text:
# Organization:National Institute of Standards and Technology

Short description: Measurement standards laboratory in the United States
Agency overview March 3, 1901; 121 years ago (as National Bureau of Standards),became NIST in 1988 100 Bureau DriveGaithersburg, Maryland, U.S.39°07′59″N 77°13′25″W / 39.13306°N 77.22361°W Approx. 3,400[1] United States dollar 1.03 billion (FY 2021)[2] Laurie E. Locascio[3], Under Secretary of Commerce for Standards and Technology and Director of NIST Department of Commerce www.nist.gov

The National Institute of Standards and Technology (NIST) is a physical sciences laboratory and non-regulatory agency of the United States Department of Commerce. Its mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement. From 1901 to 1988, the agency was named the National Bureau of Standards.[4]

## History

### Background

The Articles of Confederation, ratified by the colonies in 1781, provided:

The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective states—fixing the standards of weights and measures throughout the United States.[5]

Article 1, section 8, of the Constitution of the United States, ratified in 1789, granted these powers to the new Congress: "The Congress shall have power ... To coin money, regulate the value thereof, and of foreign coin, and fix the standard of weights and measures".[6]

In January 1790, President George Washington, in his first annual message to Congress, said, "Uniformity in the currency, weights, and measures of the United States is an object of great importance, and will, I am persuaded, be duly attended to."[7] Washington ordered Secretary of State Thomas Jefferson to prepare a Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States, later referred to informally as the Jefferson Report.

On October 25, 1791, Washington again appealed Congress:

A uniformity of the weights and measures of the country is among the important objects submitted to you by the Constitution and if it can be derived from a standard at once invariable and universal, must be no less honorable to the public council than conducive to the public convenience.

In 1821, President John Quincy Adams declared, "Weights and measures may be ranked among the necessities of life to every individual of human society."[8].

Nevertheless, it was not until 1838 that the United States government adopted a uniform set of standards.[6]

From 1830 until 1901, the role of overseeing weights and measures was carried out by the Office of Standard Weights and Measures, which was part of the U.S. Coast and Geodetic Survey in the Department of the Treasury.[9][10][11]

### Bureau of Standards (1901-1988)

In 1901, in response to a bill proposed by Congressman James H. Southard (R, Ohio), the National Bureau of Standards was founded with the mandate to provide standard weights and measures, and to serve as the national physical laboratory for the United States. (Southard had previously sponsored a bill for metric conversion of the United States.) [12]

Chart of NBS activities, 1915

### Metric system

The Congress of 1866 made use of the metric system in commerce a legally protected activity through the passage of Metric Act of 1866.[17] On May 20, 1875, 17 out of 20 countries signed a document known as the Metric Convention or the Treaty of the Meter, which established the International Bureau of Weights and Measures under the control of an international committee elected by the General Conference on Weights and Measures.[18]

## Organization

Advanced Measurement Laboratory Complex in Gaithersburg
Aerial view of the Gaithersburg campus in 2019
Boulder Laboratories

NIST is headquartered in Gaithersburg, Maryland, and operates a facility in Boulder, Colorado, which was dedicated by President Eisenhower in 1954.[19][20][21] NIST's activities are organized into laboratory programs and extramural programs. Effective October 1, 2010, NIST was realigned by reducing the number of NIST laboratory units from ten to six.[22] NIST Laboratories include:[23]

• Communications Technology Laboratory (CTL)[24]
• Engineering Laboratory (EL)[25]
• Information Technology Laboratory (ITL)[26]
• Center for Neutron Research (NCNR)[27]
• Material Measurement Laboratory (MML)[28]
• Physical Measurement Laboratory (PML)[29]

Extramural programs include:

• Hollings Manufacturing Extension Partnership (MEP),[30] a nationwide network of centers to assist small and mid-sized manufacturers to create and retain jobs, improve efficiencies, and minimize waste through process improvements and to increase market penetration with innovation and growth strategies;
• Technology Innovation Program (TIP), a grant program where NIST and industry partners cost share the early-stage development of innovative but high-risk technologies;
• Baldrige Performance Excellence Program, which administers the Malcolm Baldrige National Quality Award, the nation's highest award for performance and business excellence.

NIST's Boulder laboratories are best known for NIST‑F1, which houses an atomic clock. NIST‑F1 serves as the source of the nation's official time. From its measurement of the natural resonance frequency of cesium—which defines the second—NIST broadcasts time signals via longwave radio station WWVB near Fort Collins, Colorado, and shortwave radio stations WWV and WWVH, located near Fort Collins and Kekaha, Hawaii, respectively.[31]

NIST also operates a neutron science user facility: the NIST Center for Neutron Research (NCNR). The NCNR provides scientists access to a variety of neutron scattering instruments, which they use in many research fields (materials science, fuel cells, biotechnology, etc.).

The SURF III Synchrotron Ultraviolet Radiation Facility is a source of synchrotron radiation, in continuous operation since 1961. SURF III now serves as the US national standard for source-based radiometry throughout the generalized optical spectrum. All NASA-borne, extreme-ultraviolet observation instruments have been calibrated at SURF since the 1970s, and SURF is used for measurement and characterization of systems for extreme ultraviolet lithography.

The Center for Nanoscale Science and Technology (CNST) performs research in nanotechnology, both through internal research efforts and by running a user-accessible cleanroom nanomanufacturing facility. This "NanoFab" is equipped with tools for lithographic patterning and imaging (e.g., electron microscopes and atomic force microscopes).

### Committees

NIST has seven standing committees:

• Technical Guidelines Development Committee (TGDC)
• Advisory Committee on Earthquake Hazards Reduction (ACEHR)
• Information Security and Privacy Advisory Board (ISPAB)
• Visiting Committee on Advanced Technology (VCAT)
• Board of Overseers for the Malcolm Baldrige National Quality Award (MBNQA Board of Overseers)
• Manufacturing Extension Partnership National Advisory Board (MEPNAB)

## Projects

A 40 nm wide NIST logo made with cobalt atoms

### Measurements and standards

As part of its mission, NIST supplies industry, academia, government, and other users with over 1,300 Standard Reference Materials (SRMs). These artifacts are certified as having specific characteristics or component content, used as calibration standards for measuring equipment and procedures, quality control benchmarks for industrial processes, and experimental control samples.

### Handbook 44

NIST publishes the Handbook 44 each year after the annual meeting of the National Conference on Weights and Measures (NCWM). Each edition is developed through cooperation of the Committee on Specifications and Tolerances of the NCWM and the Weights and Measures Division (WMD) of the NIST. The purpose of the book is a partial fulfillment of the statutory responsibility for "cooperation with the states in securing uniformity of weights and measures laws and methods of inspection".

NIST has been publishing various forms of what is now the Handbook 44 since 1918 and began publication under the current name in 1949. The 2010 edition conforms to the concept of the primary use of the SI (metric) measurements recommended by the Omnibus Foreign Trade and Competitiveness Act of 1988.[32][33]

### Homeland security

NIST is developing government-wide identity document standards for federal employees and contractors to prevent unauthorized persons from gaining access to government buildings and computer systems.

### World Trade Center collapse investigation

In 2002, the National Construction Safety Team Act mandated NIST to conduct an investigation into the collapse of the World Trade Center buildings 1 and 2 and the 47-story 7 World Trade Center. The "World Trade Center Collapse Investigation", directed by lead investigator Shyam Sunder,[34] covered three aspects, including a technical building and fire safety investigation to study the factors contributing to the probable cause of the collapses of the WTC Towers (WTC 1 and 2) and WTC 7. NIST also established a research and development program to provide the technical basis for improved building and fire codes, standards, and practices, and a dissemination and technical assistance program to engage leaders of the construction and building community in implementing proposed changes to practices, standards, and codes. NIST also is providing practical guidance and tools to better prepare facility owners, contractors, architects, engineers, emergency responders, and regulatory authorities to respond to future disasters. The investigation portion of the response plan was completed with the release of the final report on 7 World Trade Center on November 20, 2008. The final report on the WTC Towers—including 30 recommendations for improving building and occupant safety—was released on October 26, 2005.[35]

### Election technology

NIST works in conjunction with the Technical Guidelines Development Committee of the Election Assistance Commission to develop the Voluntary Voting System Guidelines for voting machines and other election technology.

### Cybersecurity Framework

In February 2014 NIST published the NIST Cybersecurity Framework that serves as voluntary guidance for organizations to manage and reduce cybersecurity risk.[36] It was later amended and Version 1.1 was published in April 2018.[37] Executive Order 13800, Strengthening the Cybersecurity of Federal Networks and Critical Infrastructure, made the Framework mandatory for U.S. federal government agencies.[36]

## People

Four scientific researchers at NIST have been awarded Nobel Prizes for work in physics: William Daniel Phillips in 1997, Eric Allin Cornell in 2001, John Lewis Hall in 2005 and David Jeffrey Wineland in 2012, which is the largest number for any US government laboratory. All four were recognized for their work related to laser cooling of atoms, which is directly related to the development and advancement of the atomic clock. In 2011, Dan Shechtman was awarded the Nobel Prize in chemistry for his work on quasicrystals in the Metallurgy Division from 1982 to 1984. In addition, John Werner Cahn was awarded the 2011 Kyoto Prize for Materials Science, and the National Medal of Science has been awarded to NIST researchers Cahn (1998) and Wineland (2007). Other notable people who have worked at NBS or NIST include:

## Directors

Since 1989, the director of NIST has been a Presidential appointee and is confirmed by the United States Senate,[38] and since that year the average tenure of NIST directors has fallen from 11 years to 2 years in duration. Since the 2011 reorganization of NIST, the director also holds the title of Under Secretary of Commerce for Standards and Technology. Fifteen individuals have officially held the position (in addition to four acting directors who have served on a temporary basis).

## Patents

The NIST holds patents on behalf of the Federal government of the United States,[39] with at least one of them being custodial to protect public domain use, such as one for a Chip-scale atomic clock, developed by a NIST team as part of a DARPA competition.[40]

## Controversy regarding NIST standard SP 800-90

In September 2013, both The Guardian and The New York Times reported that NIST allowed the National Security Agency (NSA) to insert a cryptographically secure pseudorandom number generator called Dual EC DRBG into NIST standard SP 800-90 that had a kleptographic backdoor that the NSA can use to covertly predict the future outputs of this pseudorandom number generator thereby allowing the surreptitious decryption of data.[41] Both papers report[42][43] that the NSA worked covertly to get its own version of SP 800-90 approved for worldwide use in 2006. The whistle-blowing document states that "eventually, NSA became the sole editor". The reports confirm suspicions and technical grounds publicly raised by cryptographers in 2007 that the EC-DRBG could contain a kleptographic backdoor (perhaps placed in the standard by NSA).[44]

NIST responded to the allegations, stating that "NIST works to publish the strongest cryptographic standards possible" and that it uses "a transparent, public process to rigorously vet our recommended standards".[45] The agency stated that "there has been some confusion about the standards development process and the role of different organizations in it...The National Security Agency (NSA) participates in the NIST cryptography process because of its recognized expertise. NIST is also required by statute to consult with the NSA."[46] Recognizing the concerns expressed, the agency reopened the public comment period for the SP800-90 publications, promising that "if vulnerabilities are found in these or any other NIST standards, we will work with the cryptographic community to address them as quickly as possible”.[47] Due to public concern of this cryptovirology attack, NIST rescinded the EC-DRBG algorithm from the NIST SP 800-90 standard.[48]

## Publications

Guide to NIST in PDF Format

## References

1. "NIST General Information". National Institute of Standards and Technology. December 24, 2008.
2. "FY 2022: Presidential Budget Request Summary". National Institute of Standards and Technology. June 8, 2021.
3. "Dr. James K. Olthoff". United States Department of Commerce.
4. Articles of Confederation of 1781, article IX, paragraph 4.
5. NBS special publication 447 -Retrieved September 28, 2011
6. Records of the National Institute of Standards and Technology (NIST) , National Archives and Records Administration website, (Record Group 167), 1830–1987.
7. John Perry, The Story of Standards, Funk and Wagnalls, 1953, Library of Congress Cat. No. 55-11094, p. 123
8. sarah.henderson@nist.gov (2019-12-17). "NIST on a Chip Introduction" (in en).
9. NIST General Information. Retrieved on August 21, 2010.
10. "NIST Budget, Planning and Economic Studies". National Institute of Standards and Technology. October 5, 2010.
11. "Ike dedicates lab, voices peace hopes". Deseret News. United Press ((Salt Lake City, Utah)): p. A1. September 14, 1954.
12. "Ike dedicates two labs;'New type of frontier'". Meriden Record. Associated Press ((Connecticut)): p. 22. September 15, 1954.
13. "Significant papers from the first 50 years of the Boulder Labs". United States Department of Commerce: Boulder Laboratories. August 2004. p. 4.
14. "NIST Strengthens Laboratory Mission Focus with New Structure". September 28, 2010. Archived from the original on August 28, 2016.
15. NIST Laboratories . National Institute of Standards and Technology. Retrieved on May 10, 2016.
16. [1]. NIST. Retrieved on March 18, 2014.
17. Handbook 44 - "Forward; page 5" Retrieved: September 28, 2011
18. 100th Congress (1988) (June 16, 1988). "H.R. 4848". Legislation. GovTrack.us. "Omnibus Trade and Competitiveness Act of 1988"
19. Eric Lipton (August 22, 2008). "Fire, Not Explosives, Felled 3rd Tower on 9/11, Report Says". New York Times.
20. "Final Reports of the Federal Building and Fire Investigation of the World Trade Center Disaster". National Institute of Standards and Technology. October 2005.
21. "Cybersecurity Framework Documents". February 5, 2018.
22. Ost, Laura (2 December 2011). "Success Story: Chip-Scale Atomic Clock". National Institute of Standards and Technology.
23. Konkel, Frank (September 6, 2013). "What NSA's influence on NIST standards means for feds". FCW. 1105 Government Information Group.
24. James Borger; Glenn Greenwald (September 6, 2013). "Revealed: how US and UK spy agencies defeat internet privacy and security". The Guardian.
25. Nicole Perlroth (September 5, 2013). "N.S.A. Able to Foil Basic Safeguards of Privacy on Web". The New York Times.
26. Schneier, Bruce (November 15, 2007). "Did NSA Put a Secret Backdoor in New Encryption Standard?". Wired (Condé Nast). Retrieved September 10, 2013.
27. Office of the Director, NIST (September 10, 2013). "Cryptographic Standards Statement". National Institute of Standsards in Technology.
28. "NIST Removes Cryptography Algorithm from Random Number Generator Recommendations". National Institute of Standards and Technology. April 21, 2014.


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Rule

# Hinge Theorem

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Two sides in the left triangle are congruent to two sides in the right triangle. $m\angle A>m\angle B \quad \Rightarrow \quad a>b$

format: plain


text:
tkzMarkAngle changes size of tikzpicutre

I am trying to label some 3D figures. Here is a MWE:

\documentclass[tikz]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[scale=2.54,tdplot_main_coords]
\def\a{0.5}
\draw[->] (0,0,0) -- (1,0,0) node[anchor=north east]{x};
\draw[->] (0,0,0) -- (0,1,0) node[anchor=north west]{y};
\draw[,->] (0,0,0) -- (0,0,1) node[anchor=south]{z};
\coordinate (E) at (\a,0,0);
\coordinate (A) at (0,0,0);
\coordinate (B) at (0,\a,0);
\coordinate (C) at (0,0,\a);
\tkzMarkAngle[size=0.2cm,draw=red](B,A,C);
%   \tkzMarkAngle[size=0.2cm,draw=blue](C,A,E);
\end{tikzpicture}
\end{document}

This works as I'd hope: However, uncovering the commented line causes extra whitespace to be introduced to the left of the image. Is there any way I can disable this? I have a much more complicated image and I want to label different angles in turn, but I can't have the size changing each time:


text:
Free Version
Easy

# Constant Multiple Of Series

APCALC-XOVKWH

Find the value of the following:

$$\sum _{ n=1 }^{ \infty }{ \cfrac { 4 }{ { 5 }^{ n } } }$$

A

$0$

B

$\cfrac{4}{5}$

C

$\cfrac{5}{4}$

D

$1$


text:
# The most Decentralized Proof of Stake (POS) system.

All too often I see people making the claim that Delegated Proof of Stake is too centralized, but centralization is all relative. Today I would like to explore the meaning of decentralization as it relates to Proof of Stake systems and compare the top 3 approaches: BitShares, Nxt, and Peercoin. My aim is to be as objective as possible.

## What is Proof of Stake?

Proof of stake is any system that is secured by the owners of the shares, coins, or tokens. The idea is that those with a stake in the system have a financial interest in securing the system against attack. Because stake is limited, attacking a proof of stake system would require buying up a large stake in the network at great expense.

There are many ways that stake can be used and how it is used will ultimately determine the level of decentralization that will result. Peercoin uses stake like a virtual mining machine, the more stake you have the easier it is for your computer to mine. Nxt uses a deterministic algorithm for deciding who will produce the next block that randomly selects among users proportional to their stake. Recently Nxt added leased forging which allows one user to delegate their forging power to another user.

Delegated proof of stake used by BitShares elects 101 delegates with approval voting of the shareholders. These delegates are randomly shuffled every 101 blocks and then take turns producing blocks every 10 seconds.

## Decentralization Isn’t Free

For the sake of this article, I am going to define decentralization as the total number of unique individuals participating in the validation process such that no one individual is responsible for a disproportionate amount of blocks.

I am going to present some example numbers below, but do not take the numbers too seriously because they exist to demonstrate the extreme cases for the sake of contrast.

Nothing in life is free. If you want to have a million users participate in the consensus process then you will require a million computers all connected to the internet and consuming bandwidth. Assuming an impossibly low cost per computer of $1 per month, you are looking at a total cost of$12,000,000 per year just to break even.

Costs don’t start adding up until you attempt to scale these systems to the size of VISA or Master Card. If you assume everyone is running a dedicated machine processing 1000 transactions per second at 512 kb per transaction, then each machine will require 64 Megabit upload and download internet connection that can easily sustain that data rate, a hard drive growing at over 2 TB per week, and over 256 GB of RAM and a high end CPU. The cost of such a system and Internet connection is easily $1000 per month or more. At scale you are talking about a total cost of$12 billion dollars per year to maintain decentralization of 1 million validators. This would assume a minimum transaction fee of $3.60 per transaction just to cover network infrastructure. If you were to reduce the number of validators from a million to just a single fully centralized node, then the total cost of validating the transactions would fall to just$12,000 per year and transactions would be essentially free.

## Marginal Utility of Decentralization

The law of marginal utility states that as a person increases consumption of a product there is a decline in the marginal utility that person derives from consuming each additional unit of that product. Each additional validator provides less and less value to the network despite costing the network the same. How much value is there going from 1,000,000 validators to 1,000,001?

From this we can conclude that there exists an ideal number of validators such that the marginal utility of adding the last validator equals the operational costs. The only question that remains to be decided is what is the value of each additional validator. This is a value judgement that will differ with every person in the market.

## What the Market will Bear

To cover operating expenses a crypto currency network must charge transaction fees. The higher the fees, the lower the adoption and the fewer transactions. Assuming a desire to maximize profits, a network would aim to balance fees, transaction volume, and operating costs while competing against competitors attempting to offer better service for lower fees with higher margins.

Ultimately all costs flow on to the customer and the customer picks the service that provides what they need. Most customers want the lowest cost service that reliably gets the job done. For example, most people would buy a cheaper car with standard glass over an otherwise identical car with bullet proof glass that cost 10 times as much. So those of us designing crypto-currency systems must attempt to gauge how much the market is willing to pay for additional decentralization. Too much or too little decentralization could kill a crypto currency.

## Decentralization of Nxt and Peercoin

Some users of these early proof of stake systems claim that they have greater decentralization than BitShares. In other words, they claim that there are more than 101 unique validators none of which are responsible for more than 1% of the block production. For this to hold true, these networks would need to pay the minimal hosting costs for 102 full time validators entirely from transaction fees. I will assume a minimal VPS system costs $30 per month for the purpose of this discussion. This means Peercoin and Nxt would need to generate about$36,000 in transaction fees per year or about 1 transaction per second at a minimum. Obviously these currencies are not generating enough transaction fees to cover 102 unique individuals on a break-even basis.

Unfortunately, an individual could only break even at 1 transaction per second if all coins were held equally by exactly 102 individuals. This is not a realistic scenario. Instead what you have is a wealth distribution that follows a bell curve. Because transaction fees are distributed proportional to balance, we can assume that anyone with less than 1% of the stake will not be able to produce profitably and thereby be excluded from the consensus process. If there is even a single person with more than 1%, then we can conclude that there must be someone with less than 1%. Hence, both Nxt and Peercoin are unable to support 101 validators even if their transaction fees and volume were high enough because the rich validators are steeling profits at the expense of the poor validators.

If you look closely you will discover that the more distributed the currency becomes, the more centralized the validation becomes. In fact, if you had a million users each with an equal share of Nxt and Peercoin then no one could validate profitably. To resolve this only 1 out of 10,000 users could participate in validating the network so that the fees would be concentrated enough to cover their costs. This would result in just 1% of all stake actively securing the network, the other 99% would have to volunteer to sit out. This means that an attacker can take over the network with a mere 1.1% of the stake. Nxt has some ability to use leased forging which would help a little bit in this scenario.

The obvious argument that will be made is that many validators use their home PC and internet connection and thus the true cost of being a validator is much less than \$30 per month. This is only true while the network is small. If the network were to gain any serious traction then few people would want to bog down their home internet connection and run their CPU a full speed around the clock. We should not rely upon an assumption of ‘free’ resources when attempting to compare networks.

## Delegated Proof of Stake

For the sake of comparison I am going to assume Nxt, Peercoin, and BitShares all have equal revenue from transaction fees that is sufficient to fund 101 unique, full time validators.

With delegated proof of stake the network can remain secure even if the currency was evenly distributed among 1 million users. These million users would delegate to the top 101 which in theory could all have 100% approval and thus require someone to buy up 51% of the stake in order to take over the network.

Only delegated proof of stake has the power to leverage the stake of millions of individual users to secure the network. Nxt, Peercoin, and likely Ethereum all depend upon a wealthy elite with enough stake to profitably validate the network.

## Profits Don’t Matter

Some people will claim that profits don’t matter and that the costs are so low that people will validate at a loss. All these networks need to do is find 102 volunteers who don’t care about profits to partake in the process. Unfortunately, even if a small stakeholder with just .01% of the stake wanted to participate at a loss, they would be selected so infrequently that it wouldn’t even matter. Those with larger stakes would be the only ones effectively participating in the consensus process and they could easily ignore the one block per month produced by the combined efforts of 1000 small volunteer shareholders operating at a loss.

If you have 1 validator producing 99% of the blocks and 1000 validators producing the other 1% then have you really achieved decentralization? What we really care about is the ratio of validators to blocks produced. Under DPOS we have the ideal ratio, 101 validators each producing about 1% of the blocks. Nxt and Peercoin systems are more likely to have 10% of the validators producing 90% of the blocks. Under such a system you would require over 900 validators to equal the same level of decentralization that BitShares can get with just 101. In other words Nxt and Peercoin must charge 9x the transaction fees to maintain the same level of decentralization as BitShares assuming the 90/10 ratio in wealth distribution. This has the side effect of causing the poorest validator to break even while the richest validator rakes in 900% margins.

## Conclusion

Based upon the analysis in this post, it is clear that only Delegated Proof of Stake can be secure with an evenly distributed currency among a large user base at any scale. It is also clear that the uneven wealth distribution that is natural in all economic systems forces traditional Proof of Stake systems to fund several times more validators just to keep the largest stake holders from producing more than 1% of the blocks.

At the end of the day the numbers and economics do not lie. BitShares with Delegated Proof of Stake is the most decentralized network by far.

Update: Research into Nxt has shown they have about 250 unique forgers at any time. Unfortunately no information was available about the distribution of blocks among those 250 due to wealth disparities nor about the profitability of those forgers. If the forgers are not profitable then it is not sustainable.

http://freevisitorcounters.com


text:
# Maharashtra Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.2

## Maharashtra State Board Class 9 Maths Solutions Chapter 2 Real Numbers Practice Set 2.2

Question 1.
Show that 4√2 is an irrational number.
Solution:
Let us assume that 4√2 is a rational number .
So, we can find co-prime integers ‘a’ and ‘b’ (b ≠ 0) such that
4√2 = $$\frac { a }{ b }$$
∴ √2 = $$\frac { a }{ 4b }$$
Since, a and b are integers, $$\frac { a }{ 4b }$$ is a rational number and so √2 is a rational number.

Alternate Proof:
Let us assume that 4√2 is a rational number.
So, we can find co-prime integers ‘a’ and ‘b’ (b ≠ 0) such that

Since, 32 divides a2, so 32 divides ‘a’ as well.
So, we write a = 32c, where c is an integer.
∴ a2 = (32c)2 … [Squaring both the sides]
∴ 32b2 = 32 x 32c2 …[From(i)]
∴ b2 = 32c2
∴ c2 = $$\frac { { b }^{ 2 } }{ 32 }$$
Since, 32 divides b2, so 32 divides ‘b’.
∴ 32 divides both a and b.
a and b have at least 32 as a common factor.
But this contradicts the fact that a and b have no common factor other than 1.
∴ Our assumption that 4√2 is a rational number is wrong.
∴ 4√2 is an irrational number.

Question 2.
Prove that 3 + √5 is an irrational number.
Solution:
Let us assume that 3 + √5 is a rational number.
So, we can find co-prime integers ‘a’ and ‘b’ (b ≠ 0) such that

Since, a and b are integers, $$\frac { a }{ b }$$ – 3 is a rational
number and so √5 is a rational number.
But this contradicts the fact that √5 is an irrational number.
∴ Our assumption that 3 – √5 is a rational number is wrong.
3 + √5 is an irrational number.

Question 3.
Represent the numbers √5 and √10 on a number line.
Solution:
i. Draw a number line and take point A at 2.
Draw AB perpendicular to the number line such that AB = 1 unit.
In ∆OAB, m∠OAB = 90°
∴ (OB)2 = (OA)2 + (AB)2 … [Pythagoras theorem]
= (2)2 + (1)2
∴ (OB)2 = 5
∴ OB = √5 units. … [Taking square root of both sides]
With O as centre and radius equal to OB, draw an arc to intersect the number line at C.

The coordinate of the point C is √5 .

ii. Draw a number line and take point Pat 3.
Draw PR perpendicular to the number line such that PR = 1 unit.
In ∆OPR, m∠OPR = 90°
∴ (OR)2 = (OP)2 + (PR)2 … [Pythagoras theorem]
= (3)2 + (1)2
∴ (OR)2 = 10
∴ OR= √10units. … [Taking square root of both sides]
With O as centre and radius equal to OR, draw an arc to intersect the number line at Q.

The coordinate of the point Q is √10 .

Question 4.
Write any three rational numbers between the two numbers given below.
i. 0.3 and – 0.5
ii. – 2.3 and – 2.33
iii. 5.2 and 5.3
iv. – 4.5 and – 4.6
Solution:
i. 0.3 = 0.30 and -0.5 = -0.50
We know that,
0. 30 >0.29 >….. >0.10>.. > – 0.10>…. > -0.30>…> -0.50
∴ the three rational numbers between 0.3 and -0.5 are -0.3, -0.1 and 0.1.

Alternate Method:
A rational number between two rational numbers a and b

∴ the three rational numbers between 0.3 and -0.5 are -0.3, -0.1 and 0.1.

ii. -2.3 = -2.300 and -2.33 = -2.330
We know that,
-2.300 > -2.301>… > -2.310>…> -2.320>…> -2.330
∴ the three rational numbers between -2.3 and -2.33 are -2.310, -2.320 and -2.325.

iii. 5.2 = 5.20 and 5.3 = 5.30
We know that,
5.20 < 5.21 < 5.22 < 5.23 < … < 5.30
∴ the three rational numbers between 5.2 and 5.3 are 5.21, 5.22 and 5.23.

iv. -4.5 = -4.50 and -4.6 = -4.60 We know that,
-4.50 > -4.51 > -4.52 >… > – 4.55 >…>- 4.60
∴ the three rational numbers between -4.5 and -4.6 are -4.51, -4.52 and -4.55.


text:
# How to put address in the same level?

\documentclass[a4paper,12pt]{article}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{ragged2e}
\begin{document}

\begin{flushleft}
\textbf{Riyam Sen} \\
Department of Mathematical Sciences, Aligarh University \\
Napaam, Sonitpur, Delhi-110025, India. \\
e-mail:  ri45.das@gmail.com
\end{flushleft}

\begin{flushright}
\textbf{Pronoy Pratim Dutta} \\
Statistics and Mathematics Unit, Indian Statistical Institute,\\
Bangalore, R. V. College Post, Bangalore 560059,
India. \\
e-mail:  brijk5897@gmail.com
\end{flushright}

\end{document}

In this code I am trying to put the name and addresses in the same level .But one is little up and one is little down.

How we can put them in the same level?

• There's nothing about biblatex in the code, so this needs to be retagged. The final text shouldn't be formatted as code, but it's unclear to me how this was formatted, so an attempt to fix it failed. What I think you want is to put two addresses side by side. To do that, put each address in a minipage with a width of .45\textwidth, get rid of the blank line that separates them and replace it by \hfil. Apr 15 '20 at 20:44

## 1 Answer

If you want a user friendly "programming" interface i would suggest you to use the tcolorbox package for tasks like this.

The following example is a good starting point.

(Maybe i have to much fantasy but i guess you are looking for something like this)

\documentclass[a4paper,12pt]{article}
\usepackage{lipsum}
\usepackage{tcolorbox}

\tcbuselibrary{skins}

\setlength\parindent{0pt}

\newtcolorbox{heading}{%
blankest,
sidebyside,
enlarge left by  = -1cm,
enlarge right by = 2cm,
width            = \linewidth+2cm,
halign lower     = flush right,
after            = \bigskip\bigskip,
top              = 4mm,
bottom           = 4mm,
sidebyside align = top seam,
borderline north = {1.8pt}{0pt}{black},
borderline south = {1.0pt}{0pt}{black}
}

\begin{document}

\begin{heading}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\textbf{Riyam Sen} \\
Department of Mathematical Sciences, Aligarh University \\
Napaam, Sonitpur, Delhi-110025, India. \\
e-mail:  ri45.das@gmail.com
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\tcblower
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\textbf{Pronoy Pratim Dutta} \\
Statistics and Mathematics Unit\\
Indian Statistical Institute\\
Bangalore, R. V. College Post\\
Bangalore 560059 India \\
e-mail:  brijk5897@gmail.com
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{heading}

\lipsum

\end{document}


text:
Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, April 15, 2014.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2014             April 2014              May 2014
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1          1  2  3  4  5                1  2  3
2  3  4  5  6  7  8    6  7  8  9 10 11 12    4  5  6  7  8  9 10
9 10 11 12 13 14 15   13 14 15 16 17 18 19   11 12 13 14 15 16 17
16 17 18 19 20 21 22   20 21 22 23 24 25 26   18 19 20 21 22 23 24
23 24 25 26 27 28 29   27 28 29 30            25 26 27 28 29 30 31
30 31

Tuesday, April 15, 2014

1:00 pm in Altgeld Hall 243,Tuesday, April 15, 2014

#### Evolving structures and uniform growth rate

###### Kasra Rafi (University of Toronto)

Abstract: During his 60th birthday conference, Thurston asserted that the growth rate of mapping class group is independent of genus. In this talk, we attempt to understand why and to what extend this is true. It turns out, given the right choice of generating sets, the mapping class group, Out(F_n) and SL(n,Z) all have uniform growth rates. We use the ideas and the work of Sleator-Tarjan-Thurston.

1:00 pm in 345 Altgeld Hall,Tuesday, April 15, 2014

#### Buchi's Problem and Uniform Undecidability for rings of functions of positive characteristic

###### Thanases Pheidas (Purdue/University of Crete)

Abstract: We address the question: Is there an algorithm which can decide, given a polynomial equations (in many variables), with coefficients in F_p[z] (polynomials over z, with coefficients in the finite field with p elements, p a prime), whether the polynomial has solutions in F_p(z) for almost all primes p (or for infinitely many p, or for all primes p congruent to 1 mod 4)? We will present a negative answer to this question. A critical element of the proof is the solution to an analogue of Buchi's problem, a problem in Number Theory of independent interest.

1:00 pm in 347 Altgeld Hall,Tuesday, April 15, 2014

#### Layered Media Scattering: Fokas Integral Equations and Boundary Perturbation Methods

###### David Nicholls (UIC)

Abstract: In this talk we describe a class of Integral Equations to compute Dirichlet-Neumann operators for the Helmholtz equation on periodic domains inspired by the recent work of Fokas and collaborators on novel solution formulas for boundary value problems. These Integral Equations have a number of advantages over standard alternatives including: (i.) ease of implementation (high-order spectral accuracy is realized without sophisticated quadrature rules), (ii.) seamless enforcement of the quasiperiodic boundary conditions (no periodization of the fundamental solution, e.g. via Ewald summation, is required), and (iii.) reduced regularity requirements on the interface proles (derivatives of the deformations do not appear explicitly in the formulation). We show how these can be efficiently discretized and utilized in the simulation of scattering of linear acoustic waves by families of periodic layered media which arise in geoscience applications.

2:00 pm in 241 Altgeld Hall,Tuesday, April 15, 2014
###### Canceled

2:00 pm in Altgeld Hall 347,Tuesday, April 15, 2014

#### Poincar\'e inequalities in Noncommutative $L_p$ spaces

###### Qiang Zeng (UIUC Math)

Abstract: It is known in probability theory that good estimates of moments of random variables lead to concentration inequalities. The Poincar\'e inequalities provide upper bounds for the moments of random variables using their derivatives. In this talk, I will first give some motivating examples of $L_p$ Poincar\'e inequalities with satisfactory constants in classical probability and Fourier analysis. Then I will explain the consequences of these inequalities and a general theory in the context of noncommutative $L_p$ spaces. The talk is based on joint work with Marius Junge.

3:00 pm in 347 Altgeld Hall,Tuesday, April 15, 2014

#### Replication and Optimization in Causal Inference

###### Wendy K. Tam Cho (UIUC Political Science/Statistics)

Abstract: A common thread throughout scientific endeavors is the desire to identify and understand causal relationships. Randomized experiments are the gold standard for isolating treatment effects and identifying causal relationships. When experiments are not practical or not possible, researchers sometimes turn to observational data. Matching methods comprise one strategy for making causal inferences with observational data. We present a new paradigm and method for making causal inferences in the absence of experimental data. Our method incorporates an optimization approach that illuminates important scientific notions of replication. While observational studies have obvious pitfalls, we demonstrate how our computational approach highlights previously unseen opportunities with these data.

3:00 pm in 241 Altgeld Hall,Tuesday, April 15, 2014

#### Online Ramsey Theory for Planar Graphs

###### Sarka Petrickova (UIUC Math)

Abstract: An online Ramsey game $(G,\mathcal{H})$ is a game between Builder and Painter, alternating in turns. During each turn, Builder draws an edge, and Painter colors it blue or red. Builder's goal is to force Painter to create a monochromatic copy of $G$, while Painter's goal is to prevent this. The only limitation for Builder is that after each of his moves, the resulting graph has to belong to the class of graphs $\mathcal{H}$. It was conjectured by Grytczuk, Haluszczak, and Kierstead (2004) that if $\mathcal{H}$ is the class of planar graphs, then Builder can force a monochromatic copy of a planar graph G if and only if G is outerplanar. Here we show that the only if'' part does not hold while the if'' part does.

3:00 pm in 243 Altgeld Hall,Tuesday, April 15, 2014

#### Holomorphic one-forms on varieties of general type

###### Mihnea Popa (UIC Math)

Abstract: I will explain recent work with C. Schnell, in which we prove that every holomorphic one-form on a variety of general type has non-empty zero locus (together with a suitable generalization to arbitrary Kodaira dimension). The proof makes use of generic vanishing theory for Hodge D-modules on abelian varieties.

4:00 pm in Altgeld Hall,Tuesday, April 15, 2014

#### Schemes as Functors

###### Matej Penciak (UIUC Math)

Abstract: Replacing schemes with their functor of points offers a useful perspective to tackle moduli problems. In this talk I will explain this interpretation of schemes, characterize the functors that come from this construction, and try to motivate this viewpoint through various examples. Along the way I will discuss the Quot and Hilbert schemes--two schemes that represent common moduli problems.


text: openmp = True OMP_NUM_THREADS=2 python dssm_keras. get_regularization_loss() loss += l2_loss Edit: Thanks Zeke Arneodo, Tom and srcolinas I added, the last bit on your feedback so that the accepted answer provides the complete solution. Intuitively, the process of adding regularization is straightforward. Let’s discuss where should you put dropout and spatial dropout layers in your keras model to make your regularization work well avoiding overfitting. 关于本篇正则化的具体路径是： 正则化作业. There are plenty of deep learning toolkits that work on top of it like Slim, TFLearn, Sonnet, Keras. l2_regularizer(scale=0. 01, ** kwargs) A regularizer that applies a L2 regularization penalty. The regularizers are provided under keras. In this section, you will learn about these regularization methods in detail, along with how to implement them in Keras. 01) By default, no regularizer is used in any layers. W_constraint: instance of the constraints module (eg. In Keras, this is specified with a bias_regularizer argument when creating an LSTM layer. regularizers. These tasks include. l1 and l2 Regularization (3/3) I l2 regression: R(w) = P n i=1 w 2 is added to thecost function. Then, we create a function called create_regularized_model() and it will return a model similar to the one we built before. The L1 regularization seems to work fine, but whenever I add the L2 regularization's penalty term to the loss function, it returns nan. py: 489: UserWarning: theano. Playing with Keras and L2 regularization in machine learning. We learned earlier about overfitting and what it looks like. Since the l1 regularization parameter acts as a feature selector, it is able to reduce the coefficient of features to zero. Optimizer that implements the Adam algorithm. Keras makes it very easy to architect complex algorithms, while also exposing the low-level TensorFlow plumbing. 5): '''Calculate L1 and L2 penalties for a Keras layer This follows the same formulation as in the R package glmnet and Sklearn Args: alpha ([float]): amount of regularization. This type of regularization is called weight regularization and has two different variations: L2 regularization and L1 regularization. Now, I'm using the code below:. Use Keras to build simple logistic regression models, deep neural networks, recurrent neural networks, and convolutional neural networks Apply L1, L2, and dropout regularization to improve the accuracy of your model. the sum of the squared of the coefficients, aka the square of the Euclidian distance, multiplied by ½. These are shortcut functions available in keras. 01) By default, no regularizer is used in any layers. 01)：l为正则化因子，默认为0. The annotated box represents the formula for L2 regularization where lambda is the regularization hyperparameters. keras import regularizers model. Use Rectified Linear The rectified linear activation function, also called relu, is an activation function that is now widely used in the hidden layer of deep neural networks. Example weights: in a linear model or in a neural network. Overfitting is a phenomenon that occurs when a Machine Learning model is constraint to training set and not able to perform well on unseen data. The digits have been size-normalized and centered in a fixed-size image. (GAM smoothing regularization) l2: (float) L2 regularization strength for the spline base coefficients. Introduction. 01 against the baseline model. reduce_mean(cross_entropy) # using l2 regularization l2_reg = tf. Here is an overview of key methods to avoid overfitting, including regularization (L2 and L1), Max norm constraints and Dropout. What can i do to reduce the training MAE with regularization?. regularizers. you can have a look on this code as well in R language. keras A collection of 1,625 posts. For the LASSO one would need a soft-thresholding function, as correctly pointed out in the original post. Overfitting occurs when you train a neural network too long. sigmoid ) ]) 내가 아는 한이 방법으로 정규화 손실을 수동으로 추가 할 필요가 없습니다. keras_ssg_lasso Documentation, Release 0. models import Model, Sequential from keras. Try reducing lambda from 0. kernel_reg = regularizers. l2(lambda)keras. 03 (without regularization it was much lower at 0. Use Keras to build simple logistic regression models, deep neural networks, recurrent neural networks, and convolutional neural networks; Apply L1, L2, and dropout regularization to improve the accuracy of your model; Implement cross-validate using Keras wrappers with scikit-learn; Understand the limitations of model accuracy. Ai-Nimals; Private. 1 regularization in tensorflow 将正则化加入了所有可以训练的weights参数上 cross_entropy = tf. 他の正則化の説明については今回は省略する． python layers. This, however, makes the cost function more complicated. These examples are extracted from open source projects. However, we show that L2 regularization has no regularizing effect when combined with normalization. datasets import mnist (x_train, y_train), (x_test, y_test) = mnist. In this section, you will learn about these regularization methods in detail, along with how to implement them in Keras. The CIFAR-10 data consists of 60,000 (32×32) color images in 10 classes, with 6000 images per class. (Updated on July, 24th, 2017 with some improvements and Keras 2 style, but still a work in progress) CIFAR-10 is a small image (32 x 32) dataset made up of 60000 images subdivided into 10 main categories. 01 determines how much we penalize higher parameter values. models import Sequential from keras. So it is computationally more efficient to do L2 regularization. 01) a later. visualization training dropout vgg16 imagery keras-neural-networks l2-regularization ships resnet-50 satellite-images Updated Jan 16, 2020 Jupyter Notebook. “A Keras model has two modes: training and testing. Instead, regularization has an influence on the scale of weights, and thereby on the effective. Parameters. /home/ samuele /. Weight penalty is standard way for regularization, widely used in training other model types. regularizers. Below is the sample code to apply L2 regularization to a Dense layer. Ai-Nimals; Private. In this post we will use Keras to classify duplicated questions from Quora. Use Keras to build simple logistic regression models, deep neural networks, recurrent neural networks, and convolutional neural networks; Apply L1, L2, and dropout regularization to improve the accuracy of your model; Implement cross-validate using Keras wrappers with scikit-learn; Understand the limitations of model accuracy. 001), activation = tf. l2: Activity is calculated as the sum of the squared values. keras is TensorFlow's implementation of the Keras API specification. For example, sqrt(x1^2+x2^2)+sqrt(y1^2+y2^2), and sqrt(x1^2+x2^2+y1^2+y2^2), suppose that x vector is the weights of layer 1 and y is the weights of layer 2. L2 The L2 regularization factor. In Section 6, we exploit the label-independence of the noising penalty and use unlabeled data to tune our estimate of R(). Stronger regularization ###pushes coefficients more and more towards zero, though coefficients never ###become exactly zero. 마찬가지로, 확률적 경사하강법 의 여러 변형은 순볼록 함수의 최저점에 가까운 점을 찾을 가능성이 높지만 항상 보장되지는 않습니다. models import Sequential from keras. W_constraint: instance of the constraints module (eg. 01 applied to the bias vector. L2 regularization penalizes weight values. The regularization technique I'm going to be implementing is the L2 regularization technique. L2 regularization improves again to 64. Keras is a high-level API to build and train deep learning models. 01)) 16/73. regularizers import l2 In [31]: reg = l2 () model = Sequential () model. 在设计深度学习模型的时候，我们经常需要使用正则化（Regularization）技巧来减少模型的过拟合效果，例如 L1 正则化、L2 正则化等。在Keras中，我们可以方便地使用三种正则化技巧： keras. Use Rectified Linear The rectified linear activation function, also called relu, is an activation function that is now widely used in the hidden layer of deep neural networks. This Keras. L2 norm (L2 regularization, Ridge) If the loss is MSE, then cost function with L2 norm can be solved analytically. Below is the sample code to apply L2 regularization to a Dense layer. We learned earlier about overfitting and what it looks like. regularizers. L2 regularization will penalize the weights parameters without making them sparse since the penalty goes to zero for small weights. The second term is computed analytically, and then added to the layer as a regularization loss — similar to how we’d specify something like an L2 regularization. The main data structure you'll work with is the Layer. function was asked to create a function computing outputs given certain inputs, but the provided input variable at index 1 is not part of the computational graph needed to compute the outputs: keras_learning_phase. Overfitting occurs when you train a neural network too long. (Updated on July, 24th, 2017 with some improvements and Keras 2 style, but still a work in progress) CIFAR-10 is a small image (32 x 32) dataset made up of 60000 images subdivided into 10 main categories. Improve model accuracy with L1, L2, and dropout regularization Who this book is for If you know the basics of data science and machine learning and want to get started with advanced machine learning technologies like artificial neural networks and deep learning, then this is the book for you. Output shape. The L1 regularization penalty is computed as: loss = l1 * reduce_sum(abs(x)) The L2 regularization penalty is computed as loss = l2 * reduce_sum(square(x)) L1L2 may be passed to a layer as a string identifier: dense = tf. This is a high-level API to build and train models that includes first-class support for TensorFlow-specific functionality, such as eager execution, tf. layers import Input, Conv2D, Lambda, merge, Dense, Flatten, MaxPooling2D from keras. 2 The Power Iteration Method starts with an initial random vector, call it ν0, and. 0), but with f(x) = x for x > theta or f(x) = x for x < -theta, f(x) = 0. 2) to stabilize the estimates especially when there's collinearity in the data. class L2: A regularizer that applies a L2 regularization penalty. We learned earlier about overfitting and what it looks like. Ai-Nimals; Private. Practically, I think the biggest reasons for regularization are 1) to avoid overfitting by not generating high coefficients for predictors that are sparse. openmp = True OMP_NUM_THREADS=2 python dssm_keras. Lab intro Keras Functional API 1m Lab: Introducing the Keras Functional API 0m Neural Networks with Keras Functional API 10m Regularization: Dropout 5m Regularization: L1, L2, and Early Stopping 5m Regularization: The Basics 5m Serving models in the Cloud 3m Training neural networks with Tensorflow 2 and Keras Functional API: Readings 0m. magic so that the notebook will reload external python modules % load_ext watermark % load_ext autoreload % autoreload 2 import numpy as np import pandas as pd from keras. Use regularization; Getting more data is sometimes impossible, and other times very expensive. 一、keras内置3种正则化方法keras. For non-linear kernels, this corresponds to a non-linear function in the original space. 01)) # A linear layer with L2 regularization of factor 0. I am trying to replicate (a way smaller version) of the AlphaGo Zero system. Code Deep sparse but training with noise is the same thing as the Tikhonov Regularization (L2 Reg). Note that playing with regularization can be a good way to increase the performance of a network, particularly when there is an evident situation of overfitting. L2 regularization makes your decision boundary smoother. 0) Lambda value for L2-regularization. callbacks import EarlyStopping from keras. one reason why L2 is more common. L2 regularization（权重衰减） L2正则化就是在代价函数后面再加上一个正则化项： C0代表原始的代价函数，后面那一项就是L2正则化项，它是这样来的：所有参数w的平方的和，除以训练集的样本大小n。λ就是正则项系数，权衡正则项与C0项的比重。. Adding regularization is easy:. Use Keras to build simple logistic regression models, deep neural networks, recurrent neural networks, and convolutional neural networks Apply L1, L2, and dropout regularization to improve the accuracy of your model. Does this mean that we should always apply Elastic Net regularization? Of course not — this is entirely dependent on your dataset and features. 这篇文章主要介绍了TensorFlow keras卷积神经网络 添加L2正则化方式，具有很好的参考价值，希望对大家有所帮助。一起跟随小编过来看看吧. one reason why L2 is more common. In L1, we have:. Keras overfitting Keras overfitting. using L1 or L2 o the vector norm (magnitude). Keras Fundamentals for Deep Learning •Input Data •Regularization •L1 Regularization •L2 Regularization •Dropout Regularization. b_regularizer: instance of WeightRegularizer, applied to the bias. regularizers. Machine Learning을 공부하기 시작하면, 꼭 마주치는 L1, L2. There is weight decay that pushes all weights in a node to be small, e. However, later we will use cross validation to find the optimal $\lambda$ value for our data. When I used L1 or L2 regularization technique my problem (overfitting problem) got worst. how to change the regularization parameter in keras layer without rebuild a new model in R 0 I want to fine tuning my L2 parameter in my last keras layer using a for loop approach. Let's train this model for 100 epochs (with the added regularization the model is less likely to overfit and can be trained longer). This set of experiments is left as an exercise for the interested reader. pandas, which provides an easy way to represent datasets in memory. use_bias: boolean; should we add a bias to the transition; bias_initializer: bias initializer - from keras. The regularization term is the squared magnitude of the weight parameter (L2 norm) as a penalty term. L2 weight regularization with very small regularization hyperparameters such as (e. Now, I'm using the code below:. Use Rectified Linear The rectified linear activation function, also called relu, is an activation function that is now widely used in the hidden layer of deep neural networks. regularizer_l1 (l = 0. regularizers. For more details on the maths, these article by Raimi Karim and Renu Khandelwal present L1 and L2 regularization maths reasonably. Applying dropout to the final fully-connected layers effectively ensemble the entire network, including all previous layers. com Recap: what are L1, L2 and Elastic Net Regularization? In our blog post “What are L1, L2 and Elastic Net Regularization in neural networks?”, we looked at the concept of regularization and the L1, L2 and Elastic Net Regularizers. activity_regularizer: instance of ActivityRegularizer, applied to the network output. The regularization term is the squared magnitude of the weight parameter (L2 norm) as a penalty term. The digits have been size-normalized and centered in a fixed-size image. Introduction. 01 applied to the kernel matrix: layers. It looks like we are done. add (Dense (nb_classes, activation = 'softmax', W_regularizer = l2 (l2_alpha))) # compile model model_l2. Practically, I think the biggest reasons for regularization are 1) to avoid overfitting by not generating high coefficients for predictors that are sparse. openmp = True OMP_NUM_THREADS=2 python dssm_keras. 01 against the baseline model. l2_regularization_strength: A float value, must be greater than or equal to zero. reduce_mean(cross_entropy) # using l2 regularization l2_reg = tf. After 20 epochs the. 0005 for i in range (8): # penalize the L2-norm of the weight matrix model_l2. Then, we will code. In Keras, there are 2 methods to reduce over-fitting. WordContextProduct(input_dim, proj_dim= 128, init= 'uniform', activation= 'sigmoid', weights= None). In contrast, L1 regularization’s shape is diamond-like and the weights are lower in the corners of the diamond. Also note that TensorFlow supports L1, L2, and ElasticNet regularization. Lab intro Keras Functional API 1m Lab: Introducing the Keras Functional API 0m Neural Networks with Keras Functional API 10m Regularization: Dropout 5m Regularization: L1, L2, and Early Stopping 5m Regularization: The Basics 5m Serving models in the Cloud 3m Training neural networks with Tensorflow 2 and Keras Functional API: Readings 0m. 0005 or 5 x 10^−4) may be a good starting point. And that’s all there is to implementing various regularization techniques within neural networks. maxnorm, nonneg), applied to the embedding matrix. 2020 at 04:31 Image SourceBy using the early stopping callback, which is available in Keras, we can monitor specific metrics like validation loss or accuracy. 0 (default) epochs : int (default: 500) Number of passes over the training set. No regularization if l1=0. Rolba Posted on March 15, 2020 March 15, 2020 Categories Regularization Tags keras, L2, python, regularization Use your spatial dropout regularization layer wisely. The following are 30 code examples for showing how to use keras. regularizers. L2 Regularization. The option bias_regularizer is also available but not recommended. In this Applied Machine Learning & Data Science Recipe (Jupyter Notebook), the reader will find the practical use of applied machine learning and data science in Python programming: How to add a Weight Regularization (l2) to a Deep Learning Model in Keras. com Recap: what are L1, L2 and Elastic Net Regularization? In our blog post “What are L1, L2 and Elastic Net Regularization in neural networks?”, we looked at the concept of regularization and the L1, L2 and Elastic Net Regularizers. Stop training when a monitored metric has stopped improving. Exercise: Implement compute_cost_with_regularization() which computes the cost given by formula (2). regularization > 0. 7 as of this writing), which looks very similar to keras, and was wondering how to configure regularization. 0001 Big Data 6 Conclusion/Future Work Loss 8. 01) a later. Use your spatial dropout regularization layer wisely. regularizers. The regularizer is defined as an instance of the one of the L1, L2, or L1L2 classes. Therefore, I would expect that regularization would be defined as part of the specification of the model's loss function. First off, the documentation on Keras is among the best I've seen in a deep learning library, so congrats to those responsible. L2 regularization (called ridge regression for linear regression) adds the L2 norm penalty ($$\alpha \sum_{i=1}^n w_i^2$$) to the loss function. More details here: Keras Usage of Regularizers; In this experiment, we will compare L1, L2, and L1L2 with a default value of 0. models import Sequential from keras. Isn't there L2-regularization misssing? In the mentioned paper they write: The training was regularised by weight decay (the L2 penalty multiplier set to 5 · 10−4) and dropout regularisation for the first two fully-connected layers (dropout ratio set to 0. relu), keras. What are some situations to use L1,L2 regularization instead of dropout layer?. The annotated box represents the formula for L2 regularization where lambda is the regularization hyperparameters. Overfitting is a phenomenon that occurs when a Machine Learning model is constraint to training set and not able to perform well on unseen data. L2 regularization factor for the input weights, specified as a numeric scalar or a 1-by-4 numeric vector. 01)) 16/73. 01): L1 weight regularization penalty, also known as LASSO; l2(l=0. 这篇文章主要介绍了TensorFlow keras卷积神经网络 添加L2正则化方式，具有很好的参考价值，希望对大家有所帮助。一起跟随小编过来看看吧. WeightRegularizer(). model_ : Keras Object The underlying AutoEncoder in Keras. how to change the regularization parameter in keras layer without rebuild a new model in R 0 I want to fine tuning my L2 parameter in my last keras layer using a for loop approach. you change the keras. 01, ** kwargs) A regularizer that applies a L2 regularization penalty. In this post you will discover the dropout regularization technique and how to apply it to your models in Python with Keras. l2_smooth: (float) L2 regularization strength for the second order differences in positional bias' smooth splines. L2 regularization is also called weight decay in the context of neural networks. 视频中会介绍什么是 overfitting, 怎么使用l1, l2 regularization terms. 01): L1-L2 regularization penalty, also known as ElasticNet. Use Keras to build simple logistic regression models, deep neural networks, recurrent neural networks, and convolutional neural networks; Apply L1, L2, and dropout regularization to improve the accuracy of your model; Implement cross-validate using Keras wrappers with scikit-learn; Understand the limitations of model accuracy. Um, What Is a Neural Network? It’s a technique for building a computer program that learns from data. Final thoughts. py source:. Finally, Elastic Net, which combines both L1 and L2 regularization obtains the highest accuracy of 64. What is L2-regularization actually doing?: L2-regularization relies on the assumption that a model with small weights is simpler than a model with large weights. 0) Lambda value for L2-regularization. one reason why L2 is more common. A weight regularizer can be added. Check whether the l2 regularization is not too large; If you are facing the exploding gradient problem you can either: re-design the network or use gradient clipping so that your gradients have a certain “maximum allowed model update”. add ( layer = Dense ( 1 , input_dim = X. L2 regularization 0 10^-5 … 10^-1, powers of 10 Dropout 0 0. “A Keras model has two modes: training and testing. Use the keyword argument input_shape (tuple of integers, does not include the samples axis) when using this layer as the first layer in a model. l2 (l2 = 0. local / lib / python2. sigmoid ) ]) 내가 아는 한이 방법으로 정규화 손실을 수동으로 추가 할 필요가 없습니다. Everything works fine when I remove the term l2_penalty * l2_reg_param from the last line below. beta_regularizer: instance of WeightRegularizer, applied to the beta vector. random as rng import numpy as np import os import dill as pickle import matplotlib. l1(lambda)keras. l2() denotes the L2 regularizers. No regularization if l2=0. The add_loss() API. It provides L2 based regularization. layers import Input, Conv2D, Lambda, merge, Dense, Flatten, MaxPooling2D from keras. Also note that TensorFlow supports L1, L2, and ElasticNet regularization. In Keras, this is specified with a bias_regularizer argument when creating an LSTM layer. This is shown in some of the layers below. multiplicitive factor to apply to the the penalty term. CIFAR-10 is an established computer-vision dataset used for object recognition. 2) to stabilize the estimates especially when there's collinearity in the data. # def make_shared_layers (self): if self. The L1 regularization seems to work fine, but whenever I add the L2 regularization's penalty term to the loss function, it returns nan. Here are the same filters again, using only L2 decay, multiplying the image pixels by 0. L2 regularization (called ridge regression for linear regression) adds the L2 norm penalty ($$\alpha \sum_{i=1}^n w_i^2$$) to the loss function. (GAM smoothing regularization) l2: (float) L2 regularization strength for the spline base coefficients. Parameters. Use the keyword argument input_shape (tuple of integers, does not include the samples axis) when using this layer as the first layer in a model. The following are 5 code examples for showing how to use keras. Here's the regularized cross-entropy:. Now keras can use both of them for running, and you can switch it easily. The annotated box represents the formula for L2 regularization where lambda is the regularization hyperparameters. 0001 and comparing your results. l2(lambda)keras. Keras also provides a lot of built-in neural network related functions to properly create the Keras model and Keras layers. Before you go, check out these stories! 0. It relies strongly on the implicit assumption that a model with small weights is somehow simpler than a network with large weights. Situation was the same as I would use l2 regularization, which I did not now. regularizers. L2 Regularization. See full list on sthalles. There are 50,000 training images and 10,000 test images in the official data. L2 regularization: The cost added is proportional to the square of the value of the weight’s coefficients. The regularizer is defined as an instance of the one of the L1, L2, or L1L2 classes. models import Sequential from keras. "Swish : A Self-Gated Activation Function" is a new paper from google brain. 1 fit_predict(X, y) Fit the model using X and y and then use the ﬁtted model to predict X. from tensorflow. 0; gaussian_noise_injection_std_dev (float, optional) – the standard deviation of the Gaussian noise added to parameters post update, defaults to 0. Check the web page in the reference list in order to have further information about it and download the whole set. 001), activation = tf. In this section I describe one of the most commonly used regularization techniques, a technique sometimes known as weight decay or L2 regularization. Machinecurve. Ridge regression adds “squared magnitude” of coefficient as penalty term to the loss function. This article won’t focus on the maths of regularization. First, this picture below: The green line (L2-norm) is the unique shortest path, while the red, blue, yellow (L1-norm) are all same length (=12) for the same route. l2: L2 regularization factor (positive float). To calculate , use : np. 01): L2 weight regularization penalty, also known as weight decay, or Ridge; l1l2(l1=0. However, when I use the same parameters in keras, I get nan as loss starting in the first epoch. 01 applied to the bias vector. In Keras, you can do Dense(64, use_bias=False) or Conv2D(32, (3, 3), use_bias=False) We add the normalization before calling the activation function. l2_regularizer(scale=0. A weight regularizer can be added. This set of experiments is left as an exercise for the interested reader. Discover how to leverage Keras, the powerful and easy-to-use open source Python library for developing and evaluating deep learning models. Corresponds to the Keras Activity Regularization Layer. This concludes the lesson “Training Deep Neural Nets. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. W_constraint: instance of the constraints module (eg. L2 regularization（权重衰减） L2正则化就是在代价函数后面再加上一个正则化项： C0代表原始的代价函数，后面那一项就是L2正则化项，它是这样来的：所有参数w的平方的和，除以训练集的样本大小n。λ就是正则项系数，权衡正则项与C0项的比重。. 01) # test in functional API x = Input (shape = (3,)) z = core. A layer encapsulates both a state (the. The prefix is complemented by an index suffix to obtain a unique layer name. WordContextProduct keras. L2 regularization are added to the hidden layers, but not the output layer. The key difference between these two is the penalty term. Check whether the l2 regularization is not too large; If you are facing the exploding gradient problem you can either: re-design the network or use gradient clipping so that your gradients have a certain “maximum allowed model update”. L1 and L2 regularization showing increased MSE with added vars (that eventually decreases) I am attempting to run Ridge, LASSO, and Elastic Net regression as the regularization approaches are commonly used in the problem I'm working to solve. This is because the output layer has a linear activation function with only one node. Here's the regularized cross-entropy:. A regression. ai Installing fastai. 01) a later. fit を使う場合は，自動的にこれらの正則化項を含めて. Use your spatial dropout regularization layer wisely. Practically, I think the biggest reasons for regularization are 1) to avoid overfitting by not generating high coefficients for predictors that are sparse. Let's add L2 weight regularization now. ) 开发新的正则项 任何以权重矩阵作为输入并返回单个数值的函数均可以作为正则项，示例：. Regularization •New loss function to be minimized •Find a set of weight not only minimizing original cost but also close to zero 2 2 1 L cT L T O T Original loss (e. As the name implies they use L1 and L2 norms respectively which are added to your loss function by multiplying it with a parameter lambda. add ( layer = Dense ( 1 , input_dim = X. set regularization like l1, l2, l1_l2; Regularization adds item to loss function and prevent from parameters to become too big. A guide to advances in machine learning for financial professionals, with working Python code Key Features Explore advances in machine learning and how to put them to work in financial … - Selection from Machine Learning for Finance [Book]. W_constraint: instance of the constraints module (eg. Keras provides an implementation of the l1 and l2 regularizers that we will utilize in some of the hidden layers in the code snippet below. For more details on the maths, these article by Raimi Karim and Renu Khandelwal present L1 and L2 regularization maths reasonably. 01)) # A linear layer with L2 regularization of factor 0. io Find an R package R language docs Run R in your browser R Notebooks. L2 regularization improves again to 64. from keras import regularizers model. 003 for our Keras model, achieved finally train and validation accuracy of. regularizers. L1 and L2 regularization regularizer_l1: L1 and L2 regularization in keras: R Interface to 'Keras' rdrr. The CIFAR-10 data consists of 60,000 (32×32) color images in 10 classes, with 6000 images per class. Although the present study is preliminary, the results indicated that deep learning may be applied to classify colposcopy images. Regularization L1 and. Weight penalty is standard way for regularization, widely used in training other model types. 5 Keras assumes the network always has inputs and outputs, and outputs. A shared layer means its learned parameters # are the same no matter where the layer is used in the neural network. Overfitting is a phenomenon that occurs when a Machine Learning model is constraint to training set and not able to perform well on unseen data. 구현은 아래 링크들을 참고했다. These examples are extracted from open source projects. This article won't focus on the maths of regularization. First, by viewing BN as an. I am trying to replicate (a way smaller version) of the AlphaGo Zero system. Here are the same filters again, using only L2 decay, multiplying the image pixels by 0. In Keras, there are 2 methods to reduce over-fitting. 机器学习中的正则化(Regularization) 文中部分图片摘自吴恩达deeplearning课程的作业，代码及课件在我的github： DeepLearning 课件及作业. (L2 weight regularization は別名 weight decayとも呼ばれる）. First, this picture below: The green line (L2-norm) is the unique shortest path, while the red, blue, yellow (L1-norm) are all same length (=12) for the same route. L2 regularization is a classic method to reduce over-fitting, and consists in adding to the loss function the sum of the squares of all the weights of the model, multiplied by a given hyper-parameter (all equations in this article use python, numpy, and pytorch notation):. 0005 for i in range (8): # penalize the L2-norm of the weight matrix model_l2. 视频中会介绍什么是 overfitting, 怎么使用l1, l2 regularization terms. regularizers import l2 from keras. After you install tensorflow, theano and keras. The Keras regularization implementation methods can provide a parameter that represents the regularization hyperparameter value. L1 regularization coefficient. Use your spatial dropout regularization layer wisely. Keras provides an implementation of the l1 and l2 regularizers that we will utilize in some of the hidden layers in the code snippet below. A guide to advances in machine learning for financial professionals, with working Python code Key Features Explore advances in machine learning and how to put them to work in financial … - Selection from Machine Learning for Finance [Book]. The dataset first appeared in the Kaggle competition Quora Question Pairs and consists of approximately 400,000 pairs of questions along with a column indicating if the question pair is considered a duplicate. local / lib / python2. l2_regularization_weight (float, optional) – the L2 regularization weight per sample, defaults to 0. The new cost function along with L2 regularization is: Here, λ is the regularization parameter that you need to tune. regularizers. It consists of appropriately modifying your cost function, from: To: Let's modify your cost and observe the consequences. There are multiple types of weight regularization, such as L1 and L2 vector norms, and each requires a hyperparameter that must be configured. For example: keras. L2 regularization penalizes the sum of the squared values of the weights. import tensorflow. Overfitting is a major problem for Predictive Analytics and especially for Neural Networks. It consists of appropriately modifying your cost function, from: To: Let's modify your cost and observe the consequences. It has the effect of simulating a large number of networks with very different network […]. Also note that TensorFlow supports L1, L2, and ElasticNet regularization. Each takes the regularizer hyperparameter as an argument. If you split any values by max value, it is enough. multiplicitive factor to apply to the the l2 penalty term. regularizers. Optimizer that implements the Adam algorithm. Finally, we provide a set of questions that may help you decide which regularizer to use in your machine learning project. Below is the sample code to apply L2 regularization to a Dense layer. These examples are extracted from open source projects. To calculate , use : np. 7 / site-packages / keras / backend / theano_backend. In contrast, L1 regularization’s shape is diamond-like and the weights are lower in the corners of the diamond. Situation was the same as I would use l2 regularization, which I did not now. Enabled Keras model with Batch Normalization Dense layer. The models ends with a train loss of 0. mixture: A number between zero and one (inclusive) that is the proportion of L1 regularization (i. b_constraint: instance of the constraints module, applied to the bias. shape [ 1 ], activation = 'sigmoid' , kernel_regularizer = reg )). Weight decay fix: decoupling L2 penalty from gradient. 01): L2 weight regularization penalty, also known as weight decay, or Ridge; l1l2(l1=0. These are shortcut functions available in keras. [code]# Original loss function (ex: classification using cross entropy) unregularized_loss = tf. history_: Keras Object The AutoEncoder training history. 01))) Summary and Further Reading In this article, we start by understanding what is vanishing/exploding gradients followed by the solutions to handle the two issues with Keras API code. 0005 for i in range (8): # penalize the L2-norm of the weight matrix model_l2. The dataset first appeared in the Kaggle competition Quora Question Pairs and consists of approximately 400,000 pairs of questions along with a column indicating if the question pair is considered a duplicate. chdir (path) # 1. 01))) As optional argument, you can add regularization. If this option is unchecked, the name prefix is derived from the layer type. This differs from L2 above in that the L2 above is a stabilization. See full list on mc. problem: run dssm_keras. keras_ssg_lasso Documentation, Release 0. May 2020; March 2020; January 2020; December 2019; November 2019; October 2019; September 2019; Categories. Input shape. 我试图理解为什么Keras中的正则化语法看起来像它那样。 粗略地说，正则化是通过在损失函数中加入一个与模型权值的函数成正比的惩罚项来减少过度拟合的方法，因此，我认为正则化将被定义为模型损失函数规范的一部分。. The L2 regularization penalty is computed as: loss = l2 * reduce_sum(square(x)) L2 may be passed to a layer as a string identifier: dense = tf. ƛ is the regularization parameter which we can tune while training the model. regularizers. Dense(512, activation='elu', kernel_regularizer=regularizers. l2 (self. In keras, we can directly apply regularization to any layer using the regularizers. utils import shuffle def W_init (shape, name = None): """Initialize weights as in paper""" values. The regularization term is the squared magnitude of the weight parameter (L2 norm) as a penalty term. 01): L1-L2 regularization penalty, also known as ElasticNet. The results for these are shown here L2 regularized result. L1 The L1 regularization factor. L1 regularization formula does not have an analytical solution but L2 regularization does. Tensorflow is a powerful and flexible tool, but coding large neural architectures with it is tedious. L 2 정규화(L2 regularization) 경사하강법 의 여러 가지 변형은 순볼록 함수의 최저점에 가까운 점을 찾도록 보장합니다. L2 regularization will penalize the weights parameters without making them sparse since the penalty goes to zero for small weights. ) Shortcuts. class L1L2: A regularizer that applies both L1 and L2 regularization penalties. In this video, you will learn about these regularization methods in detail, along with how to implement them in Keras. verbose = 1 num_classes = 7 patience = 50 base_path = 'models/' l2_regularization=0. These tasks include. Use Keras to build simple logistic regression models, deep neural networks, recurrent neural networks, and convolutional neural networks Apply L1, L2, and dropout regularization to improve the accuracy of your model. Developed by Daniel Falbel, JJ Allaire, François Chollet, RStudio, Google. keras, weight regularization is added by passing weight regularizer instances to layers as keyword arguments. If you can't find a good parameter setting for L2, you could try dropout regularization instead. Dense(3, kernel_regularizer='l1_l2') In this case, the default. Loss functions applied to the output of a model aren't the only way to create losses. regularizers import l2 from keras. Regularisasi L 2 membantu mendorong bobot pencilan (bobot dengan nilai positif tinggi atau negatif rendah) lebih dekat ke 0 tetapi tidak benar-benar 0. In contrast, L1 regularization’s shape is diamond-like and the weights are lower in the corners of the diamond. The L1 regularization penalty is computed as: loss = l1 * reduce_sum(abs(x)) The L2 regularization penalty is computed as loss = l2 * reduce_sum(square(x)) L1L2 may be passed to a layer as a string identifier: dense = tf. L1 or L2 regularization), applied to the main weights matrix. you can have a look on this code as well in R language. /home/ samuele /. This set of experiments is left as an exercise for the interested reader. l1_l2: Activity is calculated. These examples are extracted from open source projects. We analyze BN by using a basic block of neural networks, consisting of a kernel layer, a BN layer, and a nonlinear activation function. Note that playing with regularization can be a good way to increase the performance of a network, particularly when there is an evident situation of overfitting. L2 may be passed to a layer as a string identifier: dense = tf. Through the parameter λ we can control the impact of the regularization term. Rolba Posted on March 15, 2020 March 15, 2020 Categories Regularization Tags keras, L2, python, regularization Use your spatial dropout regularization layer wisely. keras as keras #keras. kinds such as L1 and L2 regularization and soft weight sharing (Nowlan and Hinton, 1992). GMOインターネット 次世代システム研究室が新しい技術情報を配信しています | こんにちは。次世代システム研究室のJK (男)です。 突然ですが書籍の「ゼロから作るDeep Learning」読みましたか？基礎からクリアに説明されていて、個人的にはとても面白かったです。これまでLSTM, 強化学習の […]. history_: Keras Object The AutoEncoder training history. 01)) 16/73. W_constraint: instance of the constraints module (eg. bias_reg = regularizers. you change the keras. The loss function I am supposed to implement is the following: . By those, the model can get generalization performance. 001) reg_term = tf. l2_regularization_strength: A float value, must be greater than or equal to zero. In fact, what was accomplished in the previous tutorial in TensorFlow in around 42 lines* can be replicated in only 11 lines* in Keras. Unfortunately, L2 regularization also comes with a disadvantage due to the nature of the regularizer (Gupta, 2017). 01))) As optional argument, you can add regularization. The trained model predicts very well on the training data (often nearly 100% accuracy) but when presented with new data the model predicts poorly. See full list on sthalles. They are from open source Python projects. May 2020; March 2020; January 2020; December 2019; November 2019; October 2019; September 2019; Categories. Introduction. It contains all the supporting project files necessary to work through the course from start to finish. Additionally, I'm able to perform L1 regularization on the hidden layer l_hid1 without any issues. Everything works fine when I remove the term l2_penalty * l2_reg_param from the last line below. models import Sequential from keras. from the University of Toronto in their 2012 paper titled “ ImageNet Classification with Deep Convolutional Neural Networks ” developed a deep CNN model for the ImageNet dataset. The add_loss() API. L2 norm (L2 regularization, Ridge) If the loss is MSE, then cost function with L2 norm can be solved analytically There you can see that we just add an eye matrix (ridge) multiplied by λ in order to obtain a non-singular matrix and increase the convergence of the problem. def l1l2_penalty_reg (alpha = 1. This is because its calculations include gamma and beta variables that make the bias term unnecessary. add ( layer = Dense ( 1 , input_dim = X. 0005 or 5 x 10^−4) may be a good starting point. This is a high-level API to build and train models that includes first-class support for TensorFlow-specific functionality, such as eager execution, tf. 0 (default) epochs : int (default: 500) Number of passes over the training set. bias_reg = regularizers. 01): L1-L2 weight regularization penalty, also. 机器学习中的正则化(Regularization) 文中部分图片摘自吴恩达deeplearning课程的作业，代码及课件在我的github： DeepLearning 课件及作业. The second term is computed analytically, and then added to the layer as a regularization loss — similar to how we’d specify something like an L2 regularization. Regularization is a standard technique used in neural network training. l2_regularizer(scale=0. Use regularization; Getting more data is sometimes impossible, and other times very expensive. The results for these are shown here L2 regularized result. My focus is on tips that apply to any problem and any neural network architecture, and in fact, some of these tips apply more generally to any machine learning algorithm. Loss functions applied to the output of a model aren't the only way to create losses. 0005 for i in range (8): # penalize the L2-norm of the weight matrix model_l2. Keras overfitting Keras overfitting. L2 The L2 regularization factor. This is a summary of the official Keras Documentation. Specifically, the L1 norm and the L2 norm differ in how they achieve their objective of small weights, so understanding this can be useful for deciding which to use. problem: run dssm_keras. visualization training dropout vgg16 imagery keras-neural-networks l2-regularization ships resnet-50 satellite-images Updated Jan 16, 2020 Jupyter Notebook. 0001 Big Data 6 Conclusion/Future Work Loss 8. Following this, you’ll proceed to understand how to apply L1, L2, and dropout regularization techniques to improve the accuracy of your model. L2 regularization penalizes the sum of the squared values of the weights. References. In Section 6, we exploit the label-independence of the noising penalty and use unlabeled data to tune our estimate of R(). L2 regularization is also called weight decay in the context of neural networks. 01): L1 weight regularization penalty, also known as LASSO; l2(l=0. com L1 Regularization. The MAE for test is close to training which is good. how to change the regularization parameter in keras layer without rebuild a new model in R 0 I want to fine tuning my L2 parameter in my last keras layer using a for loop approach. L1,L2 regularization or dropout layer. keras as keras #keras. What can i do to reduce the training MAE with regularization?. Keras/TF implementation of AdamW, SGDW, NadamW, and Warm Restarts, based on paper Decoupled Weight Decay Regularization - plus Learning Rate Multipliers. Following this, you’ll proceed to understand how to apply L1, L2, and dropout regularization techniques to improve the accuracy of your model. from keras. 01): L1 regularization penalty, also known as LASSO l2 (l=0. This is the parameter in Keras, as shown below:. There are two good choices for running deep learning , one is theano and another one is tensorflow. ActivityRegularizer(l1=0. regularizers module: l1: Activity is calculated as the sum of absolute values. I know that a regularization strength of 1e4 is quite high but in my numpy network the loss in the 1st iteration is only around 700 and it reaches higher accuracies than anything I could train in keras. function was asked to create a function computing outputs given certain inputs, but the provided input variable at index 1 is not part of the computational graph needed to compute the outputs: keras_learning_phase. As alternatives to L2 regularization, you could use one of the following Keras weight regularizers: {r, echo=TRUE, results='hide'} # L1 regularization regularizer_l1(0. In this example, 0. use_bias: boolean; should we add a bias to the transition; bias_initializer: bias initializer - from keras. 我试图理解为什么Keras中的正则化语法看起来像它那样。 粗略地说，正则化是通过在损失函数中加入一个与模型权值的函数成正比的惩罚项来减少过度拟合的方法，因此，我认为正则化将被定义为模型损失函数规范的一部分。. keras is TensorFlow's implementation of the Keras API specification. from keras import regularizers model. datasets Download MNIST. Keras provides an implementation of the l1 and l2 regularizers that we will utilize in some of the hidden layers in the code snippet below. The regularization term for the L2 regularization is defined as i. This, however, makes the cost function more complicated. CIFAR-10 Task – Object Recognition in Images. l2_shrinkage_regularization_strength: A float value, must be greater than or equal to zero. Regularization •New loss function to be minimized •Find a set of weight not only minimizing original cost but also close to zero 2 2 1 L cT L T O T Original loss (e. For non-linear kernels, this corresponds to a non-linear function in the original space. 2) L2 regularization(=weight decay) : 가중치의 제곱에 비례하는 비용이 추가됨(가중치의 L2 norm) [keras] 정확한 평가를 위한 검증. 0; gaussian_noise_injection_std_dev (float, optional) – the standard deviation of the Gaussian noise added to parameters post update, defaults to 0. Since the coefficients are squared in the penalty expression, it has a different effect from L1-norm, namely it forces the coefficient values to be spread out more equally. regularizers import l1_l2: def set_kernel_reg (model, lambdal1 = 0, lambdal2 = 0): """ Apply kernel regularization to keras model: Args: model: Instance of Model not compiled yet: lambda1 (float): L1 regularization factor: lambda2 (float): L2 regularization factor. l2: L2 regularization factor (positive float). regularizers. As a kernel regularization, we will use the L2 regularization method. The regularization technique I’m going to be implementing is the L2 regularization technique. ; l2: L2 regularization factor (positive float). This is a summary of the official Keras Documentation. Ai-Nimals; Private. how to change the regularization parameter in keras layer without rebuild a new model in R 0 I want to fine tuning my L2 parameter in my last keras layer using a for loop approach. L2 Regularization Technique using Keras 50 xp Defining the regularizer 100 xp Compiling and fitting the model 100 xp Evaluating the L2 regularization model. The following are 30 code examples for showing how to use keras. L2 The L2 regularization factor. 01): L2 weight regularization penalty, also known as weight decay, or Ridge; l1l2(l1=0. Activity Regularization in Keras. Unfortunately, L2 regularization also comes with a disadvantage due to the nature of the regularizer (Gupta, 2017). But it has some problems. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. As the name implies they use L1 and L2 norms respectively which are added to your loss function by multiplying it with a parameter lambda. The regularizer is defined as an instance of the one of the L1, L2, or L1L2 classes. After 20 epochs the. In Keras, we can add a weight regularization by including using including kernel_regularizer=regularizers. L2 regularization penalizes the sum of the squared values of the weights. (GAM smoothing regularization) l2: (float) L2 regularization strength for the spline base coefficients. you can have a look on this code as well in R language. It is model interpretability: due to the fact that L2 regularization does not promote sparsity, you may end up with an uninterpretable model if your dataset is high-dimensional. Next, you’ll learn to evaluate your model by cross-validating it using Keras Wrapper and scikit-learn. Then, we will code. L2 regularization is also known as weight decay as it forces the weights to decay towards zero (but not exactly zero). regularizers. Therefore, regularization is a common method to reduce overfitting and consequently improve the model’s performance. Note that playing with regularization can be a good way to increase the performance of a network, particularly when there is an evident situation of overfitting. magic so that the notebook will reload external python modules % load_ext watermark % load_ext autoreload % autoreload 2 import numpy as np import pandas as pd from keras. py, but only one core is running. Regularization penalizes larger values in the weight matrices and bias vectors to help prevent over-fitting. 0 but L1 regularization doesn’t easily work with all forms of training. 001), activation = tf. l2(lambda)keras. where on the right denotes the complex modulus. Advanced Deep Learning with Keras is a comprehensive guide to the advanced deep learning techniques available today, so you can create your own cutting-edge AI. 0), but with f(x) = x for x > theta or f(x) = x for x < -theta, f(x) = 0. Don't let the different name confuse you: weight decay is mathematically the exact same as L2 regularization. 5): '''Calculate L1 and L2 penalties for a Keras layer This follows the same formulation as in the R package glmnet and Sklearn Args: alpha ([float]): amount of regularization. Now, I'm using the code below:. regularizers import l2. add(Dense( 64 , input_dim= 64 , kernel_regularizer=regularizers. The trained model predicts very well on the training data (often nearly 100% accuracy) but when presented with new data the model predicts poorly. The key difference between these two is the penalty term. Ai-Nimals; Private. L1 or L2 regularization), applied to the embedding matrix. Regularization techniques work by limiting the capacity of models—such as neural networks, linear regression, or logistic regression—by adding a parameter norm penalty Ω(θ) to. Some of the function are as follows − Activations module − Activation function is an important concept in ANN and activation modules provides many activation function like softmax, relu, etc. ActivityRegularizer(l1=0. 001)  ## Adding dropout `{r, eval=FALSE} # At training time: we drop out 50% of the. These examples are extracted from open source projects. Use regularization; Getting more data is sometimes impossible, and other times very expensive. There are two different types of regularization, namely L1 and L2. multiplicitive factor to apply to the the l1 penalty term. add ( Conv2D ( 64 , ( 3 , 3 ), kernel_regularizer = regularizers. The standard way to avoid overfitting is called L2 regularization. regularizers.


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# Revision history [back]

### Reading pixel values from a binary file

I have a series of 128x128 pixel sized frames stored in a binary file. Each pixel has 32 bits of information, I am interested in the last 12 bits of each pixel, these 12 bits should provide me with a grayscale image.

I know openCV doesn't support 12-bit, so I tried to do the masking using 0xfff, not sure if that is right. In my attempt I am looking at the 99th frame of the video, there is a 1024 byte header in each file that I am skipping, and each frame has 66960 bytes, hence the 66960*99 to skip to the 99th frame. I also skip a reserved 4 bytes which is in each.

The resulting image I get looks almost right, except it seems like there is a gray mask over the whole image. I have both what I am getting and what it should look like at the bottom attached.

My attempt is below, I know I am getting the pixel information right because I am checking pixel values by using another software, I believe the problem is in the way I am using the data types and Mat image type (unsigned int, short etc and CV_16U, CV_16S, CV_32). Please help with how to pad the pixel data and/or what type Mat to use. Thanks.

    file = fopen("binary_file", "rb");
fseek(file, 0, SEEK_END);

//frame loop
unsigned int buffer[65536];
fseek(file,4+1024+66960*99, SEEK_SET);


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Situation 55.9.3. Let $R$ be a discrete valuation ring with fraction field $K$, residue field $k$, and uniformizer $\pi$. Let $C$ be a smooth projective curve over $K$ with $H^0(C, \mathcal{O}_ C) = K$. Let $X$ be a regular proper model of $C$. Let $C_1, \ldots , C_ n$ be the irreducible components of the special fibre $X_ k$. Write $X_ k = \sum m_ i C_ i$ as in Lemma 55.9.1.

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# Annual income of A and B are in the ratio of 4:3 and their annual expances are in the ratio of 3:2. If each of them saves Rs 600 at the end of the year

## Word Problem 2

Problem 2: Annual income of A and B are in the rat... »

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## Thinking Mathematically (6th Edition)

We can find the total patient load. total load = 119 + 165 + 216 = 500 We can find the standard divisor. $standard~divisor = \frac{total~load}{number~of~ doctors}$ $standard~divisor = \frac{500}{10}$ $standard~divisor = 50$ The standard divisor is 50


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## Distribution of points on arcs.(English)Zbl 1156.11310

Let $$z_1,\dots, z_N$$ be complex numbers situated on the unit circle $$\mathbb U:=\{z\in \mathbb C\mid |z| = 1\}$$, and write $$S := z_1 +\cdots+ z_N$$. In 1962 G. A. Freiman [Izv. Vyssh. Uchebn. Zaved., Mat. 1962, No. 6(31), 131–144 (1962; Zbl 0171.00803)] established a lemma showing that if $$z_1,\dots, z_N\in \mathbb U$$ are “uniformly distributed on arcs of length $$\pi$$”, then the sum $$z_1 +\cdots+ z_N$$ is small in absolute value, $$S\leq 2n-N$$. The assumption “any open arc of $$\mathbb U$$ of length $$\pi$$ contains at most $$n$$ of the numbers $$z_1,\dots, z_N$$” implies readily that $$N\leq 2n$$.
In practice, an analog of Lemma 1 is needed with the arcs of length $$\pi$$ replaced by arcs of other prescribed lengths; see for instance [B. Green and I. Z. Ruzsa, Bull. Lond. Math. Soc. 38, No. 1, 43–52 (2006; Zbl 1155.11307), T. Schoen, Integers 3, Paper A17, 6 p., electronic only (2003; Zbl 1089.11009)]. The author generalizes Freiman’s result as follows:
Theorem 1: Suppose that any open arc of length $$\phi\in (0, \pi]$$ of the unit circle contains at most $$n$$ of the numbers $$z_1,\dots, z_N$$. Then
$|S|\leq 2n-N+2(N-n) \cos(\phi/2).$
Theorem 1 is sharp, at least in the range $$N/2\leq n \leq N$$: the bound is attained, for instance, if $$2n-N$$ of the numbers $$z_j$$ equal one, $$N-n$$ equal $$\exp(i\phi/2)$$, and $$N-n$$ equal $$\exp(-i\phi/2)$$.
Theorem 2: Suppose that any open arc of length $$\pi$$ of the unit circle contains at most $$n$$ of the numbers $$z_1,\dots, z_N$$ and suppose, in addition, that for any $$1\leq i< j\leq N$$ the length of the (shortest) arc between $$z_i$$ and $$z_j$$ is at least $$\delta > 0.$$ Then $|S|\leq\frac{\sin (n-N/2)\delta}{\sin \delta/2}$
provided that $$n\delta\leq \pi$$. Theorem 2 is also sharp.
Finally the author notices that from Theorem 1 one can deduce the following more general result.
Theorem 1’. Let $$\lambda\leq 1/2$$ and $$\nu$$ be positive real numbers and let $$\mu$$ be a probabilistic measure on the torus group $$\mathbb R/\mathbb Z$$. Suppose that $$\mu(I) \leq \nu$$ for any open interval $$I \subseteq\mathbb R/\mathbb Z$$ of length $$|I| = \lambda$$. Then $\biggl|\int_{\mathbb R/\mathbb Z}\exp(it)\, d\mu\biggr| \leq 2\nu-1 + 2(1-\nu)\cos(\pi\lambda).$

### MSC:

 11J71 Distribution modulo one 11K36 Well-distributed sequences and other variations

### Citations:

Zbl 0171.00803; Zbl 1155.11307; Zbl 1089.11009
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