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We study label flip attacks against log-linear DPO. We first illustrate that flipping one preference label induces a parameter-independent shift in the DPO gradient. Using this key property, we can then convert the targeted poisoning problem into a structured binary sparse approximation problem. To solve this problem, we develop two attack methods: Binary-Aware Lattice Attack (BAL-A) and Binary Matching Pursuit Attack (BMP-A). BAL-A embeds the binary flip selection problem into a binary-aware lattice and applies Lenstra-Lenstra-Lov\\'asz reduction and Babai's nearest plane algorithm; we provide sufficient conditions that enforce binary coefficients and recover the minimum-flip objective. 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BAL-A embeds the binary flip selection problem into a binary-aware lattice and applies Lenstra-Lenstra-Lov\\'asz reduction and Babai's nearest plane algorithm; we provide sufficient conditions that enforce binary coefficients and recover the minimum-flip objective. 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