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Current paradigms in Self-Supervised Learning (SSL) achieve state-of-the-art results through complex, heuristic-driven pretext tasks such as contrastive learning or masked image modeling. This work proposes a departure from these heuristics by reframing SSL through the fundamental principle of Minimum Description Length (MDL). We introduce the MDL-Autoencoder (MDL-AE), a framework that learns visual representations by optimizing a VQ-VAE-based objective to find the most efficient, discrete compression of visual data. We conduct a rigorous series of experiments on CIFAR-10, demonstrating that this compression-driven objective successfully learns a rich vocabulary of local visual concepts. However, our investigation uncovers a critical and non-obvious architectural insight: despite learning a visibly superior and higher-fidelity vocabulary of visual concepts, a more powerful tokenizer fails to improve downstream performance, revealing that the nature of the learned representation dictates the optimal downstream architecture. We show that our MDL-AE learns a vocabulary of holistic object parts rather than generic, composable primitives. Consequently, we find that a sophisticated Vision Transformer (ViT) head, a state-of-the-art tool for understanding token relationships, consistently fails to outperform a simple linear probe on the flattened feature map. This architectural mismatch reveals that the most powerful downstream aggregator is not always the most effective. To validate this, we demonstrate that a dedicated self-supervised alignment task, based on Masked Autoencoding of the discrete tokens, resolves this mismatch and dramatically improves performance, bridging the gap between generative fidelity and discriminative utility. Our work provides a compelling end-to-end case study on the importance of co-designing objectives and their downstream architectures, showing that token-specific pre-training is crucial for unlocking the potential of powerful aggregators.