[Paper] Multi-Column RBF Neural Network Using Adaptive and Non-Adaptive Particle Swarm Optimization

Source: arXiv - 2606.05150v1

Overview

Ammar Hoori and Yuichi Motai present a fresh take on training Radial Basis Function Neural Networks (RBFNs) by marrying them with Particle Swarm Optimization (PSO). Their multi‑column architecture splits a large dataset into spatial chunks, lets each chunk train its own small RBFN with either classic PSO or its adaptive variant (APSO), and then stitches the specialist models together at inference time. The result is a faster, more accurate, and more scalable alternative to traditional gradient‑based RBFN training methods.

Key Contributions

• Multi‑column RBFN framework for PSO: Introduces MC‑PSO (standard PSO) and MC‑APSO (adaptive PSO) that train several lightweight RBFNs in parallel on disjoint data subsets.
• Specialist‑expert model selection: At test time, only the RBFNs whose training region contains the query point are consulted, reducing inference cost.
• Scalability improvements: Demonstrates that the parallel, column‑wise approach mitigates the kernel‑computation bottleneck that plagues monolithic RBFNs on large datasets.
• Comprehensive empirical evaluation: Benchmarks on multiple public datasets show MC‑PSO/MC‑APSO outperform classic ErrCor, vanilla PSO, APSO, and the prior multi‑column RBFN (MCRN) in both accuracy/recall and training/testing speed.
• Open‑source‑ready design: The algorithms are described in a way that can be directly implemented with existing PSO libraries and standard RBFN toolkits.

Methodology

1. Data partitioning – The full training set is divided into spatial clusters (e.g., via k‑means or a simple grid). Each cluster becomes the training domain for one “column.”
2. Independent RBFN training – For each column, a small RBFN is instantiated. Its parameters (centers, spreads, output weights) are optimized by a swarm of particles:
   • PSO updates particle velocities using fixed inertia, cognitive, and social coefficients.
   • APSO dynamically tunes these coefficients based on swarm performance, accelerating convergence.
3. Specialist selection at inference – When a new sample arrives, the algorithm identifies which columns’ training regions contain the sample’s nearest neighbors. Only those columns generate outputs, which are then aggregated (e.g., weighted average) to produce the final prediction.
4. Evaluation protocol – The authors run repeated cross‑validation on benchmark classification/regression datasets, measuring classification accuracy, recall, training time, and test latency.

The approach is deliberately kept modular: swapping the clustering method, the PSO variant, or the aggregation rule can be done without redesigning the whole system.

Results & Findings

• Accuracy/Recall: Both MC‑PSO and MC‑APSO beat every baseline, with MC‑APSO leading the pack.
• Speed: Parallel training of small columns reduces overall kernel calculations, cutting both training and inference times by roughly half compared with the monolithic approaches.
• Robustness: The adaptive coefficient scheme in APSO yields more stable convergence across datasets of varying size and dimensionality.

Practical Implications

• Edge & IoT deployments: The column‑wise design enables a developer to distribute tiny RBFN specialists across constrained devices, each handling a local data slice, while the central aggregator only queries the relevant nodes.
• Fast prototyping for tabular data: Data scientists can replace heavyweight gradient‑descent pipelines with MC‑APSO to get quicker turnaround on large, noisy datasets without sacrificing predictive power.
• Hybrid AI systems: The method can be combined with other ensemble techniques (e.g., stacking) because each column is a self‑contained model with a clear API.
• Scalable cloud services: In a micro‑service architecture, each column can be a separate container that scales horizontally; PSO’s population‑based search also maps nicely to distributed compute frameworks (Spark, Ray).
• Interpretability boost: Since each column is trained on a localized region, developers can inspect the learned RBF centers to understand region‑specific patterns—a useful feature for compliance‑heavy industries.

Limitations & Future Work

• Clustering dependency: The quality of the spatial partition heavily influences performance; poorly chosen clusters can lead to under‑utilized columns.
• Memory overhead: Maintaining multiple RBFNs increases model footprint, which may be a concern on very low‑memory devices.
• Parameter tuning: While APSO reduces manual tuning, the swarm size and number of columns still require empirical selection.
• Future directions suggested by the authors include: exploring adaptive clustering that evolves during training, integrating deep feature extractors before the RBF layer, and extending the framework to regression‑heavy domains such as time‑series forecasting.

Authors

• Ammar Hoori
• Yuichi Motai

Paper Information

• arXiv ID: 2606.05150v1
• Categories: cs.NE, cs.AI
• Published: June 3, 2026
• PDF: Download PDF