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Low-income households (LIH), exposed to the uncertain modern grid, bear greater energy burdens and face inequitable access to reliable power compared to high-income households (HIH). This paper proposes a two-stage stochastic community-based microgrid planning (CMP) framework to boost energy justice within the system. To reduce the negative impact of income levels, a weighted energy cost model for households within the microgrid (MG) is designed. To address the multisource uncertainty during the operation period, a two-stage stochastic framework is developed. Moreover, to assess the proposed method, the unbalanced IEEE 123 node system is employed and modified as an isolated MG. The analysis reveals the proposed model can achieve a risk-averse solution while economic optimality is guaranteed. Additionally, the designed weighted method improves the LIH’s impact rate to 67.95% and decreases the total planning cost by 22.43%. 

Offline preference alignment for language models such as Direct Preference Optimization (DPO) is favored for its effectiveness and simplicity, eliminating the need for costly reinforcement learning. Various offline algorithms have been developed for different data settings, yet they lack a unified understanding. In this study, we introduce Pior-Informed Preference Alignment (PIPA), a unified, RL-free probabilistic framework that formulates language model preference alignment as a Maximum Likelihood Estimation (MLE) problem with prior constraints. This method effectively accommodates both paired and unpaired data, as well as answer and step-level annotations. We illustrate that DPO and KTO are special cases with different prior constraints within our framework. By integrating different types of prior information, we developed two variations of PIPA: PIPA-M and PIPA-N. Both algorithms demonstrate a 3∼10% performance enhancement on the GSM8K and MATH benchmarks across all configurations, achieving these gains without additional training or computational costs compared to existing algorithms. 

Low-income households (LIH), exposed to the uncertain modern grid, bear greater energy burdens and face inequitable access to reliable power compared to high-income households (HIH). This paper proposes a two-stage stochastic community-based microgrid planning (CMP) framework to boost energy justice within the system. To reduce the negative impact of income levels, a weighted energy cost model for households within the microgrid (MG) is designed. To address the multisource uncertainty during the operation period, a two-stage stochastic framework is developed. Moreover, to assess the proposed method, the unbalanced IEEE 123 node system is employed and modified as an isolated MG. The analysis reveals the proposed model can achieve a risk-averse solution while economic optimality is guaranteed. Additionally, the designed weighted method improves the LIH’s impact rate to 67.95% and decreases the total planning cost by 22.43%. 

The paper explores the performance of LLMs in the context of multi-dimensional analytic writing assessments, i.e. their ability to provide both scores and comments based on multiple assessment criteria. Using a corpus of literature reviews written by L2 graduate students and assessed by human experts against 9 analytic criteria, we prompt several popular LLMs to perform the same task under various conditions. To evaluate the quality of feedback comments, we apply a novel feedback comment quality evaluation framework. This framework is interpretable, cost-efficient, scalable, and reproducible, compared to existing methods that rely on manual judgments. We find that LLMs can generate reasonably good and generally reliable multi-dimensional analytic assessments. We release our corpus and code\footnote{\url{https://github.com/jaaack-wang/multi-dimensional-analytic-writing-assessments}.} for reproducibility. 

As prompts become central to Large Language Models (LLMs), optimizing them is vital. Textual Stochastic Gradient Descent (TSGD) offers a data-driven approach by iteratively refining prompts using LLM-suggested updates over minibatches. We empirically show that increasing training data initially improves but can later degrade TSGD's performance across NLP tasks, while also raising computational costs. To address this, we propose Textual Stochastic Gradient Descent with Momentum (TSGD-M)—a scalable method that reweights prompt sampling based on past batches. Evaluated on 9 NLP tasks across three domains, TSGD-M outperforms TSGD baselines for most tasks and reduces performance variance. 

Training large language models (LLMs) increasingly relies on geographically distributed accelerators, causing prohibitive communication costs across regions and uneven utilization of heterogeneous hardware. We propose HALoS, a hierarchical asynchronous optimization framework that tackles these issues by introducing local parameter servers (LPSs) within each region and a global parameter server (GPS) that merges updates across regions. This hierarchical design minimizes expensive inter-region communication, reduces straggler effects, and leverages fast intra-region links. We provide a rigorous convergence analysis for HALoS under non-convex objectives, including theoretical guarantees on the role of hierarchical momentum in asynchronous training. Empirically, HALoS attains up to 7.5x faster convergence than synchronous baselines in geo-distributed LLM training and improves upon existing asynchronous methods by up to 2.1x. Crucially, HALoS preserves the model quality of fully synchronous SGD-matching or exceeding accuracy on standard language modeling and downstream benchmarks-while substantially lowering total training time. These results demonstrate that hierarchical, server-side update accumulation and global model merging are powerful tools for scalable, efficient training of new-era LLMs in heterogeneous, geo-distributed environments.