{
  "abstract": "Post-training reasoning LLMs often requires making a tradeoff between costly supervision and compute inefficiency: supervised finetuning typically requires reasoning traces, which is data inefficient since in many applications one only has prompt-answer tuples and lacks the groundtruth chain-of-thought (CoT) sequence. On the other hand, reinforcement learning (with verifiable rewards, for example) can operate without CoT data but it is much more compute-inefficient since it requires multiple autoregressive completions per optimization step, none of which are guaranteed to give a non-zero policy gradient. In this work we explore a middleground, a self-distillation technique that uses answer-only data, treating CoT as latent variables. This relies on training a partner ``inverse reasoning LLM\" that generates the original's reasoning traces conditioned on the answer. The inverse model is trained once and reused across incoming batches of answer-only data, with all generation happening offline and up front, making the approach particularly suited to continual post-training. Using Qwen3-0.6B on the Countdown and GSM8K tasks, we show that after GRPO training has saturated, a single offline distillation round from the inverse model roughly doubles pass@1 on hard prompts and, on Countdown, outperforms rejection-sampling self-distillation on every hard-tail metric at every mix ratio (with smaller gains on GSM8K); rejection sampling by construction has no signal on problems the model never solves on its own. Continued GRPO on the fresh data retains an edge at hard pass@1 but trails distillation at pass@8 and pass@32 while regenerating rollouts at every step. As an added bonus we see that the inverse model has a second application as an accurate verifier of correctness. When used for best-of-$n$ selection at test time, it raises selection accuracy on Countdown from 0.753 (majority voting) to 0.969.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18878",
  "author_total": 1,
  "authors": [
    {
      "name": "Eric O. Korman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56smt8ed3wdh9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18878",
  "fulltext_url": null,
  "id": "56smt8ed3wdh9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18878",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Topic Modeling"
    ]
  ],
  "openalex": "W7221873653",
  "pdf_url": "https://arxiv.org/pdf/2610.18878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56smt8ed3wdh9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.18878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Inverse Reasoning Models for Efficient Post-Training and Verification from Answer-Only Data",
  "title_text": "Inverse Reasoning Models for Efficient Post-Training and Verification from Answer-Only Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/56smt8ed3wdh9",
  "venue": "arXiv",
  "versions": []
}