Our gifting experts are obsessively searching for holiday gifts that are unique, thoughtful and suitable for any budget. Apple's first touchscreen MacBook is days away - with another OLED surprise Apple reportedly set a date to unveil its new touchscreen MacBooks. Here's what else we expect. Kyle Kucharski is a Brooklyn-based writer and Senior Editor at ZDNET. Apple appears to be announcing its touchscreen OLED MacBooks on Oct. 28.

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Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check whether a formal proof is correct or not almost instantaneously, but generating a completely correct formal proof with large language models (LLMs) remains a formidable task. The usual approach in the literature is to prompt the LLM many times (up to several thousands) until one of the generated proofs passes the verification system.

GPT-5.4 mini brings some of the smarts of OpenAI's latest model to ChatGPT Free and Go users The new model offers performance improvements in reasoning, multimodal understanding and more. The ChatGPT icon, as seen on iPhone 12 running iOS. When OpenAI released GPT-5.4 at the start of March, the company said the new model was designed primarily for professional work like programming and data analysis. Now OpenAI is launching GPT-5.4 mini and nano, and while it is once again highlighting the usefulness of these new systems for tasks like coding, one of the new models is available to Free and Go users . What's more, that model, GPT-5.4 mini, even offers performance that approaches GPT-5.4 in a handful of areas.

Both the discounted and total reward episodic settings are amenable to function approximation.

As a valuable by-product, the regret analysis used in this paper can improve several existing results by a factor ofO(logK).

Many important datasets contain samples that are missing one or more feature values. Maintaining the interpretability of machine learning models in the presence of such missing data is challenging. Singly or multiply imputing missing values complicates the model's mapping from features to labels. On the other hand, reasoning on indicator variables that represent missingness introduces a potentially largenumber ofadditional terms, sacrificing sparsity.