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[ "<thought>\nThe cut occurs mid-phrase inside an expectation expression, specifically at the end of the subscript for the expectation operator: `p(\\boldsymbol{\\theta}|\\mathcal{`. The next token must be a closing parenthesis to complete the subscript. The next few tokens will likely complete the expectation by int...
[ 0 ]
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[ "<thought>\nThe cut occurs at the end of a long mathematical derivation, with the last token being the right parenthesis of an expectation expression. The next tokens will likely close the outer parentheses of the expectation expression and continue the algebraic manipulation. The next 8 tokens will most likely inc...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-sentence in the phrase \"we used in equation (\\ref{eq:post_identy}) the posterior identity\", which implies the next few tokens will begin the definition or explanation of the referenced posterior identity. The next 8 tokens are likely the opening of the equation block, specifically ...
[ 0 ]
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[ "<thought>\nThe text is mid-way through the expression for the denominator $ p(\\vec{x}|\\boldsymbol{\\theta}, \\mathcal{D}) $, having just written $ \\int_{-\\infty}^{\\infty} $, suggesting the next tokens must be the integrand and possibly the differential. Given the context of a likelihood term in a Bayesian fra...
[ 0 ]
[ false ]
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[ "<thought>\nThe cut occurs mid-sentence inside the equation for $ p(\\vec{x}|\\boldsymbol{\\theta}, \\mathcal{D}) $, specifically in the integrand of a conditional probability term. The next token must complete the expression $ p(\\vec{x}|\\boldsymbol{\\theta},\\vec{y},\\mathcal{D}) $, likely followed by $ p(\\vec{...
[ 0 ]
[ false ]
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[ "<thought>\nThe text is mid-notation, continuing the definition of a matrix $\\Phi_h$, which appears to be a concatenation of transposed submatrices $\\Phi_h^1, \\Phi_h^2, \\ldots$. The next 8 tokens will most likely complete the transpose operation of the first submatrix and begin listing the others, likely contin...
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[ "<thought>\nThe text is mid-equation, following a multi-line alignment with the use of the ampersand and double backslash indicating the end of a line in LaTeX math mode. The current line begins with \"& \\math\", which implies the continuation is the start of a new mathematical symbol or function. The most likely ...
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[ "<thought>\nThe cut occurs mid-definition of $\\Lambda_h^k$, specifically after $(\\Phi_{0,h}^k,\\Phi_{1,h}$. The next token must be a comma or a continuation of the tuple, likely $\\Phi_{2,h}^k$, as such constructions often iterate over indices. The notation suggests a sequence of matrices or vectors indexed by a ...
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