ResonatorLM, audited

An independent, from-scratch replication of ResonatorLM (arXiv:2607.05583).

Setup

The paper’s 6M-parameter budget, WikiText-2 characters, one seed, 2,000 steps (the paper used 10,000 and six seeds), on an Apple M5.

Findings

• The paper’s ordering reproduces: ResonatorLM 3.322 perplexity and 64.33% accuracy against the Transformer’s 3.401 and 63.60%. Absolute numbers differ from the paper’s, and came out better, which is unexplained.
• Decoding memory is constant: about 30 KiB of state, as claimed.
• ResonatorLM is a diagonal complex state-space model.
• Eq. 4 has a phase-sign error.
• The baseline’s collapse is a positional-encoding artifact. With RoPE, perplexity at 1,024 tokens drops from 20.00 to 5.59.
• Memory half-life caps usable context far below the benchmarked lengths.
• The sign error was reported to the authors on 2026-09-10. No reply yet.

Data and code

resonatorlm-audit is public.

@misc{paul2026resonatorlmaudit,
  author = {Paul, Kanishk},
  title = {ResonatorLM, audited},
  year = {2026},
  howpublished = {Research page, kanishkpaul.com},
  url = {https://www.kanishkpaul.com/research/resonatorlm-audit},
  note = {Code and data: https://github.com/kanishkpaul/resonatorlm-audit},
}