Memorisation and forgetting in a learning Hopfield neural network: bifurcation mechanisms, attractors and basins

• URL: http://arxiv.org/abs/2508.10765v1
• Date: Thu, 14 Aug 2025 15:48:39 GMT
• Title: Memorisation and forgetting in a learning Hopfield neural network: bifurcation mechanisms, attractors and basins
• Abstract summary: We analyse mechanisms of memory formation in an 81-neuron Hopfield network undergoing Hebbian learning.<n>We show that, by affecting evolution of connection weights, the applied stimuli induce a pitchfork and then a cascade of saddle-node bifurcations.<n>This creates new attractors with their basins that can code true or spurious memories, and an abrupt disappearance of old memories.
• Score: 41.94295877935867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Despite explosive expansion of artificial intelligence based on artificial neural networks (ANNs), these are employed as "black boxes'', as it is unclear how, during learning, they form memories or develop unwanted features, including spurious memories and catastrophic forgetting. Much research is available on isolated aspects of learning ANNs, but due to their high dimensionality and non-linearity, their comprehensive analysis remains a challenge. In ANNs, knowledge is thought to reside in connection weights or in attractor basins, but these two paradigms are not linked explicitly. Here we comprehensively analyse mechanisms of memory formation in an 81-neuron Hopfield network undergoing Hebbian learning by revealing bifurcations leading to formation and destruction of attractors and their basin boundaries. We show that, by affecting evolution of connection weights, the applied stimuli induce a pitchfork and then a cascade of saddle-node bifurcations creating new attractors with their basins that can code true or spurious memories, and an abrupt disappearance of old memories (catastrophic forgetting). With successful learning, new categories are represented by the basins of newly born point attractors, and their boundaries by the stable manifolds of new saddles. With this, memorisation and forgetting represent two manifestations of the same mechanism. Our strategy to analyse high-dimensional learning ANNs is universal and applicable to recurrent ANNs of any form. The demonstrated mechanisms of memory formation and of catastrophic forgetting shed light on the operation of a wider class of recurrent ANNs and could aid the development of approaches to mitigate their flaws.

Related papers

• Concept-Guided Interpretability via Neural Chunking [64.6429903327095]
  We show that neural networks exhibit patterns in their raw population activity that mirror regularities in the training data.<n>We propose three methods to extract recurring chunks on a neural population level.<n>Our work points to a new direction for interpretability, one that harnesses both cognitive principles and the structure of naturalistic data.
  arXiv  Detail & Related papers  (2025-05-16T13:49:43Z)
• Semi-parametric Memory Consolidation: Towards Brain-like Deep Continual Learning [59.35015431695172]
  We propose a novel biomimetic continual learning framework that integrates semi-parametric memory and the wake-sleep consolidation mechanism.<n>For the first time, our method enables deep neural networks to retain high performance on novel tasks while maintaining prior knowledge in real-world challenging continual learning scenarios.
  arXiv  Detail & Related papers  (2025-04-20T19:53:13Z)
• Discovering Chunks in Neural Embeddings for Interpretability [53.80157905839065]
  We propose leveraging the principle of chunking to interpret artificial neural population activities.<n>We first demonstrate this concept in recurrent neural networks (RNNs) trained on artificial sequences with imposed regularities.<n>We identify similar recurring embedding states corresponding to concepts in the input, with perturbations to these states activating or inhibiting the associated concepts.
  arXiv  Detail & Related papers  (2025-02-03T20:30:46Z)
• Storing overlapping associative memories on latent manifolds in low-rank spiking networks [5.041384008847852]
  We revisit the associative memory problem in light of advances in understanding spike-based computation.<n>We show that the spiking activity for a large class of all-inhibitory networks is situated on a low-dimensional, convex, and piecewise-linear manifold.<n>We propose several learning rules, and demonstrate a linear scaling of the storage capacity with the number of neurons, as well as robust pattern completion abilities.
  arXiv  Detail & Related papers  (2024-11-26T14:48:25Z)
• Enhancing learning in spiking neural networks through neuronal heterogeneity and neuromodulatory signaling [52.06722364186432]
  We propose a biologically-informed framework for enhancing artificial neural networks (ANNs) Our proposed dual-framework approach highlights the potential of spiking neural networks (SNNs) for emulating diverse spiking behaviors. We outline how the proposed approach integrates brain-inspired compartmental models and task-driven SNNs, bioinspiration and complexity.
  arXiv  Detail & Related papers  (2024-07-05T14:11:28Z)
• In search of dispersed memories: Generative diffusion models are associative memory networks [6.4322891559626125]
  Generative diffusion models are a type of generative machine learning techniques that have shown great performance in many tasks. We show that generative diffusion models can be interpreted as energy-based models and that, when trained on discrete patterns, their energy function is identical to that of modern Hopfield networks. This equivalence allows us to interpret the supervised training of diffusion models as a synaptic learning process that encodes the associative dynamics of a modern Hopfield network in the weight structure of a deep neural network.
  arXiv  Detail & Related papers  (2023-09-29T14:48:24Z)
• Meta-Learning in Spiking Neural Networks with Reward-Modulated STDP [2.179313476241343]
  We propose a bio-plausible meta-learning model inspired by the hippocampus and the prefrontal cortex. Our new model can easily be applied to spike-based neuromorphic devices and enables fast learning in neuromorphic hardware.
  arXiv  Detail & Related papers  (2023-06-07T13:08:46Z)
• Spiking neural network for nonlinear regression [68.8204255655161]
  Spiking neural networks carry the potential for a massive reduction in memory and energy consumption. They introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. A framework for regression using spiking neural networks is proposed.
  arXiv  Detail & Related papers  (2022-10-06T13:04:45Z)
• Topological Continual Learning with Wasserstein Distance and Barycenter [0.0]
  Continual learning in neural networks suffers from a phenomenon called catastrophic forgetting. We propose a novel topological regularization that penalizes cycle structure in a neural network during training. We demonstrate that our method is effective in both shallow and deep network architectures for multiple image classification datasets.
  arXiv  Detail & Related papers  (2022-10-06T03:46:20Z)
• Reducing Catastrophic Forgetting in Self Organizing Maps with Internally-Induced Generative Replay [67.50637511633212]
  A lifelong learning agent is able to continually learn from potentially infinite streams of pattern sensory data. One major historic difficulty in building agents that adapt is that neural systems struggle to retain previously-acquired knowledge when learning from new samples. This problem is known as catastrophic forgetting (interference) and remains an unsolved problem in the domain of machine learning to this day.
  arXiv  Detail & Related papers  (2021-12-09T07:11:14Z)
• Learning by Active Forgetting for Neural Networks [36.47528616276579]
  Remembering and forgetting mechanisms are two sides of the same coin in a human learning-memory system. Modern machine learning systems have been working to endow machine with lifelong learning capability through better remembering. This paper presents a learning model by active forgetting mechanism with artificial neural networks.
  arXiv  Detail & Related papers  (2021-11-21T14:55:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.