# VoxtLM: Unified decoder-only models for consolidating speech recognition,
synthesis and speech, text continuation tasks

###### Abstract

We propose a decoder-only language model, VoxtLM, that can perform four tasks:
speech recognition, speech synthesis, text generation, and speech
continuation. VoxtLM integrates text vocabulary with discrete speech tokens
from self-supervised speech features and uses special tokens to enable
multitask learning. Compared to a single-task model, VoxtLM exhibits a
significant improvement in speech synthesis, with improvements in both speech
intelligibility from 28.9 to 5.6 and objective quality from 2.68 to 3.90.
VoxtLM also improves speech generation and speech recognition performance over
the single-task counterpart. VoxtLM is trained with publicly available data
and training recipes and model checkpoints will be open-sourced to make fully
reproducible work.

Index Terms—  Multitask, speech synthesis, speech recognition, spoken language
model

##  1 Introduction

In recent years text language models (textLMs) have emerged as a powerful
generative model in natural language processing (NLP) [1, 2, 3]. These textLMs
can accommodate multiple tasks within a single model, leading to improvement
in performance across a variety of tasks. On the other hand, with advances in
discrete speech representations speech language models (speechLMs) [4, 5] have
also been proposed. However, prior speechLMs focus on individual tasks, such
as speech continuation or text-to-speech (TTS) [6, 7]. Our hypothesis is that
by unifying diverse speech tasks into a generative language model (LM), we can
potentially address multiple speech tasks using a single model with improved
generalization thanks to multitask learning.

Traditionally, speech applications such as automatic speech recognition (ASR)
and text-to-speech (TTS) use encoder-decoder architectures [8, 9, 10]. These
architectures consist of an encoder, for input processing and a decoder, for
generating the output. For example, speech-to-text involves a speech encoder
and a text decoder, whereas text-to-speech employs a text encoder and a speech
decoder. Integrating task-specific and modality-specific encoder-decoder
components complicates the incorporation of multiple tasks [11, 12]. In
contrast, we can simplify multitask integration with a joint speech-text
decoder-only model (depicted in Fig. 1).

In this work, we investigate two main questions. Firstly, can we cast diverse
speech tasks as language modeling? ASR and TTS are used as example speech
tasks. Secondly, can we combine speech tasks in a joint speech-text language
modeling framework? To this purpose, we introduce a novel LM framework VoxtLM
(Voice-text Language Model). VoxtLM combines multiple speech tasks within a
single autoregressive decoder model. Specifically, we combine four tasks:
speech recognition (speech-to-text), speech synthesis (text-to-speech), text
generation (text-to-text), and speech generation (speech-to-speech). We create
a Voxt (voice + text) vocabulary by merging self-supervised discrete speech
tokens with the text vocabulary and incorporate sub-word modeling to
efficiently process long sequences of speech. We show that VoxtLM can model
both ASR and TTS as conditioned language model. Moreover, combining four tasks
leads to improvement in speech generation, ASR, and TTS. Most significant
improvement is observed in the TTS task with improvement in both
intelligibility (28.9 to 5.6) and neural-predicted quality (2.68 to 3.90).
Additionally, we demonstrate improved initialization with pretrained textLM
and scaling model parameters helps in ASR. To ensure reproducibility, we use
publicly available datasets and will open-source our training and inference
procedures along with model checkpoints using the open-source toolkit
ESPnet.111https://github.com/ESPnet/ESPnet TTS samples are also
available.222https://soumimaiti.github.io/icassp24_voxtlm/

Fig. 1: ASR and TTS use encoder-decoder architecture while VoxtLM is decoder-
only. In VoxtLM, all parameters are shared between speech and text modalities,
compared to separate encoder/ decoder for speech and text. Table 1: Voxt data
format for different tasks: training and inference. Inference: provided
conditions for generating prediction.

Task | Training | Inference
---|---|---
|  | Condition | Prediction
TextLM |  $\langle$generate-text$\rangle,Y$ | $\langle\texttt{generate-text}\rangle,Y^{\text{test}}$ | $\hat{Y}$
SpeechLM |  $\langle$generate-speech$\rangle,D$ | $\langle\texttt{generate-speech}\rangle,D^{\text{test}}$ | $\hat{D}$
ASR |  $\langle$start-speech$\rangle$, $D$, $\langle$generate-text$\rangle$, $Y$ | $\langle\texttt{start-speech}\rangle,D^{\text{test}},\langle\texttt{generate-text}\rangle$ | $\hat{Y}$
TTS |  $\langle$start-text$\rangle,Y,\langle$generate-speech$\rangle,D$ | $\langle\texttt{start-text}\rangle,Y^{\text{test}},\langle\texttt{generate-speech}\rangle$ | $\hat{D}$

##  2 Related Work

Discrete speech representations. Speech signals can be represented as two
types of discrete tokens: semantic tokens and acoustic tokens. Semantic tokens
are quantized from self-supervised learning features (e.g., HuBERT [13],
w2v-BERT [14]) through clustering, which mostly captures the linguistic
content. Acoustic tokens are generated by audio codec models [15, 16]. They
capture rich acoustic information which is suitable for high-quality speech
synthesis, but they consist of multiple code streams and are thus difficult to
model. In this work, we follow GSLM [4] to use semantic tokens derived from
HuBERT.

Joint modeling of speech and text. Several studies [11, 17, 12] propose to
learn shared speech-text representations in a self-supervised manner. However,
they employ separate encoders and decoders for different modalities. They also
require additional losses like an alignment loss to encourage cross-modal
transfer between speech and text. Recent concurrent studies employ a single
model for multiple speech and text conversion tasks [18, 19, 20], which are
similar to our approach.333These works have only been published in a pre-print
form and have not undergone the peer-review process. SpeechGPT [20] uses a
three-stage adaptation to combine audio generation with textLMs. PolyVoice
[18] applies speechLM to speech-to-speech translation (S2ST) with three
decoder-only LMs. VioLA [19] extends VALL-E [7] for ASR and S2ST. Among them,
VioLA is the most related method to this work. However, VioLA does not
incorporate speech or text continuation tasks and requires additional sequence
modeling for speech representations, which makes it more complicated than our
approach. Moreover, we utilize textually pre-trained OPT [21] for better
initialization inspired by [22] and leverage different speech tokens. Also in
comparison to other works, our work is fully reproducible.

Fig. 2: Overview of VoxtLM, an autoregressive decoder-only LM incorporating
speech and text within vocabulary $\mathcal{V}_{\text{voxt}}$. Two additional
modules are used: the speech tokenizer for converting continuous signals into
discrete speech tokens and the speech token decoder used to generate speech
waveforms from speech tokens.

##  3 Method

Consider $Y=(y_{i}\in\mathcal{V}_{\text{txt}}|i=1,\cdots,{t_{\text{txt}}})$ is
a text utterance from a vocabulary $\mathcal{V}_{\text{txt}}$ with length
$t_{\text{txt}}$. The probability of $Y$ can be expressed as
$p(Y)=\Pi_{i=1}^{t_{\text{txt}}}p(y_{i}|y_{1},\cdots,y_{i-1}).$ Now, when
dealing with a continuous speech signal, we can convert it into discrete
speech tokens (dst), represented as
$D=(d_{i}\in\mathcal{V}_{\text{dst}}|i=1,\cdots,t_{\text{dst}})$ using a
tokenizer. In this context $\mathcal{V}_{\text{dst}}$ is the vocabulary of
discrete speech tokens. These discrete speech tokens can be treated as spoken
language within $\mathcal{V}_{\text{dst}}$ and modeled in a manner similar to
text. We combine text and speech in a new vocabulary Voxt vocabulary by
$\mathcal{V}_{\text{voxt}}=\mathcal{V}_{\text{txt}}\cup\mathcal{V}_{\text{dst}}$.
Therefore, we can model the probability of both speech and text tokens as $Z$,
where $Z=(z_{i}\in\mathcal{V}|i=1,\cdots,t)$. This probability is expressed
as:

$p(Z)=\Pi_{i=1}^{t}p(z_{i}|z_{1},\cdots,z_{i-1}).$ (1)

Here, $Z$ can represent discrete speech tokens
$D(\mathcal{V}=\mathcal{V}_{\text{dst}})$ or text tokens
$Y(\mathcal{V}=\mathcal{V}_{\text{txt}})$ or various combinations of $Y$ and
$D$.

###  3.1 VoxtLM

Fig. 2 illustrates the model’s overall architecture. Input of VoxtLM can be
both speech and text within the $\mathcal{V}_{\text{voxt}}$ vocabulary. To
process speech, we use two additional modules to convert between continuous
and discrete domains in speech. The speech tokenizer maps $X$ to $D$, while
the speech token decoder maps generated $\hat{D}$ back to $\hat{X}$. Similar
to [4], our speech tokenizer uses $k$-means clustering to derive discrete
features from the pretrained HuBERT [13]. It is worth noting that selecting a
small $k$ value may capture linguistic information effectively, but might fall
short in representing other acoustic aspects particularly crucial for speech
synthesis. We experiment with different $k$ to assess the impact. Furthermore,
within $\mathcal{V}_{\text{voxt}}$ vocabulary, we apply subword modeling [23,
24, 25] to replace frequent patterns with metatokens. Such subword modeling
technique is used to include more contextual information in text [1] or to
reduce the long sequence length of speech [26].

####  3.1.1 Data format

We use special tokens to guide the model in performing various tasks. There
are four such tokens used. $\langle$start-text$\rangle$ and $\langle$start-
speech$\rangle$ indicate the beginning of text or speech conditioning in the
language model. $\langle$generate-speech$\rangle$ and $\langle$generate-
text$\rangle$ instruct the model whether to generate speech or text. Table 1
shows examples of the Voxt data format for various tasks during training.
Ideally, we can extend to more tasks with additional task-specific tokens.

####  3.1.2 Training

VoxtLM consists of an embedding layer and a series of transformer [27] decoder
layers. The embedding layer maps input $Z$ (in Eq. 1) into $F$-dimensional
feature space, $E=(e_{i}\in\mathbb{R}^{F}|i=1,\cdots,t)$ using an embedding
table of size $|\mathcal{V}_{\text{voxt}}|\times F$. We use $L$ transformer
decoder layers with $H$ attention heads. The model’s output includes a linear
layer followed by softmax, generating a probability distribution over the
tokens in $\mathcal{V}_{\text{voxt}}$. VoxtLM is trained as an autoregressive
language model. In training, teacher forcing is used for the preceding tokens.
Given $Z$, at each timestep $i$, predicted distribution is
$\hat{p}_{i}=\text{VoxtLM}(z_{1},\cdots,z_{i-1})$. Given true probability
distribution $p_{i}$, the loss is calculated using cross-entropy as
$L_{\text{CE}}(p_{i},\hat{p}_{i})=-\sum_{c=1}^{\mathcal{V}_{\text{voxt}}}p_{i}(c)\log\hat{p}_{i}(c)$.

Table 2: Number of utterances used in training of different VoxtLM setups.
Bal: balanced data for four tasks; and 3M: uses the same number (3M) of text-
only and speech-only utterances, a balanced setup for total text and total
speech data.

Source | Unpaired | Paired | Configuration
---|---|---|---
Speech | Text | ASR | TTS
$\mathcal{D}_{\text{Bal}}$ | 300K | 300K | 281K | 404K | LL+LS+LT+VC
$\mathcal{D}_{\text{3M}}$ |  3M |  3M | 281K | 404K | LL+LS+LT+VC
$\mathcal{D}_{\text{Set}}$ |  12M |  40M | 281K | 404K | LL+LS+LT+VC
$\mathcal{D}_{\text{Set+}}$ |  12M |  40M |  11M | 404K | LL+LS+LT+VC+MLS

Table 3: Experimental results comparing multitasking VoxtLM against four
single-task VoxtLM for textLM, speechLM, ASR and TTS. We use token size ($k$)
50 for all models. Single-task models are trained with all available data, for
VoxtLM we report different training data (Table 2) cases . For ASR we report
test-clean/test-other results. $\mathcal{D}_{\text{Set}}^{*}$: four single-
task models whereas other rows depict multitask model.

Source | # params | TextLM | SpeechLM | ASR | TTS
---|---|---|---|---|---
PPL($\downarrow$) |  sWUGGY($\uparrow$) |  sBLIMP($\uparrow$) |  PPL($\downarrow$) |  sWUGGY($\uparrow$) |  sBLIMP($\uparrow$) |  WER($\downarrow$) |  CER($\downarrow$) |  MOSNet($\uparrow$)
$\mathcal{D}_{\text{Set}}^{*}$ | 125M | 18.3 | 77.1 | 80.3 | 73.8 | 62.9 | 53.9 |  8.8 / 21.4 | 28.9 | 2.68
$\mathcal{D}_{\text{Bal}}$ | 125M | 15.4 | 77.7 | 66.7 | 68.5 | 60.7 | 52.7 |  8.6 / 20.9 |  5.6 | 3.76
$\mathcal{D}_{\text{3M}}$ | 125M | 13.5 | 77.9 | 68.0 | 58.1 | 63.6 | 55.2 | 11.0 / 24.4 |  7.0 | 3.90
$\mathcal{D}_{\text{Set}}$ | 125M | 11.1 | 80.3 | 74.2 | 62.1 | 62.8 | 54.1 | 21.0 / 37.4 |  8.8 | 3.86

Initialization with pretrained textLM. Previous work [22] shows that, in
speechLM initializing with a pretrained textLM achieves better performance and
faster convergence. Motivated by this approach, we use the pretrained textLM
OPT [21] to initialize VoxtLM weights and learn the embedding table from
scratch. The same model configuration is used as the pretrained model except
for $|\mathcal{V}_{\rm voxt}|$. OPT is used due to training on publicly
available data and availability of smaller pretrained models.

####  3.1.3 Inference

Given the trained VoxtLM model, we use beam search in the inference phase.
Prediction from the VoxtLM is expressed as:

$\text{prediction}\leftarrow p(\cdot|\text{condition}).$ (2)

For TTS, the provided condition is test text utterance $Y^{\text{test}}$ and
speech tokens $\hat{D}$ are predicted. In the case of ASR, the condition is
test speech tokens $D^{\text{test}}$ and prediction is the recognized text
$\hat{Y}$. For speech continuation, the condition involves prefix speech
tokens $D^{\text{test}}$ and prediction is continued speech tokens $\hat{D}$.
For text continuation, the condition is the text $Y^{\text{test}}$ and
prediction is continued text $\hat{Y}$. The inference conditions are shown in
Table 1.

Speech token decoder. The speech token decoder takes both $\hat{D}$ and a
speaker embedding $s_{\text{spk}}\in\mathbb{R}^{N}$ of dimensionality $N$ as
inputs and produces $\hat{X}$. We use the HiFiGAN [28] as the architecture and
x-vector [29] as speaker embedding vector.

###  3.2 Evaluation Metrics

We use the following evaluation metrics.

  * •

For speech and text generation, we use sWUGGY and sBLIMP using dev dataset as
proposed in [30] and perplexity (PPL).444PPL is only compared between models
with the same vocabulary size. Only text is used for text generation
evaluation and we do not use corresponding audio.

  * •

In the case of ASR, we use the WER.

  * •

Regarding TTS, we measure intelligibility with CER and quality using neural-
predicted MOS quality score MOSNet [31, 32].

##  4 Experiments

Dataset. We use a combination of speech-only, text-only, and paired speech-
text datasets from public corpora.

  * •

Speech-only data: we use LibriLight (LL) [33] with 60K hours of audiobook
speech from 7K speakers (12M utterances).

  * •

Text-only data: we use the Librispeech (LS) [34] external textLM dataset (40M
text utterances).

  * •

Speech-text paired data:

    * –

For ASR, we mainly use Librispeech [34] with 960 hours of data ( 281K
utterances). For an additional supervised data experiment, we use English
Multilingual Librispeech (MLS) [35] with 44K hours of data from 5490 speakers
(11M utterances).

    * –

For TTS, we use LibriTTS (LT) and VCTK (VC). LT [36] contains 580 hours of
audiobook data from 2456 speakers. VC [37] contains 44 hours of studio
recorded data from 109 speakers (404K utterances).

We standardized the data by downsampling speech to a 16kHz rate, converting
text to lowercase, and removing punctuation. We use separate test/dev sets for
each task. For textLM and speechLM, we use the test set from LS and dev sets
from sWUGGY and sBLIMP, text for textLM, and speech counterpart for speechLM.
For ASR we use speech-text test set from LS test-clean and test-other and
report both test-clean/test-other separately. In TTS for computational
efficiency, we create a test set of 100 utterances from two speakers from the
LT test-clean. The test speakers are chosen via random sampling (specifically,
speaker ids 1089 and 1284).

Experimental setup. To train the sub-word model, we use paired text-speech
from ASR and TTS datasets. We experiment with three $k$ values (introduced in
Sec. 3.1), 50, 200, and 1000, denoted as VoxtLM-$k$. We also vary BPE sizes,
setting them at $2\text{K}$, $5\text{K}$, and $10\text{K}$ for $k$ values 50,
100 and 200, respectively. We use three configurations, small ($L$=12,
$F$=768, $H$=12), medium ($L$=24, $F$=1024, $H$=16), and large ($L$=24,
$F$=2048, $H$=32), with $L$, $H$ and $F$ detailed in Sec. 3.1.2. We use 4 A100
GPUs for training small/medium and 8 A100 GPUs for large with Adam optimizer
[38] and warmup learning rate schedule. Training data size varies considerably
between different tasks. For example, the paired data for ASR and TTS are
$100\times$ smaller than text-only data and $40\times$ smaller than speech-
only data. We can assume that achieving optimal performance across all tasks
requires balanced data for each of them. It is also worth noting that text-
only data is more readily available compared to speech-only and paired data.
Nonetheless, to assess the effect of different dataset sizes for tasks, we
consider balanced and unbalanced data sets for training, as summarized in
Table 2.

Table 4:  Experimental results comparing with and without initialization with
pretrained (PT) textLM for VoxtLM-$k$50 with $\mathcal{D}_{\text{Set}}$.

Name |  # params | TextLM | SpeechLM | ASR | TTS
---|---|---|---|---|---
PPL($\downarrow$) |  PPL($\downarrow$) |  WER($\downarrow$) |  CER($\downarrow$) |  MOSNet($\uparrow$)
w/o PT | 125M | 11.1 | 62.1 | 21.0 / 37.4 |  8.8 | 3.86
w/ PT | 125M | 10.4 | 58.8 |  13.1 / 28.8 |  9.4 | 3.92

Table 5: Experimental results comparing speech token size $k$ for VoxtLM. We
compare the two conditions: $\mathcal{D}_{\text{Bal}}$ and
$\mathcal{D}_{\text{Set}}$ (Table 2). † denotes initialization with OPT.

Name | Source |  # params | TextLM | SpeechLM | ASR | TTS
---|---|---|---|---|---|---
PPL($\downarrow$) |  sWUGGY($\uparrow$) |  sBLIMP($\uparrow$) |  PPL($\downarrow$) |  sWUGGY($\uparrow$) |  sBLIMP($\uparrow$) |  WER($\downarrow$) |  CER($\downarrow$) |  MOSNet($\uparrow$)
VoxtLM-$k$50 | $\mathcal{D}_{\text{Bal}}$ | 125M | 15.4 | 77.7 | 66.7 | 68.5 | 60.7 | 52.7 |  8.6 / 20.9 | 5.6 | 3.76
VoxtLM-$k$200 | $\mathcal{D}_{\text{Bal}}$ | 125M | 21.6 | 77.3 | 67.9 | 58.6 | 61.6 | 52.1 |  6.1 / 15.4 | 3.2 | 4.36
VoxtLM-$k$1000 | $\mathcal{D}_{\text{Bal}}$ | 125M | 26.3 | 76.4 | 67.6 | 38.7 | 60.7 | 52.5 |  5.4 / 14.5 | 2.6 | 4.30
VoxtLM-$k$50† | $\mathcal{D}_{\text{Set}}$ | 350M | 10.3 | 81.0 | 75.1 | 68.2 | 62.7 | 53.8 | 13.5 / 27.2 | 6.6 | 3.91
VoxtLM-$k$200† | $\mathcal{D}_{\text{Set}}$ | 350M | 12.7 | 80.2 | 78.8 | 45.7 | 65.5 | 55.3 |  6.5 / 17.6 | 3.5 | 4.36

Table 6: Experimental results comparing larger model size and more supervised
data for VoxtLM. † denotes initialization with OPT.

Name | Source |  # params | TextLM | SpeechLM | ASR | TTS
---|---|---|---|---|---|---
PPL($\downarrow$) |  sWUGGY($\uparrow$) |  sBLIMP($\uparrow$) |  PPL($\downarrow$) |  sWUGGY($\uparrow$) |  sBLIMP($\uparrow$) |  WER($\downarrow$) |  CER($\downarrow$) |  MOSNet($\uparrow$)
VoxtLM-$k$200† | $\mathcal{D}_{\text{Set}}$ | 350M | 12.7 | 80.2 | 78.8 | 45.7 | 65.5 | 55.3 |  6.5 / 17.6 | 3.5 | 4.36
VoxtLM-$k$200† | $\mathcal{D}_{\text{Set}}$ |  1.3B | 11.4 | 80.9 | 80.2 | 42.1 | 66.1 | 56.7 |  4.6 / 12.1 | 3.9 | 4.33
VoxtLM-$k$200† | $\mathcal{D}_{\text{Set+}}$ | 350M | 13.6 | 80.1 | 77.0 | 45.5 | 64.1 | 55.0 |  3.5 / 8.7 | 3.5 | 4.33
VoxtLM-$k$200† | $\mathcal{D}_{\text{Set+}}$ |  1.3B | 12.1 | 81.2 | 80.0 | 40.9 | 65.6 | 57.1 |  2.7 / 6.5 | 3.6 | 4.33
VoxtLM-$k$1000† | $\mathcal{D}_{\text{Set+}}$ | 125M | 18.3 | 77.3 | 75.2 | 36.7 | 60.7 | 51.3 |  4.7 / 11.9 | 3.9 | 4.28
VoxtLM-$k$1000† | $\mathcal{D}_{\text{Set+}}$ | 350M | 16.4 | 79.6 | 77.8 | 32.3 | 62.1 | 53.2 |  3.5 / 8.6 | 6.1 | 4.27

Table 7: SpeechLM and ASR results: Comparison with the state-of-the-art models
with VoxtLM. † denotes initialization with OPT.

Name | Source |  # params | SpeechLM | ASR
---|---|---|---|---
sWUGGY($\uparrow$) |  sBLIMP($\uparrow$) |  WER($\downarrow$)
GSLM-$k$50 [4] |  LL | 172M | - | 55.9 | \- / -
GSLM-$k$200 [4] |  LL | 172M | - | 53.0 | \- / -
AudioLM [5] |  LL | 900M | 71.5 | 64.7 | \- / -
ASR-Fbank |  LS | 149M | - | - |  2.2 / 4.6
dst-ASR-Hubert |  LS |  39M | - | - |  4.2 / 10.8
VoxtLM-$k$200† | $\mathcal{D}_{\text{Set}}~{}~{}~{}\>$ |  1.3B | 66.1 | 56.7 |  4.6 / 12.1
VoxtLM-$k$200† | $\mathcal{D}_{\text{Set+}}$ |  1.3B | 65.6 | 57.1 |  2.7 / 6.5

Table 8:  Comparison with the state-of-the-art baseline for TTS with VoxtLM. †
denotes initialization with OPT.

Name | Source |  # params | TTS
---|---|---|---
CER($\downarrow$) |  MOSNet($\uparrow$)
VITS [39] | LT |  97M | 7.7 | 4.20
VoxtLM-$k$200† | $\mathcal{D}_{\text{Set}}$ |  350M | 3.5 | 4.36
VoxtLM-$k$1000 | $\mathcal{D}_{\text{Bal}}$ |  125M | 2.6 | 4.30

###  4.1 Results

Single vs multitask. We compare a multitask and four single-task models using
VoxtLM-$k$50\. The single-task LMs are trained separately on all data for each
task, ASR, TTS, speechLM, and textLM and reported in the first row of Table 3,
each column is a separate single-task model. Compared to single-task, VoxtLM
shows competitive results for all four tasks although the best model differs.
For textLM $\mathcal{D}_{\text{Set}}$ exhibits a higher sWUGGY but a lower
sBLIMP score. In speechLM, $\mathcal{D}_{\text{3M}}$ has the best scores in
both sWUGGY and sBLIMP, followed by $\mathcal{D}_{\text{Set}}$. In TTS across
all multitask models show improvement compared to single task. ASR reports
improvement in $\mathcal{D}_{\text{Bal}}$. We note that ASR is most affected
in the unbalanced case: likely due to the lower ASR data ratio to
textLM/speechLM ($100\times$/$40\times$ less). The least degradation in ASR is
seen with $\mathcal{D}_{\text{3M}}$ where ASR data ratio to textLM/speechLM is
relatively better ($10\times$ less).

Initialization with pretrained textLM. We compare the VoxtLM-$k$50 with the
$\mathcal{D}_{\text{Set}}$ with and without initialization with OPT and report
in Table 4. Initialization improves the performance of three tasks: textLM,
speechLM, and ASR. For TTS, a slight degradation in CER is observed, whereas
objective quality improves. Notably, better initialization aids ASR
performance in the unbalanced scenario (reducing test-clean WER from 21.0 to
13.1).

Effect of token vocabulary size. We compare $k$=50, 200, and 1000, as outlined
in Table 5. Comparisons are made with $\mathcal{D}_{\text{Bal}}$ and
$\mathcal{D}_{\text{Set}}$. For ASR and TTS, $k$=50 performance are notably
worst. For speechLM with $\mathcal{D}_{\text{Set}}$ best sWUGGY and sBLIMP
scores are observed with the $k$=200 model. TextLM, as expected, shows no
significant pattern with varying $k$.

Scalability. Next, we explore if model size can help with data balancing by
comparing medium and large models with $k$=200, presented in Table 6. TextLM,
speechLM, and ASR all metrics show improvement with larger model. TTS shows a
very small degradation in intelligibility ($0.4$) and quality ($0.03$). To
mitigate the smaller ratio of paired data, we incorporate more supervised data
for ASR in $\mathcal{D}_{\text{Set+}}$. We compare this with both $k$=200 and
$k$=1000 and observe improvement in the ASR task.

Comparison with baselines. Furthermore, we conduct comparisons with well-
established models in TTS, ASR, and speechLM. It is important to note that
comparison models are not fully comparable due to differences in training
data, strategies, and architecture. For speechLM, we compare with GSLM [4] and
AudioLM [5]. For TTS, we compare with VITS [39] and we use a pretrained VITS
model with LibriTTS. For ASR, we compare two models using state-of-the-art
architecture E-Branchformer [40]. One model is spectrogram-based (ASR-Fbank).
The second one is discrete speech tokens-based (dst-ASR-Hubert), trained
following the procedure [26] and the same speech tokenizer as VoxtLM-$k$1000.

For speechLM (Table 7), sBLIMP score of VoxtLM is higher than that of
GSLM-$k$200 reported. However, AudioLM has a higher score in both sWUGGY and
sBLIMP. This suggests potential for further improvement in performance with
hierarchical tokens and multistage training. For ASR, we observe lower WER
compared to dst-ASR-Hubert. Compared to ASR-Fbank, WER is higher (2.7 against
2.2 in test-clean). In the case of TTS (Table 8), compared to VITS, VoxtLM
reports better intelligibility (CER 7.7 to 2.6) and quality (MOSNet 4.20 to
4.30). Though VoxtLM was trained with larger dataset compared to VITS, it is
noteworthy that for TTS models, having diverse training data with more noise
and more speakers (as is the case with our datasets except VCTK) degrades
rather than improves.

To summarize, we show that both ASR and TTS can be modeled as a language
modeling task. Using special tokens we can combine ASR and TTS with speech-
text joint language modeling framework. Although the four tasks are quite
different, combining four tasks leads to improvement.

##  5 Conclusion

The integration of speech and text tasks within a unified language modeling
framework presents a promising avenue for advancing speech processing. We
present a special token-based approach to combine four speech and text tasks:
speech recognition, speech synthesis, text and speech generation. Our results
demonstrate that by integrating different speech tasks into one generative
model, we can improve the performance of the tasks. Specially TTS show
impressive performance compared to state-of-the-art VITS. We will expand this
work to include more speech tasks in future.

## References

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# Analyzing Distribution System Load Flow Through Linearization of Non-
Holomorphic Functions

Ibrahim Habiballah, Wasiu Sulaimon, and Fahad Al-Ismail

###### Abstract

This letter presents a novel non-iterative power flow solution for radial
distribution systems. In the pursuit of a linear power flow solution that
seamlessly integrates into other power system operations, an approximate
solution via complex linearization of non-holomorphic functions, making no
assumptions about the network’s parameters was developed. This approach can be
readily adapted to different load models, and its accuracy is comparable to
other established conventional radial load flow analysis tools.

###### Index Terms:

Load flow analysis, unbalanced distribution system, complex linearization,
holomorphic function.

## Nomenclature

$n,m$

Number of nodes and branches.

$V\in\mathbb{R}^{n}$

Node voltages.

$V_{S}$

Specified voltage at the slack node.

$V_{M}\in\mathbb{R}^{n-1}$

Node voltages except the slack node.

$I_{M}\in\mathbb{R}^{n-1}$

Bus injections except the slack node.

$A\in\mathbb{R}^{m\times n}$

Incidence matrix.

$1_{M}\in\mathbb{R}^{n-1}$

Unity column vector.

$\left(\cdot\right)^{\ast}$

Complex conjugate.

$\odot$

Hadamard product.

##  I Introduction

The objective of the load flow program is to compute the steady state of nodal
voltages and angles, as well as the active and reactive power flow across all
lines, based on the provided power injections at specific buses, generator
outputs, and network conditions, as discussed in [1]. To accomplish this,
numerical techniques are frequently utilized to identify suitable operating
points essential for both offline and real-time operations. Nevertheless, it’s
essential to note that, in general, addressing the problem in the context of
both transmission and distribution system analysis is regarded as NP-hard, as
highlighted in [2].

Specifically within the context of distribution networks, dedicated iterative
load flow techniques have been successfully developed for radial network
configurations. One foundational approach for circuit analysis, which relies
on the principles of Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law
(KVL), was introduced in [3]. Similarly, the recursive method based on the bi-
quadratic equation describing the relationship between bus voltage magnitude
and line flows was presented in [4]. This latter approach has served as a
benchmark for several other iterative methods. An alternative, faster, and
more efficient direct approach, rooted in network topology, eliminates the
necessity for both an admittance matrix and a Jacobian matrix, as outlined in
[5]. This approach entirely bypasses the requirement for backward-forward
sweep (BFS) methods. A comprehensive overview of all these iterative
techniques can be found in [6].

This key contribution of this letter lies in the development of an innovative,
rapid, and linear load flow technique achieved through linearization of non-
holomorphic functions in the complex plane. Moreover, this approach is
adaptable to the ZIP model and can be seamlessly integrated into the
optimization of power system operations.

##  II Methodology

###  II-A Problem Formulation

Consider a generic radial feeder in Fig.1 represented as directed graph
$\mathcal{G}\left(N,L\right)$ where $N$ and $L$ are the number of nodes and
branches respectively with the property that

$N=L+1.$ (1)

Figure 1: A generic distribution system radial feeder network.

The goal of the load flow problem is to explicitly express the nodal voltages
as a function of the bus injections. In this case, we rewrite the nodal
voltages, nodal current injections, and the incidence matrix as
$V=\begin{bmatrix}V_{S}&V_{M}\end{bmatrix}^{T}$,
$I=\begin{bmatrix}I_{S}&I_{M}\end{bmatrix}^{T}$, and
$A=\begin{bmatrix}A_{S}&A_{M}\end{bmatrix}$ respectively, where
$A_{S}\in\mathbb{R}^{m}$ and $A_{M}\in\mathbb{R}^{m\times n-1}$.

$e=AV$ (2) $e=ZI_{F}$ (3) $I=A^{T}I_{F}.$ (4)

where $I_{F}$ and $e$ are the vectors of the current flows and voltage drops
in the lines respectively. Exploiting (2)-(3) by eliminating the $I_{F}$ and
$e$ and with the assumption that the slack node is known with no current
injections, we have

$A_{M}^{-1}A_{S}V_{S}+V_{M}=A_{M}^{-1}Z\left(A_{M}^{T}\right)^{-1}I_{M}$ (5)

where $Z\in\mathbb{C}^{m\times m}$ is a diagonal matrix with entries as the
impedance of each line. We can further simplify it by having the following
result

$V_{M}-1_{M}\cdot V_{S}=D\cdot I_{M}$ (6)

where matrix $D$ is $A_{M}^{-1}Z\left(A_{M}^{T}\right)^{-1}$ and
$A_{M}^{-1}A_{S}V_{S}$ simplifies to a negative unity column matrix.
Consequently, the $Y_{bus}$ matrix of the whole network in terms of the
incidence matrix is $A^{T}CA$ which can fully expressed as

$Y_{bus}=\begin{pmatrix}A_{S}^{T}Z^{-1}A_{S}&A_{S}^{T}Z^{-1}A_{M}\\\
A_{M}^{T}Z^{-1}A_{S}&A_{M}^{T}Z^{-1}A_{M}\end{pmatrix}$ (7)

where $C=Z^{-1}$ is a diagonal matrix of all the line admittances.

###  II-B ZIP Load Formulation

Since the current injections are not usually specified, they can be rewritten
(6) as in terms of complex power injections for ZIP load models at bus $k$ as

$I_{k}=h^{2}\cdot S_{Zk}^{\ast}\cdot V_{k}+h\cdot
S_{Ik}^{\ast}+\frac{S_{Pk}^{\ast}}{V_{k}^{\ast}}$ (8)

where $h=1/V_{base}$ and unity for per unit analysis. Moreover, (8) indicates
that the ony source of non-linearity is introduced by the constant power load
injections. Therefore, this necessitates a very accurate linearization
approach for a non-iterative solution.

####  II-B1 Constant Power Load

For the case of constant power load the expression in (6) can be reformulated
for each node $k$ as

$V_{k}\cdot V_{k}^{\ast}-V_{S}\cdot V_{k}^{\ast}=\sum_{j=2}^{n}D_{kj}\cdot
S_{Pk}^{\ast}$ (9)

The power flow problem in (9) has non-linear term
$f(V)=\left|V_{k}\right|^{2}$ with respect to the nodal voltages. Moreover,
these terms are non-holomorphic and cannot be linearized using the
conventional linearization because it does not fulfil the Cauchy-Reimann
condition for differentiability i.e ${f}^{\prime}_{\bar{V}}\neq 0$. Using
Wirtinger derivatives as discussed in [7], linearization of non-holomorphic
function $f\left(V\right)$ around $V_{0}$ is given below as

$f\left(V\right)\approx
f\left(V_{0}\right)+\left(V-V_{0}\right){f}^{\prime}_{V}\left(V_{0}\right)+\left(\bar{V}-V_{0}\right){f}^{\prime}_{\bar{V}}\left(V_{0}\right)$
(10)

Then from (9), the non-linear terms can be linearized around a voltage of
$1+0j$ according to (10) as

$V_{k}\cdot V_{k}^{\ast}\approx V_{k}+V_{k}^{\ast}-1,\quad\forall
k\in\mathcal{N}$ (11)

where $\mathcal{N}$ is the set of all nodes except the slack bus.

From (9) and (11) the final form for the linearized load flow can be expressed
as

$\alpha V_{M}^{\ast}-V_{M}=D\cdot S_{PM}^{\ast}+1_{M}.$ (12)

where $\alpha$ is $V_{S}-1$. Since $V_{S}$ is most of the time around 1.0 p.u,
then the linearized form of (9) can be expressed as

$V_{M}=D\cdot S_{PM}^{\ast}+1_{M}.$ (13)

####  II-B2 Constant Impedance Load

In the case of constant impedance load, from (8), the expression for the node
voltage at each bus and the compact form for all buses are shown below

$V_{k}-V_{S}=\sum_{j=2}^{n}D_{kj}\cdot S_{Zk}^{\ast}\cdot V_{k}$ (14)

$\left(1_{M}-h^{2}\cdot D\cdot S_{ZM}^{\ast}\right)\odot V_{M}=1_{M}\cdot
V_{S}$ (15)

####  II-B3 Constant Current Load

Similarly, for the constant current load injections, the resulting formulation
is shown below

$V_{k}-V_{S}=h\cdot\sum_{j=2}^{n}D_{kj}\cdot S_{Ik}^{\ast}$ (16)

$V_{M}=h\cdot D\cdot S_{IM}^{\ast}+1_{M}\cdot V_{S}$ (17)

###  II-C ZIP Linearized Formulation

Since the load flow formulation is rendered as a linear system, it is possible
to superimpose the three formulations to form a generalized load flow
equation. The compact form can be expressed below as

$V_{M}=A^{-1}B.$ (18)

where

$\displaystyle A$ $\displaystyle=diag\left(1_{M}-h^{2}\cdot D\cdot
S_{ZM}^{\ast}\right)$ (19) $\displaystyle B$ $\displaystyle=D\cdot
S_{PM}^{\ast}+h\cdot D\cdot S_{IM}^{\ast}+1_{M}\cdot V_{S}$ (20)

##  III Results

The development above is easily extensible to a three-phase unbalanced system.
A simple modification is to convert phase voltages to line voltages in the
case of delta connected loads similar to the transformation in [8]. The
evaluation metric to be adopted is the percentage line voltage unbalance rate
as stated in [9] which can be expressed for a three phase node as

$\%LUVR=\frac{\left|V_{max}-V_{avg}\right|}{V_{avg}}$ (21)

###  III-A Case 1

Initially, the accuracy of the proposed method is demonstrated through a
comparison with established linear distribution system power flow results
documented in [10, 4]. The network under examination is a balanced 30-bus
radial feeder, with the source voltage set at $1.05$ p.u. To illustrate how
the load flow results are influenced by the chosen linearization point in the
model, the proposed method is formulated at two different linearization
points: $1.05$ p.u. and $1.0$ p.u. Table I shows a decrease in accuracy in
basic some basic metrics when the linearization point is established at $1.0$
p.u., which diverges significantly from the source voltage of $1.05$ p.u. The
results provides additional insights into the sensitivity of the proposed
technique making comparisons with other methods and underscoring the
significance of selecting a linearization point in proximity to the specified
source voltage.

TABLE I: Results comparison with other methods Method |  $V_{S}$ (p.u.) |  $V_{min}$ (p.u.) |  $P_{Loss}$ (p.u.) |  $Q_{Loss}$ (p.u.)
---|---|---|---|---
[10] | 1.05 | - | 0.3778 | 0.3618
[4] | 1.05 | 0.9147 | 0.3849 | 0.3659
Proposed | 1.05 | 0.9067 | 0.4119 | 0.3911
($V_{0}=1.0$)
Proposed | 1.05 | 0.9180 | 0.3513 | 0.3340
($V_{0}=V_{S}$)
Figure 2: Error between the forward-backward sweep and the proposed method TABLE II: Simulation for balanced ZIP load model Method |  $V_{S}$ (p.u.) |  $V_{min}$ (p.u.) |  $P_{Loss}$ (p.u.) |  $Q_{Loss}$ (p.u.)
---|---|---|---|---
BFS | 1.0 | 0.9716 | 0.0293 | 0.0231
[8] | 1.0 | 0.9713 | 0.0297 | 0.0234
Proposed | 1.0 | 0.9717 | 0.0291 | 0.0230
Figure 3: LUVR comparison between the forward-backward sweep and the proposed
method

###  III-B Case 2

In this scenario, the proposed method is demonstrated within the context of
the ZIP model for both balanced and unbalanced case case. The data used for
the load flow analysis in the balanced case is provided in [8] and all
algorithms are implemented in Python environment. The evaluation metric is
$\epsilon_{k}$ which is the absolute difference between the BFS algorithm and
the linearized load flow at node $k$. Figure 2 shows that the average error
difference is very small which indicates how the proposed algorithm is
significantly similar to the iterative approach. Moreover, Table II further
shows comparison with the iterative approach and a linear method proposed in
[8] to demonstrate the accuracy of the proposed method.

For the unbalanced scenario, IEEE 37-bus test feeder data from [11] were
utilized. The system is very unbalanced and has all its load delta connected.
Figure 3 shows the percentage LUVR for both BFS and the proposed method. The
number of nodes with LUVR exceeding $1\%$ is the same for both algorithms. The
$1\%$ voltage unbalance benchmark is for derating motor loads due to system
unbalance.

##  IV Conclusion

An innovative, simple, and effective linear power flow model for radial
distribution systems has been presented. The non-linearity associated with
constant power loads was reformulated as a function of complex non-holomorphic
terms which is then linearized with specialized complex derivatives. The
accuracy of this method aligns satisfactorily with iterative techniques for
both balanced and unbalanced distribution systems.

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