Centroid-Based Speaker Consistency Loss

• Centroid-based speaker consistency loss is a method that uses the mean of speaker embeddings to enforce compact intra-speaker representations.
• It computes centroids from multiple utterances and penalizes proximity to other speakers' centroids, ensuring clear separation in the embedding space.
• The approach enhances verification, diarization, voice conversion, and extraction performance, particularly under domain shift and few-shot conditions.

Centroid-based speaker consistency loss is a class of objective functions and regularization strategies that explicitly enforce intra-speaker embedding compactness and speaker identity stability across utterances, tasks, or synthesized/generated audio. By leveraging centroid (mean) representations in the speaker embedding space, these losses improve system performance in verification, diarization, speaker-conditioned generation, voice conversion, anti-spoofing, and extraction, especially in scenarios involving domain shift, few-shot learning, or challenging mixtures.

1. Core Concept and Mathematical Formulation

Centroid-based speaker consistency loss is designed to draw utterance-level speaker embeddings toward a reference point—the centroid—computed from multiple utterances belonging to the same speaker. This centroid becomes a robust representative "prototype" of each speaker in the embedding space. Conversely, the loss penalizes proximity to centroids of other speakers, enforcing separation and discrimination.

A canonical example, as instantiated in the Generalized End-to-End (GE2E) loss (Wan et al., 2017), computes for a mini-batch with $N$ speakers and $M$ utterances per speaker:

• Speaker centroid for speaker $k$:

$c_k = \frac{1}{M} \sum_{m=1}^M e_{k m}$

where $e_{k m}$ is the embedding of the $m$-th utterance for speaker $k$.

• Leave-one-out centroid for the true speaker $j$ (to prevent bias):

$c_j^{(-i)} = \frac{1}{M-1} \sum_{m\neq i} e_{j m}$

• Similarity between an embedding $e_{j i}$ and centroid $c_k$:

$S_{j i, k} = w \cdot \cos(e_{j i}, c_k) + b$

where $w > 0$ and $b$ are learnable parameters.

The softmax-based loss per sample becomes:

$$L(e_{j i}) = -S_{j i, j} + \log\left[\sum_{k=1}^N \exp(S_{j i, k})\right]$$

This process is analogous conceptually to Prototypical Network Loss (Wang et al., 2019), where class prototypes are derived from the support set, and the task is formulated as distance-based classification against these prototypes.

2. Extensions and Methodological Variants

Centroid-based objectives pervade several method families, each differing in the way centroids are constructed, used in scoring, or optimized:

• Prototypical Networks (PNL): Episodically computed centroids are used for few-shot query classification (Wang et al., 2019) with the loss:

$$\mathcal{L}_{\mathrm{PNL}} = -\sum_{(x_j, y_j)\in Q} \log \frac{ e^{-d(f(x_j), c_{y_j})} }{ \sum_{k'} e^{-d(f(x_j), c_{k'})} }$$

where $d(\cdot, \cdot)$ is a distance metric (e.g., squared Euclidean distance or negative cosine).

• Speaker Basis Vectors: The output layer weights themselves are interpreted as "global" speaker centroids/bases (Heo et al., 2019), allowing for min-batch-independent loss terms to maximize inter-speaker discrimination and perform batch-global hard negative mining:

$\mathcal{L}_{BC} = \sum_{i\neq j} \cos(W_i, W_j)$

$$\mathcal{L}_H = \sum_{i} \sum_{W_h \in \mathcal{H}_i} \log \left( 1 + \exp(\cos(W_h, e_i) - \cos(W_{y_i}, e_i)) \right )$$

• Large Margin Losses: Additive/angular margin Softmax losses and center losses (Liu et al., 2019, Coria et al., 2020) induce centroid-based compactness and class separation in the hyperspherical geometry, targeting the angle/distance between embeddings and class centers.
• Cycle Consistency and Reconstruction-Centroid Losses: In voice conversion and source separation, centroid or embedding consistency losses operate at the utterance level by (1) reconstructing audio using the class centroid or (2) directly minimizing the L1 or L2 norm between speaker embeddings extracted from reference and synthesized/converted speech (Du et al., 2020, Guo et al., 2023, Makishima et al., 2022).

3. Empirical Performance and Task-Specific Applications

Centroid-based losses have demonstrated empirical gains across several domains:

• Speaker Verification and Identification: Significant improvements in equal error rate (EER)—up to 19% relative on unseen speakers for prototypical loss over triplet loss (Wang et al., 2019); up to a 15% reduction in EER and major minDCF gains with large margin losses (Liu et al., 2019, Coria et al., 2020).
• Voice Conversion & Synthesis: Used in joint or cycle-consistency losses, they yield higher mean opinion scores (MOS) for speaker similarity and naturalness, especially in non-parallel, cross-lingual, or expressive VC tasks (Kwon et al., 2020, Guo et al., 2023, Yang et al., 2021).
• Speaker Extraction: Direct improvements in Scale-Invariant SDR, accuracy, and speaker similarity (as measured by embedding cosine) for Target Speaker Extraction pipelines—simultaneously addressing the "speaker confusion" problem (Wu et al., 13 Jul 2025).
• Robustness and Domain Generalization: MultiReader and other joint training strategies aggregate centroids across domains (keywords, dialects), regularizing the embedding space for cross-dataset robustness (Wan et al., 2017).

Task	Loss Type	Principle	Documented Impact
Verification	GE2E, PNL, Margin	Centroid-pull, separation	EER/minDCF improvements
Speaker Extraction	C-SC loss	Prototype similarity, suppression	SI-SDR, similarity, accuracy
Voice Conversion	Consistency/cycle	Utterance-centroid alignment	Higher MOS, similarity, less confusion

4. Challenges and Optimization Strategies

The deployment of centroid-based speaker consistency loss introduces several considerations:

• Batch/Global vs. Mini-batch Centroids: Global "speaker bases" are less susceptible to batch variation but may incur higher computational or memory costs for large speaker sets (Heo et al., 2019).
• Loss Scheduling and Suppression: Excessively strong consistency objectives may overfit or degrade extraction/separation front-ends. Conditional loss suppression—where the centroid loss is inhibited above a cosine similarity threshold—helps to balance optimization (Wu et al., 13 Jul 2025).
• Margin and Hyperparameter Tuning: Margin values, centroid update rates, and the trade-off with reconstruction or cross-entropy losses must be tuned task-specifically to optimize intra-class compactness without sacrificing generalization (Liu et al., 2019, Makishima et al., 2022).
• Unsupervised and Few-Shot Regimes: Centroid-anchored methods are particularly robust to label scarcity or high label cardinality, subsuming few-shot and open-set recognition paradigms (Wang et al., 2019, Mun et al., 2020).

5. Integration with Modern Neural Architectures

Centroid-based losses are architecture-agnostic and appear in various deep models:

• TDNN/x-vector/ECAPA-TDNN: Widely used in verification and anti-spoofing pipelines, where the network output can be compared both locally (mini-batch) and globally (table-wide centroid) (Zhang et al., 2023, Wan et al., 2017).
• End-to-end diarization, extraction, and separation models: Jointly trained speaker encoders and separation modules (e.g., BSRNN backbone) can optimize SI-SDR, speaker classification, and centroid alignment in a compositional loss function (Wu et al., 13 Jul 2025).
• Auto-encoder/Disentanglement frameworks: Structured separation of speaker and non-speaker factors supports centroid-based regularization for disentangled and robust representation (Kwon et al., 2020).

6. Extensions to Adversarial and Hybrid Losses

Recent work blends centroid-based objectives with adversarial or composite losses to address more nuanced problems:

• Adversarial Speaker Classifiers & Embedding Consistency: In multilingual VC and code-switching tasks, embedding consistency loss suppresses source speaker traits and strengthens target speaker identity alignment, even under adversarial pressure (gradient reversal) (Yang et al., 2021).
• Temporal and Distributional Consistency for Anti-Spoofing: Modeling the frame-to-frame (temporal) and utterance-level (distributional) consistency of embeddings distinguishes bonafide from synthetic speech (Zhang et al., 2023), setting the path for hybrid loss functions that target both moment-to-moment and global speaker consistency.

7. Broader Impacts and Future Directions

Centroid-based speaker consistency losses have expedited advances in speaker verification robustness, voice conversion quality, anti-spoofing detectability, and extraction system reliability. Their ability to compact intra-speaker representations and accentuate between-speaker separation underlies gains observed across effectual and perceptual metrics.

Future trajectories include:

• Adapting centroid objectives to multi-modal biometrics and extremely low-resource regimes (Wan et al., 2017).
• Extending centroid-based consistency to unsupervised/self-supervised representation learning and pre-training (Mun et al., 2020).
• Further combination with perceptual, adversarial, or task-specific auxiliary losses to balance generalization, separation, and naturalness.

Centroid-based speaker consistency loss thus encapsulates a broad set of strategies that unify speaker representation, discrimination, and stability, yielding tangible benefits across the modern landscape of speaker-aware speech processing systems.