Language models (LMs) can generate hallucinations and incoherent outputs, which highlights their weak context dependency. Cache-LMs, which augment LMs with a memory of recent history, can increase context dependency and have shown remarkable performance in diverse language generation tasks. However, we find that even with training, the performance gain stemming from the cache component of current cache-LMs is suboptimal due to the misalignment between the current hidden states and those stored in the memory. In this work, we present HistAlign, a new training approach to ensure good cache alignment such that the model receives useful signals from the history. We first prove our concept on a simple and synthetic task where the memory is essential for correct predictions, and we show that the cache component of HistAlign is better aligned and improves overall performance. Next, we evaluate HistAlign on diverse downstream language generation tasks, including prompt continuation, abstractive summarization, and data-to-text. We demonstrate that HistAlign improves text coherence and faithfulness in open-ended and conditional generation settings respectively. HistAlign is also generalizable across different model families, showcasing its strength in improving context dependency of LMs in diverse scenarios. Our code is publicly available at https://github.com/meetdavidwan/histalign

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