---
license: mit
library_name: transformers
pipeline_tag: text-generation
---

# Correct Answers, Invalid Traces

The models of *Correct Answers, Invalid Traces: What Verifiable Grade-School
Math Reveals About Chain-of-Thought Traces* (Puduppully, Misra, Iyer, Kalwar,
Palod and Kambhampati, 2026). Each is a 12-layer GPT-NeoX model (124M
parameters) trained from scratch on iGSM for 100k steps at batch 512. They differ
only in the trace that followed the problem during training. Code and the
evaluation protocol are at https://github.com/ratishsp/igsm-trace-validity.

| folder | training trace |
|---|---|
| `clean-run-a` | minimal valid trace (the paper's main model) |
| `clean-run-b` | the same recipe, second run |
| `clean-run-c-200k` | the same recipe, 200k steps |
| `swapped` | trace of a different problem |
| `swapped-op-matched` | trace of a different problem with the same op count |
| `shuffled-10`, `-30`, `-50`, `-75`, `-100` | the first 10 to 100 percent of the trace's tokens shuffled |
| `no-trace` | answer only |
| `non-minimal` | valid trace with unnecessary steps |
| `non-minimal-90` | non-minimal for 90 percent of problems, minimal otherwise |
| `seed43/*` | seed-43 replicates of swapped, swapped-op-matched, shuffled-30 and non-minimal |

```python
from transformers import GPTNeoXForCausalLM
model = GPTNeoXForCausalLM.from_pretrained("ratishsp/igsm-trace-validity", subfolder="clean-run-a")
```

The tokenizer is GPT-2's, with iGSM's special tokens 222, 223 and 224 for
`[PROB]`, `[SOL]` and `[ANS]`. `evaluate.py` in the code repository runs the
paper's evaluation on any of these folders.

## Citation

```bibtex
@article{puduppully2026correct,
  title   = {Correct Answers, Invalid Traces: What Verifiable Grade-School Math Reveals About Chain-of-Thought Traces},
  author  = {Puduppully, Ratish and Misra, Pranabendu and Iyer, Paarth and Kalwar, Durgesh and Palod, Vardhan and Kambhampati, Subbarao},
  journal = {arXiv preprint},
  year    = {2026}
}
```