I don’t believe it’s accurate what you claim.

The training of LLMs I believe has a well defined loss function with a measurable value on a specific input set. I actually already discussed this problem extensively with GPT-4 itself so I’ll leave you with parts of that discussion:

> Me: Do LLMs have a well defined loss function that they optimize over?

> GPT-4 Assistant: Yes, large language models (LLMs) have a well-defined loss function that they optimize over during the training process. The choice of loss function depends on the specific task the model is designed for and the architecture used. For LLMs like GPT-3, which are based on the transformer architecture and designed for natural language processing tasks, the most commonly used loss function is the cross-entropy loss.

> Cross-entropy loss measures the difference between the model's predicted probability distribution over the possible output tokens (words, subwords, or characters, depending on the tokenization used) and the true probability distribution, which assigns a probability of 1 to the correct output token and 0 to all other tokens. The goal of the training process is to minimize the cross-entropy loss, which essentially means making the model's predicted probabilities as close as possible to the true probabilities.

> During training, the LLM processes input sequences (e.g., sentences or paragraphs) and generates output token probabilities based on its current weights. The cross-entropy loss is computed using these probabilities and the true target tokens, and then the gradients of the loss with respect to the model's weights are calculated using backpropagation. The weights are updated using an optimization algorithm, such as stochastic gradient descent (SGD) or one of its variants like Adam or Adagrad, in order to minimize the loss.

> The process of iteratively updating the model's weights to minimize the loss function is what allows LLMs to learn patterns and structure in the training data, ultimately enabling them to generate coherent text, answer questions, or perform other language-related tasks.

> Me: Is it possible to restrict the training with a rules that says only these weights, say specific slices, are allowed to change, keep all other weights fixed? Is this how LLMs can be trained in a distributed fashion?

> GPT-4 Assistant: Yes, it is possible to restrict the training of an LLM to specific slices or subsets of weights while keeping other weights fixed. This is a common approach used in distributed and parallel training scenarios, where multiple devices or nodes work on different parts of the model simultaneously. This approach is known as model parallelism.

> In model parallelism, the model's weights are divided into smaller subsets or partitions, with each partition being assigned to a different device or node. During training, each device works only on updating the weights in its assigned partition while keeping the weights in the other partitions fixed. The gradients are computed for each partition separately, and the updates are performed locally on each device.

> Once all devices complete their local updates, they communicate their updated weights with one another to synchronize the model's state. This communication can be done through various methods, such as parameter server architecture or all-reduce algorithms. The key to effective model parallelism is balancing the computational workload among the devices while minimizing the communication overhead.

> Adapting this concept for the proposed proof of work and LLM training combination could involve assigning different subsets of weights to miners and having them work on updating these subsets. This would essentially turn the mining process into a form of distributed LLM training, with each miner contributing to a portion of the model's weights. However, coordinating and synchronizing the updates among miners in a decentralized environment, while maintaining the integrity and security of the blockchain, would be a significant challenge that needs to be addressed in the design.