Continual Learning in Modern Hopfield Networks with an Application to Diffusion Models

Generative models, including diffusion models, are increasingly used as foundation models and adapted through sequential fine-tuning, making continual learning an essential problem setting. However, continual learning in such generative models remains poorly understood: after a task change, what aspects of the learned distribution are most easily lost, and what replay samples should be prioritized? We address these questions through the modern Hopfield energy. Recent links between modern Hopfield networks (MHNs) and diffusion models allow analyses in MHNs to be transferred to diffusion models. We introduce intrinsic forgetting as an increase in Hopfield energy after the task change. In tractable settings in an MHN, we prove that high-energy, outlier-like samples undergo a larger energy increase than cluster-like samples, implying that samples located in sharp, isolated basins are more forgettable. We further analyze memory replay and show that replay is particularly effective for high-energy samples, enabling an energy-based selection of replay samples. We validate these predictions in experiments on MHNs and two diffusion models under continual-learning settings: Stable Diffusion and a pixel-space DDPM. In these diffusion models, Hopfield energy tracks reconstruction-based forgetting, and replay experiments reveal energy-dependent mitigation of forgetting that is consistent with the MHN analysis.

Investigating Fine- and Coarse-grained Structural Correspondences Between Deep Neural Networks and Human Object Image Similarity Judgments Using Unsupervised Alignment

The learning mechanisms by which humans acquire internal representations of objects are not fully understood. Deep neural networks (DNNs) have emerged as a useful tool for investigating this question, as they have internal representations similar to those of humans as a byproduct of optimizing their objective functions. While previous studies have shown that models trained with various learning paradigms - such as supervised, self-supervised, and CLIP - acquire human-like representations, it remains unclear whether their similarity to human representations is primarily at a coarse category level or extends to finer details. Here, we employ an unsupervised alignment method based on Gromov-Wasserstein Optimal Transport to compare human and model object representations at both fine-grained and coarse-grained levels. The unique feature of this method compared to conventional representational similarity analysis is that it estimates optimal fine-grained mappings between the representation of each object in human and model representations. We used this unsupervised alignment method to assess the extent to which the representation of each object in humans is correctly mapped to the corresponding representation of the same object in models. Using human similarity judgments of 1,854 objects from the THINGS dataset, we find that models trained with CLIP consistently achieve strong fine- and coarse-grained matching with human object representations. In contrast, self-supervised models showed limited matching at both fine- and coarse-grained levels, but still formed object clusters that reflected human coarse category structure. Our results offer new insights into the role of linguistic information in acquiring precise object representations and the potential of self-supervised learning to capture coarse categorical structures.