Given that NeSS achieves impressive results on synthetic natural language benchmarks in our evaluation, one question is whether it could also improve the performance on commonly used natural language datasets, e.g., large-scale machine translation benchmarks. However, note that most existing natural language benchmarks are not designed for evaluating the compositional generalization performance of models. Instead, the main challenge of those datasets is to handle the inherently ambiguous and potentially noisy natural language inputs. Specifically, their training and test sets are usually from the same distribution, and thus do not evaluate compositional generalization. As a result, we did not run experiments on these datasets.

We thank all reviewers for constructive comments. We added an ablation study on the SCAN length split to demonstrate its importance. For example, in the test set, there is a new pattern "jump around right thrice" that does not appear in the training set. Recursion and sequence manipulation supported by NeSS are critical to learn such parsing rules to generalize. NeSS is 100% in 2 runs, and 62.5% in 3 runs. When the model predicts the alternative translation, the exact match accuracy becomes lower.

The discovery of neural architectures from simple building blocks is a long-standing goal of Neural Architecture Search (NAS). Hierarchical search spaces are a promising step towards this goal but lack a unifying search space design framework and typically only search over some limited aspect of architectures. In this work, we introduce a unifying search space design framework based on context-free grammars that can naturally and compactly generate expressive hierarchical search spaces that are 100s of orders of magnitude larger than common spaces from the literature. By enhancing and using their properties, we effectively enable search over the complete architecture and can foster regularity. Further, we propose an efficient hierarchical kernel design for a Bayesian Optimization search strategy to efficiently search over such huge spaces. We demonstrate the versatility of our search space design framework and show that our search strategy can be superior to existing NAS approaches.

We thank all reviewers for constructive comments. We added an ablation study on the SCAN length split to demonstrate its importance. For example, in the test set, there is a new pattern "jump around right thrice" that does not appear in the training set. Recursion and sequence manipulation supported by NeSS are critical to learn such parsing rules to generalize. NeSS is 100% in 2 runs, and 62.5% in 3 runs. When the model predicts the alternative translation, the exact match accuracy becomes lower.

We introduce Reasoning Core, a new scalable environment for Reinforcement Learning with Verifiable Rewards (RLVR), designed to advance foundational symbolic reasoning in Large Language Models (LLMs). Unlike existing benchmarks that focus on games or isolated puzzles, Reasoning Core procedurally generates problems across core formal domains, including PDDL planning, first-order logic, context-free grammar parsing, causal reasoning, and system equation solving. The environment is built on key design principles of high-generality problem distributions, verification via external tools, and continuous difficulty control, which together provide a virtually infinite supply of novel training instances. Initial zero-shot evaluations with frontier LLMs confirm the difficulty of Reasoning Core's tasks, positioning it as a promising resource to improve the reasoning capabilities of future models.

Constrained decoding enables Language Models (LMs) to produce samples that provably satisfy hard constraints. However, existing constrained-decoding approaches often distort the underlying model distribution, a limitation that is especially problematic in applications like program fuzzing, where one wants to generate diverse and valid program inputs for testing purposes. We propose a new constrained sampling framework based on Markov Chain Monte Carlo (MCMC) that simultaneously satisfies three core desiderata: constraint satisfying (every sample satisfies the constraint), monotonically converging (the sampling process converges to the true conditional distribution), and efficient (high-quality samples emerge in few steps). Our method constructs a proposal distribution over valid outputs and applies a Metropolis-Hastings acceptance criterion based on the LM's likelihood, ensuring principled and efficient exploration of the constrained space. Empirically, our sampler outperforms existing methods on both synthetic benchmarks and real-world program fuzzing tasks.

Large language models (LLMs) are increasingly expected to perform tasks based only on a specification of the task provided in context, without examples of inputs and outputs; this ability is referred to as instruction following. We introduce the Recognition of Languages In-Context (RELIC) framework to evaluate instruction following using language recognition: the task of determining if a string is generated by formal grammar. Unlike many standard evaluations of LLMs' ability to use their context, this task requires composing together a large number of instructions (grammar productions) retrieved from the context. Because the languages are synthetic, the task can be increased in complexity as LLMs' skills improve, and new instances can be automatically generated, mitigating data contamination. We evaluate state-of-the-art LLMs on RELIC and find that their accuracy can be reliably predicted from the complexity of the grammar and the individual example strings, and that even the most advanced LLMs currently available show near-chance performance on more complex grammars and samples, in line with theoretical expectations. We also use RELIC to diagnose how LLMs attempt to solve increasingly difficult reasoning tasks, finding that as the complexity of the language recognition task increases, models switch to relying on shallow heuristics instead of following complex instructions.

Large Language Models (LLMs) have shown remarkable capabilities, yet ensuring their outputs conform to strict structural or grammatical constraints remains challenging, which is critical in function calls and domain-specific language (DSL) generation. Constrained decoding with context-free grammar is a flexible approach to guarantee LLMs' adherence to a specific format by dynamically building a token logits mask. However, creating this mask requires checking the validity of all tokens in the LLM vocabulary at every decoding step, which often incurs significant overheads in existing constrained decoding engines. To address this challenge, we propose $\textbf{ZapFormat}$, a novel $\textbf{dynamic pruning}$ strategy based on the Earley algorithm that identifies and eliminates invalid or redundant Earley states in real-time, significantly reducing memory occupation of the Earley algorithm's states. This further enables us to use a state cache to speed up structured generations on a large number of queries. We implemented ZapFormat in a new constrained decoding engine called Formatron which also incorporates existing optimizations. Through comprehensive experiments on structured generation tasks, including JSON generation, JSON Schema validation, and semantic parsing, we demonstrate that Formatron not only $\textbf{consistently maintains}$ high-precision compliant outputs but also achieves $\textbf{significant improvements}$ in inference speed up to 2x compared to state-of-the-art implementations. More importantly, Formatron is generally applicable across various LLM architectures. We release Formatron as open source at https://github.com/Dan-wanna-M/formatron.