OPBO: Order-Preserving Bayesian Optimization

Bayesian optimization is an effective method for solving expensive black-box optimization problems. Most existing methods use Gaussian processes (GP) as the surrogate model for approximating the black-box objective function, it is well-known that it can fail in high-dimensional space (e.g., dimension over 500). We argue that the reliance of GP on precise numerical fitting is fundamentally ill-suited in high-dimensional space, where it leads to prohibitive computational complexity. In order to address this, we propose a simple order-preserving Bayesian optimization (OPBO) method, where the surrogate model preserves the order, instead of the value, of the black-box objective function. Then we can use a simple but effective OP neural network (NN) to replace GP as the surrogate model. Moreover, instead of searching for the best solution from the acquisition model, we select good-enough solutions in the ordinal set to reduce computational cost. The experimental results show that for high-dimensional (over 500) black-box optimization problems, the proposed OPBO significantly outperforms traditional BO methods based on regression NN and GP. The source code is available at https://github.com/pengwei222/OPBO.

Bottom-up Policy Optimization: Your Language Model Policy Secretly Contains Internal Policies

Existing reinforcement learning (RL) approaches treat large language models (LLMs) as a single unified policy, overlooking their internal mechanisms. Understanding how policy evolves across layers and modules is therefore crucial for enabling more targeted optimization and raveling out complex reasoning mechanisms. In this paper, we decompose the language model policy by leveraging the intrinsic split of the Transformer residual stream and the equivalence between the composition of hidden states with the unembedding matrix and the resulting samplable policy. This decomposition reveals Internal Layer Policies, corresponding to contributions from individual layers, and Internal Modular Policies, which align with the self-attention and feed-forward network (FFN) components within each layer. By analyzing the entropy of internal policy, we find that: (a) Early layers keep high entropy for exploration, top layers converge to near-zero entropy for refinement, with convergence patterns varying across model series. (b) LLama's prediction space rapidly converges in the final layer, whereas Qwen-series models, especially Qwen3, exhibit a more human-like, progressively structured reasoning pattern. Motivated by these findings, we propose Bottom-up Policy Optimization (BuPO), a novel RL paradigm that directly optimizes the internal layer policy during early training. By aligning training objective at lower layer, BuPO reconstructs foundational reasoning capabilities and achieves superior performance. Extensive experiments on complex reasoning benchmarks demonstrates the effectiveness of our method. Our code is available at https://github.com/Trae1ounG/BuPO.

M-STAR: Multi-Scale Spatiotemporal Autoregression for Human Mobility Modeling

Modeling human mobility is vital for extensive applications such as transportation planning and epidemic modeling. With the rise of the Artificial Intelligence Generated Content (AIGC) paradigm, recent works explore synthetic trajectory generation using autoregressive and diffusion models. While these methods show promise for generating single-day trajectories, they remain limited by inefficiencies in long-term generation (e.g., weekly trajectories) and a lack of explicit spatiotemporal multi-scale modeling. This study proposes Multi-Scale Spatio-Temporal AutoRegression (M-STAR), a new framework that generates long-term trajectories through a coarse-to-fine spatiotemporal prediction process. M-STAR combines a Multi-scale Spatiotemporal Tokenizer that encodes hierarchical mobility patterns with a Transformer-based decoder for next-scale autoregressive prediction. Experiments on two real-world datasets show that M-STAR outperforms existing methods in fidelity and significantly improves generation speed. The data and codes are available at https://github.com/YuxiaoLuo0013/M-STAR.

Virtual Width Networks

We introduce Virtual Width Networks (VWN), a framework that delivers the benefits of wider representations without incurring the quadratic cost of increasing the hidden size. VWN decouples representational width from backbone width, expanding the embedding space while keeping backbone compute nearly constant. In our large-scale experiment, an 8-times expansion accelerates optimization by over 2 times for next-token and 3 times for next-2-token prediction. The advantage amplifies over training as both the loss gap grows and the convergence-speedup ratio increases, showing that VWN is not only token-efficient but also increasingly effective with scale. Moreover, we identify an approximately log-linear scaling relation between virtual width and loss reduction, offering an initial empirical basis and motivation for exploring virtual-width scaling as a new dimension of large-model efficiency.

EPO: Diverse and Realistic Protein Ensemble Generation via Energy Preference Optimization

Accurate exploration of protein conformational ensembles is essential for uncovering function but remains hard because molecular-dynamics (MD) simulations suffer from high computational costs and energy-barrier trapping. This paper presents Energy Preference Optimization (EPO), an online refinement algorithm that turns a pretrained protein ensemble generator into an energy-aware sampler without extra MD trajectories. Specifically, EPO leverages stochastic differential equation sampling to explore the conformational landscape and incorporates a novel energy-ranking mechanism based on list-wise preference optimization. Crucially, EPO introduces a practical upper bound to efficiently approximate the intractable probability of long sampling trajectories in continuous-time generative models, making it easily adaptable to existing pretrained generators. On Tetrapeptides, ATLAS, and Fast-Folding benchmarks, EPO successfully generates diverse and physically realistic ensembles, establishing a new state-of-the-art in nine evaluation metrics. These results demonstrate that energy-only preference signals can efficiently steer generative models toward thermodynamically consistent conformational ensembles, providing an alternative to long MD simulations and widening the applicability of learned potentials in structural biology and drug discovery.

Bias-Restrained Prefix Representation Finetuning for Mathematical Reasoning

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.

SR-KI: Scalable and Real-Time Knowledge Integration into LLMs via Supervised Attention

This paper proposes SR-KI, a novel approach for integrating real-time and large-scale structured knowledge bases (KBs) into large language models (LLMs). SR-KI begins by encoding KBs into key-value pairs using a pretrained encoder, and injects them into LLMs' KV cache. Building on this representation, we employ a two-stage training paradigm: first locating a dedicated retrieval layer within the LLM, and then applying an attention-based loss at this layer to explicitly supervise attention toward relevant KB entries. Unlike traditional retrieval-augmented generation methods that rely heavily on the performance of external retrievers and multi-stage pipelines, SR-KI supports end-to-end inference by performing retrieval entirely within the models latent space. This design enables efficient compression of injected knowledge and facilitates dynamic knowledge updates. Comprehensive experiments demonstrate that SR-KI enables the integration of up to 40K KBs into a 7B LLM on a single A100 40GB GPU, and achieves strong retrieval performance, maintaining over 98% Recall@10 on the best-performing task and exceeding 88% on average across all tasks. Task performance on question answering and KB ID generation also demonstrates that SR-KI maintains strong performance while achieving up to 99.75% compression of the injected KBs.

A PDE Perspective on Generative Diffusion Models

Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only partially understood, particularly regarding the stability and consistency of the underlying stochastic and partial differential equations governing their dynamics. In this work, we develop a rigorous partial differential equation (PDE) framework for score-based diffusion processes. Building on the Li--Yau differential inequality for the heat flow, we prove well-posedness and derive sharp $L^p$-stability estimates for the associated score-based Fokker--Planck dynamics, providing a mathematically consistent description of their temporal evolution. Through entropy stability methods, we further show that the reverse-time dynamics of diffusion models concentrate on the data manifold for compactly supported data distributions and a broad class of initialization schemes, with a concentration rate of order $\sqrt{t}$ as $t \to 0$. These results yield a theoretical guarantee that, under exact score guidance, diffusion trajectories return to the data manifold while preserving imitation fidelity. Our findings also provide practical insights for designing diffusion models, including principled criteria for score-function construction, loss formulation, and stopping-time selection. Altogether, this framework provides a quantitative understanding of the trade-off between generative capacity and imitation fidelity, bridging rigorous analysis and model design within a unified mathematical perspective.

InfoFlow: Reinforcing Search Agent Via Reward Density Optimization

Reinforcement Learning with Verifiable Rewards (RLVR) is a promising approach for enhancing agentic deep search. However, its application is often hindered by low \textbf{Reward Density} in deep search scenarios, where agents expend significant exploratory costs for infrequent and often null final rewards. In this paper, we formalize this challenge as the \textbf{Reward Density Optimization} problem, which aims to improve the reward obtained per unit of exploration cost. This paper introduce \textbf{InfoFlow}, a systematic framework that tackles this problem from three aspects. 1) \textbf{Subproblem decomposition}: breaking down long-range tasks to assign process rewards, thereby providing denser learning signals. 2) \textbf{Failure-guided hints}: injecting corrective guidance into stalled trajectories to increase the probability of successful outcomes. 3) \textbf{Dual-agent refinement}: employing a dual-agent architecture to offload the cognitive burden of deep exploration. A refiner agent synthesizes the search history, which effectively compresses the researcher's perceived trajectory, thereby reducing exploration cost and increasing the overall reward density. We evaluate InfoFlow on multiple agentic search benchmarks, where it significantly outperforms strong baselines, enabling lightweight LLMs to achieve performance comparable to advanced proprietary LLMs.

The Zero-Step Thinking: An Empirical Study of Mode Selection as Harder Early Exit in Reasoning Models

Reasoning models have demonstrated exceptional performance in tasks such as mathematics and logical reasoning, primarily due to their ability to engage in step-by-step thinking during the reasoning process. However, this often leads to overthinking, resulting in unnecessary computational overhead. To address this issue, Mode Selection aims to automatically decide between Long-CoT (Chain-of-Thought) or Short-CoT by utilizing either a Thinking or NoThinking mode. Simultaneously, Early Exit determines the optimal stopping point during the iterative reasoning process. Both methods seek to reduce the computational burden. In this paper, we first identify Mode Selection as a more challenging variant of the Early Exit problem, as they share similar objectives but differ in decision timing. While Early Exit focuses on determining the best stopping point for concise reasoning at inference time, Mode Selection must make this decision at the beginning of the reasoning process, relying on pre-defined fake thoughts without engaging in an explicit reasoning process, referred to as zero-step thinking. Through empirical studies on nine baselines, we observe that prompt-based approaches often fail due to their limited classification capabilities when provided with minimal hand-crafted information. In contrast, approaches that leverage internal information generally perform better across most scenarios but still exhibit issues with stability. Our findings indicate that existing methods relying solely on the information provided by models are insufficient for effectively addressing Mode Selection in scenarios with limited information, highlighting the ongoing challenges of this task. Our code is available at https://github.com/Trae1ounG/Zero_Step_Thinking.