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Exploring Learnability in Memory-Augmented Recurrent Neural Networks: Precision, Stability, and Empirical Insights

Shrabon Das, Ankur Mali

TL;DR

Theoretical analysis suggests that freezing memory stabilizes temporal dependencies, leading to robust convergence, and the need for stable memory designs and long-sequence evaluations to understand RNNs true learnability limits is stressed.

Abstract

This study explores the learnability of memory-less and memory-augmented RNNs, which are theoretically equivalent to Pushdown Automata. Empirical results show that these models often fail to generalize on longer sequences, relying more on precision than mastering symbolic grammar. Experiments on fully trained and component-frozen models reveal that freezing the memory component significantly improves performance, achieving state-of-the-art results on the Penn Treebank dataset (test perplexity reduced from 123.5 to 120.5). Models with frozen memory retained up to 90% of initial performance on longer sequences, compared to a 60% drop in standard models. Theoretical analysis suggests that freezing memory stabilizes temporal dependencies, leading to robust convergence. These findings stress the need for stable memory designs and long-sequence evaluations to understand RNNs true learnability limits.

Exploring Learnability in Memory-Augmented Recurrent Neural Networks: Precision, Stability, and Empirical Insights

TL;DR

Theoretical analysis suggests that freezing memory stabilizes temporal dependencies, leading to robust convergence, and the need for stable memory designs and long-sequence evaluations to understand RNNs true learnability limits is stressed.

Abstract

This study explores the learnability of memory-less and memory-augmented RNNs, which are theoretically equivalent to Pushdown Automata. Empirical results show that these models often fail to generalize on longer sequences, relying more on precision than mastering symbolic grammar. Experiments on fully trained and component-frozen models reveal that freezing the memory component significantly improves performance, achieving state-of-the-art results on the Penn Treebank dataset (test perplexity reduced from 123.5 to 120.5). Models with frozen memory retained up to 90% of initial performance on longer sequences, compared to a 60% drop in standard models. Theoretical analysis suggests that freezing memory stabilizes temporal dependencies, leading to robust convergence. These findings stress the need for stable memory designs and long-sequence evaluations to understand RNNs true learnability limits.
Paper Structure (16 sections, 5 theorems, 35 equations, 3 figures, 7 tables)

This paper contains 16 sections, 5 theorems, 35 equations, 3 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Methodology
  4. Theoretical Analysis of Stability of Memory Augmented Neural Network
  5. Experimental Setup
  6. Discussion and Conclusion
  7. Conclusion.
  8. Appendix A: Related Work
  9. Appendix B: Additional Results
  10. Appendix C: Evaluating Stability in Practice
  11. Error Bounds Across Sequence Lengths
  12. Consistency of Error Across Sequence Lengths
  13. Performance Degradation Over Long Sequences
  14. Generalization to Unseen Sequence Patterns
  15. Analyzing Error Growth
  16. ...and 1 more sections

Key Result

Theorem 3.3

Let $L$ be a formal language recognized by a Pushdown Automaton (PDA) $M = (Q, \Sigma, \Gamma, \delta, q_0, Z_0, F)$. Consider a Recurrent Neural Network (RNN) $f$ augmented with a stack that models the PDA $M$. The RNN $f$ is said to be stable if it satisfies the following conditions: The RNN $f$ is unstable if any of the conditions above are violated.

Figures (3)

  • Figure 1: Performance of various models using 4 configuration (none = fully trained model, m = only memory is trained, c = only controller is trained and cm = controller and memory are frozen and only classifier is trainable. We report performance on language modeling task and report perplexity (PPL) on Penn tree bank (PTB) dataset.
  • Figure 2: Performance of top 3 models on test sets across 7 context free languages, when models are fully trained (none) and when only memory (m) is frozen.
  • Figure 3: Performance of top 2 memory-augmented models on test sets across 7 context free languages, when models are fully trained (none) and when only memory (m) is frozen.

Theorems & Definitions (10)

  • Definition 3.1: Stability
  • Definition 3.2: Stability of a Pushdown Automaton (PDA) Model
  • Theorem 3.3: Stability of Stack-Augmented RNNs
  • proof
  • Theorem 3.4
  • proof
  • Theorem 3.5: Learnability of Gradient-Descent Trained Systems
  • proof
  • Theorem 3.6: Frozen RNN with Trainable Memory Outperforms an Unstable Fully-Trained Model
  • Theorem 3.7: Error Bounds of an Unstable System