feat: support Beam search ("Best of") setting

[walking-octopus]

• I have searched the existing issues

Is your feature request related to a problem? Please describe it

Beam search is a known technique used to enhance LLM inference, especially in tasks requiring reasoning, at a great cost to performance. ChatGPT has been suspected of using it.

Describe the solution

llama.cpp does support it. All that would be needed is to add somewhere in inference config.

Teachability, documentation, adoption, migration strategy

No response

What is the motivation / use case for changing the behavior?

Example: mathematical problems. Global probability maximization allows the model to catch and prune erroneous paths, since eventually they lead to less probable chains of thought than their incorrect counterparts.

[dan-menlo]

@walking-octopus I am merging this into #3508 (Jan) and menloresearch/cortex.cpp#1151 (Cortex.cpp)

• If Beam is supported in main branch of llama.cpp, we will support
• See epic: llama.cpp params are settable via API call or model.yaml cortex.cpp#1151 (comment)