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Logarithmic Memory Networks (LMNs): Efficient Long-Range Sequence Modeling for Resource-Constrained Environments

Mohamed A. Taha

TL;DR

The paper introduces Logarithmic Memory Networks (LMNs) to tackle long-range sequence modeling in resource-constrained environments by replacing quadratic attention with a hierarchical logarithmic memory and a single-vector attention mechanism. The approach combines embedding, parallelizable memory construction, a summarizer for hierarchical summaries with implicit relative positioning, and a dual-mode operation (parallel training and sequential inference) to balance throughput and memory efficiency. Empirical results show competitive parameter efficiency and reduced memory/computation compared with GPT-2, with clear advantages on long sequences and mobile/edge contexts, supported by PyTorch implementations and benchmarking notebooks. Overall, LMNs offer a scalable, practical solution for long-range dependencies, enabling efficient deployments without substantial performance loss and opening avenues for further optimization and extension in memory management frameworks.

Abstract

Long-range sequence modeling is a crucial aspect of natural language processing and time series analysis. However, traditional models like Recurrent Neural Networks (RNNs) and Transformers suffer from computational and memory inefficiencies, especially when dealing with long sequences. This paper introduces Logarithmic Memory Networks (LMNs), a novel architecture that leverages a hierarchical logarithmic tree structure to efficiently store and retrieve past information. LMNs dynamically summarize historical context, significantly reducing the memory footprint and computational complexity of attention mechanisms from O(n2) to O(log(n)). The model employs a single-vector, targeted attention mechanism to access stored information, and the memory block construction worker (summarizer) layer operates in two modes: a parallel execution mode during training for efficient processing of hierarchical tree structures and a sequential execution mode during inference, which acts as a memory management system. It also implicitly encodes positional information, eliminating the need for explicit positional encodings. These features make LMNs a robust and scalable solution for processing long-range sequences in resource-constrained environments, offering practical improvements in efficiency and scalability. The code is publicly available under the MIT License on GitHub: https://github.com/AhmedBoin/LogarithmicMemory.

Logarithmic Memory Networks (LMNs): Efficient Long-Range Sequence Modeling for Resource-Constrained Environments

TL;DR

The paper introduces Logarithmic Memory Networks (LMNs) to tackle long-range sequence modeling in resource-constrained environments by replacing quadratic attention with a hierarchical logarithmic memory and a single-vector attention mechanism. The approach combines embedding, parallelizable memory construction, a summarizer for hierarchical summaries with implicit relative positioning, and a dual-mode operation (parallel training and sequential inference) to balance throughput and memory efficiency. Empirical results show competitive parameter efficiency and reduced memory/computation compared with GPT-2, with clear advantages on long sequences and mobile/edge contexts, supported by PyTorch implementations and benchmarking notebooks. Overall, LMNs offer a scalable, practical solution for long-range dependencies, enabling efficient deployments without substantial performance loss and opening avenues for further optimization and extension in memory management frameworks.

Abstract

Long-range sequence modeling is a crucial aspect of natural language processing and time series analysis. However, traditional models like Recurrent Neural Networks (RNNs) and Transformers suffer from computational and memory inefficiencies, especially when dealing with long sequences. This paper introduces Logarithmic Memory Networks (LMNs), a novel architecture that leverages a hierarchical logarithmic tree structure to efficiently store and retrieve past information. LMNs dynamically summarize historical context, significantly reducing the memory footprint and computational complexity of attention mechanisms from O(n2) to O(log(n)). The model employs a single-vector, targeted attention mechanism to access stored information, and the memory block construction worker (summarizer) layer operates in two modes: a parallel execution mode during training for efficient processing of hierarchical tree structures and a sequential execution mode during inference, which acts as a memory management system. It also implicitly encodes positional information, eliminating the need for explicit positional encodings. These features make LMNs a robust and scalable solution for processing long-range sequences in resource-constrained environments, offering practical improvements in efficiency and scalability. The code is publicly available under the MIT License on GitHub: https://github.com/AhmedBoin/LogarithmicMemory.
Paper Structure (30 sections, 2 equations, 10 figures, 1 table)

This paper contains 30 sections, 2 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Recurrent Neural Networks and Their Limitations
  4. Memory-Augmented Networks
  5. Transformers and Their Impact
  6. State Space Models (SSMs)
  7. Methodology (LMNs)
  8. Architecture Overview
  9. Memory Construction
  10. Summarizer Layer
  11. Parallel Memory Construction
  12. Sequential Memory Construction
  13. Single Vector Attention
  14. Multi-Bank Memory
  15. Path-Through Positional Encoding
  16. ...and 15 more sections

Figures (10)

  • Figure 1: Logarithmic Memory and its capability to train as a transformers and inference as a recurrent
  • Figure 2: Visualization of parallel memory construction. The nodes are summarized from the bottom up. Nodes from different levels are combined to form the final output.
  • Figure 3: Visualization of sequential memory construction. The pointer keeps track of the input sequence. The bitmask determines whether to summarize or simply a copy of the previous one if no summarization is needed.
  • Figure 4: Visualization of the Single Vector Attention mechanism. Q, K and V are generated from the input, and scores are generated by performing matrix multiplication between Q and the transpose of first vector of K, then normalized and masked. Finally, softmax is performed on the result and then weighted sum of the value vector is used to generate the final output
  • Figure 5: Multi-Memory Banks Visualization.
  • ...and 5 more figures