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[]
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[]
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[ "<thought>\nThe text is mid-reference to an equation, specifically \"Eq.~(\\ref{\" which is a LaTeX command for citing an equation. The next tokens will almost certainly be the label of the equation being referenced, likely starting with a letter and possibly including numbers or other standard label characters. Th...
[ 0 ]
[ false ]
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[ -78.87567901611328 ]
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false
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[ "<thought>\nThe text is mid-sentence, introducing the Wiener filter interpretation of a given equation, and has just mentioned the term \"gain\". The next few tokens are likely to either define or specify this gain, possibly in mathematical terms or by introducing a variable or expression that represents it. The ne...
[ 0 ]
[ false ]
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[ -41.47145080566406 ]
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false
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[ "<thought>\nThe text is mid-sentence, following \"For fixed,\" and is likely to be followed by a noun or noun phrase that specifies what is being held constant in the upcoming analysis or derivation. Given the context of gain $\\mathbf{g}_k$ depending on $\\alpha^2$ and $\\gamma_c(\\omega_k)$, the next tokens are l...
[ 0 ]
[ false ]
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[ -51.97867202758789 ]
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false
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[]
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null
[]
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false
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[]
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[ "<thought>\nThe sentence is mid-clause, with the last token being \"to\", suggesting a comparison or convergence is about to be completed. The structure implies a comparison between the magnitude of $\\gamma_c(\\omega_k)$ and the proximity of $\\mathbf{g}_k$ to a specific value or limit. The likely next 8 tokens ar...
[ 0 ]
[ false ]
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[ -44.54006576538086 ]
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true
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[ [ 13708, 2450, 397, 785, 11652, 374, 71026, 264, 58457, 16148, 911, 279, 7709, 315, 57960, 10374, 13233, 90, 70, 19444, 74, 3, 304, 12687, 311, 57960, 32214, 666, 11520, 32696, 4698, 8, ...
[ "<thought>\nThe sentence is concluding a causal explanation about the behavior of $\\mathbf{g}_k$ in relation to $\\gamma_c(\\omega_k)$. The next tokens will likely continue the \"Therefore,\" clause, completing the grammatical structure with a result or implication. The most plausible next tokens are a subject (po...
[ 0 ]
[ false ]
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[ -52.018310546875 ]
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false
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null
[]
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[]
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[]
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[]
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[ "<thought>\nThe sentence is mid-illustration setup, having introduced a figure reference and the phrase \"how different\". The next 8 tokens must logically introduce the variable or condition being varied in the figure. Given the context of $\\mathbf{g}_k$ and $\\gamma_c(\\omega_k)$, the most likely continuation is...
[ 0 ]
[ false ]
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[ -21.760757446289062 ]
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false
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[]
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[]
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[]
[]
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[]
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[]
[]
[]
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null
[]
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[]
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[]
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false
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[]
[]
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null
[]
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false
00a6a450-fc6d-46ff-b0c0-8878fe844cf9
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[]
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null
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[]
[]
[]
[]
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null
[]
[]
false
00a6a450-fc6d-46ff-b0c0-8878fe844cf9
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[]
[]
[]
[]
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null
[]
[]
false
00a6a450-fc6d-46ff-b0c0-8878fe844cf9
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1,312
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[]
[]
[]
[]
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null
[]
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[ "<thought>\nThe text is mid-phrase, with the phrase \"This suggests that GPCDL shares the\" ending in the middle of a noun phrase. Given the prior context, which draws a connection between the Wiener filter interpretation, the gain behavior, and Bayesian learning, the next few tokens are likely to introduce a prope...
[ 0 ]
[ false ]
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[ -41.01194763183594 ]
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false
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[]
[]
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[]
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null
[]
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false
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[]
[]
[]
[]
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null
[]
[]
false
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[]
[]
[]
[]
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null
[]
[]
false
00a6a450-fc6d-46ff-b0c0-8878fe844cf9
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1,472
1,504
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[]
[]
[]
[]
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null
[]
[]
false
00a6a450-fc6d-46ff-b0c0-8878fe844cf9
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1,504
1,536
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[]
[]
[]
[]
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null
[]
[]
false
00a6a450-fc6d-46ff-b0c0-8878fe844cf9
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1,536
1,568
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[]
[]
[]
[]
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null
[]
[]
false
00a6a450-fc6d-46ff-b0c0-8878fe844cf9
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1,568
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[]
[]
[]
[]
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[]
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[ "<thought>\nThe next 8 tokens must continue the clause \"the gain is determined a posteriori from the balance between the likelihood\" and are likely to introduce the second term in the balance, which is the prior. The most probable continuation is \"and the prior,\" completing the grammatical structure and alignin...
[ 0 ]
[ false ]
-40.124065
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[ -44.258705139160156 ]
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false
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[]
[]
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[]
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[ "<thought>\nThe figure caption is mid-sentence, ending at \"The filter gain $\\\", which is the start of a mathematical expression for the gain. The next token must be the variable or symbol representing the gain, likely $\\mathbf{g}$ or $g$, followed by a subscript or functional notation (e.g., $\\mathbf{g}_k$ or ...
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