Este documento presenta 22 apartados que describen diferentes operaciones matemáticas con funciones y el cálculo de sus dominios resultantes. Se explican sumas, restas, productos, composiciones, divisiones y raíces de funciones polinómicas y racionales. Para cada operación, se identifican las funciones involucradas, se describe la operación matemática y se determina el dominio resultante basado en las propiedades de las funciones y los números que hacen cero al denominador.
A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to the uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition[4] or speech recognition. The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replaced with a strictly feedforward neural network, while an infinite impulse recurrent network is a directed cyclic graph that can not be unrolled.
Additional stored states and the storage under direct control by the network can be added to both infinite-impulse and finite-impulse networks. The storage can also be replaced by another network or graph if that incorporates time delays or has feedback loops. Such controlled states are referred to as gated state or gated memory, and are part of long short-term memory networks (LSTMs) and gated recurrent units. This is also called Feedforward Neural Network (FNN). Recurrent neural networks are theoretically Turing complete and can run arbitrary programs to process arbitrary sequences of inputs.
This presentation is Part 2 of my September Lisp NYC presentation on Reinforcement Learning and Artificial Neural Nets. We will continue from where we left off by covering Convolutional Neural Nets (CNN) and Recurrent Neural Nets (RNN) in depth.
Time permitting I also plan on having a few slides on each of the following topics:
1. Generative Adversarial Networks (GANs)
2. Differentiable Neural Computers (DNCs)
3. Deep Reinforcement Learning (DRL)
Some code examples will be provided in Clojure.
After a very brief recap of Part 1 (ANN & RL), we will jump right into CNN and their appropriateness for image recognition. We will start by covering the convolution operator. We will then explain feature maps and pooling operations and then explain the LeNet 5 architecture. The MNIST data will be used to illustrate a fully functioning CNN.
Next we cover Recurrent Neural Nets in depth and describe how they have been used in Natural Language Processing. We will explain why gated networks and LSTM are used in practice.
Please note that some exposure or familiarity with Gradient Descent and Backpropagation will be assumed. These are covered in the first part of the talk for which both video and slides are available online.
A lot of material will be drawn from the new Deep Learning book by Goodfellow & Bengio as well as Michael Nielsen's online book on Neural Networks and Deep Learning as well several other online resources.
Bio
Pierre de Lacaze has over 20 years industry experience with AI and Lisp based technologies. He holds a Bachelor of Science in Applied Mathematics and a Master’s Degree in Computer Science.
https://www.linkedin.com/in/pierre-de-lacaze-b11026b/
A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to the uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition[4] or speech recognition. The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replaced with a strictly feedforward neural network, while an infinite impulse recurrent network is a directed cyclic graph that can not be unrolled.
Additional stored states and the storage under direct control by the network can be added to both infinite-impulse and finite-impulse networks. The storage can also be replaced by another network or graph if that incorporates time delays or has feedback loops. Such controlled states are referred to as gated state or gated memory, and are part of long short-term memory networks (LSTMs) and gated recurrent units. This is also called Feedforward Neural Network (FNN). Recurrent neural networks are theoretically Turing complete and can run arbitrary programs to process arbitrary sequences of inputs.
This presentation is Part 2 of my September Lisp NYC presentation on Reinforcement Learning and Artificial Neural Nets. We will continue from where we left off by covering Convolutional Neural Nets (CNN) and Recurrent Neural Nets (RNN) in depth.
Time permitting I also plan on having a few slides on each of the following topics:
1. Generative Adversarial Networks (GANs)
2. Differentiable Neural Computers (DNCs)
3. Deep Reinforcement Learning (DRL)
Some code examples will be provided in Clojure.
After a very brief recap of Part 1 (ANN & RL), we will jump right into CNN and their appropriateness for image recognition. We will start by covering the convolution operator. We will then explain feature maps and pooling operations and then explain the LeNet 5 architecture. The MNIST data will be used to illustrate a fully functioning CNN.
Next we cover Recurrent Neural Nets in depth and describe how they have been used in Natural Language Processing. We will explain why gated networks and LSTM are used in practice.
Please note that some exposure or familiarity with Gradient Descent and Backpropagation will be assumed. These are covered in the first part of the talk for which both video and slides are available online.
A lot of material will be drawn from the new Deep Learning book by Goodfellow & Bengio as well as Michael Nielsen's online book on Neural Networks and Deep Learning as well several other online resources.
Bio
Pierre de Lacaze has over 20 years industry experience with AI and Lisp based technologies. He holds a Bachelor of Science in Applied Mathematics and a Master’s Degree in Computer Science.
https://www.linkedin.com/in/pierre-de-lacaze-b11026b/
CHARACTER RECOGNITION USING NEURAL NETWORK WITHOUT FEATURE EXTRACTION FOR KAN...Editor IJMTER
Handwriting recognition has been one of the active and challenging research areas in the
field of pattern recognition. It has numerous applications which include, reading aid for blind, bank
cheques and conversion of any hand written document into structural text form[1]. As there are no
sufficient number of works on Indian language character recognition especially Kannada script
among 15 major scripts in India[2].In this paper an attempt is made to recognize handwritten
Kannada characters using Feed Forward neural networks. A handwritten kannada character is resized
into 60x40 pixel.The resized character is used for training the neural network. Once the training
process is completed the same character is given as input to the neural network with different set of
neurons in hidden layer and their recognition accuracy rate for different kannada characters has been
calculated and compared. The results show that the proposed system yields good recognition
accuracy rates comparable to that of other handwritten character recognition systems.
GUI based handwritten digit recognition using CNNAbhishek Tiwari
This project is to create a model which can recognize the digits as well as also to create GUI which is user friendly i.e. user can draw the digit on it and will get appropriate output.
DISTINGUISH BETWEEN WALSH TRANSFORM AND HAAR TRANSFORMDip transformsNITHIN KALLE PALLY
walsh transform-1D Walsh Transform kernel is given by:
n - 1
g(x, u) = (1/N) ∏ (-1) bi(x) bn-1-i(u)
i = 0
where, N – no. of samples
n – no. of bits needed to represent x as well as u
bk(z) – kth bits in binary representation of z.
Thus, Forward Discrete Walsh Transformation is
N - 1 n - 1
W(u) = (1/N) Σ f(x) ∏ (-1) bi(x) b(u) x = 0 i = 0
Cubic curves are commonly used in graphics because curves of lower order commonly have too little flexibility, while curves of higher order are usually considered unnecessarily complex and make it easy to introduce undesired wiggles.
classify images from the CIFAR-10 dataset. The dataset consists of airplanes, dogs, cats, and other objects.we'll preprocess the images, then train a convolutional neural network on all the samples. The images need to be normalized and the labels need to be one-hot encoded.
CHARACTER RECOGNITION USING NEURAL NETWORK WITHOUT FEATURE EXTRACTION FOR KAN...Editor IJMTER
Handwriting recognition has been one of the active and challenging research areas in the
field of pattern recognition. It has numerous applications which include, reading aid for blind, bank
cheques and conversion of any hand written document into structural text form[1]. As there are no
sufficient number of works on Indian language character recognition especially Kannada script
among 15 major scripts in India[2].In this paper an attempt is made to recognize handwritten
Kannada characters using Feed Forward neural networks. A handwritten kannada character is resized
into 60x40 pixel.The resized character is used for training the neural network. Once the training
process is completed the same character is given as input to the neural network with different set of
neurons in hidden layer and their recognition accuracy rate for different kannada characters has been
calculated and compared. The results show that the proposed system yields good recognition
accuracy rates comparable to that of other handwritten character recognition systems.
GUI based handwritten digit recognition using CNNAbhishek Tiwari
This project is to create a model which can recognize the digits as well as also to create GUI which is user friendly i.e. user can draw the digit on it and will get appropriate output.
DISTINGUISH BETWEEN WALSH TRANSFORM AND HAAR TRANSFORMDip transformsNITHIN KALLE PALLY
walsh transform-1D Walsh Transform kernel is given by:
n - 1
g(x, u) = (1/N) ∏ (-1) bi(x) bn-1-i(u)
i = 0
where, N – no. of samples
n – no. of bits needed to represent x as well as u
bk(z) – kth bits in binary representation of z.
Thus, Forward Discrete Walsh Transformation is
N - 1 n - 1
W(u) = (1/N) Σ f(x) ∏ (-1) bi(x) b(u) x = 0 i = 0
Cubic curves are commonly used in graphics because curves of lower order commonly have too little flexibility, while curves of higher order are usually considered unnecessarily complex and make it easy to introduce undesired wiggles.
classify images from the CIFAR-10 dataset. The dataset consists of airplanes, dogs, cats, and other objects.we'll preprocess the images, then train a convolutional neural network on all the samples. The images need to be normalized and the labels need to be one-hot encoded.
El cálculo, son todas aquellas operaciones en su mayoría matemáticas que nos permite llegar a una solución partiendo solamente de algunos datos; por ende tiene muchas herramientas fundamentales que permite la resolución del mismo.
3. Apartado A
Sabiendo que f(x)= 3x+3 y g(x)= x^2-7 la operación f(x)+g(x) consiste en sumar
los miembros de ambas funciones. Para calcular el dominio, debemos realizar
la intersección de los dos dominios.
4. Apartado B
Sabemos que f(x)=3x-3; g(x)=x^2-7 , por ello, usamos la fórmula de resta de
funciones, y tendremos el dominio del resultado:
5. Apartado C
Sabemos que f(x)=3x+3 y que h(x)=(x+5)/4, por tanto, su producto se obtendrá
realizando la intersección de sus dominios.
6. Apartado D
El producto de estas funciones es y su dominio R ya
que los dominios de g(x) y f(x) son R. Dom=R
7. Apartado E
Sabiendo que f(x)= 3x+3 y g(x)= x^2-7, para calcular f compuesta de g, hay
que sustituir x por g en la función f(x). Finalmente hallaremos su dominio.
8. Apartado F
Sabemos que f(x)=3x-3; g(x)=x^2-7, por ello, para obtener "g" compuesta de
"f",vamos a introducir la función f(x) en la función g(x) , y finalmente hallaremos
su dominio:
Al ser el resultado una
función polinómica,
el dominio son todos los
números reales.
9. Apartado G
Sabemos que g(x)=(x^2)-7 y que h(x)= (x+5)/4 por tanto, para obtener "g"
compuesta de "h(x)", introducimos la función h(x) en la función g(x).
A continuación,
calculamos el dominio
de la función resultante.
En este caso se trata de
una función racional con
un polinomio en su
numerador, siendo su
dominio el conjunto de
los números reales.
10. Apartado H
El resultado de la composición es el indicado en la imagen y su dominio es el
conjunto de todos os números reales exceptuando el 0, ya que no puede ser
nunca un cero el denominador de una fracción. dom=R-(0)
11. Apartado I
Sabiendo que h(x)= x+5/4 y t(x)= -4/x para hacer la multiplicación de ambas,
hay que multiplicar los miembros de ambas funciones y posteriormente calcular
sus dominios.
12. Apartado J
Sabemos que h(x)=x+5/4; t(x)=-4/x, por ello, para obtener "t" compuesta de "h",
vamos a introducir la función h(x) en la función t(x) , y finalmente hallaremos su
dominio:
Al conocer que el resultado es
una función racional, su dominio
será todos los números reales
menos aquellos que hagan 0
al denominador.En nuestro caso,
el dominio del resultado son todos
los números reales menos el -5.
13. Apartado K
Sabemos que t(x)= -4/4 y que g(x)=(x^2)-7, por tanto su diferencia se calculará
realizando la intersección de sus dominios. En el caso de la primera función, al
ser racional, el único número que hace 0 al denominador es 0. Por tanto su
dominio es el conjunto de los reales menos el 0. La intersección con el dominio
de la otra función (todos los reales) hace que el resultado sea:
14. Apartado L
El resultado de la operación es el indicado en la imagen y su dominio el
conjunto de todos los números reales, esto se debe a que en una división la
única manera de que se excluyan números en el dominio es que el
denominador se haga 0 y en este ejercicio no es posille que sea 0.
Dom=R
15. Apartado M
Sabiendo que f(x)= 3x+3 y g(x)= x^2-7 para hacer esta multiplicación, basta
con hacer la x de f(x) negativa y elevarla al cuadrado. Posteriormente
multiplicamos este resultado con g(x). Por último, realizaremos el dominio de la
función.
16. Apartado N
Sabemos que f(x)=3x-3; g(x)=x^2-7, por ello,para realizar el producto,primero
debemos multiplicar a f(x) por 3, e imponer (x^2-1) en g(x). A continuación,
calculamos su dominio:
17. Apartado Ñ
Siendo f(x)= 3x+3 y g(x)=(x^2)-7, calculamos su diferencia realizando la
intersección de sus dominios. Antes de ello multiplicamos cada función por su
coeficiente y no operamos ni simplificamos. Al tratarse finalmente de dos
funciones polinómicas, su dominio hace que sea el conjunto de los reales.
18. Apartado O
El dominio de la operación es el conjunto de números comprendidos entre el
[-1,+∞) , esto se debe a que no es posible que el argumento de una raíz de
exponente par sea negativo y por ello los únicos valores que no dan negativo
son[-1,+∞)
Dom=[-1,+∞)
19. Apartado Q
Sabiendo que f(x)= 3x+3 y g(x)= x^2-7 realizamos la división de ambas
funciones dentro de una raíz cuadrada. Por último, calculamos el dominio de la
función.
20. Apartado R
Debemos de calcular el cociente de las raíces cuadradas de f(x) y de g(x)
conocemos que f(x)=3x-3 , g(x)=x^2-7; A continuación, se realiza el cociente:
Su dominio son todos los números reales comprendidos en el intervalo citado.
21. Apartado S
El cociente entre dos funciones se calcula realizando la intersección entre el
dominio del numerador, el dominio del denominador y la resta de aquel valor
que hace 0 al denominador. El numerador es un polinomio por lo que su
dominio es el conjunto de los números reales. El denominador tiene una
función irracional por lo que se buscan los valores mayores o iguales que 0.
Finalmente,
el único valor
que hace 0 el
denominador
es el -1.
El resultado
final es un
intervalo que
va desde el
-1 (no
incluído) al
infinito.
22. Apartado T
El resultado de la operación es y su dominio es el
indicado en la imagen, esto se debe a que sólo pueden valores positivos
dentro de las raíces de exponente par.