arXiv:2602.18449v1 Announce Type: cross Abstract: We propose a diffusion-based framework for prompt optimization that leverages Diffusion Language Models (DLMs) to iteratively refine system prompts through masked denoising. By conditioning on interaction traces, including user queries, model responses, and optional feedback, our method enables flexible, span-level prompt updates without requiring gradient access or modifying the downstream language model. Across diverse benchmarks (e.g., $\tau$-bench, SST-2, SST-5), DLM-optimized prompts consistently improve the performance of a frozen target LLM (e.g., GPT-4o-mini). We further show that moderate diffusion step counts provide the best balance between refinement quality and stability. These results highlight diffusion-based prompt optimization as a general, model-agnostic, and scalable approach for enhancing LLM performance through iterative prompt refinement.

arXiv:2512.07805v4 Announce Type: replace-cross Abstract: We present GRAPE (Group Representational Position Encoding), a unified framework for positional encoding based on group actions. GRAPE unifies two families of mechanisms: (i) multiplicative rotations (Multiplicative GRAPE) in $\operatorname{SO}(d)$ and (ii) additive logit biases (Additive GRAPE) arising from unipotent actions in the general linear group $\mathrm{GL}$. In Multiplicative GRAPE, a position $n \in \mathbb{Z}$ (or $t \in \mathbb{R}$) acts as $\mathbf{G}(n) = \exp(n \, \omega \, \mathbf{L})$ with a rank-2 skew-symmetric generator $\mathbf{L} \in \mathbb{R}^{d \times d}$, yielding a relative, compositional, norm-preserving map with a closed-form matrix exponential. RoPE is recovered exactly when the $d/2$ planes correspond to canonical coordinate pairs with a log-uniform spectrum. Learned commuting subspaces and compact non-commuting mixtures strictly extend this geometry to capture cross-subspace feature coupling at $O(d)$ and $O(r d)$ cost per head, respectively. In Additive GRAPE, additive logits arise from rank-1 (or low-rank) unipotent actions, recovering ALiBi and the Forgetting Transformer (FoX) as exact special cases while preserving an exact relative law and streaming cacheability. Overall, GRAPE provides a principled design space for positional geometry in long-context models, subsuming RoPE and ALiBi as special cases. Project page: https://github.com/model-architectures/GRAPE.

arXiv:2601.04205v2 Announce Type: replace-cross Abstract: Diffusion Language Models (DLMs) enable parallel decoding via iterative denoising, where remasking strategies play a critical role in balancing inference speed and output quality. Existing methods predominantly rely on static confidence thresholds, overlooking the spatial-temporal dynamics of token confidence, causing unnecessary remasking. We propose Spatial-Temporal Token-Dynamics-Aware Responsive Remasking (STaRR), a training-free framework that dynamically adapts remasking decisions based on token confidence evolution. STaRR introduces two metrics, temporal variance and spatial deviance, to guide fine-grained, step-wise dynamic thresholding. We further introduce a step-wise dynamic thresholding strategy, further enhanced with responsiveness optimizations for scalability and robustness. Experiments show that STaRR achieves an average speedup of 4.1 and up to 8.9 while maintaining comparable accuracy.