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Lattice-Based Pruning in Recurrent Neural Networks via Poset Modeling

Rakesh Sengupta

TL;DR

This work addresses the computational burden of recurrent neural networks by introducing a poset-based lattice framework for pruning. By modeling RNNs as dependency lattices and identifying meet-irreducible elements (and centrality), it guides pruning while preserving essential connectivity, using both binary and continuous adjacency representations. The authors provide thorough complexity analyses for hierarchical multilayer RNNs and validate the approach on MNIST with LSTM, revealing a trade-off: binary adjacency yields ~50% sparsity with >98% accuracy, while continuous adjacency achieves near-total sparsity with noticeable accuracy loss. The framework offers a rigorous, scalable path to efficient, hierarchical RNNs and has potential implications for computational neuroscience and machine learning applications requiring real-time performance.

Abstract

Recurrent neural networks (RNNs) are central to sequence modeling tasks, yet their high computational complexity poses challenges for scalability and real-time deployment. Traditional pruning techniques, predominantly based on weight magnitudes, often overlook the intrinsic structural properties of these networks. We introduce a novel framework that models RNNs as partially ordered sets (posets) and constructs corresponding dependency lattices. By identifying meet irreducible neurons, our lattice-based pruning algorithm selectively retains critical connections while eliminating redundant ones. The method is implemented using both binary and continuous-valued adjacency matrices to capture different aspects of network connectivity. Evaluated on the MNIST dataset, our approach exhibits a clear trade-off between sparsity and classification accuracy. Moderate pruning maintains accuracy above 98%, while aggressive pruning achieves higher sparsity with only a modest performance decline. Unlike conventional magnitude-based pruning, our method leverages the structural organization of RNNs, resulting in more effective preservation of functional connectivity and improved efficiency in multilayer networks with top-down feedback. The proposed lattice-based pruning framework offers a rigorous and scalable approach for reducing RNN complexity while sustaining robust performance, paving the way for more efficient hierarchical models in both machine learning and computational neuroscience.

Lattice-Based Pruning in Recurrent Neural Networks via Poset Modeling

TL;DR

This work addresses the computational burden of recurrent neural networks by introducing a poset-based lattice framework for pruning. By modeling RNNs as dependency lattices and identifying meet-irreducible elements (and centrality), it guides pruning while preserving essential connectivity, using both binary and continuous adjacency representations. The authors provide thorough complexity analyses for hierarchical multilayer RNNs and validate the approach on MNIST with LSTM, revealing a trade-off: binary adjacency yields ~50% sparsity with >98% accuracy, while continuous adjacency achieves near-total sparsity with noticeable accuracy loss. The framework offers a rigorous, scalable path to efficient, hierarchical RNNs and has potential implications for computational neuroscience and machine learning applications requiring real-time performance.

Abstract

Recurrent neural networks (RNNs) are central to sequence modeling tasks, yet their high computational complexity poses challenges for scalability and real-time deployment. Traditional pruning techniques, predominantly based on weight magnitudes, often overlook the intrinsic structural properties of these networks. We introduce a novel framework that models RNNs as partially ordered sets (posets) and constructs corresponding dependency lattices. By identifying meet irreducible neurons, our lattice-based pruning algorithm selectively retains critical connections while eliminating redundant ones. The method is implemented using both binary and continuous-valued adjacency matrices to capture different aspects of network connectivity. Evaluated on the MNIST dataset, our approach exhibits a clear trade-off between sparsity and classification accuracy. Moderate pruning maintains accuracy above 98%, while aggressive pruning achieves higher sparsity with only a modest performance decline. Unlike conventional magnitude-based pruning, our method leverages the structural organization of RNNs, resulting in more effective preservation of functional connectivity and improved efficiency in multilayer networks with top-down feedback. The proposed lattice-based pruning framework offers a rigorous and scalable approach for reducing RNN complexity while sustaining robust performance, paving the way for more efficient hierarchical models in both machine learning and computational neuroscience.

Paper Structure

This paper contains 24 sections, 9 theorems, 33 equations, 1 figure, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Methods
  4. Key Lattice-Theoretic Tools
  5. Pruning and Scaling Strategy
  6. Example: Toy RNN Lattice
  7. Complexity Analysis for Hierarchical Lattice-Based Pruning in Multilayer RNNs
  8. Pruning Efficiency
  9. Additional Complexity Analyses
  10. Graph-Theoretic Analysis
  11. Information-Theoretic Analysis
  12. Example: Cohen–Grossberg Type RNNs.
  13. Dynamical Systems Analysis
  14. Example: Cohen–Grossberg RNNs.
  15. Continuity of the Lyapunov Exponent.
  16. ...and 9 more sections

Key Result

Theorem 3.1

Let $\mathcal{R}$ be an RNN that is either a Cohen–Grossberg network or an LSTM, with the dependency relation $\preceq$ defined as above. Then the dependency structure of $\mathcal{R}$ forms a modular lattice. In particular, for any $a, b, c \in L$ with $a \preceq c$, the following modular law holds

Figures (1)

  • Figure 1: Dependency lattice of a toy RNN with neurons $\{a, b, c\}$. The meet-irreducible elements $a$ and $b$ (in blue) are critical, while $c = a \vee b$ represents the output neuron.

Theorems & Definitions (23)

  • Definition 3.1: RNN Poset
  • Definition 3.2: Dependency Lattice
  • Theorem 3.1: Lattice based Representation for Cohen–Grossberg and LSTM networks
  • proof
  • Definition 3.3: Meet-Irreducible
  • Theorem 3.2: Irreducible Pruning Stability
  • proof
  • Lemma 3.1: Bottleneck Identification
  • proof
  • Theorem 3.3: Pruning Efficiency
  • ...and 13 more