Author: Sharath Paper Link Overview Curriculum learning is inspired by the way human learns, where the examples are shown in the increasing order of the difficulty. More sepcifically te network is exposed to the easier examples in the early stages of training and then gradually to the tougher ones. This paper studies the benifits of showing this sequential ordered eamples to the network and comments about when it works and when it doesn't. Contributions: This paper introduces a phenomenon called implicit curricula. One of the claims they make is that the the ordered learning (curriculum, anti-curriculum and random) almost performs same in the standard settings. Curricula is benificial when there is a limited time budget and in noisy regime
7/4/2021Author: Sharath Overview This paper discusses how the BNNs behave as we scale to the large models. This paper discusses the "soap-bubble" issue in case of high dimensional probability spaces and how MFVI suffers from this. As a way to tackle this issue, the authors propose a new variational posterior approximation in hyperspherical coordinate system and show that this overcomes the soap-bubble issue when we sample from this posterior. The geometry of high dimensional spaces One of the properties of high dimensional spaces is that there is much more volume outside any given neighbourhood than inside of it. Betacount et al explained this behaviour visually with two intuitive examples. For first example let us consider partitioning our parameter space in equal rectangular intervals as shown below. We can see that as we increase the dimensions the distribution of volume around the center decreases. This becomes almost negligible as compared to the its neighbourhood in high dimensional cases where $D$ is very large. We can observe a similar behaviour if we consider spherical view of parameter space, where the exterior volume grows even larger than the interior in high dimensional spaces as shown in the figure. . How this intuition of volumes in high dimensions explain soap bubble phenomenon?
7/4/2021Author: Sharath What is a convex function? Let's try to define a convex function formally and geometrically. Formally, a function $f$ is said to be a convex function if the domain of $f$ is a convex set and if it satisfies the following $\forall x \ \text{and} \ y \in \text{dom} f$; \begin{equation} f(\theta x + (1 - \theta)y) \leq \theta f(x) + (1 - \theta)f(y) \end{equation} Geometrically it means that the value of a function at the convex combination of two points of the function always lies below the convex combination of the values at the corresponding points. It means that if we draw a line at any two points $(x, y) \in \text{dom} f$, then this line/chord always lies above the function $f$.
7/4/2021Author: Sharath What is a dynamical system? It is any system that evolves and changes through time governed by a set of rules. Using dynamical systems we can study the long term behavior of an evolving system. Formally, it is a triplet $(X, T, \phi)$ where $X$ denotes the state space, $T$ denotes the time space and $\phi: X \times T \rightarrow X$ is the flow (this is the rule that governs the evolution). There are few properties of flow: $\phi(X, 0) = X$ Principle of compositionality: $\phi(\phi(x, t), s) = \phi(x, t+s)$
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