05deepak/demo

LinAlg-Bench: A Forensic Benchmark Revealing Structural Failure Modes in LLM Mathematical Reasoning

A diagnostic benchmark evaluating 10 frontier LLMs on linear algebra computation across a strict dimensional gradient (3×3, 4×4, 5×5 matrices), with automated three-stage forensic error classification revealing that LLM mathematical failure is structurally constrained by algorithm family and matrix dimension rather than random.

Overview

LinAlg-Bench is a diagnostic dataset of LLM responses and forensic error annotations on linear algebra computation tasks. It covers 660 problems across three matrix sizes (3×3, 4×4, 5×5) and nine operation types (determinant, eigenvalues, rank, nullity, trace, multiplication, matrix power, matrix-vector product, transpose), evaluated on 10 frontier models. Each failure is annotated with a fine-grained error tag and subtype via a three-stage automated forensic pipeline (Gemini-3.1-Pro judge + meta-auditor).

Data Structure

data/
├── benchmark/                      # Problem definitions (SymPy-certified ground truth)
│   ├── train-00000.parquet        # 3×3: 220 unique problems
│   ├── train-00001.parquet        # 4×4: 220 unique problems
│   └── train-00002.parquet        # 5×5: 220 unique problems
├── model_outputs/                  # Stage 1: Raw model responses and correct status
│   ├── train-00000.parquet        # 3×3: model inference on 220 Problem_IDs for 10 models
│   ├── train-00001.parquet        # 4×4: model inference on 220 Problem_IDs for 10 models
│   └── train-00002.parquet        # 5×5: model inference on 220 Problem_IDs for 10 models
├── error_annotations/              # Stage 3: Forensic error labels (validated)
│   ├── train-00000.parquet        # 3×3: 335 failures classified
│   ├── train-00001.parquet        # 4×4: 879 failures classified
│   └── train-00002.parquet        # 5×5: 1,335 failures classified
└── results/                        # Aggregated summaries per size
    ├── accuracy/                   # Model accuracy by task/size
    ├── error_tags/                 # Error tag distribution per subcategory (10–14 tags by size)
    ├── sign_subtypes/              # Sign error breakdown (8–9 subtypes by size)
    └── hallucination_subtypes/     # Hallucination breakdown (4–6 subtypes by size)

Data Notes

Model naming convention : Model names are inconsistent across splits. model_outputs and results/accuracy use long-form provider slugs (e.g. google/gemma-3-12B-it, qwen/qwen-2.5-14b-instruct), while error_annotations uses short-form names (e.g. Gemma-3-12B, Qwen2.5-14B). A direct join between the two on (Problem_ID, Model) will not match any model. Normalize names before joining. The mapping is:

model_outputs / results	error_annotations
google/gemma-3-4b-it	Gemma-3-4B
google/gemma-3-12B-it	Gemma-3-12B
google/gemma-3-27b-it	Gemma-3-27B
meta-llama/llama-3.1-8b-instruct	Llama-3.1-8B
mistralai/ministral-8b-2512	Mistral-8B
mistralai/ministral-14b-2512	Mistral-14B
mistralai/mistral-small-24b-instruct-2501	Mistral-24B
qwen/qwen-2.5-7b-instruct	Qwen2.5-7B
qwen/qwen-2.5-14b-instruct	Qwen2.5-14B
qwen/qwen-2.5-32b-instruct	Qwen2.5-32B

Usage Examples

Load with Hugging Face Datasets

from datasets import load_dataset

# Load full dataset
ds = load_dataset("05deepak/demo")

# Load specific splits
benchmark = ds['benchmark']           # Problem definitions
model_outputs = ds['model_outputs']   # Stage 1 responses
errors = ds['error_annotations']      # Forensic labels
results = ds['results']               # Aggregated summaries

# Access a records
record = model_outputs[0]
print(f"Problem: {record['Problem_ID']}")
print(f"Model: {record['Model']}")
print(f"Task: {record['Subcat']}")
print(f"Correct: {record['Correct']}")

# Access an error annotation
error = errors[0]
print(f"Error tag: {error['Final_tags']}")
print(f"Validated: {error['validated']}")

Limitations

1. Domain-specific: Linear algebra only. Generalization to other mathematical domains is out of scope for the present research.

2. Snapshot in time: All inferences performed May 2026. Model updates or API changes after this date are not reflected.

3. Scale limit: Maximum 5×5 matrices. Behaviour at larger scales is out of scope for the present research.

Ethical Considerations & Responsible Use

Recommended Use Cases

✅ Research on symbolic reasoning in LLMs
✅ Analyzing systematic error patterns and failure modes
✅ Identifying mechanistic bottlenecks (working memory, strategy rigidity)
✅ Developing better post-training curricula for mathematical reasoning

Caution / Not Recommended For

❌ Definitive model ranking — single benchmark is insufficient for production decisions
❌ Knowledge claims — this measures execution under specific conditions (T=0, no tools)
❌ General reasoning ability assessment — linear algebra is narrow domain
❌ Marketing claims — benchmark results are domain-specific diagnostics, not overall capability metrics

Known Biases

• Synthetic problems: Small integer entries [-10, 10] may not reflect real-world distribution
• Format bias: LaTeX consistently helps at recursive levels (model-specific)
• Training data: Newer models (those with larger training corpora) may have seen more matrix problems

File Manifest

File	Rows	Columns	Purpose
benchmark/train-000{00,01,02}.parquet	220 each	5	Unique problems per size (LaTeX)
model_outputs/train-000{00,01,02}.parquet	2,200 each	20	All model responses + metadata
error_annotations/train-000{00,01,02}.parquet	335/879/1,335	23	Failures with forensic labels
results/accuracy/train-000{00,01,02}.parquet	10 rows each	5	Model accuracy per task
results/error_tags/train-000{00,01,02}.parquet	8/9/9 rows	15/16/12	Error tag distribution per subcategory
results/sign_subtypes/train-000{00,01,02}.parquet	5/7/6 rows	10/10/11	Sign error breakdown per subcategory
results/hallucination_subtypes/train-000{00,01,02}.parquet	3/8/7 rows	6/8/8	Hallucination breakdown per subcategory

Citation

@inproceedings{linalgbench2026,
  title={LinAlg-Bench: A Forensic Benchmark Revealing Structural Failure Modes in LLM Mathematical Reasoning},
  author={Anonymous},
  booktitle={Advances in Neural Information Processing Systems (NeurIPS) - Datasets and Benchmarks Track},
  year={2026}
}

License

CC BY 4.0 — freely available for research and commercial use with attribution.

Acknowledgments

• Model API Access: OpenAI, Google DeepMind, Mistral, Qwen, Meta
• SymPy Verification: Symbolic mathematics backend for ground truth
• Annotation: Three-stage automated pipeline (Gemini-3.1-Pro judge + meta-auditor)

Contact & Support

Issues/Questions: Open issue on GitHub or discussion on HF Hub
Dataset Updates: Check release notes for new versions, bug fixes, model additions
Cite This Work: See citation section above

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Dataset Hub: 05deepak/demo
Paper: NeurIPS 2026 Datasets & Benchmarks Track
Code & Reproduction: GitHub Repository