Many applications today provide users with multiple auto-complete drafts as they type, including GitHub's code completion, Gmail's smart compose, and Apple's messaging auto-suggestions.

Current state-of-the-art document retrieval solutions mainly follow an indexretrieve paradigm, where the index is hard to be directly optimized for the final retrieval target.

Parallel sampling promises substantial gains in test-time scaling, but its effectiveness is sharply limited by diversity collapse, where models concentrate on a few modes and repeated samples produce the same mistakes. We propose the mode-conditioning (ModC) framework, which explicitly allocates test-time compute across reasoning modes using either specialist models or mode-specific prefixes. ModC consistently improves scaling across controlled graph-search tasks and large-scale reasoning benchmarks, spanning model families and sizes from 0.5B to 7B. On OpenThoughts, fine-tuning Qwen2.5-7B with ModC achieves a 4x efficiency gain over standard training while also improving the maximum attainable Pass@k. We further show that gradient clustering enables ModC without explicit mode labels, yielding up to 10% gains on datasets such as NuminaMath. Finally, we show that ModC improves reinforcement learning (RL) and can further boost diversity-inducing RL methods. These results demonstrate that standard training underutilizes the diversity in data, and that ModC provides a simple, effective remedy for unlocking the full benefits of diversity in test-time scaling.

Large language models, trained on massive corpora, are prone to verbatim memorization of training data, creating significant privacy and copyright risks. While previous works have proposed various definitions for memorization, many exhibit shortcomings in comprehensively capturing this phenomenon, especially in aligned models. To address this, we introduce a novel framework: multi-prefix memorization. Our core insight is that memorized sequences are deeply encoded and thus retrievable via a significantly larger number of distinct prefixes than non-memorized content. We formalize this by defining a sequence as memorized if an external adversarial search can identify a target count of distinct prefixes that elicit it. This framework shifts the focus from single-path extraction to quantifying the robustness of a memory, measured by the diversity of its retrieval paths. Through experiments on open-source and aligned chat models, we demonstrate that our multi-prefix definition reliably distinguishes memorized from non-memorized data, providing a robust and practical tool for auditing data leakage in LLMs.

In order to predict the next token, LLMs must represent semantic and surface-level information about the current word. Previous work identified two types of attention heads that disentangle this information: (i) Concept induction heads, which copy word meanings, and (ii) Token induction heads, which copy literal token representations (Feucht et al., 2025). We show that these heads can be used to identify subspaces of model activations that exhibit coherent semantic structure in Llama-2-7b. Specifically, when we transform hidden states using the attention weights of concept heads, we are able to more accurately perform parallelogram arithmetic (Mikolov et al., 2013) on the resulting hidden states, e.g., showing that "Athens" - "Greece" + "China" = "Beijing". This transformation allows for much higher nearest-neighbor accuracy (80%) than direct use of raw hidden states (47%). Analogously, we show that token heads allow for transformations that reveal surface-level word information in hidden states, allowing for operations like "coding" - "code" + "dance" = "dancing".

In agentic LLM scenarios, an agent's interaction process during a single rollout often exhibits branching behaviors. Due to memory retrieval and concurrent tool executions at certain decision points, the token trajectory of one task evolves into a tree-like structure rather than a linear sequence. However, current training pipelines decompose such tree-structured trajectories into separate linear segments, treating each branch as an independent sequence. As a result, shared prefixes across these branches are repeatedly recomputed during both forward and backward passes. To address this inefficiency, we propose Tree Training, a paradigm that computes each shared prefix only once and reuses its intermediate results across related branches during both forward and backward passes, substantially improving computation efficiency in large-scale agentic training. This is achieved via (i) Tree Packing, which efficiently reuses shared computations across trajectories, and (ii) Gradient Restoration, which ensures correct gradient propagation across reused prefixes. Experiments on multiple open-source models demonstrate up to 3.9x reduction in total training time, enabling more efficient agentic LLM SFT and RL training.

Beyond simple text generation, Large Language Models (LLMs) have evolved into agentic systems capable of planning and interacting with external tools to solve complex tasks. This evolution involves fine-tuning LLMs on agent-specific tasks to enhance their proficiency. However, safety concerns are frequently overlooked during this fine-tuning process. In this work, we show that aligned LLMs can become unintentionally misaligned, leading to a higher likelihood of executing harmful tasks and a reduced tendency to refuse them when fine-tuned to execute agentic tasks. To address these safety challenges, we propose Prefix INjection Guard (PING), a simple yet effective method that prepends automatically generated natural language prefixes to agent responses, guiding them to refuse harmful requests while preserving performance on benign tasks. Specifically, we introduce an iterative approach that alternates between (1) generating candidate prefixes and (2) selecting those that optimize both task performance and refusal behavior. Experimental results demonstrate that PING significantly enhances the safety of fine-tuned LLM agents without sacrificing their effectiveness. PING consistently outperforms existing prompting approaches across diverse benchmarks in both web navigation and code generation tasks. Our analysis of internal hidden states via linear probes reveals that prefix tokens are crucial for behavior modification, explaining the performance gains. WARNING: This paper contains contents that are unethical or offensive in nature.

Parameter-Efficient finetuning (PEFT) enhances model performance on downstream tasks by updating a minimal subset of parameters. Representation finetuning (ReFT) methods further improve efficiency by freezing model weights and optimizing internal representations with fewer parameters than PEFT, outperforming PEFT on several tasks. However, ReFT exhibits a significant performance decline on mathematical reasoning tasks. To address this problem, the paper demonstrates that ReFT's poor performance on mathematical tasks primarily stems from its struggle to generate effective reasoning prefixes during the early inference phase. Moreover, ReFT disturbs the numerical encoding and the error accumulats during the CoT stage. Based on these observations, this paper proposes Bias-REstrained Prefix Representation FineTuning (BREP ReFT), which enhances ReFT's mathematical reasoning capability by truncating training data to optimize the generation of initial reasoning prefixes, intervening on the early inference stage to prevent error accumulation, and constraining the intervention vectors' magnitude to avoid disturbing numerical encoding. Extensive experiments across diverse model architectures demonstrate BREP's superior effectiveness, efficiency, and robust generalization capability, outperforming both standard ReFT and weight-based PEFT methods on the task of mathematical reasoning. The source code is available at https://github.com/LiangThree/BREP.

Reinforcement Learning with Human Feedback (RLHF) has emerged as a key paradigm for task-specific fine-tuning of language models using human preference data. While numerous publicly available preference datasets provide pairwise comparisons of responses, the potential for biases in the resulting reward models remains underexplored. In this work, we introduce novel methods to detect and evaluate prefix bias -- a systematic shift in model preferences triggered by minor variations in query prefixes -- in LLM-based reward models trained on such datasets. We leverage these metrics to reveal significant biases in preference models across racial and gender dimensions. Our comprehensive evaluation spans diverse open-source preference datasets and reward model architectures, demonstrating susceptibility to this kind of bias regardless of the underlying model architecture. Furthermore, we propose a data augmentation strategy to mitigate these biases, showing its effectiveness in reducing the impact of prefix bias. Our findings highlight the critical need for bias-aware dataset design and evaluation in developing fair and reliable reward models, contributing to the broader discourse on fairness in AI.