Machine-Perception

Recurrent Neural Networks allows us to model arbitrarily long sequence dependencies, at least in theory. This is very handy, and has many interesting theoretical implication. But here we are also interested in the practical applicability, so we may need to analyze common architectures used to implement these models, the main limitation and drawbacks, the nice properties and some applications. These network can bee seen as chaotic systems (non-linear dynamical systems), see Introduction to Chaos Theory. ...

Backpropagation is perhaps the most important algorithm of the 21st century. It is used everywhere in machine learning and is also connected to computing marginal distributions. This is why all machine learning scientists and data scientists should understand this algorithm very well. An important observation is that this algorithm is linear: the time complexity is the same as the forward pass. Derivatives are unexpectedly cheap to calculate. This took a lot of time to discover. See colah’s blog. Karpathy has a nice resource for this topic too! ...

The perceptron is a fundamental binary linear classifier introduced by (Rosenblatt 1958). It maps an input vector $\mathbf{x} \in \mathbb{R}^n$ to an output $y \in \{0,1\}$ using a weighted sum followed by a threshold function. The Mathematical Definition Given an input vector $\mathbf{x} = (x_1, x_2, \dots, x_n)$ and a weight vector $\mathbf{w} = (w_1, w_2, \dots, w_n)$, the perceptron computes: $$ z = \mathbf{w}^\top \mathbf{x} + b = \sum_{i=1}^{n} w_i x_i + b $$where $b$ is the bias term. The output is determined by the Heaviside step function: ...