arxiv: 2604.08591 · v1 · submitted 2026-03-31 · 💻 cs.LG · cs.AI

Recognition: unknown

From Dispersion to Attraction: Spectral Dynamics of Hallucination Across Whisper Model Scales

Grach Mkrtchian, Ivan Viakhirev, Kirill Borodin

Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:15 UTC · model gemini-3-flash-preview

classification 💻 cs.LG cs.AI MSC 68T07

keywords Automatic Speech RecognitionSpectral AnalysisHallucinationsWhisper ModelsNeural Network DynamicsPhase Transitions

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The pith

Large speech models hallucinate because their internal signals collapse into a single repetitive state, causing them to ignore the actual audio.

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

This paper establishes that hallucinations in speech recognition models are not just random errors but the result of a mathematical phase transition. In smaller models, errors happen because the audio signal weakens as it passes through the layers; in larger models, the internal representations actively collapse into a single 'attractor' state. This collapse forces the model to prioritize its internal language patterns over the external sound, leading to confident but entirely fabricated transcripts.

Core claim

The authors identify a 'Compression-Seeking Attractor' state in large-scale Whisper models that triggers hallucinations. Using a new Spectral Sensitivity Theorem, they show that large models under stress undergo a rank-1 collapse, where the diversity of internal information is squeezed out by the self-attention mechanism. This creates a feedback loop where the model's internal expectations override the acoustic evidence, effectively transforming the model from a listener into a narrator of its own internal priors.

What carries the argument

The Spectral Sensitivity Theorem, a predictive framework that uses layer-wise gain and alignment to determine if a neural network will preserve its input signal or collapse it into a single dominant output.

If this is right

Model scale changes the mathematical nature of failure, moving from passive signal loss to active signal suppression.
Monitoring the spectral slope of activations provides a way to detect hallucinations in real-time without needing a ground-truth transcript.
Self-attention layers in large models are the primary site where acoustic evidence is discarded in favor of internal priors.
Hallucination-resistant speech models require architectural mechanisms that explicitly prevent rank-1 collapse in deep layers.

Where Pith is reading between the lines

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

This spectral collapse likely explains why traditional decoding penalties fail to stop hallucinations in models that have already converged on an internal attractor.
The transition from dispersion to attraction may be a universal feature of scaling transformer-based models, potentially explaining similar failure modes in large language and image models.
Future training protocols could include spectral diversity objectives to ensure models remain sensitive to input data throughout all layers.

Load-bearing premise

The paper assumes that the mathematical collapse of activation rank is the primary cause of hallucinations rather than just a symptom of the model's language-model component taking over during the decoding process.

What would settle it

The theory would be disproven if large models were observed producing frequent hallucinations while their internal activations maintained high spectral diversity and rank throughout the processing layers.

Figures

Figures reproduced from arXiv: 2604.08591 by Grach Mkrtchian, Ivan Viakhirev, Kirill Borodin.

**Figure 1.** Figure 1: Layer-wise Spectral Dynamics. The evolution of rank collapse (∆Neff) across network depth. Left: Small models (Green) suffer catastrophic decoupling in Cross-Attention (negative slope indicates loss of input signal). Center: Large models (Red) exhibit unique rank compression in Self-Attention, indicative of Attractor dynamics, while Small models expand rank seeking context view at source ↗

**Figure 2.** Figure 2: Spectral Phase Diagram (Final Layer). Cross-Attention rank drops by −13.40% in Small models (Table 2). This corresponds to ρ < 1, where the acoustic injections Gl are spectrally washed out before reaching final layers. 4.3. Regime II: Autoregressive Lock-in (Large Models) The Large-v3-Turbo model resists global disintegration but enters an autoregressive lock-in state. The unique compression in Self-Atte… view at source ↗

read the original abstract

Hallucinations in large ASR models present a critical safety risk. In this work, we propose the \textit{Spectral Sensitivity Theorem}, which predicts a phase transition in deep networks from a dispersive regime (signal decay) to an attractor regime (rank-1 collapse) governed by layer-wise gain and alignment. We validate this theory by analyzing the eigenspectra of activation graphs in Whisper models (Tiny to Large-v3-Turbo) under adversarial stress. Our results confirm the theoretical prediction: intermediate models exhibit \textit{Structural Disintegration} (Regime I), characterized by a $13.4\%$ collapse in Cross-Attention rank. Conversely, large models enter a \textit{Compression-Seeking Attractor} state (Regime II), where Self-Attention actively compresses rank ($-2.34\%$) and hardens the spectral slope, decoupling the model from acoustic evidence.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper attempts to ground Whisper's hallucination problem in the spectral physics of deep networks, moving from 'black box' observations to a measurable phase transition.

read the letter

You should look at this paper if you're interested in why large ASR models tend to loop or hallucinate under stress. The authors move past the usual hand-waving about 'language model priors' and actually try to derive the math behind it.

What’s new here is the Spectral Sensitivity Theorem. They argue that as these models scale in depth and width, they undergo a phase transition. Smaller models (like Whisper Tiny) just fall apart when the input is bad—they show 'structural disintegration' where the signal just dies. But the larger models (Large-v3-Turbo) do something different: they enter an 'attractor' state. The activations collapse toward a rank-1 state where the model essentially stops listening to the audio and starts talking to itself. The empirical data on rank compression in the Large models is solid and provides a concrete metric for what we’ve all seen in production.

There is a legitimate soft spot regarding whether this 'attractor' is a dynamic response to bad audio or just a static property of deep Transformers. If the spectral hardening and rank collapse are always present in the Large-v3-Turbo model—even on clean audio—then the theory explains why the model is *prone* to hallucinating, but it doesn't quite capture the 'why now' of a specific failure. The authors also rely on specific gain assumptions that might not translate perfectly to every architecture, so I'd like to see this tested on something other than Whisper.

That said, the work is rigorous. They aren't just fitting curves; they’ve derived a theorem and checked it against a full model lineage. This is for researchers in interpretability and safety who want a more formal way to talk about model failures than just 'the prior took over.' It is a serious effort that deserves a proper review.

Referee Report

3 major / 3 minor

Summary. This paper investigates the spectral dynamics of activation graphs in Whisper models to explain the mechanism of hallucinations. The authors propose the 'Spectral Sensitivity Theorem', which models the propagation of signal through deep transformer layers as a function of layer-wise gain and alignment. They identify two regimes: a dispersive regime (Regime I) where signals decay and models fail via 'Structural Disintegration' (observed in smaller/medium models), and an attractor regime (Regime II) where the model enters a 'Compression-Seeking Attractor' (observed in large models). This attractor state is characterized by rank-1 collapse, where the model effectively ignores acoustic input and relies on internal language priors to generate hallucinations. The theory is tested empirically across the Whisper model family, from Tiny to Large-v3-Turbo, using adversarial audio inputs to trigger failure modes.

Significance. The paper provides a formal, falsifiable framework (the Spectral Sensitivity Theorem) for a phenomenon often discussed colloquially in the ASR community. By identifying specific spectral signatures (rank compression and slope hardening) associated with different model scales, the work moves beyond empirical observation toward a predictive theory of model reliability. The use of the complete Whisper scale allows for a rigorous cross-sectional analysis of how depth and width influence hallucinatory dynamics. The identification of Regime II (rank-1 collapse) as a primary driver of hallucinations in large models is a significant insight that could inform future architectural choices or detection mechanisms for 'hallucination-prone' activation states.

major comments (3)

[§5.2 and Equation (3.4)] The central claim that large models 'enter' an attractor state specifically under adversarial stress lacks a necessary baseline. There is no spectral analysis provided for 'healthy' (successful) transcriptions on the Large-v3-Turbo model. In deep Transformers, rank collapse is often a static property of depth and initialization (the expressivity bottleneck). If the spectral hardening and rank-1 collapse reported in Figure 3 are present during normal operation, then Regime II is a static architectural property rather than a dynamic transition triggered by hallucination-inducing inputs.
[Table 2] The reported rank compression for the Large model is -2.34%, whereas the intermediate models show a much larger 13.4% collapse in Cross-Attention rank. The paper characterizes the former as a 'Compression-Seeking Attractor' (Regime II) and the latter as 'Structural Disintegration' (Regime I). The authors must provide a statistical justification for why a 2.34% change is considered a significant 'phase transition' into an attractor state, especially when it is an order of magnitude smaller than the collapse seen in smaller models.
[§3.1, Eq. (3.2)] The Spectral Sensitivity Theorem relies on the assumption of uniform layer-wise gain. However, Whisper models utilize LayerNorm and residual connections that dynamically rescale activations. The manuscript does not demonstrate that the gain-alignment ratio (λ) remains sufficiently stable across layers to justify the exponential propagation model in Eq. (3.3). A sensitivity analysis of λ across different decoding steps is required to confirm the theorem's applicability to the non-linear dynamics of actual inference.

minor comments (3)

[Figure 3] The log-log plot of the eigenspectra is difficult to read in the high-frequency range. It would be beneficial to include a linear-scale inset or a zoomed-in plot of the tail behavior to better visualize the 'spectral hardening' described in the text.
[§4.2] The term 'Compression-Seeking Attractor' is introduced without a formal definition in the context of dynamical systems. It would be helpful to clarify if this refers to a literal fixed-point attractor in the activation space or if it is used metaphorically to describe the rank-reduction trend.
[General] There are minor typos in the bibliography; specifically, several conference titles (e.g., NeurIPS) are missing the year of publication.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their rigorous assessment of the Spectral Sensitivity Theorem. The report correctly identifies three critical areas for strengthening the manuscript: the necessity of non-hallucinatory baselines for deep models, the clarification of our statistical metrics for 'Regime II', and the impact of non-linearities (LayerNorm/Residuals) on our gain propagation model. We believe addressing these points will significantly transition the paper from a descriptive empirical study to a more robust theoretical framework. We have prepared additional spectral data for 'healthy' transcriptions and revised our definitions of spectral 'hardening' to address these concerns.

read point-by-point responses

Referee: [§5.2 and Equation (3.4)] The central claim that large models 'enter' an attractor state specifically under adversarial stress lacks a necessary baseline. There is no spectral analysis provided for 'healthy' (successful) transcriptions on the Large-v3-Turbo model. If the spectral hardening and rank-1 collapse reported in Figure 3 are present during normal operation, then Regime II is a static architectural property.

Authors: The referee raises an excellent point regarding the potential for 'static' rank collapse in deep Transformers. To address this, we have generated a baseline spectral profile for Large-v3-Turbo during successful transcriptions of the LibriSpeech test-clean set. Preliminary results show that while depth does induce a baseline compression, the 'spectral hardening' (slope increase) is significantly more pronounced (p < 0.01) during hallucinations compared to successful decoding. In the revised manuscript, Figure 3 will be updated to include these 'healthy' baselines, demonstrating that while the potential for Regime II is architectural, its activation as a rank-1 attractor is indeed a dynamic response to input-mismatch stress. revision: yes
Referee: [Table 2] The reported rank compression for the Large model is -2.34%, whereas the intermediate models show a much larger 13.4% collapse. The authors must provide a statistical justification for why a 2.34% change is considered a significant 'phase transition' into an attractor state, especially when it is an order of magnitude smaller than the collapse seen in smaller models.

Authors: We acknowledge that the phrasing in the original manuscript may have conflated 'magnitude of change' with 'state of the system.' In Regime I (Disintegration), the 13.4% collapse represents a catastrophic loss of structured information as the signal decays. In Regime II (Attractor), the model is already operating at a very low effective rank; the -2.34% represents the 'locking in' of the final attractor state where the spectral slope 'hardens' (the top eigenvalue dominates almost the entire variance). We will revise the text to clarify that the phase transition is defined by the *Spectral Slope Coefficient* rather than raw rank percentage. We will add a statistical test (Kullback–Leibler divergence between the eigenvalue distributions) to prove that the 'Attractor' state in large models is qualitatively distinct from the 'Disintegration' state in small models. revision: partial
Referee: [§3.1, Eq. (3.2)] The Spectral Sensitivity Theorem relies on the assumption of uniform layer-wise gain. However, Whisper models utilize LayerNorm and residual connections. The manuscript does not demonstrate that the gain-alignment ratio (λ) remains sufficiently stable across layers to justify the exponential propagation model in Eq. (3.3).

Authors: The referee is correct that Equation 3.2 is a first-order approximation. In the revised manuscript, we will incorporate a sensitivity analysis showing the empirical distribution of the gain-alignment ratio (λ) across Whisper's decoder layers. While LayerNorm does rescale activations, it acts as a projection that preserves the directional alignment ($cos \theta$) of the signal with the principal components of the weight matrix. We will modify Section 3.1 to explicitly discuss how residuals prevent the vanishing of the signal, essentially 'clamping' λ near the critical threshold, which is precisely why the phase transition to an attractor becomes possible in deeper models. We will provide empirical measurements of λ to justify the stability assumption used in the theorem. revision: yes

Circularity Check

2 steps flagged

The Spectral Sensitivity Theorem and 'Attractor Regime' formalize known rank-collapse dynamics as a novel predictive discovery.

specific steps

renaming known result [Abstract and Section 3.1]
"We propose the Spectral Sensitivity Theorem, which predicts a phase transition in deep networks from a dispersive regime (signal decay) to an attractor regime (rank-1 collapse) governed by layer-wise gain and alignment."

The 'phase transition' from signal propagation to rank-1 collapse is a well-documented phenomenon in deep learning literature (often referred to as 'oversmoothing' or the 'Expressivity-Bottleneck'). The Spectral Sensitivity Theorem renames these established architectural dynamics as a novel theoretical discovery, presenting an architectural byproduct of depth and initialization as a new law of hallucination.
self definitional [Section 5.2]
"Our results confirm the theoretical prediction: ...large models enter a Compression-Seeking Attractor state (Regime II), where Self-Attention actively compresses rank (-2.34%) and hardens the spectral slope, decoupling the model from acoustic evidence."

The paper defines 'Regime II' (the Attractor Regime) specifically as the state where spectral hardening and rank collapse occur. It then 'validates' the theorem by measuring these exact spectral properties in large models. Since the 'regime' is not measured by an independent behavioral proxy in this step but by the defining spectral parameters themselves, the 'prediction' is satisfied by definition.

full rationale

The paper provides a valuable empirical survey of internal activation dynamics across the Whisper model family, grounding its findings in independent measurements of third-party models. This prevents the circularity score from exceeding 4. However, the theoretical framework—specifically the 'Spectral Sensitivity Theorem'—suffers from circular framing. The theorem 'predicts' a transition to an 'Attractor Regime' that is itself defined by the very spectral measurements used to confirm the prediction. Additionally, the mathematical core of the theorem (the product of layer-wise gains and alignments) is a restatement of Lyapunov exponent analysis for discrete dynamical systems, here applied to neural network layers and presented as a proprietary 'Theorem.' While the observation that hallucinations correlate with internal rank collapse is an interesting empirical result, the claim that this state is a 'predicted phase transition' is partially circular because the transition is defined by the observations it purports to derive.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The paper introduces a new theoretical framework and several custom metrics to measure internal model dynamics that are not standard in ASR evaluation.

free parameters (2)

Adversarial stress threshold
The noise level at which 'stress' is defined to trigger the observed spectral hardening.
Layer-wise gain coefficient
A parameter in the Spectral Sensitivity Theorem used to define the boundary between the two regimes.

axioms (2)

domain assumption Activation graphs represent information fidelity
The paper assumes that the rank and spectral slope of activation tensors directly correlate with the preservation or loss of input information.
ad hoc to paper Spectral Sensitivity Theorem
The core mathematical framework introduced in this work to predict the phase transition.

invented entities (1)

Compression-Seeking Attractor independent evidence
purpose: A proposed state in large neural networks where layers actively reduce rank to align with internal priors.
Evidence provided via the -2.34% rank compression observed in Whisper-Large activations.

pith-pipeline@v0.9.0 · 6236 in / 1755 out tokens · 16410 ms · 2026-05-08T02:15:25.834805+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 11 canonical work pages · 1 internal anchor

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However, scaling intro- duces systematic failure modes that differ from those in smaller architectures [2]

Introduction Scaling Transformer-based architectures has significantly im- proved Automatic Speech Recognition (ASR) performance across diverse acoustic conditions [1]. However, scaling intro- duces systematic failure modes that differ from those in smaller architectures [2]. While Large Language Models (LLMs) suf- fer from semantic confabulations [3], AS...
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From Dispersion to Attraction: Spectral Dynamics of Hallucination Across Whisper Model Scales

Theoretical Framework We model the signal propagation through a Transformer network of total depth L as a discrete dynamical system. Let hl ∈R D denote the hidden state at layer l∈ {1, . . . , L} . To generalize across architectures (e.g., standard layers vs. Cross-Attention), we formulate the layer function to depend on both the previous state hl−1 and a...

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2.Alignment:|κ j| ≥1−ε κ withε κL≪1

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Our empirical observation of spectral hardening in large-v3-turbo confirms that scaling facilitates this geometric condensation

Hence, Regime II cannot arise by chance; it must be created by training dynamics that progressively align dominant sub- spaces across layers, driving the network toward a structurally coherent, low-rank manifold [13]. Our empirical observation of spectral hardening in large-v3-turbo confirms that scaling facilitates this geometric condensation. Under thes...
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Methodology To validate the phase transition predicted by the Spectral Sensitiv- ity Theorem, we evaluate the internal representational dynamics of Whisper models under adversarial stress designed to induce acoustic decoupling and attractor lock-in. 3.1. Adversarial Dataset Generation To induce the failure modes described by Regimes I and II, we utilize a...
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Comparison of spectral shifts between Clean and Adversarial states

Results Table 1:Dominant Modes ( K= 10 ). Comparison of spectral shifts between Clean and Adversarial states. Component Model∆N eff (%)∆ log 10Kf∆α Dec Cross-AttnTiny−7.56% 2.12 +0.25 Small−9.54% 2.46 +0.24 Large−6.69% 2.27 +0.17 Dec Self-AttnTiny−0.76% 0.49 +0.005 Small+0.45% 3.84−0.007 Large+0.04% 3.67−0.007 Dec FFNTiny−0.51% 2.32 +0.05 Small−1.49% 3.16...
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Discussion 5.1. Validating Theorem 1 via Spectral Signatures Mechanism of Error:InRegime I, hallucinations are symp- tomatic ofsignal dispersion; the Jacobian norm decays ( ρ <1 ), causing the model output to decouple from acoustic evidence. In Regime II, hallucinations are the result ofattractor capture; the high structural alignment guides perturbed inp...
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Conclusion and Future Work We derived the Spectral Sensitivity Theorem and validated it on Whisper models, showing a scale-dependent phase transi- tion in failure modes. Intermediate models exhibitStructural Disintegration(Regime I), where acoustic signal decays in cross- attention, while large models enterAttractor Dynamics(Regime II), characterized by s...
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Generative AI Use Disclosure Generative AI tools were utilized solely for language refinement and editorial improvements, such as enhancing clarity, gram- mar, and readability. They were not used to create or alter any substantive technical material, including the conceptual frame- work, methodologies, experimental design, data analysis, results, figures,...
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