# Rhythm of the Deep: Two-tier acoustic organization of sperm-whale codas from click waveforms to second-order sequence dependence

arXiv: https://arxiv.org/abs/2606.16084 · HTML: https://mlsanity.com/paper/2606.16084/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [BEATs: Audio Pre-Training with Acoustic Tokenizers](https://mlsanity.com/paper/2212.09058/) (2022)
- [VampNet: Music Generation via Masked Acoustic Token Modeling](https://mlsanity.com/paper/2307.04686/) (2023)
- [AVES: Animal Vocalization Encoder based on Self-Supervision](https://mlsanity.com/paper/2210.14493/) (2022)
- [Global birdsong embeddings enable superior transfer learning for bioacoustic classification](https://mlsanity.com/paper/2307.06292/) (2023)
- [Machine learning in acoustics: theory and applications](https://mlsanity.com/paper/1905.04418/) (2019)
- [AVEX: What Matters for Animal Vocalization Encoding](https://mlsanity.com/paper/2508.11845/) (2025)
- [WhAM: Towards A Translative Model of Sperm Whale Vocalization](https://mlsanity.com/paper/2512.02206/) (2025)

## Abstract (arXiv)

Sperm-whale codas are conventionally characterized by click count and inter-click intervals (ICIs), leaving recurring differences in constituent click waveforms unresolved. This study tests whether acoustic organization is nested across two scales: within codas, where recurring click-waveform differences may complement ICI timing, and across codas, where recurring whole-coda forms may themselves carry sequence dependence. Candidate recurring click and whole-coda groupings were identified from 1,483 codas without prespecifying waveform categories, then evaluated with native-rate spectral/envelope measurements, exact nuisance matching, held-out timing contrasts, and sequence controls. At the first tier, recurring click-waveform groups differed in spectral slope, bandwidth, flatness, high/low-band energy, and envelope structure within matched date, social unit, individual, and sample-rate strata. Their composition added information about whole-coda grouping beyond timing, while timing remained informative when click composition was fixed. The richer description also carried held-out social-unit-associated information beyond timing. At the second tier, direct native-rate waveform summaries recovered the recurring whole-coda forms well above context-preserving nulls, whereas conventional timing did not; the forms also cross-cut published timing-defined coda types. The preceding two-coda context then added held-out predictive information beyond the immediately preceding coda, while a third preceding coda provided no reliable further gain. Together, these results support two-tier acoustic organization: recurring waveform differences and ICI timing jointly organize individual codas, and acoustically grounded whole-coda forms in turn show bounded second-order predictive dependence across sequences.