Notations used in the paper.
∝	proportional to
$x\sim p(·)$	$x\sim p\left(x\right)$
${\left|\right|x\left|\right|}_2$	Euclidian norm of x
t	timestep
$Const$	arbitrary constant
A	set of possible actions
S	set of possible states
$a\in A$	action
$s\in S$	state
$s_0\in S$	first state of a trajectory
$s_f\in S$	final state of a trajectory
$s^{\prime }\in S$	state following a tuple $(s,a)$
h	history of interactions $(s_0,a_0,s_1,\cdots )$
$\widehat{s}$	predicted states
$g\in G$	goal
$s_g\in S$	state used as a goal
$S_b$	set of states contained in b
$\tau \in \mathcal{T}$	trajectory
$u\left(\tau \right)$	function that extracts parts of the trajectory $\tau$
$R(s,a,s^{\prime })$	reward function
$d_t^{\pi }\left(s\right)$	t-steps state distribution
$d_{0:T}^{\pi }\left(S\right)$	stationary state-visitation distribution of $\pi$ over a horizon T
	$\frac{1}{T}{\sum }_{t=1}^T{d}_t^{\pi }\left(S\right))$
f	representation function
z	compressed latent variable, $z=f\left(s\right)$
$\rho \in \mathrm{P}$	density model
$\varphi \in \mathsf{\Phi }$	forward model
${\varphi }_T\in {\mathsf{\Phi }}_T$	true forward model
$q_{\omega }$	parameterized discriminator
$\pi$	policy
${\pi }^g$	policy conditioned on a goal g
$n{n}_k(S,s^{\prime })$	k-th closest state to $s^{\prime }$ in S
$D_{KL}\left(p\left(x\right)\right||p^{\prime }\left(x\right))$	Kullback–Leibler divergence
	${\mathbb{E}}_{x\sim p(·)}log\frac{p\left(x\right)}{p^{\prime }\left(x\right)}$
$H\left(X\right)$	$-{\int }_{X}p\left(x\right)logp\left(x\right)$
$H\left(X\right|S)$	$-{\int }_{S}p\left(s\right){\int }_{X}p\left(x\right|s)logp\left(x\right|s)dxds$
$I(X;Y)$	$H\left(X\right)-H\left(X\right|Y)$
$I(X;Y|S)$	$H\left(X\right|S)-H(X|Y,S)$
$IG(h,A,S^{\prime },S,\mathsf{\Phi })$	Information gain
	$I(S^{\prime };\mathsf{\Phi }|h,A,S)$