From 3188a05c6aa65e7ecb3915e69d586f2dd8ed6da4 Mon Sep 17 00:00:00 2001 From: Mars Ultor Date: Tue, 29 Apr 2025 22:38:13 -0500 Subject: [PATCH] cooked --- EEMLA.aux | 17 +- EEMLA.bbl | 482 ------------------------------------------------- EEMLA.bcf | 3 + EEMLA.blg | 18 +- EEMLA.log | 262 +++++++++++++++++++++------ EEMLA.pdf | Bin 116835 -> 131155 bytes EEMLA.run.xml | 4 +- EEMLA.tex | 33 ++++ references.bib | 18 ++ 9 files changed, 279 insertions(+), 558 deletions(-) delete mode 100644 EEMLA.bbl diff --git a/EEMLA.aux b/EEMLA.aux index a48c08f..1b430a2 100644 --- a/EEMLA.aux +++ b/EEMLA.aux @@ -20,11 +20,12 @@ \abx@aux@segm{0}{0}{hendrycks2021measuringmathematicalproblemsolving} \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Comparison of LLM Sizes and Their Computational Requirements}}{5}{}\protected@file@percent } \newlabel{tab:model-sizes}{{1}{5}{}{table.1}{}} -\abx@aux@read@bbl@mdfivesum{C2B7A906B5BBD5BA46851A4078C3BC58} -\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}{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{7} +\abx@aux@cite{0}{ahn2024largelanguagemodelsmathematical} +\abx@aux@segm{0}{0}{ahn2024largelanguagemodelsmathematical} +\abx@aux@cite{0}{cobbe2021trainingverifierssolvemath} +\abx@aux@segm{0}{0}{cobbe2021trainingverifierssolvemath} +\abx@aux@cite{0}{cobbe2021trainingverifierssolvemath} +\abx@aux@segm{0}{0}{cobbe2021trainingverifierssolvemath} +\abx@aux@read@bbl@mdfivesum{nohash} +\abx@aux@read@bblrerun +\gdef \@abspage@last{8} diff --git a/EEMLA.bbl b/EEMLA.bbl deleted file mode 100644 index 5ebcdd0..0000000 --- a/EEMLA.bbl +++ /dev/null @@ -1,482 +0,0 @@ -% $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.3 $ -% Do not modify the above lines! -% -% This is an auxiliary file used by the 'biblatex' package. -% This file may safely be deleted. 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Output to EEMLA.bbl -[169] Biber.pm:131> WARN - legacy month field 'Oct' in entry 'Wang2024' is not an integer - this will probably not sort properly. -[169] Biber.pm:133> INFO - WARNINGS: 1 +[39] biber:340> INFO - === Tue Apr 29, 2025, 22:30:03 +[47] Utils.pm:410> ERROR - EEMLA.bcf is malformed, last biblatex run probably failed. 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[5] +LaTeX Font Info: Trying to load font information for TS1+ptm on input line 1 +52. + (/usr/share/texmf-dist/tex/latex/psnfss/ts1ptm.fd +File: ts1ptm.fd 2001/06/04 font definitions for TS1/ptm. +) + +LaTeX Warning: Citation 'ahn2024largelanguagemodelsmathematical' on page 6 unde +fined on input line 162. + + +LaTeX Warning: Citation 'cobbe2021trainingverifierssolvemath' on page 6 undefin +ed on input line 162. + + +LaTeX Warning: Citation 'cobbe2021trainingverifierssolvemath' on page 6 undefin +ed on input line 162. + + Package fancyhdr Warning: \headheight is too small (12.0pt): @@ -579,6 +705,17 @@ Package fancyhdr Warning: \headheight is too small (12.0pt): (fancyhdr) \addtolength{\topmargin}{-2.49998pt}. [6] +! Undefined control sequence. +l.167 ...le-based function } \mathcal{R} : \mathbb + {R}^{n \times d} \rightarr... + +? +! 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z+F#G~+BWhm*EQ4faMO@z$F2O%rn{YMUnIme?%pQ-%>PN9R3Ud)3*v)_d0fj)i~r z9yrzWm+_1F&R0)YzLiq=DPI&=e+J&B&*hq~bCHpw-crFpAwMaL%f^OFKcuoCRY5-@ zC^d~s-!m^IwL&4A zEnmUh0?Khwh_-Qdva~RCc6Bo~F?2GpG_Wu>wy-obwQw=v-^ ]> - + latex EEMLA.bcf @@ -64,7 +64,7 @@ english-mla.lbx - + biber biber diff --git a/EEMLA.tex b/EEMLA.tex index c344c37..5f849f2 100644 --- a/EEMLA.tex +++ b/EEMLA.tex @@ -26,6 +26,7 @@ % \usepackage{fancyhdr} \usepackage{float} +\usepackage{amsmath} \pagestyle{fancy} \lhead{} \chead{} @@ -143,6 +144,38 @@ This research aims to investigate the potential integration of rule-based tensor \textbf{RQ:} How can deterministic rule-based tensor mutations be embedded within LLM architectures to enable more accurate and efficient mathematical operations? \end{quote} +The significance of this line of inquiry lies in its potential to address a fundamental limitation of current generative AI systems like ChatGPT, Anthropic's Claude, etc. While specialized numeric compute systems exist (e.g. RAG with Wolphram Alpha), they operate independently of the SIMD, low-latency systems of LLMS, leading to sizable latency in communication. This is especially prevalent in workflows involving both mathematical and linguistic reasoning. The integration of computational resources required for such workflows within LLMs could substantially reduce the computational resources required for complex tasks that involve both natural and language processing and mathematical reasoning. + +This infestation focuses specifically on the following mathematical operations: + +\begin{itemize} +\item Basic arithmetic (addition, subtraction, multiplication, division) +\item Matrix Operations (multiplication, inversion, determinant) +\item Binary Opertaions (XOR, AND, NAND, left shift, right shift, OR, complement) +\item Array Operations (array sum, as well as the mean, median, mode, standard deviation, variance, and other single variable metrics of a data set) +\end{itemize} + +Furthermore, as previously mentioned, the scope of the experiment is limited to implementing these operations within existing open source LLM architectures of moderate scale (1-7 Billion Parameters) as opposed to developing entirely new architectures. This is both because it is desirable to eliminate all sources of subject variability to help ascertain statistical significance, and because of the readily available weights. Namely, the target model for this paper is the Llama-3-3B model, due to its lightweight and fully open source nature. + +{\raggedright \normalsize \textbf{Related Works}} + +Prior research has explored various approaches to improving mathematical reasoning capabilities in LLMs, including specialized training on mathematical corpora \parencite[4]{ahn2024largelanguagemodelsmathematical}. Additionally, other work has been done to fine-tune responses to mathematically demanding prompts using reinforcement learning \parencite[1]{cobbe2021trainingverifierssolvemath}. Others still have tried to add secondary inferences or \textit{Verifiers} to determine accuracy of model outputs when containing computations \parencite[2]{cobbe2021trainingverifierssolvemath}. The immediately evident disadvantage to these approaches is the need for extended training cycles and copious amounts of new corpora. Furthermore, training corpora are required to be similar to testing samples since the strategies outlined above fail to grant models a mechanical performance edge. + +{\raggedright \normalsize \textbf{Methodology}} +$$ +\begin{aligned} +&\text{Define a rule-based function } \mathcal{R} : \mathbb{R}^{n \times d} \rightarrow \mathbb{R}^{n \times d} \text{ such that:} \\ +&\mathcal{R}(\mathbf{X})_i = +\begin{cases} +\mathbf{X}_i + \mathbf{X}_{i+1}, & \text{if rule is "sum with right neighbor"} \\ +\det(\mathbf{X}_{i:i+2, j:j+2}), & \text{if rule is "3$\times$3 determinant over submatrix"} \\ +\mathbf{X}_i, & \text{otherwise} +\end{cases} \\ +&\text{Then pass } \mathcal{R}(\mathbf{X}) \text{ into the modified attention layer: } \mathbf{Z} = \text{Attention}(\mathcal{R}(\mathbf{X})) +\end{aligned} +$$ + + %%%%Works cited \newpage \begin{center} diff --git a/references.bib b/references.bib index c58cd5a..a30a7dc 100644 --- a/references.bib +++ b/references.bib @@ -50,3 +50,21 @@ DOI = {10.3390/app14020744} primaryClass={cs.LG}, url={https://arxiv.org/abs/2103.03874}, } +@misc{ahn2024largelanguagemodelsmathematical, + title={Large Language Models for Mathematical Reasoning: Progresses and Challenges}, + author={Janice Ahn and Rishu Verma and Renze Lou and Di Liu and Rui Zhang and Wenpeng Yin}, + year={2024}, + eprint={2402.00157}, + archivePrefix={arXiv}, + primaryClass={cs.CL}, + url={https://arxiv.org/abs/2402.00157}, +} +@misc{cobbe2021trainingverifierssolvemath, + title={Training Verifiers to Solve Math Word Problems}, + author={Karl Cobbe and Vineet Kosaraju and Mohammad Bavarian and Mark Chen and Heewoo Jun and Lukasz Kaiser and Matthias Plappert and Jerry Tworek and Jacob Hilton and Reiichiro Nakano and Christopher Hesse and John Schulman}, + year={2021}, + eprint={2110.14168}, + archivePrefix={arXiv}, + primaryClass={cs.LG}, + url={https://arxiv.org/abs/2110.14168}, +}