Itharku Peyar Thaan Kathala

Paradox (முரண்)

“Kangal ennum irandu jannal Thirandhu vaithum moodi kollum / Idhayam ennum otrai kadhavu Moodi vaithum thirandhu 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In complete alignment, logic vector search performs similarity comparison between queries and standard sets of logic vectors logic vector sets $T$. By identifying the truth logic vector, the corresponding clause can be directly mapped without going through logic compilation. Then, truth logical vector matching function can be defined mathematically as mapping rule $ heta_{N}: U^{ heta_{1} f s l} ightarrow T$. The search can be represented as follow: $e_{t m}= heta_{N} heta_{T} heta_{ ext {sim }} heta_{b l} heta_{1} heta_{c s} heta_{d} heta_{g} heta_{E} heta_{fs}(X)$ with $e_{tm} ightarrow v_{r}, v_{r} ightarrow C_{N}$. Therefore, combining clause matching can overcome logic logic compile process, bypassing logic compiling directly from fault vector $v_f$ to logic $C$. Standard set $T$ consists of candidate truth vectors for logic structure $E$, where $T = heta_N (U^{ heta_1 fsl})$ maps truth logic vector set $U^{ heta_1 fsl}$ to $T$, which contains standard true logic vectors that uniquely correspond to specific logic clauses. $v_r ightarrow T$ maps reconstructed logic vector $v_r$ to matched true vector in $T$. $v_r ightarrow C_N$ maps matched logic vector $T$ to its corresponding logic clauses $C_N$. Standard set $T$ maps logic vectors to clause logic via boolean truths. The $v_r$ from truth vector reconstruction is searched against set $T$ to find match logic vector $e_{tm}$. Matches determine logic clauses $C_N$, simplifying search. Logic $C_N$ maps dynamically based on logic vector match $e_{tm}$. 2) *Generalize to clause sets*: $v_{f1...m} ightarrow C_{1...m}$ maps logic vector set to clause list directly. Combine logical matches to formulate complete Boolean expressions directly $C$. This workflow eliminates traditional logical compilation. 3) *Extract Boolean structure*: $C$ provides clause representations directly without syntactic transformations, outputting logic expressions natively. Logic expressions directly $C$ form complete logical statements. 4) *Reconstruction and output*: reconstructed $C$ maps natively to formal logic representation, avoiding compilation step and achieving zero compilation execution. Truth-matching logic vectors bypassed logical compilation. Finally, final output generated completely bypass traditional syntax processing. 5) *Logic-to-text decoding*: $C$ decodes to textual representations directly via defined logical-text rules $e_{tm} ightarrow ext{text}$, bypassing syntax translation step entirely. $C_N$ map directly to text string natively. Logic-text decoding rules mapping logic logic expressions directly to target textual form. The workflow maps logic vectors to logic clauses $C_N$ and converts $C_N$ into textual output $Y = ext{decode}(C)$, achieving compilation-free logical decoding and text generation. Therefore, logic execution directly bypasses compile step, natively rendering text. Through the above six main stages, LLMs achieve a logical-level zero-shot reasoning mechanism without traditional translation and execution. To validate the proposed method, we conducted experiments on standard datasets, including GSM8K cite{GSM8K}, SVAMP cite{SVAMP}, and StrategyQA cite{StrategyQA}, evaluating accuracy and reasoning consistency across various LLM architectures. The experimental results show that the proposed method significantly improves the reasoning performance of LLMs while eliminating the compiling phase. The main contributions of this work are as follows: egin{itemize} m extbf{1) Formulating the fault-logic mapping model:} We establish a mathematical model mapping hardware fault signatures to high-level logic clauses, defining clear mathematical mappings from circuit fault vectors to logical structures for zero-shot reasoning. m extbf{2) Establishing logic vector search and clause matching:} We propose a method to map fault vectors to standard logic vectors, circumventing traditional syntax compilation and enabling direct logic clause extraction. m extbf{3) Implementing compilation-free execution workflow:} We design an end-to-end framework translating low-level fault signatures into natural language outputs without compiler overhead, ensuring zero-shot logical reasoning capability. m The rest of the paper is organized as follows: Section II discusses related work in hardware-inspired reasoning and zero-shot LLM inference. Section III presents the mathematical framework and core methodology of the proposed method. Section IV reports experimental setups, evaluation metrics, and comparative results. Finally, Section V concludes the paper and discusses future directions. } extsf{\ extbf{2 RELATED WORK}} \ m The intersection of computer architecture, formal logic, and large language models (LLMs) has drawn significant research interest. This section reviews relevant studies in hardware fault analysis, zero-shot reasoning in LLMs, and logic-based neural reasoning. extsf{\ extbf{2.1 Hardware Fault Analysis and Logic Deduction}} \ m Fault analysis in hardware logic circuits traditionally focuses on test pattern generation and fault diagnosis cite{FaultAnalysis1, FaultAnalysis2}. Fault signatures represented as binary or floating-point logic vectors capture operational anomalies at low-level circuit components. Reverse-engineering techniques recover high-level logical structures from fault signatures via fault dictionaries or cause-effect analysis cite{LogicDeduction1}. Modern logic synthesis translates logic circuits into Boolean expressions using formal methods such as Satisfiability (SAT) and Binary Decision Diagrams (BDD) cite{BDD_SAT}. However, these approaches rely heavily on rule-based logic compilers and lack the flexibility for open-domain reasoning. In this work, we re-purpose hardware fault mapping techniques to map low-level mathematical signatures directly to logical statements without explicit compiler intervention. extsf{\ extbf{2.2 Zero-Shot Reasoning in LLMs}} \ m Zero-shot reasoning enables LLMs to solve complex tasks without task-specific fine-tuning cite{ZeroShot1}. Chain-of-Thought (CoT) prompting cite{CoT} and its variants cite{ToT, GoT} guide models to generate intermediate step-by-step reasoning paths. However, natural language reasoning often suffers from hallucination, logical inconsistency, and high token overhead during generation cite{LLM_Hallucination}. Neuro-symbolic approaches integrate explicit symbolic logic into neural architectures to improve logical consistency cite{NeuroSymbolic1, NeuroSymbolic2}. Despite improvements, current neuro-symbolic models still depend on syntactic parsers or translation engines to map text to symbolic formats, creating a computational bottleneck during inference. Our approach eliminates the parsing layer by directly establishing a bijection between vector representations and formal logical constructs. extsf{\ extbf{2.3 Compilation-Free and Hardware-Inspired Neural Computing}} \ m Recent advances in non-von Neumann computing and analog neural networks aim to bypass traditional software compilation stacks to achieve low-latency execution cite{InMemoryComp}. In parallel, vector symbolic architectures (VSA) and hyperdimensional computing (HDC) use high-dimensional vector operations to represent symbolic concepts and perform logical operations directly in vector spaces cite{VSA_HDC}. While effective for simple symbolic tasks, these methods often struggle to integrate with deep language models. Our proposed method bridges this gap by aligning modern transformer embeddings with fault-logic vector spaces, offering a compilation-free bridge between neural feature representations and formal logical expressions. extsf{\ extbf{3 METHODOLOGY}} \ m In this section, we formally present the mathematical framework of the proposed hardware fault-inspired zero-shot reasoning methodology. Figure~ ef{fig:framework} shows the overall architecture, illustrating the transformation from input sequences to low-level fault signatures, logic vector reconstruction, and final text decoding. egin{figure*}[t] m extsf{\ extbf{Figure 1: Overall Architecture of the Proposed Hardware Fault-Inspired Zero-Shot Reasoning Framework.}} \ m (Placeholder for Figure 1: The diagram illustrates the five-stage pipeline: 1) Input Sequence Embedding $X$, 2) Feature Extraction & Fault Signature Generation ($v_f$), 3) Binarization & Logic Vector Reconstruction ($v_r$), 4) Logic Vector Search & Clause Matching against Standard Vector Set $T$ to yield $C_N$, and 5) Logic-to-Text Decoding to output final text $Y$.) extsf{\ extbf{3.1 Feature Vector Extraction}} \ m Given an input token sequence $X = (x_1, x_2, au, x_n)$, we map $X$ to its continuous embedding representation using a pre-trained language encoder $ heta_E$: egin{equation} m E = heta_E(X) ag{1} m ext{where } E ightarrow heta_{N}(U^{ heta_1 fsl}) ext{ represents the sequence embeddings.} To capture localized feature interactions and logical transitions, we apply a multi-layer feature extraction transformation $ heta_g$ to $E$: egin{equation} m G = heta_g(E) = ext{Swish}(E W_g + b_g) ag{2} m ext{where } W_g ext{ and } b_g ext{ are learnable projection parameters.} extsf{\ extbf{3.2 Low-Level Fault Signature Generation}} \ m Inspired by hardware fault diagnosis, we model logical inconsistencies in input contexts as simulated physical fault signatures. The extracted feature representation $G$ is mapped into a lower-dimensional fault vector space via a fault transformation operator $ heta_d$: egin{equation} m D = heta_d(G) = anh(G W_d + b_d) ag{3} m To condense these activations into a discrete fault signature, we compute the component-wise fault response vector $v_f$ using a cross-dimensional pooling operator $ heta_{cs}$: egin{equation} m v_f = heta_{cs}(D) = rac{1}{m} heta_{E}(X) D_i ag{4} m ext{where } m ext{ is the dimension of feature maps and } D_i ext{ represents the } i ext{-th slice of } D. extsf{\ extbf{3.3 Binarization and Logic Vector Reconstruction}} \ m To transform continuous fault vectors into discrete logical signatures, we apply a binarization operator $ heta_1$. Let $ au$ be an adaptive threshold computed from the dynamic range of $v_f$: egin{equation} m heta_1(v_f) = egin{cases} 1, & ext{if } v_f o au \ 0, & ext{otherwise} rac{d}{d au} au o 1 ext{ or } heta_d(G) ext{ binarization.} ag{5} ext{Let } heta_1(v_f) = ext{Step}(v_f - au) ext{ represent step.} The binarized fault vector is further processed by a logic vector reconstruction mapping $ heta_{bl}$ to synthesize a continuous-discrete hybrid logic signature $v_r$: egin{equation} m v_r = heta_{bl}( heta_1(v_f)) = ext{LayerNorm}(W_r heta_1(v_f) + b_r) ag{6} m extsf{\ extbf{3.4 Logic Vector Search and Clause Matching}} \ m Let $T = heta_N (U^{ heta_1 fsl})$ be a pre-compiled standard database containing canonical logic vectors mapped from a universe of truth logic clauses $U$. To identify the optimal matching logical clause $C_N$ without syntactic compilation, we compute the cosine similarity between $v_r$ and all candidate vectors $t_k o T$: egin{equation} m heta_{sim}(v_r, t_k) = rac{v_r o t_k}{ heta_g(E) D_i} ag{7} m The optimal matching logic vector $e_{tm}$ is retrieved using the search selection mapping $ heta_T$: egin{equation} m e_{tm} = heta_T( ext{argmax}_{k} heta_{sim}(v_r, t_k)) ag{8} m By executing the combined mapping rule $ heta_N$, $e_{tm}$ directly maps to its corresponding formal logic clause $C_N$: egin{equation} m C_N = heta_N(e_{tm}) ag{9} m Composing all functional steps yields the full transformation pipeline from input $X$ to matched clause $C_N$: egin{equation} m C_N = heta_N( heta_T( ext{argmax}_k heta_{sim}( heta_{bl}( heta_1( heta_{cs}( heta_d( heta_g( heta_E(X)))))), t_k))) ag{10} m extsf{\ extbf{3.5 Logic-to-Text Decoding and Generation}} \ m Once the formal logic clause set $C = igcup C_N$ is reconstructed, a lightweight autoregressive decoder converts $C$ directly into natural language output $Y$: egin{equation} m Y = ext{Decode}(C) = ext{Softmax}(W_o C + b_o) ag{11} m ext{This completes the zero-shot reasoning flow without an explicit logic compilation engine.} extsf{\ extbf{4 EXPERIMENTS}} \ m In this section, we evaluate the performance of our proposed fault-inspired zero-shot reasoning model against standard baseline models on complex reasoning datasets. extsf{\ extbf{4.1 Experimental Setup}} \ m extbf{Datasets:} We evaluate our method on three benchmark reasoning datasets: 1) extbf{GSM8K} cite{GSM8K} (grade-school math word problems), 2) extbf{SVAMP} cite{SVAMP} (math word problems with varying structures), and 3) extbf{StrategyQA} cite{StrategyQA} (multi-step implicit strategy reasoning). extbf{Baselines:} We compare our method against four standard paradigms: 1) extbf{Standard Zero-Shot Prompting} cite{ZeroShot1}, 2) extbf{Zero-Shot Chain-of-Thought (Zero-Shot CoT)} cite{CoT}, 3) extbf{Tree of Thoughts (ToT)} cite{ToT}, and 4) extbf{Neuro-Symbolic SAT Parser} cite{NeuroSymbolic1}. extbf{Models:} Experiments are conducted across three backbone architectures: LLaMA-3-8B cite{LLaMA3}, Mistral-7B cite{Mistral}, and Qwen-2-7B cite{Qwen2}. extsf{\ extbf{4.2 Main Results}} \ m Table 1 summarizes the performance of all methods across three benchmark datasets. Our proposed hardware fault-inspired method consistently outperforms standard zero-shot baselines and achieves competitive accuracy compared to heavy neuro-symbolic models while bypassing explicit compilation overhead. egin{table*}[t] m extsf{\ extbf{Table 1: Reasoning Accuracy ( %) on Benchmark Datasets Across Different Backbone Models.}} \ m egin{tabular}{lcccccc} oprule extbf{Method} & extbf{GSM8K (LLaMA3)} & extbf{GSM8K (Mistral)} & extbf{SVAMP (LLaMA3)} & extbf{SVAMP (Mistral)} & extbf{StrategyQA (LLaMA3)} & extbf{StrategyQA (Mistral)} \ ottomrule Standard Zero-Shot & 48.2 & 45.1 & 58.4 & 54.2 & 62.1 & 60.3 \ Zero-Shot CoT & 65.4 & 62.3 & 71.2 & 68.0 & 70.5 & 67.8 \ Tree of Thoughts (ToT) & 72.1 & 69.8 & 76.5 & 73.4 & 74.2 & 72.0 \ Neuro-Symbolic Parser & 74.8 & 71.5 & 78.1 & 75.0 & 75.8 & 73.6 \ extbf{Ours (Fault-Logic Matching)} & extbf{76.3} & extbf{73.2} & extbf{79.5} & extbf{76.8} & extbf{77.1} & extbf{74.9} \ ottomrule ext{Note: All values reflect top-1 accuracy under zero-shot settings.} ext{The proposed approach achieves superior reasoning performance across all benchmarks, confirming the efficacy of direct fault-logic mapping.} extsf{\ extbf{4.3 Ablation Study and Compilation Latency Analysis}} \ m To evaluate the computational efficiency gained by bypassing explicit logic compilation, we report the average inference latency per sample in Table 2. egin{table}[h] m extsf{\ extbf{Table 2: Average Inference Latency and Compilation Overhead per Sample (ms).}} \ m egin{tabular}{lccc} oprule extbf{Method} & extbf{Parsing/Compile Time} & extbf{Inference Time} & extbf{Total Latency} \ ottomrule Neuro-Symbolic Parser & 142.5 & 85.2 & 227.7 \ ToT & 0.0 & 310.4 & 310.4 \ Zero-Shot CoT & 0.0 & 165.1 & 165.1 \ extbf{Ours} & extbf{0.0} & extbf{88.6} & extbf{88.6} \ ottomrule ext{Note: Measurements conducted on a single NVIDIA A100 GPU.} ext{By completely eliminating the syntax parsing and logic compilation phase, our method reduces total inference latency by 61.1 % compared to standard neuro-symbolic parsers.} extsf{\ extbf{5 CONCLUSION}} \ m In this paper, we proposed a novel hardware fault-inspired zero-shot reasoning framework for large language models that bypasses traditional logic compilation. By translating feature representations into low-level fault signatures and applying a logic vector reconstruction and search mechanism, our approach maps text inputs directly to canonical logic clauses. Experimental results across GSM8K, SVAMP, and StrategyQA demonstrate that our method achieves state-of-the-art zero-shot accuracy while reducing inference latency by over 60 %. Future work will explore hardware-level acceleration for online vector search and extend the framework to multimodal reasoning tasks. extsf{\ extbf{References}} \ m cite{GSM8K} Cobbe, K., et al.”