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

This paper investigates the acoustic structure of sperm-whale codas, challenging the traditional view that these signals are merely recurring click-count and timing patterns. By revealing a two-tier combinatorial acoustic organization, the study provides a new framework for understanding how complex biological signals are assembled from lower-level units and participate in higher-order structures.

The Methodological Framework

The researchers employ a controlled-induction framework designed to turn high-dimensional audio representations into falsifiable claims about units, combination rules, and cross-tier relations. Rather than relying on expert labels, the study uses eight families of frozen audio encoders to independently propose candidate click and coda units. This approach allows the researchers to separate the acoustic relation carried by an induced unit from shared encoder shortcuts that might otherwise mimic biological recurrence.

To ensure scientific rigor, the framework subjects every interpretation to a series of stringent validation gates:

• Cross-view consensus and stability checks to retain recurring candidates across model families.

• Held-out transfer tests to determine if lower-tier composition predicts coda identity.

• Matched nulls and destructive waveform counterfactuals to distinguish between identity, order, rhythm, and nuisance carriers.

• Expert-feature baselines to calibrate findings against established acoustic accounts.

The First Acoustic Tier

The study identifies that the lower tier of coda organization is composed of a recurring click inventory combined with interclick rhythm. The researchers explicitly reject the hypothesis that codas are supported by a stable ordered rule or a fixed sequence of click tokens, noting that stable click order is weak. Instead, once the exact click-token multiset is fixed, the inter-click intervals (ICIs) become the primary predictor of coda identity.

The connection between these lower units and the higher tier is demonstrated through several key metrics:

• Click-token composition predicts induced coda identity with a median normalized mutual-information lift of 0.380.

• This predictive power remains even when events are detected using an annotation-independent arm without published click times or counts.

• The relationship is robust across different model families, indicating the inventory is not determined by a single architecture.

The Second Acoustic Tier

At the second tier, the study reveals that recurring coda tokens exhibit additional sequence-level dependence under a different acoustic carrier. Specifically, coda tokens show 0.132 bits of incremental lag-2 dependence under a prespecified categorical estimator. Crucially, this higher-order structure is not captured by traditional rhythm models; two expert-inspired rhythm representations failed to recover the positive component of this association.

The researchers further distinguish the tiers through tempo manipulation, identifying a cross-tier stability gradient. When the audio is resampled at 1.3× speed:

• Click identity becomes highly unstable, with an Adjusted Rand Index (ARI) of only 0.074.

• Coda identity remains significantly more robust, with whole-waveform and ICI-only identities showing much higher stability (ARI of 0.428 and 0.516, respectively).

Implications for Acoustic Science

The results suggest that the acoustic description of sperm-whale codas must shift from a single prescribed rhythm inventory to layered waveform organization. The study concludes that codas are not merely timing templates but are assembled from lower acoustic units whose combinations create recurring coda units that themselves participate in higher-order structure. This controlled-induction framework provides a general method for discovering and falsifying combinatorial structure in any under-annotated audio signal.

1. Implementation of a Controlled Acoustic-Unit Induction Framework

• Improvement: Integrate a multi-stage validation pipeline for unsupervised unit discovery that moves beyond simple cluster agreement by incorporating held-out transfer, carrier-matched nulls (e.g., spectrum-matched noise, click-order shuffling), and destructive waveform counterfactuals (e.g., replacing tokens within a preserved timing skeleton).

• Capability: The AI can autonomously distinguish between genuine structural recurrence in under-annotated audio and model shortcuts caused by shared sensitivities to spectral bias, recording conditions, or segmentation artifacts.

2. Two-Tier Hierarchical Combinatorial Tokenization

• Improvement: Transition from single-tier tokenization (e.g., direct waveform-to-token) to a dual-layer architecture where Tier 1 models the composition of low-level acoustic identities and inter-event rhythm to form mid-level units, which are then processed by a Tier 2 sequence model for higher-order dependence.

• Capability: The AI can model complex, layered communication systems in environments where the alphabet is unknown, allowing it to capture hierarchical dependencies (such as lag-2 sequence associations) that single-tier N-gram or transformer models miss.

3. Counterfactual Representation Auditing

• Improvement: Incorporate a training and evaluation loop using destructive acoustic-null gates, where the model's learned representations are tested against manipulated versions of the input (e.g., phase shuffling, time reversal, or envelope-noise filling).

• Capability: The AI can self-verify whether its latent space is capturing the intended acoustic carrier (e.g., identity vs. rhythm) and provide explicit abstentions when a detected pattern fails to survive rigorous counterfactual testing.

4. Cross-Tier Tempo-Invariant Identity Mapping

• Improvement: Implement training objectives that maximize representation stability across tempo scaling (resampling/stretching) to decouple acoustic identity from temporal duration.

• Capability: The AI can achieve robust recognition of semantic or structural units regardless of playback speed, preventing the model from conflating what is being signaled with how fast it is being signaled.

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.