Softmax takes in an n-dimensional vector x = R and outputs another n-dimensional vector y R...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Softmax takes in an n-dimensional vector x = R" and outputs another n-dimensional vector y R" with the ith element y(i) = n k=1 expx(i) expx(k) Vi E {1, 2,...,n}. In this problem, please calculate the gradient of y with respect to x. Let di.j 1. (5 Points): Please derive an expression for dii, where i = {1, 2, ..., n}. Hint: Recall that for a general function in the form of h(x): respect to the variable x is (3) y (i) - ax(j) f(x) = 9(x)' its derivative h(x) af (x) g(x) ag(x) : f(x) n (9(x)) 2(x(i)) 2. (5 Points): In a similar way, please derive the expression for di,j, where i j and i, j = {1, 2,...,n}. Softmax takes in an n-dimensional vector x = R" and outputs another n-dimensional vector y R" with the ith element y(i) = n k=1 expx(i) expx(k) Vi E {1, 2,...,n}. In this problem, please calculate the gradient of y with respect to x. Let di.j 1. (5 Points): Please derive an expression for dii, where i = {1, 2, ..., n}. Hint: Recall that for a general function in the form of h(x): respect to the variable x is (3) y (i) - ax(j) f(x) = 9(x)' its derivative h(x) af (x) g(x) ag(x) : f(x) n (9(x)) 2(x(i)) 2. (5 Points): In a similar way, please derive the expression for di,j, where i j and i, j = {1, 2,...,n}.
Expert Answer:
Related Book For
Introduction to Econometrics
ISBN: 978-0133595420
3rd edition
Authors: James H. Stock, Mark W. Watson
Posted Date:
Students also viewed these mathematics questions
-
The Cost of Debt and Flotation Costs Suppose a company will issue new 20-year debt with a par value of $1,000 and a coupon rate of 9%, paid annually. The issue price will be $1,000. a) The tax rate...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Q1. You have identified a market opportunity for home media players that would cater for older members of the population. Many older people have difficulty in understanding the operating principles...
-
Assume electricity is generated by three technologies: a base load technology with cost function C b (x b ) and proportional emission coefficient b ; gas turbines with cost function C g (x g ) and...
-
Ripley Shirt Company sells on credit and manages its own receivables. Average experience for the past three years has been the following: Jack Rivers, the owner, is considering whether to accept...
-
Air at 1 atm and 40C flows in a 8-cm-diameter pipe at a rate of 2500 L/min. The friction factor is determined from the Moody chart to be 0.027. The required power input to overcome the pressure drop...
-
\(\mu=1275, \sigma=6, n=1000\) In Exercises 1-4, a population has a mean \(\mu\) and a standard deviation \(\sigma\). Find the mean and standard deviation of the sampling distribution of sample means...
-
Sunspot Beverages, Ltd., of Fiji makes blended tropical fruit drinks in two stages. Fruit juices arc extracted from fresh fruits and then blended in the Blending Department. The blended juices are...
-
24. Accrued Intererst: You purchase a bond with a coupon rate of6.4 percent, a par value of $1,000. The bond has a coupon rate of5.3 percent, and there are four months to the next semiannualcoupon 2...
-
What is information systems analysis and design?
-
In an international project, the bill of quantities stipulates that white cement should be used for mosaic jointing in the toilet, but the technical specifications indicate that ordinary Portland...
-
A liquid of density 1397 kg/m flows with speed 2.5 m/s into a pipe of diameter 0.17 m. The diameter of the pipe decreases to 0.05 m at its exit end. The exit end of the pipe is 7.04 m lower than the...
-
What are integrated marketing communication strategies used by Amazon using print advertising, digital advertising, social media advertising and tv advertising?
-
In a construction job that is expected to last 4 years, a conveyor with a cost of $ 10,000 is proposed as an alternative for handling materials; with annual operating expenses of $ 7,000. The analyst...
-
1.If $961.00 accumulates t o$1185.89 in two years six months compounded quarterly what is the effective annual rate of interest ? the effective annual rate of interest is ? 2.A car was purchaed for...
-
Classify the following goods in terms of their own-price elasticity: (elastic, inelastic, unit-elastic, perfectly elastic, and perfectly inelastic) (a) Emergency Air Travel = 0.1. (b) Recreational...
-
How does risk assessment in environmental contexts differ from industrial and engineering applications, particularly in terms of assessing the impact on ecosystems and public health ?
-
The MIT Sloan School of Management is one of the leading business schools in the U.S. The following table contains the tuition data for the masters program in the Sloan School of Management. a. Use...
-
(Review of summation notation) Let x1, . . . xn denote a sequence of numbers. y1, . . . ,yn denote another sequence of numbers, and a, b, and c denote three constants. Show that (a) (b) (c) (d)...
-
a. In the fixed effects regression model, are the fixed entity effects, i, consistently estimated as n with T fixed? b. If n is large (say, n = 2000) but T is small (say, T = 4), do you think that...
-
In a given population, 11 % of the likely voters are African American. A survey using a simple random sample of 600 landline telephone numbers finds 8% African Americans. Is there evidence that the...
-
Rationalize the denominator of the following: 1. \(\frac{5}{\sqrt{7}}\) 2. \(\frac{3 \sqrt{6}}{2 \sqrt{10}}\)
-
Perform the following operations without a calculator. Simplify if possible. 1. \(3 \sqrt{15} \div(8 \sqrt{3})\) 2. \(14.7 \sqrt{135} \div(3 \sqrt{5})\).
-
Identify all subsets of the real numbers to which the following real numbers belong: 1. 14 2. -14.223 3. \(\sqrt{17}\)
Study smarter with the SolutionInn App