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Variable remuneration of retail banking staff
Banking businesses in Australia need to ensure that any incentive payments or employee remuneration schemes comply with new requirements and in particular are designed to avoid incentivising poor practices and negative consumer outcomes.
Mortgage Broker reforms introduced by the Australian Parliament are intended to have a similar effect.
The Sedgwick Review
In April 2016, the Australian Bankers' Association (as it then was) commissioned former Public Service Commissioner Stephen Sedgwick AO to conduct a review of, and make recommendations in relation to, ABA member banks' variable remuneration and incentive arrangements covering their bank staff and third parties selling retail banking products such as deposit accounts, mortgages, and credit cards. The Review was commissioned as part of a broader plan to address bank culture issues in response to sustained industry criticism.[1]
The Sedgwick Review Final Report, completed in April 2017, recommended that incentives no longer be paid to any retail staff of banks based directly or solely on sales performance. Its specific recommendations in relation to remuneration structures for retail bank staff were as follows:
Banks should remove variable reward payments and campaign-related incentives that are directly linked to sales or the achievement of sales targets (including but not limited to cross-sales, referral targets, and profit and revenue targets) [Rec. 2];
Staff eligibility to receive any variable reward payment should be based on an overall assessment against a range of factors that reflect the breadth of the responsibilities of each role [Rec. 3].
Any financial measures included in an overall assessment consistent with Recommendation 3 should be product-neutral (i.e. not encourage the sale of one product over another) [Rec. 4].
Where a performance scorecard system is used, all financial measures together should attract a maximum effective weight of 50% as quickly as systems and other changes can be introduced, falling to 33% or less by 2020 [Rec. 4].
All customer measures should be genuinely customer-centric and tailored to the role being assessed; and they should progressively reflect a focus on customer outcomes not just customer loyalty/ satisfaction [Rec. 5].
Credible behavioural or equivalent values gateways (e.g. gateways relating to ethical behaviour, customer focus etc.) should be applied to determine whether an individual can access variable rewards to which they would otherwise be entitled [Rec. 6].
Variable rewards payment regimes should no longer include financial measure-related "accelerators" [rec. 7].
Variable rewards payment regimes should no longer include financial gateways, including gateways relating to the number or value of cross sells [rec. 7].
Mr. Sedgwick said these changes should be implemented by no later than each bank's 2020 performance year [Rec 1]. He also made recommendations regarding the remuneration of third parties (mortgage brokers and aggregators); as well as broader recommendations around governance, culture, and performance management.
ABA member banks' response to the Sedgwick Review
On behalf of its members, the ABA committed to implementing the Review recommendations following the release of the Sedgwick Report.
A follow-up implementation assessment, also undertaken by Mr. Sedgwick[2] and released in 2019, found that, although considerable work remained to be done in implementing the recommendations in full, "substantial progress" had been made in delinking sales directly to reward for front line staff, including for specialist bankers such as home lenders and their managers.
According to the ABA website [https://www.ausbanking.org.au/policy/earning-back-trust/remuneration/]:
By the end of 2020, the industry will have reformed its remuneration structures to minimise the prevalence of financial targets as core indicators of staff performance. The revised structures will be balanced with other measures such as customer outcomes achievement and risk focus.
In addition, several banks have announced changes in recent years that go further than the Sedgwick Review recommendations. For instance, several have discontinued the payment of variable remuneration to tellers altogether, and some ABA members have removed, or are in the process of removing, variable remuneration for other customer-facing staff as well.
The most recent example of this is Westpac's decision, announced in August 2020 [https://www.westpac.com.au/about-westpac/media/media-releases/2020/19-august/], to remove all short-term incentives for, and increase the fixed pay of, over 4,000 branch and "customer care" employees of the bank and its subsidiary brands from 1 October 2020. This follows Westpac's decision in 2019 to move to a fixed pay only remuneration structure for all its tellers.
FSRC critique of sales incentive payments and recommendations on staff remuneration
The Final Report of the Financial Services Royal Commission [FSRC], released in February 2019[3], identifies commission payments and variable remuneration structures at all levels as a key driver (if not the key driver) of the poor practices and negative consumer outcomes identified by the Commission. As the Report states:
Very often, the conduct has broken the law. And if it has not broken the law, the conduct has fallen short of the kind of behaviour the community not only expects of financial services entities but is also entitled to expect of them…
Rewarding misconduct is wrong. Yet incentive, bonus and commission schemes throughout the financial services industry have measured sales and profit, but not compliance with the law and proper standards. Incentives have been offered, and rewards have been paid, regardless of whether the sale was made, or profit derived, in accordance with law.
To address his concerns regarding the distorting impact of industry remuneration structures, Commissioner Hayne called for, among other things, a radical overhaul of the way mortgage brokers are paid, including a phasing out of all commission-based remuneration. He also called for APRA to overhaul its prudential standards and guidance in relation to the remuneration systems of ADIs and other APRA-regulated entities and to give elevated attention to non-financial risk factors. These aspects are further discussed under Related Developments below.
In relation to the remuneration of front line or customer-facing staff, Hayne's approach (set out on pages 367 – 374 of the Final Report) was more incremental. The Final Report notes evidence of, and acknowledges, that "Banks have recently made, and are continuing to make, significant changes to the ways in which they remunerate front line staff" as they implement the recommendations of the Sedgwick Review Report, discussed above.
The "full" implementation of the Sedgwick recommendations "both in spirit and letter" was, the Report continues, an "important first step towards improving front line remuneration practices", highlighting various aspects of those recommendations. However, implementation of the Sedgwick recommendations should only be seen as a first step:
… As I have sought to emphasise above, banks must continue to give frequent and considered thought to how their variable remuneration systems are structured: to whether they are geared not only to what employees do but how they do it.[4]
The commentary then proceeds to highlight evidence of bank practices and proposed changes that Commissioner Hayne regards as appropriately geared to the how as well as the what, following which two summary recommendations are set out:
At least once a year, all financial services entities should review the design and implementation of their remuneration systems for front line staff to ensure that the design and implementation of those systems focus on not only what staff do, but also how they do it (Rec. 5.4)
Banks should implement fully the recommendations of the Sedgwick Review (Rec 5.5).
Government response to the FSRC recommendations on staff remuneration
In its initial response to the FSRC Final Report[5], the Government indicated that it "supported" the Commission's recommendations relating to staff remuneration. It went somewhat further in its follow-up Financial Services Royal Commission Implementation Roadmap (August 2019)[6], stating that it "expected" banks to implement the Sedgwick recommendations "as soon as possible".
Beyond indicating its expectations, the Government did not commit to, and has not since taken any further action in relation to, the recommendations.
Following the publication of the Implementation Roadmap, Commonwealth Treasury advised the Customer Owned Banking Association that the Government's expectation that banks would fully implement the recommendations of the Sedgwick Report extended to all ADIs, not just ABA member banks.
Related developments
In response to recommendations of the FSRC Final Report, legislation was enacted early in 2020 to amend the National Credit Act to require mortgage brokers to act in the best interests of consumers when providing credit assistance. This legislation also bans brokers and aggregators from receiving (and credit providers, employers, and intermediaries from giving) conflicted remuneration as prescribed by the Regulations.
Regulations are currently being developed to address various aspects of broker commission arrangements, as recommended by Commissioner Hayne, including banning campaign and volume-based commissions and payments, limiting soft dollar benefits, and requiring the value of up front commissions to be linked to the amount drawn down by the borrower (instead of the loan amount). After intense advocacy by the broker industry, the Government decided not to enact the FSRC recommendation that the payment of up front and trail commissions to brokers be phased out altogether. A further review of this issue will be undertaken in 2022.
The mortgage broker reforms are scheduled to commence on 1 January 2021, following a six-month deferral announced by ASIC in May 2020 in response to the impact of the COVID-19 pandemic.
APRA prudential Standard CPS 511
In July 2019, APRA commenced consulting on a new cross-industry Prudential Standard on remuneration, releasing a consultation paper and draft Standard CPS511 [https://www.apra.gov.au/consultation-on-remuneration-requirements-for-all-apra-regulated-entities]. APRA's stated intention was to strengthen reporting entities' remuneration frameworks and incentive structures so they "better align with the long-term interests of entities and their stakeholders, including customers and shareholders".
APRA indicated that the development of the new Standard responded to previous reviews it has undertaken (including its Inquiry into CBA completed in 2018), as well as the recommendations of the FSRC's Final Report (Recs 5.1 – 5.3).
APRA has indicated that it intends to resume work on the CPS 511 consultation in Q2 of FY 20-21, after suspending this work (and nearly all its policy reform consultations) in March2020 as part of its response to the impact of the COVID-19 pandemic.
In light of the developments outlined above, all banking institutions that have remuneration incentive arrangements in place for their staff should ensure their arrangements align with the recommendations of the Sedgwick Review Report.
[1] See the Review website [https://www.retailbankingremreview.com.au/] for further information about its terms of reference, consultation processes, the submissions it received, and Final Report
[2] Retail Remuneration Review – Assessment of progress (February 2019) is available here: https://www.ausbanking.org.au/wp-content/uploads/2020/07/Remuneration-Assessment-Paper-Final.pdf
[3] Available here: https://financialservices.royalcommission.gov.au/Pages/default.html
[4] This picks up an earlier comment at p.368: "Focusing only on what is to be sold is not enough. How the employee does the job is at least as important as what the employee does."
[5] Restoring trust in Australia's financial system, available here: https://treasury.gov.au/sites/default/files/2019-03/FSRC-Government-Response-1.pdf
[6] See Roadmap, pp. 13 – 14, available here: https://treasury.gov.au/p2019-399667
A Christmas season message from our CEO, Julian Fenwick: what to look forward to in 2021
Measuring Compliance Training Effectiveness
In this article, Thomas Fox, Compliance Evangelist based in Houston, TX, addresses the question, "What if you want to take your post-training analysis to a higher level and begin a more robust consideration of the effectiveness of compliance training?"


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Home Salon Care Enrich Salon pauses expansion plan, sees 25% fall in revenue this year
Enrich Salon pauses expansion plan, sees 25% fall in revenue this year
Hair and beauty salon chain Enrich has put on hold its store expansion plan for the year due to the coronavirus pandemic, and expects to close the ongoing fiscal with around 22-25 per cent fall in revenue, according to a top company official.
With the recovery from lockdown slow on account of poor consumer sentiment, the company wants government support in the form of "some consideration or some credit back of the GST of what all the companies would have paid in the last two years".
"Recovery is slower than what we thought. In terms of expansion, we had quite aggressive plans to grow to become a bigger format (player), get more products, more on and offline. Of that, at least adding new stores is currently on hold," Enrich Salon founder Vikram Bhatt told PTI.
In the past two years, the company has been adding almost 20-plus stores every year, he said adding that "I don't think we will be adding any more stores at least till March, till we get back on track".
Stressing that this will be a year of consolidation with focus on both offline and online, Bhatt said, "We are going to ensure that we first get back on track. In fact, we have shut down four stores…we are also into the second phase of evaluation. We will be shutting down another three to four stores. So, from 86 stores to 78 is what we feel we would end the year."
He added that the closure of the stores is primarily for the reason that centres are not affordable. Even though some of the owners are ready to give consideration, it is not good enough and the business does not look feasible at the store level, Bhatt said.
When asked about the expected impact on revenue due to the pandemic, he said, "This year, we will end up doing 75-odd per cent of last year from the same stores, about 22-25 per cent decline. This is based on our first five months' performance; we are projecting for the next seven months."
The company had clocked a total revenue of Rs 225 crore.
Bhatt said recovery of business has been slow as consumers have been really cautious and focussing more on savings with spending on beauty and salons being discretionary.
Moreover, he said that in Maharashtra, where the company has the highest number of outlets, there are still restrictions on services like facial and beard trimming, thereby limiting options for customers.
Besides, he said customers are wary about the safety aspects of COVID-19, although Enrich customers "are aware that we are quite ahead as far as safety and hygiene is concerned. We have been using single use towels and disposable items for years."
The company has quality audit and mystery audit process to ensure safety and hygiene, Bhatt added.
Seeking support from the government, he said, "My request to the government would be to give us some consideration or some credit back of the GST of what all the companies would have paid in the last two years."
Bhatt further said, "We are the people who have paid taxes religiously and honestly. In today's time if the government wants to give any stimulus or financial aid, I strongly feel the GST credit can be of real help.
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El I Festival de la Cançó d'Intervisió va ser la primera edició del festival d'Europa de l'Est i es va celebrar a Sopot (on se celebrava el festival de Sopot) del 24 al 27 d'agost. Els actes d'interval van ser Sofia Rotaru, Pegi Marš, Marie Myriam, Linda Lewis i The Ritchie Family. El festival va ser guanyat per l'artista txeca Helena Vondráčková de Txecoslovàquia (ara República Txeca).

Països participants
La primera edició va comptar amb onze països.

Curiositats
 Tant Txecoslovàquia com la Unió Soviètica no van participar a Eurovisió 1977 (ni en cap any) però la Televisió Txecoslovaca (ČST) i la Televisió Central Soviètica (ЦТ СССР) van retransmetre aquesta edició del festival. També a la БНТ (que en aquell moment no era membre de la UER).
 Aquesta edició s'asembla a la primera edició d'Eurovisió, ja que en tenim un nombre gran de artistes però un petit nombre de països participants.

Vegeu també
 Festival de la Cançó d'Eurovisió (1977)
 Festival de Sopot

Referències

1977

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Patricia Ann "Dr. Patt" VanDyke has passed away
Category: Obituary
Patricia Ann "Dr. Patt" VanDyke, Maryville, MO, was born on March 29, 1937, to Tice John and Thelma Mildred Gibson VanDyke, in Wyoming, IA. She passed away at her home in Maryville, MO, on March 13, 2017. Patt grew up in Hanover, IL, a beautiful little town on the Apple River. Education was always very important part of her life. She joked that she was enrolled in school very early because she kept chewing through the rope that her mother tied her to the clothes line with. She graduated Valedictorian of the Hanover High School class of 1954. Following high school, she attended Northern Illinois University and then transferred to Wisconsin State University at Platteville, where she earned her Bachelor's degree in 1958. She then earned both her Masters (1962) and Ph.D.. (1972) from the University of Wisconsin at Madison. Prior to coming to Maryville and Northwest Missouri State University, Patt was a field worker for the Dictionary of American Regional English. She traveled throughout upper Midwestern and western states gathering data for this project. She also taught high school in New Glarus and Monroe, WI.
Dr. Patt came to Northwest Missouri State University in 1969. She had planned for this to only be a short stop. But like most others, she fell in love with the school and the community. During her years at Northwest she served as a professor of English, Director of the Talent Development Center, Interim Vice President for Academic Affairs, and Dean of Libraries. She was honored with the Tower Service Award in 1994 and the Northwest Commitment to Quality Award in 1998. She was proud of her role in developing the principles that became foundation for the University's Culture of Quality. And, she was also honored to serve as an examiner for the Missouri Quality Award. She was respected for her intellect, honesty, loyalty, fairness, and integrity. She retired from Northwest in 2001.
She was a published poet and author. And, she was an athlete and participated in college sports long before Title IX. After coming to Maryville, she enjoyed playing city league softball, basketball, and volleyball. She recently shared that her list of accomplishments should include the fact she once pitched a one-hitter slow pitch game.
Patt was preceded in death by her parents and younger sister, Norma Jean Blair. She is survived by aunts, Janice Gibson, Washington, IA, and Bernice Gibson, Keosauqua, IA; her brother in law, Robert Blair, Sr, Greentown, IN; a niece, Robin Baker, Huntington, IN; nephews, Robert Blair, Jr. Kokoma, IN, and Tim Blair, Garden City, ID; three great nieces and a horde of rowdy cousins. She is also survived by her Maryville family, Margaret Nelson, Amee and Brian Wilmes, Keenan Joiner, Dyllan Nelson, Briley Wilmes, Alyxis Beltz, and Anderson James "Sprout" Joiner.
For more information, visit Legacy.com.


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Crossley People
[vimeo_video id="54848338" height="" width="1040"]
[pullquote align="left"]One of the most complicated things I've learned is riding a unicyle… and making people laugh[/pullquote]
Edoardo, artist, juggler, unicyle-rider… a self-described creative freelancer. Inspired by the people he meets and the places he goes, his work changes from one day to the next.
www.edoardonardin.it
What's your job?
Juggler. I started for fun with my twin brother, and then my older brother started doing it too. At the beginning it was just for fun, then it became a job. At first it was a way to pay for my vices during university, and then it became a job. I actually do other things too, like paintings, photos…there is also a visual part to my work. I describe myself as a creative freelancer. Today I'll do performance, tomorrow I'll make a painting, and the day after that I'll invent something for someone else.
How do you start your day?
Breakfast.
What's the last thing you do every day?
I add a drawing to this wardrobe, which is like a diary. Every day I add an object, a memory, a person…so I draw something, I read and then go to sleep. You guys can't see him, but right now I'm drawing the cameraman.
Which is the hardest discipline that you've learned?
As far the juggling, acrobatics and the circus part of my work, I think one of the most complicated things I've learned is to ride a unicycle. It's not an immediate skill, it's tough, and you have to be really determined to learn. And another thing is making people laugh…I think that's one of the hardest things to do. As for everything else, I don't think it's difficult. If you want to learn, you can learn anything, with a bit of determination.
Definitely Pop Art, Andy Warhol. For now I do a lot of different things, and I need to do them all. One thing influences another. My aesthetic, my taste, I think I have my taste, my experience because of everything that I see and everything that I do. I feel complete by doing all of these things.
If we opened your fridge right now, what would we find?
A bottle of beer, a bit of cheese, some salad, and some fruit.
What kind of music do you like?
I think that adolescence is a fundamental moment for anyone. I listened to punk, ska punk. Pulp? I don't know who they are.
What place would you say has influenced you most?
I really like traveling, and I've been lucky enough to travel quite a lot. This year I've been to Japan. I've also been to Africa, to America, New York. It's hard to say because all of these places are different and they each fascinated me for different reasons.
Shirt or t-shirt?
During the day, a t-shirt, in the evening, a shirt.
Bye, thanks for listening. And if by chance you're in the area, ring the bell, and who knows, maybe you'll end up on my wardrobe too.
Crossley People	8 years, 11 months ago 0
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GSA common acquisition platform in progress, but no firm timeline set
The General Services Administration's launch of a common acquisition platform to reduce wasteful practices in government procurement is well into its beta stage, but GSA officials leading the program's rollout said there's no grand and official unveiling scheduled.
Kevin Youel Page, GSA's assistant commissioner for integrated award environment and common acquisition, said Monday at ACT-IAC's Executive Leadership Conference though his office is currently hard at work developing several layers of the platform, "I don't have firm timelines for when we're going to have ubiquitous, end-to-end user experience and contracting."
Under GSA's common acquisition platform, procurement officers specializing in, say, cloud computing would act as category managers, helping others who have less experiences in that area. (Credit: iStockphoto.com)
GSA's common acquisition platform is a move toward a more efficient procurement style based on category management. Instead of asking procurement officers to become subject matter experts on anything their agency needs to buy, this system suggests that, somewhere out there in the government, somebody is an expert at procuring a given item.
Speaking on the panel with Youel Page, Tom Sharpe, GSA's Federal Acquisition Service commissioner, said a common acquisition platform can relieve some of the stress and difficulty related to tightening budgets, a time when "flat is the new up for funding."
"Right now, there are 61,000 people working in the federal government doing acquisitions on behalf of federal agencies, and many of them are working in a bubble without knowledge of what their counterparts across the government are doing," Sharpe said. "They're very clearly not acting as one. We're operating like 500 different small businesses suboptimizing the purchasing power of the federal government." He went on to call it "an incredible waste of human capital and money."
The solution? "It's as simple as acting as one," Sharpe said.
"This is really the federal challenge," Youel Page said. "How do we get the 61,000 people out there who individually are doing really smart things to provide their view and get them to take advantage of each other's wisdom?" Somewhere deep in an agency, he said there's likely someone already doing the exact thing other procurement officers need to get done. "There's somebody splitting an atom on how to buy cloud services. You just need to find those people who know what they're doing and bring them into light," he said.
Those atom-splitters, as Youel Page called them, are vital to the common acquisition platform, and they'll act as category managers, helping those less experienced with a certain topic navigate and procure it.
But interagency sharing may be easier in theory than in practice. Mary Davie, GSA's assistant commissioner for integrated technology services, said category management won't work unless agencies are unbiased or agnostic. Even GSA must be open to the idea that other agencies may have a better acquisition solutions for certain things, and those will be featured on the common acquisition platform as well an offering as well.
So far in its beta, the platform has three "hallways," what GSA's calls the different categories, for IT software, IT hardware and office supplies. But over the next year, said Laura Stanton, a director of the common acquisition platform, "what we're going to be putting in this acquisition platform are a number of other categories; this tool is going to be expanding."
Still, Stanton said there's no set time period for the launch, but that's because they want to do it the right way, she said.
"What you will see is a slow and daily update to the platform," she said. "So as we find the appropriate pieces and we integrate them in, we're not going to suddenly pull back the curtain. We want to make sure we do it the right way."
Agencies, big data, Common Acquisition Platform, data analytics, Departments, General Services Administration (GSA), Government IT News, Information sharing environment, Innovation, Kevin Youel Page, Management & Budget, Mary Davie, Sequestration, shared services, Tech, Tom Sharpe


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The Case of the Vanishing Justice Department E-Mail
Posted by Craig in Justice Department, Obama, Politics, torture
interrogation techniques, John Yoo, Justice Department, missing e-mail
The legacy of Rose Mary Woods is alive and well at the Justice Department:
"Large batches of e-mail records from the Justice Department lawyers who worked on the 2002 legal opinions justifying the Bush administration's brutal interrogation techniques are missing, and the Justice Department told lawmakers Friday that it would try to trace the disappearance."
And in a stroke of what I'm sure is pure coincidence, what's missing just happens to be from a crucial time period:
"The Justice Department's Office of Professional Responsibility…pushed to get access to a range of e-mail records and other internal documents from the Justice Department to aid in its investigation.
But it discovered that many e-mail messages to and from John Yoo, who wrote the bulk of the legal opinions for the Justice Department's Office of Legal Counsel, were missing…Also deleted were a month's worth of e-mail files from the summer of 2002 for Patrick Philbin, another Justice Department lawyer who worked on the interrogation opinions. Those missing e-mail messages came during a period when two of the critical interrogation memos were being prepared."
But never fear, the Obama DoJ is on the case. Kinda, sorta, maybe:
"Gary Grindler, the acting deputy attorney general who represented the Justice Department at Friday's hearing, said he did not think there was "anything nefarious" about the deletion of the e-mail messages, but he could not explain what happened to them.
He said he had directed administrative personnel at the Justice Department to review the situation and determine whether there were problems in the department's system for automatically archiving internal documents. He said the review would also seek to recover the missing e-mail messages if possible."
Why do I get the feeling that in the spirit of the cover-up looking forward, not back, recovering the missing messages will be found impossible. Just a hunch.


This article presents lists of the literary events and publications in 1823.
February 7 – The Bannatyne Club is inaugurated by Sir Walter Scott and others as a text publication society to print by subscription rare texts relating to the history, literature and traditions of Scotland.
October – Thomas De Quincey's classic essay On the Knocking at the Gate in Macbeth appears in this month's issue of The London Magazine.
May 23 – Russian writer Alexander Pushkin begins work on his verse novel Eugene Onegin.
December – Samuel Taylor Coleridge, suffering from opium addiction, takes up residence at No. 3, The Grove, Highgate, a house owned by Dr James Gillman.
December 23 – Clement Clarke Moore's poem, A Visit from St. Nicholas is published anonymously in the Troy, New York, Sentinel, and introduces the character named "Santa Claus".
The discovery of the First Quarto edition of 1603 of William Shakespeare's Hamlet (a so-called "bad quarto"), by Sir Henry Bunbury, causes excitement among the scholarly community.
London actor Edmund Kean reinstates the original tragic ending of Shakespeare's play King Lear, not generally used since 1681, in performance, although it is not well received.
The London publisher C. Baldwyn brings out the first English translation of Grimms' Fairy Tales as German Popular Stories. Translated from the Kinder und Haus Märchen collected by MM. Grimm from Oral Tradition. The anonymous translations were made by two lawyers, Edgar Taylor and David Jardine, and the illustrations by George Cruikshank, who is beginning to focus on this medium.
^ Hasty, Olga Peters (1999). Pushkin's Tatiana. University of Wisconsin Press. p. 14.
^ McVeigh, Daniel (2005). "ESTESE and Doblado: Coleridge, Blanco White, and the Church of Rome". In Marshall, Donald G. (ed.). The Force of Tradition. Rowman & Littlefield. p. 165.
^ William Shakespeare (April 2001). Hamlet. Classic Books Company. p. 13. ISBN 978-0-7426-5285-9.
^ Bloom, Harold (2008). Bloom's Shakespeare Through the Ages: King Lear. Infobase Publishing. p. 53.
^ Chapelle, Niamh (2001). "The Translator's Tale" (PDF). p. 72. Retrieved 2013-11-22.
^ James Fenimore Cooper (1852). The Pioneers: Or, the Sources of the Susquehanna. Stringer and Townsend. p. 8.
^ Tenney, Charles R.; Lewis, Leo Rich (1898). Church Harmonies New and Old: A Book of Spiritual Song for Christian Worshippers (Public domain ed.). Universalist Publishing House. pp. 393–.
^ Hill, Thomas Edie (1891). Hill's Album of Biography and Art: Containing Portraits and Pen-sketches of Many Persons who Have Been and are Prominent as Religionists, Military Heroes, Inventors, Financiers, Scientists, Explorers, Writers, Physicians, Actors, Lawyers, Musicians, Artists, Poets, Sovereigns, Humorists, Orators and Statesmen, Together with Chapters Relating to History, Science, and Important Work in which Prominent People Have Been Engaged at Various Periods of Time (Public domain ed.). Danks. pp. 270–.
^ Stone, Herbert Stuart (1893). First Editions of American Authors: A Manual for Book-lovers (Public domain ed.). Stone & Kimball. pp. 76–.
^ The Annual Register 1823.


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It is no secret that we can design what you want and need. However, we also take great pleasure in knowing that what we offer provides our customers with optimum efficiency. Our technicians test your system over and over again to ensure that it lives up to the expectations of our customers. Our technicians provide the most precise technology to achieve their overall goals. Building a computer is no problem but many service providers fall short of being able to provide a system that offers efficiency. Our technicians do it all from designing the framework to controlling conveyance. While we leave it up to our customers to tell us what they are looking for, we are also happy to offer our expertise by making recommendations based on what our customers want.
Our technicians at Computer Repair Voorhees will check your system for strength and bottleneck problems. We have a list of tests that every pc must pass before we release it into the hands of our customers. You only get the best from our service technicians and this is why they adhere to strict testing procedures. The benchmarks they use to identify any problems that you might experience with memory, the processor, graphics cards, power issues or storage problems. If a problem is detected, it is immediately resolved and retested by another technician. When you want the best, you'll find it when you turn to our qualified computer repair technicians in Voorhees, NJ.
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text:
package com.andela.voluminotesapp.adapters.views;

import android.support.v7.widget.CardView;
import android.support.v7.widget.RecyclerView;
import android.view.View;
import android.widget.TextView;

import com.andela.voluminotesapp.R;

public class MasterViewHolder extends RecyclerView.ViewHolder {
    public TextView text, date;
    public CardView cardView;

    public MasterViewHolder(View itemView) {
        super(itemView);
        text = (TextView) itemView.findViewById(R.id.text);
        date = (TextView) itemView.findViewById(R.id.date);
        cardView = (CardView) itemView.findViewById(R.id.item);
    }
}

redpajama_set_name: RedPajamaGithub


Conjunctival melanoma arises when melanocytes in the conjunctival epithelium become malignant.
These malignant melanocytes can multiply and spread within the epithelium, forming 'malignant melanocytic intra-epithelial neoplasia' or 'melanoma in situ'.
Melanoma in situ can break through into the tissues beneath the epithelium to form an invasive melanoma.
de novo (i.e., 'out of the blue').
from a pre-existing nevus or 'mole'.
Conjunctival melanoma is more common in individuals with a fair complexion with a tendency to freckling and sunburn.
the deeper tissues beneath the epithelium.
the orbit around the eye.
through the blood vessels to other parts of the body (i.e., 'hematogenous metastasis').
Located in the caruncle (i.e., the fleshy lump near the inner corner of the eye).
Involving the tarsal conjunctiva (i.e., on the inside of the eyelids).
Any nodules of melanoma are treated by surgical excision. This is done under local or general anesthesia, depending on the extent of the tumor. If possible, the surgical wound is closed by suturing the conjunctival edges together (i.e., 'by primary intention'). If this is not possible, then an amniotic membrane graft may be necessary.
Many surgeons administer cryotherapy to the wound edges to reduce the chances of tumor recurrence. At UCSF, we prefer to administer topical chemotherapy with mitomycin C if the tumor shows signs of spreading or seeding superficially in the epithelium. This topical chemotherapy can interfere with wound healing so that the treatment is delayed until healing is complete (i.e., more than 2 weeks post-operatively).
If the tumor shows deep invasion, some (including ocular oncologists at UCSF) advocate adjunctive radiotherapy to ensure that the entire tumor has been eradicated. This can be administered with a radioactive plaque or proton beam. Unlike radiotherapy of intraocular tumors, conjunctival radiotherapy is performed without opening the conjunctiva. If a plaque is used, this is sutured to the ocular surface and left in place for about a day. If proton beam radiotherapy is administered, this is done without the use of tantalum markers.
Lifelong surveillance is required after completion of the treatment so that any tumor recurrence is treated promptly.


text:
\section{Experiments details}
\subsection{Estimating $U_k^s$} \label{app:details_uk}
Estimations of the average sample low-resolution pairwise distance $U_k^s$ \eqref{eq:uk} displayed in Figure ~\ref{fig:uk} are computed with Monte-Carlo sampling.
In practice, $50$ different full latent codes $\bm{z}^{(i)}$ are sampled from the prior:
\begin{equation}
    \bm{z}^{(i)} \sim \pt{\bm{z}}.
\end{equation}
For each latent code $\bm{z}^{(i)}$ and each number of fixed groups $k$, $5$ different images are sampled
\begin{equation}
\bm{x}^{(i,k,l)} \sim \pt{\bm{x}|\z_{<k}^{(i)}}.
\end{equation}
The average sample pairwise distance estimation is then computed as:
\begin{equation}
    \hat{U_k^s} = \sum_{i=1}^{50} \sum_{1\leq l < m \leq 5}\rmse{H_s\bm{x}^{(i,k,l)}}{H_s\bm{x}^{(i,k,m)}},
\end{equation}
where $H_s$ is the downsampling operator associated to the downscaling factor $s$.

\section{Connection between the training criterion and the model conditional log-likelihood} \label{sec:applb}
In this part we detail the result about the lower-bound on the model conditional log-likelihood given in proposition \ref{prop:lb},
and we link the introduced lower-bound to the training criterion.
The conditional log-likelihood of the super-resolution model is defined as:
\begin{equation}
    \label{eq:condll}
    \E{\pd{\bm{x}, \bm{y}}}{\log \psr{\bm{x}|\bm{y}}}.
\end{equation}

\begin{propn}[\ref{prop:lb}]
    The conditional log-likelihood of the super-resolution model on a joint distribution $\pd{\bm{x},\bm{y}}$ is lower-bounded by
   \begin{align}
       \label{eq:condlb}
       \mathcal{O}(\psi)
       & =
       \mathbb{E}_{\pd{\bm{x}, \bm{y}}}\E{\qp{\bm{z}_{<k}| \bm{x}}}
       {
           \log \frac{\pt{\bm{x}|\bm{z}_{<k}}\qh{\bm{z}_{<k}|\bm{y}}}{\qp{\bm{z}_{<k}|\bm{x}}}
       } \\
       & \leq \E{\pd{\bm{x}, \bm{y}}}{\log \psr{\bm{x}|\bm{y}}}.
   \end{align}
\end{propn}
\begin{proof}
It is shown in \cite{harvey2022conditional} that, for a conditional model writen as:
\begin{equation}
 p_{cond}(\bm{x}|\bm{y}) := \E{\qp{\bm{z}|\bm{y}}}{\pt{\bm{x}|\bm{z}}},
\end{equation}
the conditional log-likelihood on a paired data distribution $\pd{\bm{x}, \bm{y}}$ is lower-bounded as\footnote[1]{In \cite{harvey2022conditional}, the lower bound is also defined as a function of the VAE encoder and decoder $\mathcal{O}(\theta, \phi, \psi)$. We omit the dependance on $\theta$ and $\phi$ since we keep those parameters constant.}:
\begin{align}
    \label{eq:condlbharvey}
    \mathcal{O}(\psi)
    & =
    \mathbb{E}_{\pd{\bm{x}, \bm{y}}}\E{\qp{\bm{z}| \bm{x}}}
    {
        \log \frac{\pt{\bm{x}|\bm{z}}\qh{\bm{z}|\bm{y}}}{\qp{\bm{z}|\bm{x}}}
    } \\
    & \leq \E{\pd{\bm{x}, \bm{y}}}{\log \psr{\bm{x}|\bm{y}}}.
\end{align}
Applying relation \eqref{eq:condlbharvey} to the truncated VAE $\pt{\bm{x}|\z_{<k}}$, $\qh{\z_{<k}|\bm{y}}$ and the truncated latent restoration model $\psr{\bm{x}|\bm{y}}$ \eqref{eq:psr}, we then have:
\begin{align}
\mathcal{O}(\psi)
& =
\mathbb{E}_{\pd{\bm{x}, \bm{y}}}\E{\qp{\bm{z}_{<k}| \bm{x}}}
{
    \log \frac{\pt{\bm{x}|\bm{z}_{<k}}\qh{\bm{z}_{<k}|\bm{y}}}{\qp{\bm{z}_{<k}|\bm{x}}}
} \\
& \leq \E{\pd{\bm{x}, \bm{y}}}{\log \psr{\bm{x}|\bm{y}}}.
\end{align}
\end{proof}
The lower bound can be rewritten as:

\begin{align}
    \mathcal{O}(\psi)  & = \mathbb{E}_{\pd{\bm{x}, \bm{y}}}\E{\qp{\bm{z}_{<k}| \bm{x}}}
    {
        \log \pt{\bm{x}|\bm{z}_{<k}}
    } \\
    & +
    \mathbb{E}_{\pd{\bm{x}, \bm{y}}}\E{\qp{\bm{z}_{<k}| \bm{x}}}
    {
        \log \frac{\qh{\bm{z}_{<k}|\bm{y}}}{\qp{\bm{z}_{<k}|\bm{x}}}
    } \\
    & = C - \mathcal{L}(\psi).
\end{align}
Therefore, for fixed $\theta$ and $\phi$, minimizing $\mathcal{L}(\psi)$ amounts to maximizing the lower bound $\mathcal{O}(\psi)$ in $\psi$.

\section{Expected consistency of the super-resolution model}\label{app:proofP1}
In this section we demonstrate Proposition \ref{prop:expcons2} on the expected consistency of the super-resolution model. To that end, we first give an intermediate result concerning optimal VAEs. %

\begin{proposition} [Optimal VAE]%
The ELBO loss of a VAE \eqref{eq:elbo} can be written as:
\begin{equation}
    \label{eq:elbo2}
    \mathcal{L}_{elbo}(\theta, \phi) = -\mathcal{H}\mleft(\pd{\bm{x}}\mright) - \KL{\pd{\bm{x}}\qp{\bm{z}|\bm{x}}}{\pt{\bm{z}}\pt{\bm{x}|\bm{z}}},
\end{equation}
where $\mathcal{H}\mleft(\pd{\bm{x}}\mright)$ is the entropy of the data distribution.
\end{proposition}
\begin{proof}
This result is demonstrated in appendix B.1 of \cite{harvey2022conditional}.
\end{proof}
The formulation \eqref{eq:elbo2} indicates that maximizing the ELBO loss amounts to reducing the KL divergence from $\pd{\bm{x}}\qp{\bm{z}|\bm{x}}$  to $\pt{\bm{z}, \bm{x}}$.

\subsection{Optimal low-resolution encoder}
We remind the reader that we denote
\begin{equation}
\tag{\ref{eq:r}}
r(\bm{z}_{<k}, \bm{x}, \bm{y}):= \pd{\bm{x}, \bm{y}}\qp{\bm{z}_{<k}|\bm{x}}
\end{equation}
 the joint distribution of high-resolution and low-resolution image pairs $(\bm{x},\bm{y})$, and their latent variable $\bm{z}$ given by the high-resolution encoder, and $r(\bm{z}_{<k}|\bm{y})$ the corresponding conditional distribution.
We now recall the technical assumptions made in section \ref{ssec:expcons}.

 \begin{assumn}[\ref{assum:1}] %
    There exists $\psi \in \Psi$ which satisfies
    $r(\bm{z}_{<k}|\bm{y})
    =\qh{\bm{z}_{<k}|\bm{y}}$ for all $\bm{y}$ in the support of $\pd{\bm{y}}$.
 \end{assumn}

 \begin{assumn}[\ref{assum:2}] %
    The low-resolution encoder parameters $\psi$ are minimizers of the training criterion \eqref{eq:loss}:
    \begin{equation}
    \psi \in \arg\min_{\tilde{\psi}} \mathcal{L}(\tilde{\psi})
    \tag{\ref{eq:a2}}
    \end{equation}
 \end{assumn}

 \begin{assumn}[\ref{assum:vae}] %
    The VAE encoder $\qp{\bm{x}|\bm{z}}$ and generative model $\pt{\bm{x}, \bm{z}}$ have enough capacity and are trained well enough so that $\phi$ and $\theta$ reaches the upper bound $-\mathcal{H}\mleft(\pd{\bm{x}}\mright)$ of the ELBO loss \eqref{eq:elbo2}:
    \begin{equation}
        \KL{\pd{\bm{x}}\qp{\bm{z}|\bm{x}}}{\pt{\bm{z}}\pt{\bm{x}|\bm{z}}} = 0.
    \end{equation}
\end{assumn}

In the next proposition, we give the value of the optimal low-resolution encoder.
\begin{proposition}
\label{prop:opt_lrenc}
Under assumptions \ref{assum:1} and \ref{assum:2}, we have:
\begin{align}
\qh{\bm{z}_{<k}|\bm{y}} = r(\bm{z}_{<k}|\bm{y})
\end{align}
for all $\bm{y}$ in the support of $\pd{\bm{y}}$.
\end{proposition}

\begin{proof}%
    The training criterion  \eqref{eq:loss} can be written as:
    \begin{align}
        \mathcal{L}(\psi) & = \E{\pd{\bm{x}, \bm{y}}}{ \E{\qp{\bm{z}_{<k}|\bm{x}}}{\log \frac{\qp{\bm{z}_{<k}|\bm{x}}}{\qh{\bm{z}_{<k}|\bm{y}}}}} \\
        & = \E{\pd{\bm{x}, \bm{y}}}
        {
            \E{\qp{\bm{z}_{<k}|\bm{x}}}{\log \frac{\qp{\bm{z}_{<k}|\bm{x}}}{r(\bm{z}_{<k}|\bm{y})}}
            +
            \E{\qp{\bm{z}_{<k}|\bm{x}}}{\log \frac{r(\bm{z}_{<k}|\bm{y})}{\qh{\bm{z}_{<k}|\bm{y}}}
        }
        }\\
        & = \E{\pd{\bm{x}, \bm{y}}}{ \E{\qp{\bm{z}_{<k}|\bm{x}}}
        {
            \log \frac{\qp{\bm{z}_{<k}|\bm{x}}}{r(\bm{z}_{<k}|\bm{y})}
        } }
        +
        \E{\pd{\bm{y}}}
        {
            \KL{r(\bm{z}_{<k}|\bm{y})}{\qh{\bm{z}_{<k}|\bm{y}}}
        }.
        \label{eq:decomploss}
    \end{align}
    Thus $\mathcal{L}(\psi)$ is lower-bounded by the first term of the right handside of \eqref{eq:decomploss}. If the encoder has enough capacity (\ref{assum:1}) and by non-negativity of the KL-divergence, the lower bound is reached (\ref{assum:2}) if and only if the second term of the right handside of  \eqref{eq:decomploss} is zero, or equivalently $r(\bm{z}_{<k}|\bm{y})
    =\qh{\bm{z}_{<k}|\bm{y}}$ for all $\bm{y}$ in the support of $\pd{\bm{y}}$.
\end{proof}

Proposition \ref{prop:opt_lrenc} states that, if the low-resolution encoder $\qh{\z_{<k}|\bm{y}}$ has enough capacity and is trained so that it minimizes the training criterion \eqref{eq:loss}, it matches the intractable distribution $r(\bm{z}_{<k}|\bm{y})$ for all images of the training distribution.

With a slight abuse of notation, let us now denote:
\begin{equation}
    \label{eq:pt}
    \pt{\bm{z}, \bm{x}, \bm{y}} = \pt{\bm{z}}\pt{\bm{x}|\bm{z}}p(\bm{y}|\bm{x})
\end{equation}
the VAE model distribution of the latent variables $\bm{z}$ and the generated high-resolution images $\bm{x}$, combined with their low-resolution counterpart $\bm{y}$ given by the degradation model \eqref{eq:forward}.
In the next proposition we show that, under additional hypothesis on the pretrained VAE, the low-resolution encoder $\qh{\z_{<k}|\bm{y}}$  matches the conditional $\pt{\z_{<k}|\bm{y}}$ of the model distribution $\eqref{eq:pt}$.

\begin{proposition}
    \label{prop:opt_vae}
    Under assumptions \ref{assum:1}, \ref{assum:2} and \ref{assum:vae},
    we have
    \begin{equation}
       \qh{\bm{z}_{<k}|\bm{y}} =  \pt{\bm{z}_{<k}|\bm{y}}
    \end{equation}
    for all $\bm{y}$ in the support of $\pd{\bm{y}}$.
\end{proposition}

\begin{proof}%
    Refering to the definition of $r(\bm{x}, \z_{<k}, \bm{y})$ \eqref{eq:r} and $p_{\theta}(\z_{<k}, \bm{x}, \bm{y})$ \eqref{eq:pt}, we have, from assumption \ref{assum:vae}:
    \begin{align}
        \KL{r(\bm{z}, \bm{x})}{p_{\theta}(\bm{z}, \bm{x})} = 0 &\implies r(\bm{z}, \bm{x}) = p_{\theta}(\bm{z}, \bm{x}) \\
        &\implies r(\bm{z}, \bm{x})\pd{\bm{y}|\bm{x}} = p_{\theta}(\bm{z}, \bm{x})\pd{\bm{y}|\bm{x}}\\
        &\implies r(\bm{z}, \bm{x}, \bm{y}) = p_{\theta}(\bm{z}, \bm{x}, \bm{y}) \\
        &\implies r(\bm{z}| \bm{y}) = p_{\theta}(\bm{z}| \bm{y}).
    \end{align}
    Furthermore, using proposition \ref{prop:opt_lrenc}, assumptions \ref{assum:1} and \ref{assum:2} imply that $r(\bm{z}_{<k}|\bm{y})
    =\qh{\bm{z}_{<k}|\bm{y}}$ for all $\bm{y}$ in the support of $\pd{\bm{y}}$.
    Thus, we have:
    \begin{align}
        r(\bm{z}_{<k}|\bm{y}) & =\qh{\bm{z}_{<k}|\bm{y}} \\
        & = p_{\theta}(\bm{z}| \bm{y}),
    \end{align}
    for all $\bm{y}$ in the support of $\pd{\bm{y}}$.
\end{proof}

Proposition \ref{prop:opt_vae} shows that, if the VAE encoder and decoder and the low-resolution encoder have enough capacity and are trained well enough to optimize their respective training criterion, the low-resolution encoder matches the intractable conditional $\pt{\z_{<k}|\bm{y}}$ of the VAE model distribution~\eqref{eq:pt}.

\subsection{Expected consistency of the super-resolution model}

In the next proposition, we establish a general formula to estimate of the expected consistency error.
\begin{proposition}
    \label{prop:expcons}
    Under assumptions \ref{assum:1} and \ref{assum:2}, we have:
    \begin{equation}
        \label{eq:cons1}
        CE(k) = \mathbb{E}_{\pd{\bm{x}}}
        \mathbb{E}_{\qp{\z_{<k}|\bm{x}}}
        \mathbb{E}_{\pt{\bm{\tilde{x}}|\z_{<k}}} \left[
            \rmse{H_s\bm{\tilde{x}}}{H_s\bm{x}}
            \right].
    \end{equation}
\end{proposition}

\begin{proof}%
    Assumptions \ref{assum:1} and \ref{assum:2} imply that $r(\bm{z}_{<k}|\bm{y})
    =\qh{\bm{z}_{<k}|\bm{y}}$ for all $\bm{y}$ in the support of $\pd{\bm{y}}$.
    Notice that, by definition of $r(\z_{<k}, \bm{x}, \bm{y})$ \eqref{eq:r}, the marginals satisfy $r(\bm{y}) = \pd{\bm{y}}$ and $r(\bm{x})=\pd{\bm{x}}$.
    Consequently:
    \begin{align}
        CE(k) &= \mathbb{E}_{\pd{\bm{y}}}
        \mathbb{E}_{r(\bm{z}_{<k}|\bm{y})}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
        \right] \\
        &= \mathbb{E}_{r(\bm{z}_{<k}, \bm{y})}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
        \right] \\
        &=  \mathbb{E}_{r(\bm{\tilde{x}})}
        \mathbb{E}_{r(\bm{z}_{<k}, \bm{y}| \bm{\tilde{x}})}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
        \right] \\
        &= \mathbb{E}_{\pd{\bm{\tilde{x}}}}
        \mathbb{E}_{\pd{\bm{y}|\bm{\tilde{x}}}}
        \mathbb{E}_{\qh{\z_{<k}|\bm{\tilde{x}}}}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
        \right].
    \end{align}
\end{proof}

According to Proposition \ref{prop:opt_lrenc}, the assumption $\qh{\z_{<k}|\bm{y}} = r(\z_{<k}|\bm{y})$ is satisfied when the low-resolution encoder has enough capacity and is trained to optimality. The quantity \eqref{eq:cons1} can be estimated with Monte-Carlo sampling, without using the low-resolution encoder. Thus, Proposition \ref{prop:expcons}  gives us a way to estimate the potential consistency error of a super-resolution model before training the low-resolution encoder.

We can now show Proposition \ref{prop:expcons2}, which states that under the additional hypothesis \ref{assum:vae} on the VAE inference and generative model, the expected consistency error of the super-resolution model can be estimated only as a function of the VAE generative model $\pt{\bm{z}|\bm{x}}$.

\begin{propn}[\ref{prop:expcons2}]
    Under assumptions \ref{assum:1}, \ref{assum:2} and \ref{assum:vae},
    the expected consistency error is:
    \begin{equation}
    CE(k) = \mathbb{E}_{\pt{\z_{<k}}}
    \mathbb{E}_{\pt{\bm{x}|\z_{<k}}}
        \mathbb{E}_{\pt{\bm{\tilde{x}}|\bm{z}_{<k}}} \left[
        \rmse{H_s\bm{\tilde{x}}}{H_s\bm{x}}
        \right].
        \tag{\ref{eq:cons2}}
    \end{equation}
\end{propn}

\begin{proof}%
    First, assumption \ref{assum:vae} implies that the marginals of the model distribution \eqref{eq:pt} match the respective data distributions:
    \begin{align}
        \pt{\bm{x}}&= \pd{\bm{x}}\\ \label{eq:ptpd}
        \pt{\bm{y}}&= \pd{\bm{y}} \\
        \pt{\bm{x}|\bm{y}} &= \pd{\bm{x}|\bm{y}}.
    \end{align}

    Second, from assumptions \ref{assum:1} and \ref{assum:2}, proposition \ref{prop:opt_vae} can be applied, and we have:
    \begin{align}
        \qh{\z_{<k}|\bm{y}} &= \pt{\z_{<k}|\bm{y}} \\
        &= \E{\pt{\bm{\tilde{x}}|\bm{y}}}{\pt{\z_{<k}|\bm{\tilde{x}}, \bm{y}}}\\
        &= \E{\pd{\bm{\tilde{x}}|\bm{y}}}{\pt{\z_{<k}|\bm{\tilde{x}}}}. \label{eq:qh}
    \end{align}

    Thus we get:
    \begin{align}
        CE(k)
        &= \mathbb{E}_{\pd{\bm{y}}}
        \mathbb{E}_{\pt{\bm{z}_{<k}|\bm{y}}}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
            \right]\label{eq:p21} \\
        &= \mathbb{E}_{\pd{\bm{y}}}
        \mathbb{E}_{\pd{\bm{\tilde{x}}|\bm{y}}}
        \mathbb{E}_{\pt{\bm{z}_{<k}|\bm{\tilde{x}}}}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
            \right]\label{eq:p22} \\
        &= \mathbb{E}_{\pd{\bm{\tilde{x}}}}
        \mathbb{E}_{\pd{\bm{y}|\bm{\tilde{x}}}}
        \mathbb{E}_{\pt{\bm{z}_{<k}|\bm{\tilde{x}}}}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
            \right] \label{eq:p23} \\
        &= \mathbb{E}_{\pt{\bm{\tilde{x}}}}
        \mathbb{E}_{\pt{\bm{z}_{<k}|\bm{\tilde{x}}}}
        \mathbb{E}_{\pd{\bm{y}|\bm{\tilde{x}}}}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
            \right] \label{eq:p24} \\
        &= \mathbb{E}_{\pt{\bm{z}_{<k}}}
        \mathbb{E}_{\pt{\bm{\tilde{x}}|\bm{z}_{<k}}}
        \mathbb{E}_{\pd{\bm{y}|\bm{\tilde{x}}}}
        \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
            \rmse{H_s\bm{x}}{\bm{y}}
            \right], \label{eq:p25}
    \end{align}

where \eqref{eq:p22} comes from relation \eqref{eq:qh}, and \eqref{eq:p24} comes from relation \eqref{eq:ptpd}.
Therefore, using the fact that $\pd{\bm{y}|\bm{\tilde{x}}} = \delta_{\{\bm{y}=H_s\bm{\tilde{x}}\}}$, we obtain:
\begin{align}
    CE(k)
        &= \mathbb{E}_{\pt{\z_{<k}}}
        \mathbb{E}_{\pt{\bm{\tilde{x}}|\z_{<k}}}
            \mathbb{E}_{\pt{x|\bm{z}_{<k}}} \left[
                \rmse{H_s\bm{\tilde{x}}}{H_s\bm{x}}
            \right],
\end{align}
\end{proof}

Proposition \ref{prop:expcons2} show that, under  adequate assumptions,
the expected consistency of the super-resolution model~\eqref{eq:cons2} only depends on the generative model $\pt{\bm{x}, \bm{z}}$.
It follows that it can be estimated before the training of the low-resolution encoder.
Notice that the quantity \eqref{eq:cons2} is equal to the low-resolution consistency $U_k^s$ \eqref{eq:uk}.

\subsection{Training criterion of the low-resolution encoder}
We introduce a low-resolution encoder $\qh{\bm{z}_{<k}|\bm{y}}$, which is a neural network parametrized by $\psi \in \Psi$, where $\Psi$ is the parameter space of the network. Considering a joint training distribution of clean-degraded image pairs $\pd{\bm{x},\bm{y}}$, we can show that the conditional log-likelihood of the super-resolution model  has a lower-bound.

\begin{proposition}
    \label{prop:lb}
 The conditional log-likelihood of the super-resolution model on a joint distribution $\pd{\bm{x},\bm{y}}$ is lower-bounded by
\begin{align}
    \tag{\ref{eq:condlb}}
    \mathcal{O}(\psi)
    & =
    \mathbb{E}_{\pd{\bm{x}, \bm{y}}}\E{\qp{\bm{z}_{<k}| \bm{x}}}
    {
        \log \frac{\pt{\bm{x}|\bm{z}_{<k}}\qh{\bm{z}_{<k}|\bm{y}}}{\qp{\bm{z}_{<k}|\bm{x}}}
    } \\
    & \leq \E{\pd{\bm{x}, \bm{y}}}{\log \psr{\bm{x}|\bm{y}}}.
\end{align}
\end{proposition}
\begin{proof}
This result comes from applying the lower-bound introduced in \cite{harvey2022conditional} to the truncated VAE $\qp{\z_{<k}|\bm{x}}$, $\pt{\bm{x}|\z_{<k}}$ (a detailed proof is given in appendix \ref{sec:applb}).
\end{proof}

Furthermore, as also detailed in appendix~\ref{sec:applb}, maximizing the lower-bound $ \mathcal{O}(\psi)$ in relation \eqref{eq:condlb} is equivalent to minimizing the criterion:
\begin{equation}
    \label{eq:loss}
    \mathcal{L}(\psi) = \E{\pd{\bm{x}, \bm{y}}}{\KL{\qp{\bm{z}_{<k}|\bm{x}}}{\qh{\bm{z}_{<k}|\bm{y}}}}.
\end{equation}
 In other words, to maximize the lower-bound $ \mathcal{O}(\psi) $, the low-resolution encoder has to minimize the $KL$ divergence between the LR and the HR encoder on LR-HR images pairs.
We set $\mathcal{L}(\psi)$ to be the training criterion of the low-resolution encoder.

\subsection{Expected consistency of the super-resolution model}
\label{ssec:expcons}
In this part, we derive a criterion to select the number of latent groups $k$ to be predicted by the low-resolution encoder, based on the expected consistency error of the super-resolution model. Without loss of generality, we measure the consistency error between a high-resolution and a low-resolution image as the root mean square error between the downsampled HR image and the LR image $\rmse{H_s\bm{x}}{\bm{y}}$.
 We define the consistency error of the super-resolution model as

\begin{equation}
    \label{eq:consistency}
    CE(k) = \mathbb{E}_{\pd{\bm{y}}}
    \mathbb{E}_{\psr{\bm{x}|\bm{y}}} \left[
        \rmse{H_s\bm{x}}{\bm{y}}
    \right].
\end{equation}

We show in the next proposition that the consistency error of the super-resolution model \eqref{eq:consistency} can be predicted without using the low-resolution encoder, when the low-resolution encoder is trained with the criterion \eqref{eq:loss}.
First, we introduce
\begin{equation}
\label{eq:r}
r(\bm{z}_{<k}, \bm{x}, \bm{y}):= \pd{\bm{x}, \bm{y}}\qp{\bm{z}_{<k}|\bm{x}},
\end{equation}
 the joint distribution of high-resolution and low-resolution image pairs $(\bm{x},\bm{y})$, and their latent variable $\bm{z}$ given by the high-resolution encoder, and $r(\bm{z}_{<k}|\bm{y})$ the corresponding conditional distribution.
We also consider the following assumptions:

\begin{assum}%
    \label{assum:1}
    There exists $\psi \in \Psi$ which satisfies
    $r(\bm{z}_{<k}|\bm{y})
    =\qh{\bm{z}_{<k}|\bm{y}}$ for all $\bm{y}$ in the support of $\pd{\bm{y}}$.
 \end{assum}

 \begin{assum}%
    \label{assum:2}
    The low-resolution encoder parameters $\psi$ are minimizers of the training criterion \eqref{eq:loss}:
    \begin{equation}
        \label{eq:a2}
    \psi \in \arg\min_{\tilde{\psi}} \mathcal{L}(\tilde{\psi}).
    \end{equation}
 \end{assum}

 \begin{assum} %
    \label{assum:vae}
    The VAE encoder $\qp{\bm{x}|\bm{z}}$ and generative model $\pt{\bm{x}, \bm{z}}$ have enough capacity and are trained well enough so that $\phi$ and $\theta$ reaches the upper bound of the ELBO loss \eqref{eq:elbo}.
\end{assum}

Assumption~\ref{assum:1} is met if the low-resolution encoder has enough capacity while assumption~\ref{assum:2} is met if the low-resolution encoder is trained well. In the next proposition, we show that the expected consistency of the super-resolution model can be expressed only as a function of the generative model $\pt{\bm{x}, \bm{z}}$.
\begin{proposition}[Proof in Appendix \ref{app:proofP1}]
    \label{prop:expcons2}
Under assumptions \ref{assum:1}, \ref{assum:2} and \ref{assum:vae},
 the expected consistency error is equal to the average low-resolution pairwise distance $U_k^s$ \eqref{eq:uk}:
\begin{equation}
    \label{eq:cons2}
CE(k) = \mathbb{E}_{\pt{\z_{<k}}}
\mathbb{E}_{\pt{\bm{x}|\z_{<k}}}
    \mathbb{E}_{\pt{\bm{\tilde{x}}|\bm{z}_{<k}}} \left[
    \rmse{H_s\bm{\tilde{x}}}{H_s\bm{x}}
    \right]
    = U_k^s.
\end{equation}
\end{proposition}
Proposition~\ref{prop:expcons2} shows that, if a low-resolution encoder $\qh{\z_{<k}|\bm{y}}$ has enough capacity and is trained perfectly, it is possible to estimate the expected consistency error of a super resolution model relying on $\qh{\z_{<k}|\bm{y}}$ without actually using the low-resolution encoder. It implies that $CE(k)$ can be estimated before training the low-resolution encoder, using relation \eqref{eq:cons2}. Therefore, the formulation \eqref{eq:cons2} can be used as a criterion to select the number of latent groups $k$ to be predicted by the low-resolution encoder, as a function of the desired consistency. Furthermore, the expected consistency as defined in~\eqref{eq:cons2} is equal to the average low-resolution pairwise distance of the conditional generative model $U_k^s$ \eqref{eq:uk}, displayed in Figure~\ref{fig:uk}.

\subsection{Low-resolution encoder architecture}

The low-resolution encoder architecture is built similarly to the VD-VAE\xspace encoder, but it contains a reduced number of blocks due to the smaller number of latent variable groups to predict.
Specifically, the low-resolution encoder is composed of a deterministic bottom-up path that extracts different levels of representation, and a top-down path that sequentially infers each latent group $\bm{z}_{l}$, using the representations extracted by the bottom-up path. The bottom-up path is composed of simple residual blocks, while the top-down path is composed of residual top-down blocks \cite{kingma2016improved}. Both residual blocks and residual top-down blocks follow the same design as in VD-VAE\xspace.
Furthermore, following a common practice in hierarchical VAE design \cite{LVAE, kingma2016improved, child2021deep, vahdat2020nvae}, the top-down path of the low-resolution encoder shares its parameters with VD-VAE\xspace generative model, as described in Figure \ref{fig:vdvae_sr}. Only the parameters of the low-resolution encoder (in red in Figure \ref{fig:vdvae_sr}) are trained, while the shared parameters (in blue in Figure \ref{fig:vdvae_sr}) are set to the value of the corresponding parameters in the pretrained VD-VAE\xspace generative model, and remain frozen during training.

\begin{figure}
    \begin{subfigure}[b]{1\linewidth}
        \centering
        \includegraphics[scale=0.8]{figures/vdvae-w-lrenc-new.pdf}
    \caption{VDVAE architecture with the low-resolution encoder}
    \label{fig:vdvae_lrenc}
    \end{subfigure}
    \begin{subfigure}[b]{1\linewidth}
        \centering
        \includegraphics[scale=0.6]{figures/td-block-w-lrenc-new.pdf}
        \caption{Top-down block}
        \label{fig:tdblock}
    \end{subfigure}
    \caption{Super-resolution model based on a pretrained VD-VAE\xspace model. The low-resolution encoder $\qh{\z_{<k}|\bm{y}}$ (in red) is trained to match VD-VAE\xspace pretrained encoder $\qp{\z_{<k}|x}$ (in green). Both encoders share parameters with VD-VAE\xspace generative model $\pt{\bm{z}, \bm{x}}$ (in blue) in the top-down path. To super-resolve an image $y$, we sequentially sample $\z_{<k} \sim \qh{\z_{<k}|\bm{y}}$ and $\bm{x} \sim \pt{\bm{x}|\z_{<k}}$.}
    \label{fig:vdvae_sr}
\end{figure}

\subsection{Enforcing consistency of the super-resolution}
By definition of the downsampling model \eqref{eq:forward}, the super-resolved version of a LR image $\bm{y}$ should belong to the space of consistent solutions $\{\bm{x} | \bm{y}=H_s\bm{x}\}$.
However, as many learning based super-resolution methods, our super-resolution model does not explicitly enforce this condition.
According to Proposition~\ref{prop:expcons2} and the estimated average LR pairwise distance in Figure \ref{fig:uk}, the consistency error of our super-resolution model should be small, but remains positive. The lack of consistency can also be due to the assumption of Proposition \ref{prop:expcons2} not being met in practice, that is to say, the encoders and the decoder not having enough capacity and/or not being trained well enough. In particular, if the encoder $\qp{\bm{z}|\bm{x}}$ does not match the intractable posterior $\pt{\bm{z}|\bm{x}}$, the reconstruction error of the VAE will propagate to the low-resolution encoder and hurt the consistency of the super-resolution.

In order to generate super-resolved images  consistent with respect to the low resolution input, we apply a post-processing step  by projecting the output of the generative network to the space of consistent solutions $\{\bm{x} | \bm{y}=H_s\bm{x}\}$, as previously proposed in \cite{bahat2020explorable}. Given a potentially unconsistent image $\hat{\bm{x}}$, the consistent solution $\hat{\bm{x}}_p$ is obtained as
\begin{equation}
    \label{eq:cycle_consistency}
    \hat{\bm{x}}_{p} = (I - H_s^T(H_s\Hs^T)^{-1}H_s)\hat{\bm{x}} +  H_s^T(H_s\Hs^T)^{-1}\bm{y}.
\end{equation}
In practice, the filter $(H_s\Hs^T)$ can be efficiently inversed in the frequency domain using a discrete fourier transform \cite{bahat2020explorable}.

\subsection{Practical details}
We test our method for super-resolution on the FFHQ dataset \cite{karras2019style}, with image of resolution $256\times256$.
We build our work upon the official VD-VAE\xspace codebase \cite{child2021deep}, and we reuse the pretrained networks provided by the authors.
All models are trained with Adam optimizer and the learning rate is divided by $10$ when the validation loss is on a plateau.
More details about the training can be found on Table \ref{tab:tdetails}.

In practice, the number of predicted latent groups $k$ for each resolution is set so that each low-resolution encoder only predicts the latent groups $z_l$ of spatial dimension lower than or equal to the dimension of the LR input. We found that training the low-resolution encoder to predict more groups would make the training of the low-resolution encoder harder, yielding super-resolved samples more consistent with the input but also containing more artefacts. Overall, with our choice of the number of latent groups to be predicted, super-resolved samples are consistent enough with the LR input, so that the projection \eqref{eq:cycle_consistency} does not introduce visible artifacts.

To enforce the consistency of the super-resolution at inference \eqref{eq:cycle_consistency}, we use the cycle-consistency module implementation provided in the official explorable super-resolution Github repository \cite{bahat2020explorable}.

\begin{table}
    \caption{Training details of the low-resolution encoder for each upsampling factors.}
    \centering
    \label{tab:tdetails}
    \begin{tabular}{c|c|c|c}
        upsampling factor & $\times 4$ & $\times 8$ & $\times 16$ \\
        \hline
        $k$ & 57 & 43 & 21 \\
        batch size & 8 & 16 & 32\\
        learning rate & $0.00001$ & $0.00004$ & $0.0001$\\
        iterations & 150K & 150K & 300K \\
    \end{tabular}
\end{table}

\subsection{Results}
Samples from our super-resolution models are displayed on Figure \ref{fig:srx8}. For small upscaling factors ($\times 4$ and $\times 8$), our super-resolution model is able to generate diverse textures (skin, hairs) and to generate different image details (mouth, eyes). For larger upscaling factors ($\times 16$) our method is able to produce semantically diverse super-resolutions (age, face expression).

\newlength{\picwidth}
\settowidth{\picwidth}{\pgfimage[interpolate=false]{figures/demo_x4/36_LR.png}}

\tikzstyle{closeupD} = [
    opacity=1.0,          %
    green,
    magnification=3,     %
    height=0.5\picwidth, %
    width=0.5\picwidth %
  ]

\tikzstyle{closeupG} = [
    opacity=1.0,          %
    red,
    magnification=2,
    height=0.5\picwidth, %
    width=0.5\picwidth %
    ]

\tikzstyle{largewindowD} = [green]
\tikzstyle{largewindowG} = [red]
\tikzstyle{smallwindow} = [blue, line width=0.20mm]

\newcommand{\imagewzooms}[6]{
    \resizebox{#6}{!}{
        \begin{tikzpicture}[spy using outlines={rectangle}]
            \node[inner sep=0.1pt, anchor=south west] (img) at (0,0) {\pgfimage[interpolate=false, width=\picwidth]{#1}};
            \coordinate (posG) at (#2, #3);
            \coordinate (posD) at (#4, #5);
            \spy [closeupG ] on (posG)
                in node[largewindowG,anchor=north west] at (img.south west);
            \spy [closeupD] on (posD)
                in node[largewindowD,anchor=north east] at (img.south east);
        \end{tikzpicture}
    }
}

\newcommand{0.25 \linewidth}{0.25 \linewidth}
\begin{figure}
    \begin{subfigure}[t]{1\linewidth}
       \centering
       \begin{adjustbox}{max width=\textwidth}
            \begin{tabular}{ccccc}
                    \imagewzooms{figures/demo_x4/36_LR.png}{1.1}{1.6}{1.1}{0.5}{0.25 \linewidth} &
                    \imagewzooms{figures/demo_x4/36_sample000.png}{1.1}{1.6}{1.1}{0.5}{0.25 \linewidth} &
                    \imagewzooms{figures/demo_x4/36_sample001.png}{1.1}{1.6}{1.1}{0.5}{0.25 \linewidth} &
                    \imagewzooms{figures/demo_x4/36_sample002.png}{1.1}{1.6}{1.1}{0.5}{0.25 \linewidth} &
                    \imagewzooms{figures/demo_x4/36.png}{1.1}{1.6}{1.1}{0.5}{0.25 \linewidth} \\
                    \imagewzooms{figures/demo_x4/29_LR.png}{0.5}{0.4}{0.85}{1.2}{0.25 \linewidth} &
                    \imagewzooms{figures/demo_x4/29_sample000.png}{0.5}{0.4}{0.85}{1.2}{0.25 \linewidth} &
                    \imagewzooms{figures/demo_x4/29_sample001.png}{0.5}{0.4}{0.85}{1.2}{0.25 \linewidth} &
                    \imagewzooms{figures/demo_x4/29_sample002.png}{0.5}{0.4}{0.85}{1.2}{0.25 \linewidth} &
                    \imagewzooms{figures/demo_x4/29.png}{0.5}{0.4}{0.85}{1.2}{0.25 \linewidth} \\
            \end{tabular}
        \end{adjustbox}
        \caption{$\times 4$}
    \end{subfigure}
    \begin{subfigure}[t]{1\linewidth}
        \centering
        \begin{adjustbox}{max width=\textwidth}
             \begin{tabular}{ccccc}
                     \imagewzooms{figures/demo_x8/32_LR.png}{1.15}{0.6}{1.45}{1.2}{0.25 \linewidth} &
                     \imagewzooms{figures/demo_x8/32_sample000.png}{1.15}{0.6}{1.45}{1.2}{0.25 \linewidth} &
                     \imagewzooms{figures/demo_x8/32_sample001.png}{1.15}{0.6}{1.45}{1.2}{0.25 \linewidth} &
                     \imagewzooms{figures/demo_x8/32_sample004.png}{1.15}{0.6}{1.45}{1.2}{0.25 \linewidth} &
                     \imagewzooms{figures/demo_x8/32.png}{1.15}{0.6}{1.45}{1.2}{0.25 \linewidth} \\
                     \imagewzooms{figures/demo_x8/35_LR.png}{0.8}{0.6}{0.95}{1.75}{0.25 \linewidth} &
                     \imagewzooms{figures/demo_x8/35_sample000.png}{0.8}{0.6}{0.95}{1.75}{0.25 \linewidth} &
                     \imagewzooms{figures/demo_x8/35_sample001.png}{0.8}{0.6}{0.95}{1.75}{0.25 \linewidth} &
                     \imagewzooms{figures/demo_x8/35_sample002.png}{0.8}{0.6}{0.95}{1.75}{0.25 \linewidth} &
                     \imagewzooms{figures/demo_x8/35.png}{0.8}{0.6}{0.95}{1.75}{0.25 \linewidth} \\
             \end{tabular}
         \end{adjustbox}
         \caption{$\times 8$}
     \end{subfigure}
     \begin{subfigure}[t]{1\linewidth}
        \centering
        \begin{adjustbox}{max width=\textwidth}
             \begin{tabular}{ccccc}
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00005_LR.png} &
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00005_sample000.png} &
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00005_sample001.png} &
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00005_sample002.png} &
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00005.png} \\
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00028_LR.png}&
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00028_sample000.png}&
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00028_sample001.png}&
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00028_sample002.png}&
                \includegraphics[width=0.25 \linewidth]{figures/demo_x16/00028.png}\\
             \end{tabular}
            \end{adjustbox}
            \caption{$\times 16$}
        \end{subfigure}
        \caption{\label{fig:srx8}Results of our super-resolution method for different upscaling factor. Left : LR input, middle : diverse super-resolved samples, right : original.}
\end{figure}

\subsection{Discussion}
Our method is able to succesfully produce diverse super-resolved sample for upscaling factors $\times 4$, $\times 8$ and $\times 16$.
In particular, our method provides realistic visual results for large upscaling factors ($\times 16$).
To the best of our knowledge, no other conditional latent variable generative models have been proposed for super-resolution with such large upsampling factors.
Our results are in line with previous works based on reusing pretrained generative models for image restoration \cite{menon2020pulse,harvey2022conditional}, showing that restoration methods reusing pretrained generative models are particularly succesfull for restoration problems  when an important part of the information is missing
(\textit{e.g.} super-resolution with large downsampling factor, or inpainting with large image parts missing).

 As for today, even the best VAEs are limited to the generation of $256\times256$ images, on datasets with specific structures, such as FFHQ, while requiring a large amount of computing resources for training (2.5 weeks on 32 v100 gpu for VD-VAE\xspace trained on FHQ256).
 Therefore, for computational burden, we decided to exploit existing VAES and to limit our study to the super-resolution of image faces.
 However, recent works indicate that improved implementation strategies \cite{hazami2022less} or more powerfull architectures \cite{apostolopoulou2021deep} could help to reduce the training time of  deep hierarchical VAE.
 This opens the way to a democratization of deep hierarchical VAEs, %
that have the potential to improve downstream applications, %
as we have demonstrated with super-resolution.

\subsection{What information is encoded within each latent group?}

The generative model of VD-VAE\xspace provides a rich hierarchical latent representation of images. The effect of each latent group of the hierarchy on the generated image can be vizualized by sampling images from $\pt{\bm{x}|\bm{z}_{<k}}$, for different values of the group level $k$. Indeed, attributes that are common to all samples from $\pt{\bm{x}|\bm{z}_{<k+1}}$, but not to all samples from $\pt{\bm{x}|\bm{z}_{<k}}$, are most likely to be encoded in the latent group $\bm{z}_{k}$.

Experiments in previous works \cite{child2021deep} suggest that the low-frequency information of images generated by VD-VAE\xspace is mostly controlled by the latent variables at the top of the hierarchy, while the image high-frequency details are dependent on the latent variables at the bottom of the hierarchy.
Similar properties were observed for other hierarchical VAE architectures \cite{vahdat2020nvae, Havtorn2021HierarchicalVK}.

\newcommand{0.16\linewidth}{0.16\linewidth}
\begin{figure}[h]
    \centering
    \begin{tabular}{b{2cm}|cccc}
        \multirow{3}{*}{samples}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_4_sample_0.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_21_sample_0.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_43_sample_0.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_57_sample_0.png}
        \\
         &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_4_sample_1.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_21_sample_1.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_43_sample_1.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_57_sample_1.png}
        \\
         &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_4_sample_2.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_21_sample_2.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_43_sample_2.png}
        &
        \includegraphics[width=0.16\linewidth]{figures/demo_consistency/2_HR_k_57_sample_2.png}
        \\  \addlinespace \hline \addlinespace
        pixel-wise standard deviation
         &
        \begin{subfigure}[t]{0.16\linewidth}
            \includegraphics[width=\linewidth]{figures/demo_consistency/2_k_4_std.png}
            \end{subfigure} &
        \begin{subfigure}[t]{0.16\linewidth}
            \includegraphics[width=\linewidth]{figures/demo_consistency/2_k_21_std.png}
        \end{subfigure} &
        \begin{subfigure}[t]{0.16\linewidth}
            \includegraphics[width=\linewidth]{figures/demo_consistency/2_k_43_std.png}
        \end{subfigure} &
        \begin{subfigure}[t]{0.16\linewidth}
            \includegraphics[width=\linewidth]{figures/demo_consistency/2_k_57_std.png}
        \end{subfigure}
        \\
        & $k=4$ & $k=21$ & $k=43$ & $k=57$ \\
    \end{tabular}
    \caption{Samples and pixel-wise standard deviation of VD-VAE\xspace hierarchical generative model $\pt{\bm{x}|\z_{<k}}$ (when fixing the $k$ first latent groups of the hierarchy), for different values of $k$.
    High level semantic information and image low-frequency components is mostly controlled by the first groups of the hierarchy ($k<21$), while image high frequency details (hairs, edges) are determined by the last latent groups ($k\geq 43$).}
    \label{fig:std}
\end{figure}

Our experiments are in line with those observations. We study the VD-VAE\xspace model provided by the author \cite{child2021deep}, trained on FFHQ256 \cite{karras2019style} with $L=66$ groups in the latent hierarchy. Figure \ref{fig:std} shows sampled images from the conditional generative model $\pt{\bm{x}|\z_{<k}}$, where $\z_{<k}$ are $k$ fixed latent groups at the top of the hierarchy.
For a few fixed latent groups ($k=4$), generated images share high level semantic information such as gender, skin tone or face orientation, indicating that those attributes are most likely to be encoded into the $k=4$ first groups of the latent hierarchy.
When more latent groups are fixed, generated images share the same low-frequency information, and the variation between samples is mostly due to variation of high frequency details in textures (hairs, background) or edges (face shape, eyes, mouth).
Therefore, it appears that the hierarchical latent representation learned by VD-VAE\xspace implicitly separates the image low-frequency information from the high-frequency details.
Hence, latent groups at the top of the hierarchy  monitor the low-frequency information, whereas the latent groups at the bottom of the hierarchy control high-frequency details.

\subsection{Is VD-VAE\xspace implictly a Super-resolution network?}
Our previous experiments suggest that VD-VAE\xspace implicitly encodes the distribution of high frequency details conditional on low-frequency information via the hierarchical structure imposed on the prior model $\pt{\bm{z}}$.
We recall that image super-resolution is the task of recovering high-frequency details from the low-frequency information contained within a low-resolution image.
We formulate the hypothesis that VD-VAE\xspace conditional generative models $\pt{\bm{x}|\z_{<k}}$ are implicit super-resolution models,  generating diverse super-resolved versions of one particular low-resolution image $y$.
To validate this hypothesis, we measure how close the image generated by the conditional models $\pt{\bm{x}|\z_{<k}}$ are with each other, when they are downsampled with different downscaling factors. Without loss of generality, we consider the root mean square error (RMSE) as a measure of distance between samples.
  Thus, we estimate:
\begin{equation}
    \label{eq:uk}
  U_k^s := \mathbb{E}_{\pt{\bm{z}_{<k}}} \mathbb{E}_{\pt{\bm{x}|\bm{z}_{<k}}} \mathbb{E}_{\pt{\bm{\tilde{x}}|\bm{z}_{<k}}} \left[ \rmse{H_s\bm{x}}{H_s\bm{\tilde{x}}} \right],
\end{equation}
the average low-resolution pairwise distance of the generative model $\pt{\bm{x}|\z_{<k}}$, when samples are downsampled by a factor $s$.
 $U_k^s$ measures how much images sampled from $\pt{\bm{x}|\z_{<k}}$ differs from each other when they are downsampled.

\begin{figure}
    \begin{centering}
        \begin{tikzpicture}
            \centering
            \begin{axis}[
                grid=major,
                xmin=0, xmax=67,
                grid style={dashed,gray!30},
                xlabel=$k$,
                ylabel=$U_k^s$,
                xtick distance=10,
                xlabel style={yshift=0cm},
                ylabel style={yshift=-0.3cm},
                legend image post style={scale=1},
                ymode=log,
                legend pos=outer north east,
            ]
            \addlegendimage{empty legend} %
            \addplot table[x=k, y=rmse_16_mean, col sep=comma]{"data/consistency_diversity_generator.csv"};
            \addplot table[x=k, y=rmse_32_mean, col sep=comma]{"data/consistency_diversity_generator.csv"};
            \addplot table[x=k, y=rmse_64_mean, col sep=comma]{"data/consistency_diversity_generator.csv"};
            \addplot table[x=k, y=rmse_mean, col sep=comma]{"data/consistency_diversity_generator.csv"};
            \legend{$s$, $\times 16$, $\times 8$, $\times 4$, $\times 1$};
            \end{axis}
        \end{tikzpicture}
    \end{centering}
    \caption{Average low-resolution pairwise distance, $U_k^s$ \eqref{eq:uk} between samples from the conditional generative model $\pt{\bm{x}|\bm{z}_{<k}}$ of VD-VAE\xspace, for downscaling factors $s= 1, 4 , 8 , 16 $. Image with pixel values in $[0, 255]$.}
    \label{fig:uk}
\end{figure}

Practical details about the estimation of the average low-resolution pairwise distance $U_k^s$ are given in appendix \ref{app:details_uk}.
In Figure \ref{fig:uk} we estimate the value of $U_k^s$ for different downsampling factors. Non surpisingly, results illustrate that, as the number of fixed group $k$ increases, the generated images get more similar.
Furthermore, for a given number of fixed groups $k$, the low-resolution pairwise distance decreases as the downsampling factor $s$ increases, indicating that there is more variation in the HR samples than in their LR conterparts.
The gap between the average sample pairwise distance in high resolution ($s=1$), and low-resolution ($s \in \{4, 8, 16\}$) gets larger as the number of fixed groups $k$ increases, indicating that fixing a large number of groups $k$ yields samples that are close at low-resolution but different at high-resolution.
The average low-resolution pairwise distance $U_k^s$ gets closer to zero as $k$ increases. While there is no value of $k$ so that $U_k^s=0$, we argue that for a large enough value of $k$, $U_k^s$ becomes negligible compared to the pixel intensity range (0-255), for instance $U_{60}^4 < 0.5$.
Those results show that the downsampling of any image synthesized from the conditional generative model $\pt{\bm{x}|\bm{z}_{<k}}$ are consistent with one low-resolution image $\bm{y}$ with a certain precision inversely proportional to $k$.
Thus, we conclude that, for a large enough value of $k$, all images sampled from $\pt{\bm{x}|\z_{<k}}$ are diverse super-resolved versions of one LR image $\bm{y}$,  %
which is in line with the hypothesis that $\pt{\bm{x}|\z_{<k}}$ is implicitly a diverse super-resolution model.

\section{Introduction}\label{sec:intro}
\input{introduction.tex}

\section{Related works}\label{sec:related_works}
\input{related_works.tex}

\section{Preliminaries}\label{sec:prelim}
\input{preliminaries.tex}

\section{Analysing the hierarchical latent representation of VD-VAE\xspace}\label{sec:analysing}
\input{low_frequency_info_vdvae.tex}

\section{Diverse super-resolution with VD-VAE\xspace}\label{sec:diverse_sr}
\input{diverse_sr_w_vdvae.tex}

\section{Experiments}\label{sec:exp}
\input{experiments.tex}

\section{Conclusion}\label{sec:ccl}
\input{conclusion.tex}

\bibliographystyle{plain}

\subsection{Diverse super-resolution}
In this work we tackle the problem of diverse super-resolution: given a low-resolution (LR) image $\bm{y} \in \mathbb{R}^m$,
 our goal is to synthetize high-resolution (HR) images $\bm{x} \in \mathbb{R}^n$ that are both {\em realistic} and {\em plausible} with respect to the observed $\bm{y}$.
 The degradation process we consider writes:
\begin{equation}
    \label{eq:forward}
    \bm{y} = H_s\bm{x},
\end{equation}
where $H_s$ is a linear operator corresponding to the composition of a low-pass filter
and a subsampling operation with downsampling factor $s$. The goal of super-resolution is to recover the high-frequency details of $\bm{x}$ erased by the degradation process \eqref{eq:forward}.
Image super-resolution is an ill-posed inverse problem, as there can be many HR images consistent with an LR image, \textit{i.e.}, that satisfy \eqref{eq:forward}.
The objective of diverse super-resolution is to sample from the posterior distribution $p(\bm{x}|\bm{y}) \propto p(\bm{y}|\bm{x})p(\bm{x})$.
The data-fidelity term $p(\bm{y}|\bm{x})$, dealing with the plausibility  of the reconstruction, is given by the degradation model \eqref{eq:forward}.
On the other hand, the prior distribution term  modeling realistic  high-resolution images, $p(\bm{x})$, is unknown.
In the following, we investigate the parameterization of $p(\bm{x})$ using deep image generative models such as variational autoencoders.

\subsection{Variational autoencoders}
The variational autoencoder (VAE) framework \cite{kingma2013auto,rezende2014stochastic} provides an efficient way of learning a deep latent variables generative model :
\begin{equation}
	\pt{\bm{x}} = \int \pt{\bm{x}|\bm{z}}\pt{\bm{z}}d\bm{z}
\end{equation}
VAE can successfully model complex image distributions, while providing a latent representation of images useful for downstream applications.
A VAE is composed of a prior distribution on the latent space $\pt{\bm{z}}$, a decoder $\pt{\bm{x}|\bm{z}}$ parametrized by $\theta \in \Theta$, and an approximate posterior (encoder) $\qp{\bm{z}|\bm{x}}$ parametrized by $\phi \in \Phi$.
VAE encoder and decoder are usually parametrized by neural-networks, while the prior is set to be a centered isotropic multivariate gaussian distribution.
The VAE parameters $\theta$ and $\phi$ are jointly trained to maximize the Evidence Lower BOund (ELBO), which is a lower bound on the intractable model log-likelihood:
	\begin{align}\label{eq:elbo}
	 \mathcal{L}_{elbo}(\theta, \phi) &= \E{\pd{\bm{x}}}{\E{\qp{\bm{z}|\bm{x}}}{\pt{\bm{x}|\bm{z}}}
	+ \KL{\qp{\bm{x}|\bm{z}}}{\pt{\bm{z}}}} \\
    & \leq \E{\pd{\bm{x}}}{\log \pt{\bm{x}}},
	\end{align}
where $\pd{x}$ is a training data distribution.

\subsection{VD-VAE\xspace}

In this work, we use VD-VAE\xspace, a VAE architecture that provides state-of-the art results on image modelling \cite{child2021deep}.
VD-VAE\xspace is a hierarchical VAE (HVAE): the latent variables $\bm{z}$ are partitionned into  $L+1$ groups $\bm{z} = (\bm{z}_0, \bm{z}_1, \cdots, \bm{z}_L)$, and the prior $\pt{\bm{z}}$ is set to have a hierarchical structure, in which each group  depends on  previous groups:
\begin{equation}
	\label{eq:hdec}
	\pt{\bm{z}} = \pt{\bm{z}_0} \prod_{l=1}^L \pt{\bm{z}_l|\bm{z}_{<l}},
\end{equation}
where we denote $\bm{z}_{<l} = (\bm{z}_0, \cdots, \bm{z}_{l-1})$.
Each latent group is a 3-dimensional tensor $\bm{z}_l \in \mathbb{R}^{C^l \times H^l \times W^l}$, where $C^l$ is the number of channel and $(H^l, W^l)$ are the spatial dimensions.
The conditional prior is set to be a multivariate gaussian distribution with diagonal covariance
\begin{equation}
	\pt{\bm{z}_l|\bm{z}_{<l}} = \mathcal{N}\left(\bm{z}_l; \mu_{\theta}\left(\bm{z}_{<l}\right), \Sigma_{\theta}\left(\bm{z}_{<l}\right)\right),
\end{equation}
where $\mu_{\theta}\left(\bm{z}_{<l}\right)$ and $\Sigma_{\theta}\left(\bm{z}_{<l}\right)$ are parametrized by residual blocks.
VD-VAE\xspace inference network is composed of a deterministic bottom-up path, followed by a top-down path, sharing parameters with the generative model $\pt{\bm{z}, \bm{x}}$. The inference network $\qp{\bm{z}|\bm{x}}$ infers the latent groups in the same order as in the generative model:
\begin{equation}
	\label{eq:henc}
	\qp{\bm{z}|\bm{x}} = \qp{\bm{z}_0|\bm{x}}\prod_{l=1}^L \qp{\bm{z}_l|\bm{z}_{<l}, \bm{x}}.
\end{equation}
We refer the reader to  VD-VAE\xspace original paper \cite{child2021deep} for more details about the network architecture.

redpajama_set_name: RedPajamaArXiv


text:
Posted on January 23, 2020 December 19, 2019 by acmag
Technicolour Adelaide
Technicolor's new post production studio in Adelaide, its first in the Southern Hemisphere, is up and running – by Slade Phillips
Technicolor is a series of colour motion picture processes, the first version dating back to 1916, and followed by improved versions over several decades of cinema history. It was the second major colour process, after Britain's Kinemacolor, and the most widely used colour process in Hollywood from 1922 to 1952. Now, Technicolor works with creative and technology leaders in content creation, distribution and consumption to seamlessly deliver experiences worldwide.
Operating under the Mill Film banner, the South Australian visual effects studio has already attracted three-hundred creatives, well on its way to the goal of employing five-hundred people within five years.
The studio joins a growing number of post-production companies in Adelaide, helping the South Australian capital emerge as a screen industry hub. Others include Kojo, which worked on projects such as Hotel Mumbai (2018) as well as Top End Wedding (2019), and Rising Sun Pictures, the visual effects producer behind many of the X-Men films. E. Bennet Walsh's upcoming Mortal Kombat film will also be shot in South Australia by Germain McMicking ACS and is set to become South Australia's largest ever film production.
Technicolor has recently announced it would build a $26 million, 3000sqm visual effects studio in Adelaide. Managing director of Mill Film, Mark Thorley, said he expected to reach the goal of five-hundred creatives in Adelaide much faster than the five-year timeframe originally forecast. "It's been a long time since there's been some new investment into the visual effects market in Australia so people are seeing it as an opportunity to join something new and exciting," Thorley said.
The decision to locate the studio in South Australia followed a $6 million grant from the State Government's Economic Investment Fund, which expects the project to have an economic benefit of more than $250 million over a decade. The South Australian Government also offers a 10% rebate for post-production, digital and visual effects work, designed to attract international film business. This is on top of a similar federal measure, set at 30 per cent of growth expenditure.
Thorley said the decision to move Mill Film into Adelaide was also aided by access to talent. "Australia has had a rich history of good visual effects talent and I think over a number of years many Australians have gone offshore to continue their careers in visual effects, so this was a great opportunity to bring those Australians back home," Thorley says.
The Technicolor Academy is also located in Adelaide, which focuses on animation, lighting and environment work. Technicolor Academy is a fully-paid, intensive program which aims to improve artists' skills in lighting, effects, compositing and animation. "We look for young talent who have had some experience, whether that be from an educational institution or just naturally talented individuals," explains Thorley.
Located in the Adelaide CBD, the Mill Film studio has been fitted out over three floors of open-plan artist spaces and production offices. While the Adelaide studio is Mill Film's only Southern Hemisphere location, the company has studios in Montreal, Los Angeles and a partnership with Technicolor Bangalore.
Thorley said the Adelaide studio recently worked with Technicolor partner MPC in London to deliver its first significant milestone: 443 shots for the Dora the Explorer film Dora and the Lost City of Gold (2019). The studio is also working on films for Paramount, Universal and Amblin.
Slade Phillips is a writer based in Sydney.
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There's an old wooden barn in the middle of an open field. You start to hear the faint sounds of the last remnants of humanity within. A baby crying. The clicking of automatic weapons being readied. Even the occasional laugh. Then you hear it. "Woah-ohhhhhh….. Trust issues….. Woah-oh-ohhhhhh… Trust issues…" Rick Grimes, the trusted leader of this group of survivors is sitting in the fetal position, rocking back and forth as he mumbles his new theme song.
Okay, things didn't exactly go down that way. But in the latest episode of AMC's The Waking Dead, entitled, "The Distance," Rick definitely shows how severe his trust issues and paranoia have become.
Picking up where we left off last week, Maggie and Sasha bring Aaron, a wanderer who approached them in the woods, back to the group to let him have his say. Aaron claims to be a scout from a stable society with walls made of steel that nothing alive or dead can breach. After following the group for who knows how long, he chose to approach them and invite them to "audition for membership." During his first pitch, Rick, who has been giving him the stink eye the entire time, hits him dead in the jaw with a right cross rivaled only by the power of Roman Reigns' Superman Punch.
At this point, the entire group realizes that Rick's gone off the deep end when it comes to trusting strangers, and with good reason. From when we first met Rick five seasons ago everyone new (and some old) that he's tried to trust have tried to kill him, feed him to zombies, eat him or endanger his family and friends more times than he'd like to count. So his paranoia is on a completely new level. After hearing that there's at least one person out there looking for him, and a car, a group consisting of Glenn, Maggie, Michonne, Abraham and Rosita head out to investigate further. They find out that at least half of Aaron's story is true, there is an RV big enough to carry the group wherever they have to go.
They come back to report their findings to a frustrated Rick, who is resistant to give any trust to his captive. The rest of the group explains that its more of a danger at this point to ignore the possibility of another safe haven than to keep wandering the roads until something comes along. Realizing that he's pretty much the only person that feels so strongly about this, he decided on letting the group head to their new destination. On the night-time drive (who thought this was a good idea?), Glenn, Michonne, Rick and Aaron end up driving through enough walkers to fill up a city block. They realize the rest of the group is no longer trailing them and see a flare light up the sky, presumably from someone in Aaron's group. Realizing that everyone else will head there, they fight through a horde of walkers in the woods. One even gets a sparking headshot from a flare gun to the eye socket.
Everyone eventually meets up at a warehouse and we meet Eric, Aaron's partner, in both scouting for survivors and in romance. We finally have our first openly gay characters in the show. And it's about damn time. The next morning the group heads out to Alexandria, Virginia, the camp that Aaron and Eric claim as their home.But only after Rick stores a spare gun at a nearby vacant house. During a one-on-one conversation with Michonne, Rick explained that he's not sure if he can let his people walk into a new camp. It would essentially come down the first thing he hears when he gets to the gate. When he gets to Alexandria, the first thing he hears is the sound of children playing. For the first time in a while, Rick, and the group as a whole, have hope.
This week's episode doesn't quite make up for last week's slow pace, but it's a start. My main concerns come down to two things. One, how are they going to make this new place, "too good to be true." It would be a pretty boring show if no challenges presented itself. Secondly, going back to the fact that everyone has to "audition for membership" into this group, there's a strong chance that not everyone in the group is going to pass. So what happens after that?


text:
Welwyn Garden City dance starlets to take to the world stage
PUBLISHED: 10:57 13 February 2019
Andrew Brookes
Dancers from North Star Academy in Welwyn Garden City will represent Team England at the 2019 Dance World Cup Finals in Braga, Portugal. Picture: James Copeman.
Young dancers from Welwyn Garden City are reaching for the stars as they prepare to take to the world stage.
Knightsfield-based dance school North Star Academy have qualified 22 boys and girls to compete in the 2019 Dance World Cup Finals in Braga, Portugal, in June and July.
The starlets, aged from 11 to 18, were chosen from thousands of dancers that auditioned to represent Team England this year.
They will be compete among more than 5000 dancers from across the world.
North Star Academy teacher and choreographer Sophia Melvin said: "We are so unbelievably proud of our starlets. It is not only a huge honour to represent your country at such a prestigious competition, but also a massive achievement out of the thousands of dancers that auditioned for the very few spots on Team England for 2019.
"They will be performing in some of the most difficult and competitive categories, including contemporary, modern technique and tap, which just highlights their consistent hard work and dedication to their craft.
"They really are an incredible group of stars and excellent role models for their generation."
The school is raising funds and hoping to attract sponsorship for the trip.
Email northstaracademy17@gmail.com if you are interested in sponsoring or donating.