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Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions

Parth Patil, Dhruv Kumar, Yash Sinha, Murari Mandal · Apr 8, 2026 · Citations: 0

Automatic Metrics
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How to use this page

Low trust

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

What to verify

Validate the evaluation procedure and quality controls in the full paper before operational use.

Evidence quality

Low

Derived from extracted protocol signals and abstract evidence.

Abstract

Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause. When a model fails an algebraic problem, a single accuracy score cannot reveal whether the expression was too deeply nested, the operator too uncommon, the intermediate state count too high, or the dependency chain too long. Prior work has studied individual failure modes in isolation, but no framework has varied each complexity factor independently under strict experimental control. No prior system has offered automatic generation and verification of problems of increasing complexity to track model progress over time. We introduce a nine-dimension algebraic complexity framework in which each factor is varied independently while all others are held fixed, with problem generation and verification handled by a parametric pipeline requiring no human annotation. Each dimension is grounded in a documented LLM failure mode and captures a structurally distinct aspect of algebraic difficulty, including expression nesting depth, simultaneous intermediate result count, sub-expression complexity, operator hardness, and dependent reasoning chain length. We evaluated seven instruction-tuned models spanning 8B to 235B parameters across all nine dimensions and find that working memory is the dominant scale-invariant bottleneck. Every model collapses between 20 and 30 parallel branches regardless of parameter count, pointing to a hard architectural constraint rather than a solvable capacity limitation. Our analysis further identifies a minimal yet diagnostically sufficient subset of five dimensions that together span the full space of documented algebraic failure modes, providing a complete complexity profile of a model's algebraic reasoning capacity.

Abstract-only analysis — low confidence

All signals on this page are inferred from the abstract only and may be inaccurate. Do not use this page as a primary protocol reference.

  • This paper looks adjacent to evaluation work, but not like a strong protocol reference.
  • The available metadata is too thin to trust this as a primary source.
Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub

Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A secondary eval reference to pair with stronger protocol papers.

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Trust level

Low

Usefulness score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

Usefulness for eval research

Adjacent candidate

Extraction confidence 35%

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause."

Evaluation Modes

partial

Automatic Metrics

Includes extracted eval setup.

"Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause."

Quality Controls

missing

Not reported

No explicit QC controls found.

"Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause."

Reported Metrics

partial

Accuracy

Useful for evaluation criteria comparison.

"When a model fails an algebraic problem, a single accuracy score cannot reveal whether the expression was too deeply nested, the operator too uncommon, the intermediate state count too high, or the dependency chain too long."

Human Feedback Details

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Not reported
  • Expertise required: General

Evaluation Details

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Not reported
  • Evidence quality: Low
  • Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

accuracy

Research Brief

Metadata summary

Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause.
  • When a model fails an algebraic problem, a single accuracy score cannot reveal whether the expression was too deeply nested, the operator too uncommon, the intermediate state count too high, or the dependency chain too long.
  • Prior work has studied individual failure modes in isolation, but no framework has varied each complexity factor independently under strict experimental control.

Researcher Actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Validate inferred eval signals (Automatic metrics) against the full paper.
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

Accuracy

Research Summary

Contribution Summary

  • Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause.
  • When a model fails an algebraic problem, a single accuracy score cannot reveal whether the expression was too deeply nested, the operator too uncommon, the intermediate state count too high, or the dependency chain too long.
  • We introduce a nine-dimension algebraic complexity framework in which each factor is varied independently while all others are held fixed, with problem generation and verification handled by a parametric pipeline requiring no human…

Why It Matters For Eval

  • Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause.
  • We introduce a nine-dimension algebraic complexity framework in which each factor is varied independently while all others are held fixed, with problem generation and verification handled by a parametric pipeline requiring no human…

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Pass: Metric reporting is present

    Detected: accuracy

Related Papers

Papers are ranked by protocol overlap, extraction signal alignment, and semantic proximity.

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