FAIRBANKS, AK For the first time in the history of Alaska an appellate court judge will reside in Fairbanks.
Judge Bethany Harbison was appointed to be a Judge of the Court of Appeals by former Governor Bill Walker in November and her installation ceremony was held Thursday, March 14th.
Judge Bethany Harbison was appointed to be a Judge of the Court of Appeals by former Governor Bill Walker in November and her installation ceremony was held Thursday, March 14th. Judge Harbison grew up in the North East and after getting her undergraduate degree decided to study law at Harvard.
"It's just really neat I think for Fairbanks, like I said, I am a Fairbanks forever person, and just having a third appellate judge in our community I think will really help, it's good for the community", said Harbison.
She went on to talk about her love of the outdoors and how her want to visit Alaska led her to intern at the public defender office in Fairbanks one summer; never thinking she would stay but in the end falling in love with Alaska and especially Fairbanks.
After going on to intern in Portland, Maine, she realized she missed Alaska and when she was offered a position with the Fairbanks public defender's office, she decided to move.
When asked about her decision to come back she said, "I am so glad that I did, because I loved living in Fairbanks and I am a Fairbanks forever kind of person and once I got here I am not planning to move."
In 2005 she applied to be a Magistrate Judge, from there she moved up to a Trail Court judge for a short time and then became a Superior Court judge for six years before becoming an Appellate Court judge last November.
"It's also really nice to be a neutral and to be thinking really about, to advocate essentially for what is the correct answer, which is what a neutral arbiter does, so I am enjoying the neutrality now", said Harbison about being a judge in lieu of being an attorney.
Though her new position doesn't come without its challenges.
"An appellate court judge is reviewing the transcript and the record from the trial court, so now the job is still very high volume, very busy, but the busyness is very much by oneself in the office reading and writing all day."
These are challenges she looks forward to overcoming as she continues to serve Fairbanks in her new role.
Tune in to the CBS News13 tonight at 5PM AKST for the full interview.


Solar energy production is growing worldwide – overall capacity increased by a third in 2016, with the global installed photovoltaic (PV) capacity reaching 301 GW. As PV becomes more cost effective and a commoditized alternative for electricity production, many building owners are seeking to incorporate PV systems for self-consumption—consuming the energy as it is being produced. This post explains the remarkably simple operation of an electrical installation with a photovoltaic system for self-consumption.
During the day, while the sunlight and PV panels are producing electricity, the electrical installation is powered both by the grid and the PV system. These two sources operate in parallel, with no transfer of supply from one source to the other.
To facilitate this, inverters convert the DC electricity produced by the solar panels into AC electricity. The PV inverters synchronize their output power with the grid voltage and frequency to avoid mismatch and stability issues. They also perform several other important control functions.
Beyond that, there is no need for specific equipment to manage the flow of electrons – this happens naturally, following the basic electrical principles of voltage, resistance, and current.
The PV-produced power goes to the loads, as the electricity takes the path of least resistance. The loads consume the local PV production and draw any additional electricity, if needed, from the grid. If the PV production exceeds the load consumption—on weekends, for example—the excess electricity goes to the grid, for which compensation also may be possible. (See "What to do with photovoltaic renewable energy and why your decision matters" for further explanation.) If, however, the contract with the energy supplier does not allow injection of electricity to the grid, PV production should be curtailed at these times.
Figure 1-Electrical installation with PV production for self-consumption.
At night, when there is no PV production, the PV inverters do not operate and the electrical installation is supplied by the grid only.
When there is a loss of electrical power from the grid side, and if no other local source is able to provide backup power, the grid-tie PV inverters disconnect rapidly and the electrical installation is no longer supplied. Although this may at first seem counterintuitive, it addresses a serious safety concern. In case of utility supply loss, installations with local generation are required to guarantee that they do not inject power into the grid to keep utility workers safe.
For installations with PV production operating only grid-connected, this safety feature can be met by a dedicated protection device installed at the local sources' feeders, at the incoming utility line of the electrical installation, or by the PV inverter(s). Most PV inverters have integrated anti-islanding protection, which disconnects the PV inverter in the event of a power outage. The presence of this protection and its standard compliance is provided by the PV manufacturer.
Schneider Electric, for example, offers several types of inverters designed specifically for PV installations. Click to learn about our string inverter for commercial buildings and our adaptable single-phase and three-phase hybrid inverter for residential and commercial, grid-tie and backup power applications.
Today PV installations cannot ensure standalone operation of the electrical installation in off-grid mode because the PV energy produced is volatile, predictable but unplannable, and has limited control capabilities. To provide an off-grid operation, PV installations must be associated with another major and stable source such as storage or a generator. Operation of such an electrical installation in both grid-connected and off-grid mode is more complex, and will require a specific electrical installation design, an additional control system, and an effective protection plan for each operating mode.
To design the right PV system, specifiers and consulting engineers need to understand how to size the system, what equipment is required, how to integrate the PV to the electrical installation, how their customers want to operate the PV system, and more. Read the new Photovoltaic chapter of the online Electrical Installation Guide, which includes typical architectures and state-of-the-art sizing guidelines.
Future posts will further explain the details of PV system operation.
Why You Should Design Your Renewable Energy System for Self-Consumption (Vive la Difference!) What to do with photovoltaic renewable energy and why your decision matters Photovoltaic equipment: What are the hazards and how can you prevent them? Photovoltaic equipment safety: Always err on the side of caution!


This Iowa game is the best I've seen so far.
Stress test in O.T. and they look like they are a pickup team and the gym. God that is horrid and sloppy.
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Home > Entertainment > Celebrity
Tom Hanks Has Had Diabetes For Years, but Some Are Concerned About His Hands
By Joseph Allen
Jun. 15 2022, Published 9:45 a.m. ET
As one of the most beloved actors in Hollywood, Tom Hanks is someone that many people want to protect fiercely. He was among the first famous people to test positive for COVID-19, but he recovered well, and most people have not been concerned about the actors health in the years since. Now, following the premiere of Elvis, many are concerned about whether Tom is facing health issues.
Tom Hanks's hands were shaking at the premiere of 'Elvis.'
The concern over Tom's health started after some noticed that he was having trouble controlling shaking in his right hand while walking the red carpet at the Elvis premiere in Sydney, Australia. Tom plays the titular rock star's manager Colonel Tom Parker in the film.
While on the red carpet, he gave an address to the audience in which he discussed what it had been like to shoot the film in Australia.
"There is no better place in the world to make a motion picture than right here on the Gold Coast," Tom said while holding a microphone in his right hand. "I've shot films in Morocco and Los Angeles and New York City and Seattle and in Berlin. None of them have what the Gold Coast have, and what is that? Two words. None of those other cities have Dan Murphy. What a man, who I got to know quite well."
It was at this point that Tom's right hand began to shake, and he appeared to have some trouble controlling it. He eventually placed his left hand on top of his right hand, which was still holding the microphone, and then eventually swapped hands completely. He then continued with his remarks, saying that he had a magnificent time filming the movie along with his co-stars and director Baz Luhrmann.
Tom Hanks has looked thin at recent events.
In addition to his shaking hands, fans have also been concerned about the actor because he's shown up to several recent events related to Elvis looking remarkably thin. Tom's weight has fluctuated throughout his career, but some were concerned that his newly thin frame could be an indication that he is facing some health issues that he has not publicly disclosed.
Tom Hanks has type 2 diabetes.
In 2013, Tom revealed that he had been diagnosed with type 2 diabetes, and he's been open about it in the years since that diagnosis.
"I'm part of the lazy American generation that has blindly kept dancing through the party and now finds ourselves with a malady," Tom said during a 2016 interview with Radio Times. "I was heavy. You've seen me in movies, you know what I looked like. I was a total idiot."
It's unclear whether Tom's shaking hands were in any way connected to his diabetes, but it's certainly possible. Regardless of what the reason might be, most people are just hoping that the beloved actor remains healthy and active for years to come.
Tom Hanks Has Four Kids — but Two of Them Aren't With Rita Wilson
This Detail in Tom Hanks' 'Saving Private Ryan' Performance Has Perplexed Fans of the Film
Is Tom Hanks a Democrat? He's Been Politically Active for Years
Latest Celebrity News and Updates

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142091 Omerblaes è un asteroide della fascia principale. Scoperto nel 2002, presenta un'orbita caratterizzata da un semiasse maggiore pari a 2,4171676 UA e da un'eccentricità di 0,1216226, inclinata di 6,30980° rispetto all'eclittica.

Collegamenti esterni

Omerblaes
Corpi celesti scoperti nel 2002

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Home News Why do we never hear stories about working-class South Asian women?
Why do we never hear stories about working-class South Asian women?
News George Holan · June 30, 2022 · 0 Comment
There's a reason why east is east was such a hit. It showed us something we hardly ever see on stage or screen: a working-class Muslim family. Ayub Khan-Din's play, produced by Tamasha in 1996 (also a hit film in 1999) was set in the Seventies, but the action still feels so alive and relevant today. It's a kitchen sink family drama centered around a culture that society hasn't connected with the kitchen sink genre. In fact, the everyday struggles of ordinary people that define the kitchen sink genre are extremely common in working-class South Asian homes. There have been a number of depictions of conservative South Asian households on our televisions. These haven't been wrong, necessarily – but it's a restricted kind of representation. Failing to cast a broader lens on lesser shown pockets within the culture means that we're missing the chance to see the complicated, roaring, non-subservient South Asian women.
I wanted to bring those women to the stage when I came to write my play, pleasewhich is opening at the Bush Theater this week. It's a story about a working-class Muslim family living in Ilford who are impacted by the criminal justice system and addiction. It's centered around three generations of women and how they survive the impact and understand the consequences of both of those things.
I wanted to write a play about single mothers. The portrayal of South Asian families has often been defined by a patriarchal foundation: the fathers, brothers and the many forms of uncles. I came from a long line of single mothers who raised their children on their own. The notion or idea of a father seemed like a bonus rather than a necessity, which is something I wanted to capture in the play. It's not about women lyricizing endlessly about men being absent, but instead working from a matriarchal foundation instead and finding a new way of prevailing. My childhood was one of ferocious women who held their space alone with rage, desire, sadness, intellect, addiction, humour, intensity, and strength. Which is what I hope pours out from the characters in please.
I was commissioned to write the play by Clean Break, a theater company that works with women with lived experience of the criminal justice system or are at risk of entering it. To tell this story, I was introduced to a number of organizations who are integral in helping South Asian women who have been impacted by the criminal justice system – including the Southall Black Sisters, and the Muslim Women in Prison Project run by Sofia Buncy. Although my initial idea came from a much more personal place, the reports and case studies I encountered around South Asian women in prison (such as the 2014 Muslim Women in Prison report) gave me a real sense of urgency to tell this story. Many of the reports I read stated that Muslim women who left the prison system felt a great deal of judgment and shame when returning back to their communities, often describing it as 'serving a second sentence', whilst men would return home and be celebrated.
(Michael Shelford)
The other big theme in the play is addiction. While carrying out research before writing the play, it became known to me that many members within South Asian communities had a lower participation in alcohol/drug prevention health services compared to other demographics. This didn't surprise me, based on my own personal connection to someone who suffered with addiction. It was clear to me that shame and judgment were at the core of the reasoning behind this and that it was something I wanted to tackle in the play. Our lead character is repeatedly muzzled by her mother de ella in order to clamber back the families 'izzat' (honour). This shortens the string on the big block of dynamite which is about to explode. The consequences and ramifications of silencing women are two things I explore.
please is being brought to the stage by a group of brilliant women, from the cast to the directors, to the stage managers, to the producers, across to the sound, set and lighting designer. It's been an emotionally freeing space. I have been working alongside Róisín McBrinn (outgoing Joint Artistic Director of Clean Break) over the past three years on this play, as well working with her as an actress on the late Sonya Hale's play BLIS-TA (which is available to listen to on Clean Break's website – with a moving introduction from Clean Break patron Lucy Kirkwood) and carrying out playwriting courses in New Hall Prison alongside her.
please was born out of urgency. I felt compelled to tell these women's stories. And although it's centered around a South Asian family, my hope is that its impact will be universal. It's distinctive, provocative, and passionate. We can't wait to share it with the world.
Favor is at Bush Theater until 6 August


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\section{Introduction}\label{sec:introduction}}
\IEEEPARstart{V}{isual} Speech Recognition (VSR) technology \cite{zhou2013compact,saenko2004articulatory,matthews2002extraction} is developed for recognizing speech into text solely depending on visual information (\textit{e}.\textit{g}., lip movements) from an input talking face video. It can be regarded as a counterpart of Audio-based automatic Speech Recognition (ASR) that utilizes speech sound as inputs, and is also called lip reading. Even though the technology has drawn big attention \cite{saenko2009multistream,petridis2018end,afouras2018deep,ma2021lira,kim2021cromm,kim2022distinguishing,ma2022visual,shi2022avhubert} with its attractive applications \cite{ke2018computer,cohen2004semisupervised} such as recognizing speech without sound input thus robust to auditory noises and can be utilized in environments that need to be quiet, it is still hard to find that VSR technology is being employed in real-world applications. This is because the VSR system is inherently sensitive to personal lip appearances and movements \cite{assael2016lipnet}, and it shows degraded performances when applied to unseen speakers even if it is developed using a large-scale database with large speaker variations \cite{yang2020SIlipreading,kim2021lip,zhang2021SIlipreading,kim2022udp}.

In order to mitigate this problem, a speaker-adaptive VSR system can be developed in analogy to speaker adaptation technologies developed for ASR systems \cite{neto1995lin,anastasakos1997mllr,miao2014towardsSAT,klejch2019meta,huang2020SAspeechsynthesis}. Speaker adaptation method is for narrowing the gap between training and testing data distributions by fitting a trained model to unseen test speakers to improve performances during test time. The method attempts to optimize the speech recognition performance by transforming pre-trained models to well operate on one particular speaker or modifying the encoded features of the target speaker to match the pre-trained model, by using a small amount of adaptation data. The most intuitive way is finetuning the pre-trained model on the adaptation data of the target speaker. However, it is not feasible to store and handle each user-specific model since it yields the total number of parameters the same as that of one model multiplicated by the number of speakers. In addition, it requires a relatively large number of adaptation data to achieve optimal performance for the target speaker as the method tunes a large number of parameters. Therefore, an efficient way to adapt the pre-trained VSR model to diverse speakers is necessary, with a small number of parameters and adaptation data.

Recently, Input transformation \cite{elsayed2018AR1,chen2021AR2,dinh2022AR3,zheng2021AR4,neekhara2022AR5,yu2022defending} and Prompting \cite{brown2020gpt3,zhou2022conditional,li2021prompttuning,liu2021prompting,liu2021prompttuning,jia2022vpt,xu2022prompting,smith2022coda,zhou2022learning} have shown the effectiveness of input-level modification of pre-trained models on adapting the models on different tasks or data distributions without modifying the learned weight parameters of pre-trained models. By introducing learnable external parameters to the input of Deep Neural Networks (DNNs), a pre-trained model can perform different tasks from training \cite{elsayed2018AR1,lester2021prompttuning} or be adapted to shifted data distribution \cite{gao2022visual}. Inspired by the recent advances in Input transformation and Prompting, we propose a novel speaker-adaptive VSR framework that utilizes prompt tuning. Specifically, we propose three different types of prompts, addition form, padding form, and concatenation form, which can be jointly utilized for VSR models. Different from the previous prompt tuning methods that are mainly developed with Transformer variant architecture \cite{liu2021prompting,li2021prompttuning,liu2021prompttuning,lester2021prompttuning,jia2022vpt}, the proposed method can also be employed for CNN from the input level to the intermediate layer level.

Moreover, distinct from the previous speaker adaptation methods that modified the extracted feature by introducing additional layers \cite{xue2014fastadaptation,abdel2013codeicassp,miao2015SATivector,abdel2013codecnn}, the proposed prompt tuning does not introduce an additional adaptation network and does not require finetuning of the pre-trained model. It has the advantage of simplifying the adaptation steps so direct adaptation from a pre-trained model is possible, while the previous works need to train an adaptation network after attaching it to the pre-trained model. Finally, the prompt has a much less number of parameters compared to the pre-trained model, so it can be stored and easily handled for each user (\textit{i}.\textit{e}., speaker).

Specifically, we propose three different prompts, i) addition form prompt, ii) padding form prompt, and iii) concatenation form prompt. The addition form prompt is the input-level prompt for CNN and has the same shape as the input video frame. It is added to all input video frames consistently to transform the encoded visual feature to well operate on the target speaker. The padding form prompt is the intermediate feature-level prompt for CNN. It operates by replacing the padding of pre-trained CNN that usually has zero, constant, and reflect values. As the padding of CNN is also convolved with convolution kernels, the padding prompt can adapt the encoded visual feature at each intermediate CNN layer to the target speaker. Finally, the concatenation form prompt is similar to Prompting in NLP \cite{li2021prompttuning,liu2021prompting,liu2021prompttuning} and it is concatenated to the input of Transformer in the temporal dimension. We examine the effect of the combinations of the three different prompts and show that by just tuning the prompt, we can improve the performance of the pre-trained VSR model for unseen speakers. Moreover, by analyzing the performance and the number of parameters required for each speaker, we show that the proposed method is preferred over finetuning methods when only a small number of adaptation data is available. We extensively validate the effectiveness of the proposed method in both word- and sentence-level VSR databases, LRW \cite{chung2016lrw} and GRID \cite{cooke2006grid}. Especially, since there is no speaker-annotated VSR dataset obtained in the wild, we annotate the speaker information for LRW \cite{chung2016lrw} dataset and utilize it to confirm the effectiveness of the proposed method in a real-world setting.

The major contributions of this paper are as follows.
\begin{itemize}
    \item To the best of our knowledge, this is the first work to explore the effectiveness of prompt tuning in VSR. We show that just finetuning prompts can largely improve the performance of VSR model for unseen speakers.
    \item We propose and analyze different types of prompts, the addition prompt, the padding prompt, and the concatenation prompt, that can be jointly utilized for general VSR models which are composed of both CNN and Transformer.
    \item We evaluate the effectiveness of the proposed method with comprehensive experiments on different adaptation data sizes and different prompt types, and we show that the proposed method can even outperform the finetuning method by just introducing about 0.5\% additional parameters compared to the full model.
\end{itemize}

\section{Related Work}
\subsection{Visual Speech Recognition}
Visual Speech Recognition (VSR), also known as lip reading, is the task of predicting speech in the text by watching a silent talking face video \cite{lafon2006data,saenko2005visual,saenko2005production}. Due to the insufficient information and homophene problems, it is regarded as a challenging problem. With the great development of deep learning \cite{hinton2012deep,sainath2015deep}, the performance of VSR has improved significantly \cite{kim2021lip, ma2021end, shi2022avhubert}.

In word-level VSR, \cite{stafylakis2017resnetlstm} proposed a model architecture with a combination of 3D CNN and 2D CNN for a visual feature encoder and Bi-LSTM as a temporal encoder. Following studies \cite{weng2019twostream, xiao2020deformation} proposed to utilize dynamic information with two-stream CNN \cite{simonyan2014two,ma2019ts,xu2019two} that models the speech from RGB frames and optical flows. \cite{martinez2020mstcn} proposed to model the temporal dynamics using temporal convolutions by proposing Multi-Scale Temporal Convolutional Network (MS-TCN) which has multi-scale temporal receptive fields. \cite{kim2021mmbridge} proposed to use a cross-modal memory network to complement the insufficient information of the visual-only model. In sentence-level VSR, \cite{assael2016lipnet} firstly proposed an end-to-end VSR framework using Connectionist Temporal Classification (CTC) training objective \cite{graves2006ctc} and evaluated their framework on GRID \cite{cooke2006grid} dataset. \cite {chung2017lrs2} proposed a dataset, LRS2, constructed in the wild environment and Sequence-to-Sequence (Seq2Seq) architecture \cite{sutskever2014sequence} which can model the language with its decoder. \cite{afouras2018deep} significantly improved VSR performance by proposing to utilize Transformer \cite{vaswani2017attention} for the temporal encoder (\textit{i}.\textit{e}., back-end) and the decoder. Recently, \cite{ma2021end} improved the temporal encoder with Conformer \cite{gulati2020conformer} which is shown improved performance in speech recognition with its local convolution and global self-attention mechanism. \cite{prajwal2022vtp} focused on improving visual front-end architecture by introducing attention so that the model can extract the most salient region from the talking face video.

Some studies have improved VSR performances by focusing on designing training mechanisms for the models \cite{ma2022visual}. \cite{afouras2020asrisallyouneed,zhao2020hearing,ren2021learningfrommaster,ma2021towards} proposed to use knowledge distillation \cite{hinton2015distilling} so the student VSR model can learn from the teacher ASR model or powerful VSR model. \cite{kim2021cromm,kim2022distinguishing} proposed a method that can learn visual-to-audio mapping functions and bring audio representations through the learned mapping using cross-modal memory networks. \cite{chung2016syncnet,ma2021lira,shi2022avhubert} proposed to pre-train the backbone models in a self-supervised way that can utilize large-scale audio-visual databases, and showed its effectiveness with the powerful VSR performances.

Even with the progress in VSR, speaker-adaptive VSR has not well been studied. Since VSR only utilizes visual information, especially lip movements, it is inherently sensitive to personal lip appearances and movements. It makes the pre-trained VSR model show degraded performances when it is applied to unseen speakers that do not appear in the training dataset \cite{assael2016lipnet,kim2022udp}. In this paper, we try to mitigate the speaker-dependency problem of VSR by developing a speaker-adaptive VSR method. Specifically, we introduce prompt tuning methods to VSR, so we can adapt a pre-trained VSR model to the target speaker without modifying the pre-trained model parameters but just tuning the proposed prompts.

\input{./Figure/Figure1.tex}

\subsection{Speaker Adaptation}
Speaker adaptation \cite{miao2015SATivector} is mainly developed for ASR. \cite{liao2013trainpart1} propose to finetune different parts of the network to adapt the model to the target speakers. However, as the finetuning methods modify a large number of parameters, they can be suffered from overfitting problems when the adaptation data is not enough. In order to mitigate the overfitting problem, \cite{yu2013kldregularized} proposed a regularization method for speaker adaptation. Some works \cite{seide2011addlayer1, li2010addlayer2} proposed augmenting the pre-trained speech recognition model with additional speaker-dependent layers. \cite{swietojanski2014lhuc} proposed to add a speaker-dependent vector to every pre-trained hidden layer which will be adapted to the test speaker.
\cite{abdel2013codecnn,abdel2013codeicassp,xue2014fastadaptation} proposed to use speaker codes which are additional inputs depending on speakers. They firstly train an adaptation network by attaching it to the pre-trained model on the train set, and then the speaker codes are optimized for each target speaker on the adaptation set. Therefore, the methods require speaker annotations for both training and adaptation data.
Recently, meta-learning \cite{klejch2019meta} and speech synthesis \cite{huang2020SAspeechsynthesis} based speaker adaptation methods were explored.

A few works handled speaker adaptation for VSR. \cite{almajai2016lipreadingmllt} proposed to utilize traditional speaker adaptation methods of ASR \cite{gopinath1998mllt,anastasakos1997mllr} into VSR. \cite{kandala2019SAlipreading} proposed to bring the concept of i-vector \cite{dehak2010ivector} in VSR. \cite{kim2022udp} proposed to use user-dependent padding for each speaker. In this paper, we propose a novel speaker-adaptive VSR method that utilizes prompt tuning. Different from the previous methods, the proposed method does not need any additional network and has simpler adaptation steps. Moreover, the proposed method requires the speaker information for the target speaker only.

\subsection{Input Transformation}
Recently, input transformation methods attract large attention \cite{chen2021AR2, dinh2022AR3,zheng2021AR4,neekhara2022AR5} with its potential to reprogram a pre-trained model to perform different tasks from training. By surrounding the input image with noises, \cite{elsayed2018AR1} showed that the model originally trained to classify ImageNet \cite{deng2009imagenet} classes can perform hand-written digit classification. Recently, \cite{yu2022defending} showed that using the input transformation, defense against the adversarial perturbs can be achieved. In this paper, we utilize the input transformation concept to develop a speaker-adaptive VSR model, we add learnable parameters to the input video frames for transforming the encoded visual feature to represent well for the unseen target speaker.

\subsection{Prompt Tuning}
Prompting is firstly introduced by \cite{brown2020gpt3} to prepend text instruction to the input to make a pre-trained language model understand a given task. By the prepended text, prompt, the performance of a pre-trained language model can be varied \cite{li2022bridge} and previous works \cite{jiang2020can,shin2020autoprompt,radford2021learning} tried to find the better prompt formula. Recent works \cite{liu2021prompting,li2021prompttuning,liu2021prompttuning,lester2021prompttuning,zhou2022conditional,zhou2022learning} proposed learning the prompt by gradient descent which is named prompt tuning. The prompt tuning is developed mainly for Transformer-based language models and has much fewer parameters compared to the full model parameters but can achieve strong performances. Beyond the language model, the prompt is started to be utilized in visual applications \cite{jia2022vpt,bahng2022visual}. However, the visual prompt was limitedly explored for Visual Transformer (ViT) architecture \cite{dosovitskiy2020vit} and input of CNN \cite{bahng2022visual}.

In this paper, we utilize prompt tuning to adapt a pre-trained VSR model to the target unseen speaker. Different from the previous works, we propose three different types of prompts, addition form, padding form, and concatenation form, which can be jointly utilized for DNNs composed of CNN and Transformer variant architecture. Especially, we introduce intermediate feature-level prompts for CNN through a padding form prompt and show its effectiveness becomes larger according to the model size of CNN.

\input{./Figure/Figure2.tex}

\section{Prompt Tuning for Speaker-adaptive Visual Speech Recognition}
As shown in Fig. \ref{fig:1}(a), VSR models usually consist of a visual front-end $\mathcal{F}$ which has CNN-based architecture, a back-end $\mathcal{B}$ which has RNN- or Transformer-based architecture, and predictor $\mathcal{P}$ that predicts the transcription. We denote all the learnable weight parameters of the VSR model including the visual front-end, the back-end, and the predictor as $\theta$. With a large-scale training dataset $\mathcal{T}=\{(\mathbf{X}^t, \mathbf{Y}^t)\}=\{(x^t_i, y^t_i)\}_{i=1}^{N_t}$ composed of $N_t$ pairs of input video $x^t_i$ and ground-truth text $y^t_i$, we can develop a VSR model having optimized parameter $\theta^*$, as follows,
\begin{align}
    \label{eq:1}
    \theta^* = \argmin_\theta\mathcal{L}(\mathbf{Y}^t, \hat{\mathbf{Y}}),
\end{align}
\begin{align}
    \label{eq:2}
    \hat{\mathbf{Y}} = (\mathcal{P}\circ \mathcal{B}\circ \mathcal{F})_\theta(\mathbf{X}^t),
\end{align}
where $\mathcal{L}$ is the objective function of VSR such as Connectionist Temporal Classification (CTC) \cite{graves2006ctc} and Cross Entropy, and $\circ$ denotes function composition.

Our objective is to maximize the performance of the pre-trained VSR model, $\theta^*$, on unseen speakers that did not appear in the training dataset $\mathcal{T}$. To this end, we utilize a small number of adaptation data $\mathcal{A}_s=\{(\mathbf{X}^{a_s}, \mathbf{Y}^{a_s})\}=\{(x^{a_s}_i, y^{a_s}_i)\}_{i=1}^{N_{a_s}}$ to adapt the pre-trained VSR model on the target speaker $s$. Here, we assume the amount of adaptation data is much smaller (\textit{i}.\textit{e}., 1$\sim$5 minutes) than the data used during training, $N_{a_s} \ll N_t$, which is the feasible data amount to obtain for each speaker in the real-world scenario. Specifically, we introduce prompts, $p$, and only optimize them to adapt the pre-trained model on unseen speakers instead of updating the learned weight parameters of the model. The proposed prompts have three different forms, addition, padding, and concatenation, which are illustrated in Fig. \ref{fig:1}(b). In the following subsections, we will describe details of how each prompt can be incorporated for developing speaker-adaptive VSR systems.

\subsection{Add Prompt: Addition to the input of CNN}
By adding some perturbations to the input of CNN, we can reprogram a pre-trained model to perform different tasks from those originally trained for. Motivated by these prior works \cite{elsayed2018AR1,chen2021AR2,dinh2022AR3,zheng2021AR4,neekhara2022AR5,yu2022defending}, we try to adapt a pre-trained VSR model to perform well on unseen speakers by adding a prompt to the input video. Therefore, only the prompt to be added to the input video is optimized by using a small amount of adaptation data of the target speaker. To this end, the prompt has the same size as the input video frame and it can be written as $p\in \mathbb{R}^{H\times W\times C}$, where the input video with $T$ frames can be written as $x_i^{a_s}\in \mathbb{R}^{T\times H\times W\times C}$. The prompt $p$ is added to the entire $T$ frames consistently and optimized to transform the input video of the target speaker to be operated well on the pre-trained VSR model. The optimization of the addition formula prompt for target speaker $s$ can be written as follows,
\begin{align}
    \label{eq:3}
    p_s^* = \argmin_{p_s}\mathcal{L}(\mathbf{Y}^{a_s}, \hat{\mathbf{Y}}),
\end{align}
\begin{align}
    \label{eq:4}
    \hat{\mathbf{Y}} = (\mathcal{P}\circ \mathcal{B}\circ \mathcal{F})_{\theta^*}(\mathbf{X}^{a_s} + p_s),
\end{align}
where the input of the pre-trained VSR model with parameter $\theta^*$ is now the video added with the prompt $p_s$ and the optimization is performed for the prompt while the model parameter $\theta^*$ is kept frozen. Please note that different from the adversarial examples \cite{goodfellow2014explaining}, the addition form prompt has no constraints with its value so that it can have a value out of range of the image similar to \cite{bahng2022visual}. The addition form prompt is illustrated in Fig. \ref{fig:2}(a). Since the learned weight parameters are maintained, we can naturally have the regularization effects \cite{li2006l2regularized,yu2013kldregularized} and it has a low risk for the model to be overfitted.

\input{./Table/LRW_ID.tex}

\subsection{Replace Prompt: Padding of CNN}
Since the addition form prompt is applied at the input level, it can have insufficient representation power to transform the entire pre-trained model, especially if the model has large architecture. This problem is also shown in prompting in NLP, and previous work \cite{liu2021prompttuning} inserts the prompts into all layers of Transformer to enhance the representation power of the prompt. Taking inspiration from the prompting in NLP \cite{liu2021prompttuning}, we try to make the prompt can affect the intermediate layers of CNN. To this end, we propose to utilize the padding region of a convolution layer. Usually, padding is utilized in CNN to control the size of the output feature map, and to fill the padding region, zero, constant, and reflect values are employed. As the padding is also convolved with the learned convolution kernel, we replace these padding regions with the prompts to affect the encoded visual feature, and adapt the pre-trained VSR model to the unseen target speaker. Specifically, the prompts have the same size as the pre-defined padding size of each convolution layer. For example, the prompt for target speaker $s$ at $l$-th convolution layer can be written as $p_s^l \in \mathbb{R}^{S^l\times C^l}$, where $S^l=H^l(L^l+R^l)+W^l(U^l+B^l)+(L^l+R^l)(U^l+B^l)$ is the size of padding region, $L^l$, $R^l$, $B^l$, $U^l$ represent the padding size of left, right, bottom, and top, $H^l$, $W^l$, and $C^l$ are the height, width, and channel size of feature map of $l$-th layer. Then, the prompt tuning for the padding form can be written as follows,
\begin{align}
    \label{eq:5}
    \mathbf{P}_s^* = \argmin_{\mathbf{P}_s}\mathcal{L}(\mathbf{Y}^{a_s}, \hat{\mathbf{Y}}),
\end{align}
\begin{align}
    \label{eq:6}
    \hat{\mathbf{Y}} = (\mathcal{P}\circ \mathcal{B}\circ \mathcal{F})_{\theta^*}(\mathbf{X}^{a_s}, \mathcal{R}(\mathbf{P}_s)),
\end{align}
where $\mathbf{P}_s=\{p_s^l\}_1^{N_l}$ is the set of prompts for $N_l$ convolution layers and $\mathcal{R}(\cdot)$ is the operation of replacement the padding of visual front-end $\mathcal{F}$ with the prompts. Applying the padding form prompt is illustrated in Fig. \ref{fig:2}(b). Even if the padding is applied to the outer area of the feature map, it can affect the inner area of the feature map and even the entire feature map when the CNN layers are deep enough, with their enlarged receptive fields.

\subsection{Concatenate Prompt: Concatenation to Transformer input}
Recently, Transformer-based networks \cite{vaswani2017attention,gulati2020conformer} are proven to be more effective to model temporal data than RNN-based networks \cite{hochreiter1997lstm,chung2014gru,fragkiadaki2015recurrent}. Therefore, recently developed VSR models and state-of-the-art models \cite{ma2021end,afouras2018deep,hong2022visual,shi2022avhubert} are also utilizing Transformer-based back-end modules, and this makes it possible to utilize the prompting methods developed in NLP \cite{liu2021prompting,lester2021prompttuning} which are mainly for the Transformer-based architecture. Specifically, we concatenate the prompt to the input of back-end $\mathcal{B}$, the feature encoded from visual front-end $\mathcal{F}$, in the temporal dimension. The prompt has the same dimension as that of the encoded feature and can be denoted as $p_s\in\mathbb{R}^{N_p\times D}$, where $N_p$ is the length of prompts and $D$ is the dimension of the encoded feature. Then, through the self-attention layers in the back-end, the prompts can affect the features encoded by the back-end. The optimization of concatenation form prompts can be written as follows,
\begin{align}
    \label{eq:7}
    p_s^* = \argmin_{p_s}\mathcal{L}(\mathbf{Y}^{a_s}, \hat{\mathbf{Y}}),
\end{align}
\begin{align}
    \label{eq:8}
    \hat{\mathbf{Y}} = (\mathcal{P}\circ \mathcal{B})_{\theta^*}(\mathcal{F}(\mathbf{X}^{a_s})_{\theta^*} \oplus p_s),
\end{align}
where $\oplus$ represents concatenation in the temporal dimension. The concatenation form prompt is illustrated in Fig. \ref{fig:2}(c).

The three types of prompts, addition form, padding form, and concatenation form, can be jointly utilized for a pre-trained VSR model to adapt the model to an unseen target speaker. We evaluate the effectiveness of each prompt method and the combination of them through extensive experiments in the following sections.

\section{Experimental Setup}
For the experiments, we utilize both word- and sentence-level audio-visual datasets, LRW \cite{chung2016lrw} and GRID \cite{cooke2006grid}. We evaluate the proposed method by adapting a pre-trained model on unseen speakers by using different amounts of adaptation data. The following subsections describe the details of data settings and implementation details for each dataset.
\subsection{Dataset}
\subsubsection{GRID}
GRID \cite{cooke2006grid} is a sentence-level audio-visual corpus dataset following a fixed grammar. It consists of videos uttered by 33 speakers. Each speaker contains about 1,000 videos and each video is 3 seconds long. We follow the unseen speaker split of \cite{assael2016lipnet} so that speakers 1, 2, 20, and 22 are used for testing while the remainder is utilized for training. The data of the test speakers are divided into half to build adaptation sets and test sets. Since each video is 3 seconds long, every 20 videos from the adaptation set compose 1 minute of adaptation data. For the pre-processing and data augmentation, the lip ROI is cropped and resized into a size of 64$\times$128 similar to \cite{assael2016lipnet}, and random horizontal flipping, time masking, and random spatial region erasing are employed similar to \cite{kim2022distinguishing}. For the performance metric, Word Error Rate (WER, \%) which measures the prediction error compared to ground truth is utilized for the dataset. Therefore, the lower WER values indicate better VSR performances.

\subsubsection{LRW-ID}
LRW \cite{chung2016lrw} is a word-level audio-visual corpus dataset captured in television programs, thus datasets have large pose and illumination variations that are close to the real-world setting. It consists of 500 word classes and each word class contains 1,000 training videos. Since the dataset doesn't contain the speaker information, we annotate the speaker by using face recognition \cite{barr2012face,he2005face} technology with a pre-trained model \cite{deng2019arcface}. The annotated speakers are 17,580 which is very large compared to the GRID dataset. To build the speaker-adaptation setting, we set 20 speakers for testing while the remainder is utilized for training, and named the modified split as LRW-ID. The data information of 20 test speakers of LRW-ID is shown in Table \ref{table:1}. S\# represents the speaker index and the number in the blanket represents the speaker ID. Compared to GRID dataset, each speaker has different amounts of adaptation data, and the adaptation set may not cover the entire word classes in the test set, which is closer to a real-world scenario. Since each video is 1.16 seconds long, 52, 155, and 259 videos compose 1, 3, and 5 minutes of adaptation data. The lip ROI is cropped and resized into 112$\times$112, and the cropped frames are converted into grayscale. The same data augmentation is applied as GRID dataset. For the performance metric, word accuracy (ACC, \%) is employed so the large value of ACC refers to better VSR performance.

\input{./Table/Table1.tex}

\input{./Table/Table2.tex}

\subsection{Implementation details}
The basic architecture of VSR models is similar as illustrated in Fig. \ref{fig:1}(a). For the GRID dataset, we modify the architecture of \cite{assael2016lipnet}. The visual front-end is composed of three 3D convolutions and two 2D convolutions, the back-end is composed of a 4-layered Transformer \cite{vaswani2017attention} with a hidden dimension size of 256, and the predictor is composed of a linear layer (Table \ref{table:2}). For training, we use word-level CTC \cite{graves2006ctc} loss function. The size of the addition prompt for GRID dataset is 64$\times$124$\times$3 which is the same as the input frame, and it is added to all input frames consistently. To insert the padding prompt, all paddings in 5 convolution layers are changed from zero paddings to the padding prompts. The detailed size of convolution layers and prompts are shown in Table \ref{table:2}. The padding prompt size is represented as [left and right padding size, top and bottom padding size] $\times$ channel size. The concatenation prompt is concatenated with the encoded visual feature before passing the back-end module in the time dimension. We use 5 for the length of the concatenation prompt (\textit{i}.\textit{e}., $N_p=5$).

For the LRW-ID dataset, we use the ResNet-18 architecture \cite{he2016resnet} whose first convolution layer is changed with 3D convolution following \cite{petridis2018end,kim2021cromm}. For the back-end module, we employ a 6-layered Transformer with a hidden size of 512, and a linear layer is utilized for the predictor (Table \ref{table:3}). For the loss function, Cross Entropy loss is applied for 500 word classes. For the LRW-ID, the addition prompt has the size of 112$\times$112$\times$1, the padding prompt is inserted for all convolution layers (\textit{i}.\textit{e}., 17 layers) in the visual front-end as described in Table \ref{table:3}, and the concatenation prompt is inserted before the back-end, with 5 lengths.

\input{./Table/Num_params.tex}

For evaluating the proposed prompt tuning method in speaker adaptation, we pre-train the VSR models on the training set whose subjects are not overlapped with the testing set. For pre-training on GRID, a batch size of 112 and a maximum learning rate of 0.008 with 5,000 warmup \cite{vaswani2017attention} steps are used. The training data consists of about 29,000 videos. For LRW-ID, a batch size of 400 and a maximum learning rate of 0.004 with 10,000 warmup steps are used, and the training data consists of 480,378 videos. With the pre-trained model, $\theta^*$, we only optimize the prompts to adapt the model to unseen speakers while the model parameter is kept frozen. During adaptation, we use a learning rate of 0.01 for the addition and padding prompts and a learning rate of 0.1 for the concatenation prompt, with a batch size of 112 and 55 for GRID and LRW-ID, respectively. For the optimization, we use AdamW \cite{kingma2014adam,loshchilov2017adamw} and TITAN RTX GPUs for both pre-train and adaptation. The number of parameters for each prompt method for adapting one target speaker is shown in Table \ref{table:4}. The percentage refers to the relative number of parameters compared to the full model parameters. It shows that the prompt has a very small number of parameters compared to the full model.

\input{./Table/GRID_MIN.tex}

\subsection{Baselines for comparisons}
In order to validate the effectiveness of the proposed prompt tuning methods in speaker-adaptive VSR, we set comparison methods including previous speaker-adaptive methods and finetuning methods.

\textit{Baseline} is a pre-trained VSR model without performing the adaptation to the unseen speakers so it shows the lower bound performance.
\textit{Speaker-invariant}\cite{meng2018sitASR} and \textit{Speaker code}\cite{abdel2013codeicassp} are the speaker-invariant and -adaptive methods developed for ASR models. We directly apply these methods to the VSR model to compare the effectiveness of the proposed method with previous speaker-invariant and -adaptive methods. Specifically, for the speaker-invariant model, we additionally attach a speaker identity classifier after the visual front-end. During training, the speaker identity classifier is guided to classify the subject identity from the encoded visual feature while the visual front-end module is guided to deceive the speaker identity classifier. Therefore, with the adversarial training \cite{ganin2015grl}, the visual front-end is eventually become a speaker-invariant model by not encoding the speaker identity information into the visual feature. For the speaker-adaptive model, \textit{Speaker code}, we additionally train the Adaptation Network and speaker code of \cite{abdel2013codeicassp} on training dataset $\mathcal{T}$ by attaching them to the pre-trained VSR model. After training, adaptation is performed by only training the speaker code on the adaptation dataset of target speaker $s$, $\mathcal{A}_s$. We use 128, 64, and 32 dimensions of speaker code for each MLP layer in the Adaptation Network for GRID dataset, and 256, 128, and 64 dimensions for LRW-ID dataset.

Moreover, to compare with the finetuning methods \cite{liao2013trainpart1}, we set three types of finetuning methods by differing the trainable parts of the pre-trained model. Firstly, \textit{FineTune-C} is the method that only the last linear layer (\textit{i}.\textit{e}., predictor) is tuned on the adaptation data, so it has the smallest number of parameters compared to other finetuning methods. \textit{FineTune-B} is the method for finetuning both the back-end and the predictor. Finally, \textit{FineTune-F} is the method that the whole pre-trained VSR model is finetuned on the adaptation dataset, hence it requires the largest parameters. For finetuning the pre-trained model, a learning rate of 1e-5 is utilized.

\section{Experimental Results}
We evaluate the effectiveness of the proposed prompt tuning in speaker-adaptive VSR by using different amounts of adaptation data. Firstly, we explore the effectiveness of the proposed method in a situation where only a small number of adaptation data is available. To this end, we use 1, 3, and 5 minutes of adaptation data for each unseen speaker to adapt the pre-trained model to the target speaker. Then, we examine the speaker adaptation performances by using different ratios of adaptation data, to validate when the prompt tuning has benefits compared to finetuning methods.

\subsection{Speaker adaptation results with small data}
In this experiment, we evaluate the effectiveness of the different types of prompts, the addition, the padding, the concatenation, and their combinations by using a small number of adaptation data with 1, 3, and 5 minutes in length. Therefore, a total of 7 methods are evaluated including, addition prompt only (Add), padding prompt only (Pad), concatenation prompt only (Cat), and their combinations (Add Pad), (Add Cat), (Pad Cat), and (Add Pad Cat). The speaker adaptation results by using the proposed prompt tuning for 4 unseen test speakers (\textit{i}.\textit{e}., S1, S2, S20, and S22) on GRID are shown in Table \ref{table:5}. Compared to the performance of Baseline which is the results obtained by using the pre-trained VSR model on unseen target speakers directly, all prompt methods largely improve the performance on the target unseen speaker. The results indicate that the VSR model is inherently sensitive to personal lip appearances and a pre-trained VSR model can show degraded performance when they are applied to unseen speakers directly. In contrast, by applying the proposed speaker adaptation method, we can improve the VSR performances with a small number of adaptation data, so that it achieves the almost similar performance obtained in seen speaker settings \cite{assael2016lipnet,chung2017lrs2}. Please note that just using 1 minute of adaptation data improves 56\% relative mean performance with the addition and concatenation prompts (Add Cat), compared to Baseline.

\input{./Table/LRW_ID_MIN_MEAN.tex}

By comparing the different prompt methods, the addition prompt achieves the best performance among the single prompt methods for the GRID dataset. It is related to the used network architecture of GRID shown in Table \ref{table:2}, which has a shallow visual front-end so the input-level prompt can affect the visual feature largely, while the padding prompt has fewer effects on the inner feature map due to the shallow layers and small receptive fields. Moreover, by additionally utilizing the concatenation prompt with the prompts for CNN (\textit{i}.\textit{e}., addition and padding prompts), the VSR performances on the target unseen speakers are improved overall. Analyzing the effect of each prompt, the addition and the padding prompts are mainly for improving the encoded visual feature so that the target speaker's personal lip appearances can be adaptively modeled, and the concatenation prompts improves the temporal encoding availability of the back-end module so that the personal lip movements can be accounted. We find that the combination of the addition and the padding prompts, (Add Pad), does not further improve the performance over the addition-only prompts (Add). A similar tendency can be seen in that the (Add Cat) and (Add Pad Cat) have similar performances.

The speaker adaptation results for 20 unseen test speakers on LRW-ID are shown in Table \ref{table:7}. Even if the pre-trained VSR model is trained with large speaker variations with 17,560 speakers, we can still improve the VSR performance by adapting the pre-trained model on the target unseen speaker. Especially, when the model has less competency for a test speaker, the effectiveness of adaptation is bigger. For example, the pre-trained VSR model shows 75.95\% ACC on speaker 11 (S11) which is lower compared to the mean ACC of 87.54\% over all speakers. In this case, by using the proposed prompt tuning (Pad Cat) with 3 minutes of adaptation data, we can improve the performance to 84.45\% ACC which is a large improvement of about 8.5\% ACC. On the other hand, we find that when the pre-trained model has enough competency, the effectiveness of the adaptation is small. This can be seen from the results of speaker 9 (S9), where the performance gain is smaller compared to the other speakers. As the purpose of the speaker adaptation is to transform a pre-trained model that cannot capture the lip appearances and movements of the target unseen speaker, the obtained tendency is natural and the effect of the adaptation can be small for the already well-captured lip appearances and movements.

\input{./Table/LRW_ID_MIN.tex}

The mean word accuracies for 20 speakers according to different types of prompts are shown in Table \ref{table:6}. The mean word accuracy of the Baseline model is 87.54\% and by utilizing just 1 minute of adaptation data with (Pad Cat, P+C) prompts, the performance is improved to 88.53\%. With more adaptation data of 3 and 5 minutes lengths, we can achieve the best word accuracies of 89.45\% and 89.99\% respectively. By comparing the different prompt methods, the padding prompt achieves the best performance among the single prompt methods for the LRW-ID dataset. This is the different tendency with that the addition prompt shows the best performance for the GRID dataset. It is related to that the visual front-end of LRW-ID is much deeper and has large parameters so that the addition prompt cannot largely affect the final encoded visual feature. On the other hand, the padding prompts can largely affect the visual feature at all intermediate CNN layers, with the large receptive field of deep CNN. Moreover, we observe similar results with GRID, the prompt (Add Pad, A+P) does not improve the performance over the padding-only prompt (Pad), and the prompt (Add Pad Cat, A+P+C) shows similar performance as (Pad Cat, P+C). The results indicate that the addition and the padding prompts have a similar role, improving the visual feature representations, thus the combination of them does not improve the performance further. However, the combination of prompts for CNN with the concatenation prompt which is for improving the temporal feature representations can boost the performance.

From the experimental results on both GRID and LRW-ID, we highlight that regardless of the types of prompts, we can improve the performance of pre-trained VSR models on the unseen target speaker by just finetuning prompts with a small number of adaptation data (\textit{i}.\textit{e}., less than 5 minutes long). In addition, when the pre-trained CNN model has deep architecture, the padding prompt has more effectiveness than the addition prompt, while the addition prompt can achieve better performance for shallow CNN. Finally, the combination of prompts for CNN and for Transformer can further improve the performance.

\subsection{Comparison with previous methods}
In this experiment, we compare the effectiveness of the proposed prompt tuning methods with previous speaker-invariant and -adaptive methods including different finetuning methods. Especially, we also compare the total number of parameters required for inferring for all target speakers. For example, the method finetuning of the whole pre-trained model (\textit{i}.\textit{e}., FineTune-F) requires the parameters of the pre-trained model multiplied by the number of target speakers.
The comparison results on GRID dataset are shown in Table \ref{table:8}. We only represent the best two prompt types (Add Cat, A+C) and (Add Pad Cat, A+P+C) among all combinations, on the table. The best performance is represented in bold and the second-best performance is underlined. Among the methods that require less than 3\% additional parameters compared to that of the pre-trained model, Speaker-invariant, Speaker code, FineTune-C, and the proposed method (A+C), the proposed prompt tuning achieves the best performance on all adaptation data ranges. This shows the effectiveness of the proposed prompt tuning with a small number of additional parameters on speaker adaptation. Moreover, it is notable that compared to the method, Speaker code \cite{abdel2013codeicassp}, the proposed method has simpler adaptation stages by directly finetuning the prompts by attaching them to the pre-trained model. On the other hand, the method, Speaker code, has more adaptation stages where Adaptation Network should be firstly trained after attaching it to the pre-trained model on the training dataset, and then the speaker code should be finetuned on the adaptation dataset. Compared with the other finetuning methods, FineTune-B and FineTune-F, which consume more than 250\% additional parameters, the proposed prompt tuning methods, (A+C) and (A+P+C), show comparable performance with much fewer additional parameters (\textit{i}.\textit{e}., less than 5\% additional parameters). The results show that the proposed method is practical and is applicable to the speaker adaptation of tens of thousands of users in the real world while finetuning methods require astronomical memory for the speaker-specific models.

The comparison results on LRW-ID dataset are shown in Table \ref{table:9}. We only represent the two best prompt types, (Pad Cat, P+C) and (Add Pad Cat, A+P+C), and the smallest prompt type, (Cat, C), in the table. Surprisingly, in the adaptation setting of using under 5 minutes of adaptation data, the proposed methods even outperform the finetuning methods on LRW-ID. This result is also related to the previous studies \cite{jia2022vpt,lester2021prompttuning} that when the pre-trained model size becomes larger, the effectiveness of the prompt is getting bigger and even outperforms the finetuning methods. Please note that the model used for LRW-ID is about 10 times larger than that for GRID. Moreover, compared to the methods that require less than 15\% additional parameters for 20 target speakers, Speaker-invariant, Speaker code, FineTune-C, and the proposed methods, the proposed methods achieve the best performances. It is notable that using the concatenation prompt which increases just 0.15\% of model parameters outperforms the previous speaker-adaptive method, Speaker code.

\input{./Table/GRID_MIN_COMP.tex}

\input{./Table/LRW_ID_MIN_COMP.tex}

\subsection{Speaker adaptation results according to the data size}

\input{./Figure/GRID_FT.tex}
\input{./Figure/LRW_ID_FT.tex}

In this experiment, we explore the performances of the proposed method without limiting the adaptation data size. Therefore, we analyze when the proposed prompt tuning is preferred over the finetuning methods. To this end, we utilize the different amounts of adaptation data proportionally to the entire adaptation set, 10\%, 30\%, 50\%, 70\%, and 100\%. Fig. \ref{fig:3} shows the adaptation results of the proposed prompt tuning and the three different finetuning methods on GRID. In overall, FineTune-B (FT-B) and FineTune-F (FT-F) outperform the other methods. Especially, the performance gap between FT-B (and FT-F) and the proposed prompt tuning gets bigger when more than 50\% adaptation data is utilized. The performance of the proposed prompt tuning (Add Pad Cat, A+P+C) with 100\% adaptation data is 3.13\% WER and the performance of the full finetuning, FineTune-F, is 2.34\% WER. Therefore, when the pre-trained model size is small, a better method can be selected by considering the model parameters and performance trade-off, based on the fact that the finetuning methods perform better while the proposed prompt tuning methods have much fewer parameters (\textit{i}.\textit{e}., 14.32M vs. 3.75M).

Fig. \ref{fig:4} shows the adaptation results on LRW-ID dataset. Compared to the finetuning methods, the proposed prompt tuning methods, (Add Pad Cat, A+P+C), (Pad Cat, P+C), (Pad, P), (Cat, C), show better results when the adaptation data is small so below 30\%. However, the finetuning methods, FineTune-B and FineTune-F outperform the prompt tuning methods when the adaptation data size becomes larger, and the performance gaps become larger according to the data size. Therefore, when the pre-trained model is large and there exist a few numbers of adaptation data, the prompt tuning method is preferred over the finetuning methods in the aspects of both performance and parameter size. When large-scale adaptation data is available for the target speaker, the trade-off between performance and additional parameters would be considered to select the appropriate speaker-adaptive method. Please note that the (A+P+C) prompt has 0.487\% parameters compared to the full model, for each speaker.

\input{./Table/Ablation_Pad.tex}

\input{./Table/Ablation_Cat.tex}

\subsection{Ablation study}
There are two hyperparameters that can be controlled, the number of CNN layers to insert the padding prompt and the length of the concatenation prompt. In order to confirm the effects of hyperparameters, we evaluate the adaptation performances by differing the number of layers (\textit{i}.\textit{e}., $N_l\in\{5,11,17\}$) that the padding prompt inserted and by differing the length of the concatenation prompt (\textit{i}.\textit{e}., $N_p\in\{1,3,5\}$). For the padding prompt ablation study, we only utilize the padding prompt without combination with other prompts to focus on the effects of the number of padding layers. Similarly, we only utilize the concatenation prompt for checking the effects of its length. The ablation results according to different padding prompt layers are shown in Table \ref{table:10}. When all padding layers are changed with the padding prompts, we can achieve the best performances for the three adaptation data settings (\textit{i}.\textit{e}., 1, 3, and 5 minutes). Moreover, we can find that the performance gains by using more layers become larger when more adaptation data is utilized. Therefore, we could further reduce the parameters for the padding prompt by inserting it for only the part of CNN layers, if the available adaptation data is less than 3 minutes. From the experimental result, we utilize all layers of CNN to insert the padding prompts in other experiments, as it shows the best results.
The ablation results according to different concatenation prompt lengths are shown in Table \ref{table:11}. For the concatenation prompt, we find that the length of the prompt does not affect the performance largely. We set the length of the concatenation prompt to 5 for other experiments, as it shows better performances overall.

\section{Conclusion}
In this paper, we proposed prompt tuning methods of DNNs for developing speaker-adaptive VSR models. With different types of prompts, the addition form, the padding form, and the concatenation form, we can adapt a pre-trained model composed of both CNN and Transformer variant architectures to the target unseen speaker. The proposed prompt has much fewer parameters compared to the full model, so it is more practical in storing and handling data for many users. Through comprehensive experimental evaluations, we showed that the padding prompt can improve the visual representations of CNN when the CNN is deep while the addition prompt is effective for shallow CNN. Moreover, by using the combination of the addition prompt and the padding prompt with the concatenation prompt, we can further increase the performance of VSR on unseen speakers. Finally, we compared the proposed method with several finetuning methods in the aspects of both the performance and the number of parameters, and showed that the proposed prompt tuning can achieve comparable VSR performances with much fewer additional parameters.

\section*{Acknowledgments}
This work was supported by Institute of Information \& communications Technology Planning \& Evaluation (IITP) grant funded by the Korea government(MSIT) (No.2022-0-00124, Development of Artificial Intelligence Technology for Self-Improving Competency-Aware Learning Capabilities)

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


"The controversy stems, in part, from recent arrest sweeps conducted by the Otsego County Sheriff's Department for Friend of the Court warrants (see related story), intended to nab individuals delinquent on child support."
It's no surprise to me that the court will go to extra efforts to prioritize the arrest of child support debtors before other actions, because they make more money enforcing child support obligations.
The Federal Government pays the court 66 cents for every dollar the court spends on child support collections (US Code Title 42, Section 655), and the federal government provides additional incentive payments (US Code Title 42 Section 658a) based on various child support collection criteria. It's my understanding that these incentive payments, along with Grants to States for Access and Visitation (US Code Title 42 Section 669b) combine with fees fully pay for Friend of the Court.
Furthermore, when debtors are in arrears, they are charged an 8% per year fee on their outstanding debt, all of which goes directly to the courts.
Courts would be foolish not to make every effort to collect as much money as possible, as they are doing here.
However, there is a dark side to this arrangement. These same courts, who go to great lengths to collect these child support payments, also have a duty to act as impartial arbiters when interpreting the laws upon which these payments are set.
Is it any wonder that a judge presiding over a divorce may be swayed by all of future income to his or her court to believe that sole custody with the lower wage earner, which gives the highest income to the court is the Court's preferred custody arrangement?
How many Friend of the Court workers can explain in detail why joint custody, in which both parents give love and attention to their child, and provides the least dollars of transfer payments under the Michigan child support formula manual, and thus the least income to the court, is a terrible, terrible arrangement for the children?
Imagine trying to explain to a Friend of the Court worker that you're out of a job not because you chose to quit, but because you were downsized, and need a reduction in your child support payments, when that FOC worker's own salary may depend on finding a reason to find a way to skirt the law by saying no to you and those like you.
It is for this and the love of their children that Dads and Moms of Michigan and others have worked to support Michigan House Bill HB 5464, which would instruct judges to prefer joint custody unless there is clear and convincing evidence that it won't work.
Please contact your Michigan House Rep and support HB 5464.


Every day brings a law suit against a church, leading Christian figure, or ministry. But, Christ told us to expect persecution (Jn. 17:18-20).
The question is: How will we respond to such attacks?
I am going to offer some general propositions which I feel are applicable and then look at and comment upon some recent and cases.
Proposition #1 is that how we act when attacked does not depend upon whether we are an individual or a corporation. I doubt God sees our corporations and organizations. He just keeps looking for one of His people, called by His name, to act as He commands, in faith, at any instant in time.
Proposition #2 is that how we act when attacked does not depend upon the attacker being a person, organization, or government, and our actions do not depend upon whether the attacker is a Christian or direct agent of Satan. We are told to be light and salt; we are told to love our neighbor as our self; we are told to love those who persecute us; and we are told that we are ambassadors for Christ, ministers of reconciliation.
Proposition #3 is that conflict is neutral. It becomes either good or bad -- for us, our opponents, and all who see us -- to the extent that we bring it under the lordship of Jesus Christ.
Proposition #4 is that the normal result of litigation conducted outside of God's rules is a defeat for us (I Cor. 6:7), may wrong others (I Cor. 6:8), may imprison us (Matt. 5:25-26), and may consume us (Gal. 5:15).
Proposition #5 is that when we are in conflict, we need spiritual counsel (generally by several counselors who are physically present with us at the same time) from outside our own organization for we have logs in our eyes and ears which impede our knowing truth.
Proposition #6 is that when a claim is launched against us, we must seek the claimant out and try to speak with them. We must do this, not our attorney. We may speak with our attorney as a part of counting the cost, before we go to the other party, but go to them we must before starting any legal defense (Matt. 5:22-24 and Matt. 18:12-15). We cannot simply turn all matters over to our attorney and allow our attorney to do what God would never allow us to do.
Proposition #8 is based on the last portion of that verse: we may not demean or degrade our opponent, or cause them pain and anguish by attacking or counter-attacking, them. If the only way we can "win" is to bite and devour them, then we must suffer the wrong and be defrauded (I Cor. 6:7), "entrusting ourselves to Him Who judges righteously" (I Pet. 2:23).
A pro-choice-in-abortion group sued the I.R.S. to revoke the tax exempt status of two Catholic organizations. The claim was that the Catholics were engaged in political activity and lobbying in the area of pro-life in violation of the law granting them tax-exemption. To prove their case, the pro-choice group got a court order for the Catholics to turn over records of expenditures and minutes of meetings where the decisions were made concerning expenditures. The Catholics refused, on the basis of legal and constitutional theories. The judge held them in contempt of court and fined them $50,000 per day until the records would be produced. Ultimately, this decision was reversed on the grounds that a tax payer did not have "standing" to sue about someone else violating tax law; only the IRS could sue.
I have a problem with the method of defense. The defense chose to use the law of man as a shield of protection rather than trust in God. Such form of defense is a poor witness to the world. (See I Pet. 3:15, Matt. 5:37, and Rom. 13:1-7.) In comparison, look at how Shadrach, Meshach and Abednego responded when they were attacked. They did not complain that the law or the king were unrighteous or un-constitutional. They respected the authority throughout (Rom. 13:1-7). And they walked free through the fire of the attack.
Yes, we may use the Constitution and laws in defense -- but only after giving account, only after responding to the questions asked. We are not to place our defense or our trust upon man, his ways, his laws, his systems -- only upon God.
Another very difficult to discuss is Nally v Grace Community Church and John McArthur. This case has been called a case of "clergy mal-practice". Briefly, the facts are that in 1979 a young adult committed suicide. Later, his parents blamed individuals and the church for the death. The church sought to resolve the matter without litigation (Matt. 5:23-26), but could not do so. The parents filed suit.
Maybe the parents would be healed of their anger, bitterness, pain, confusion, etc. if the church chose to bear the stripes. By choosing to suffer the wrong, we may lose the building, furnishings and accounts over which we see ourselves as stewards. But, first and foremost, we are to be stewards of our actions as ambassadors to the world for Jesus Christ and as ministers of reconciliation (II Cor. 5:17-20). We must never hold on to material things so as to defeat our witness.
Let us, as we face these situations, keep in mind that our church properties can be as much mammon as our personal wealth. Let us keep in mind that God does not think in terms of rights and property but of relationships, sacrifice, and bearing the burdens of others. Our example and model is Jesus Christ -- and He laid down all rights, position and properties, and died when He could have called ten thousand angels.
From what I see in the news media, and read in legal reports, I find the church, when attacked, far too often responding exactly as do the unbelievers -- without any regard for relationship, witness or impact upon others. Do we choose to respond to these attacks in the way of the world rather than the way of the Lord because of fear? Let me explain some things of the law, and then judge for yourself.
When the church receives the court papers, the papers say that the church has a limited number of days within which to appear and file an answer. If they fail to do so, they may be "defaulted". The lay person believes that "being defaulted" means that a judgment for millions of dollars will be entered against them. That is not always true. In all cases, before judgment can be entered, the plaintiffs must ask the judge for a judgment. The plaintiffs could die before that happens, or the Lord could call the elect home before then (Matt. 6:25-34). Before the judge grants judgment he must determine: (1) that the church was negligent in some manner; (2) that harm resulted; and (3) whether any monetary damages are appropriate.
Before the judge can find liability, he must find that: (1) there was a legal duty owed the plaintiff; (2) the duty was violated; and (3) the Constitution does not prohibit this type of case. The judge must decide these things even if no one defends.
The judge can require the plaintiff to present evidence proving liability and can decide that no wrong act was done, or that a wrong act was done but there was no duty owed, or that there was a wrong act and duty but the Constitution forbids judgment. Before the judge can award damages, plaintiffs must prove that they were damaged. In Nally, the judge could have decided that any wrong of the church died with the young adult man and the parents suffered no loss.
My point is this: God calls us to act according to His commands by taking one step down an unknown road, in faith that He is sovereign and working, being aware that we might die tonight before anything could possibly happen to us as a result of that one step. We fail to take the one step for fear that it will result in something horrible later.
A final case I want to consider involves a bankruptcy. I must confess that my knowledge on this case is more scanty than the others, and thus the analysis could be quite inadequate as to the actual facts.
A couple, members of a church, had a business which went into bankruptcy. This apparently also caused them to personally take bankruptcy. The Trustee in Bankruptcy sought to recover from the Church the tithes and offerings of the couple during the year prior to bankruptcy on the base that they were voidable transfers, given without adequate consideration. Such transfers are called "voidable preferences" and are not based upon any fraudulent or evil state of mind; it is a mere "thou shalt not do this" concept. Much money was spent fighting the case and, at an appellate level, the church won.
Should the church have fought, or simply turned over the money? I confess that my bias is to turn over the money lest the name of Christ be held up to scorn. However my issues and questions focus first on the acts of the couple and the church before the bankruptcy.
When this couple saw bankruptcy looming, did they "go to the law or to the saints"? (I Cor. 6:1-8) [See May we Sue? Shall We Sue? Whom May We Sue?] It seems to me that this is what God would require. At that time, the saints can help analyze "how did we get to this place". If there were patterns in sin in the lives of the couples, those patters need to be dealt with lest they continue on and reappear in some other guise at a later date. The saints are also best suited to help make decision on filing bankruptcy vs arranging a payoff of creditors. The saints are best in the position to help determine whether the saints should "bear the burden" and see to the satisfaction of the creditors even if the couple have no resources. Unfortunately, when I asked these questions of the church involved, no response was given.
Let us assume the couple did not come to the church but merely went to law. Once the church became aware of this, what did the church do? I believe it should have conducted the same inquiry, asked the same questions, and considered the same options -- plus one another: refund the preference.
My final concern is that the Court initially make a judgment that the church had failed to show that the couple received anything of value for their tithes and offerings. Such a judicial ruling should, I believe, cause us all pause, for we do give massive amounts to keep our religious institutions afloat.
I know that the way I look at things is, in part, born our of my own experiences of life. In November, 1981, facing a suit to remove me from the position of judge, and strip me of my license to practice law, I felt the Lord call me to fire my attorney and cease all defense, trusting only in Him. I did so. I found freedom in the fire, and became free to minister as I was no longer spending all of my time, energy, emotions, and finances defending myself. I still have a license, am well fed, sheltered and alive.
But I do not demand that others accept my view; I merely hope they can consider with an open mind the totality of Scripture when in conflict.
But, most importantly, I know God, in the End of Time, WINS!


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Wondering where you can have a family holiday trip or day out in south Florida? Riverbend Park is the place to be. The park is located in Jupiter, Palm Beach County, Florida. Fun activities are available for all ages. Here are some of the exciting activities you could carry out as you explore the 680 acres Riverbend Park.
There are meandering paths for hiking. Walking through the scrub and under the canopies offers relaxation. The environment suits all interests and abilities. It is so natural and well maintained. Carrying a camera is recommended due to the rich variety of creatures and plants you can see. There are birds of different species, live oak, alligators in the river, deer and many others. The area is very safe and is marked with signs.
There are bike trails of up to 10 miles. They are appropriate for multi-use and suit family bicycles perfectly. You could spend some hours or even a whole day cycling. You may opt to come with your own bike or rent them at the park. There are safety tips for guidance to ensure that you cycle safely in the park.
If you prefer paddling to pedaling, there is the Loxahatchee River and the perfect location along the east. There is an 8.5 mile waterway just for you. If kayaks and canoes are new to you, beginners are well catered to. There is no age limit for the activity. Gear is provided for souls taking longer trips. Life vests are provided. You will come across swamps, raccoons, wading birds, turtles and alligators. You can rent your own canoe for you and your family.
There is a fishing pier or you can fish as you canoe through the park. You can use live bait and get cool hits. Bring along your horse and enjoy about 7 miles of equestrian trails. Be sure to bring sunscreen for your skin's health.
Riverbend Park is indeed the place to be for a happy, healthy and natural exploration. Stroll along the wild and scenic Loxahatchee River, visit the Cracker Farmstead, and picnic in the shade under a Seminole chickee. Hours: 7 days a week Sunrise- Sunset.


text:
Q: Bayesian networks and joint probabilities This is my problem
My problem is modeled by a basic Bayesian Network with only two layers. So I have parent and child nodes but the children has no children. Essentially a bipartite graph. The children depend on one or more of the parents and these edges/relations have a probability. The model is also extended by completing the bipartite graph with low probability edges to account for noisy data. So in the finished model each child $(C_x)$ has a dependency on each parent $(P_x)$.
What I want to be able to do is to infer the most probable solution by maximizing,
$$ max_{P_1,P_2,\dots,P_n}(P(P_1,P_2,\dots,P_n|C_1,C_2,\dots,C_m)) $$
where $ C_i \in \{0,1\} $, $ P_j \in \{0,1\} $. For a given observation on the state of the children.
So for a observation $O=\{C_1=0, C_2=1, C_3=1\}$
I want to calculate
$$P(P_1=1,P_2=0,P_3=0|C_1=0, C_2=1, C_3=1)$$
$$P(P_1=0,P_2=1,P_3=0|C_1=0, C_2=1, C_3=1)$$
$$P(P_1=1,P_2=1,P_3=0|C_1=0, C_2=1, C_3=1)$$
and so on.
Here is how I try to solve it
I want to be thorough so I will explain how I try to solve this. I'm not sure that I'm doing it right. Please point out to med if I'm doing this wrong.
What I do first is I complete the conditional distribution tables for the child nodes. From the model I have the CPT as for a child node $C_x$ something like this, the probabilites are chosen to make the example easy.
\begin{array}{ l l l|l l }
P_1 & P_2 & P_3 & P & \lnot P \\
  \hline
 0 & 0 & 0 & 0 & 1 \\
 0 & 0 & 1 & 0.1 & 0.9 \\
 0 & 1 & 0 & 0.4 & 0.6 \\
 1 & 0 & 0 & 0.2 & 0.8 \\
\end{array}
And I complete this table by calculating
\begin{array}{ l l l|l l }
P_1 & P_2 & P_3 & P & \lnot P \\
  \hline
 0 & 1 & 1 & (1- \lnot P) & 0.9 \times 0.6 \\
 1 & 0 & 1 & (1- \lnot P) & 0.9 \times 0.8 \\
 1 & 1 & 0 & (1- \lnot P) & 0.6 \times 0.8 \\
 1 & 1 & 1 & (1- \lnot P) & 0.9 \times 0.6 \times 0.8 \\
\end{array}
And then I calculate the joint conditional probability by doing something like
$$P(P_1=1,P_2=0,P_3=0|C_1=0, C_2=1, C_3=1) = $$
$$P(P_1=1,P_2=0,P_3=0|C_1=0) \times$$
$$P(P_1=1,P_2=0,P_3=0|C_2=1) \times$$
$$P(P_1=1,P_2=0,P_3=0|C_3=1)$$
Basically I'm not convinced that the last step is correct. Any help or comments is greately appreciated!
Yes, this is school related but it is not regular homework. It is a part of a thesis project I'm doing at a company.
Graph update on request

Here is a graph example of my model. The regular edges are direct dependencies and the dotted edges are noisy or guess edges added to allow for noisy data. Guess edges has a low probability of $p = 0.0001$ and the regular edges all have the probability $(1-p)$. In my problem I do not care for the probability of individual events like $P(L_1)$ or $P(C_2)$, so they are assumed to be $1$. I make an observation on the state of the variables $C_1...C_n$ and given the graph model above I want to infer to most plausible cause. The possible causes  are $P_1...P_n$ or a combination of them that is most likely. Like I stated earlier on the example observation above.
Here is an example of the basic truth tables for this graph.
\begin{array}{ l|l l }
C_1 & T & F \\
  \hline
 P_1 & 0.9999 & 0.0001 \\
 P_2 & 0.9999 & 0.0001 \\
 P_3 & 0.9999 & 0.0001 \\
\end{array}
\begin{array}{ l|l l }
C_2 & T & F \\
  \hline
 P_1 & 0.0001 & 0.9999 \\
 P_2 & 0.9999 & 0.0001 \\
 P_3 & 0.9999 & 0.0001 \\
\end{array}
\begin{array}{ l|l l }
C_3 & T & F \\
  \hline
 P_1 & 0.0001 & 0.9999 \\
 P_2 & 0.0001 & 0.9999 \\
 P_3 & 0.9999 & 0.0001 \\
\end{array}
Does that make it any clearer?

A: First of all, your CPT's are not correct. You must have $2^3=8$ rows for all possible combinations of $P_i=\{\text{True}, \text{False}\}$, $i=1,2,3$ which are parent nodes of each $C_i$, $i=1,2,3$. For example,
$$
\begin{array}{c|c|c|c}
P_1 & P_2 & P_3 & Pr(C_1=\text{T}|P_1,P_2,P_3) \\
\hline
\text{T} & \text{T} & \text{T} & 0.4 \\
\text{T} & \text{T} & \text{F} & 0.5 \\
\text{T} & \text{F} & \text{T} & 0.3 \\
\text{T} & \text{F} & \text{F} & 0.7 \\
\text{F} & \text{T} & \text{T} & 0.1 \\
\text{F} & \text{T} & \text{F} & 0.9 \\
\text{F} & \text{F} & \text{T} & 0.2 \\
\text{F} & \text{F} & \text{F} & 0.6 \\
\end{array}
$$
As I understand the problem from your BN graph, you are looking for the maximum probable state of $P_i$'s given $C_i$'s,
$$\text{max } Pr(P_1,P_2,P_3|C_1,C_2,C_3)$$
Your Bayesian Network joint probability can be written as,
$$Pr_{BN} = Pr(P_1,P_2,P_3,C_1,C_2,C_3)=\prod_{i=1}^3 Pr(C_i|P_1,P_2,P_3) \tag{  1}$$
and
$$Pr_{BN} = Pr(P_1,P_2,P_3|C_1,C_2,C_3)Pr(C_1,C_2,C_3)$$
You can find $Pr(C_1,C_2,C_3)$ by marginalizing $Pr(P_1,P_2,P_3,C_1,C_2,C_3)$.
$$Pr(C_1,C_2,C_3)=\sum_{P_1=\{\text{T},\text{F}\}}\sum_{P_2=\{\text{T},\text{F}\}}\sum_{P_3=\{\text{T},\text{F}\}}Pr(P_1,P_2,P_3,C_1,C_2,C_3)\tag{2}$$
So here are the steps:
1) Redesign CPT's correctly
2) Compute $Pr_{BN}$ using formual (1)
3) Compute $Pr(C_1,C_2,C_3)$ by marginalizing $Pr_{BN}$ using formula (2)
4) Compute $Pr(P_1,P_2,P_3|C_1,C_2,C_3) = \dfrac{Pr_{BN}}{Pr(C_1,C_2,C_3)}$
5) Compute the maximum of $Pr(P_1,P_2,P_3|C_1,C_2,C_3)$ and observe which set of $\{P_1, P_2, P_3\}$ maximizes the probability. That set is the answer.
Edit 1: The way you are estimating CPT's is not correct. I assume that the events $P_i$'s are independent and that they are conditionally independent given the event $C_i$, hence,
$$
\begin{align}
Pr(P_1,P_2,P_3|C_i) & = Pr(P_1|C_i)Pr(P_2|C_i)Pr(P_3|C_i) \\
 & = \frac{Pr(C_i|P_1)P(C_i|P_2)Pr(C_i|P_3)Pr(P_1)Pr(P_2)Pr(P_3)}{[Pr(C_i)]^3}\tag{3}
\end{align}
$$
on the other hand from Bayes rule we have,
$$
\begin{align}
Pr(C_i|P_1,P_2,P_3) &= \frac{Pr(P_1,P_2,P_3|C_i)Pr(C_i)}{Pr(P_1,P_2,P_3)}\\
&=\frac{Pr(P_1,P_2,P_3|C_i)Pr(C_i)}{Pr(P_1)Pr(P_2)Pr(P_3)}\tag{4}
\end{align}
$$
From (3) and (4),
$$Pr(C_i|P_1,P_2,P_3) = \alpha Pr(C_i|P_1)P(C_i|P_2)Pr(C_i|P_3)\tag{5}$$
where $\alpha = \frac{1}{[Pr(C_i)]^2}$.
Your approach has two flaws. First, you don't take into account the effect of $\alpha$, and second in general,
$$Pr(C_i|P_1=1,P_2=0,P_3=0)\neq Pr(C_i|P_1=1)$$
In other words,
$$Pr(C_i=1|P_1=1,P_2=0,P_3=0)=0.2, Pr(C_i=1|P_1=0,P_2=1,P_3=0)=0.4 \not\Rightarrow Pr(C_i=1|P_1=1,P_2=1,P_3=0) = 0.2\times 0.4$$

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(Annews24- Uganda Kampala) A team lead by the Executive Director Musisi has visited the Uganda parliament to present their resolutions for the city and what has been Done.
Members of Parliament interacting with a team from KCCA led by the Executive Director, Jennifer Musisi.
The team is at Parliament to update members about KCCA's accomplishments in the 7 years and the plans for developing the city. Musisi applauds KCCA for improvements in: Street vending, traffic management, greening the city, garbage collection and management, hygiene and sanitation and health service delivery at KCCA facilities.
They were received by the speaker Of parliament Hon Kadaga Rebecca and the the Honourable member of Parliament who were in the house .
The Speaker advised the the KCCA to arrest all those cutting down the trees.
Musisi: I want to see someone arrested for cutting down a tree, I am interested in the preservation of environment.
Speaker @RebeccaKadaga to @KCCAED Musisi: I want to see someone arrested for cutting down a tree, I am interested in the preservation of environment.
This happened while the bank of Uganda was also being cautioned about the closure of other banks COSASE.