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Emergence Engagements
Video Meditations
Schuyler Brown
The Art of Emergence
About Schuyler Brown
Growing up in Kentucky I learned what it's like to live on the land. How it feels to be broke, but not poor. What the ancient Appalachian mountains have to teach us. How to saddle and ride a horse. How to chew tobacco and shoot a gun. How to sing around the campfire and make biscuits and square dance. I learned how to tell a good story, because some nights you're the entertainment and people love a good story. In Kentucky, I learned to listen and to feel.
Of course, I didn't know it as a kid but these essential skills would serve me well. Not because I frequently make biscuits or shoot guns or ride horses, but because I can work with my hands, I know the safety in responsibility, and I know how to respond with extreme sensitivity to other beings.
Floral Decor
School taught me to play the game of life. I quickly learned what was expected of me and how to make people happy. I learned to climb ladders and navigate power structures. I was good at it. These are skills that still come in handy, but they no longer serve me or humanity. They're for a simpler time.
What really interested me as I grew through adolescence and early adulthood was the quest for Spirit, mystery, the unknown, self-expression through writing and art. I was highly intuitive and empathic, but had no one to support the unfolding of these gifts. It wouldn't be until much later that I'd begin to understand and revere the meaning of the numinous in life and how the culture devalues what it can't measure or see.
Much of my dharma is around bringing *magic* back into the world. For me, and I believe many others, the loss of magic (we know it as children!) is a tragic blow to human imagination and ingenuity. We need it now more than ever as things escalate in complexity. We are entering an era where we can't think our way through our problems anymore. We need higher and more subtle skills.
My interest in business started when I got my first job out of college. Until that moment, I'd wanted to have a career in the arts, but I moved to San Francisco and needed to make a decent living right away. So, I got a job with the branding agency, Landor Associates.
I was hooked. It was a wonderful time to work at Landor, a company at the height of its powers, well-run, with a healthy culture. I was surrounded by smart people and we were doing work for the world's biggest brands. It all felt important. I realized how much money moved through the economy as a result of marketing, communications, branding. I felt the power of capitalism. I felt safe.
At Landor I started my career as a trendspotter. My intuitive skills coupled with my innate love of culture made me a crack strategist and accurate predictor of the tastes of the market. This led me to the east coast where I was hired by a real estate developer to improve the "coolness factor" of his malls around the country. That led me eventually to New York City where I was hired as a strategist and futurist at one of the largest ad agencies in the world. I enjoyed the high stakes, the travel, the fame...for a while.
The work I was doing was exciting, but absolutely soulless and worse: extractive, extravagant, shallow. It ate at me. By grace, I never let my spiritual interests die. In fact, the busier I got at work, the more I turned to yoga, meditation and Buddhist studies. I craved an antidote to the emptiness I felt as a result of what was supposed to be sustaining me: my so-called success!
At a certain point (in 2006, to be exact), the tension between my deepening spiritual life and my accelerating professional life came to a breaking point. I could no longer work so far out of alignment with my values, or justify spending most of my day working to sell harmful products. I became aware of and then obsessed with the severity of the climate crisis. I quit.
My previous definition of success was now in the rearview mirror. I could see the futility of so much of what I'd spent my time, imagination, and life force on; how much I'd compromised in the name of business. I could see all of this and felt a great deal of remorse for the harm I'd caused. And I couldn't yet see the next step. Still, I had my integrity back. I had my Self.
I thought I might become a yoga teacher or spiritual teacher. I dove deep into the spiritual world. Studied one-on-one most days of the week with Mystical teachers, Buddhist teachers, Vedanta teachers, Tantra teachers. I learned Sanskrit so I could read the great books of India in the original language. I studied trauma and did shadow work, went on pilgrimage, suffered, witnessed the miraculous in everyday life, integrated my feminine dimension and learned to listen to my own inner guidance. I married and had a daughter. Motherhood was (and still is) it's own spiritual path...
Through it all, I kept one foot in the business world. I think it somehow still made me feel safe, but also I knew I had work to do there. I thought I was alone in my conviction that work could and should be a place of growth and healing. But, soon I found like-minded people. I found a community of spiritual friends dedicated to the transformation of work.
Which brings me to the current moment and the launch of The Art of Emergence.
My motivation is not to climb the ladder or shatter any glass ceilings. It's to shatter the illusion of "reality," the norms, and the ideas of status quo that are inherently out of balance, extractive and harmful to all living beings and the planet. My work now is to find and collaborate with leaders and people in positions of power who are ready to fundamentally change the way we do business and the way we treat each other when we're at work. I want work to be a place of healing for all people; a place where individuals can individuate, develop, mature and express their fullest version of self.
I hope we get a chance to know each other.
Let's weave...
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Home Relationships Becoming Single Again!
out who you are and what you want in life!
with you if you didn't have all these emotions and thought patterns coming out of a relationship.
definitely are NOT ready to start dating again. It's time to work on YOU…..
may not be. Aim to please and not disappoint, yourself and those you are dating, (in the emotionally sense).
dating, how do you know those you are dating are actually ready to date again?
flags' before you get in deep. If you get my drift.
and getting to know who you really are and what you want.
What are your unrealised dreams and expectations in life?
honest about what you are really looking for out of life and from a future life partner.
What are your core requirements in a relationship?
What are your red flags?
What are you not willing to compromise on?
then start with being open and honest with YOU first.
of time and angst in the long run, believe me! I'm speaking from experience!
Dating, Divorce, loneliness, love, Relationships, Single. Bookmark.
Find the JOY in your relationship – by letting go of perfection.


Advertising and Marketing Services, Consumer Products, Media and Entertainment, Retail and Apparel, and Travel/Hospitality/Leisure.
Aviation, Automotive, Diversified Manufacturing, Chemicals, Energy, Power, and Construction.
Oil and Gas, Mining, Forestry, Agriculture, and Plantation.
Medical Devices, Pharmaceuticals, Life Science, and Biotechnology.
Telecommunication, IT Services, and Electronics.
Please feel free to drop your comprehensive CV or resume (in DOC or PDF file) via Candidates section at Headhunter: Indonesia website.


A relatively new member of the Swans setup, Jordi Amat is a centre half who has been at the club for just two seasons. A young and enthusiastic member of the side, Amat joined the club for £2.5 million from Espanyol, and has since gone on to make 27 Premier League appearances.
The former Spanish Under-21 international has found game time a little limited at the Liberty with Federico Fernandez and Ashley Williams ahead of him in the pecking order, but the player himself is seemingly happy in South Wales having signed a contract extension back in March.
Amat struggled for game time last year and racked up just 10 league appearances all year, with Fernandez and Williams blocking his path into the first team. He is considered third choice at the club currently, but will face stern competition from Kyle Bartley for the role next season. But, the 23 year-old may need to calm down in his defensive duties if he is to impress as he made three defensive errors and collected a total of three cautions in just 10 appearances last season, this in comparison to just one error in 17 appearances in the previous year.


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Whistleblowers have 2 weeks left to expose Tower Hamlets malpractice after Rahman's fall
Published: 7:00 AM November 23, 2016 Updated: 8:46 AM October 14, 2020
Disgraced Tower Hamlets ex-Mayor Lutfur Rahman - Credit: Archant
An independent "clear up" team headed by a top civil servant has been set up to deal with any outstanding allegations of Town Hall dodgy dealings in London's East End where disgraced mayor Lutfur Rahman was banned from office for malpractice.
Sir Ken Knight (right) chairing a Town Hall grants meeting in July 2016 with current Mayor John Biggs - Credit: Archant
It follows government commissioners sent in two years ago, headed by Sir Ken Knight (pictured), to check on the way Tower Hamlets council dished out grants from the public coffers and where the money went to.
Two weeks are left for residents or Town Hall whistleblowers to come forward with serious complaints about any issues between October, 2010, and June this year.
The council wants to improve its transparency following Rahman's five-year administration which was slammed in the High Court last year for its secrecy and "bunker mentality" when he was banned from office for five years for election fraud and malpractice.
Now Civil servant James Richardson has been appointed as the troubled authority's 'Clear Up project manager' to encourage anyone to come forward over matters of concern during the Rahman administration which have not yet been looked into.
'Cean up' team at Tower Hamlets Council - Credit: Archant
"We are seeking to protect where possible the anonymity of those who want to come forward," Mr Richardson assured.
"This is a completely independent process. There is an opportunity for council staff as well as residents to raise specific concerns."
Allegations can be posted to Clear Up Team, Mulberry Place, Town Hall, 5 Clove Crescent, E14 2BG, emailed to clearupteam@towerhamlets.gov.uk or sent directly to the Commissioners at the Town Hall.
The deadline for raising outstanding issues is December 8, after which allegations have to go through the council's own whistleblowing process or sent to individual ward councillors or to local MPs Jim Fitzpatrick and Rushanara Ali.

redpajama_set_name: RedPajamaCommonCrawl


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SWLA's Premier Wine & Food Event will return October 30, 2021
ROUGE ET BLANC 2021 is NOW SOLD OUT!
PARKING & MAP
Ham Reid Rd entrance only. Nelson Rd entrance will be closed to thru traffic.
Paved parking on-site is reserved for patrons who purchased a VIP Parking Pass.
Grass lot will be free festival-style parking. Limited spaces available to first in.
Once the grass lot is full, an auxiliary lot is available at Trinity Baptist Church (1800 Country Club Rd), and shuttle service will be available.
IMBIBE, DON'T DRIVE: Search Rouge et Blanc or Oak Crossing (5656 Nelson Rd) on Uber or Lyft rideshare services.
Ride-share vouchers are available for pick-up from the event. Visit the main order table on-site at The Gazebo for info!
Banners staff is closely monitoring the continuing pandemic and are taking steps to host the safest event possible, in consideration of any and all health guidelines previously released.
Heading into the August 6 ticket day, we assure our patrons that Rouge et Blanc is moving forward, unless it cannot.
Though Rouge et Blanc is a non-refundable event, if we are mandated to cancel, or through any extenuating circumstances must cancel, ticketholders will have the option to donate their purchase to the Banners Series / McNeese Foundation or to request a refund by the date of event (October 30, 2021).
We are humbled and grateful that so many of our patrons, both businesses and individuals, have donated since March of last year, in support of the unique cultural and educational programming that Banners offers.
Stay safe, Lake Area. We look forward to sipping wine with you all again under the beautiful oaks at Oak Crossing.
A huge thank-you to all these essential supporters, sponsors, and champions of the Lake Area arts community!
Rouge et Blanc attracts thousands of food & wine lovers annually to enjoy the best the region has to offer.
The main event, sold out thirteen years running, is a four-hour tasting extravaganza.
2021 Imbiber Pre-sale begins July 5
Details and weblinks emailed to Imbiber patrons
2021 Red Ticket Day: August 6
Tickets will only be available online this year
Rouge et Blanc is made possible through the generosity of area sponsors, restaurants, wine vendors, expert presenters, and patrons. A group of community volunteers also make this annual event possible through their tireless work and dedication to celebrating culture and diversity in Southwest Louisiana.
Rouge et Blanc serves as the flagship fundraiser for Banners at McNeese State University, allowing for funding to the annual Cultural Series in March & April, as well as off-season educational components through the Banners Engages program.
IMBIBER PROGRAM
Imbibers: Purchase $250-$499 in wine (pre-tax) from the previous cycle of Rouge events.
Imperial Imbibers: Purchase $500+ in wine (pre-tax) from the previous cycle of Rouge events.
Imbiber Perks
Access to two gold tickets during pre-sale.
Large wine glass during Main Tasting
Opportunity to purchase one VIP Parking Pass and VIP tables while supplies last
Rouge et Blanc 2019 - Downtown Lake Charles
Rouge et Blanc 2018 - McNeese State University
Interested in special VIP perks? Click here for sponsor packages!
Lost or Stolen Tickets
Please treat your ticket as you would any other valuable or cash. Each ticket issued has a unique number, which is recorded by patron. The physical ticket is required for entrance. Once patron accepts receipt of physical ticket, Banners at McNeese is no longer responsible and cannot refund or replace the ticket.
We do not keep a waiting list. People will generally sell their tickets on our Rouge et Blanc Facebook page if their plans change.
What is Rouge et Blanc?
Rouge et Blanc is an event series and celebration of food and wine hosted annually by Banners at McNeese State University. This event is the flagship fundraiser for Banners, an arts and cultural program that serves the five-parish area in Southwest Louisiana.
Many wine experts and renowned area chefs volunteer to share their expertise with attendees. The Banners staff and community volunteers work hard to keep the wine dinners, seminars, and other events fresh and engaging each year.
How did Rouge et Blanc start?
The idea was born as a fundraiser to support the mission of Banners, which promotes lifelong learning and cultural diversity while enhancing the quality of life throughout Southwest Louisiana.
Lost in Transit
If your ticket was lost in postal transit, contact the Banners at McNeese office prior to the event. Because each ticket has a unique number, we will verify if that ticket is used at the event. We will require a credit card or alternate form of payment that will be processed only if that ticket number is used.
No One Under 21 Admitted
We do not allow anyone under the age of 21 on site. This means babies, toddlers, and teenagers. No exceptions.
What Should I Expect at the Grand Tasting?
Rouge et Blanc is an outdoor event. This is a tasting with each restaurant and wine vendor giving you a small sample of their best food and wine.
The Grand Tasting will occur regardless of the weather. Alternate plans are in place in case of adverse conditions.
Ticket holders will be notified via email of any updates.
Each patron who purchases $250 or more of wine (not including tax) at a qualifying Rouge et Blanc event becomes a member of the Imbiber program. The totals are compiled on a pre-tax basis under the name used on the order forms. Benefits include the opportunity to purchase two gold tickets to the following year's event.
More than 20 years later, Banners at McNeese State University continues to fulfill its initial mission - bringing the best of arts and humanities to Southwest Louisiana.


No progress has been made over Sunday to resolve the crisis in the coalition, with both sides standing firm on their positions.
This causes further postponement of the Knesset's vote on the appointment of Yisrael Beiteinu Chairman MK Avigdor Lieberman as Defense Minister, which has already been delayed several times. As of now, the vote is scheduled to take place on Wednesday.
Over the weekend, in an attempt to resolve the dispute, Netanyahu unilaterally announced the establishment of a committee which would examine the Cabinet's performance and publish its recommendations within three weeks. This did not satisfy Bennett, who publicly rejected this proposal and called it a "spin" that wouldn't do anything to save human lives.
HaBayit Hayehudi officials claimed on Sunday that all of the Cabinet ministers agree with Bennett's position "off the record" but are not willing to declare it. They say Bennett's requests are legitimate and that Netanyahu is being stubborn for no reason.


We wrote about a particular economic phenomenon referred to in this post about economic cycles and particularly the Kuznets swing; which we find the most interesting and thought provoking cycle. The reason for this is that it is a generational cycle, only lasting or more accurately stated lasting anywhere between 15 – 25 years.
So where are we on this cycle and what does it mean for me, should be the two most obvious questions to answer?
Lets address both separately below.
Firstly we believe we are now around seven years into a downward phase of the Kuznets cycle, therefore to some analysts it would mean that we are either almost half way or to others around a third of the way through this cycle.
We believe that the downward phase of a Kuznets swing is the 'exuberance' correcting phase; when markets and other factors of productions contributing to mostly normal market clearing activity 'got slightly out of kilter'. The Kuznets swing is always there to bring these factors of production into alignment. It is a consolidation phase of the cycle and interestingly for this particular phase, it coincides with disruptive technological advances around Cloud Computing, dis-aggregation of intermediaries, especially in labour markets with labour or skills exchanges appearing everywhere. Examples include, Elance, oDesk, PeoplePerHour, etc..
Furthermore, and this is the most import action point for our readers to understand and appreciate, this consolidation and technological advance has a severe impact of wages levels and the distribution of where actual 'work' is being performed.
Hence headlines like the one we spotted this morning regarding real wages in Britain declining relative to other (very unproductive EU cousins) are not helpful without the pundit exploring and engaging n deeper analysis of the underlying drivers for the pressure.
Understand that the world of work is changing much faster than we had ever become used to in previous generations. As active able and willing participants in this market for labour and skills we have clear choices: Up-skill, be competitive appreciate and plan for volatility in the labour supply market, by ensuring flexibility in location, skills and prices. It is especially painful to suffer real wage declines, but remember this is the market's subtle way of signalling a problem or challenge in that particular market and a way of adjusting in order to restore the natural balance and clearing prices.
We believe every interfering politician and educating commentator should always bear this in mind.


It's hard to overstate what I feel I've gotten from hypnosis. Simply, it has changed my life and I will use the tools I've learned here in the process of being more me. For the first time in 40 years I can recognize emotions other than anger, anxious and stressed.


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Hydroxyurea-induced HbF production in anemic primates: Augmentation by erythropoietin, hematopoietic growth factors, and sodium butyrate
K. T. McDonagh, G. J. Dover, R. E. Donahue, D. G. Nathan, B. Agricola, E. Byrne, A. W. Nienhuis
Hydroxyurea, a cell-cycle-specific cytotoxic agent, has been shown to increase fetal hemoglobin (HbF) production. This property makes it an attractive drug for treatment of sickle cell disease and severe beta thalassemia. Its potential efficacy is limited because of a variable and often suboptimal response. Combinations of hydroxyurea and other drugs may induce more clinically significant increases in HbF. We have utilized chronically phlebotomized rhesus monkeys, treated with oral hydroxyurea, to investigate the capacity of several other agents to further augment HbF synthesis. Recombinant human erythropoietin, in super-pharmacologic doses, increased F-reticulocyte production when given on a weekly sequential schedule (3 of 7 days) with hydroxyurea (4 of 7 days), but it was less effective on an alternate day schedule when hydroxyurea was given daily. Neither recombinant human interleukin 3 (IL-3) nor recombinant human granulocyte-macrophage colony-stimulating factor (GM-CSF), when infused individually, increased F-reticulocytes in animals receiving daily hydroxyurea. Sequential, overlapping infusions of IL-3 and GM-CSF produced a small but statistically significant increase in F-reticulocytes in one of two hydroxyurea-treated animals. Infusions of sodium butyrate produced a substantial augmentation in F-reticulocyte production in animals chronically treated with hydroxyurea. Thus, our studies have identified several agents that may prove useful in combination with hydroxyurea to achieve clinically beneficial levels of HbF.
Experimental Hematology
GM-CSF
Dive into the research topics of 'Hydroxyurea-induced HbF production in anemic primates: Augmentation by erythropoietin, hematopoietic growth factors, and sodium butyrate'. Together they form a unique fingerprint.
Butyric Acid Medicine & Life Sciences 100%
Erythropoietin Medicine & Life Sciences 84%
Primates Medicine & Life Sciences 74%
Intercellular Signaling Peptides and Proteins Medicine & Life Sciences 65%
Reticulocytes Medicine & Life Sciences 42%
Interleukin-3 Medicine & Life Sciences 21%
Granulocyte-Macrophage Colony-Stimulating Factor Medicine & Life Sciences 18%
McDonagh, K. T., Dover, G. J., Donahue, R. E., Nathan, D. G., Agricola, B., Byrne, E., & Nienhuis, A. W. (1992). Hydroxyurea-induced HbF production in anemic primates: Augmentation by erythropoietin, hematopoietic growth factors, and sodium butyrate. Experimental Hematology, 20(10), 1156-1164.
Hydroxyurea-induced HbF production in anemic primates : Augmentation by erythropoietin, hematopoietic growth factors, and sodium butyrate. / McDonagh, K. T.; Dover, G. J.; Donahue, R. E.; Nathan, D. G.; Agricola, B.; Byrne, E.; Nienhuis, A. W.
In: Experimental Hematology, Vol. 20, No. 10, 1992, p. 1156-1164.
McDonagh, KT, Dover, GJ, Donahue, RE, Nathan, DG, Agricola, B, Byrne, E & Nienhuis, AW 1992, 'Hydroxyurea-induced HbF production in anemic primates: Augmentation by erythropoietin, hematopoietic growth factors, and sodium butyrate', Experimental Hematology, vol. 20, no. 10, pp. 1156-1164.
McDonagh KT, Dover GJ, Donahue RE, Nathan DG, Agricola B, Byrne E et al. Hydroxyurea-induced HbF production in anemic primates: Augmentation by erythropoietin, hematopoietic growth factors, and sodium butyrate. Experimental Hematology. 1992;20(10):1156-1164.
McDonagh, K. T. ; Dover, G. J. ; Donahue, R. E. ; Nathan, D. G. ; Agricola, B. ; Byrne, E. ; Nienhuis, A. W. / Hydroxyurea-induced HbF production in anemic primates : Augmentation by erythropoietin, hematopoietic growth factors, and sodium butyrate. In: Experimental Hematology. 1992 ; Vol. 20, No. 10. pp. 1156-1164.
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abstract = "Hydroxyurea, a cell-cycle-specific cytotoxic agent, has been shown to increase fetal hemoglobin (HbF) production. This property makes it an attractive drug for treatment of sickle cell disease and severe beta thalassemia. Its potential efficacy is limited because of a variable and often suboptimal response. Combinations of hydroxyurea and other drugs may induce more clinically significant increases in HbF. We have utilized chronically phlebotomized rhesus monkeys, treated with oral hydroxyurea, to investigate the capacity of several other agents to further augment HbF synthesis. Recombinant human erythropoietin, in super-pharmacologic doses, increased F-reticulocyte production when given on a weekly sequential schedule (3 of 7 days) with hydroxyurea (4 of 7 days), but it was less effective on an alternate day schedule when hydroxyurea was given daily. Neither recombinant human interleukin 3 (IL-3) nor recombinant human granulocyte-macrophage colony-stimulating factor (GM-CSF), when infused individually, increased F-reticulocytes in animals receiving daily hydroxyurea. Sequential, overlapping infusions of IL-3 and GM-CSF produced a small but statistically significant increase in F-reticulocytes in one of two hydroxyurea-treated animals. Infusions of sodium butyrate produced a substantial augmentation in F-reticulocyte production in animals chronically treated with hydroxyurea. Thus, our studies have identified several agents that may prove useful in combination with hydroxyurea to achieve clinically beneficial levels of HbF.",
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T2 - Augmentation by erythropoietin, hematopoietic growth factors, and sodium butyrate
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AU - Donahue, R. E.
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N2 - Hydroxyurea, a cell-cycle-specific cytotoxic agent, has been shown to increase fetal hemoglobin (HbF) production. This property makes it an attractive drug for treatment of sickle cell disease and severe beta thalassemia. Its potential efficacy is limited because of a variable and often suboptimal response. Combinations of hydroxyurea and other drugs may induce more clinically significant increases in HbF. We have utilized chronically phlebotomized rhesus monkeys, treated with oral hydroxyurea, to investigate the capacity of several other agents to further augment HbF synthesis. Recombinant human erythropoietin, in super-pharmacologic doses, increased F-reticulocyte production when given on a weekly sequential schedule (3 of 7 days) with hydroxyurea (4 of 7 days), but it was less effective on an alternate day schedule when hydroxyurea was given daily. Neither recombinant human interleukin 3 (IL-3) nor recombinant human granulocyte-macrophage colony-stimulating factor (GM-CSF), when infused individually, increased F-reticulocytes in animals receiving daily hydroxyurea. Sequential, overlapping infusions of IL-3 and GM-CSF produced a small but statistically significant increase in F-reticulocytes in one of two hydroxyurea-treated animals. Infusions of sodium butyrate produced a substantial augmentation in F-reticulocyte production in animals chronically treated with hydroxyurea. Thus, our studies have identified several agents that may prove useful in combination with hydroxyurea to achieve clinically beneficial levels of HbF.
AB - Hydroxyurea, a cell-cycle-specific cytotoxic agent, has been shown to increase fetal hemoglobin (HbF) production. This property makes it an attractive drug for treatment of sickle cell disease and severe beta thalassemia. Its potential efficacy is limited because of a variable and often suboptimal response. Combinations of hydroxyurea and other drugs may induce more clinically significant increases in HbF. We have utilized chronically phlebotomized rhesus monkeys, treated with oral hydroxyurea, to investigate the capacity of several other agents to further augment HbF synthesis. Recombinant human erythropoietin, in super-pharmacologic doses, increased F-reticulocyte production when given on a weekly sequential schedule (3 of 7 days) with hydroxyurea (4 of 7 days), but it was less effective on an alternate day schedule when hydroxyurea was given daily. Neither recombinant human interleukin 3 (IL-3) nor recombinant human granulocyte-macrophage colony-stimulating factor (GM-CSF), when infused individually, increased F-reticulocytes in animals receiving daily hydroxyurea. Sequential, overlapping infusions of IL-3 and GM-CSF produced a small but statistically significant increase in F-reticulocytes in one of two hydroxyurea-treated animals. Infusions of sodium butyrate produced a substantial augmentation in F-reticulocyte production in animals chronically treated with hydroxyurea. Thus, our studies have identified several agents that may prove useful in combination with hydroxyurea to achieve clinically beneficial levels of HbF.
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text:
\section{Introduction}
\label{sec:intro}

Scaling transformations are as pervasive in natural image data as translations. In any natural scene, the size of the projection of an object on the retina or a digital sensor varies continuously with the distance between the object and the observer.
Convolutional neural networks (CNNs) already encode structural assumptions about translation invariance and locality.
A vanilla CNN is, however, not designed for multi-scale processing, since the fixed size of the filters together with the depth and max-pooling strategy applied implies a preferred scale.
Encoding structural priors about visual transformations, including scale or affine invariance, is an integrated part of a range of successful classical computer vision approaches. There is also a growing body of work on invariant CNNs, especially concerning invariance to 2D/3D rotations and flips (see e.g. \cite{BruMal-TPAMI2013,CohWel-ICML2016,LapSavBuh-CVPR2016}).
The possibilities for CNNs to generalise to previously unseen scales have, however, not been well explored. We propose that structural assumptions about scale could, similarly to translation covariance, be a useful prior in convolutional neural networks.
\emph{Scale-invariant CNNs} could enable both multi-scale processing and predictable behaviour when encountering objects at novel scales, without the need to fully span all possible scales in the training set.

One of the simplest CNN architectures used for covariant and invariant image processing is a channel network (also referred to as siamese network) \cite{LapSavBuh-CVPR2016}.
In such an architecture, transformed copies of the input image are processed in parallel by different ``channels" (subnetworks) corresponding to a set of image transformations. If combined with weight sharing and max or average pooling over the output from the channels, this approach can enable invariant recognition for finite transformation groups.

An \emph{invariant scale channel network} is a natural extension of invariant channel networks for rotations  \cite{LapSavBuh-CVPR2016}.  It can equivalently be seen as a way of extending ideas underlying the classical scale-space methodology \cite{Iij62-TR,Wit83,Koe84-BC,lindeberg1993-scspbook,lindeberg1994-scsparticle,Flo97-book,scalespaceJapan_weickert99,haarromeny-04book} to deep learning. It should be noted that a channel architecture for scale-invariant recognition poses additional challenges compared to recognition over finite groups. First, scaling transformations are, as opposed to 2D or 3D rotations, not a compact group (intuitively, there is no smallest or largest scale). Second, scaling implies a change in image size and resolution for discrete image data.
The subject of this paper is to investigate the possibility for CNNs to generalise to previously unseen scales by means of a scale channel architecture.

\subsection{Contribution and novelty}
The key contributions of our work are as follows:
\begin{itemize}
\item We perform a theoretical analysis of invariance and covariance properties of scale channel networks.
\item We present a new family of invariant foveated scale channel networks.
\item We evaluate different types of scale channel networks and a standard CNN on the task of \emph{scale generalisation over wide scale ranges}, using a new variation of the MNIST dataset with large scale variations.
\item We demonstrate inherent limitations of previous scale channel approaches.
\item We show that our proposed foveated networks can enable very good generalisation to unseen scales and improvements in the small sample regime.
\end{itemize}
This is, to our knowledge, the first study to evaluate and demonstrate means for CNNs to \emph{generalise to unseen scales over significant scale ranges}.

\subsection{Related work}
In classical scale-space theory \cite{Iij62-TR,Wit83,Koe84-BC,lindeberg1993-scspbook,lindeberg1994-scsparticle,Flo97-book,scalespaceJapan_weickert99,haarromeny-04book},
a multi-scale representation of an input image is created by convolving the image with a set of rescaled Gaussian kernels and Gaussian derivative filters, which are then often combined in non-linear ways. The scale channel networks described in this paper  can be seen as an extension of this philosophy of
 processing an image \emph{at all scales simultaneously}, but using deep non-linear feature extractors learned from data.

CNNs can give impressive performance but they are sensitive to scale variations. Performance degrades for scales not present in the training set \cite{EngTsiSchMad-ICML2019,FawFro-BMVC2015,SinDav-CVPR2018}, different network structure is optimal for small vs large images \cite{SinDav-CVPR2018} and it is possible to construct adversarial examples by means of small translations rotations and scalings \cite{EngTsiSchMad-ICML2019,FawFro-BMVC2015}.
State-of-the-art CNN based object detection approaches
all employ different mechanisms to deal with scale variability, e.g. branching off classifiers at different depths \cite{CaiFanFerVas-ECCV2016}, learning to transform the input or the filters \cite{JadSimZisKav-NIPS2015,YuKol-ICLR2016}, or using different types of image pyramids \cite{SerEigZha-arXiv2013,Gir-ICCV2015,LinDolGirhe-CVPR2017}.
The goal of these approaches has, however, not been to generalise to \emph{previously unseen scales} and they lack the structure necessary for true scale invariance.

Examples of handcrafted scale invariant hierarchical descriptors are \cite{SifMal-CVPR2013,Lin2020provably}. We are, here, interested in combining scale invariance with learning. There exist some previous work aimed explicitly at scale invariant recognition in CNNs  \cite{XuXiaZhaYan-arXiv2014,KanShaJac-arXiv2014,MarKelLob-arXiv2018,WorWel-NIPS2019}. These approaches have, however, either not been evaluated for the task of generalisation to scales \emph{not present in the training set} \cite{KanShaJac-arXiv2014,MarKelLob-arXiv2018,WorWel-NIPS2019} or only across a very limited scale range \cite{XuXiaZhaYan-arXiv2014}. Previous scale channel networks exist, but are explicitly designed for multi-scale processing \cite{FarCouNajLeC-2013,NooPos-PR2016} rather than scale invariance or have not been evaluated with regard to their ability to generalise to unseen scales over any significant scale range \cite{SerEigZha-arXiv2013,XuXiaZhaYan-arXiv2014}.

\section{Theory}
\label{sec:theory}
In this section, we will introduce a mathematical framework for scale channel networks based on a continuous model of the image space. This model enables straightforward analysis of the covariance and invariance properties of the channel networks that are later approximated in a discrete implementation. We, here, generalise previous analysis of invariance properties of channel networks \cite{LapSavBuh-CVPR2016} to scale channel networks. We further analyse covariance properties and additional options for aggregating information across transformation channels.

\subsection{Images and image transformations}
We consider images $f: \mathbb{R}^N \to \mathbb{R}$ that are measurable functions in $L_\infty(\bbbr^N)$ and denote this space of images as $V$.
A \emph{group of image transformations} corresponding to a group $G$ is a family of image transformations $\mathcal{T}_g$ ($g \in G$) with a group structure.
We denote the combination of two group elements $g,h \in G$ by $gh$ and the cardinality of $G$ as $|G|$.
Formally, a group $G$ induces an \emph{action on functions} by acting on the underlying space on which the function is defined (here the image domain). We are here  interested in the group of \emph{uniform scalings} around $x_0$ with the group action
\begin{align}
(\mathcal{S}_{s, x_0} f ) (x') &= f(x) \text{,~~~~} x' = S_s(x - x_0) + x_0
\label{eq:scale-def},
\end{align}
where $S_s = \operatorname{diag}(s)$. For simplicity, we often assume $x_0=0$  and denote $\mathcal{S}_{s,0}$ as $\mathcal{S}_s$ corresponding to
\begin{equation}
(\mathcal{S}_s f)(x) = f(S_s^{-1} x) = f_s(x).
\label{eq:scale-def2}
\end{equation}
We will also consider the translation group with the action (where $\delta \in \bbbr^N$)
\begin{align}
(\mathcal{D}_\delta f) (x') &= f(x) \text{,~~~~}  x' = x + \delta.
\label{eq:trans-def}
\end{align}

\subsection{Invariance and covariance}
Consider a general feature extractor $\Lambda: V \to \mathbb{K}$ that maps an image $f \in V$ to a feature representation $y \in \mathbb{K}$.
In our continuous model, $\mathbb{K}$ will typically correspond to a set of $M$  feature maps (functions) so that $\Lambda f \in V^M$.
This is a continuous analogue of a discrete convolutional feature map with $M$ features.

A feature extractor $\Lambda$ is \emph{covariant} to a transformation group $G$ (formally to the group action) if there exists an \emph{input independent} transformation $\tilde{\mathcal{T}}_g$ that can align the feature maps of a transformed image with those of the original image
\begin{equation}
\Lambda (\mathcal{T}_g f) = \tilde{\mathcal{T}}_g (\Lambda f)
\label{eq:covariance}
\end{equation}
for all $g \in G$ and $f \in V$.
Thus, for a covariant feature extractor it is possible to predict the feature maps of a transformed image from the feature maps of the original image.

A feature extractor $\Lambda$ is \emph{invariant} to a transformation group $G$ if the feature representation of a transformed image is \emph{equal to} the feature representation of the original image
\begin{equation}
\Lambda (\mathcal{T}_g f) = \Lambda (f)
\label{eq:invariance}
\end{equation}
for all $g \in G$ and $f \in V$.
Invariance is thus a special case of covariance where $\tilde{\mathcal{T}_g}$ is the identity transformation.

\subsection{Continuous model of a CNN}

Let $\phi:  V \to V^{M_k}$ denote a continuous CNN with $k$ layers and $M_i$ feature channels in layer $i$.
Let $\theta^{(i)}$ represent the transformation between layers $i-1$ and $i$ such that
\begin{align}
(\phi^{(i)} f)(x,c) &= (\theta^{(i)} \theta^{(i-1)} \cdots \theta^{(2)} \theta^{(1)} f)(x,c),
\label{eq:phi_i-def}
\end{align}
where $c \in \{1,2, \dots M_k\}$ denotes the feature channel and $\phi = \phi^{(k)}$.
We model the transformation $\theta^{(i)}$ between two adjacent layers $\phi^{(i-1)}f$ and $\phi^{(i)}f$ as a convolution followed by the addition of a bias term $b_{i,c} \in \bbbr$ and the application of a pointwise non-linearity $\sigma_i:\bbbr \to \bbbr$:

\begin{multline}
(\phi^{(i)} f)(x, c)\\ =  \sigma_i \left( \sum_{m=1}^{M_{i-1}} \int_{\xi \in \bbbr^N } (\phi^{(i-1)}f)(x-\xi, m)\, g^{(i)}_{m,c}(\xi) \, d\xi + b_{i,c}
\right)
\label{eq:phi_integral}
\end{multline}
where $g^{(i)}_{m,c} \in L_1(\bbbr^N)$
denotes the convolution kernel that propagates information from feature channel $m$ in layer $i-1$ to output feature channel $c$ in layer $i$.
A final fully connected classification layer with compact support can also be modelled as a convolution combined with a non-linearity $\sigma_k$ that represents \emph{a softmax operation} over the feature channels.

\begin{figure*}[hbpt]
	\begin{center}
		\includegraphics[width=0.8\textwidth]{drawing2.pdf}
	\end{center}
	\caption{\emph{Foveated scale channel networks.} a)
		Foveated scale channel network that process an image of the digit 2. Since each scale channel has a fixed size receptive field/support region in the scale channels, they will together process input regions corresponding to varying sizes in the original image (circles of corresponding colors).
		b) This corresponds to a type of foveated processing, where the center of the image is processed with high resolution, which works well to detect small objects, while larger regions are processed using gradually reduced resolution, which enables detection of larger objects. c) There is a close similarity between this model and the foveal scale space model \cite{CVAP166}, which was motivated by a combination of regular scale space axioms with a complementary assumption of a uniform limited processing capacity at all scales.
	}
	\label{fig:foveated-processing}
\end{figure*}

\subsection{Scale channel networks}
\label{sec:scale-channel-networks}
The key idea underlying \emph{channel networks} is to process transformed copies of an input image in parallel, in a set of network ``channels" (subnetworks) with shared weights. For finite transformation groups, such as discrete rotations, using one channel corresponding to each group element and applying max pooling over the channel dimension can give an invariant output code. For continuous but compact groups, invariance can instead be achieved for a discrete subgroup.

The scaling group does, however, imply additional challenges, since it is neither finite nor compact. The key question that we address here, is whether a scale channel network can still support invariant recognition.

We will define a multi-column \emph{scale channel network}
$\Lambda: V \to V^{M_k}$
for the group of scaling transformations $S$ by using a single base network $\phi: V \to V^{M_k}$ to define a set of \emph{scale channels} $\{\phi_s \}_{s \in S}$
\begin{equation}
(\phi_s f)(x,c) = (\phi\, \mathcal{S}_{s} f)(x,c) = (\phi f_s)(x,c),
\label{eq:phi_s-def}
\end{equation}
where each channel thus applies exactly the same operation to a scaled copy of the input image (see Figure \ref{fig:foveated-processing}a).
We will denote the mapping from the input image to the scale channel feature maps at depth $i$ as $\Gamma^{(i)}: V \to V^{M_i |S|}$
\begin{equation}
(\Gamma^{(i)} f)(x,c,s) =  (\phi^{(i)}_s f)(x, c)  = (\phi^{(i)} \mathcal{S}_s f)(x,c).
\label{eq:gamma_s-def}
\end{equation}
A scale channel network invariant to the continuous group of uniform scaling transformations $S = \{s \in \bbbr_+ \}$
can be constructed using an \emph{infinite} set of scale channels $\{ \phi_s \}_{s \in S}$. The following analysis also holds for a set of scale channels corresponding to a discrete subgroup of the group of uniform scaling transformations such that
$S = \{\gamma^i |  i \in {\mathbb Z}\}$, $\gamma > 1$.

The final output $\Lambda f$ from the  scale channel network is an aggregation across the scale dimension of the last layer scale channel feature maps. In our theoretical treatment, we combine the output of the scale channels by the supremum
\begin{equation}
(\Lambda_{\sup} f)(x,c) = \sup_{s \in S} \left[  ( \phi_s f)(x,c,s) \right]
\label{eq:lambda_s-def}.
\end{equation}
Other permutation invariant operators such as averaging operations, could also be used. For this construction, the network output will be invariant to \emph{rescalings around $x_0=0$ for all $x$} such that $(\Lambda_{\sup} f)(x,c) = (\Lambda_{\sup} S_{s}f)(x, c)$ (global scale invariance). This architecture is appropriate  when characterising a single centered object that might vary in scale and it is the main architecture we explore in this paper.
Alternatively, one may instead pool over \emph{corresponding image points} in the original image by operations of the form
\begin{equation}
\label{eq:lambda_s-skewed-def}
(\Lambda_{\sup}^{\operatorname{local}} f)(x, c) = \sup_{s \in S} \{ (\phi_s f)(S_s x, c) \}
\end{equation}
This descriptor instead has the invariance property
$(\Lambda_{\sup}^{\operatorname{local}} f)(x_0, c) = (\Lambda_{\sup}^{\operatorname{local}} S_{s, x_0}f)(x_0, c)$ \emph{for all $x_0$}, i.e. when scaling around an arbitrary image point, the output \emph{at that specific point} does not change (local scale invariance). This property makes it more suitable to describe scenes with multiple objects.

\subsubsection{Scale covariance}
Consider a scale channel network $\Lambda$ (\ref{eq:lambda_s-def}) that expands the input over the group of uniform scaling transformations $S$. We can relate the feature map representation $\Gamma^{(i)}$
for a scaled image copy $\mathcal{S}_t f$ for $t \in S$ and its original $f$ in terms of operator notation as
\begin{align}
&(\Gamma^{(i)} \mathcal{S}_t f)(x,c,s) = (\phi_s^{(i)} \, \mathcal{S}_t f)(x,c) \nonumber\\
&=(\phi^{(i)} \, \mathcal{S}_s \, \mathcal{S}_t f)(x,c) = (\phi^{(i)} \, \mathcal{S}_{s t} f)(x,c) \nonumber\\
&= (\phi_{st}^{(i)} f)(x,c) = (\Gamma^{(i)} f)(x,c, s t),
\label{eq:scale-covariance}
\end{align}
where we have used the definitions (\ref{eq:phi_s-def}) and (\ref{eq:gamma_s-def}) together with the fact that $S$ is a group. A scaling of an image thus only results in a multiplicative shift in the scale dimension of the feature maps. A more general and more rigorous proof using an integral representation of a scale channel network is given in Section \ref{sec:invariance-covariance-proof}.

\subsubsection{Scale invariance}
\label{sec:scale-invariance}
Consider the scale channel network $\Lambda_{\sup}$ (\ref{eq:lambda_s-def}) that selects the supremum over scales. We will show that $\Lambda_{\sup}$ is scale invariant i.e. that
\begin{equation}
(\Lambda_{\sup}\, \mathcal{S}_t f)(x,c) = (\Lambda_{\sup} f)(x,c).
\label{eq:scale-invariance}
\end{equation}
First, (\ref{eq:scale-covariance}) gives $\{\phi^{(i)}_s (\mathcal{S}_t f)\}_{s \in S} = \{ \phi_{st}^{(i)} (f) \}_{s \in S}$. Then, we note that $\{st\}_{s \in S} = St = S$.
This holds both in the case when $S = \bbbr_+$ and in the case when $S = \{\gamma^i |  i \in {\mathbb Z}\}$.
Thus, we have
\begin{multline}
\{(\phi_s^{(i)} \mathcal{S}_t f)(x,c)\}_{s \in S}
= \{(\phi^{(i)}_{s t} f)(x,c)\}_{s \in S}\\ =  \{(\phi^{(i)}_{s} f)(x,c)\}_{s \in S}
\label{eq:phi_maps_scale},
\end{multline}
i.e. \emph{the set} of outputs from the scale channels for a transformed image is equal to the set of outputs from the scale channels for its original image.
For any permutation invariant aggregation operator, such as the supremum, we have that
\begin{multline}
(\Lambda_{\sup}\, \mathcal{S}_s f)(x,c) = \sup_{s \in S} \{(\phi^{(k)}_{s t} f)(x, c)\} \\
=   \sup_{s \in S} \{(\phi^{(k)}_{s} f)(x,c)\}  = (\Lambda_{\sup} f)(x, c),
\label{eq:lambda-scale-invariant}
\end{multline}
and, thus, $\Lambda$ is invariant to uniform rescalings.

\subsection{Proof of scale and translation covariance using an integral representation of a scale channel network}
\label{sec:invariance-covariance-proof}
We, here, prove the transformation property
\begin{equation}
(\Gamma^{(i)} h)(x, s, c)  = (\Gamma^{(i)} f)(x + S_s S_t x_1 - S_t x_2, st, c)
\end{equation}
of the scale channel feature maps
under a more general combined scaling transformation and translation of the form
\begin{equation}
\label{eq-sc-transf-app-sc-cov-proof-noncent-offset}
h(x') = f(x) \quad \mbox{for} \quad x' = S_t (x - x_1) + x_2
\end{equation}
corresponding to
\begin{equation}
h(x) = f(S_t^{-1}(x - x_2) + x_1)
\label{eq:general_scaling_transformation}
\end{equation}
using an integral representation of the deep network.
In the special case when $x_1 = x_2 = x_0$, this corresponds to a
uniform scaling transformation around $x_0$ (i.e. $S_ {x_0,s}$).
With $x_1 = x_0$ and $x_2 = x_0 + \delta$, this
corresponds to a scaling transformation around $x_0$ followed by a
translation $\mathcal{D}_\delta$.

Consider a deep network $\phi^{(i)}$
 (\ref{eq:phi_i-def})
and assume the integral representation (\ref{eq:phi_integral}), where we for simplicity of notation incorporate the offsets $b_{i,c}$ into the
non-linearities $\sigma_{i,c}$.
By expanding the integral representation
of the rescaled image $h$ (\ref{eq:general_scaling_transformation}),
we have that that the feature representation in the scale channel network is given by
 (with $M_0 = 1$ for a scalar input image):

 \begin{align}
 \begin{split}
 &  (\Gamma^{(i)} h)(x, s, c)  =  \{ \mbox{definition (\ref{eq:gamma_s-def})}  \}
 = (\phi_s^{(i)} h)(x, c)
 \end{split}\nonumber\\
 \begin{split}
 & = \{ \mbox{definition (\ref{eq:phi_s-def})} \}
  = (\phi^{(i)} \, h_s)(x, c)
 = \{ \mbox{equation~(\ref{eq:phi_i-def})} \}
 \end{split}\nonumber\\
 \begin{split}
 & = (\theta^{(i)} \theta^{(i-1)} \dots \theta^{(2)} \theta^{(1)}  h_s)(x, c)
 = \{ \mbox{equation~(\ref{eq:phi_integral})} \}
 \end{split}\nonumber\\
 \begin{split}
 & =
 \sigma_{i,c}
 \left(
 \sum_{m_i=1}^{M_{i-1}}
 \int_{\xi_i \in \bbbr^N}
 \sigma_{i-1,m_i}
 \left(
 \sum_{m_{i-1}=1}^{M_{i-2}}
 \int_{\xi_{i-1} \in \bbbr^N}
 \dots
 \right.
 \right.
 \end{split}\nonumber\\
 \begin{split}
 & \phantom{\sigma_i \vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)}} \quad
 \left.
 \left.
 \sigma_{1,m_2}
 \left(
 \sum_{m_1=1}^{M_0}
 \int_{\xi_1 \in \bbbr^N}
 h_s(x - \xi_i - \xi_{i-1} -
 \dots - \xi_1) \, \times
 \right.
 \right.
 \right.
 \end{split}\nonumber\\
 \begin{split}
 & \phantom{\sigma_i \vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)}} \quad
 \left.
 \left.
 \left.
 \phantom{\left(\sum_{m_i=1}^{M_{i-1}} \right.)}
 g_{m_1,m_2}^{(1)}(\xi_1)  \, d\xi_1
 \right) \dots
 g_{m_{i-1},m_i}^{(i-1)}(\xi_{i-1})  \, d\xi_{i-1}
 \vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)}
 \right)
 \right.
 \end{split}\nonumber\\
 \begin{split}
 \label{eq-exp-int-repr-sc-cov-proof-noncent-offset}
 \left.
 \vphantom{\left(\sum_{m_i=1}^{M_{i-1}} \right.)}\quad\quad
 g_{m_i,c}^{(i)}(\xi_i)  \, d\xi_i
 \vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)} \right).
 \end{split}
 \end{align}
Under the scaling transformation (\ref{eq-sc-transf-app-sc-cov-proof-noncent-offset}), the part of the integrand
$h_s(x - \xi_i - \xi_{i-1} - \dots -\xi_1)$ transforms as follows:
\begin{align}
\begin{split}
& h_s(x - \xi_i - \xi_{i-1} - \dots - \xi_1)
\end{split}\nonumber\\
\begin{split}
& = \{ \mbox{$h_s(x) = h(S_s^{-1}x)$ according to definition (\ref{eq:scale-def2})}  \}
\end{split}\nonumber\\
\begin{split}
& = h(S_s^{-1} (x - \xi_i - \xi_{i-1} - \dots - \xi_1))
\end{split}\nonumber\\
\begin{split}
& = \{ \mbox{$h(x) = f(S_t^{-1} (x-x_2) + x_1)$ according to (\ref{eq:general_scaling_transformation}) } \}
\end{split}\nonumber\\
\begin{split}
& = f(S_t^{-1} S_s^{-1} ((x - \xi_i - \xi_{i-1} - \dots - \xi_1) - S_s x_2 + S_s S_t x_1)
\end{split}\nonumber\\
\begin{split}
& = \{ \mbox{$S_s S_t = S_{st}$ for scaling transformations} \}
\end{split}\nonumber\\
\begin{split}
& = f(S_{st}^{-1} ((x + S_s S_t x_1 - S_s x_2 - \xi_i - \xi_{i-1} - \dots - \xi_1))
\end{split}\nonumber\\
\begin{split}
& = \{ \mbox{$f_{st}(x) = f(S_{st}^{-1} x)$ according to definition (\ref{eq:scale-def2})} \}
\end{split}\nonumber\\
\begin{split}
& = f_{st}(x + S_s S_t x_1 - S_s x_2 - \xi_i - \xi_{i-1} - \dots - \xi_1).
\end{split}
\end{align}
Inserting this transformed integrand into the integral representation (\ref{eq-exp-int-repr-sc-cov-proof-noncent-offset})
gives
\begin{align}
\begin{split}
&  (\Gamma^{(i)} h)(x, s, c) =
\end{split}\nonumber\\
\begin{split}
& =
\sigma_{i,c}
\left(
\sum_{m_i=1}^{M_{i-1}}
\int_{\xi_i \in \bbbr^N}
\sigma_{i-1,m_i}
\left(
\sum_{m_{i-1}=1}^{M_{i-2}}
\int_{\xi_{i-1} \in \bbbr^N}
\dots
\right.
\right.
\end{split}\nonumber\\
\begin{split}
& \phantom{\sigma_i \vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)}} \quad
\left.
\left.
\sigma_{1,m_2}
\left(
\sum_{m_1=1}^{M_0}
\int_{\xi_1 \in \bbbr^N}
f_{st}(x + S_s S_t x_1 - S_s x_2  -
\right.
\right.
\right.
\end{split}\nonumber\\
\begin{split}
& \hphantom{\sigma_i \vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)}} \quad
\left.
\left.
\hphantom{\sigma_{1,m_2} \left(  \sum_{m_1=1}^{M_0}
	\int_{\xi_1 \in \bbbr^N} \right. } \quad\quad
\xi_i - \xi_{i-1} - \dots - \xi_1) \times
\right.
\right.
\end{split}\nonumber\\
\begin{split}
& \phantom{\sigma_i \vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)}} \quad
\left.
\left.
\left.
\phantom{\left(\sum_{m_i=1}^{M_{i-1}} \right.)}
g_{m_1,m_2}^{(1)}(\xi_1)  \, d\xi_1
\right) \dots
g_{m_{i-1},m_i}^{(i-1)}(\xi_{i-1})  \, d\xi_{i-1}
\vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)}
\right)
\right.
\end{split}\nonumber\\
\begin{split}
\left.
\vphantom{\left(\sum_{m_i=1}^{M_{i-1}} \right.)}\quad\quad
g_{m_i,c}^{(i)}(\xi_i)  \, d\xi_i
\vphantom{\left( \sum_{m_i=1}^{M_{i-1}} \right.)} \right),
\end{split}
\end{align}
which we recognize as
\begin{align}
\begin{split}
&  (\Gamma^{(i)} h)(x, s, c)
\end{split}\nonumber\\
\begin{split}
& = (\theta^{(i)} \theta^{(i-1)} \dots \theta^{(2)} \theta^{(1)} f_{st})(x + S_s S_t x_1 - S_s x_2, c)
\end{split}\nonumber\\
\begin{split}
& = (\phi^{(i)} \, f_{st})(x + S_s S_t x_1 - S_s x_2, c)
\end{split}\nonumber\\
\begin{split}
&  = (\phi_{st}^{(i)} f)(x + S_s S_t x_1 - S_s x_2, c)
\end{split}\nonumber\\
\begin{split}
&=  (\Gamma^{(i)} f)(x + S_s S_t x_1 - S_s x_2, st, c)
\end{split}
\end{align}
and which proves the result. Note that for a pure translation ($S_t = I$,  $x_1 = x_0 $  and $x_2 = x_0 + \delta$) this gives
\begin{align}
&(\Gamma^{(i)}\, \mathcal{D}_\delta\, f)(x,c,s) = (\Gamma^{(i)} f)(x - S_s \delta, s, c).
\label{eq:translation-covariance-scale}
\end{align}
Thus, translation covariance is preserved in the scale channel network but the magnitude of the spatial shift in the feature maps will depend on the scale channel.

\subsection{Relations to scale-space theory}
In classical scale-space theory \cite{Iij62-TR,Wit83,Koe84-BC,lindeberg1993-scspbook,lindeberg1994-scsparticle,Flo97-book,scalespaceJapan_weickert99,haarromeny-04book}, a multi-scale representation of an input image is created by convolving the image with a set of rescaled and normalised Gaussian kernels. The  scale channel networks described in this paper are  based on a similar philosophy of processing an image at \emph{all scales simultaneously}, although \emph{the input image}, as opposed to the filter, is expanded over scales.
For continuous image data, a representation computed by applying a fixed size filter to a set of rescaled input images is computationally equivalent to applying a set of rescaled and scale-normalised filters to a fixed size input (as done when computing a Gaussian scale-space representation). The two representations are related through a \emph{spatial rescaling} and an \emph{inverse mapping of the scale parameter} $s \mapsto s^{-1}$ (see Appendix \ref{app:relation-to-scale-space1}).

For discrete image data, a similar relation holds approximately, provided that the discrete rescaling operation is a sufficiently good approximation of the continuous rescaling operation.

A key difference compared to classical scale-space representations is that \emph{non-linear} feature extractors \emph{learned from data} are used as opposed to the mathematically derived Gaussian derivatives and differential invariants.
The outputs from the scale channels do, however, still constitute a \emph{(non-linear) scale-covariant multi-scale representation}, which implies that e.g. maxima over scale are preserved, although shifted to a different scale channel, when an input image is rescaled.

The use of \emph{supremum}, or for a discrete set of scale channels, \emph{max-pooling}, (see further Section \ref{sec:discrete-scale-channels}) over the outputs of the scale channels is structurally similar to classical methods for \emph{scale selection}, which detect maxima over scale of scale-normalised filter responses \cite{lindeberg97-IJCV,scaleselection-Lin14}. Here, max pooling is, however, done over more complex feature responses, already adapted to detect specific objects, while classical scale selection is performed in a class-agnostic way based on low-level features. This makes max-pooling in the scale channel networks also closely related to more specialized classical methods that detect maxima
 from the scales at which a supervised classifier delivers class labels with the highest posterior \cite{LiTaxLoo11-ScSp, LooLiTax09-LNCS}.
Average pooling over the outputs of a discrete set of scale channels (Section \ref{sec:discrete-scale-channels}) is structurally similar to methods for scale selection that are based on \emph{weighted averages} of filter responses at different scales \cite{Lin15-JMIV,scaleselection-Lin13JMIV}. Although there is no guarantee that the learned non-linear features will, indeed, take maxima for relevant scales, one might expect training to promote this, since a failure to do so should be detrimental to the classification performance of these networks.
In case the learned features correspond to partial \emph{Gaussian
derivatives} of some orders, then the
application of these filters to all the scale channels is, in fact, computationally equivalent to applying corresponding
	\emph{scale-normalised Gaussian derivatives} to the original image (see Appendix \ref{app:relation-to-scale-space2}).

\section{Discrete scale channel networks}
\label{sec:discrete-scale-channels}
Discrete scale channel networks are implemented by using a standard discrete CNN as the base network $\phi$. For practical applications, it is also necessary to restrict the network to include a finite number of scale channels $\hat{S} = \{ \gamma^{i}\}_{-K_{min} \leq i \leq K_{max} }$. The input image $f:{\mathbb Z}^2 \to \bbbr$ is assumed to be of finite support.
The outputs from the scale channels are, here,  aggregated using e.g. max pooling
\begin{equation}
(\Lambda_{\operatorname{max}}f)(x,c) = \operatorname{max}_{s \in \hat{S}} \{(\phi_s f)(x,c,s) \}
\label{eq:lambda-s-max}
\end{equation}
or average pooling
\begin{equation}
(\Lambda_{\operatorname{avg}} f)(x,c)= \mathop{\operatorname{avg}}_{s \in \hat{S}} \{(\phi_s f)(x,c,s) \}.
\label{eq:lambda-s-avg}
\end{equation}
We will also implement discrete scale channel networks that concatenate the outputs from the scale channels followed by an additional transformation $\varphi: \bbbr^{M_i |\hat{S}|} \to \bbbr^{M_i}$ that mixes the information from the different channels
\begin{align}
&(\Lambda_{\operatorname{conc}} f)(x, c) \nonumber \\
&=  \varphi \left( [(\phi_{s_1} f)(x,c), (\phi_{s_2} f)(x,c) \cdots  (\phi_{s_{|\hat{S}|}} f)(x,c) ] \right).
\label{eq:lambda-s-conc}
\end{align}
$\Lambda_{\operatorname{conc}}$ does not have any theoretical guarantees of invariance, but
since scale concatenation of outputs from the scale channels has been previously used with the explicit aim of scale invariant recognition \cite{XuXiaZhaYan-arXiv2014}, we will evaluate it also here.

\subsection{Foveated processing}
\label{sec:foveated-operations}
A standard convolutional neural network $\phi$ has a finite support region $\Omega$ in the input.
When rescaling an input image of fixed size/finite support in the scale channels, it is necessary to decide how to process the resulting images of varying size using a feature extractor with fixed support. One option is to process regions of \emph{constant size} in the scale channels corresponding to regions of \emph{different sizes} in the input image.
This results in \emph{foveated image operations}, where a smaller region around the center of the input image is processed with high resolution, while gradually larger regions of the input image are processed with gradually reduced resolution (see Figure~\ref{fig:foveated-processing}b-c).
We will refer to the foveated network architectures $\Lambda_{\operatorname{max}} $, $\Lambda_{\operatorname{avg}} $ and $\Lambda_{\operatorname{conc}} $ as the FovMax network, the FovAvg network and the FovConc network respectively.

\subsection{Approximation of scale invariance}
Foveated processing combined with max or average pooling
will give an approximation of the scale invariance in the continuous model (Section \ref{sec:scale-invariance}) over \emph{a limited scale range}. The numerical scale warpings of the input images in the scale channels approximate continuous scaling transformations. A discrete set of scale channels will approximate the representation for a continuous scale parameter.
A possible issue is problems at the scale boundaries of a finite scale interval.
Boundary effects can, however, be mitigated if the network learns to suppress responses for both very zoomed in and very zoomed out objects.
If including a large enough number of scale channels and training the network from scratch, this is, in fact, a likely scenario, since the network will otherwise classify based on use of object views that will hardly provide useful information.

\subsection{Sliding window processing in the scale channels}
\label{sec:sliding-window}

An alternative option for dealing with varying image sizes is to, in each scale channel, process the entire rescaled image by applying the base network in \emph{a sliding window manner}.
The output from the scale channels can then be combined by max (or average) pooling over space followed by max (or average) pooling over scales
\begin{equation}
(\Lambda_{sw,\operatorname{max}} f)(c) = \operatorname{max}_{s \in S} \operatorname{max}_{x \in \Omega_s} \{ (\phi_s f)(x, c, s)  \},
\label{eq:disc-sliding-window-pool}
\end{equation}
where $\Omega_s = \{sx | x \in \Omega \}$.
We will here only evaluate the architecture using max pooling, which is structurally similar to the popular multi-scale OverFeat detector \cite{SerEigZha-arXiv2013}. This network will be referred to as the SWMax network. For this scale channel network to support invariance, it is not enough that boundary effects resulting from using a finite number of scale channels are mitigated. When processing regions in the scale channels corresponding to only a single region in the input image, new structures can appear (or disappear) in this region for a rescaled version of the original image. With a linear approach this might be expected to not cause problems.
For a deep neural network, however, there is no guarantee that there cannot be strong erroneous responses for e.g. a partial view of a zoomed in object. We are, here, interested in studying the effects this has on generalisation in the deep learning context.

\begin{figure*}[h]
	\centering
	\subfloat[Subfigure 1 list of figures text][Standard CNN.]{
		\includegraphics[width=0.48\textwidth]{mnist_cnn_generalisation_tr1_tr2_tr4.pdf}
		\label{fig:subfig1}
}
	\subfloat[Subfigure 2 list of figures text][The FovConc network.]{
		\includegraphics[width=0.48\textwidth]{mnist_fovconc_generalisation_tr1_tr2_tr4_3ch.pdf}
		\label{fig:subfig2}
} \\
\vspace*{-1em}
	\subfloat[Subfigure 3 list of figures text][The FovMax and FovAvg networks]{
		\includegraphics[width=0.48\textwidth]{mnist_fovmaxavg_channels_tr1_tr2_tr4.pdf}
		\label{fig:subfig3}
}
	\subfloat[Subfigure 4 list of figures text][The SWMax network]{
		\includegraphics[width=0.48\textwidth]{mnist_swmax_channels_tr1_tr2_tr4_17ch_narrow.pdf}
		\label{fig:subfig4}
}
	\caption{\emph{Generalisation ability to unseen scales for a standard CNN and the different scale channel network architectures}. The networks are trained on digits of scale 1 (tr1), scale 2 (tr2) or scale 4 (tr4) and evaluated for varying rescalings of the test set. We note that the CNN (a) and the FovConc network (b) have poor generalisation ability to unseen scales, while the FovMax and FovAvg networks (c) generalise extremely well. The SWMax network (d) generalises considerably better than a standard CNN, but there is some drop in performance for scales not seen during training.
	}
	\label{fig:single-scale-generalisation}
\end{figure*}

\section{Experiments}

\subsection{The MNIST Large Scale dataset}
\label{sec:mnist-scale}
To evaluate the ability of standard CNNs and  scale channel networks to generalise to unseen scales over \emph{a wide scale range}, we have created a new version of the standard MNIST dataset \cite{MNISToriginal-1998}.
This new dataset, \emph{MNIST Large Scale}, which is available online \cite{MnistLargeScale-online}, is composed of images of size $112 \times 112$  with scale variations of a factor 16 for scale factors $s \in [0.5, 8]$ relative to the original MNIST dataset. The train and test sets for the different scale factors are created by resampling the original MNIST training and test sets using bicubic interpolation followed by smoothing and soft thresholding to reduce discretization effects. Note that for scale factors $>4$, the full digit might not be visible in the image. These scale values are nonetheless included to study the limits of generalisation. More details concerning this dataset are given in Appendix \ref{app:mnist-large-scale}.

\subsection{Network and training details}

\emph{The standard CNN} is composed of 8 conv-batchnorm-ReLU blocks followed by a fully connected layer and a final softmax layer. The number of features/filters in each layer is 16-16-16-16-32-32-32-32-100-10. A stride of 2 is used in convolutional layers 2, 4, 6 and 8. The reason for using a quite deep network is to avoid a network structure that is heavily biased towards recognising either small or large digits.

\emph{The FovMax, FovAvg, FovConc and SWMax\footnote{We noted that batchnorm impairs performance when training the SWMax network from scratch. We believe this is because the sliding window approach implies in a change
	in the feature distribution when processing data of different scales.

	We, therefore, train the SWMax network without batchnorm.}
scale channel networks} are constructed using scale channels with 4 conv-batchnorm-ReLU blocks followed by a fully connected layer and a final softmax layer. Rescaling within the scale channels is done with bilinear interpolation and applying border padding or cropping as needed. Batchnorm layers are shared across the scale channels.
The number of features/filters in each layer is 16-16-32-32-100-10. A stride of 2 is used in convolutional layers 2 and 4. All scale channel architectures have around 70\,000 parameters, while the baseline CNN has around 90\,000 parameters.

All networks are trained with 50\,000 training samples from the MNIST Large Scale dataset for 20 epochs using the Adam optimiser. During training, 15 \% dropout is applied to the first fully connected layer. The learning rate starts at $3e^{-3}$ and decays with a factor $1/e$ every second epoch towards a minimum learning rate of $5e^{-5}$. Results are reported for the MNIST Large Scale test set (10\,000 samples) as the average of training each network using three different random seeds. The remaining 10\,000 samples constitute a validation set. Numerical performance scores for Figures~2--5 are given in Appendix \ref{app:numerical}.

\subsection{Generalisation to unseen scales}
We, first, evaluate the ability of the standard CNN and the different scale channel networks to generalise to previously unseen scales. We train each network on each of the scales 1, 2, and 4
and evaluate the performance on the test set for scale factors between $1/2$ and $8$. The FovMax, FovAvg and SWMax networks have 17 scale channels spanning the scale range $[\frac{1}{2}, 8]$. The FovConc network has 3 scale channels spanning the scale range $[1,4]$.\footnote{The FovConc network performs considerably worse when including too many scale channels or spanning a too large scale range. Since we are more interested in the best case rather than the worst case scenario, we, here, picked the best network out of a large range of configurations.} The results are presented in Figure \ref{fig:single-scale-generalisation}.
We, first, note that all networks achieve similar top performance for the scales seen during training. There are, however, large differences in the abilities of the networks to generalise to unseen scales:

\subsubsection{Standard CNN}
The standard CNN shows limited generalisation ability to unseen scales with a large drop in accuracy for scale variations larger than a factor $\sqrt{2}$. This illustrates that, while the network can recognise digits of all sizes, a vanilla CNN includes no structural prior to promote scale invariance.

\subsubsection{The FovConc network}
 The generalisation ability of the FovConc network is quite similar to that of the standard CNN, sometimes slightly worse. The reason for limited generalisation is that although the scale channels share weights, when simply concatenating the outputs from the scale channels there is no structural constraint to support invariance. This is consistent with our observation that
  spanning a too large scale range or using too many channels degrades generalisation for the FovConc network. For scales \emph{not present during training}, there is, simply, no useful training signal to learn the correct weights in the fully connected layers combining the scale channel outputs.
  Note that our results are not contradictory to those previously reported for a similar network structure  \cite{XuXiaZhaYan-arXiv2014}, since they train on data that contain natural scale variations and test over a quite narrow scale range. What we do show, however, is that this network structure is \emph{not scale invariant}.

\begin{figure}[hbpt]
	\begin{center}
		\includegraphics[width=0.5\textwidth]{mnist_fovmax_fovavg_channels_denseness_zoom.pdf}
	\end{center}
	\caption{\emph{Varying the sampling density of the scale channels.} FovMax and FovAvg networks spanning the scale range $[\frac{1}{4},8]$ are trained with varying spacing between the scale channels ($2$, $2^{1/2}$ and $2^{1/4}$). All networks are trained on scale 2. There is a significant increase in the performance when reducing the spacing between the scale channels from $2$ to $2^{1/2}$ while the effect of a further reduction to $2^{1/4}$ is small.

	}
	\label{fig:denseness}
\end{figure}

\subsubsection{The FovAvg and FovMax networks}
We note that the FovMax and FovAvg networks generalise very well, independently of which scale the network is trained on. The maximum difference in performance in the scale range $[1,4]$ between training on scale 1, scale 2 or scale 4  is less than 0.2 percentage points for these network architectures.
Importantly, this shows that, if including a large enough number of scale channels and training the networks from scratch, boundary effects at the scale boundaries do not prohibit invariant recognition.
For the FovAvg and FovMax networks, we also investigate how densely it is necessary to sample the scale channels for good performance. The result is presented in Figure \ref{fig:denseness}. Accuracy is considerably improved when decreasing the distance between consecutive channels from a factor $2$ (5 channels) to a factor of $2^{1/2}$ (9 channels), while a further reduction to $2^{1/4}$ (17 channels) provide very small additional benefits.

\begin{figure*}[hbpt]

\begin{tabular}{cc}
			\includegraphics[width=0.48\textwidth]{compare_single_vs_multi_cnn_fovconc_sw.pdf}  &
				\includegraphics[width=0.48\textwidth]{compare_single_vs_multi_cnn_fovmax_fovavg.pdf}
\end{tabular}

	\caption{\emph{Multiscale image data.}
		All networks are trained on digits in the scale range $[1,4]$  (tr1-4) and evaluated for varying scale factors in the test set.
		The difference in generalisation ability between training on multiscale and single scale data (dotted lines) is striking for both the CNN and the FovConc network.
		For the FovMax and FovAvg networks, the difference is negligible between multiscale and single scale training, which illustrates the strong invariance properties of these networks.}
	\label{fig:compare_multiscale_all}
\end{figure*}

\subsubsection{The SWMax network}
We note that the SWMax network generalises considerably better than a standard CNN, but there is some drop in performance for scales not seen during training.
We believe that the main reason for this is, here, that since all scale channels are processing a fixed sized region in the input image (as opposed to for foveated processing), new structures might leave or enter this region when an image is rescaled. This might lead to erroneous high responses for unfamiliar views (Section \ref{sec:sliding-window}).
We also noted that the SWMax networks are harder to train (more sensitive to learning rate etc) compared to the foveated network architectures as well as more computationally expensive.
Thus, while the FovMax and FovAvg networks still are easy to train and the performance is not degraded when spanning a large scale range, the SWMax network seems to work best for spanning a more limited scale range where fewer scale channels are needed (as was indeed the use case in \cite{SerEigZha-arXiv2013}).

\subsection{Multiscale vs.\ single scale training}
\label{sec:multiscale_vs_singlescale}
All the scale channel architectures support multiscale processing although they might not support scale invariance. We, here, test the performance of the different scale channel networks when training on multiscale training data.
For the FovMax, FovAvg and FovSW network, the same scale channel setup (17 channels) is used as for single scale training. For the FovConc network, 5 scale channels spanning the scale range $[\frac{1}{2}, 8]$ are used, since this setup gives  better results compared to the previous setup with 3 channels.

 The results are presented in Figure \ref{fig:compare_multiscale_all}.
 The difference between training on multiscale and single scale data is striking for the standard CNN and the FovConc network. It can, however, be noted that the FovConc network does generalise slightly better than a standard CNN outside the scale range it is trained on. For the SWMax network, including multiscale data improves generalisation somewhat for larger scales but impairs generalisation somewhat for smaller scales.
The difference in generalisation ability between training on a single scale or multiscale image data is almost indiscernible for the FovMax and FovAvg networks.

\subsection{Generalisation from fewer training samples}
Another scenario of interest is when the training data does span a relevant range of scales, but there are few training samples. Theory would predict a correlation between the performance in this scenario and the ability to generalise to unseen scales.
To test this prediction, we trained the standard CNN and the different scale channel networks on multi scale training data spanning the scale range $[1,4]$, while gradually reducing the number of samples in the training set. Here, the same scale channel setup with 17 channels spanning the scale range $[\frac{1}{2}, 8]$ is used for all the architectures. The results are presented in Figure \ref{fig:mnist_few_samples}. We note that the FovConc network shows some improvement over the standard CNN. The SWMax network, on the other hand, does not, and we hypothesise that when using fewer samples, the problem with partial views of objects (see Section \ref{sec:sliding-window}) might be more severe.
 Note that the way the OverFeat detector is used is the original study \cite{SerEigZha-arXiv2013}, is more similar to our single scale training scenario, since they use base networks pretrained on ImageNet.  The FovAvg and FovMax networks show the highest robustness also in this scenario. This illustrates that these networks can give improvements when multiscale training data is available but there are few training samples.

\begin{figure}[hbpt]

	\begin{center}
		\includegraphics[width=0.45\textwidth]{mnist_few_samples_comparison.pdf}

	\end{center}
	\caption{\emph{Training  with smaller training sets with large scale variations}. All network architectures are evaluated on their ability to classify data with large scale variations while reducing the number of training samples. Both the training and test set here span the scale range $[1,4]$. The FovAvg network shows the highest robustness when decreasing the number of training samples followed by the FovMax network.

}
	\label{fig:mnist_few_samples}
\end{figure}

\section{Summary and conclusions}

We have presented a theoretical analysis of covariance and invariance properties of continuous scale channel networks. Moreover, we performed an experimental evaluation of different types of discrete scale channel networks on the task of generalising to unseen scales over wide scale ranges. The tested networks include a new family of scale channel networks that combine foveated processing with max or average pooling over the scale channels (the FovMax and FovAvg networks). The experimental evaluation illustrates the strong invariance properties of these networks in practice and limitations of previous approaches and vanilla CNNs.
We believe that our proposed foveated scale channel networks
will prove useful in situations where a simple approach that can generalise to unseen scales or learn from small datasets with large scale variations is needed. This type of foveated scale invariant processing could also be included as subparts in more complex frameworks dealing with large scale variations.

A more overarching aim of this study have been to test the limits of CNNs to generalise to unseen scales over a wide scale range. The key take home message is a proof of concept that such generalisation is possible if including structural assumptions about scale in the network design.

redpajama_set_name: RedPajamaArXiv


text:
E. Michael Jones a Kremlin tool, wittingly or unwittingly
April 8, 2021 Anno Domini
Author-turned Eurasian guest of honour E. Michael Jones completely failed at trying to dismiss last month the claim that he is a KGB asset aiding the demise of the West.
Jones attempted to dismiss the claim (made by researcher Andy Sloan on this site) using a strawman argument during a live chat on Restoring the Faith, March 6, 2021.
"Someone is now spreading this ridiculous, preposterous claim that I am a KGB agent because I was in a room with Aleksandr Dugin," Jones declared. He went on, "I am in the unfortunate position of being unable to prove a negative. I cannot prove that I am not a KGB agent, so the burden of proof lies on these people, these character assassinations (sic) who are launching this in the first place. I was at a conference in Tehran with Dugin…he gave a speech about multi-polarity. I offered an objection to that that speech saying we lived in some sense a uni-polar world, even if it's not the United States of America that's head of it. That was the extent of our discussion. This Internet breeds character assassination and this is one example of it."
First off, Sloan's article in no way based his claim merely on the fact that Jones was in the same room with Dugin (on multiple occasions, by the way). Jones then follows his strawman argument with a challenge of burden of proof, which Sloan did thoroughly provide. Jones addressed none of the many, many pieces of evidence written by Sloan. Did he even read it or is he deceiving his audience about the breadth of evidence?
Jones then claims he offered an objection to Dugin's speech about multi-polarity. But he didn't really offer an objection, though. He merely stated what he perceives as the current world geopolitical reality—that it is unipolar. Furthermore, Jones completely fails to discern (deliberately?) Dugin's meaning of multi-polarity, which is really just jargonous deception to distract from the fact that Dugin wants his Eurasian union to rule the world as a unipolar, neo-Bolshevik empire (world government). To achieve this, the Eurasianists have to break the West's seemingly unipolar rule using an appeal to the West's enemies to engage in multi-polarism (divesting from the West) and embracing the East (Eurasianism, Belt and Road initiative). If Jones genuinely can't understand this, then he is unfit to be a geopolitical analyst, especially as a self-appointed representative of the Catholic Church and the United States of America. Even Glenn Beck's audience have a better understanding of Dugin's deceptive language than does Jones, and Beck's audience could be classified as "normies".
At worst, Sloan is correct and Jones is a KGB asset wittingly distorting the evidence. Either way, Jones is carrying out the neo-Soviet Eurasianists' objective of distorting the East's true intentions as well as blaming the West for what is really Eastern subversion of it. While Jones does seem free, in his apparent KGB mission, to criticize world Jewry, he flat out denies Jewry's subdivisions: subversion by freemasonry and Soviet communist threat.
"…communism was never a threat, in general." —Jones
This is in addition to Jones being a race denialist (except when non-whites are he subject), denial of communism as a still-present threat, soft on Vatican II and its "popes", outright heretical statements concerning Islam, propping up of Putin as an anti-globalist renegade, and associations with numerous Eurasianists and socialists, like Israel Shamir and Dugin—all Soviet-friendly narratives.
Jones has become so blatant with his agenda, I have had to create a dossier just to catalogue it all. The guy smacks of shill. It's becoming more and more plain.
Aleksandr DuginCulture WarsDuginismE. Michael JonesEurasinistsGlenn BeckMulti-polarOpus DeiRoosh VSovietsuni-polar
Belt and Road / Catholic / Cointelpro / Communism / Controlled Opposition / Dossiers / Shills / Uncategorized 7 comments
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Great as always my friend. Never forget Jones said Communism was 'never a threat." That's all it took for me to be convinced. Such a stupid comment here on the eve of the rising dragon.
Yeah, I remember him saying that, but I couldn't find the video.
Ah, just found it. You posted it. https://twitter.com/FitzInfo/status/1376315127289483264
At 31:36-34:12 in the below interview, Jones says the Soviet Union ended & "The American Empire is in process of collapse & HAS UNITED THE EURASIAN LANDMASS & will bring about a NEW WORLD ORDER, to REPLACE the American Empire."
https://www.altcensored.com/watch?v=fMwc19MqDEI
and at 34:17-34:37
"China is NOT a threat to the West and trying to collaborate with the West."
At minimum, please use your common-sense folks!!
https://fitzinfo.net/2020/12/25/e-michael-jones-is-a-kgb-asset-and-guilty-of-immeasurable-treason-against-the-usa-west/
In further comment on this article, it is well to correct again the common-belief that Jones is against all Jews. This is false. His narrative is against WESTERN ZIONIST JEWS ONLY – the same as Dugin and according to Operation SIG:
Jones interview 2018:
Vendée Radio: "Do, you know, Orthodox Jews, Hasidic Jews, the more religious Jews, do they not oppose it (the Jewish revolutionary spirit)?"
Jones: "Well yeah. I mean they do. I mean there's Neturei Karta – it's a completely Anti-Zionist operation that opposes the State of Israel."
last paragraph
https://culturewars.com/podcasts/tag/Henry+Regnery
"I said to Rabbi Weiss (of anti-zionist Jewish sect Neturei Karta), I wish all Jews were like you. His organisation is anti-zionist."
9 m -9 m 44 s
https://culturewars.com/podcasts/tag/Alexander+Dugin
Dugin: "Zionism is Jewish satanism. Anti-Zionist Neturei Karta represent true Jewish tradition.
(click 'show more' for English text translation)
https://youtube.com/watch?v=xlBNLp5qXso&t=28s
Dugin:
Orthodox Christians are good; Western Christians a 'fallen branch'. Western Zionist Jews bad…the others we could presume to be different.
3m 5s – 3m 40s & 7m:31s -8m 11s
https://youtu.be/qWLABY5ZcW8?t=185
Operation SIG – Soviet defector Ion Pacepa:
"In 1972, the Kremlin decided to turn the whole Islamic world against Israel and the USA. As KGB chairman Yuri Andropov told me, a billion adversaries could inflict far greater damage on America than could a few million. We needed to instill a Nazi-style hatred for the Jews throughout the Islamic world and to turn this weapon of the emotions into a terrorist bloodbath against Israel and its main supporter, the United States. The codename of this operation was 'SIG' (Sionistskiye Gosudarstva, or 'Zionist Governments'). The task was to portray that the United States and Israel were 'fascist, imperial-Zionist countries' bankrolled by rich Jews and run by Jewish politicians, whose aim was to subordinate the entire Islamic world."
https://www.thefreelibrary.com/The+real+terror+paymasters%3A+the+KGB+has+long+sponsored+the+Muslim%E2%80%A6-a0168397212
Hence, absolutely in line, Jones on Israel Shamir (another KGB asset):
"If Shamir is a prophet, his main prophecy is left v right is obsolete (another Dugin narrative) given the new dichotomy, which is the Jewish US empire v the rest of the world."
(About half-way down)
https://shankradioworldwide.typepad.com/shankradio_world_wide/e-michael-jones/
In all, Jones' de facto narrative on Jews, given his promotion of the Eurasian world order, is the same as Dugin's:
"There will always be a place for Jewish Orientalism (Eastern Jews) in the ranks of the builders of the Great Eurasian Empire."
section 8, last paragraph
https://niqnaq.wordpress.com/2013/11/07/dugin-on-the-jews/
Elon Musk a Fraud.
https://twitter.com/nLiigjvL1GCBgnu/status/1404167508278616064
Elon Musk, CEO of SpaceX, visits Israel, with tour of Masada, and even drops in at Jerusalem pub.
https://www.israelnationalnews.com/News/News.aspx/243401
A. Gaveer says:
Same with Assange who is a Mossad asset being himself a cryptojew and can't deny it so he avoid anyone that might bring up the question.
Who believe these shills?!