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Working memory refers to a combination of components, including short-term memory and attention, that allow an individual to hold information temporarily as we perform cognitive tasks. It is an essential cognitive function that enables the execution of complex tasks such as problem-solving, comprehension, and reasoning. Unlike short-term memory, which simply involves the storage of information for a brief period, working memory involves the active manipulation and processing of this...
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Information-theoretic analysis of Hierarchical Temporal Memory-Spatial Pooler algorithm with a new upper bound for

Shiva Sanati1, Modjtaba Rouhani1, Ghosheh Abed Hodtani2

  • 1Department of Computer Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.

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Summary

Hierarchical Temporal Memory's Spatial Pooler (SP) algorithm shows noise resistance and improved performance with higher sparsity. Optimal reconstruction is achieved with 2% sparsity, demonstrating its effectiveness in encoding data.

Keywords:
Cramer-Rao lower bound (CRLB)Fisher information matrix (FIM)Hierarchical Temporal Memory (HTM)Spatial Pooler (SP)modified-information bottleneck (modified-IB)sparsitystandard information bottleneck (IB)

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Area of Science:

  • Machine Learning
  • Computational Neuroscience
  • Information Theory

Background:

  • Hierarchical Temporal Memory (HTM) is an unsupervised machine learning algorithm inspired by neocortical principles.
  • The Spatial Pooler (SP) is a core HTM component that generates sparse distributed representations from binary input streams.
  • Evaluating SP's sparsification using information theory metrics is crucial for understanding its performance.

Purpose of the Study:

  • To assess the sparsification effectiveness of the Spatial Pooler (SP) algorithm within Hierarchical Temporal Memory (HTM).
  • To introduce and utilize a modified information bottleneck (IB) measure to evaluate SP performance under varying sparsity and noise conditions.
  • To mathematically prove the positive correlation between sparsity and SP algorithm performance.

Main Methods:

  • Information-theoretic analysis using the information bottleneck (IB), Cramer-Rao lower bound, and Fisher information matrix.
  • Introduction of a novel upper bound for the IB relation, termed modified-IB.
  • Testing the SP algorithm with MNIST, Fashion-MNIST, and NYC-Taxi datasets, including introducing up to 40% noise.
  • Reconstruction of sparse SP output representations using probabilistic mapping and Hidden Markov Models.
  • Mathematical analysis of the Cramer-Rao lower bound with Cauchy distributed data.

Main Results:

  • The SP algorithm demonstrated significant resistance to noise, with up to 40% input noise causing no discernible output changes.
  • Numerical calculations using modified-IB indicated that lower noise and higher sparsity levels improve reconstruction effectiveness.
  • The SP algorithm achieved optimal results with 2% sparsity.
  • Mathematical proof confirmed that increased sparsity enhances SP algorithm performance.

Conclusions:

  • The Spatial Pooler (SP) algorithm exhibits robust performance and noise resistance, particularly at higher sparsity levels.
  • The modified-IB measure provides a valuable tool for evaluating SP performance across different sparsity and noise conditions.
  • Sparsity is a critical factor for optimizing the SP algorithm's efficiency and representational capabilities in Hierarchical Temporal Memory.