Single-Layer MeMo as a Randomized Hamming-Kernel Classifier

MeMo [Zanzotto et al. (2025)] is a recent language-model architecture that stores associations between token contexts and next tokens in a correlation matrix memory. In this work, we study its single-layer form and show that its ideal retrieval rule is a multiclass classifier based on the *positional Hamming kernel*. The MeMo architecture represents both the sequence features and the output labels with Gaussian random codes. Its score is therefore a doubly randomized sketch of the ideal classifier. Under independent input and output codebooks, we bound the errors introduced by context sketching and output decoding, characterize their dependence on model and data parameters, and give a margin-based guarantee for recovering the ideal prediction. Controlled simulations support the trends predicted by the analysis. On a restricted WikiText-2 next-token task, we compare MeMo with classical baselines and show that it can offer a useful trade-off among predictive accuracy, memory, and throughput, particularly on a GPU, where its matrix operations can be parallelized.