Large language models (LLMs) have shown promising performance across diverse domains. Many practical applications of LLMs, such as code completion and structured data extraction, require adherence to syntactic constraints specified by a formal language. Yet, due to their probabilistic nature, LLM output is not guaranteed to adhere to such formal languages. Prior work has proposed constrained decoding as a means to restrict LLM generation to particular formal languages. However, existing works are not applicable to the emerging paradigm of diffusion LLMs, when used in practical scenarios such as the generation of formally correct C++ or JSON output. In this paper we address this challenge and present the first constrained decoding method for diffusion models, one that can handle formal languages captured by context-free grammars. We begin by reducing constrained decoding to the more general additive infilling problem, which asks whether a partial output can be completed to a valid word in the target language. This problem also naturally subsumes the previously unaddressed multi-region infilling constrained decoding. We then reduce this problem to the task of deciding whether the intersection of the target language and a regular language is empty and present an efficient algorithm to solve it for context-free languages. Empirical results on various applications, such as C++ code infilling and structured data extraction in JSON, demonstrate that our method achieves near-perfect syntactic correctness while consistently preserving or improving functional correctness. Importantly, our efficiency optimizations ensure that the computational overhead remains practical.

These observations suggest the existence of a tradeoff between average robustness and robust fairness. We use var and rob.acc to denote the variance of class-wise robust accuracy, and average robust accuracy, respectively. We use var and rob.acc to denote the variance of class-wise robust accuracy, and average robust accuracy, respectively. B.1 Naturally Trained Linear model We use var and rob.acc to denote the variance of class-wise robust accuracy, and average robust accuracy, respectively. For any classifier f ( x) in Equation ( 2), we first calculate its natural risk.

Large language models lie at the center of recent advances in artificial intelligence.

Figure 5: ViTs trained only on our patch-based transformations exhibit stronger texture bias. Each bar is the texture accuracy ( %) on Conflict Stimuli (Geirhos et al., 2018), and a higher texture accuracy indicates the model has a higher bias towards texture. The "texture accuracy" is defined as the percentage of images that are classified as the "texture" label, provided the image is classified as either "texture" or "shape" label. The baseline model is ViT -B/16 in (Dosovitskiy et al., 2021) trained on original images. Other models are trained on patch-based transformed images, e.g., "P-Shuffle" stands for a ViT -B/16 model trained on patch-based shuffled images.