i'm basically done

IEEE-conference-template-062824.tex

@@ -9,6 +9,8 @@
 \usepackage{graphicx}
 \usepackage{textcomp}
 \usepackage{xcolor}
+\usepackage{booktabs}
+
 \def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
     T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
 
@@ -22,28 +24,54 @@
 \title{Rule-based Tensor Mutations Embedded within LLMs for Low-Cost Mathematical Computation}
 
 \author{\IEEEauthorblockN{Srikrishna Ayyalasomayajula}
-\IEEEauthorblockA{\textit{dept. name of organization (of Aff.)} \\
-\textit{name of organization (of Aff.)}\\
-City, Country \\
+\IEEEauthorblockA{\textit{
+Plano, Texas \\
 krishna@ayyalasomayajula.net}
 }
-
+}
 \maketitle
 
 \begin{abstract}
-Large Language Models (LLMs) have demonstrated remarkable proficiency in natural language tasks but remain inefficient and error-prone when performing deterministic mathematical computations. Existing approaches to improving mathematical reasoning rely on external symbolic engines or extensive fine-tuning on mathematical corpora, both of which introduce latency and scalability challenges. This paper proposes a novel architectural enhancement for transformer-based LLMs: the embedding of deterministic, rule-based tensor mutations directly within the model’s internal computational graph. By implementing fixed-index tensor operations—such as arithmetic functions, binary operations, and matrix computations—within the embedding space of the Llama 3 3B model, we enable low-latency mathematical reasoning without modifying the core probabilistic architecture. The proposed system leverages deterministic computation pathways optimized for GPU tensor cores, significantly reducing inference latency and improving mathematical accuracy on arithmetic and linear algebra tasks. %Experimental results on benchmark datasets demonstrate up to a 3.7× reduction in inference latency for mathematical prompts and a 24\% increase in accuracy compared to baseline LLM performance, all without additional fine-tuning. This work highlights the potential for integrating rule-based logic into neural network inference, bridging the gap between probabilistic language modeling and deterministic computation.%
+Large Language Models (LLMs) have demonstrated remarkable proficiency in natural language tasks but remain inefficient and error-prone when performing deterministic mathematical computations. Existing approaches to improving mathematical reasoning rely on external symbolic engines or extensive fine-tuning on mathematical corpora, both of which introduce latency and scalability challenges. This paper proposes a novel architectural enhancement for transformer-based LLMs: the embedding of deterministic, rule-based tensor mutations directly within the model’s internal computational graph. By implementing fixed-index tensor operations—such as arithmetic functions, binary operations, and matrix computations—within the embedding space of the Llama 3 3B model, we enable low-latency mathematical reasoning without modifying the core probabilistic architecture. The proposed system leverages deterministic computation pathways optimized for GPU tensor cores, significantly reducing inference latency and improving mathematical accuracy on arithmetic and linear algebra tasks.
 \end{abstract}
 
 \begin{IEEEkeywords}
-component, formatting, style, styling, insert.
+Multi-Layer Perceptron (MLP), Rule-based Mutation, Neural Network Architecture, Language Models, LLaMA, Long-Horizon Reasoning, Step-wise Accuracy, Model Generalization, Deep Learning, Artificial Intelligence, Training Efficiency, Inference Optimization, Neural Computation, Architecture Search, Mutated MLPs, Model Scaling, Structural Inductive Bias, Token-wise Evaluation, Parametric Efficiency, High-Performance Computing, Transformer Models, Cognitive Tasks, Reasoning Benchmarking, Neuro-Symbolic Integration.
 \end{IEEEkeywords}
 
 \section{Introduction}
 
-Large Language Models (LLMs) have rapidly advanced the field of natural language processing (NLP), achieving unprecedented success across tasks such as text generation, summarization, translation, and conversational reasoning. These models, built upon transformer architectures, learn statistical patterns in tokenized language data through extensive pretraining on vast corpora. However, despite their proficiency in language understanding, LLMs consistently underperform on tasks that require deterministic mathematical computation \cite{hendrycks2021measuringmathematicalproblemsolving, ahn2024largelanguagemodelsmathematical}. This limitation stems from the fundamentally probabilistic nature of neural network inference, which excels at pattern recognition but lacks the precise symbolic manipulation capabilities required for accurate mathematical reasoning.
+Large Language Models (LLMs) have rapidly advanced the field of natural language processing (NLP), achieving unprecedented success across tasks such as text generation, summarization, translation, and conversational reasoning. These models, built upon transformer architectures, learn statistical patterns in tokenized language data through extensive pretraining on vast corpora. However, despite their proficiency in language understanding, LLMs consistently underperform on tasks that require deterministic mathematical computation \cite{hendrycks2021measuringmathematicalproblemsolving} \cite{ahn2024largelanguagemodelsmathematical}. This limitation stems from the fundamentally probabilistic nature of neural network inference, which excels at pattern recognition but lacks the precise symbolic manipulation capabilities required for accurate mathematical reasoning.
 
 Current approaches to improving the mathematical competence of LLMs follow two main paradigms. The first involves fine-tuning models on specialized mathematical datasets \cite{cobbe2021trainingverifierssolvemath}, such as arithmetic sequences, calculus problems, or algebraic equations. While fine-tuning improves performance on familiar problems, it is both computationally expensive and brittle when generalizing to unseen operations or data distributions. The second paradigm leverages Retrieval-Augmented Generation (RAG) pipelines that offload computation to external symbolic engines such as Wolfram Alpha. Though effective in some contexts, these solutions introduce substantial inference latency due to the need for external API calls and often compromise the seamless, end-to-end nature of LLM inference pipelines.
 
+\begin{table}[htbp]
+\caption{Comparison of LLM Computational Requirements}
+\begin{center}
+\begin{tabular}{|l|c|c|c|}
+\hline
+\textbf{Model Name} & \textbf{Compute (PF-days)} & \textbf{Inference (ms/tkn.)} & \textbf{VRAM (GB)} \\
+\hline
+GPT-2            & 5.6       & 12   & 3     \\
+GPT-3            & 3,640     & 75   & 350   \\
+LLaMA-2-7B       & 184       & 18   & 14    \\
+LLaMA-2-13B      & 368       & 32   & 26    \\
+LLaMA-2-70B      & 1,720     & 145  & 140   \\
+Claude 2         & N/A       & 82   & $\sim$200 \\
+GPT-4            & $\sim$25,000 & 210  & $\sim$3,000 \\
+\hline
+\end{tabular}
+\label{tab:model-sizes}
+\end{center}
+\vspace{2mm}
+\begin{minipage}{0.95\linewidth}
+\footnotesize
+\textit{Note—} Training compute is measured in petaflop-days. Inference time is reported per token on an A100 GPU. Memory usage denotes peak VRAM during inference. Proprietary model figures are estimates.
+\end{minipage}
+\end{table}
+
+
+
 Moreover, scaling LLMs to address such shortcomings faces practical limitations. Empirical scaling laws \cite{hoffmann2022trainingcomputeoptimallargelanguage} demonstrate that beyond a certain point, increasing the number of model parameters yields diminishing returns in accuracy relative to computational cost. This is particularly evident in mathematical reasoning benchmarks, where larger models show sub-linear performance improvements despite exponential increases in compute and memory consumption. As Table~\ref{tab:model-sizes} illustrates, state-of-the-art models such as GPT-4 and Claude 2 require thousands of petaflop-days of compute and terabytes of memory, yet they still fail to achieve high accuracy on elementary arithmetic problems without external assistance.
 
 This paper addresses this gap by proposing a fundamentally different approach: embedding deterministic, rule-based tensor mutations directly within the neural network's computational graph. Instead of relying solely on statistical learning, this method introduces explicit, hard-coded mathematical operations into specific locations of the model's embedding space. By leveraging the high parallelism of modern GPUs, particularly tensor core architectures optimized for Single Instruction, Multiple Data (SIMD) workloads, these operations execute with minimal latency and no dependence on external inference pathways.