Preference optimization is widely used to align Large Language Models (LLMs) with preference feedback. However, most existing methods train on a single positive-negative pair per prompt, discarding additional supervision available in preference datasets that typically contain multiple candidate responses. Motivated by this limitation, recent work explores group-wise preference optimization, which jointly contrasts multiple responses for the same prompt, but its empirical behavior and scalability remain underexplored due to the memory overhead of group-coupled objectives. In this work, we present a unified empirical and systems study of group-wise preference optimization and develop a memory-efficient implementation for group-coupled objectives. By instantiating first-order linearization with objective-specific per-response coefficients, our implementation preserves first-order gradients while decoupling samples during backpropagation, substantially reducing peak memory usage and enabling scalable training with larger groups. Across offline and online settings, we show that leveraging multiple responses consistently outperforms single-pair training. Furthermore, incorporating a negative log-likelihood (NLL) term on positive responses is critical for both performance gains and training stability.

Reasoning-intensive retrieval often requires evidence whose relevance is not captured by keyword or embedding similarity alone, exposing a core limitation of traditional IR systems. An emerging direction known as LLM-guided hierarchical search addresses this limitation by letting an LLM directly traverse a semantic tree over the corpus. Such methods so far work well only with a frontier LLM in the search loop, which makes inference expensive. We propose HSearch-R1, a distillation recipe for learning compact (4B) LLMs that perform efficient LLM-guided hierarchical search. The recipe distils a frontier teacher’s per-step value estimates from its search trajectories into a much smaller LLM (Qwen3.5-4B) via RL, using a composite reward that matches the teacher’s ranking and score distribution at each step; this outcome-level RL distillation substantially outperforms supervised fine-tuning on teacher outputs. We further propose a retrieval-prior-informed variant of the search that injects a cheap retriever’s shortlist as a prior into the tree and adds robustness when the offline index is stale. The base HSearch-R1-4B matches or closely tracks frontier LLMs on the seven static BRIGHT-StackExchange subsets at roughly 50× lower per-query cost. Adding the retrieval prior brings HSearch-R1 to 52.5 nDCG@10 on StackExchange and 45.6 across all 12 BRIGHT subsets, within 1 nDCG of the strongest published ensembled baselines while remaining substantially cheaper.

While image-text pre-trained models, such as CLIP, have demonstrated impressive capabilities in learning robust text and image representations, a critical area for substantial improvement remains—precise color understanding. In this paper, we address this limitation by introducing PRISM, a simple yet highly effective method that extends CLIP’s capability to grasp the nuances of precise colors. PRISM seamlessly adapts to both recognized HTML colors and out-of-vocabulary RGB inputs through the utilization of our curated dataset of 100 image-text pairs, which can be effortlessly repurposed for fine-tuning with any desired color. Importantly, PRISM achieves these enhancements without compromising CLIP’s performance on established benchmarks. Furthermore, we introduce a novel evaluation framework, ColorLens, featuring both seen and unseen test sets that can be readily repurposed to assess a model’s precision in understanding precise colors. Our comprehensive evaluation and results demonstrate significant improvements over baseline models.