Slower Generalization, Faster Memorization: A Sweet Spot in Algorithmic Learning

Critical-data-size accounts of grokking suggest a natural post-threshold intuition: once training data is sufficient to identify the underlying rule, additional data should accelerate validation convergence. We show that this intuition can fail in a controlled structured-output task. In Needleman--Wunsch (NW) matrix generation, small Transformers reach high validation exact-match accuracy fastest at an intermediate dataset size, not at the largest one. Past this dataset-size sweet spot, generalization remains achievable but requires more gradient updates. Conversely, in the regime where partial validation competence first appears, larger datasets can require fewer updates to reach high training accuracy, suggesting that emerging rule structure can accelerate fitting beyond example-wise memorization. A multiplication baseline does not show the same post-threshold slowdown. These results separate the critical data size for the onset of generalization from the dataset size that optimizes update-based convergence, and identify structured-output tasks where learning the rule and completing exact-fitting can diverge.

Understanding the Reversal Curse Mitigation in Masked Diffusion Models through Attention and Training Dynamics

Autoregressive language models (ARMs) suffer from the reversal curse: after learning that "$A$ is $B$", they often fail on the reverse query "$B$ is $A$". Masked diffusion-based language models (MDMs) exhibit this failure in a much weaker form, but the underlying reason has remained unclear. A common explanation attributes this mitigation to the any-order training objective. However, observing "[MASK] is $B$" during training does not necessarily teach the model to handle the reverse prompt "$B$ is [MASK]". We show that the mitigation arises from architectural structure and its interaction with training. In a one-layer Transformer encoder, weight sharing couples the two directions by making forward and reverse attention scores positively correlated. In the same setting, we further show that the corresponding gradients are aligned, so minimizing the forward loss also reduces the reverse loss. Experiments on both controlled toy tasks and large-scale diffusion language models support these mechanisms, explaining why MDMs partially overcome a failure mode that persists in strong ARMs.