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ReLU is non-linear by definition In calculus and related areas, a linear function is a function whose graph is a straight line, that is a polynomial function of degree one or zero. Since the graph of the ReLU function $f(x) = \max(0,x)$ is not a straight line (equivalently, it cannot be expressed in the form $f(x) = mx + c$), by definition it is not ...

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I found someone that has done this thing! You can hear a good explanation in Marcus Hutter's answer to this question about rewards given to AIXI. He describes a work that seems to be referring to this paper: Universal Knowledge-Seeking Agents for Stochastic Environments I'll edit this answer later with a full explanation of the approach, but essentially ...

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The usage of the word "kernel" in the context of support vector machines probably comes from its usage in the context of integral transforms. See the article Kernel of an integral operator, and the questions What is the difference between a kernel and a function? and Why is the kernel of an integral transform called kernel?. The word "kernel" has been ...

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In short, the Jacobian matrix is a generalization of the gradient for vector-valued functions. Recall that the gradient is a vector of partial derivatives of a multi-variable function. So, consider a multi-variable function of the form $f: \mathcal{X}_1 \times \mathcal{X}_2 \times \dots \times \mathcal{X}_N \rightarrow \mathcal{Y}$. The output of this ...

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In the, presumably final, printed version the last two equal signs are approximations. This is just because over a large amount of weight updates where you have been sampling the expectation will be approximated by Monte Carlo.

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I will try to answer the question in a lesser mathematical (and hopefully correct way). NOTE: I have used $V_{\pi}$ and $v_{\pi}$ interchangeably. We start from LHS: $$\max_s \Bigl\lvert \mathbb{E}_{\pi} \left[ G_{t:t+n} \mid S_t = s \right] - v_{\pi}(s) \Bigr\rvert$$ This can be written in terms of trajectories. Say the probability of observing a $n$ ...

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