arxiv_cl 95% Match Research paper LLM researchers,AI interpretability experts,Machine learning engineers 3 weeks ago

Interpreting the Latent Structure of Operator Precedence in Language Models

large-language-models › reasoning

📄 Abstract

Abstract: Large Language Models (LLMs) have demonstrated impressive reasoning capabilities but continue to struggle with arithmetic tasks. Prior works largely focus on outputs or prompting strategies, leaving the open question of the internal structure through which models do arithmetic computation. In this work, we investigate whether LLMs encode operator precedence in their internal representations via the open-source instruction-tuned LLaMA 3.2-3B model. We constructed a dataset of arithmetic expressions with three operands and two operators, varying the order and placement of parentheses. Using this dataset, we trace whether intermediate results appear in the residual stream of the instruction-tuned LLaMA 3.2-3B model. We apply interpretability techniques such as logit lens, linear classification probes, and UMAP geometric visualization. Our results show that intermediate computations are present in the residual stream, particularly after MLP blocks. We also find that the model linearly encodes precedence in each operator's embeddings post attention layer. We introduce partial embedding swap, a technique that modifies operator precedence by exchanging high-impact embedding dimensions between operators.

Authors (7)

Dharunish Yugeswardeenoo

Harshil Nukala

Ved Shah

Cole Blondin

Sean O Brien

Vasu Sharma

+1 more

Submitted

October 14, 2025

arXiv Category

cs.CL

arXiv PDF

Key Contributions

Investigates the internal representation of operator precedence in LLMs using LLaMA 3.2-3B. By tracing intermediate computations in the residual stream via interpretability techniques (logit lens, probes, UMAP), it shows that models encode arithmetic operations, particularly after MLP blocks, shedding light on their reasoning mechanisms.

Business Value

Enhances trust and reliability in LLMs by providing insights into their reasoning processes, crucial for high-stakes applications like finance or scientific modeling.

Paper Metadata

Innovation Type

Interpretability study of arithmetic reasoning

Deployment Feasibility

High for research and understanding; direct application is in improving model design and debugging.

Limitations Addressed

LLMs' poor performance on arithmetic tasks,Lack of insight into the internal mechanisms LLMs use for computation,Focus on outputs/prompting strategies in prior work

Performance Gains

Demonstrates the presence and location of internal arithmetic computations, improving understanding of LLM reasoning.

Technical Tags

interpretabilityoperator precedencearithmetic reasoningLLM internalsresidual streamlogit lenslinear probesUMAPLLaMA 3.2-3B

Research Topics

LLM InterpretabilityArithmetic ReasoningModel InternalsComputational Linguistics

Methods & Architectures

Logit lensLinear classification probesUMAP geometric visualizationTracing intermediate computationsDataset of arithmetic expressions LLaMA 3.2-3BTransformer models

Applications & Tasks

AI Interpretability LLM Understanding Arithmetic Computation LLMs struggling with arithmetic tasksLack of understanding of internal arithmetic computation in LLMs Investigating if LLMs encode operator precedence internallyLocating intermediate arithmetic computations in the model's residual stream

Datasets & Benchmarks

Benchmarks

Dataset of arithmetic expressions with varying operator precedence

Presence of intermediate computations in residual streamAccuracy of linear probesVisualization patterns (UMAP)

Related Fields

Machine LearningNatural Language ProcessingInterpretabilityCognitive ScienceComputational Linguistics

Keywords

LLMinterpretabilityarithmeticoperator precedencereasoningresidual streamlogit lenslinear probesUMAPLLaMAtransformer

Academic Context

#LLM Interpretability#Arithmetic Reasoning#Model Internals#Computational Linguistics

Commercial Potential

Potential Products

Tools for LLM interpretabilityDebugging tools for arithmetic errors in LLMs

Target Industries

TechnologyAI ResearchFinanceScientific Computing

Use Case Examples

Understanding why LLMs fail at complex math problemsDeveloping more robust arithmetic capabilities in LLMs

Competitive Edge

Provides novel insights into the internal workings of LLMs for arithmetic tasks, a critical area of research.

Market Opportunity

Growing market for AI explainability and interpretability tools.

Revenue Models

Consulting serviceslicensing of interpretability tools.

Resource Requirements

Compute Needs

High (for running LLM inference and interpretability methods)

Data Requirements

Arithmetic expression dataset, access to LLaMA 3.2-3B model.

Deployment Constraints

Complexity of interpretability methods, model-specific findings.

Scalability

Scalable to other transformer models with similar architectures.

Regulatory Considerations

None directly.

Production Readiness

Maturity Level

Research/Interpretability

Time to Market

N/A (research focus)

Licensing

Likely open source for interpretability code

Patent Potential

Low (research methodology)

View Full Paper Back to Papers