# Comprehension Without Competence: Architectural Limits of LLMs in Symbolic Computation and Reasoning

arXiv: https://arxiv.org/abs/2507.10624 · HTML: https://mlsanity.com/paper/2507.10624/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 45 of its 72 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [What Formal Languages Can Transformers Express? A Survey](https://mlsanity.com/paper/2311.00208/) (2023)
- [Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process](https://mlsanity.com/paper/2407.20311/) (2024)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics](https://mlsanity.com/paper/2410.21272/) (2024)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)
- [Transformers Can Do Arithmetic with the Right Embeddings](https://mlsanity.com/paper/2405.17399/) (2024)
- [Alice in Wonderland: Simple Tasks Showing Complete Reasoning Breakdown in State-Of-the-Art Large Language Models](https://mlsanity.com/paper/2406.02061/) (2024)
- [On Limitations of the Transformer Architecture](https://mlsanity.com/paper/2402.08164/) (2024)

## Built on by (most cited first, 9 of 9)

- [Limited Reasoning Space: The cage of long-horizon reasoning in LLMs](https://mlsanity.com/paper/2602.19281/) (2026)
- [CircuChain: Disentangling Competence and Compliance in LLM Circuit Analysis](https://mlsanity.com/paper/2602.15037/) (2026)
- [Think Twice Before You Write -- an Entropy-based Decoding Strategy to Enhance LLM Reasoning](https://mlsanity.com/paper/2604.00018/) (2026)
- [Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism](https://mlsanity.com/paper/2606.09484/) (2026)
- [Agentic Frameworks for Reasoning Tasks: An Empirical Study](https://mlsanity.com/paper/2604.16646/) (2026)
- [Scaffolding the Strategist: Architecture-Dependent Reasoning Interventions in Hotelling Spatial Markets](https://mlsanity.com/paper/2607.09743/) (2026)
- [Solver-Hard Is Not Model-Hard: A Hardness-Controlled Diagnostic for LLM Constraint Reasoning](https://mlsanity.com/paper/2607.17047/) (2026)
- [LUMOS: Tracing Parametric Knowledge from Training Data to Behavioral Outputs in LLMs](https://mlsanity.com/paper/2610.02902/) (2026)
- [FON: A Draft-Revise Dual-Organ Language Model without Sequence-Level Quadratic Attention](https://mlsanity.com/paper/2610.16301/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) display striking surface fluency yet systematically fail at tasks requiring symbolic reasoning, arithmetic accuracy, and logical consistency. This paper offers a structural diagnosis of such failures, revealing a persistent gap between textitcomprehension and textitcompetence. Through controlled experiments and architectural analysis, we demonstrate that LLMs often articulate correct principles without reliably applying them--a failure rooted not in knowledge access, but in computational execution. We term this phenomenon the computational textitsplit-brain syndrome, where instruction and action pathways are geometrically and functionally dissociated. This core limitation recurs across domains, from mathematical operations to relational inferences, and explains why model behavior remains brittle even under idealized prompting. We argue that LLMs function as powerful pattern completion engines, but lack the architectural scaffolding for principled, compositional reasoning. Our findings delineate the boundary of current LLM capabilities and motivate future models with metacognitive control, principle lifting, and structurally grounded execution. This diagnosis also clarifies why mechanistic interpretability findings may reflect training-specific pattern coordination rather than universal computational principles, and why the geometric separation between instruction and execution pathways suggests limitations in neural introspection and mechanistic analysis.