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[ "<thought>\nThe text is mid-sentence inside a remark, and the next few tokens must continue the mathematical or verbal reasoning about the behavior of adversarial risk as $t \\to \\infty$. The phrase \"if $1 \\leq p \\leq 2$,\" is a clause setting up a condition, so the next content will likely be a mathematical ex...
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[ "<thought>\nThe cut occurs mid-phrase in an academic paper, immediately after \"eq\", which is short for \"equation\" in academic writing. The next few tokens will almost certainly be a reference to a specific equation, likely in the format \"eq. X\", \"eq. (X)\", or \"Equation (X)\", where X is a number or letter ...
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[ "<thought>\nThe cut occurs mid-sentence, within a footnote that begins \"In our experimental work we use the fair clustering data sets\". The next 8 tokens will likely name the first of these datasets, likely a standard benchmark in fair clustering. Based on typical conventions in ML papers, the next tokens will ei...
[ 0 ]
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[ "<thought>\nThe text cuts off mid-bullet point, with the phrase \"In typical fair clustering settings\" as the start of the first item in an enumerated list of experimental results. The next 8 tokens are likely to elaborate on the specific type of setting or the first key finding, such as a comparison metric, a fai...
[ 0 ]
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[ "<thought>\nThe text cuts off mid-sentence at \"quickly\". The next 8 tokens will almost certainly complete the sentence by specifying the time or training steps in which convergence occurs. Since the preceding items in the list use past tense and active voice, the next word is likely \"within\", followed by a quan...
[ 0 ]
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[ -65.86923217773438 ]
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[ "<thought>\nThe cut occurs immediately after the opening of a subsection, indicated by `\\subsection`. Since the previous section is titled \"Experiments\" and the first subsection is missing a title, the next 8 tokens will almost certainly be the title of the subsection, enclosed in curly braces and starting with ...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-way through the phrase \"We use the image source (MN\" where \"MN\" is the start of a dataset name, likely \"MNIST\" given the context. The next tokens will almost certainly complete the name as \"IST\" to form \"MNIST\", followed by a closing parenthesis or a comma, and possibly a co...
[ 0 ]
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[ "<thought>\nThe text is mid-sentence inside a paragraph describing the Reverse-MNIST dataset. It has just introduced the dataset by stating it uses the 60000 training images from MNIST and is likely to continue by specifying how the PSV (Protected Sensitive Variable) is defined for this dataset. The next 8 tokens w...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-sentence inside the dataset description for Reverse-MNIST. The sentence is introducing the dataset by stating its origin and transformation. The next 8 tokens must continue the explanation of how the dataset is constructed, likely specifying the inversion method (e.g., \"by inverting ...
[ 0 ]
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[ -8.530242919921875 ]
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[ "<thought>\nThe cut occurs mid-sentence, immediately after the citation command `\\cite{`, indicating the author is about to reference a traditional fair clustering work. The next 8 tokens are likely to be the citation key or keys used in the reference list, probably a single key like `chen2019fair` or `backurs2019...
[ 0 ]
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