Existing parameter-efficient fine-tuning (PEFT) methods for large language models (LLMs), such as LoRA and PiSSA, constrain model updates to low-rank subspaces, limiting their expressiveness and leading to suboptimal performance on complex tasks. To address this, we introduce **H**igh-rank **D**istributed **PiSSA (HD-PiSSA)**, a distributed PEFT approach that initializes **orthogonal adapters** across different devices and aggregates their delta updates collectively on (W) for fine-tuning. Unlike Data Parallel LoRA or PiSSA, which maintain identical adapters across all devices, HD-PiSSA assigns different principal components of the pre-trained weights to each GPU, significantly expanding the range of update directions. This results in over 16× higher effective updated ranks than data-parallel LoRA or PiSSA when fine-tuning on 8 GPUs with the same per-device adapter rank. Empirically, HD-PiSSA benefits from this extra optimization flexibility and outperforms both LoRA and PiSSA across a variety of challenging downstream tasks, including mathematics, code, and multi-task learning.

Accurate representation of procedures in restricted scenarios, such as non-standardized scientific experiments, requires precise depiction of constraints. Unfortunately, Domain-specific Language (DSL), as an effective tool to express constraints structurally, often requires case-by-case hand-crafting, necessitating customized, labor-intensive efforts. To overcome this challenge, we introduce the AutoDSL framework to automate DSL-based constraint design across various domains. Utilizing domain specified experimental protocol corpora, AutoDSL optimizes syntactic constraints and abstracts semantic constraints. Quantitative and qualitative analyses of the DSLs designed by AutoDSL across five distinct domains highlight its potential as an auxiliary module for language models, aiming to improve procedural planning and execution.