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Attention Is All You Need (to Avoid Spurious Oscillations)

arXiv · AI, language, vision and robotics · article · Sep 11, 2026 · UTC

Can attention move a shock across several cells in one update without breaking it? We develop a conservative, fixed grid finite-volume scheme in which a CFL-conditioned attention flux selects upstream information according to the transport required by the current time step. One-dimensional inviscid Burgers transport is used as the central mechanism test: the same learned flux remains reliable in the conventional small-step regime and, with a time step four times larger, preserves sharp shocks while using one stage per update. A standard fifth-order WENO scheme with third-order strong-stability

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