New Hopfield networks part7(Machine Learning 2024)
- Unsupervised learning architecture based on neural Darwinism and Hopfield networks recognizes symbols with high accuracy
Authors: Mario Stepanik
Abstract: This paper introduces a novel unsupervised learning paradigm inspired by Gerald Edelman’s theory of neuronal group selection (“Neural Darwinism”). The presented automaton learns to recognize arbitrary symbols (e.g., letters of an alphabet) when they are presented repeatedly, as they are when children learn to read. On a second hierarchical level, the model creates abstract categories representing the learnt symbols. The fundamental computational unit are simple McCulloch-Pitts neurons arranged into fully-connected groups (Hopfield networks with randomly initialized weights), which are “selected”, in an evolutionary sense, through symbol presentation. The learning process is fully tractable and easily interpretable for humans, in contrast to most neural network architectures. Computational properties of Hopfield networks enabling pattern recognition are discussed. In simulations, the model achieves high accuracy in learning the letters of the Latin alphabet, presented as binary patterns on a grid. This paper is a proof of concept with no claims to state-of-the-art performance in letter recognition, but hopefully inspires new thinking in bio-inspired machine learning.
2. Exploring the Temperature-Dependent Phase Transition in Modern Hopfield Networks
Authors: Felix Koulischer, Cédric Goemaere, Tom van der Meersch, Johannes Deleu, Thomas Demeester
Abstract: The recent discovery of a connection between Transformers and Modern Hopfield Networks (MHNs) has reignited the study of neural networks from a physical energy-based perspective. This paper focuses on the pivotal effect of the inverse temperature hyperparameter β on the distribution of energy minima of the MHN. To achieve this, the distribution of energy minima is tracked in a simplified MHN in which equidistant normalised patterns are stored. This network demonstrates a phase transition at a critical temperature βc, from a single global attractor towards highly pattern specific minima as β is increased. Importantly, the dynamics are not solely governed by the hyperparameter β but are instead determined by an effective inverse temperature βeff which also depends on the distribution and size of the stored patterns. Recognizing the role of hyperparameters in the MHN could, in the future, aid researchers in the domain of Transformers to optimise their initial choices, potentially reducing the necessity for time and energy expensive hyperparameter fine-tuning.
