mlsanityData to 7 Oct 2026

Complex Recurrent Spectral Network

arXiv 2312.07296 ↗First posted 12 Dec 2023cs.LG cs.NEcited by 5

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Abstract (arXiv)

This paper presents a novel approach to advancing artificial intelligence (AI) through the development of the Complex Recurrent Spectral Network (mathbbC-RSN), an innovative variant of the Recurrent Spectral Network (RSN) model. The mathbbC-RSN is designed to address a critical limitation in existing neural network models: their inability to emulate the complex processes of biological neural networks dynamically and accurately. By integrating key concepts from dynamical systems theory and leveraging principles from statistical mechanics, the mathbbC-RSN model introduces localized non-linearity, complex fixed eigenvalues, and a distinct separation of memory and input processing functionalities. These features collectively enable the mathbbC-RSN evolving towards a dynamic, oscillating final state that more closely mirrors biological cognition. Central to this work is the exploration of how the mathbbC-RSN manages to capture the rhythmic, oscillatory dynamics intrinsic to biological systems, thanks to its complex eigenvalue structure and the innovative segregation of its linear and non-linear components. The model's ability to classify data through a time-dependent function, and the localization of information processing, is demonstrated with an empirical evaluation using the MNIST dataset. Remarkably, distinct items supplied as a sequential input yield patterns in time which bear the indirect imprint of the insertion order (and of the time of separation between contiguous insertions).

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 23 of its 63 references that are in the map. First posted on arXiv 12 Dec 2023.

Builds on

23 of 63 references.

References · 23

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11 more
  1. 2020Learning from Survey Propagation: a Neural Network for MAX-E-3-SATcited by 11
  2. 2020Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemescited by 11
  3. 2023Phase transitions in the mini-batch size for sparse and dense two-layer neural networkscited by 9
  4. 2022Hard Optimization Problems have Soft Edgescited by 8
  5. 2023How a student becomes a teacher: learning and forgetting through Spectral methodscited by 5
  6. 2020Large independent sets on random d-regular graphs with fixed degree dcited by 4
  7. 2022Recurrent Spectral Network (RSN): shaping the basin of attraction of a discrete map to reach automated classificationcited by 4
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  11. 2023Stochastic Gradient Descent-like relaxation is equivalent to Metropolis dynamics in discrete optimization and inference problemscited by 3

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Cited by year

Citing papers per year: 2023: 1; 2024: 4.

5 papers.

  1. 2024Estimating Global Input Relevance and Enforcing Sparse Representations with a Scalable Spectral Neural Network Approachcited by 4
  2. 2024Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noisecited by 4
  3. 2024Learning in Wilson-Cowan model for metapopulationcited by 2
  4. 2023Engineered Ordinary Differential Equations as Classification Algorithm (EODECA): thorough characterization and testingcited by 0
  5. 2024A short review on the maximum clique problem algorithms with classical, AI, and quantum methodscited by 0