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Attention Is All You Need for KV Cache in Diffusion LLMs

Quan Nguyen-Tri, Mukul Ranjan, Zhiqiang Shen

This work studies how to adaptively recompute key–value (KV) caches for diffusion large language models (DLMs) to maximize prediction accuracy while minimizing decoding latency. Prior methods' decoders recompute QKV for all tokens at every denoising step and layer, despite KV states changing little across most steps, especially in shallow layers, leading to substantial redundancy. We make three observations: (1) distant MASK tokens primarily act as a length-bias and can be cached block-wise beyond the active prediction window; (2) KV dynamics increase with depth, suggesting that selective refresh starting from deeper layers is sufficient; and (3) the most-attended token exhibits the smallest KV drift, providing a conservative lower bound on cache change for other tokens. Building on these, we propose Elastic-Cache, a training-free, architecture-agnostic strategy that jointly decides ${when}$ to refresh (via an attention-aware drift test on the most-attended token) and ${where}$ to refresh (via a depth-aware schedule that recomputes from a chosen layer onward while reusing shallow-layer caches and off-window MASK caches). Unlike fixed-period schemes, Elastic-Cache performs adaptive, layer-aware cache updates for diffusion LLMs, reducing redundant computation and accelerating decoding with negligible loss in generation quality. Experiments on LLaDA-Instruct, LLaDA-1.5, and LLaDA-V across mathematical reasoning and code generation tasks demonstrate consistent speedups: $8.7\times$ on GSM8K (256 tokens), $45.1\times$ on longer sequences, and $4.8\times$ on HumanEval, while consistently maintaining higher accuracy than the baseline. Our method achieves significantly higher throughput ($6.8\times$ on GSM8K) than existing confidence-based approaches while preserving generation quality, enabling practical deployment of diffusion LLMs.

Prompt-MII: Meta-Learning Instruction Induction for LLMs

Emily Xiao, Yixiao Zeng, Ada Chen, Chin-Jou Li, Amanda Bertsch, Graham Neubig

A popular method to adapt large language models (LLMs) to new tasks is in-context learning (ICL), which is effective but incurs high inference costs as context length grows. In this paper we propose a method to perform instruction induction, where we take training examples and reduce them to a compact but descriptive prompt that can achieve performance comparable to ICL over the full training set. Specifically, we propose Prompt-MII, a reinforcement learning (RL) based framework to meta-learn an instruction induction model that can generate compact instructions on the fly for an arbitrary new dataset. We train on over 3,000 diverse classification datasets from the HuggingFace hub, and evaluate on 90 unseen tasks. Prompt-MII improves downstream model quality by 4-9 F1 points (10-20\% relative), matching ICL performance while requiring 3-13x fewer tokens.

Cautious Optimizers: Improving Training with One Line of Code

Kaizhao Liang, Lizhang Chen, Bo Liu, Qiang Liu

AdamW has been the default optimizer for transformer pretraining. For many years, our community searched for faster and more stable optimizers with only constrained positive outcomes. In this work, we propose a \textbf{single-line modification in Pytorch} to any momentum-based optimizer, which we rename cautious optimizer, e.g. C-AdamW and C-Lion. Our theoretical result shows that this modification preserves Adam's Hamiltonian function and it does not break the convergence guarantee under the Lyapunov analysis. In addition, a whole new family of optimizers is revealed by our theoretical insight. Among them, we pick the simplest one for empirical experiments, showing not only consistent speed-up on LLM pretraining and post-training tasks, but also better results in MAE pretraining, with minimum extra tuning on hyperparameters.

All Code, No Thought: Language Models Struggle to Reason in Ciphered Language

Shiyuan Guo, Henry Sleight, Fabien Roger

Detecting harmful AI actions is important as AI agents gain adoption. Chain-of-thought (CoT) monitoring is one method widely used to detect adversarial attacks and AI misalignment. However, attackers and misaligned models might evade CoT monitoring through *ciphered reasoning*: reasoning hidden in encrypted, translated, or compressed text. To assess this risk, we test whether models can perform ciphered reasoning. For each of 28 different ciphers, we fine-tune and prompt up to 10 models to reason in that cipher. We measure model accuracy on math problems as a proxy for reasoning ability. Across the models we test, we find an asymmetry: model accuracy can drop significantly when reasoning in ciphered text, even though models demonstrate comprehension of ciphered text by being able to translate it accurately to English. Even frontier models struggle with lesser-known ciphers, although they can reason accurately in well-known ciphers like rot13. We show that ciphered reasoning capability correlates with cipher prevalence in pretraining data. We also identify scaling laws showing that ciphered reasoning capability improves slowly with additional fine-tuning data. Our work suggests that evading CoT monitoring using ciphered reasoning may be an ineffective tactic for current models and offers guidance on constraining the development of this capability in future frontier models.

Code Driven Planning with Domain-Adaptive Selector

Zikang Tian, Shaohui Peng, Di Huang, Jiaming Guo, Ruizhi Chen, Rui Zhang, Xishan Zhang, Yuxuan Guo, Zidong Du, Qi Guo, Ling Li, Yewen Pu, Xing Hu, Yunji Chen

Large Language Models (LLMs) have been widely adopted as task planners for AI agents in sequential decision-making problems, leveraging their extensive world knowledge. However, the gap between their general knowledge and environment-specific requirements often leads to inaccurate plans. To address this, existing approaches rely on frequent LLM queries to iteratively refine plans based on immediate environmental feedback, which incurs substantial query costs. However, this refinement is typically guided by short-term environmental feedback, limiting LLMs from developing plans aligned with long-term rewards. We propose **Co**de Driven **P**lanning w**i**th Domain-Adaptive Sele**C**tor (CoPiC). Instead of relying on frequent queries, CoPiC employs LLMs to generate a diverse set of high-level planning programs, which iteratively produce and refine candidate plans. A trained domain-adaptive selector then evaluates these candidates and selects the one most aligned with long-term rewards for execution. Using high-level planning programs as planner and domain-adaptive selector as estimator, CoPiC improves planning while significantly reducing query costs. Results in ALFWorld, NetHack, and StarCraft II Unit Building show that CoPiC outperforms advanced LLM-based baselines, achieving an average (1) 19.14\% improvement in success rate and (2) 79.39\% reduction in token costs.

Kevin: Multi-Turn RL for Generating CUDA Kernels

Carlo Baronio, Pietro Marsella, Ben Pan, Simon Guo, Silas Alberti

Writing GPU kernels is a challenging task and critical for AI systems' efficiency. It is also highly iterative: domain experts write code and improve performance through execution feedback. Moreover, it presents verifiable rewards like correctness and speedup, making it a natural environment to apply Reinforcement Learning (RL). To explicitly incorporate the iterative nature of this process into training, we develop a flexible multi-turn RL recipe that addresses unique challenges encountered in real-world settings, such as learning from long trajectories and effective reward attribution across turns. We present Kevin the Kernel Writer, the first model trained with multi-turn RL for CUDA kernel generation and optimization. In our evaluation setup, Kevin shows significant gains over its base model (QwQ-32B), improving correctness of generated kernels (in pure CUDA) from 56% to 82% and mean speedup from 0.53x to 1.10x of baseline (PyTorch Eager), and surpassing frontier models like o4-mini (0.78x). Finally, we study its behavior across test-time scaling axes: we found scaling serial refinement more beneficial than parallel sampling. In particular, when given more refinement turns, Kevin shows a higher rate of improvement.

WithAnyone: Toward Controllable and ID Consistent Image Generation

Hengyuan Xu, Wei Cheng, Peng Xing, Yixiao Fang, Shuhan Wu, Rui Wang, Xianfang Zeng, Daxin Jiang, Gang Yu, Xingjun Ma, Yu-Gang Jiang

Identity-consistent (ID-consistent) generation has become an important focus in text-to-image research, with recent models achieving notable success in producing images aligned with a reference identity. Yet, the scarcity of large-scale paired datasets—containing multiple images of the same individual—forces most approaches to adopt reconstruction-based training. This reliance often leads to a failure mode we term copy-paste, where the model directly replicates the reference face rather than preserving identity across natural variations in pose, expression, or lighting. Such over-similarity undermines controllability and limits the expressive power of generation. To address these limitations, we (1) construct a large-scale paired dataset, MultiID-2M, tailored for multi-person scenarios, providing diverse references for each identity; (2) introduce a benchmark that quantifies both copy-paste artifacts and the trade-off between identity fidelity and variation; and (3) propose a novel training paradigm with a contrastive identity loss that leverages paired data to balance fidelity with diversity. These contributions culminate in WithAnyone, a diffusion-based model that effectively mitigates copy-paste while preserving high identity similarity. Extensive experiments—both qualitative and quantitative—demonstrate that WithAnyone substantially reduces copy-paste artifacts, improves controllability over pose and expression, and maintains strong perceptual quality. User studies further validate that our method achieves high identity fidelity while enabling expressive, controllable generation.

A Noise is Worth Diffusion Guidance

Donghoon Ahn, Jiwon Kang, Sanghyun Lee, Jaewon Min, Minjae Kim, Wooseok Jang, Hyoungwon Cho, Sayak Paul, SeonHwa Kim, Eunju Cha, Kyong Hwan Jin, Seungryong Kim

Diffusion models have demonstrated remarkable image generation capabilities, but their performance heavily relies on classifier-free guidance (CFG). While CFG significantly enhances image quality, evaluating both conditional and unconditional models at every denoising step leads to substantial computational overhead. Existing approaches mitigate this cost through distillation, training a student network to learn the guided predictions. In contrast, we take an orthogonal approach by refining the \textit{initial Gaussian noise}, a critical yet under-explored factor in the diffusion-based generation pipelines. Recent studies have explored noise optimization for specific tasks such as layout-conditioned generation and human preference alignment. However, whether refined noise alone can enable guidance-free high-quality image generation remains an open question. We introduce a noise refinement framework where a refining network is trained to minimize the difference between images generated by unguided sampling from the refined noise and those produced by guided sampling from the input Gaussian noise. Our method achieves CFG-like quality without modifying the diffusion model, preserving its prior knowledge and compatibility with techniques like DreamBooth LoRA. Additionally, the learned refining network generalizes across domains without retraining and seamlessly integrates with existing distilled models, further improving sample quality. Beyond its practical benefits, we provide an in-depth analysis of refined noise, offering insights into its role in the denoising process and its interaction with guidance. Our findings suggest that structured noise initialization is key to efficient and high-fidelity image synthesis. Code and weights will be publicly released.

SatDreamer360: Multiview-Consistent Generation of Ground-Level Scenes from Satellite Imagery

Xianghui Ze, Beiyi Zhu, Zhenbo Song, Jianfeng Lu, Yujiao Shi

Generating multiview-consistent $360^\circ$ ground-level scenes from satellite imagery is a challenging task with broad applications in simulation, autonomous navigation, and digital twin cities. Existing approaches primarily focus on synthesizing individual ground-view panoramas, often relying on auxiliary inputs like height maps or handcrafted projections, and struggle to produce multiview consistent sequences. In this paper, we propose SatDreamer360, a framework that generates geometrically consistent multi-view ground-level panoramas from a single satellite image, given a predefined pose trajectory. To address the large viewpoint discrepancy between ground and satellite images, we adopt a triplane representation to encode scene features and design a ray-based pixel attention mechanism that retrieves view-specific features from the triplane. To maintain multi-frame consistency, we introduce a panoramic epipolar-constrained attention module that aligns features across frames based on known relative poses. To support the evaluation, we introduce VIGOR++, a large-scale dataset for generating multi-view ground panoramas from a satellite image, by augmenting the original VIGOR dataset with more ground-view images and their pose annotations. Experiments show that SatDreamer360 outperforms existing methods in both satellite-to-ground alignment and multiview consistency.

DistillKac: Few-Step Image Generation via Damped Wave Equations

Weiqiao Han, Chenlin Meng, Christopher D Manning, Stefano Ermon

We present DistillKac, a fast image generator that uses the damped wave equation and its stochastic Kac representation to move probability mass at finite speed. In contrast to diffusion models whose reverse time velocities can become stiff and implicitly allow unbounded propagation speed, Kac dynamics enforce finite speed transport and yield globally bounded kinetic energy. Building on this structure, we introduce classifier free guidance in velocity space that preserves square integrability under mild conditions. We then propose endpoint only distillation that trains a student to match a frozen teacher over long intervals. We prove a stability result that promotes supervision at the endpoints to closeness along the entire path. Experiments demonstrate DistillKac delivers high quality samples with very few function evaluations while retaining the numerical stability benefits of finite speed probability flows.

Rethinking Uncertainty Estimation in LLMs: A Principled Single-Sequence Measure

Lukas Aichberger, Kajetan Schweighofer, Sepp Hochreiter

Large Language Models (LLMs) are increasingly employed in real-world applications, driving the need to evaluate the trustworthiness of their generated text. To this end, reliable uncertainty estimation is essential. Leading uncertainty estimation methods generate and analyze multiple output sequences, which is computationally expensive and impractical at scale. In this work, we inspect the theoretical foundations of these methods and explore new directions to enhance computational efficiency. Building on the framework of proper scoring rules, we find that the negative log-likelihood of the most likely output sequence constitutes a theoretically principled uncertainty measure. To approximate this alternative measure, we propose G-NLL, obtained using a single output sequence from greedy decoding. This approach streamlines uncertainty estimation while preserving theoretical rigor. Empirical results demonstrate that G-NLL achieves state-of-the-art performance across various scenarios. Our work lays the theoretical foundation for efficient and reliable uncertainty estimation in natural language generation, challenging the necessity of the prevalent methods that are more complex and resource-intensive.

Planned Diffusion

Daniel Mingyi Israel, Tian Jin, Ellie Y Cheng, Guy Van den Broeck, Aditya Grover, Suvinay Subramanian, Michael Carbin

A central challenge in large language model inference is the trade-off between generation speed and output quality. Autoregressive models produce high-quality text but generate tokens sequentially. Diffusion models can generate tokens in parallel but often need many iterations to match the same quality. We propose planned diffusion, a hybrid method that combines the strengths of both paradigms. Planned diffusion works in two stages: first, the model creates a short autoregressive plan that breaks the output into smaller, independent spans. Second, the model generates these spans simultaneously using diffusion. This approach expands the speed–quality Pareto frontier and provides a practical path to faster, high-quality text generation. On AlpacaEval, a suite of 805 instruction-following prompts, planned diffusion achieves Pareto-optimal trade-off between quality and latency, achieving 1.27x to 1.81x speedup over autoregressive generation with only 0.87\% to 5.4\% drop in win rate, respectively. Our sensitivity analysis shows that the planning mechanism of planned diffusion is minimal and reliable, and simple runtime knobs exist to provide flexible control of the quality-latency trade-off.

Leveraging Pretrained Knowledge at Inference Time: LoRA-Gated Contrastive Decoding for Multilingual Factual Language Generation in Adapted LLMs

Gwangseon Jang, Hongseok Choi, Chanuk lim, Kyong-Ha Lee, Mun Yong Yi

Large language models (LLMs) adapted to specific languages through continual pretraining or instruction tuning often suffer from catastrophic forgetting, which can lead to factual inaccuracies. This issue is particularly pronounced in multilingual settings, where adaptation may override general world knowledge with language-specific patterns. We propose LoRA-Gated Contrastive Decoding (LGCD), a training-free inference-time decoding framework that improves factuality in language-adapted LLMs by leveraging knowledge from the original pretrained model. LGCD operates by (1) extracting factual representations from Feed-Forward Network (FFN) layers via LoRA-based decomposition, approximating pretrained knowledge, (2) dynamically gating decoding based on token-level confidence, and (3) applying contrastive decoding with Top-K masking to revise uncertain predictions by referencing the approximated representation of pretrained knowledge. LGCD requires no additional training or access to the original pretraining data. Extensive experiments with LGCD on multilingual multiple-choice and long-form QA tasks across nine languages demonstrate its strong effectiveness in mitigating hallucinations and enhancing factual accuracy in language-adapted models. These results further indicate that pretrained knowledge can be strategically reintroduced during decoding to promote factual multilingual generation.

Any-Order Any-Subset AutoRegressive Model

Tianqi Du, Lizhe Fang, Weijie Yang, Chenheng Zhang, Zeming Wei, Yifei Wang, Yisen Wang

We propose Any-order Any-subset Autoregressive modeling (A3), a novel sequence generation framework that generalizes standard autoregressive (AR) factorization to support the prediction of arbitrary token groups in any order. A3 overcomes the limitations of conventional left-to-right decoding by enabling flexible groupwise generation while preserving probabilistic rigor and training stability. Our design combines a two-stream attention architecture with a progressive training strategy, allowing both efficient parallel decoding and robust modeling of diverse dependency structures. Empirical results demonstrate that A3 achieves a superior trade-off between generation speed, flexibility, and quality compared to state-of-the-art AR and diffusion-based methods. This work offers a unified approach for a flexible, efficient, and novel language modeling paradigm.

From Large to Small: Transferring CUDA Optimization Expertise via Reasoning Graph

Junfeng Gong, Zhiyi Wei, Junying Chen, Cheng Liu, Huawei Li

Despite significant evolution of CUDA programming and domain-specific libraries, effectively utilizing GPUs with massively parallel engines remains difficult. Large language models (LLMs) show strong potential in generating optimized CUDA code from sequential code. However, using LLMs in practice faces two major challenges: cloud-based APIs pose risks of code leakage, and local deployment is often computationally expensive and inefficient. These drawbacks have spurred interest in small language models (SLMs), which are more lightweight and privacy-friendly. Encouragingly, recent studies show that SLMs can achieve performance comparable to LLMs on specific tasks. While SLMs can match LLMs on domain-specific tasks, their limited reasoning abilities lead to suboptimal performance in complex CUDA generation according to our experiments. To bridge this gap, we propose ReGraphT, a training-free, retrieval-augmented generation framework that transfers LLM-level reasoning to smaller models. ReGraphT organizes CUDA optimization trajectories into a structured reasoning graph, modeling the combined CUDA optimizations as state transitions, and leverages Monte Carlo Graph Search (MCGS) for efficient exploration. We also present a CUDA-specific benchmark with difficulty tiers defined by reasoning complexity to evaluate models more comprehensively. Experiments show that ReGraphT outperforms HPC-specific fine-tuned models and other retrieval-augmented approaches, achieving an average 2.33× speedup on CUDAEval and ParEval. When paired with DeepSeek-Coder-V2-Lite-Instruct and Qwen2.5-Coder-7B-Instruct, ReGraphT enables SLMs to approach LLM-level performance without the associated privacy risks or excessive computing overhead.

Flow Caching for Autoregressive Video Generation

Yuexiao Ma, Xuzhe Zheng, Jing Xu, Xiwei Xu, Feng Ling, Xiawu Zheng, Huafeng Kuang, Huixia Li, Xing Wang, Xuefeng Xiao, Fei Chao, Rongrong Ji

Autoregressive models, often built on Transformer architectures, represent a powerful paradigm for generating ultra-long videos by synthesizing content in sequential chunks. However, this sequential generation process is notoriously slow. While caching strategies have proven effective for accelerating traditional video diffusion models, existing methods assume uniform denoising across all frames—an assumption that breaks down in autoregressive models where different video chunks exhibit varying similarity patterns at identical timesteps. In this paper, we present FlowCache, the first caching framework specifically designed for autoregressive video generation. Our key insight is that each video chunk should maintain independent caching policies, allowing fine-grained control over which chunks require recomputation at each timestep. We introduce a chunkwise caching strategy that dynamically adapts to the unique denoising characteristics of each chunk, complemented by an importance-based KV cache compression mechanism that maintains fixed memory bounds while preserving generation quality. Our method achieves remarkable speedups of $\textbf{2.38}\times$ on MAGI-1 and $\textbf{6.7}\times$ on SkyReels-V2, with negligible quality degradation (VBench: $0.87\uparrow$ and $0.79\downarrow$ respectively). These results demonstrate that FlowCache, successfully unlocks the potential of autoregressive models for real-time, ultra-long video generation—establishing a new benchmark for efficient video synthesis at scale. The code is available at https://anonymous.4open.science/r/FlowCache-23495iclrAnonymous

Modeling Others' Minds as Code

Kunal Jha, Aydan Yuenan Huang, Eric Ye, Natasha Jaques, Max Kleiman-Weiner

Accurate prediction of human behavior is essential for robust and safe human-AI collaboration. However, existing approaches for modeling people are often data-hungry and brittle because they either make unrealistic assumptions about rationality or are too computationally demanding to adapt rapidly. Our key insight is that many everyday social interactions may follow predictable patterns; efficient "scripts" that minimize cognitive load for actors and observers, e.g., "wait for the green light, then go." We propose modeling these routines as behavioral programs instantiated in computer code rather than policies conditioned on beliefs and desires. We introduce ROTE, a novel algorithm that leverages both large language models (LLMs) for synthesizing a hypothesis space of behavioral programs, and probabilistic inference for reasoning about uncertainty over that space. We test ROTE in a suite of gridworld tasks and a large-scale embodied household simulator. ROTE predicts human and AI behaviors from sparse observations, outperforming competitive baselines---including behavior cloning and LLM-based methods---by as much as 50% in terms of in-sample accuracy and out-of-sample generalization. By treating action understanding as a program synthesis problem, ROTE opens a path for AI systems to efficiently and effectively predict human behavior in the real-world.

OptimSyn: Influence-Guided Rubrics Optimization for Synthetic Data Generation

Zhiting Fan, Ruizhe Chen, Tianxiang Hu, Ru Peng, Zenan Huang, Haokai Xu, Yixin Chen, Jian Wu, Junbo Zhao, Zuozhu Liu

Large language models (LLMs) achieve strong downstream performance largely due to abundant supervised fine-tuning (SFT) data that imparts problem-solving capabilities. However, as applications expand, high-quality SFT data in knowledge-intensive verticals (e.g., humanities and social sciences, medicine, law, finance) is exceedingly scarce: expert curation is costly, privacy constraints are strict, and label consistency is hard to guarantee. Recent work turns to synthetic data, typically prompting a teacher model over domain documents and filtering with handcrafted rubrics. Yet, rubric design is expert-dependent and rarely transfers across domains; moreover, prevalent heuristic optimization follows a brittle loop (write rubric $\rightarrow$ synthesize $\rightarrow$ train $\rightarrow$ inspect $\rightarrow$ guess tweaks) that lacks reliable, quantitative feedback about a rubric's true contribution to downstream performance. We argue for assessing synthetic data quality through its causal impact on the target model, using this feedback to guide data generation. Inspired by classic influence functions, we repurpose an optimizer-aware estimator that uses gradient information to quantify each synthetic sample's contribution to the objective of a given target model on specific tasks. Our analysis reveals a gap: although synthetic and real samples may be close in embedding space, their influence on learning can differ substantially. Building on this insight, we propose an optimization-based synthetic data framework that adapts rubrics with target-model feedback. Instead of manually engineering domain rubrics, we supply lightweight guiding text and delegate rubric generation to a rubric-specialized model conditioned on the task; crucially, rubric (and data) selection is supervised by estimated downstream impact rather than proxy formality. Empirically, the framework yields consistent gains across domains (HSS and health), target models (e.g., Qwen and Llama families), and data generators, demonstrating broad generalization and engineering portability without task-specific tuning.

HARDTESTGEN: A High-Quality RL Verifier Generation Pipeline for LLM Algorithimic Coding

Zhongmou He, Yee Man Choi, Kexun Zhang, Ivan Bercovich, Jiabao Ji, Junting Zhou, Dejia Xu, Aidan Zhang, Yixiao Zeng, Lei Li

Verifiers provide important reward signals for reinforcement learning of large language models (LLMs). However, it is challenging to develop or create reliable verifiers, especially for code generation tasks. A well-disguised wrong solution program may only be detected by carefully human-written edge cases that are difficult to synthesize automatically. To address this issue, we propose HardTestsGen, an approach to synthesize high-quality test cases for algorithmic coding problems. We curate a comprehensive algorithmic programming dataset HardTests with 26.6k problems and high-quality synthetic tests. Compared with existing tests, HardTestsGen tests demonstrate significantly higher accuracy in verifying LLM-generated code (+11.22 percentage points in precision, the percentage of actually correct code within the predicted correct ones). We also show that downstream post-training — including rejection sampling and reinforcement learning (RL) — using HardTests verifier results in improved performance of LLM code generation.

Exploring Diverse Generation Paths via Inference-time Stiefel Activation Steering

Dongxuan Zhu, Ly Tran Ho Khanh, Andy Yat-Ming Cheung, Man-Chung Yue, Viet Anh Nguyen

Language models often default to a narrow set of high-probability outputs, leaving their generation paths homogeneous and prone to mode collapse. Sampling-based strategies inject randomness but still struggle to guarantee diversity across multiple concurrent generation runs. We address this limitation by introducing STARS (**ST**iefel-based **A**ctivation Steering for Diverse **R**ea**S**oning), a training-free, inference-time intervention method that transforms activation steering into an exploration engine. At each token, STARS collects the hidden activations of concurrent generation runs and optimizes multiple additive steering directions jointly on the Stiefel manifold. STARS maximizes the geometric volume of the steered activations, while the Stiefel manifold induces orthogonality of the steering interventions. This formulation explicitly promotes divergent activation vectors of concurrent generation runs, and implicitly promotes divergent generation trajectories. This manifold optimization formulation can be solved using a Riemannian gradient descent algorithm with convergence guarantees, but this algorithm is too time-consuming for real-time inference. To guarantee low latency, we further design a lightweight one-step update with an aggressive, closed-form stepsize. For test case generation and scientific discovery benchmarks, STARS consistently outperforms standard sampling methods, achieving greater diversity without sacrificing qualitative performance.

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