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Where can I find the proof of the universal approximation theorem?

There are multiple papers on the topic because there have been multiple attempts to prove that neural networks are universal (i.e. they can approximate any continuous function) from slightly different ...
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Yes, UCS is a special case of A*. UCS uses the evaluation function $f(n) = g(n)$, where $g(n)$ is the length of the path from the starting node to $n$, whereas A* uses the evaluation function $f(n) =... • 40.9k 6 votes Is there a rigorous proof that AGI is possible, at least, in theory? Consciousness is not well-understood As an AI practitioner and philosopher, I don't think that humans will be able to create a truly conscious silicon-based AGI. Humans are incapable of creating some ... • 169 6 votes Where can I find the proof of the universal approximation theorem? "Modern" Guarantees for Feed-Forward Neural Networks My answer will complement nbro's above, which gave a very nice overview of universal approximation theorems for different types of ... • 565 6 votes Accepted Is this proof of$\epsilon-greedy policy improvement correct? The weights do sum to one. Note that in the second line where we have $$\frac{\epsilon}{|\mathcal{A}(s)|} \sum_a q_{\pi}(s,a) + (1-\epsilon)\max_aq_{\pi}(s,a) \; ,$$ the sum is over the whole action ... • 4,920 6 votes Why are the Bellman operators contractions? The inequality \begin{align} \left\|T^{\pi} V-T^{\pi} U\right\|_{\infty} & \leq \gamma\|V-U\|_{\infty} \label{1}\tag{1}, \end{align} whereU$and$V$are two value functions, follows from the ... • 40.9k 6 votes Accepted How is this Pytorch expression equivalent to the KL divergence? The code is correct. Since OP asked for a proof, one follows. The usage in the code is straightforward if you observe that the authors are using the symbols unconventionally: ... • 473 6 votes Accepted Why policy improvement theorem can't be applied in case of function approximation? As referenced in Sutton's RL book regarding policy improvement theorem (PIT): The policy improvement theorem applies to the two policies that we considered at the beginning of this section: an ... • 2,277 5 votes Accepted How is inequality 31 derived from equality 30 in lemma 2 of the "Trust Region Policy Optimization" paper? We can start with equation (30): $$\bar{A}(s) = P(a \neq \tilde{a}) \mathbb{E}_{(a,\tilde{a})\sim(\pi,\tilde{\pi}|a\neq\tilde{a})} [A_\pi(s, \tilde{a}) - A_\pi(s, a)]$$ Taking the absolute value ... 5 votes How are the reward functions$R(s)$,$R(s, a)$and$R(s, a, s')$equivalent? Let$R(s)$denote a probability distribution over rewards that our agent may get in some MDP as a reward for entering a state$s$. The easiest case is to demonstrate that we can also choose to write ... • 10.3k 5 votes Is there a rigorous proof for finding Hopfield minima? See the paper On the Convergence Properties of the Hopfield Model (1990), by Jehoshua Bruck. In the first section of the paper, J. Bruck describes the Hopfield network (popularized by J. J. Hopfield ... • 40.9k 5 votes Is the summation of consistent heuristic functions also consistent? No, it will not necessary be consistent or admissible. Consider this example, where$s$is the start,$g$is the goal, and the distance between them is 1. s --1-- g Assume that$h_0$and$h_1$are ... • 371 5 votes Accepted Why there are only three machine learning paradigms: supervised, unsupervised, reinforcement? You can formulate RL and unsupervised learning as "some sort of supervised learning"... in the case of UL you have that the target is an handcrafted task, it being similarity learning, next ... • 2,273 4 votes Accepted How can a neural network approximate all functions when the weights are not allowed to grow exponentially? What is Proven The question references the proof of Approximation by Superpositions of a Sigmoidal Function, G. Cybenko, 1989, Mathematics of Control, Signals, and Systems. The 1989 proof stated that ... • 7,513 4 votes Accepted Can two admissable heuristics not dominate each other? This is possible. Admissibility only asserts that the heuristic will never overestimate the true cost. With that being said, it is possible for one heuristic in some cases to do better than another ... • 1,106 4 votes Are these two forms of the state value function the same? There are a few different, but equivalent, ways to express the relationships between value functions in the Bellman equations. Some differences are just notation, but in the case of the two equations ... • 32.7k 3 votes Why doesn't Q-learning converge when using function approximation? There are three problems Limited capacity Neural Network (explained by John) Non-stationary Target Non-stationary distribution Non-stationary Target In tabular Q-learning, when we update a Q-value, ... • 131 3 votes Understanding why the expectation is over the new policy$\pi'$in the proof of the Policy Improvement Theorem The expectation is over the policy$\pi'$because the action at the state$S_t = s$is taken according to$\pi'$, and, for the proof, the book text (2nd edition, paragraph below Equation 4.8) defines$...

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