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PyTorch Lightning is an open-source Python library that provides a high-level interface for PyTorch, a popular deep learning framework. [1] It is a lightweight and high-performance framework that organizes PyTorch code to decouple research from engineering, thus making deep learning experiments easier to read and reproduce.
Dominating set, a.k.a. domination number [3]: GT2 NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7
Differential dynamic programming (DDP) is an optimal control algorithm of the trajectory optimization class. The algorithm was introduced in 1966 by Mayne [1] and subsequently analysed in Jacobson and Mayne's eponymous book. [2] The algorithm uses locally-quadratic models of the dynamics and cost functions, and displays quadratic convergence ...
In September 2022, Meta announced that PyTorch would be governed by the independent PyTorch Foundation, a newly created subsidiary of the Linux Foundation. [ 24 ] PyTorch 2.0 was released on 15 March 2023, introducing TorchDynamo , a Python-level compiler that makes code run up to 2x faster, along with significant improvements in training and ...
The torch package also simplifies object-oriented programming and serialization by providing various convenience functions which are used throughout its packages. The torch.class(classname, parentclass) function can be used to create object factories ().
Another related problem is the bottleneck travelling salesman problem: Find a Hamiltonian cycle in a weighted graph with the minimal weight of the weightiest edge. A real-world example is avoiding narrow streets with big buses. [15] The problem is of considerable practical importance, apart from evident transportation and logistics areas.
NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. [2] [Note 1]
A simple example of an NP-hard problem is the subset sum problem. Informally, if H is NP-hard, then it is at least as difficult to solve as the problems in NP . However, the opposite direction is not true: some problems are undecidable , and therefore even more difficult to solve than all problems in NP, but they are probably not NP-hard ...