Datasets:
JackHsieh
/
chunk-records-example

Dataset card Data Studio Files
xet
 Community
is_thoughtful
bool
uuid
string
chunk_index
int64
chunk_start_index
int64
chunk_end_index
int64
num_scored_tokens
int64
input_ids
list
thought_text
list
g
list
truncated
list
thoughtless_log_prob_sum
float32
thoughtless_log_prob_per_token
list
thoughtful_log_prob_sum
list
thoughtful_log_prob_per_token
list
false
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[ "<thought>\nThe cut occurs mid-sentence, with the inequality being set up for a bound on some quantity related to the iterates of DMSGD. The phrase \"for all $k$\" suggests the next tokens will introduce an index or condition involving $k$, likely in the form of an inequality or a summation. The next few tokens are...
[ 0 ]
[ false ]
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[ -48.56643295288086 ]
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false
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[ "<thought>\nThe cut occurs mid-phrase in the second inequality, specifically inside the expectation term: $\\mathbb{E}[\\mathbf{x}_{k}) - \\mathcal{F}^*]$, where a closing parenthesis is missing after $\\mathbf{x}_{k}$. The next tokens must therefore be $)]$ to close the bracket and complete the expression. Immedia...
[ 0 ]
[ false ]
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[ -0.4865313768386841 ]
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false
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[ "<thought>\nThe cut occurs in the middle of a fraction denominator, specifically in the term $\\frac{1-(\\beta\\Lambda)^k}{1-\\beta\\Lambda}$, which is part of the second-to-last term in the inequality. The next tokens must complete the denominator of this fraction by appending $\\Lambda$, matching the previous den...
[ 0 ]
[ false ]
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[ -2.4974050521850586 ]
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true
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[ "<thought>\nThe cut occurs in the middle of the last equation's third term, specifically inside a fraction involving $(\\beta\\Lambda)^k$. The next 8 tokens will almost certainly complete the numerator of this fraction and begin the denominator, likely continuing with $1-(\\beta\\Lambda)^k$ or a similar expression,...
[ 0 ]
[ false ]
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[ -11.921897888183594 ]
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false
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[ "<thought>\nThe cut occurs mid-sentence within the phrase \"Based on the definition of\", which is typically followed by a term or expression that will be referenced in the proof. Given the context of the preceding theorem and the mathematical notation used, the most likely next tokens are a mathematical object or ...
[ 0 ]
[ false ]
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[ -13.043797492980957 ]
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true
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[ "<thought>\nThe cut occurs mid-sentence inside the proof, following \"we can obtain that\". The next 8 tokens must continue this clause, likely introducing a mathematical inequality or expression derived from the smoothness property. Given the context, it is most probable that the next content involves the gradient...
[ 0 ]
[ false ]
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[ -9.545223236083984 ]
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true
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[ "<thought>\nThe text is mid-sentence and mid-equation, immediately following \"we can obtain that\" and starting a new align* block. The next tokens will most likely be the beginning of a mathematical inequality or identity, likely involving the expected value of the function difference $\\mathbb{E}[\\mathcal{F}(\\...
[ 0 ]
[ false ]
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false
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null
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[]
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null
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[ "<thought>\nThe cut occurs mid-clause inside an inequality, with the inner product $\\langle \\nabla \\mathcal{F}(\\mathbf{x}_k), $ just begun. The next tokens must complete this inner product by providing the second vector or expression being dotted with the gradient. Given the context of gradient-based optimizati...
[ 0 ]
[ false ]
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[ -7.395508766174316 ]
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false
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[ "<thought>\nThe cut occurs mid-clause inside an equation, specifically in the middle of the expression `= \\langle \\nab`. The next few tokens will complete the LaTeX math mode command `\\nabla` (which was being written as `\\nab`) and continue the inner product notation. The immediate next tokens are likely `\\nab...
[ 0 ]
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[ "<thought>\nThe text is mid-equation, having just written `||\\mathbf{x}_{k+1} - \\mathbf{x}||^` and is clearly in the middle of a mathematical expression. The next token must be a superscript exponent (likely `2`) to complete the squared norm notation. Given the structure of the inequality and the previous use of ...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-expression inside an inner product: specifically, the inner product $\\langle \\nabla \\mathcal{F}(\\mathbf{x}_k), -\\alpha \\nabla$ is incomplete and must be finished immediately. The next token is almost certainly a gradient term, likely $\\nabla \\mathcal{F}(\\mathbf{x}_k)$ or a re...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-expression inside a long inner product term in the third line of the align block, specifically in the term $\\langle \\nabla \\mathcal{F}(\\mathbf{x}_k), \\alpha \\nabla \\mathcal{F}(\\mathbf{x}_k) \\rangle$, where the angle bracket has just opened after $\\alpha$. The next token must...
[ 0 ]
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[ "<thought>\nThe text is mid-sentence in a mathematical derivation, specifically in the expansion of an inner product term in the proof. The current line ends at \"$\\alpha\\mathcal{S}(\\mathbf{x}_k$\", which is an incomplete expression. The next token must be a closing parenthesis to balance the open one in $\\math...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-expression inside an inner product term in the proof's derivation. The next 8 tokens will likely continue the inner product with a closing bracket and possibly the addition of the momentum term or a continuation of the expansion. Given the structure, the next tokens are expected to be...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-expression inside a long inner product term: specifically, the last line of the align* block ends with `+ \\langle \\nabla \\mathcal{F}(\\mathbf`. The next 8 tokens must complete this opening of the inner product, likely continuing with the vector argument and operator, e.g., `x}_k, ...
[ 0 ]
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[ "<thought>\nThe cut occurs mid-expression inside a long inner product term in the third line of the align block. The current term is $\\langle \\nabla \\mathcal{F}(\\mathbf{x}_k), \\beta\\til$, with the final token being the incomplete word \"til\" likely part of the previously defined operator $\\tilde{\\Pi}$. The...
[ 0 ]
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