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jsut 200 more words

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Mars Ultor
2025-04-29 23:59:35 -05:00
parent cda8b28b7e
commit a56dacdcca
13 changed files with 1712 additions and 126 deletions
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11
EEMLA.aux
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@@ -26,13 +26,20 @@
\abx@aux@segm{0}{0}{cobbe2021trainingverifierssolvemath}
\abx@aux@cite{0}{cobbe2021trainingverifierssolvemath}
\abx@aux@segm{0}{0}{cobbe2021trainingverifierssolvemath}
\abx@aux@read@bbl@mdfivesum{DB874CC7E8DA7002F79589CE78CE1348}
\abx@aux@cite{0}{deepseekai2025deepseekv3technicalreport}
\abx@aux@segm{0}{0}{deepseekai2025deepseekv3technicalreport}
\abx@aux@cite{0}{cuda_programming_guide_2025}
\abx@aux@segm{0}{0}{cuda_programming_guide_2025}
\abx@aux@read@bbl@mdfivesum{A4BF38394F3D8B19FB0185ACC0064B31}
\abx@aux@defaultrefcontext{0}{ahn2024largelanguagemodelsmathematical}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{cobbe2021trainingverifierssolvemath}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{deepseekai2025deepseekv3technicalreport}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{hendrycks2021measuringmathematicalproblemsolving}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{hoffmann2022trainingcomputeoptimallargelanguage}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{ivanov2024}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{cuda_programming_guide_2025}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{app14020744}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{vaswani2023attentionneed}{nty/global//global/global/global}
\abx@aux@defaultrefcontext{0}{Wang2024}{nty/global//global/global/global}
\gdef \@abspage@last{9}
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\gdef \@abspage@last{10}

1257
EEMLA.bbl
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2
EEMLA.bcf
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@@ -2787,6 +2787,8 @@
<bcf:citekey order="10" intorder="1">ahn2024largelanguagemodelsmathematical</bcf:citekey>
<bcf:citekey order="11" intorder="1">cobbe2021trainingverifierssolvemath</bcf:citekey>
<bcf:citekey order="12" intorder="1">cobbe2021trainingverifierssolvemath</bcf:citekey>
<bcf:citekey order="13" intorder="1">deepseekai2025deepseekv3technicalreport</bcf:citekey>
<bcf:citekey order="14" intorder="1">cuda_programming_guide_2025</bcf:citekey>
</bcf:section>
<!-- SORTING TEMPLATES -->
<bcf:sortingtemplate name="nty">

27
EEMLA.blg
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@@ -1,17 +1,18 @@
[0] Config.pm:308> INFO - This is Biber 2.20
[0] Config.pm:311> INFO - Logfile is 'EEMLA.blg'
[38] biber:340> INFO - === Tue Apr 29, 2025, 23:04:30
[46] Biber.pm:420> INFO - Reading 'EEMLA.bcf'
[81] Biber.pm:994> INFO - Found 8 citekeys in bib section 0
[39] biber:340> INFO - === Tue Apr 29, 2025, 23:58:53
[47] Biber.pm:420> INFO - Reading 'EEMLA.bcf'
[81] Biber.pm:994> INFO - Found 10 citekeys in bib section 0
[89] Biber.pm:4463> INFO - Processing section 0
[93] Biber.pm:4654> INFO - Looking for bibtex file 'references.bib' for section 0
[94] Biber.pm:4654> INFO - Looking for bibtex file 'references.bib' for section 0
[94] bibtex.pm:1713> INFO - LaTeX decoding ...
[97] bibtex.pm:1519> INFO - Found BibTeX data source 'references.bib'
[171] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'
[171] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable'
[171] Biber.pm:4283> INFO - Sorting list 'nty/global//global/global/global' of type 'entry' with template 'nty' and locale 'en-US'
[171] Biber.pm:4289> INFO - No sort tailoring available for locale 'en-US'
[177] bbl.pm:676> INFO - Writing 'EEMLA.bbl' with encoding 'UTF-8'
[181] bbl.pm:779> INFO - Output to EEMLA.bbl
[181] Biber.pm:131> WARN - legacy month field 'Oct' in entry 'Wang2024' is not an integer - this will probably not sort properly.
[181] Biber.pm:133> INFO - WARNINGS: 1
[98] bibtex.pm:1519> INFO - Found BibTeX data source 'references.bib'
[321] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'
[321] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable'
[322] Biber.pm:4283> INFO - Sorting list 'nty/global//global/global/global' of type 'entry' with template 'nty' and locale 'en-US'
[322] Biber.pm:4289> INFO - No sort tailoring available for locale 'en-US'
[333] bbl.pm:676> INFO - Writing 'EEMLA.bbl' with encoding 'UTF-8'
[372] bbl.pm:779> INFO - Output to EEMLA.bbl
[372] Biber.pm:131> WARN - legacy month field 'Oct' in entry 'Wang2024' is not an integer - this will probably not sort properly.
[373] Biber.pm:131> WARN - legacy month field 'Feb' in entry 'cuda_programming_guide_2025' is not an integer - this will probably not sort properly.
[373] Biber.pm:133> INFO - WARNINGS: 2

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EEMLA.log
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**EEMLA.tex
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Package biblatex Info: Trying to load bibliographic data...
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(./EEMLA.bbl)
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@@ -181,6 +182,15 @@ In the above example formulation of a fixed-index mutator function coupled with
A critical aspect of the methodology is the mechanism responsible for determining which rule is applicable at each position within the input matrix $\mathbf{X}$. Rather than relying on stochastic selection, this approach implements a deterministic, location-based rule selection strategy that leverages the contextual information encoded within the model's representations. A major advantage of this fixed-index approach is the minimization of dynamic surfaces in the model's cost function, thereby reducing the amount of noise in output, as well as reducing the required amount of training as over fitting is a non-issue without randomness.
{\raggedright \normalsize \textit{Fixed-Index Architecture}}
The implementation architecture utilizes predetermined index relationships within the tensor space. For example, indices $(0,1)$ and $(1,2)$ might have a fixed relationship where their values are added together and output at index $(0,4)$. This fixed-index approach creates explicit computational pathways within the neural network architecture, allowing for deterministic mathematical operations without disturbing the stochastic nature of the remaining network. The fundamental advantage of this approach lies in its compatibility with modern hardware acceleration techniques, particularly Single Instruction Multiple Data (SIMD) operations that commonly take place on GPUs. These GPUs are already leveraged for matrix multiplication in the vast majority of existing AI/ML runtimes.
Each mathematical operation type is assigned specific input and output indices within the tensor, creating a predictable computational graph that can be optimized during compilation using the CUDA compiler, \mintinline{c}|gcc|, and manual assembler optimization like with DeepSeekV3 \parencite[16]{deepseekai2025deepseekv3technicalreport}. Addition operations, for instance, use indices $(i,j)$ and $(i+1,j)$ as inputs, with results stored at $(i,j+d/2)$, effectively partitioning the embedding space into operand and result regions. Multiplication operations utilize indices $(i,j)$ and $(i,j+1)$ as inputs, with results projected to $(i+1,j+d/2)$, maintaining a consistent pattern of spatial relationships within the tensor. More complex operations like matrix determinant calculations employ a $3\times3$ submatrix starting at index $(i,j)$ with results consolidated at $(i+3,j)$. This systematic approach to index mapping enables highly efficient computation on GPU architectures, as the fixed patterns allow for optimized memory access patterns due to hard-coded indexing at compile time, and reduced cache thrashing during tensor operations. Modern GPUs excel at these fixed-pattern operations, particularly when they can be expressed as fused operations within CUDA kernels or optimized through tensor cores designed specifically for matrix multiplication\parencite{cuda_programming_guide_2025}.
The architecture maintains parallel processing paths that preserve the dual nature of the system's capabilities. The standard language processing path continues to leverage the probabilistic, statistical nature of the transformer architecture, preserving the original LLM capabilities that have proven effective for natural language understanding and generation. Simultaneously, the mathematical computation path applies fixed-index transformations for specific operations, creating a deterministic subsystem within the larger stochastically variant network. These parallel streams capitalize on the inherent parallelism of GPU architectures, allowing different CUDA cores and cache regions to process distinct streams simultaneously. The fixed-index nature of the mathematical operations enables compiler optimizations that can allocate dedicated tensor cores for these operations, maximizing throughput and minimizing latency. Existing models, as shown in Figure \ref{tb:model-sizes} tend to use far more VRAM than cores, leading to an allocation inefficient in terms of performance per millisecond of inference. The paths are later merged through concatenation and a projection layer, a process that similarly benefits from the warp-level primitives available in modern GPU architectures for efficient tensor manipulation.
The attention mechanism serves as a noise filter and integration component, allowing the model to selectively focus on either standard language representations or mathematically transformed representations based on input context. This selective focusing behavior effectively routes information through the appropriate pathway based on the input's semantic requirements. From a hardware acceleration perspective, this mechanism benefits from the recent advancements in GPU architecture specifically designed for transformer models. The attention operations leverage dedicated tensor cores in NVIDIA's Ampere and Hopper architectures, which provide specialized hardware acceleration for matrix multiplication and accumulation operations at various precisions. The fixed-index nature of the approach enables further optimization of these operations through persistent CUDA kernels that maintain tensor data in high-bandwidth on-chip memory (L3-L4 cache), reducing expensive global memory access operations during the attention computation phase.
%%%%Works cited
\newpage

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biber EEMLA
pdflatex EEMLA.tex
pdflatex -shell-escape EEMLA.tex
pdflatex -shell-escape EEMLA.tex

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references.bib
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@@ -68,3 +68,20 @@ DOI = {10.3390/app14020744}
primaryClass={cs.LG},
url={https://arxiv.org/abs/2110.14168},
}
@misc{cuda_programming_guide_2025,
author = {NVIDIA},
title = {1. Introduction - CUDA C++ Programming Guide},
year = {2025},
month = {Feb},
url = {https://docs.nvidia.com/cuda/cuda-c-programming-guide/},
journal = {1. Introduction - CUDA C++ Programming Guide}
}
@misc{deepseekai2025deepseekv3technicalreport,
title={DeepSeek-V3 Technical Report},
author={DeepSeek-AI and Aixin Liu and Bei Feng and Bing Xue and Bingxuan Wang and Bochao Wu and Chengda Lu and Chenggang Zhao and Chengqi Deng and Chenyu Zhang and Chong Ruan and Damai Dai and Daya Guo and Dejian Yang and Deli Chen and Dongjie Ji and Erhang Li and Fangyun Lin and Fucong Dai and Fuli Luo and Guangbo Hao and Guanting Chen and Guowei Li and H. Zhang and Han Bao and Hanwei Xu and Haocheng Wang and Haowei Zhang and Honghui Ding and Huajian Xin and Huazuo Gao and Hui Li and Hui Qu and J. L. Cai and Jian Liang and Jianzhong Guo and Jiaqi Ni and Jiashi Li and Jiawei Wang and Jin Chen and Jingchang Chen and Jingyang Yuan and Junjie Qiu and Junlong Li and Junxiao Song and Kai Dong and Kai Hu and Kaige Gao and Kang Guan and Kexin Huang and Kuai Yu and Lean Wang and Lecong Zhang and Lei Xu and Leyi Xia and Liang Zhao and Litong Wang and Liyue Zhang and Meng Li and Miaojun Wang and Mingchuan Zhang and Minghua Zhang and Minghui Tang and Mingming Li and Ning Tian and Panpan Huang and Peiyi Wang and Peng Zhang and Qiancheng Wang and Qihao Zhu and Qinyu Chen and Qiushi Du and R. J. Chen and R. L. Jin and Ruiqi Ge and Ruisong Zhang and Ruizhe Pan and Runji Wang and Runxin Xu and Ruoyu Zhang and Ruyi Chen and S. S. Li and Shanghao Lu and Shangyan Zhou and Shanhuang Chen and Shaoqing Wu and Shengfeng Ye and Shengfeng Ye and Shirong Ma and Shiyu Wang and Shuang Zhou and Shuiping Yu and Shunfeng Zhou and Shuting Pan and T. Wang and Tao Yun and Tian Pei and Tianyu Sun and W. L. Xiao and Wangding Zeng and Wanjia Zhao and Wei An and Wen Liu and Wenfeng Liang and Wenjun Gao and Wenqin Yu and Wentao Zhang and X. Q. Li and Xiangyue Jin and Xianzu Wang and Xiao Bi and Xiaodong Liu and Xiaohan Wang and Xiaojin Shen and Xiaokang Chen and Xiaokang Zhang and Xiaosha Chen and Xiaotao Nie and Xiaowen Sun and Xiaoxiang Wang and Xin Cheng and Xin Liu and Xin Xie and Xingchao Liu and Xingkai Yu and Xinnan Song and Xinxia Shan and Xinyi Zhou and Xinyu Yang and Xinyuan Li and Xuecheng Su and Xuheng Lin and Y. K. Li and Y. Q. Wang and Y. X. Wei and Y. X. Zhu and Yang Zhang and Yanhong Xu and Yanhong Xu and Yanping Huang and Yao Li and Yao Zhao and Yaofeng Sun and Yaohui Li and Yaohui Wang and Yi Yu and Yi Zheng and Yichao Zhang and Yifan Shi and Yiliang Xiong and Ying He and Ying Tang and Yishi Piao and Yisong Wang and Yixuan Tan and Yiyang Ma and Yiyuan Liu and Yongqiang Guo and Yu Wu and Yuan Ou and Yuchen Zhu and Yuduan Wang and Yue Gong and Yuheng Zou and Yujia He and Yukun Zha and Yunfan Xiong and Yunxian Ma and Yuting Yan and Yuxiang Luo and Yuxiang You and Yuxuan Liu and Yuyang Zhou and Z. F. Wu and Z. Z. Ren and Zehui Ren and Zhangli Sha and Zhe Fu and Zhean Xu and Zhen Huang and Zhen Zhang and Zhenda Xie and Zhengyan Zhang and Zhewen Hao and Zhibin Gou and Zhicheng Ma and Zhigang Yan and Zhihong Shao and Zhipeng Xu and Zhiyu Wu and Zhongyu Zhang and Zhuoshu Li and Zihui Gu and Zijia Zhu and Zijun Liu and Zilin Li and Ziwei Xie and Ziyang Song and Ziyi Gao and Zizheng Pan},
year={2025},
eprint={2412.19437},
archivePrefix={arXiv},
primaryClass={cs.CL},
url={https://arxiv.org/abs/2412.19437},
}

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