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

Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic manipulation, and commonsense reasoning with increasing size of models. However, it is still unclear what the underlying capabilities of these LMs are. Surprisingly, we find that these models have limitations on certain basic symbolic manipulation tasks such as copy, reverse, and addition. When the total number of symbols or repeating symbols increases, the model performance drops quickly. We investigate the potential causes behind this phenomenon and examine a set of possible methods, including explicit positional markers, fine-grained computation steps, and LMs with callable programs. Experimental results show that none of these techniques can solve the simplest addition induction problem completely. In the end, we introduce LMs with tutor, which demonstrates every single step of teaching. LMs with tutor is able to deliver 100% accuracy in situations of OOD and repeating symbols, shedding new insights on the boundary of large LMs in induction.

In short, much of our understanding of the world is given by nature, with learning as a matter of fleshing out the details. There is an alternate, empiricist view which inverts this: symbolic manipulation is a rarity in nature, primarily arising as a learned capacity for communicating acquired gradually by our hominin ancestors over the last two million years. On this view, the primary cognitive capacities are non-symbolic learning abilities bound up with improving survival, such as rapidly recognizing prey, predicting their likely actions, and developing skillful responses. This assumes that the vast majority of complex cognitive abilities are acquired through a general, self-supervised learning capacity, one that acquires an intuitive world-model capable of the central features of common sense through experience. It also assumes that most of our complex cognitive capacities do not turn on symbolic manipulation; they make do, instead, with simulating various scenarios and predicting the best outcomes.