{
  "id": "2506.18233",
  "title": "Beyond Parameters: Exploring Virtual Logic Depth for Scaling Laws",
  "first_public": "2025-06-23",
  "paper_url": "https://arxiv.org/abs/2506.18233",
  "authors": "Ruike Zhu, Hanwen Zhang, Kevin Li, Tianyu Shi, Yiqun Duan, Chi Wang, Tianyi Zhou, Arindam Banerjee, Zengyi Qin",
  "arxiv": "2506.18233",
  "added_at": "2026-11-09",
  "venue": "arXiv",
  "provenance": "Primary-source literature review, 2026-11-09",
  "html_url": "https://arxiv.org/html/2506.18233v3",
  "lens": [
    "recurrent",
    "analysis"
  ],
  "representation": [
    "hidden-state"
  ],
  "computation": [
    "recurrent",
    "depth-wise"
  ],
  "training": [
    "pretraining",
    "supervised"
  ],
  "questions": [
    "architecture",
    "scaling",
    "capability"
  ],
  "evidence": [
    "empirical",
    "scaling"
  ],
  "modality": [
    "language",
    "symbolic"
  ],
  "summary": "Repeats transformer layers with shared parameters in several reuse patterns. Compares how added computation affects memorization and reasoning at a fixed parameter count, using synthetic tasks and language-model benchmarks.",
  "author_names": [
    "Ruike Zhu",
    "Hanwen Zhang",
    "Kevin Li",
    "Tianyu Shi",
    "Yiqun Duan",
    "Chi Wang",
    "Tianyi Zhou",
    "Arindam Banerjee",
    "Zengyi Qin"
  ],
  "record_url": "https://latent-implicit-thinking.github.io/papers/2506.18233/",
  "legacy_record_url": "https://latent-implicit-thinking.github.io/papers/#paper-2506-18233",
  "citation_date": "2025-06-23",
  "json_url": "https://latent-implicit-thinking.github.io/papers/2506.18233/record.json",
  "markdown_url": "https://latent-implicit-thinking.github.io/papers/2506.18233/index.md",
  "bibtex_url": "https://latent-implicit-thinking.github.io/papers/2506.18233/citation.bib",
  "csl_url": "https://latent-implicit-thinking.github.io/papers/2506.18233/citation.csl.json",
  "pdf_url": "https://arxiv.org/pdf/2506.18233"
}