Finding Kissing Numbers with Game-theoretic Reinforcement Learning

Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a fundamental challenge. This problem represents the local analogue of Hilbert's 18th problem on sphere packing, bridging geometry, number theory, and information theory. Although significant progress has been made through lattices and codes, the irregularities of high-dimensional geometry and exponentially growing combinatorial complexity beyond 8 dimensions, which exceeds the complexity of Go game, limit the scalability of existing methods. Here we model this problem as a two-player matrix completion game and train the game-theoretic reinforcement learning system, PackingStar, to efficiently explore high-dimensional spaces. The matrix entries represent pairwise cosines of sphere center vectors; one player fills entries while another corrects suboptimal ones, jointly maximizing the matrix size, corresponding to the kissing number. This cooperative dynamics substantially improves sample quality, making the extremely large spaces tractable. PackingStar reproduces previous configurations and surpasses all human-known records from dimensions 25 to 31, with the configuration in 25 dimensions geometrically corresponding to the Leech lattice and suggesting possible optimality. It achieves the first breakthrough beyond rational structures from 1971 in 13 dimensions and discovers over 6000 new structures in 14 and other dimensions. These results demonstrate AI's power to explore high-dimensional spaces beyond human intuition and open new pathways for the Kissing Number Problem and broader geometry problems.

Minimal Semantic Sufficiency Meets Unsupervised Domain Generalization

The generalization ability of deep learning has been extensively studied in supervised settings, yet it remains less explored in unsupervised scenarios. Recently, the Unsupervised Domain Generalization (UDG) task has been proposed to enhance the generalization of models trained with prevalent unsupervised learning techniques, such as Self-Supervised Learning (SSL). UDG confronts the challenge of distinguishing semantics from variations without category labels. Although some recent methods have employed domain labels to tackle this issue, such domain labels are often unavailable in real-world contexts. In this paper, we address these limitations by formalizing UDG as the task of learning a Minimal Sufficient Semantic Representation: a representation that (i) preserves all semantic information shared across augmented views (sufficiency), and (ii) maximally removes information irrelevant to semantics (minimality). We theoretically ground these objectives from the perspective of information theory, demonstrating that optimizing representations to achieve sufficiency and minimality directly reduces out-of-distribution risk. Practically, we implement this optimization through Minimal-Sufficient UDG (MS-UDG), a learnable model by integrating (a) an InfoNCE-based objective to achieve sufficiency; (b) two complementary components to promote minimality: a novel semantic-variation disentanglement loss and a reconstruction-based mechanism for capturing adequate variation. Empirically, MS-UDG sets a new state-of-the-art on popular unsupervised domain-generalization benchmarks, consistently outperforming existing SSL and UDG methods, without category or domain labels during representation learning.

Exploiting Layer Normalization Fine-tuning in Visual Transformer Foundation Models for Classification

LayerNorm is pivotal in Vision Transformers (ViTs), yet its fine-tuning dynamics under data scarcity and domain shifts remain underexplored. This paper shows that shifts in LayerNorm parameters after fine-tuning (LayerNorm shifts) are indicative of the transitions between source and target domains; its efficacy is contingent upon the degree to which the target training samples accurately represent the target domain, as quantified by our proposed Fine-tuning Shift Ratio ($FSR$). Building on this, we propose a simple yet effective rescaling mechanism using a scalar $\lambda$ that is negatively correlated to $FSR$ to align learned LayerNorm shifts with those ideal shifts achieved under fully representative data, combined with a cyclic framework that further enhances the LayerNorm fine-tuning. Extensive experiments across natural and pathological images, in both in-distribution (ID) and out-of-distribution (OOD) settings, and various target training sample regimes validate our framework. Notably, OOD tasks tend to yield lower $FSR$ and higher $\lambda$ in comparison to ID cases, especially with scarce data, indicating under-represented target training samples. Moreover, ViTFs fine-tuned on pathological data behave more like ID settings, favoring conservative LayerNorm updates. Our findings illuminate the underexplored dynamics of LayerNorm in transfer learning and provide practical strategies for LayerNorm fine-tuning.

PET2Rep: Towards Vision-Language Model-Drived Automated Radiology Report Generation for Positron Emission Tomography

Positron emission tomography (PET) is a cornerstone of modern oncologic and neurologic imaging, distinguished by its unique ability to illuminate dynamic metabolic processes that transcend the anatomical focus of traditional imaging technologies. Radiology reports are essential for clinical decision making, yet their manual creation is labor-intensive and time-consuming. Recent advancements of vision-language models (VLMs) have shown strong potential in medical applications, presenting a promising avenue for automating report generation. However, existing applications of VLMs in the medical domain have predominantly focused on structural imaging modalities, while the unique characteristics of molecular PET imaging have largely been overlooked. To bridge the gap, we introduce PET2Rep, a large-scale comprehensive benchmark for evaluation of general and medical VLMs for radiology report generation for PET images. PET2Rep stands out as the first dedicated dataset for PET report generation with metabolic information, uniquely capturing whole-body image-report pairs that cover dozens of organs to fill the critical gap in existing benchmarks and mirror real-world clinical comprehensiveness. In addition to widely recognized natural language generation metrics, we introduce a series of clinical efficiency metrics to evaluate the quality of radiotracer uptake pattern description in key organs in generated reports. We conduct a head-to-head comparison of 30 cutting-edge general-purpose and medical-specialized VLMs. The results show that the current state-of-the-art VLMs perform poorly on PET report generation task, falling considerably short of fulfilling practical needs. Moreover, we identify several key insufficiency that need to be addressed to advance the development in medical applications.

PAST: A multimodal single-cell foundation model for histopathology and spatial transcriptomics in cancer

While pathology foundation models have transformed cancer image analysis, they often lack integration with molecular data at single-cell resolution, limiting their utility for precision oncology. Here, we present PAST, a pan-cancer single-cell foundation model trained on 20 million paired histopathology images and single-cell transcriptomes spanning multiple tumor types and tissue contexts. By jointly encoding cellular morphology and gene expression, PAST learns unified cross-modal representations that capture both spatial and molecular heterogeneity at the cellular level. This approach enables accurate prediction of single-cell gene expression, virtual molecular staining, and multimodal survival analysis directly from routine pathology slides. Across diverse cancers and downstream tasks, PAST consistently exceeds the performance of existing approaches, demonstrating robust generalizability and scalability. Our work establishes a new paradigm for pathology foundation models, providing a versatile tool for high-resolution spatial omics, mechanistic discovery, and precision cancer research.

Structure-aware Semantic Discrepancy and Consistency for 3D Medical Image Self-supervised Learning

3D medical image self-supervised learning (mSSL) holds great promise for medical analysis. Effectively supporting broader applications requires considering anatomical structure variations in location, scale, and morphology, which are crucial for capturing meaningful distinctions. However, previous mSSL methods partition images with fixed-size patches, often ignoring the structure variations. In this work, we introduce a novel perspective on 3D medical images with the goal of learning structure-aware representations. We assume that patches within the same structure share the same semantics (semantic consistency) while those from different structures exhibit distinct semantics (semantic discrepancy). Based on this assumption, we propose an mSSL framework named $S^2DC$, achieving Structure-aware Semantic Discrepancy and Consistency in two steps. First, $S^2DC$ enforces distinct representations for different patches to increase semantic discrepancy by leveraging an optimal transport strategy. Second, $S^2DC$ advances semantic consistency at the structural level based on neighborhood similarity distribution. By bridging patch-level and structure-level representations, $S^2DC$ achieves structure-aware representations. Thoroughly evaluated across 10 datasets, 4 tasks, and 3 modalities, our proposed method consistently outperforms the state-of-the-art methods in mSSL.

Efficient Network Automatic Relevance Determination

We propose Network Automatic Relevance Determination (NARD), an extension of ARD for linearly probabilistic models, to simultaneously model sparse relationships between inputs $X \in \mathbb R^{d \times N}$ and outputs $Y \in \mathbb R^{m \times N}$, while capturing the correlation structure among the $Y$. NARD employs a matrix normal prior which contains a sparsity-inducing parameter to identify and discard irrelevant features, thereby promoting sparsity in the model. Algorithmically, it iteratively updates both the precision matrix and the relationship between $Y$ and the refined inputs. To mitigate the computational inefficiencies of the $\mathcal O(m^3 + d^3)$ cost per iteration, we introduce Sequential NARD, which evaluates features sequentially, and a Surrogate Function Method, leveraging an efficient approximation of the marginal likelihood and simplifying the calculation of determinant and inverse of an intermediate matrix. Combining the Sequential update with the Surrogate Function method further reduces computational costs. The computational complexity per iteration for these three methods is reduced to $\mathcal O(m^3+p^3)$, $\mathcal O(m^3 + d^2)$, $\mathcal O(m^3+p^2)$, respectively, where $p \ll d$ is the final number of features in the model. Our methods demonstrate significant improvements in computational efficiency with comparable performance on both synthetic and real-world datasets.

Fast on the Easy, Deep on the Hard: Efficient Reasoning via Powered Length Penalty

Large language models (LLMs) have demonstrated significant advancements in reasoning capabilities, performing well on various challenging benchmarks. Techniques like Chain-of-Thought prompting have been introduced to further improve reasoning. However, these approaches frequently generate longer outputs, which in turn increase computational latency. Although some methods use reinforcement learning to shorten reasoning, they often apply uniform penalties without considering the problem's complexity, leading to suboptimal outcomes. In this study, we seek to enhance the efficiency of LLM reasoning by promoting conciseness for simpler problems while preserving sufficient reasoning for more complex ones for accuracy, thus improving the model's overall performance. Specifically, we manage the model's reasoning efficiency by dividing the reward function and including a novel penalty for output length. Our approach has yielded impressive outcomes in benchmark evaluations across three datasets: GSM8K, MATH500, and AIME2024. For the comparatively simpler datasets GSM8K and MATH500, our method has effectively shortened output lengths while preserving or enhancing accuracy. On the more demanding AIME2024 dataset, our approach has resulted in improved accuracy.

SD-MAD: Sign-Driven Few-shot Multi-Anomaly Detection in Medical Images

Medical anomaly detection (AD) is crucial for early clinical intervention, yet it faces challenges due to limited access to high-quality medical imaging data, caused by privacy concerns and data silos. Few-shot learning has emerged as a promising approach to alleviate these limitations by leveraging the large-scale prior knowledge embedded in vision-language models (VLMs). Recent advancements in few-shot medical AD have treated normal and abnormal cases as a one-class classification problem, often overlooking the distinction among multiple anomaly categories. Thus, in this paper, we propose a framework tailored for few-shot medical anomaly detection in the scenario where the identification of multiple anomaly categories is required. To capture the detailed radiological signs of medical anomaly categories, our framework incorporates diverse textual descriptions for each category generated by a Large-Language model, under the assumption that different anomalies in medical images may share common radiological signs in each category. Specifically, we introduce SD-MAD, a two-stage Sign-Driven few-shot Multi-Anomaly Detection framework: (i) Radiological signs are aligned with anomaly categories by amplifying inter-anomaly discrepancy; (ii) Aligned signs are selected further to mitigate the effect of the under-fitting and uncertain-sample issue caused by limited medical data, employing an automatic sign selection strategy at inference. Moreover, we propose three protocols to comprehensively quantify the performance of multi-anomaly detection. Extensive experiments illustrate the effectiveness of our method.

ChromFound: Towards A Universal Foundation Model for Single-Cell Chromatin Accessibility Data

The advent of single-cell Assay for Transposase-Accessible Chromatin using sequencing (scATAC-seq) offers an innovative perspective for deciphering regulatory mechanisms by assembling a vast repository of single-cell chromatin accessibility data. While foundation models have achieved significant success in single-cell transcriptomics, there is currently no foundation model for scATAC-seq that supports zero-shot high-quality cell identification and comprehensive multi-omics analysis simultaneously. Key challenges lie in the high dimensionality and sparsity of scATAC-seq data, as well as the lack of a standardized schema for representing open chromatin regions (OCRs). Here, we present \textbf{ChromFound}, a foundation model tailored for scATAC-seq. ChromFound utilizes a hybrid architecture and genome-aware tokenization to effectively capture genome-wide long contexts and regulatory signals from dynamic chromatin landscapes. Pretrained on 1.97 million cells from 30 tissues and 6 disease conditions, ChromFound demonstrates broad applicability across 6 diverse tasks. Notably, it achieves robust zero-shot performance in generating universal cell representations and exhibits excellent transferability in cell type annotation and cross-omics prediction. By uncovering enhancer-gene links undetected by existing computational methods, ChromFound offers a promising framework for understanding disease risk variants in the noncoding genome.