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REVIEW 4 major objections 7 minor 44 references

Speech AI's internal layers follow a predictable geometry

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2026-07-08 07:13 UTC pith:NNNMDLXU

load-bearing objection Solid diagnostic toolkit for speech SSL with one load-bearing interpretive gap the 4 major comments →

arxiv 2607.06392 v1 pith:NNNMDLXU submitted 2026-07-07 cs.SD

InsideSSL: Understanding Self-Supervised Speech Representations using a Model-Centric Perspective

Samir Sadok , Xavier Alameda-Pineda This is my paper
classification cs.SD
keywords model-centriccompressioninsidesslperspectiveself-supervisedspeechtasksunderstanding
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces InsideSSL, a framework for understanding self-supervised speech models (like Wav2Vec2, HuBERT, and WavLM) by examining their internal layer-by-layer structure rather than just their performance on tasks. The authors track three properties across network depth: entropy (how compressed the information is), curvature (how smooth or tangled the representation manifold is), and robustness (how stable the representations are to audio perturbations). They find that different training objectives create distinct internal regimes. For instance, Wav2Vec2 undergoes a sharp entropy collapse in its final layers, while HuBERT and WavLM maintain steady information density throughout. The paper also introduces the Generative Compatibility Matrix (GCM), which measures how well a decoder trained on one layer can interpret representations from another layer, revealing that phonetic content forms a stable core in mid-layers while speaker identity is more volatile. By connecting these intrinsic geometric properties to linear probing results for phoneme, pitch, and speaker tasks, the authors demonstrate that low-level acoustic tasks (pitch, speaker identity) depend on early layers with high entropy and high curvature, while phoneme recognition benefits from deeper layers where the manifold has been compressed and linearized.

Core claim

The central finding is that the internal geometry of self-supervised speech models follows a predictable trajectory—early layers build complex, high-dimensional representations (high entropy, high curvature), while deeper layers compress and linearize them—and that this trajectory directly dictates which layers are optimal for different downstream tasks. Phoneme recognition peaks at mid-to-deep layers where curvature transitions from high to low (marking a shift from local acoustic detail to linearly separable abstractions), while pitch and speaker identity rely on the high-entropy, high-curvature states of early layers. The paper also shows that training objectives create distinct regimes:W

What carries the argument

von Neumann entropy of the Gram matrix (measuring informational density), average curvature of token transition vectors (measuring manifold smoothness), InfoNCE-based robustness metric, and the Generative Compatibility Matrix (cross-layer decoder transferability).

Load-bearing premise

The paper assumes that von Neumann entropy of the Gram matrix faithfully measures 'informational density' and that average curvature of token transitions faithfully measures 'manifold unfolding' in the speech domain, without independently validating that these mathematical proxies correspond to the semantic phenomena they are claimed to capture.

What would settle it

If the entropy and curvature metrics were replaced with alternative measures of compression and geometry, the correlations with downstream task performance (Figure 9) would likely weaken or vanish.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Speech model architectures could be designed with task-specific layer extraction points rather than defaulting to the final layer, improving efficiency for applications like speaker verification (early layers) vs. speech recognition (mid layers).
  • Pre-training objectives could be evaluated by their effect on internal geometry (entropy stability, curvature linearization) rather than only downstream task scores, potentially guiding the design of objectives that avoid undesirable phenomena like Wav2Vec2's late-stage entropy collapse.
  • The Generative Compatibility Matrix methodology could be applied to other modalities (vision, language) to map cross-layer functional dependencies in foundation models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If entropy and curvature are indeed faithful proxies for informational density and manifold linearization, then one could predict optimal probing layers for novel tasks without running expensive probing experiments, simply by inspecting the curvature transition point.
  • The finding that scaling model size (WavLM-LARGE) has a stronger structural effect than increasing training data suggests that architectural capacity, not data volume, is the primary driver of internal representational geometry in these models.
  • The asymmetry of the GCM (deep-layer decoders generalize to early layers but not vice versa) implies a one-way information bottleneck that could constrain the design of multi-layer feature fusion methods.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 7 minor

Summary. The paper proposes InsideSSL, a model-centric framework for analyzing self-supervised speech representation (SSL) models across their Transformer layers. The framework has two components: (1) three per-layer intrinsic metrics—von Neumann entropy of the Gram matrix (compression), average curvature of token transitions (geometry), and InfoNCE-based invariance to perturbations (robustness)—and (2) a cross-layer Generative Compatibility Matrix (GCM) that trains per-layer CFM+DiT decoders and evaluates their cross-layer transferability. The authors apply these tools to Wav2Vec2, HuBERT, WavLM, Data2Vec, and UniSpeech at BASE/PLUS/LARGE scales, and connect the intrinsic metrics to downstream phoneme, pitch, and speaker probing. The central claims are that training objectives induce distinct compression and manifold-unfolding regimes, and that phoneme recognition benefits from deep-layer compression/linearization while pitch and speaker tasks rely on early high-entropy, high-curvature states.

Significance. The paper provides a systematic and broad-coverage empirical study: five model families, three scales, fine-tuning data ablations, training-dynamics tracking, and a novel cross-layer GCM methodology. The GCM is a genuinely new contribution for audio SSL, moving beyond isolated per-layer probes to quantify inter-layer functional relationships. The provision of a project page with code and interactive audio is a positive for reproducibility. The connection of intrinsic, task-agnostic metrics to downstream probing via Pearson correlations is a reasonable bridging strategy. The paper's scope and the novelty of the GCM make it a solid contribution to the SSL interpretability literature.

major comments (4)
  1. §2.2 (Compression, Eq. 1) and §3.5: The paper interprets von Neumann entropy of the Gram matrix as 'informational density' and frames its decrease as beneficial 'compression.' However, this entropy measures spectral spread (effective rank), not information content in the Information Bottleneck sense (I(Z;X) or I(Z;Y)). A decrease in effective rank can indicate either beneficial compression (noise removal with signal preservation) or destructive collapse (loss of task-relevant information). The paper does not distinguish these cases. This is load-bearing for the central claim that 'phoneme recognition benefits from deep-layer compression and linearization.' The authors should either (a) add an independent measure of task-relevant information (e.g., mutual information estimates or probing-based proxies) to validate that the entropy decrease preserves phoneme-relevant signal, or (b) soften'
  2. Figure 9a, Wav2Vec2 row: The entropy-phoneme correlation for Wav2Vec2 is +0.33, which is positive—meaning higher entropy is associated with better phoneme accuracy. This is opposite to the paper's general claim that phoneme recognition benefits from low entropy (compression). The paper's take-away states phonemes require 'deep-layer compression,' but Wav2Vec2—the model with the most dramatic entropy collapse—shows the opposite trend. This inconsistency should be explicitly addressed. If the claim is model-dependent, the take-away should be qualified accordingly.
  3. Figure 9 and §3.5: The Pearson correlations between intrinsic metrics and probing accuracy assume a linear relationship. However, Figure 8a shows that phoneme accuracy is non-monotonic (peaking in mid-layers and declining in deep layers for most models). A linear correlation coefficient may mischaracterize a non-monotonic relationship. The authors should discuss this limitation and consider whether rank-based or non-monotonic measures would be more appropriate for the reported correlations.
  4. §3.1–§3.5: No error bars, confidence intervals, or significance tests are reported for any of the intrinsic metrics, GCM entries, or probing results. Given that the central claims rest on comparing layer-wise trajectories and correlation values across models, some quantification of variance is needed to assess whether the observed differences (e.g., Wav2Vec2's entropy collapse vs. WavLM's stability) are statistically reliable. At minimum, bootstrap confidence intervals on the entropy and curvature averages, or standard deviations across the test set, would strengthen the reported patterns.
minor comments (7)
  1. §2.2, Eq. (2): The curvature formula uses v_n^(l) but the text defines l as the layer index elsewhere. The superscript notation switches between (l) and (ℓ); consistent notation would help.
  2. §2.3: The GCM definition uses M(D^(ℓ)(Z^(k)), x) but does not specify what x is in this context (waveform? Mel-spectrogram?) at the point of definition. This is clarified later in §3.4 but should be stated at the point of definition.
  3. Table 1: The 'Task' column uses P/C/D abbreviations but UniSpeech is marked as both P and C. A brief note on UniSpeech's dual objective would help readers unfamiliar with this model.
  4. Figure 2: The y-axis label 'Average Normalized Entropy' in Fig. 2a does not specify the normalization scheme. The text mentions maxEntropy normalization in §3.1, but the figure caption should clarify this.
  5. §3.3, Figure 6: The caption says 'first training iteration of a HuBERT model, utilizing labels extracted from MFCCs.' It is unclear whether this refers to the first iteration of pre-training or the first iteration of a specific training stage. Clarification is needed.
  6. §3.4: The GCM is described as 'structurally asymmetric, strongly favoring the lower triangular region.' The text should clarify the matrix convention (row = training layer, column = evaluation layer) at this point to make the asymmetry claim more precise.
  7. References [18] and [19] appear to be the same arXiv preprint (arXiv:2501.05310) cited twice with slightly different author lists. This should be corrected.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the thorough and constructive report. The referee correctly identifies the GCM as a novel contribution and acknowledges the breadth of our study. The four major comments raise substantive points about (1) the interpretation of von Neumann entropy as 'compression,' (2) the Wav2Vec2 sign inconsistency in entropy-phoneme correlation, (3) the appropriateness of linear Pearson correlation for non-monotonic relationships, and (4) the absence of error bars and significance tests. We address each below and commit to revisions for all four points.

read point-by-point responses

  1. Referee: §2.2 (Compression, Eq. 1) and §3.5: The paper interprets von Neumann entropy of the Gram matrix as 'informational density' and frames its decrease as beneficial 'compression.' However, this entropy measures spectral spread (effective rank), not information content in the Information Bottleneck sense (I(Z;X) or I(Z;Y)). A decrease in effective rank can indicate either beneficial compression (noise removal with signal preservation) or destructive collapse (loss of task-relevant information). The paper does not distinguish these cases. This is load-bearing for the central claim that 'phoneme recognition benefits from deep-layer compression and linearization.' The authors should either (a) add an independent measure of task-relevant information (e.g., mutual information estimates or probing-based proxies) to validate that the entropy decrease preserves phoneme-relevant signal, or (b) soften.

    Authors: The referee is correct that von Neumann entropy of the Gram matrix measures spectral spread (effective rank) rather than mutual information in the Information Bottleneck sense, and that a decrease in effective rank is ambiguous between beneficial compression and destructive collapse. We agree this distinction is important and that our current framing overstates what the entropy metric alone can establish. We will revise the manuscript in two ways. First, we will soften the language throughout: 'informational density' will be replaced with 'effective dimensionality' or 'spectral spread,' and we will explicitly state that entropy decrease is consistent with—but does not prove—beneficial compression. Second, we will note that our linear probing results (Section 3.5, Figure 8a) serve as an independent, task-relevant proxy: phoneme accuracy does not catastrophically decline in the deep layers for HuBERT, WavLM, and UniSpeech, which is consistent with beneficial rather than destructive compression for those models. However, we acknowledge that for Wav2Vec2, the entropy collapse coincides with a decline in phoneme accuracy in the final layers, which may indeed reflect partial destructive collapse. We will state this explicitly. We will not claim that entropy alone validates beneficial compression. revision: yes

  2. Referee: Figure 9a, Wav2Vec2 row: The entropy-phoneme correlation for Wav2Vec2 is +0.33, which is positive—meaning higher entropy is associated with better phoneme accuracy. This is opposite to the paper's general claim that phoneme recognition benefits from low entropy (compression). The paper's take-away states phonemes require 'deep-layer compression,' but Wav2Vec2—the model with the most dramatic entropy collapse—shows the opposite trend. This inconsistency should be explicitly addressed. If the claim is model-dependent, the take-away should be qualified accordingly.

    Authors: The referee has identified a genuine inconsistency that we had not adequately addressed. The +0.33 correlation for Wav2Vec2 is indeed opposite in sign to the negative average correlation (-0.46) and to the trends observed for HuBERT (-0.82), Data2Vec (-0.74), and UniSpeech (-0.72). This is not a minor discrepancy: Wav2Vec2 is the model with the most dramatic entropy collapse, and it is the one model where higher entropy is associated with better phoneme accuracy. We agree that the take-away should be qualified. In the revised manuscript, we will explicitly discuss this Wav2Vec2 exception, noting that the entropy collapse in Wav2Vec2's final layers may represent destructive rather than beneficial compression—consistent with the concurrent decline in phoneme accuracy and the GCM's semantic rupture at layer 11. The general claim will be restated as model-dependent: for masked-prediction models (HuBERT, WavLM, UniSpeech), phoneme accuracy correlates negatively with entropy, but for Wav2Vec2's contrastive objective, the relationship reverses. The take-away will be revised to reflect this qualification. revision: yes

  3. Referee: Figure 9 and §3.5: The Pearson correlations between intrinsic metrics and probing accuracy assume a linear relationship. However, Figure 8a shows that phoneme accuracy is non-monotonic (peaking in mid-layers and declining in deep layers for most models). A linear correlation coefficient may mischaracterize a non-monotonic relationship. The authors should discuss this limitation and consider whether rank-based or non-monotonic measures would be more appropriate for the reported correlations.

    Authors: This is a valid methodological concern. The phoneme accuracy curves in Figure 8a are indeed non-monotonic—peaking in mid-layers and declining in deep layers—so Pearson correlation, which captures only linear association, can mischaracterize the relationship between entropy/curvature and phoneme accuracy. We will address this in two ways. First, we will add an explicit discussion of this limitation in Section 3.5, noting that Pearson correlations may understate or misrepresent non-monotonic relationships. Second, we will compute Spearman rank correlations as a supplementary measure and report them alongside the Pearson values. We expect that rank-based measures will better capture the monotonic component of the relationship (e.g., the general trend that lower entropy layers tend to have higher phoneme accuracy for masked-prediction models), while also being more honest about the non-monotonic structure. If the Spearman correlations differ substantially from the Pearson values, we will report both and discuss the discrepancy. revision: yes

  4. Referee: §3.1–§3.5: No error bars, confidence intervals, or significance tests are reported for any of the intrinsic metrics, GCM entries, or probing results. Given that the central claims rest on comparing layer-wise trajectories and correlation values across models, some quantification of variance is needed to assess whether the observed differences (e.g., Wav2Vec2's entropy collapse vs. WavLM's stability) are statistically reliable. At minimum, bootstrap confidence intervals on the entropy and curvature averages, or standard deviations across the test set, would strengthen the reported patterns.

    Authors: The referee is right that the absence of variance estimates is a weakness, particularly given that the central claims rest on comparing layer-wise trajectories across models. We will add bootstrap confidence intervals for the intrinsic metrics (entropy, curvature, InfoNCE) computed over the test-clean set. For the GCM entries, we will report standard deviations across the evaluation set. For the linear probing results, we will report standard deviations across multiple random seeds for probe training. We note that for the intrinsic metrics, the patterns we report (e.g., Wav2Vec2's entropy collapse, the curvature transition point) are visually dramatic and consistent across the 2,620 utterances in test-clean, so we expect the confidence intervals to be narrow and the patterns to remain significant. However, we agree that this should be verified empirically rather than assumed, and we will include the variance estimates in the revised figures. revision: yes

Circularity Check

0 steps flagged

No significant circularity: metrics are computed from embeddings without fitting to target results, and the central derivation is self-contained against external benchmarks.

full rationale

The paper's derivation chain is largely self-contained. The three per-layer metrics (entropy Eq. 1, curvature Eq. 2, InfoNCE Eq. 3) are computed directly from the SSL model embeddings Z^(l) without fitting any parameters to the downstream task results they are later correlated with. The GCM decoders (Section 2.3) are trained on reconstruction loss (L1, SpeechBERTScore, etc.), not on phoneme/pitch/speaker task performance. The linear probes (Section 3.5) are standard and independent — trained on frozen embeddings to predict external labels. The Pearson correlations in Figure 9 are post-hoc statistical relationships between independently computed quantities, not predictions forced by construction. The main external citation is to Skean et al. [20] ('Layer by layer'), from which the implementation of intrinsic metrics is adapted; this is a methodological adaptation of published, externally-available tools, not a self-citation. The paper's authors (Sadok, Alameda-Pineda) do not appear in the author list of [20]. The interpretive claims (entropy as 'informational density,' curvature decrease as 'manifold unfolding') are assumptions that could be questioned on correctness grounds — the von Neumann entropy of the Gram matrix measures spectral diversity rather than information-theoretic mutual information — but this is a validity concern, not circularity. No step in the derivation chain reduces to its own inputs by definition or by fitted parameter. The framework computes intrinsic metrics, computes task performance, and correlates them; none of these steps is tautological.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities, particles, forces, or dimensions. The Generative Compatibility Matrix (GCM) is a new methodological tool, not an invented entity. The free parameters are standard hyperparameters (temperature, augmentation probability, decoder architecture choices) chosen by hand, not fitted to recover the target result. The axioms are domain assumptions about the interpretability of information-theoretic and geometric proxies, which are standard in representation analysis literature but unvalidated for the specific claims made here.

free parameters (4)
  • InfoNCE temperature τ = 0.1
    Set to 0.1 in §3.1 for the robustness metric. Not fitted to data but chosen by hand; standard value in contrastive learning.
  • Augmentation trigger probability p = 0.7
    Each transformation triggered with p=0.7 in §3.1. Chosen by hand for the robustness analysis pipeline.
  • DiT hidden dimension = 512
    Decoder hidden dimension for GCM in §3.4. Chosen by hand.
  • DiT number of layers = 6
    Decoder depth for GCM in §3.4. Chosen by hand.
axioms (4)
  • domain assumption Von Neumann entropy of the Gram matrix is a faithful proxy for representational information density/diversity.
    Invoked in §2.2 Compression: 'High entropy values indicate that embeddings are spread across many dimensions (high diversity), whereas low entropy values suggest that the representation lies in a low-dimensional subspace.' This interpretation is assumed, not proven for speech embeddings.
  • domain assumption Average curvature of token transitions is a faithful proxy for manifold unfolding and linear separability.
    Invoked in §2.2 Geometry: 'a decrease in curvature indicates smoother, more linear trajectories, often associated with the abstraction of global, semantically coherent structures.' The link between curvature and semantic abstraction is assumed.
  • domain assumption InfoNCE loss between augmented views approximates mutual information and thus measures robustness/invariance.
    Invoked in §2.2 Robustness: 'Minimizing this objective is equivalent to maximizing a lower bound on the mutual information between the latent representations of the invariant views.' Standard CPC assumption [25] applied here.
  • standard math Linear probing accuracy reflects the immediate accessibility of task-relevant information in a layer.
    Standard assumption in interpretability research, invoked in §3.5. The probe is restricted to a linear mapping to quantify accessibility.

pith-pipeline@v1.1.0-glm · 17288 in / 3027 out tokens · 388954 ms · 2026-07-08T07:13:56.451070+00:00 · methodology

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read the original abstract

Self-supervised learning (SSL) models, such as Wav2Vec2, HuBERT, and WavLM, have become foundational across a wide range of speech and audio tasks. Despite their success, understanding their internal layer-wise dynamics remains an ongoing challenge. To address this, we propose a two-part model-centric framework called InsideSSL. First, we establish a task-agnostic analysis from three intrinsic per-layer perspectives: compression (entropy), geometry (curvature), and robustness to perturbations. We show that varying training objectives induce distinct regimes of acoustic compression and manifold unfolding. Second, we introduce the cross-layer Generative Compatibility Matrix (GCM) to evaluate functional transferability, exposing stable phonetic cores, identity volatility, and deep-layer semantic pruning. In addition to these evaluations, linear probing connects the model-centric perspective to downstream tasks, demonstrating how layer topology dictates phoneme, pitch, and speaker encoding.

Figures

Figures reproduced from arXiv: 2607.06392 by Samir Sadok, Xavier Alameda-Pineda.

Figure 1
Figure 1. Figure 1: Systematic layer-wise evaluation of SSL speech rep￾resentations using a model-centric perspective framework. It tracks the evolution of entropy, curvature, and invariance across layer depth to characterize how information is compressed, or￾ganized, and abstracted within the Transformer hierarchy. (i) Compression perspective: Guided by the Information Bot￾tleneck principle [21, 22, 23, 20], we investigate t… view at source ↗
Figure 2
Figure 2. Figure 2: Layer-wise analysis of SSL models across the three model-centric perspectives: compression (entropy), geometry (curvature), and robustness (invariance to input perturbations). baseline is included as a reference for raw acoustic features. Complementing these trajectories, the bottom row (Figs. 2d–2f) displays inter-model correlation matrices. These heatmaps quantify the pairwise similarity of layer-wise be… view at source ↗
Figure 3
Figure 3. Figure 3: The impact of training data (WAVLM-PLUS) and model size (WAVLM-LARGE) on SSL audio representations, showing how layer-wise properties (compression, geometry, and robustness) vary across models of different scales. (a) Compression (entropy) (b) Geometry (curvature) (c) Robustness (InfoNCE) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of ASR fine-tuning scale (10 min, 100 h, 960 h) on DATA2VEC representations, illustrating how layer-wise properties (compression, geometry, and robustness) evolve after task adaptation. Robustness perspective. Figure 2c tracks the average InfoNCE loss, serving as a proxy for assessing the robustness/invariance of SSL models to various perturbations (see Section 3.1). Most architectures (e.g., HUBERT… view at source ↗
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: Robustness analysis–Layer-wise impact of diverse perturbations on representation invariance. We report Average InfoNCE for WAVLM (a) and WAV2VEC2 (b) across layers. ble variation across data regimes. This stability implies that the informational density and effective dimensionality of the repre￾sentations are determined primarily by pre-training, remaining invariant to the scale of downstream supervision. … view at source ↗
Figure 7
Figure 7. Figure 7: The cross-layer Generative Compatibility Matrix (GCM) comparison between Wav2Vec2-base (top) and WavLM-base (bot￾tom). Each cell (ℓ, k) represents the performance of a decoder trained on layer ℓ and evaluated on layer k. subsequently reconstructs the final speech waveform without being updated during training. All decoders are trained for 400 epochs on a single GPU using the train-clean-100 subset, ensurin… view at source ↗
Figure 8
Figure 8. Figure 8: Task probing across layers for phoneme classification, pitch regression, and speaker classification. Results show how task￾relevant information is distributed across the network hierarchy. Entropy Curvature Invariance Wav2vec2 Wavlm Hubert-ls960 Data2vec-audio Unispeech-sat Average 0.33 -0.06 -0.47 -0.38 -0.56 -0.93 -0.82 -0.72 -0.82 -0.74 -0.83 0.16 -0.72 -0.70 -0.63 -0.46 -0.57 -0.54 1.00 0.75 0.50 0.25 … view at source ↗
Figure 9
Figure 9. Figure 9: Pearson correlation between layer-wise probing accuracy (PPGs, pitch, speaker identity) and representation properties (entropy, curvature, invariance) across self-supervised speech models. Higher absolute values indicate stronger relationships. layers over-compress the signal. This layer-wise phonetic spe￾cialization is consistent with previous studies [5, 17] reporting that intermediate transformer layers… view at source ↗

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Reference graph

Works this paper leans on

44 extracted references · 44 canonical work pages · 14 internal anchors

  1. [1]

    Introduction Self-supervised speech representation learning (SSL) has be- come a cornerstone of modern audio processing [1, 2], with models such as WAVLM [3], WAV2VEC2 [4], and HUBERT

    work page

  2. [2]

    InsideSSL: Understanding Self-Supervised Speech Representations using a Model-Centric Perspective

    achieving remarkable performance across speech recogni- tion [4, 3], speaker verification [6, 3, 7], emotion recognition [8, 9, 7] and speech enhancement tasks [10, 11]. By leveraging unlabeled audio data, these models learn representations that capture meaningful semantic and acoustic information with- out relying on explicit supervision. However, despit...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  3. [3]

    P” for predictive (masked prediction), “C

    Experiments 3.1. Per-Layer Analysis: Experimental Setup We evaluate our model-centric perspective on several widely used SSL models. For each model, we extract hidden represen- tations at every layer and analyze them according to the three perspectives described in Section 2. Models.All self-supervised learning models examined in this study utilize a bidi...

    work page

  4. [4]

    flattens

    The results show that scaling model size has a stronger struc- tural effect than simply increasing the amount of training data: the trajectories ofWAVLM-BASEandWAVLM-BASE-PLUSare closely aligned, whereasWAVLM-LARGEexhibits a markedly different behavior. In terms of entropy,WAVLM-LARGEex- hibits a distinct trajectory: starting at a value of0.70in layer 1, ...

    work page

  5. [5]

    In terms of phonetic content (SpeechBERTScore), both SSL models display a broad region of high SpeechBERTScore values, indicating a stable phonetic encoding

    for semantic content, Resemblyzer similarity [35] for speaker identity, STOI for audio quality, andL1loss for Mel-spectrogram reconstruction. In terms of phonetic content (SpeechBERTScore), both SSL models display a broad region of high SpeechBERTScore values, indicating a stable phonetic encoding. For instance, in WAV2VEC2, layers1through10 consistently ...

    work page

  6. [6]

    Our analysis revealed dis- tinct optimization regimes, notably the late-stageentropy col- lapsein Wav2Vec2, contrasting with the geometric stability of WavLM

    Conclusion In this work, we introduced theINSIDESSL framework, a uni- fied,task-agnostic and model-centricapproach to analyze SSL speech representations first through three per-layer lenses: com- pression, geometry, and robustness. Our analysis revealed dis- tinct optimization regimes, notably the late-stageentropy col- lapsein Wav2Vec2, contrasting with ...

    work page

  7. [7]

    Acknowledgments This work was granted access to the HPC resources of IDRIS under the allocation Grant 2025-A0181016041 made by GENCI

    work page 2025

  8. [8]

    They did not contribute to the scientific content, analyses, or conclusions of this work

    Generative AI Use Disclosure Generative AI tools were used exclusively for language edit- ing and stylistic improvements. They did not contribute to the scientific content, analyses, or conclusions of this work. All au- thors take full responsibility for the manuscript, have approved its submission, and confirm that no generative AI system is listed as a ...

    work page

  9. [9]

    Audio self-supervised learning: A survey,

    S. Liu, A. Mallol-Ragolta, E. Parada-Cabaleiro, K. Qian, X. Jing, A. Kathan, B. Hu, and B. W. Schuller, “Audio self-supervised learning: A survey,”Patterns, vol. 3, no. 12, 2022

    work page 2022

  10. [10]

    Self-supervised speech representation learning: A review,

    A. Mohamed, H.-y. Lee, L. Borgholt, J. D. Havtorn, J. Edin, C. Igel, K. Kirchhoff, S.-W. Li, K. Livescu, L. Maaløeet al., “Self-supervised speech representation learning: A review,”IEEE Journal of Selected Topics in Signal Processing, vol. 16, no. 6, pp. 1179–1210, 2022

    work page 2022

  11. [11]

    Wavlm: Large-scale self- supervised pre-training for full stack speech processing,

    S. Chen, C. Wang, Z. Chen, Y . Wu, S. Liu, Z. Chen, J. Li, N. Kanda, T. Yoshioka, X. Xiaoet al., “Wavlm: Large-scale self- supervised pre-training for full stack speech processing,”IEEE Journal of Selected Topics in Signal Processing, vol. 16, no. 6, pp. 1505–1518, 2022

    work page 2022

  12. [12]

    wav2vec 2.0: A framework for self-supervised learning of speech repre- sentations,

    A. Baevski, Y . Zhou, A. Mohamed, and M. Auli, “wav2vec 2.0: A framework for self-supervised learning of speech repre- sentations,”Advances in neural information processing systems, vol. 33, pp. 12 449–12 460, 2020

    work page 2020

  13. [13]

    Hubert: Self-supervised speech represen- tation learning by masked prediction of hidden units,

    W.-N. Hsu, B. Bolte, Y .-H. H. Tsai, K. Lakhotia, R. Salakhutdi- nov, and A. Mohamed, “Hubert: Self-supervised speech represen- tation learning by masked prediction of hidden units,”IEEE/ACM transactions on audio, speech, and language processing, vol. 29, pp. 3451–3460, 2021

    work page 2021

  14. [14]

    Exploring wav2vec 2.0 on speaker verification and language identification

    Z. Fan, M. Li, S. Zhou, and B. Xu, “Exploring wav2vec 2.0 on speaker verification and language identification,”arXiv preprint arXiv:2012.06185, 2020

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  15. [15]

    A Fine-tuned Wav2vec 2.0/HuBERT Benchmark For Speech Emotion Recognition, Speaker Verification and Spoken Language Understanding

    Y . Wang, A. Boumadane, and A. Heba, “A fine-tuned wav2vec 2.0/hubert benchmark for speech emotion recognition, speaker verification and spoken language understanding,”arXiv preprint arXiv:2111.02735, 2021

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  16. [16]

    Emotion Recognition from Speech Using Wav2vec 2.0 Embeddings

    L. Pepino, P. Riera, and L. Ferrer, “Emotion recognition from speech using wav2vec 2.0 embeddings,”arXiv preprint arXiv:2104.03502, 2021

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  17. [17]

    Exploring wav2vec 2.0 fine tuning for improved speech emotion recognition,

    L.-W. Chen and A. Rudnicky, “Exploring wav2vec 2.0 fine tuning for improved speech emotion recognition,” inICASSP 2023-2023 IEEE international conference on acoustics, speech and signal processing (ICASSP). IEEE, 2023, pp. 1–5

    work page 2023

  18. [18]

    Boosting Self-Supervised Embeddings for Speech Enhancement

    K.-H. Hung, S.-w. Fu, H.-H. Tseng, H.-T. Chiang, Y . Tsao, and C.-W. Lin, “Boosting self-supervised embeddings for speech en- hancement,”arXiv preprint arXiv:2204.03339, 2022

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  19. [19]

    Investigating self-supervised learning for speech enhancement and separation,

    Z. Huang, S. Watanabe, S.-w. Yang, P. Garc´ıa, and S. Khudanpur, “Investigating self-supervised learning for speech enhancement and separation,” inICASSP 2022-2022 IEEE International Con- ference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2022, pp. 6837–6841

    work page 2022

  20. [20]

    Layer-wise analysis of a self-supervised speech representation model,

    A. Pasad, J.-C. Chou, and K. Livescu, “Layer-wise analysis of a self-supervised speech representation model,” in2021 IEEE Auto- matic Speech Recognition and Understanding Workshop (ASRU). IEEE, 2021, pp. 914–921

    work page 2021

  21. [21]

    What all do audio transformer models hear? Probing Acoustic Representations for Language Delivery and its Structure

    J. Shah, Y . K. Singla, C. Chen, and R. R. Shah, “What all do audio transformer models hear? probing acoustic represen- tations for language delivery and its structure,”arXiv preprint arXiv:2101.00387, 2021

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  22. [22]

    Phone and speaker spatial organization in self-supervised speech represen- tations,

    P. Riera, M. Cerdeiro, L. Pepino, and L. Ferrer, “Phone and speaker spatial organization in self-supervised speech represen- tations,” in2023 IEEE International Conference on Acoustics, Speech, and Signal Processing Workshops (ICASSPW). IEEE, 2023, pp. 1–5

    work page 2023

  23. [23]

    Exploration of a self- supervised speech model: A study on emotional corpora,

    Y . Li, Y . Mohamied, P. Bell, and C. Lai, “Exploration of a self- supervised speech model: A study on emotional corpora,” in2022 IEEE Spoken Language Technology Workshop (SLT). IEEE, 2023, pp. 868–875

    work page 2023

  24. [24]

    What do self-supervised speech and speaker mod- els learn? new findings from a cross model layer-wise analysis,

    T. Ashihara, M. Delcroix, T. Moriya, K. Matsuura, T. Asami, and Y . Ijima, “What do self-supervised speech and speaker mod- els learn? new findings from a cross model layer-wise analysis,” inICASSP 2024-2024 IEEE International Conference on Acous- tics, Speech and Signal Processing (ICASSP). IEEE, 2024, pp. 10 166–10 170

    work page 2024

  25. [25]

    Comparative layer-wise anal- ysis of self-supervised speech models,

    A. Pasad, B. Shi, and K. Livescu, “Comparative layer-wise anal- ysis of self-supervised speech models,” inICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023, pp. 1–5

    work page 2023

  26. [27]

    A large-scale probing analysis of speaker-specific at- tributes in self-supervised speech representations,

    A. Y . F. Chiu, K. C. Fung, R. T. Y . Li, J. Li, and T. Lee, “A large-scale probing analysis of speaker-specific at- tributes in self-supervised speech representations,”arXiv preprint arXiv:2501.05310, 2025

    work page arXiv 2025

  27. [28]

    Layer by Layer: Uncovering Hidden Representations in Language Models

    O. Skean, M. R. Arefin, D. Zhao, N. Patel, J. Naghiyev, Y . LeCun, and R. Shwartz-Ziv, “Layer by layer: Uncovering hidden repre- sentations in language models,”arXiv preprint arXiv:2502.02013, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  28. [29]

    The information bottleneck method

    N. Tishby, F. C. Pereira, and W. Bialek, “The information bottle- neck method,”arXiv preprint physics/0004057, 2000

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  29. [30]

    Opening the Black Box of Deep Neural Networks via Information

    R. Shwartz-Ziv and N. Tishby, “Opening the black box of deep neural networks via information,”arXiv preprint arXiv:1703.00810, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  30. [31]

    To compress or not to compress—self-supervised learning and information theory: A review,

    R. Shwartz Ziv and Y . LeCun, “To compress or not to compress—self-supervised learning and information theory: A review,”Entropy, vol. 26, no. 3, p. 252, 2024

    work page 2024

  31. [32]

    Large language models implic- itly learn to straighten neural sentence trajectories to construct a predictive representation of natural language

    E. Hosseini and E. Fedorenko, “Large language models implic- itly learn to straighten neural sentence trajectories to construct a predictive representation of natural language.”Advances in Neu- ral Information Processing Systems, vol. 36, pp. 43 918–43 930, 2023

    work page 2023

  32. [33]

    Representation Learning with Contrastive Predictive Coding

    A. v. d. Oord, Y . Li, and O. Vinyals, “Representation learning with contrastive predictive coding,”arXiv preprint arXiv:1807.03748, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  33. [34]

    LiDAR: Sensing Linear Probing Performance in Joint Embedding SSL Architectures

    V . Thilak, C. Huang, O. Saremi, L. Dinh, H. Goh, P. Nakkiran, J. M. Susskind, and E. Littwin, “Lidar: Sensing linear probing performance in joint embedding ssl architectures,”arXiv preprint arXiv:2312.04000, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  34. [35]

    DiME: Maximizing Mutual Information by a Difference of Matrix-Based Entropies

    O. Skean, J. K. H. Osorio, A. J. Brockmeier, and L. G. S. Gi- raldo, “Dime: Maximizing mutual information by a difference of matrix-based entropies,”arXiv preprint arXiv:2301.08164, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  35. [36]

    Multivari- ate extension of matrix-based r ´enyi’s alpha-order entropy func- tional,

    S. Yu, L. G. S. Giraldo, R. Jenssen, and J. C. Principe, “Multivari- ate extension of matrix-based r ´enyi’s alpha-order entropy func- tional,”IEEE transactions on pattern analysis and machine intel- ligence, vol. 42, no. 11, pp. 2960–2966, 2019

    work page 2019

  36. [37]

    Data2vec: A general framework for self-supervised learning in speech, vision and language,

    A. Baevski, W.-N. Hsu, Q. Xu, A. Babu, J. Gu, and M. Auli, “Data2vec: A general framework for self-supervised learning in speech, vision and language,” inInternational conference on ma- chine learning. PMLR, 2022, pp. 1298–1312

    work page 2022

  37. [38]

    Lib- rispeech: an asr corpus based on public domain audio books

    V . Panayotov, G. Chen, D. Povey, and S. Khudanpur, “Lib- rispeech: an asr corpus based on public domain audio books.” IEEE, 2015, pp. 5206–5210

    work page 2015

  38. [39]

    Flow Matching for Generative Modeling

    Y . Lipman, R. T. Chen, H. Ben-Hamu, M. Nickel, and M. Le, “Flow matching for generative modeling,”arXiv preprint arXiv:2210.02747, 2022

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  39. [40]

    Scalable diffusion models with transform- ers,

    W. Peebles and S. Xie, “Scalable diffusion models with transform- ers,” inProceedings of the IEEE/CVF international conference on computer vision, 2023, pp. 4195–4205

    work page 2023

  40. [41]

    Hifi-GAN: Generative adversarial networks for efficient and high fidelity speech synthesis,

    J. Kong, J. Kim, and J. Bae, “Hifi-GAN: Generative adversarial networks for efficient and high fidelity speech synthesis,” 2020

    work page 2020

  41. [42]

    SpeechBERTScore: Reference-Aware Automatic Evaluation of Speech Generation Leveraging NLP Evaluation Metrics

    T. Saeki, S. Maiti, S. Takamichi, S. Watanabe, and H. Saruwatari, “Speechbertscore: Reference-aware automatic evaluation of speech generation leveraging nlp evaluation metrics,”arXiv preprint arXiv:2401.16812, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  42. [43]

    Generalized end- to-end loss for speaker verification,

    L. Wan, Q. Wang, A. Papir, and I. L. Moreno, “Generalized end- to-end loss for speaker verification,” 2018

    work page 2018

  43. [44]

    High-fidelity neural phonetic posteriorgrams,

    C. Churchwell, M. Morrison, and B. Pardo, “High-fidelity neural phonetic posteriorgrams,” inICASSPW, 2024

    work page 2024

  44. [45]

    Crepe: A convo- lutional representation for pitch estimation,

    J. W. Kim, J. Salamon, P. Li, and J. P. Bello, “Crepe: A convo- lutional representation for pitch estimation,” in2018 IEEE Inter- national Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018, pp. 161–165

    work page 2018