Appendix D on the web

Symbol index

91 symbols, A to Z. Each row gives the symbol, its meaning in words, its type and the sections where it is used.

What is real here. The rows come from registry/symbols.json, copied into src/data/symbols.json. Symbols are rendered with KaTeX. Section lists come from the loaded chapters, so this fixture build records only chapter 1 uses.

Search the symbol index

Search runs in this browser. No query is sent anywhere.

91 entries shown.

A

$A$ : a matrix

a matrix

Type: matrix

Sections:

$|x|$ : the absolute value of x, or the size of a finite set

the absolute value of x, or the size of a finite set

Type: function

Sections: no section recorded yet

$alpha$ : a learning rate or a significance level, as labelled at use

a learning rate or a significance level, as labelled at use

Type: scalar

Sections:

$a l p h a_{N}$ : a step-size coefficient at stage N

a step-size coefficient at stage N

Type: scalar

Sections:

c24.s03 · Scaling laws

$and$ : conjunction

conjunction

Type: logic

Sections: no section recorded yet

B

$b$ : a bias or a vector

a bias or a vector

Type: vector

Sections:

$B$ : a matrix, a budget, or a number of runs

a matrix, a budget, or a number of runs

Type: matrix

Sections:

$b e t a$ : a coefficient, a discount factor, or a momentum constant

a coefficient, a discount factor, or a momentum constant

Type: scalar

Sections:

c22.s04 · Diffusion

$b e t a_{0}$ : an intercept

an intercept

Type: scalar

Sections:

c14.s01 · Fitting a line

$b e t a_{1}$ : a slope or a momentum constant

a slope or a momentum constant

Type: scalar

Sections:

c14.s01 · Fitting a line

C

$c$ : a coefficient or a count

a coefficient or a count

Type: scalar

Sections:

c08.s04 · The normal equations

$C$ : the complex numbers (rare; used only where stated)

the complex numbers (rare; used only where stated)

Type: set

Sections:

c24.s03 · Scaling laws

D

$d$ : the number of features (dimension); never a distance

the number of features (dimension); never a distance

Type: count

Sections:

$D$ : the dataset you hold: a finite indexed family of items

the dataset you hold: a finite indexed family of items

Type: set

Sections:

$:=$ : is defined to be

is defined to be

Type: relation

Sections: no section recorded yet

$D e l t a$ : a change in a quantity

a change in a quantity

Type: operator

Sections:

$c d o t$ : the dot product

the dot product

Type: operator

Sections:

c08.s01 · Dot products and angles

E

$E$ : expectation of a random variable

expectation of a random variable

Type: operator

Sections:

c22.s03 · The variational autoencoder

$ell$ : the pointwise loss: the cost of one answer

the pointwise loss: the cost of one answer

Type: function

Sections:

$emptyset$ : the empty set

the empty set

Type: set

Sections: no section recorded yet

$e p s i l o n$ : a small positive constant

a small positive constant

Type: scalar

Sections:

$eta$ : a learning rate

a learning rate

Type: scalar

Sections:

$exists$ : there exists

there exists

Type: logic

Sections:

c03.s01 · Claims with quantifiers

F

$f$ : a function

a function

Type: function

Sections:

$ma t h c a l I$ : Fisher information

Fisher information

Type: matrix

Sections:

c13.s04 · How much can one observation tell you?

$forall$ : for all

for all

Type: logic

Sections:

c03.s01 · Claims with quantifiers

G

$gamma$ : a discount factor between zero and one

a discount factor between zero and one

Type: scalar

Sections:

$nab l a$ : the gradient vector

the gradient vector

Type: vector

Sections:

c10.s04 · Gradients in many dimensions

H

$h$ : a candidate predictor

a candidate predictor

Type: function

Sections:

$H$ : Shannon entropy, in bits when the logarithm is base two

Shannon entropy, in bits when the logarithm is base two

Type: function

Sections:

$H$ : the candidate class, also called the hypothesis class

the candidate class, also called the hypothesis class

Type: set

Sections:

c02.s06 · What learning will mean

I

$i$ : the index over items, from 1 to n

the index over items, from 1 to n

Type: index

Sections: no section recorded yet

$I$ : mutual information between two random variables

mutual information between two random variables

Type: function

Sections:

c16.s03 · Mutual information

$iff$ : the left and right hold together or not at all

the left and right hold together or not at all

Type: logic

Sections: no section recorded yet

$implies$ : if the left holds then the right holds

if the left holds then the right holds

Type: logic

Sections: no section recorded yet

$in$ : is a member of

is a member of

Type: relation

Sections:

c03.s04 · Sets, functions and relations

$1[.]$ : the indicator of an event: one if it holds, zero otherwise

the indicator of an event: one if it holds, zero otherwise

Type: function

Sections: no section recorded yet

K

$k$ : the number of neighbours consulted

the number of neighbours consulted

Type: count

Sections:

$k a pp a$ : a condition number

a condition number

Type: scalar

Sections:

c17.s04 · Convergence under convexity

$D_{K} L$ : Kullback-Leibler divergence from one distribution to another

Kullback-Leibler divergence from one distribution to another

$m$ : a number of examples, rows, or features

a number of examples, rows, or features

Type: count

Sections:

$M$ : the number of distinct labels

the number of distinct labels

Type: count

Sections: no section recorded yet

$f: A -> B$ : a function from domain A to codomain B

a function from domain A to codomain B

Type: function

Sections: no section recorded yet

N

$n$ : the number of items in the table you hold; the number of labelled examples

the number of items in the table you hold; the number of labelled examples

Type: count

Sections:

$N$ : the whole numbers, zero included

the whole numbers, zero included

Type: set

Sections:

$l V er t c d o t r V er t$ : a norm

a norm

Type: function

Sections:

c08.s01 · Dot products and angles

$N (m u, s i g m a^{2})$ : the Gaussian distribution with mean mu and variance sigma squared

the Gaussian distribution with mean mu and variance sigma squared

Type: distribution

Sections: no section recorded yet

$not$ : negation

negation

Type: logic

Sections: no section recorded yet

O

$or$ : disjunction

disjunction

Type: logic

Sections: no section recorded yet

P

$p$ : a probability or a parameter

a probability or a parameter

Type: scalar

Sections:

$P$ : a probability measure

a probability measure

Type: function

Sections:

$p hi$ : a feature map or a parameter

a feature map or a parameter

Type: function

Sections:

c22.s03 · The variational autoencoder

$pi$ : a policy: a rule or distribution over actions

a policy: a rule or distribution over actions

Type: function

Sections:

c23.s06 · Policy gradients

$A^{+}$ : the pseudoinverse

the pseudoinverse

Type: matrix

Sections:

c08.s05 · The pseudoinverse

$o p er a t or nam e p r o j$ : a projection

a projection

Type: function

Sections:

c08.s02 · The shadow of a vector

Q

$q$ : a query vector or a probability

a query vector or a probability

Type: vector

Sections:

$Q$ : an action-value function

an action-value function

Type: function

Sections:

c09.s04 · The spectral theorem

R

$R$ : the real numbers

the real numbers

Type: set

Sections:

c15.s01 · Why training error lies

$Rhat$ : the empirical risk: average loss over the items you hold

the empirical risk: average loss over the items you hold

Type: scalar

Sections:

$rho$ : a distance between two inputs

a distance between two inputs

Type: function

Sections:

c02.s02 · The nearest neighbour

$R$ : the true risk of a predictor on unseen items

the true risk of a predictor on unseen items

Type: scalar

Sections: no section recorded yet

$r$ : a run index

a run index

Type: index

Sections:

c04.s01 · A result and its luck

a standard deviation, or a sigma-algebra where the context says so

Type: scalar

Sections:

$Σ$ : the diagonal matrix of singular values

the diagonal matrix of singular values

Type: matrix

Sections:

c09.s06 · The SVD

$subset$ : is a subset of

is a subset of

Type: relation

Sections:

c03.s04 · Sets, functions and relations

T

$t$ : a step, time, or a parameter index

a step, time, or a parameter index

Type: index

Sections:

$T$ : a transpose, a horizon or a temperature, as labelled at use

a transpose, a horizon or a temperature, as labelled at use

Type: operator

Sections: no section recorded yet

$T_{n}$ : a Taylor polynomial of degree n

a Taylor polynomial of degree n

Type: function

Sections:

c10.s03 · Taylor approximation and curvature

$theta$ : a parameter vector

a parameter vector

Type: vector

Sections:

the input space

Type: set

Sections: no section recorded yet

$x_{i}$ : the feature vector of item i

the feature vector of item i

Type: vector

Sections: no section recorded yet

Y

$y$ : an output or a label

an output or a label

Type: scalar

Sections:

c09.s05 · When is a quadratic form a bowl?

$Y$ : the label set

the label set

Type: set

Sections: no section recorded yet

$yhat$ : the value a predictor returns

the value a predictor returns

Type: scalar

Sections:

$y_{i}$ : the recorded answer for item i

the recorded answer for item i

Type: scalar

Sections: no section recorded yet

Z

$z$ : a score, a latent variable, or a complex number

a score, a latent variable, or a complex number

Type: scalar

Sections:

$Z$ : the integers

the integers

Type: set

Sections: no section recorded yet

A

A: a matrix

|x|: the absolute value of x, or the size of a finite set

alpha: a learning rate or a significance level, as labelled at use

alphaN​: a step-size coefficient at stage N

and: conjunction

B

b: a bias or a vector

B: a matrix, a budget, or a number of runs

beta: a coefficient, a discount factor, or a momentum constant

beta0​: an intercept

beta1​: a slope or a momentum constant

C

c: a coefficient or a count

C: the complex numbers (rare; used only where stated)

D

d: the number of features (dimension); never a distance

D: the dataset you hold: a finite indexed family of items

:=: is defined to be

Delta: a change in a quantity

cdot: the dot product

E

E: expectation of a random variable

ell: the pointwise loss: the cost of one answer

emptyset: the empty set

epsilon: a small positive constant

eta: a learning rate

exists: there exists

F

f: a function

mathcalI: Fisher information

forall: for all

G

gamma: a discount factor between zero and one

nabla: the gradient vector

H

h: a candidate predictor

H: Shannon entropy, in bits when the logarithm is base two

H: the candidate class, also called the hypothesis class

I

i: the index over items, from 1 to n

I: mutual information between two random variables

iff: the left and right hold together or not at all

implies: if the left holds then the right holds

in: is a member of

1[.]: the indicator of an event: one if it holds, zero otherwise

K

k: the number of neighbours consulted

kappa: a condition number

DK​L: Kullback-Leibler divergence from one distribution to another

L

L: a loss, a length, or a Lipschitz constant

lambda: a regularisation strength or an eigenvalue, as labelled at use

log: a logarithm; base two in information contexts, base e in calculus contexts, always stated

M

m: a number of examples, rows, or features

M: the number of distinct labels

f: A -> B: a function from domain A to codomain B

N

n: the number of items in the table you hold; the number of labelled examples

N: the whole numbers, zero included

lVertcdotrVert: a norm

N(mu,sigma2): the Gaussian distribution with mean mu and variance sigma squared

not: negation

O

or: disjunction

P

p: a probability or a parameter

P: a probability measure

phi: a feature map or a parameter

pi: a policy: a rule or distribution over actions

A+: the pseudoinverse

operatornameproj: a projection

Q

q: a query vector or a probability

Q: an action-value function

R

R: the real numbers

Rhat: the empirical risk: average loss over the items you hold

rho: a distance between two inputs

$A$ : a matrix

$|x|$ : the absolute value of x, or the size of a finite set

$alpha$ : a learning rate or a significance level, as labelled at use

$a l p h a_{N}$ : a step-size coefficient at stage N

$and$ : conjunction

$b$ : a bias or a vector

$B$ : a matrix, a budget, or a number of runs

$b e t a$ : a coefficient, a discount factor, or a momentum constant

$b e t a_{0}$ : an intercept

$b e t a_{1}$ : a slope or a momentum constant

$c$ : a coefficient or a count

$C$ : the complex numbers (rare; used only where stated)

$d$ : the number of features (dimension); never a distance

$D$ : the dataset you hold: a finite indexed family of items

$:=$ : is defined to be

$D e l t a$ : a change in a quantity

$c d o t$ : the dot product

$E$ : expectation of a random variable

$ell$ : the pointwise loss: the cost of one answer

$emptyset$ : the empty set

$e p s i l o n$ : a small positive constant

$eta$ : a learning rate

$exists$ : there exists

$f$ : a function

$ma t h c a l I$ : Fisher information

$forall$ : for all

$gamma$ : a discount factor between zero and one

$nab l a$ : the gradient vector

$h$ : a candidate predictor

$H$ : Shannon entropy, in bits when the logarithm is base two

$H$ : the candidate class, also called the hypothesis class

$i$ : the index over items, from 1 to n

$I$ : mutual information between two random variables

$iff$ : the left and right hold together or not at all

$implies$ : if the left holds then the right holds

$in$ : is a member of

$1[.]$ : the indicator of an event: one if it holds, zero otherwise

$k$ : the number of neighbours consulted

$k a pp a$ : a condition number

$D_{K} L$ : Kullback-Leibler divergence from one distribution to another

$L$ : a loss, a length, or a Lipschitz constant

$lambda$ : a regularisation strength or an eigenvalue, as labelled at use

$log$ : a logarithm; base two in information contexts, base e in calculus contexts, always stated

$m$ : a number of examples, rows, or features

$M$ : the number of distinct labels

$f: A -> B$ : a function from domain A to codomain B

$n$ : the number of items in the table you hold; the number of labelled examples

$N$ : the whole numbers, zero included

$l V er t c d o t r V er t$ : a norm

$N (m u, s i g m a^{2})$ : the Gaussian distribution with mean mu and variance sigma squared

$not$ : negation

$or$ : disjunction

$p$ : a probability or a parameter

$P$ : a probability measure

$p hi$ : a feature map or a parameter

$pi$ : a policy: a rule or distribution over actions

$A^{+}$ : the pseudoinverse

$o p er a t or nam e p r o j$ : a projection

$q$ : a query vector or a probability

$Q$ : an action-value function

$R$ : the real numbers

$Rhat$ : the empirical risk: average loss over the items you hold

$rho$ : a distance between two inputs

$R$ : the true risk of a predictor on unseen items

$r$ : a run index

$B$ : the number of independent runs

$s$ : a singular value, a step, or a seed

$S$ : a sum, a set of examples, or a singular value

$o p er a t or nam e se$ : a standard error

$s$ : a random seed: the recorded value that fixes every arbitrary choice in a run

$sigma$ : a standard deviation, or a sigma-algebra where the context says so

$Σ$ : the diagonal matrix of singular values

$subset$ : is a subset of

$t$ : a step, time, or a parameter index

$T$ : a transpose, a horizon or a temperature, as labelled at use

$T_{n}$ : a Taylor polynomial of degree n

$theta$ : a parameter vector

$ha t t h e t a$ : an estimate of a parameter

$U$ : left singular vectors

$ma t hb f v$ : a vector