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tags :: category theory
source :: ACT4E - Session 2 - Connection
A function is a special type of relation
A relation is a function if it satisfies the two following conditions:
$\forall x \in X \exists y \in Y : \langle x,y \rangle \in R$
every element of the source X gets mapped by f to some element of the target Y
$\exists \langle x_1,y_1 \rangle, \langle x_2,y_2 \rangle \in R$ holds: $x_1 x_2 \Rightarrow y_1 y_2$
Like categories and subsequently relations, functions can also be composed.
A free function is a programming languageconstruct where a functionis not bound to a particular object, such as a method
In the following example, f is a free function while obj.m is a method
(obj.m can reference this1):
function f() {
return "f";
}
const obj = {
m: function () {
return "m";
},
};
1This example is somewhat misleading because in JavaScripta free function can become a method. Consider the following example:
function f() {
return this.name;
}
const obj = {
name: 'obj',
};
console.log('free func:\t', f());
obj.f = f;
console.log('method:\t', obj.f());
free func: undefined method: obj undefined
Further, in JavaScript this can be set in free functions:
function f() {
return `my name is ${this.name}`;
}
console.log(f.call({name: 'foo'}));
: my name is foo : undefined
Go to [[Week 2 - Introduction]] or back to the [[Main AI Page]]
Part of the page on [[Neural Networks]]
An activation function determines how a node responds to its inputs.
#ToDo Expand on the definition of Activation function.
Go back to the [[AI Glossary]]
A function (for example, ReLU or sigmoid) that takes in the weighted sum of all of the inputs from the previous layer and then generates and passes an output value (typically nonlinear) to the next layer.
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A function in which the region above the graph of the function is a convex set. The prototypical convex function is shaped something like the letter U. For example, the following are all convex functions:
A typical convex function is shaped like the letter ‘U’.
By contrast, the following function is not convex. Notice how the region above the graph is not a convex set:
A strictly convex function has exactly one local minimum point, which is also the global minimum point. The classic U-shaped functions are strictly convex functions. However, some convex functions (for example, straight lines) are not U-shaped.
A lot of the common loss functions, including the following, are convex functions:
Many variations of gradient descent are guaranteed to find a point close to the minimum of a strictly convex function. Similarly, many variations of stochastic gradient descent have a high probability (though, not a guarantee) of finding a point close to the minimum of a strictly convex function.
The sum of two convex functions (for example, L2 loss + L1 regularization) is a convex function.
Deep models are never convex functions. Remarkably, algorithms designed for convex optimization tend to find reasonably good solutions on deep networks anyway, even though those solutions are not guaranteed to be a global minimum.
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In TensorFlow, a function that returns input data to the training, evaluation, or prediction method of an Estimator. For example, the training input function returns a batch of features and labels from the training set.
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The function within an Estimator that implements machine learning training, evaluation, and inference. For example, the training portion of a model function might handle tasks such as defining the topology of a deep neural network and identifying its optimizer function. When using premade Estimators, someone has already written the model function for you. When using custom Estimators, you must write the model function yourself.
For details about writing a model function, see the Creating Custom Estimators chapter in the TensorFlow Programmers Guide.
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The mathematical formula or metric that a model aims to optimize. For example, the objective function for linear regression is usually squared loss. Therefore, when training a linear regression model, the goal is to minimize squared loss.
In some cases, the goal is to maximize the objective function. For example, if the objective function is accuracy, the goal is to maximize accuracy.
See also loss.
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#rl
In reinforcement learning, the function that predicts the expected return from taking an action in a state and then following a given policy.
Q-function is also known as state-action value function.
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A function that maps logistic or multinomial regression output (log odds) to probabilities, returning a value between 0 and 1. The sigmoid function has the following formula:
where $\sigma$ in logistic regression problems is simply:
In other words, the sigmoid function converts
into a probability between 0 and 1.
In some neural networks, the sigmoid function acts as the activation function.
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#rl
Synonym for Q-function.
In this book, Plantinga introduces the notion of warrant as an alternative to justification and discusses topics like self-knowledge, memories, perception, and probability.[1] Plantinga’s "proper function" account argues that as a necessary condition of having warrant, one’s "belief-forming and belief-maintaining apparatus of powers" are functioning properlyβ"working the way it ought to work".[2] Plantinga explains his argument for proper function with reference to a "design plan", as well as an environment in which one’s cognitive equipment is optimal for use. Plantinga asserts that the design plan does not require a designer: "it is perhaps possible that evolution (undirected by God or anyone else) has somehow furnished us with our design plans",[3] but the paradigm case of a design plan is like a technological product designed by a human being (like a radio or a wheel). Ultimately, Plantinga argues that epistemological naturalism- i.e. epistemology that holds that warrant is dependent on natural faculties β is best supported by supernaturalist metaphysics β in this case the belief in a creator God or designer who has laid out a design plan that includes cognitive faculties conducive to attaining knowledge.[4]
I’m not really a fan of this, the whole "designer" bullshit [[bullshido]]
In this book, Plantinga introduces the notion of warrant as an alternative to justification and discusses topics like self-knowledge, memories, perception, and probability.[1] Plantinga’s "proper function" account argues that as a necessary condition of having warrant, one’s "belief-forming and belief-maintaining apparatus of powers" are functioning properlyβ"working the way it ought to work".[2] Plantinga explains his argument for proper function with reference to a "design plan", as well as an environment in which one’s cognitive equipment is optimal for use. Plantinga asserts that the design plan does not require a designer: "it is perhaps possible that evolution (undirected by God or anyone else) has somehow furnished us with our design plans",[3] but the paradigm case of a design plan is like a technological product designed by a human being (like a radio or a wheel). Ultimately, Plantinga argues that epistemological naturalism- i.e. epistemology that holds that warrant is dependent on natural faculties β is best supported by supernaturalist metaphysics β in this case the belief in a creator God or designer who has laid out a design plan that includes cognitive faculties conducive to attaining knowledge.[4]
I’m not really a fan of this, the whole "designer" bullshit [[bullshido]]
In this book, Plantinga introduces the notion of warrant as an alternative to justification and discusses topics like self-knowledge, memories, perception, and probability.[1] Plantinga’s "proper function" account argues that as a necessary condition of having warrant, one’s "belief-forming and belief-maintaining apparatus of powers" are functioning properlyβ"working the way it ought to work".[2] Plantinga explains his argument for proper function with reference to a "design plan", as well as an environment in which one’s cognitive equipment is optimal for use. Plantinga asserts that the design plan does not require a designer: "it is perhaps possible that evolution (undirected by God or anyone else) has somehow furnished us with our design plans",[3] but the paradigm case of a design plan is like a technological product designed by a human being (like a radio or a wheel). Ultimately, Plantinga argues that epistemological naturalism- i.e. epistemology that holds that warrant is dependent on natural faculties β is best supported by supernaturalist metaphysics β in this case the belief in a creator God or designer who has laid out a design plan that includes cognitive faculties conducive to attaining knowledge.[4]
I’m not really a fan of this, the whole "designer" bullshit [[bullshido]]
In this book, Plantinga introduces the notion of warrant as an alternative to justification and discusses topics like self-knowledge, memories, perception, and probability.[1] Plantinga’s "proper function" account argues that as a necessary condition of having warrant, one’s "belief-forming and belief-maintaining apparatus of powers" are functioning properlyβ"working the way it ought to work".[2] Plantinga explains his argument for proper function with reference to a "design plan", as well as an environment in which one’s cognitive equipment is optimal for use. Plantinga asserts that the design plan does not require a designer: "it is perhaps possible that evolution (undirected by God or anyone else) has somehow furnished us with our design plans",[3] but the paradigm case of a design plan is like a technological product designed by a human being (like a radio or a wheel). Ultimately, Plantinga argues that epistemological naturalism- i.e. epistemology that holds that warrant is dependent on natural faculties β is best supported by supernaturalist metaphysics β in this case the belief in a creator God or designer who has laid out a design plan that includes cognitive faculties conducive to attaining knowledge.[4]
I’m not really a fan of this, the whole "designer" bullshit [[bullshido]]