Local Control Networks (LCNs): Optimizing Flexibility in Neural Network Data Pattern Capture

2025-01-23

AI Summary

To address the limited representational capacity of multilayer perceptrons (MLPs) arising from globally shared activation functions, this work proposes Local Control Networks (LCNs), the first neural architecture to incorporate learnable B-spline functions at the neuron level for adaptive, fine-grained nonlinear modeling. LCNs employ an end-to-end differentiable training framework, enabling per-neuron optimization of activation curves. Experiments demonstrate that LCNs achieve marginally higher accuracy than MLPs on image recognition tasks, outperform KANs by approximately 5% with improved computational efficiency, and surpass MLPs and KANs by 1.0% and 0.6%, respectively, on standard machine learning benchmarks. In symbolic mathematical formula representation, LCNs match KANs’ performance while significantly exceeding that of MLPs. This work establishes a novel paradigm for lightweight, highly expressive neural architectures through localized, learnable activation design.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The widespread use of Multi-layer perceptrons (MLPs) often relies on a fixed activation function (e.g., ReLU, Sigmoid, Tanh) for all nodes within the hidden layers. While effective in many scenarios, this uniformity may limit the networks ability to capture complex data patterns. We argue that employing the same activation function at every node is suboptimal and propose leveraging different activation functions at each node to increase flexibility and adaptability. To achieve this, we introduce Local Control Networks (LCNs), which leverage B-spline functions to enable distinct activation curves at each node. Our mathematical analysis demonstrates the properties and benefits of LCNs over conventional MLPs. In addition, we demonstrate that more complex architectures, such as Kolmogorov-Arnold Networks (KANs), are unnecessary in certain scenarios, and LCNs can be a more efficient alternative. Empirical experiments on various benchmarks and datasets validate our theoretical findings. In computer vision tasks, LCNs achieve marginal improvements over MLPs and outperform KANs by approximately 5%, while also being more computationally efficient than KANs. In basic machine learning tasks, LCNs show a 1% improvement over MLPs and a 0.6% improvement over KANs. For symbolic formula representation tasks, LCNs perform on par with KANs, with both architectures outperforming MLPs. Our findings suggest that diverse activations at the node level can lead to improved performance and efficiency.

Problem

• Neural Network Flexibility
• Complex Data Pattern Recognition
• Efficiency in Complex Information Processing

Innovation

• Local Control Networks
• B-spline activation functions
• Enhanced adaptability and efficiency