Phone and speaker spatial organization in self-supervised speech representations

TL;DR

This paper investigates how self-supervised speech representations encode phone and speaker information across different layers without relying on downstream models, revealing task-dependent encoding patterns.

Contribution

It introduces methods to analyze spatial organization of speech attributes in representations without downstream models, highlighting task-dependent differences.

Findings

Different layers encode formants and pitch variably.

Representations cluster speech samples by phone and speaker.

Encoding patterns depend on pretraining tasks.

Abstract

Self-supervised representations of speech are currently being widely used for a large number of applications. Recently, some efforts have been made in trying to analyze the type of information present in each of these representations. Most such work uses downstream models to test whether the representations can be successfully used for a specific task. The downstream models, though, typically perform nonlinear operations on the representation extracting information that may not have been readily available in the original representation. In this work, we analyze the spatial organization of phone and speaker information in several state-of-the-art speech representations using methods that do not require a downstream model. We measure how different layers encode basic acoustic parameters such as formants and pitch using representation similarity analysis. Further, we study the extent to which each representation clusters the speech samples by phone or speaker classes using non-parametric statistical testing. Our results indicate that models represent these speech attributes differently depending on the target task used during pretraining.

Tables

Table 1. Table 1 : Self-supervised speech models considered in the analysis and their main characteristics. Here LS means LibriSeech dataset, and Mix is a dataset introduced in the WavLM work that combines different datasets.

Model	Dataset	Input Format	Encoder	Loss	Target
Mockingjay [11]	LS 360 hr	mel-spectrogram	Transformer	L1 loss	mel-spectrogram
DeCoAR2 [12]	LS 960 hr	log mel-spectrogram	Transformer	L1 loss	mel-spectrogram
HuBERT Base [13]	LS 960 hr	raw waveform	1D CNN + Transformer	Contrastive loss	K-Means MFCC
WavLM Base+ [14]	Mix 94k hr	raw waveform	1D CNN + Transformer	Contrastive loss	K-Means MFCC
wav2vec 2.0 Base [15]	LS 960 hr	raw waveform	1D CNN + Transformer	InfoNCE	Internal
data2vec [16]	LS 960 hr	raw waveform	1D CNN + Transformer	L1/L2 Loss	Internal

Equations

$$U_x=\frac{\max (R_1-\frac{n_1(n_1+1)}{2},R_2-\frac{n_2(n_2+1)}{2})}{n_1{n}_2},$$

Full text

Index Terms—  Speech Representations, Self-Supervised Learning, Representation Analyses

1 Introduction

In recent years, many new deep-learning-based speech representations have been proposed and used for a variety of applications. Most of these models are trained with self-supervised approaches [1], making it hard to understand which information is being preserved in the resulting representations. Consequently, several recent works have focused on analyzing how the properties of a speech signal are encoded in these representations [2, 3]. These works rely on different techniques for probing speech representations. Some of them are based on evaluating downstream tasks involving training a machine learning model that takes the representations from the pre-trained model as input. The output labels are characteristics derived from the speech signal, such as phone class [2], pronunciation quality, fluency, or other speech properties [4]. These approaches tell us whether a certain representation encodes a particular speech property, but they do not specifically tackle the question of the structure of the representation in the embedding space.

For example, an interesting situation arises when analyzing phone and speaker classes. A given representation cannot cluster well both phones and speakers since clustering by speaker implies that phone information must be ignored and conversely. Nonetheless, by non-linearly transforming the embeddings with a specific downstream model for each case, it may be possible to classify both phones and speakers with the same embeddings. In this work, though, our goal is to understand the underlying organization of the embeddings as they come out of the model. For this reason, we avoid the use of downstream models.

One way of analyzing the structure of a representation is by comparing it with another one. A comparison of two representations can be made using methods from Representation Similarity Analysis (RSA) [5]. One of these methods is centered kernel alignment (CKA), which measures the similarity of the geometric structure of two representations and it has been used to identify correspondences in representations that were trained using different initializations. RSA techniques have been used to compare representations extracted from different hidden layers within the same neural network. In [6], they found that wav2vec2.0 layers best encoded phonetic information in the middle layers. Using CKA, [7] found that the learning objective of self-supervised speech models affects the similarity more than the architecture does.

A different approach for analyzing a representation structure involves measuring how members of the same class (for example, phones) are clustered in that space. One way of computing a metric for this is by using an ABX discrimination task [8] where every sample X is classified as being of class A or not by comparing the distances in the representation space of samples A, B, with X, with B in a different class from A. This method has been used to measure the intrinsic quality of a speech representation to perform a certain classification task [9, 10].

In this work, we analyze how different self-supervised speech models represent phone and speaker information using methods that do not require downstream models. First, we analyze the similarity of a set of acoustic features with the representations generated by the models’ layers using linear CKA. Second, using non-parametric statistical testing, we measure how speech samples from the same class (phone or speaker) cluster together in the space. Specifically, given a speech sample, we measure to what extent its nearest neighbors belong to the same class using a multivariate Wilcoxon-Mann-Whitney (WMW) test. Our analysis suggests that representations with the same learning strategy (i.e., trained for the same self-supervised task) tend to represent the same type of information, regardless of their specific architecture.

2 Speech Representations

The success of transformer models and self-supervised learning in NLP inspired many of the recently proposed neural-network-based speech representations. Specifically, most of these models are based on the masked language modeling pretext task from BERT [17], which consists in reconstructing masked regions from the input signal. In this work, we analyze a variety of self-supervised speech representations. Table 1 shows the list of models used in this work, including their distinguishing characteristics.

Mockingjay [11] follows the same transformer architecture used in BERT (12 layers of 768 dimensions and 12 attention heads). The model masks a portion of the mel-spectrogram input features and then learns to predict the masked frames using the transformer’s last layer and L1 loss. Similarly, DeCoAR2 [12] learns to reconstruct a masked gap from the input log mel-spectrogram using a transformer encoder, but they include a Gumbel-Softmax quantization layer before the prediction head. The authors show that the quantization layer boosts performance when the model is fine-tuned for ASR.

Using the same masked language modeling pretext task, in HuBERT [13], the targets are generated by k-means clustering of MFCCs. WavLM [14] follows the same strategy, but they introduce a speech-denoising task by generating mixtures of speech and noise. The pretext task predicts the targets generated using the unmasked clean speech from the noisy masked speech.

In wav2vec 2.0 [15], a CNN encoder generates the inputs to the transformer applied to the speech waveform, and they use Gumbel-Softmax quantization [18] to generate the targets and minimize a contrastive loss. In data2vec [16], the model itself generates the contextualized targets. To train data2vec, the unmasked speech signal is forwarded to a teacher model, which has an exponential moving average of the weights of the student model, and the student model has to predict the activations of the teacher model from the masked speech signal by minimizing a regression loss.

Finally, we also include, for the analysis, classic speech features such as 13-dimensional MFCC with their deltas and double deltas, 80 bins mel-spectrogram, and Kaldi’s filter bank features [19].

All of the transformer-based architectures mentioned above have 12 layers. In the results presented below, we also include the projection layer that adapts the input to the transformer block as layer zero. In this paper, we consider every instance of a phone as a sample and the neural representations and acoustic features are averaged over all the frames in each phone for our analyses.

3 Methods and metrics

In this work, we use two methods to analyze the spatial structure of the representation. The first method measures the similarity between the representation under analysis and acoustic representations like formants. In Figure 1, we find a visualization that motivates this analysis. In the left plot, we see the average F1 and F2 values for each vowel in the L2Arctic dataset. The colors are determined based on the coordinates. In the right plot, we see the UMAP [20] 2D visualization of the 4th layer of the WavLM model (averaged over all frames within each vowel) for the same samples using the same color for each point as in the left plot. We can see that, while the overall structure differs, neighbors appear to be preserved across the two spaces.

To capture this phenomenon, we measure the similarity between the acoustic and neural representations using Linear Central Kernel Alignment (CKA) from the literature on representation similarity analysis [5]. Given a matrix $X$ where the rows correspond to the samples (phones in our case) and the columns to the representation dimensions, this index computes the correlation of the dot-product self-similarity matrices for each representation $X$ and $Y$: $CKA(X,Y)=\mathrm{corr}(\mathrm{vec}(XX^{T}),\mathrm{vec}(YY^{T}))$, where $\mathrm{vec}$ indicates the flattening of the matrix. This metric allows us to compare representations with different dimensionality. Linear CKA takes values between 0 and 1 and measures to which degree the pairwise distance between samples is preserved between both representations. The CKA index between the two representations in Figure 1 is 0.5. While the local structure appears to be mostly preserved, the change in global structure reduces the value of CKA.

The second method used for analysis in this paper quantifies how speech segments are clustered depending on their attributes, like phone or speaker class. This is illustrated in figure 2, which shows the UMAP projections of the 12th layer of the DeCoAR2 model. In each plot, each point corresponds to a vowel, and its color corresponds to a different characteristic of the sample: the database, the gender, the speaker, and the phone. We can see that the samples from the same speaker, dataset, and gender, for this representation, tend to cluster together. On the other hand, samples from the same phone but different speakers do not cluster together, though phones from the same speaker tend to appear nearby. For our analysis, we would like to measure whether the points belonging to a class are organized in clusters or distributed in different regions. To this end, we use a multivariate version of the Wilcoxon-Mann-Whitney (WMW) test. For each point $x$ of a given class, we create the distance rankings to all other points and compute the statistic:

[TABLE]

where $R_{1}$ is the sum of the rankings for the $n_{1}$ points of the same class as $x$, and $R_{2}$ is the sum of the rankings for the $n_{2}$ points of a different class than $x$. This statistic increases when the points of the same class as $x$ are closer to $x$ than the points of all other classes. Finally, we compute the mean of $U_{x}$ for all the points $x$, which we will call $AvgU$. This statistic lies in the range $0.5-1$, and the univariate WMW is equivalent to the AUC [21]. The computation of the presented statistic is a variant of the multivariate statistic presented in [22].

The datasets used in our analyses are the L2Arctic [23], and TIMIT [24] datasets, both of which have manually-checked phone alignments, and use the ARPABET phone dictionary. A significant difference between these datasets is that L2Arctic is composed of English utterances from non-native speakers, while TIMIT only has native English speakers.

4 Acoustic vs Neural representations

Our first analysis compares basic acoustic features, F0, F1, F2, and spectral centroid [25], with the various neural speech representations in Table 1. The goal is to analyze whether neural representations are organized similarly for vowels as these standard acoustic features. We separate the analysis of these variables into two groups to test their representation correspondence separately. We group F0 and spectral centroid, which are features known to contain information about the speaker identity, and F1 and F2, which correlate with the vowel identity (see the left plot in Figure 1).

Figure 3 shows the results for L2Arctic and TIMIT vowels. We measure Linear CKA between F0 and centroid features (top) and F1 and F2 features (bottom) versus six neural representations with 1 projection layer (layer 0 in our plots) and 12 transformer layers, and 3 classic speech features: MFCC, mel-spectrogram, and Kaldi’s filter bank. The trends for L2Arctic and TIMIT are similar, though L2Arctic shows smaller CKA values for the F0 and centroid case. This could be happening due to inaccurate F0 values for some of the L2Arctic data. Alternatively, this may suggest that the pre-trained models do not represent these acoustic features as well for native (TIMIT) than for non-native speakers (L2Arctic).

For the F0 and centroid features, we can see that the WavLM, wav2vec2.0, HuBERT, and data2vec representations preserve the acoustic information structure in the initial layers and partially lose it throughout the successive layers. The trend is different for DeCoAR2, and Mockingjay, where the last layers have similar or greater CKA values than the first ones. These models’ targets are the same as their input features. Interestingly HuBERT and WavLM behave similarly, which could be related to the fact that both models use the same target type: quantized MFCCs. The last two layers of wav2vec2.0 and data2vec also have similar behavior. This could be due to the fact that these models’ reconstruction targets are internally learned, and the last layers may not necessarily be organized by acoustics features. In the case of Mockingjay, a dip can be seen in the 5th layer, which may be related to the architecture having different dimension size in the linear projection matrix for that layer. Overall, there appears to be a strong relationship between the organization of the last layer and the model’s learning objective during pretraining.

For F1 and F2, we can see that the similarity value is larger than for F0 and centroid. This behavior is expected since these representations are good at encoding phone information, in this case, vowels. While some representations like data2vec and Mockingjay present the same curve trend as in the F0 and centroid case, HuBERT, WavLM, wav2vec2.0, and DeCoAR2 have peaks of similarity between the layers 2 to 4. These layers appear to preserve the phone information best, as shown in the next section’s results. We also analyzed the use of articulation features and obtained similar results to those of F1 and F2 (results not shown due to lack of space).

5 Encoding of speaker and phone classes

For the second analysis, we want to measure if a point of a given class (speaker or phone) is near other points of the same class, for which we use the $AvgU$ metric defined in section 3. Figure 5 shows the $AvgU$ scores for speaker (top) and phone (bottom) classes for each representation layer for L2Arctic (left) and TIMIT (right). Both databases present similar results, with TIMIT values being somewhat higher in the case of phones. This shows some stability of the representations to non-native pronunciations, supporting the hypothesis that the differences between L2Arctic and TIMIT in Figure 3 were due to inaccuracies in the features rather than a degradation in the representations for non-native speakers.

For the metric computed by speaker (top plots), we can see that data2vec, WavLM, and HuBERT, have larger values in their first layers and then decline, while DeCoAR2 and wav2vec2.0 increase the value in their last layers. We see that the phone $AvgU$ is larger than the speaker $AvgU$ for any specific representation, meaning the points tend to be clustered into phone classes. This is expected as the learned task for these models is to predict a masked target using the context, which can be improved by learning the phone regularities in the language. Interestingly, we see a clear trade-off between speaker and phone $AvgU$ values for the same representation. If a representation clusters speakers, the phones will be dispersed between the clusters corresponding to each speaker. If, on the other hand, a certain representation clusters phones together, then the points corresponding to different speakers will overlap. Figure 2 shows a case where the speakers are clustered, and the phones are segregated.

For the metric computed by phone (bottom plots in Figure ), we observe that the peak values depend on the model. For models like WavLM and HuBERT there is a peak in the last layers. This may be explained by the fact that these models are trained to predict quantized MFCCs, which are known to be good for phone classification. We see that the final layers have lower values for DeCoAR2, Mockingjay, wav2vec2.0, and data2vec. These models are trained to predict either mel-spectrogram or internal representations where the phone information may not be as readily available as in MFCCs. We can also see that the models that use internally-generated targets, wav2vec2.0 and data2vec, have distinct last layer values. In particular, data2vec value is the lowest, meaning that the targets used to train it are not well organized by phone.

Another interesting result occurs when the representations are normalized. The normalization is done by taking all the phones in a database, subtracting the mean from each representation dimension, and dividing by the standard deviation. Figure 5 shows the difference in $AvgU$ value for normalized versus unnormalized representations. A slightly positive value for the speakers indicates that the normalization favored speaker clusterization. For the phone case, negative values indicate the opposite.

Finally, we can compare the values of $AvgU$ with the performance obtained on downstream tasks. To this end, we use the performances reported in the SUPERB benchmark [26][27] computing their correlation with the maximum $AvgU$ over the layers for each downstream task, over the self-supervised models analyzed in this paper. For the $AvgU$ of phones, we obtained a correlation of 0.84 ($p=0.018$) with the performance on the phone recognition task. Similarly, for the $AvgU$ of speakers, the correlation with the performance on the speaker identification task was 0.75 ($p=0.05$). This indicates that each $AvgU$ is able to predict which of the self-supervised models is best for the class for which they are computed.

6 Conclusions

In this work, we analyze phone and speaker spatial organization in speech representations obtained from self-supervised models using two techniques that do not rely on training downstream models. In the first case, we compare acoustic features and neural representations using the representational similarity index, linear CKA. Next, we introduce a multivariate test to measure whether phones and speakers are clustered in the representations. We observe that the performance on these tasks depends heavily on what type of learning objective was used in the pretraining. Our analyses suggest that the first few layers encode the information available in the transformer input while the middle layers organize the space in a way that helps phone representation, and the last layers favor a representation that matches the target task used for pretraining.