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It includes the Zero Redundancy Optimizer (ZeRO) for training models with 1 trillion or more parameters. [4] Features include mixed precision training, single-GPU, multi-GPU, and multi-node training as well as custom model parallelism. The DeepSpeed source code is licensed under MIT License and available on GitHub. [5]
Messages are always transmitted with FEC parity data (and error-detection redundancy). A receiver decodes a message using the parity information and requests retransmission using ARQ only if the parity data was not sufficient for successful decoding (identified through a failed integrity check).
[4] [5] The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors. Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth.
The simple checksums described above fail to detect some common errors which affect many bits at once, such as changing the order of data words, or inserting or deleting words with all bits set to zero.
In engineering and systems theory, redundancy is the intentional duplication of critical components or functions of a system with the goal of increasing reliability of the system, usually in the form of a backup or fail-safe, or to improve actual system performance, such as in the case of GNSS receivers, or multi-threaded computer processing.
"Don't repeat yourself" (DRY), also known as "duplication is evil", is a principle of software development aimed at reducing repetition of information which is likely to change, replacing it with abstractions that are less likely to change, or using data normalization which avoids redundancy in the first place.
Note that, while this procedure perfectly corrects the output when zero or one flips are introduced by the channel, if more than one qubit is flipped then the output is not properly corrected. For example, if the first and second qubits are flipped, then the syndrome measurement gives the outcome P 3 {\displaystyle P_{3}} , and the third qubit ...
These two variations serve the purpose of detecting zero bits added to the message. A preceding zero bit adds a leading zero coefficient to (), which does not change its value, and thus does not change its divisibility by the generator polynomial. By adding a fixed pattern to the first bits of a message, such extra zero bits can be detected.