Training a Hopfield Variational Autoencoder with Equilibrium Propagation

On dedicated analog hardware, equilibrium propagation is an energy-efficient alternative to backpropagation. In spite of its theoretical guarantees, its application in the AI domain remains limited to the discriminative setting. Meanwhile, despite its high computational demands, generative AI is on the rise. In this paper, we demonstrate the application of Equilibrium Propagation in training a variational autoencoder (VAE) for generative modeling. Leveraging the symmetric nature of Hopfield networks, we propose using a single model to serve as both the encoder and decoder which could effectively halve the required chip size for VAE implementations, paving the way for more efficient analog hardware configurations.Comment: Associative Memory & Hopfield Networks in 2023 (NeurIPS 2023 workshop

Exploring the Temperature-Dependent Phase Transition in Modern Hopfield Networks

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 $\beta$ 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 $\beta_{\text{c}}$, from a single global attractor towards highly pattern specific minima as $\beta$ is increased. Importantly, the dynamics are not solely governed by the hyperparameter $\beta$ but are instead determined by an effective inverse temperature $\beta_{\text{eff}}$ 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.Comment: Accepted as poster for Associative Memory and Hopfield Networks workshop at NeurIPS2