PCWorld reports that Microsoft is enhancing Copilot with new user controls, including read-only options and the ability to lock the AI assistant to specific document sections. Microsoft is expanding Copilot's prompt box with contextually aware suggestions for Word and PowerPoint, while unifying commercial and consumer versions under single leadership. These updates aim to make AI assistance more helpful and less overwhelming for productivity tasks, with features currently being tested internally before reaching consumers. Google made headlines a short time ago for a plan to expand its Gemini prompt box as it combines AI and search. Microsoft is taking a different tack: it's also dynamically expanding its prompt box, but with an eye towards improving its productivity apps instead. Right now, Microsoft's efforts are traversing the outer reaches of its productivity solar system, being tested internally with a few targeted corporate partners, Fast Company reports .

First, as R4 suggested, "symbolic35 tree" was more approachable for people in the ML community. Second, the symbolic tree is declared by the user using36 decorators and serves to represent high-level program constructs, which is different from the AST that represents all37 the syntactic structures for the program. For example, the full Python AST contains information about objects' class38 methods, whereas our symbolic representation does not.39 R4: "Second, most of their tool/language design could be summarized as adding some kind of non determinis-40 tic/parametric choice ... It's extension to ML does not introduce anything particularly new ..."41 We agree with R4 that symbolic programming and non-deterministic programming are well-studied topics in the PL42 community. However, we would like to emphasize that this work is the first to introduce such concepts to AutoML43 to significantly reduce engineering effort, which is a novel and useful contribution. For example, PyGlove leverages44 symbolic manipulation to decouple the search algorithm, search space and child program, which enabled us to unify45 the interface among search methods with and without weight sharing. To enable symbolic programming in Python,46 PyGlove implements an object model for maintaining the consistency of program state during symbolic manipulation.47 R4 "Provide the grammar in the main text"48 We understand the "grammar" here as a reference to the formal definition of the search space specification. We will49 revise current Appendix Table 3 into a formal definition, and add it to the "search space" sub-section.50

We thank the reviewers for their encouraging and constructive comments. We are pleased that they find the paper well1 written and acknowledge the novelty and originality of the proposed task, which "has a potential to spark interest"2 (R1) and "may lead to future papers studying it" (R2). Regarding the proposed framework, R1 and R2 not only find it3 "sound" and "novel" but also stress the "re-implementation ease" from which "practitioners may benefit" (R1). Still,4 the reviewers raise points of improvement (R1, R3) and suggest a discussion about a related task (R2). We carefully5 address these comments below.

We sincerely appreciate the reviewers for their careful reading, constructive questions and suggestions. We would very1 much like further exchanges to improve our work, but the following is our best effort within the current limits.2 First, we address questions appeared at least twice. We write P1, P2 for paragraph reference, and Rx for reviewers.3 We discuss two main motivations here: lack of graph loss, and empirical failure4 of distinguishing power.

Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study largescale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NATURALPROVER,a language model that generates proofs by conditioning on background references (e.g.