Exploring the Hierarchical Reasoning Model for Small Natural-Image Classification Without Augmentation

Abstract

This paper asks whether the Hierarchical Reasoning Model (HRM) with the two Transformer-style modules $(f_L,f_H)$, one step (DEQ-style) training, deep supervision, Rotary Position Embeddings, and RMSNorm can serve as a practical image classifier. It is evaluated on MNIST, CIFAR-10, and CIFAR-100 under a deliberately raw regime: no data augmentation, identical optimizer family with one-epoch warmup then cosine-floor decay, and label smoothing. HRM optimizes stably and performs well on MNIST ($\approx 98\%$ test accuracy), but on small natural images it overfits and generalizes poorly: on CIFAR-10, HRM reaches 65.0\% after 25 epochs, whereas a two-stage Conv--BN--ReLU baseline attains 77.2\% while training $\sim 30\times$ faster per epoch; on CIFAR-100, HRM achieves only 29.7\% test accuracy despite 91.5\% train accuracy, while the same CNN reaches 45.3\% test with 50.5\% train accuracy. Loss traces and error analyses indicate healthy optimization but insufficient image-specific inductive bias for HRM in this regime. It is concluded that, for small-resolution image classification without augmentation, HRM is not competitive with even simple convolutional architectures as the HRM currently exist but this does not exclude possibilities that modifications to the model may allow it to improve greatly.