Transformers have achieved state-of-the-art performance across various tasks, but suffer from a notable quadratic complexity in sequence length due to the attention mechanism. In this work, we propose MonarchAttention-a novel approach to sub-quadratic attention approximation via Monarch matrices, an expressive class of structured matrices. Based on the variational form of softmax, we describe an efficient optimization-based algorithm to compute an approximate projection of softmax attention onto the class of Monarch matrices with Θ(N Nd) computational complexity and Θ(Nd)memory/IO complexity.

The authors would like to thank Ulrich-Michael, Frances, James, Maryam, and Mandolyn for their help in labeling the dataset. The work at the Université de Montréal was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (Paull), an NSERCPGS DScholarship (Morin) and an FRQNT Doctoral Scholarship (Morin). Moreover, this research was enabled in part by compute resources provided by Mila (mila.quebec). The work at the University of Freiburg was funded by an academic grant from NVIDIA. The work at the University of Oxford was supported by a Royal Society University Research Fellowship (Fallon, Kassab), a Sellafield Robotics and AICentre of Excellence Grant, and EPSRCC2CGrant EP/Z531212/1 (Mattamala), and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)(No.

Large language models (LLMs) have achieved unprecedented performance by leveraging vast pretraining corpora, yet their performance remains suboptimal in knowledge-intensive domains such as medicine and scientific research, where high factual precision is required. While synthetic data provides a promising avenue for augmenting domain knowledge, existing methods frequently generate redundant samples that do not align with the model's true knowledge gaps. To overcome this limitation, we propose a novel Structural Entropy-guided Knowledge Navigator (SENATOR) framework that addresses the intrinsic knowledge deficiencies of LLMs. Our approach employs the Structure Entropy (SE) metric to quantify uncertainty along knowledge graph paths and leverages Monte Carlo Tree Search (MCTS) to selectively explore regions where the model lacks domain-specific knowledge. Guided by these insights, the framework generates targeted synthetic data for supervised fine-tuning, enabling continuous self-improvement. Experimental results on LLaMA-3 and Qwen2 across multiple domain-specific benchmarks show that SENATOR effectively detects and repairs knowledge deficiencies, achieving notable performance improvements.

We study the problem of estimating the mean reward of the best arm in a multiarmed bandit (MAB) setting. Specifically, given a target precision εand confidence level 1 δ, the goal is to return an ε-accurate estimate of the largest mean reward with probability at least 1 δ, while minimizing the number of samples. We first establish an instance-dependent lower bound on the sample complexity, which requires handling the infinitely many possible candidates of the estimated best mean. This lower bound is expressed in a non-convex optimization problem, which becomes the main difficulty of this problem, preventing the direct application of standard techniques such as Track-and-Stop to provably achieve optimality. To overcome this difficulty, we introduce several new algorithmic and analytical techniques and propose an algorithm that achieves the asymptotic lower bound with matching constants in the leading term. Our method combines a confidence ellipsoid-based stopping condition with a two-phase sampling strategy tailored to manage non-convexity proposed algorithm is simple, nearly free of hyperparameters, and achieves the instance-dependent, asymptotically optimal sample complexity. Experimental results support our theoretical guarantees and demonstrate the practical effectiveness of our method.

Recent years have witnessed a surge of interest in solving combinatorial optimization problems (COPs) using machine learning techniques. Motivated by this trend, we propose a learning-augmented exact approach for tackling an NP-hard COP, the Orienteering Problem with Time Windows, which aims to maximize the total score collected by visiting a subset of vertices in a graph within their time windows. Traditional exact algorithms rely heavily on domain expertise and meticulous design, making it hard to achieve further improvements. By leveraging deep learning models to learn effective relaxations of problem restrictions from data, our approach enables significant performance gains in an exact dynamic programming algorithm. We propose a novel graph convolutional network that predicts the directed edges defining the relaxation. The network is trained in a supervised manner, using optimal solutions as high-quality labels. Experimental results demonstrate that the proposed learning-augmented algorithm outperforms the state-of-the-art exact algorithm, achieving a 38% speedup on Solomon's benchmark and more than a sevenfold improvement on the more challenging Cordeau's benchmark.

Diffusion-based virtual staining methods of histopathology images have demonstrated outstanding potential for stain normalization and cross-dye staining (e.g., hematoxylin-eosin to immunohistochemistry). However, achieving pathology-correct cross-dye virtual staining with versatile tone controls poses significantchallenges due to the difficulty of decoupling the given pathology and tone con-ditions.

Transformers and their attention mechanism have been revolutionary in the field of Machine Learning. While originally proposed for the language data, they quickly found their way to the image, video, graph, etc. data modalities with various signal geometries. Despite this versatility, generalizing the attention mechanism to scenarios where data is presented at different scales from potentially different modalities is not straightforward. The attempts to incorporate hierarchy and multimodality within transformers are largely based on ad hoc heuristics, which are not seamlessly generalizable to similar problems with potentially different structures. To address this problem, in this paper, we take a fundamentally different approach: we first propose a mathematical construct to represent multi-modal, multi-scale data. We then mathematically derive the neural attention mechanics for the proposed construct from the first principle of entropy minimization. We show that the derived formulation is optimal in the sense of being the closest to the standard Softmax attention while incorporating the inductive biases originating from the hierarchical/geometric information of the problem. We further propose an efficient algorithm based on dynamic programming to compute our derived attention mechanism. By incorporating it within transformers, we show that the proposed hierarchical attention mechanism not only can be employed to train transformer models in hierarchical/multi-modal settings from scratch, but it can also be used to inject hierarchical information into classical, pre-trained transformer models post training, resulting in more efficient models in zero-shot manner.

Visual Place Recognition (VPR) enables robust localization through image retrieval based on learned descriptors. However, drastic appearance variations of images at the same place caused by viewpoint changes can lead to inconsistent supervision signals, thereby degrading descriptor learning. Existing methods either rely on manually defined cropping rules or labeled data for view differentiation, but they suffer from two major limitations: (1) reliance on labels or handcrafted rules restricts generalization capability; (2) even within the same view direction, occlusions can introduce feature ambiguity. To address these issues, we propose MutualVPR, a mutual learning framework that integrates unsupervised view self-classification and descriptor learning. We first group images by geographic coordinates, then iteratively refine the clusters using K-means to dynamically assign place categories without orientation labels. Specifically, we adopt a DINOv2-based encoder to initialize the clustering.

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics--InfoBias and InfoGain--to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

Large Language Model (LLM) agents are capable of task execution across various domains by autonomously interacting with environments and refining LLM responses based on feedback. However, existing model serving systems are not optimized for the unique demands of serving agents. Compared to classic model serving, agent serving has different characteristics: predictable request pattern, increasing quality requirement, and unique prompt formatting. We identify a key problem for agent serving: LLM serving systems lack session-awareness. They neither perform effective KV cache management nor precisely select the cheapest yet competent model in each round. This leads to a cost-quality tradeoff, and we identify an opportunity to surpass it in an agent serving system. To this end, we introduce AGSERVE for AGile AGent SERVing.