a 100% property-satisfaction rate for teacher corrections. This approach enables more trustworthy, explainable AIoT systems by integrating domain-specific temporal reasoning into privacy-preserving distributed learning.

Abstract

Recent advancements in federated learning (FL) have greatly facilitated the development of decentralized collaborative applications, particularly in the domain of Artificial Intelligence of Things (AIoT). However, a critical aspect missing from the current research landscape is the ability to enable data-driven client models with symbolic reasoning capabilities. Specifically, the inherent heterogeneity of participating client devices poses a significant challenge, as each client exhibits unique logic reasoning properties. Failing to consider these device-specific specifications can result in critical properties being missed in the client predictions, leading to suboptimal performance. In this work, we propose a new training paradigm that leverages temporal logic reasoning to address this issue. Our approach involves enhancing the training process by incorporating mechanically generated logic expressions for each FL client. Additionally, we introduce the concept of aggregation clusters and develop a partitioning algorithm to effectively group clients based on the alignment of their temporal reasoning properties. We evaluate the proposed method on two tasks: a real-world traffic volume prediction task consisting of sensory data from fifteen states and a smart city multi-task prediction utilizing synthetic data. The evaluation results exhibit clear improvements, with performance accuracy improved by up to 54% across all sequential prediction models.

Formal Logic Enabled Personalized Federated Learning Through Property Inference

TL;DR

FedSTL addresses the absence of symbolic temporal reasoning in federated learning by automatically inferring temporal logic properties for each client and dynamically clustering clients based on property alignment. It introduces a teacher-student mechanism to correct predictions toward the inferred STL properties and employs a hierarchical update scheme that preserves personalization while enabling cluster-level learning. Across real-world highway traffic and SUMO-based smart-city data, FedSTL achieves substantial improvements in predictive accuracy and property satisfaction, including up to a 54% reduction in MSE and a 100% property-satisfaction rate for teacher corrections. This approach enables more trustworthy, explainable AIoT systems by integrating domain-specific temporal reasoning into privacy-preserving distributed learning.

Abstract

Recent advancements in federated learning (FL) have greatly facilitated the development of decentralized collaborative applications, particularly in the domain of Artificial Intelligence of Things (AIoT). However, a critical aspect missing from the current research landscape is the ability to enable data-driven client models with symbolic reasoning capabilities. Specifically, the inherent heterogeneity of participating client devices poses a significant challenge, as each client exhibits unique logic reasoning properties. Failing to consider these device-specific specifications can result in critical properties being missed in the client predictions, leading to suboptimal performance. In this work, we propose a new training paradigm that leverages temporal logic reasoning to address this issue. Our approach involves enhancing the training process by incorporating mechanically generated logic expressions for each FL client. Additionally, we introduce the concept of aggregation clusters and develop a partitioning algorithm to effectively group clients based on the alignment of their temporal reasoning properties. We evaluate the proposed method on two tasks: a real-world traffic volume prediction task consisting of sensory data from fifteen states and a smart city multi-task prediction utilizing synthetic data. The evaluation results exhibit clear improvements, with performance accuracy improved by up to 54% across all sequential prediction models.
Paper Structure (41 sections, 4 theorems, 13 equations, 3 figures, 5 tables, 2 algorithms)

This paper contains 41 sections, 4 theorems, 13 equations, 3 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Notations
  3. Problem Formulation
  4. Temporal Reasoning Property Inference
  5. Temporal Logic Specification
  6. Logic Inference Through Observed Data
  7. Logic inference
  8. Logic-Enabled Federated Learning
  9. Enhancing STL-based Logic Reasoning Property
  10. Client model prediction correction
  11. Dynamic Temporal Logic-Based Clustering
  12. Hierarchical Logic Reasoning Strengthening
  13. Evaluation
  14. Experiment Setup
  15. Baseline Methods
  16. ...and 26 more sections

Key Result

Theorem 1

For any positive number $\lambda >0$, objective function $F_i(\theta_i) = \mathcal{L} (\mathcal{Y}, \hat{\mathcal{Y}}) + \lambda \, \mathcal{L}_{p} (\varphi_i, \hat{\mathcal{Y}})$ is strongly convex if the following conditions hold.

Figures (3)

  • Figure 1: FedSTL consists of $\mathcal{S}$ cluster devices, and $\mathcal{C}$ client devices. During each communication round, client models are partitioned into clusters. Then, inferred temporal reasoning properties are enhanced on predictive models.
  • Figure 2: The training workflow for one iteration in the framework involves the inference of client logic properties $\{ \varphi_i\}$ and cluster logic properties $\{ \varphi_j\}$. Based on the alignment of these properties, clients are partitioned into clusters. Then, our framework enhances personalized FL by incorporating both client and cluster reasoning properties during training.
  • Figure 3: Comparison on MSE by enhancing intra-task reasoning properties. A higher position on the y-axis indicates a smaller MSE value.

Theorems & Definitions (13)

  • Definition 1: STL syntax
  • Definition 2: STL property inference
  • Example 1: An example of STL inference
  • Definition 3: STL property inference with a tight bound
  • Theorem 1
  • Lemma 1
  • proof
  • proof
  • Theorem 2: Convergence of stochastic gradient descentshamir2013stochastic
  • Lemma 2
  • ...and 3 more