LUCID: Attention with Preconditioned Representations

• URL: http://arxiv.org/abs/2602.10410v1
• Date: Wed, 11 Feb 2026 01:46:32 GMT
• Title: LUCID: Attention with Preconditioned Representations
• Authors: Sai Surya Duvvuri, Nirmal Patel, Nilesh Gupta, Inderjit S. Dhillon,
• Abstract summary: We introduce LUCID Attention, an architectural modification that applies a preconditioner to the attention probabilities.<n>This preconditioner, derived from exponentiated key-key similarities, minimizes overlap between the keys in a Reproducing Kernel Hilbert Space.<n>We validate our approach by training 1 billion parameter language models evaluated on up to 128K tokens.
• Score: 14.98859684869003
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Softmax-based dot-product attention is a cornerstone of Transformer architectures, enabling remarkable capabilities such as in-context learning. However, as context lengths increase, a fundamental limitation of the softmax function emerges: it tends to diffuse probability mass to irrelevant tokens degrading performance in long-sequence scenarios. Furthermore, attempts to sharpen focus by lowering softmax temperature hinder learnability due to vanishing gradients. We introduce LUCID Attention, an architectural modification that applies a preconditioner to the attention probabilities. This preconditioner, derived from exponentiated key-key similarities, minimizes overlap between the keys in a Reproducing Kernel Hilbert Space, thus allowing the query to focus on important keys among large number of keys accurately with same computational complexity as standard attention. Additionally, LUCID's preconditioning-based approach to retrieval bypasses the need for low temperature and the learnability problems associated with it. We validate our approach by training ~1 billion parameter language models evaluated on up to 128K tokens. Our results demonstrate significant gains on long-context retrieval tasks, specifically retrieval tasks from BABILong, RULER, SCROLLS and LongBench. For instance, LUCID achieves up to 18% improvement in BABILong and 14% improvement in RULER multi-needle performance compared to standard attention.

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