Update README.md

README.md

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 ---
 license: cc-by-4.0
 ---
+---
+language: en
+lic-ense: cc-by-4.0
+tags: [linear-algebra, llm-evaluation, error-analysis, mathematical-reasoning, benchmark]
+size_categories: [1K<n<10K]
+configs:
+  features:
+    - name: Problem_ID
+      dtype: string
+    - name: Model
+      dtype: string
+    - name: Subcat
+      dtype: string
+    - name: problem_latex
+      dtype: string
+    - name: answer_latex
+      dtype: string
+    - name: Model_Response
+      dtype: string
+    - name: Correct
+      dtype: string
+    - name: Error_Tag
+      dtype: string
+    - name: validated
+      dtype: bool
+  splits:
+    - name: benchmark
+      num_examples: 660
+    - name: model_outputs
+      num_examples: 6600
+    - name: error_annotations
+      num_examples: 2549
+    - name: results
+  config_name: "default"
+---
+
+# 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
+
+```python
+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
+
+```bibtex
+@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
+
+---
+
+**Dataset Hub**: [05deepak/demo](https://huggingface.co/datasets/05deepak/demo)  
+**Paper**: [NeurIPS 2026 Datasets & Benchmarks Track](https://neurips.cc)  
+**Code & Reproduction**: [GitHub Repository](https://github.com/05deepak/LinAlg-Bench)