Exploring the Temperature-Dependent Phase Transition in Modern Hopfield Networks
This work provides insights into hyperparameter optimization for Transformers, potentially reducing fine-tuning costs, though it is incremental in nature.
The paper investigates the effect of the inverse temperature hyperparameter on energy minima distributions in Modern Hopfield Networks, revealing a phase transition at a critical temperature that shifts from a global attractor to pattern-specific minima as temperature decreases.
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 $β_{\text{c}}$, 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 $β_{\text{eff}}$ 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.