Skip to content
← Back to explorer

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
Open arXiv Find Implementation RSS feed Shortlist (0)

Data freshness

Extraction: Fresh

Check recency before relying on this page for active eval decisions. Use stale pages as context and verify against current hub results.

Metadata refreshed

Apr 8, 2026, 8:12 AM

Fresh

Extraction refreshed

Apr 10, 2026, 7:11 AM

Fresh

Extraction source

Persisted extraction

Confidence 0.35

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.

Low-signal caution for protocol decisions

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.35 (below strong-reference threshold).
Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub

HFEPX Relevance Assessment

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

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit 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

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

If you are doing eval pipeline work, start here:

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

Field Provenance & Confidence

Each key protocol field shows extraction state, confidence band, and data source so you can decide whether to trust it directly or validate from full text.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: 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

Confidence: Low Source: Persisted extraction evidenced

Includes extracted eval setup.

Evidence snippet: 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

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: 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

Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: 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

Confidence: Low Source: Persisted extraction evidenced

Useful for evaluation criteria comparison.

Evidence snippet: 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.

Rater Population

missing

Unknown

Confidence: Low Source: Persisted extraction missing

Rater source not explicitly reported.

Evidence snippet: 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.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: General
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.35
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

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

Reported Metrics

accuracy

Research Brief

Deterministic synthesis

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. HFEPX signals include Automatic Metrics with confidence 0.35. Updated from current HFEPX corpus.

Generated Apr 10, 2026, 7:11 AM · Grounded in abstract + metadata only

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…
  • 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…

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Identify benchmark choices from full text before operationalizing conclusions.
  • Validate metric comparability (accuracy).

Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

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

Category-Adjacent Papers (Broader Context)

These papers are nearby in arXiv category and useful for broader context, but not necessarily protocol-matched to this paper.

Need human evaluators for your AI research? Scale annotation with expert AI Trainers.

Post a Job Get a Quote