Inertial 2-blocks with abelian defect groups
L. Puig defined inertial blocks. In this paper, we prove that 2-blocks with defect group $C_{2^{n_1}}\times C_{2^{n_2}}\times...\times C_{2^{n_t}}$ are inertial, where $n_i\geq 2$ for all $i$.
math.GR↗
arXiv subjects
Kun Zhang
Publications and source records attributed to Kun Zhang.
On the Sum of Squares of Irreducible Brauer Character Degrees in Blocks
We study a weakened version of the Holm--Willems Local Conjecture. The problem is reduced to quasi-simple groups under the assumption that the defect group is abelian. Complete proofs are provided in the case \(p = 2\).
math.GR↗
Advancing Reasoning in Diffusion Language Models with Denoising Process Rewards
Diffusion-based large language models offer a non-autoregressive alternative for text generation, but enabling them to perform complex reasoning remains challenging. Reinforcement learning has recently emerged as an effective post-training strategy for improving their performance; however, existing methods rely primarily on outcome-based rewards, which provide no direct supervision over the denoising process and often result in poorly structured reasoning that is difficult to interpret and inconsistently supports the final prediction. To address this limitation, we introduce \emph{denoising process reward}, a process-level reinforcement signal defined over the denoising trajectory of diffusion language models. This reward is obtained by estimating the contribution of intermediate denoising intervals to the final task outcome, encouraging the model to favor reasoning trajectories that consistently guide generation toward correct predictions. We further propose an efficient stochastic estimator that reuses standard training rollouts, enabling practical process-level supervision at scale. Experiments on challenging reasoning benchmarks demonstrate that our approach yields consistent improvements in reasoning stability, interpretability, and overall task performance.
cs.AI↗
2-blocks with abelian defect groups and inertial quotient of prime order
In this paper, we classify all $2$-blocks for which the defect groups are abelian and the inertial quotient has prime order. As a consequence, we prove that Broué's abelian defect group conjecture holds for all blocks under consideration here.
math.GR↗
Causal Discovery in Linear Models with Unobserved Variables and Measurement Error
The presence of unobserved common causes and measurement error poses two major obstacles to causal structure learning, since ignoring either source of complexity can induce spurious causal relations among variables of interest. We study causal structure learning in linear systems where both challenges may occur simultaneously. We introduce a causal model called LV-SEM-ME, which contains four types of variables: directly observed variables, variables that are not directly observed but are measured with error, the corresponding measurements, and variables that are neither observed nor measured. Under a separability condition-namely, identifiability of the mixing matrix associated with the exogenous noise terms of the observed variables-together with certain faithfulness assumptions, we characterize the extent of identifiability and the corresponding observational equivalence classes. We provide graphical characterizations of these equivalence classes and develop recovery algorithms that enumerate all models in the equivalence class of the ground truth. We also establish, via a four-node union model that subsumes instrumental variable, front-door, and negative-control-outcome settings, a form of identification robustness: the target effect remains identifiable in the broader LV-SEM-ME model even when the assumptions underlying the specialized identification formulas for the corresponding submodels need not all hold simultaneously.
cs.LG↗
Towards Effective Long Video Understanding of Multimodal Large Language Models via One-shot Clip Retrieval
Due to excessive memory overhead, most Multimodal Large Language Models (MLLMs) can only process videos of limited frames. In this paper, we propose an effective and efficient paradigm to remedy this shortcoming, termed One-shot video-Clip based Retrieval-Augmented Generation (OneClip-RAG). Compared with existing video RAG methods, OneClip-RAG makes full use of the merits of video clips for augmented video understanding in terms of both knowledge integrity and semantic coherence. Besides, it is also equipped with a novel query-guided video chunking algorithm that can unify clip chunking and cross-modal retrieval in one processing step, avoiding redundant computations. To improve instruction following, we further propose a new dataset called SynLongVideo and design a progressive training regime for OneClip-RAG. OneClip-RAG is plugged into three recent MLLMs and validated on a set of long-video benchmarks. Experimental results not only show the obvious performance gains by OneClip-RAG over MLLMs, e.g., boosting Qwen3-VL 8B to the level of GPT-5 on MLVU, but also show its superior efficiency in handling long videos. e.g., enabling LLaVA-Video understand up to an hour of videos in less than 1.2 minutes on a single 4090 GPU.
cs.CV↗
PDF Retrieval Augmented Question Answering
This paper presents an advancement in Question-Answering (QA) systems using a Retrieval Augmented Generation (RAG) framework to enhance information extraction from PDF files. Recognizing the richness and diversity of data within PDFs--including text, images, vector diagrams, graphs, and tables--poses unique challenges for existing QA systems primarily designed for textual content. We seek to develop a comprehensive RAG-based QA system that will effectively address complex multimodal questions, where several data types are combined in the query. This is mainly achieved by refining approaches to processing and integrating non-textual elements in PDFs into the RAG framework to derive precise and relevant answers, as well as fine-tuning large language models to better adapt to our system. We provide an in-depth experimental evaluation of our solution, demonstrating its capability to extract accurate information that can be applied to different types of content across PDFs. This work not only pushes the boundaries of retrieval-augmented QA systems but also lays a foundation for further research in multimodal data integration and processing.
cs.CL↗
SmartCLIP: Modular Vision-language Alignment with Identification Guarantees
Contrastive Language-Image Pre-training (CLIP)~\citep{radford2021learning} has emerged as a pivotal model in computer vision and multimodal learning, achieving state-of-the-art performance at aligning visual and textual representations through contrastive learning. However, CLIP struggles with potential information misalignment in many image-text datasets and suffers from entangled representation. On the one hand, short captions for a single image in datasets like MSCOCO may describe disjoint regions in the image, leaving the model uncertain about which visual features to retain or disregard. On the other hand, directly aligning long captions with images can lead to the retention of entangled details, preventing the model from learning disentangled, atomic concepts -- ultimately limiting its generalization on certain downstream tasks involving short prompts. In this paper, we establish theoretical conditions that enable flexible alignment between textual and visual representations across varying levels of granularity. Specifically, our framework ensures that a model can not only \emph{preserve} cross-modal semantic information in its entirety but also \emph{disentangle} visual representations to capture fine-grained textual concepts. Building on this foundation, we introduce \ours, a novel approach that identifies and aligns the most relevant visual and textual representations in a modular manner. Superior performance across various tasks demonstrates its capability to handle information misalignment and supports our identification theory. The code is available at https://github.com/Mid-Push/SmartCLIP.
cs.CV↗
Optimal Procurement Design: A Reduced-Form Approach
Standard procurement models assume that the buyer knows the quality of the good at the time of procurement; however, in many settings, the quality is learned only long after the transaction. We study procurement problems in which the buyer's valuation of the supplied good depends directly on its quality, which is unverifiable and unobservable to the buyer. For a broad class of procurement problems, we identify procurement mechanisms maximizing any weighted average of the buyer's expected payoff and social surplus. The optimal mechanism can be implemented via an auction that restricts sellers to submitting bids within specific intervals.
econ.TH↗
Beyond the Black Box: Identifiable Interpretation and Control in Generative Models via Causal Minimality
Deep generative models, while revolutionizing fields like image and text generation, largely operate as opaque ``black boxes'', hindering human understanding, control, and alignment. While methods like sparse autoencoders (SAEs) show remarkable empirical success, they often lack theoretical guarantees, risking subjective insights. Our primary objective is to establish a principled foundation for interpretable generative models. We demonstrate that the principle of causal minimality -- favoring the simplest causal explanation -- can endow the latent representations of modern generative models with clear causal interpretation and robust, component-wise identifiable control. We introduce a novel theoretical framework for hierarchical selection models, where higher-level concepts emerge from the constrained composition of lower-level variables, better capturing the complex dependencies in data generation. Under theoretically derived minimality conditions, we show that learned representations can be equivalent to the true latent variables of the data-generating process. Empirically, applying these constraints to leading text-to-image diffusion models allows us to extract their innate hierarchical concept graphs, offering fresh insights into their internal knowledge organization. Furthermore, these causally grounded concepts serve as levers for fine-grained model steering, paving the way for transparent, reliable systems.
cs.LG↗
Scaling the Long Video Understanding of Multimodal Large Language Models via Visual Memory Mechanism
Long video understanding is a key challenge that plagues the advancement of \emph{Multimodal Large language Models} (MLLMs). In this paper, we study this problem from the perspective of visual memory mechanism, and proposed a novel and training-free approach, termed \emph{Flexible Memory} (\textbf{FlexMem}). In principle, FlexMem aims to mimic human behavior of video watching, \emph{i.e.}, continually watching video content and recalling the most relevant memory fragments to answer the question. In this way, FlexMem can help MLLMs achieve video understanding of infinite lengths, unlike previous methods that process all video information at once and have input upper-limit. Concretely, FlexMem first consider the visual KV caches as the memory sources, and realize the effective memory transfer and writing via a dual-pathway compression design. Afterwards, FlexMem also explores different memory reading strategies for the diverse video understanding tasks, including the popular streaming one. To validate FlexMem, we apply it to two popular video-MLLMs, and conduct extensive experiments on five long video and one streaming video task. The experimental results show that on \textbf{a single 3090 GPU}, our FlexMem can achieve obvious improvements than existing efficient video understanding methods and process more than \textbf{1k frames}, which also helps the base MLLMs achieve comparable or even better performance than SOTA MLLMs on some benchmarks, \emph{e.g.} , GPT-4o and Gemini-1.5 Pro.
cs.CV↗
CausalEvolve: Towards Open-Ended Discovery with Causal Scratchpad
Evolve-based agent such as AlphaEvolve is one of the notable successes in using Large Language Models (LLMs) to build AI Scientists. These agents tackle open-ended scientific problems by iteratively improving and evolving programs, leveraging the prior knowledge and reasoning capabilities of LLMs. Despite the success, existing evolve-based agents lack targeted guidance for evolution and effective mechanisms for organizing and utilizing knowledge acquired from past evolutionary experience. Consequently, they suffer from decreasing evolution efficiency and exhibit oscillatory behavior when approaching known performance boundaries. To mitigate the gap, we develop CausalEvolve, equipped with a causal scratchpad that leverages LLMs to identify and reason about guiding factors for evolution. At the beginning, CausalEvolve first identifies outcome-level factors that offer complementary inspirations in improving the target objective. During the evolution, CausalEvolve also inspects surprise patterns during the evolution and abductive reasoning to hypothesize new factors, which in turn offer novel directions. Through comprehensive experiments, we show that CausalEvolve effectively improves the evolutionary efficiency and discovers better solutions in 4 challenging open-ended scientific tasks.
cs.LG↗
Selection, Reflection and Self-Refinement: Revisit Reasoning Tasks via a Causal Lens
Due to their inherent complexity, reasoning tasks have long been regarded as rigorous benchmarks for assessing the capabilities of machine learning models, especially large language models (LLMs). Although humans can solve these tasks with ease, existing models, even after extensive pre-training and post-training at scale, still fail to perform reasoning reliably. In this paper, we revisit reasoning tasks from a causal perspective, seeking to understand their behavior in latent space and to offer insights for addressing their challenges. Specifically, we cast reasoning tasks as a selection mechanism, in which high-level logical concepts function as selection operators on the given observations, such as, identifying the correct answer in a math problem or filling the appropriate entry in Sudoku. We emphasize two key properties of this formulation that shed light on the difficulty of reasoning tasks. First, the latent space exceeds the observation space in complexity, even when the correct answer is fully determined by the observed input. Second, the latent variables, corresponding to logical thought, are densely structured and exhibit strong dependencies. Building on this formulation, we introduce a framework, called SR$^2$, that incorporates the estimated latent variables as feedback into the selection mechanism, thereby facilitating the learning of dense dependencies among latent representations. The framework consists of three key modules: reflective representation learning, dependency self-refinement, and periodic intermediate alignment. Experimentally, we show that our approach yields significant gains in reasoning accuracy, for example, attaining over 10$\%$ improvement in performance with 8$\times$ fewer parameters on the Sudoku and Maze tasks over the recent advances.
cs.AI↗
Solar Wind Reflected Ion Properties at Earth's Bow Shock: Dependence on Upstream Conditions and Shock Geometry
Solar wind ion reflection at collisionless shocks regulates foreshock plasma dynamics, yet the quantitative dependence of reflected ion properties on upstream and shock-related parameters remains unclear, causing difficulties in predicting foreshock disturbances. We present a statistical study of solar wind reflected ions near the Earth's bow shock using THEMIS observations from 59 well-defined shock crossings between 2016 and 2019. Reflected ion moments are derived after removal of the solar wind core and compared with upstream and shock parameters. The reflection ratio decreases with increasing angle between interplanetary magnetic field and shock normal, and increases with magnetic compression ratio, indicating that shock geometry and magnetic compression primarily regulate ion reflection. Reflected ion energies deviate from individual idealized reflection models: the adiabatic model overestimates total ion energy, whereas the specular model captures the perpendicular component. A combined adiabatic-specular representation improves the linear energy correspondence, and model-observation agreement increases under quasi-perpendicular shock conditions for all comparisons. Reflected ion temperature correlates with upstream magnetic field strength and solar wind temperature, and shows a substantially stronger dependence on magnetic field fluctuation energy. Overall, reflected ion properties are primarily governed by upstream conditions and shock structure, with magnetic field fluctuations contributing to ion thermalization, providing observational constraints on ion reflection and heating at Earth's bow shock.
physics.space-ph↗
DiffVP: Differential Visual Semantic Prompting for LLM-Based CT Report Generation
While large language models (LLMs) have advanced CT report generation, existing methods typically encode 3D volumes holistically, failing to distinguish informative cues from redundant anatomical background. Inspired by radiological cognitive subtraction, we propose Differential Visual Prompting (DiffVP), which conditions report generation on explicit, high-level semantic scan-to-reference differences rather than solely on absolute visual features. DiffVP employs a hierarchical difference extractor to capture complementary global and local semantic discrepancies into a shared latent space, along with a difference-to-prompt generator that transforms these signals into learnable visual prefix tokens for LLM conditioning. These difference prompts serve as structured conditioning signals that implicitly suppress invariant anatomy while amplifying diagnostically relevant visual evidence, thereby facilitating accurate report generation without explicit lesion localization. On two large-scale benchmarks, DiffVP consistently outperforms prior methods, improving the average BLEU-1-4 by +10.98 and +4.36, respectively, and further boosts clinical efficacy on RadGenome-ChestCT (F1 score 0.421). All codes will be released at https://github.com/ArielTYH/DiffVP/.
cs.CV↗
Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning
Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalence class and develop an algorithm to recover models from data up to such equivalence. To our knowledge, this is the first equivalence characterization with latent variables in any parametric setting without structural assumptions, and hence the first structural-assumption-free discovery method. Code and an interactive demo are available at https://equiv.cc.
cs.LG↗
QCAgent: An agentic framework for quality-controllable pathology report generation from whole slide image
Recent methods for pathology report generation from whole-slide image (WSI) are capable of producing slide-level diagnostic descriptions but fail to ground fine-grained statements in localized visual evidence. Furthermore, they lack control over which diagnostic details to include and how to verify them. Inspired by emerging agentic analysis paradigms and the diagnostic workflow of pathologists,who selectively examine multiple fields of view, we propose QCAgent, an agentic framework for quality-controllable WSI report generation. The core innovations of this framework are as follows: (i) it incorporates a customized critique mechanism guided by a user-defined checklist specifying required diagnostic details and constraints; (ii) it re-identifies informative regions in the WSI based on the critique feedback and text-patch semantic retrieval, a process that iteratively enriches and reconciles the report. Experiments demonstrate that by making report requirements explicitly prompt-defined, constraint-aware, and verifiable through evidence-grounded refinement, QCAgent enables controllable generation of clinically meaningful and high-coverage pathology reports from WSI.
cs.CV↗
Beyond DAGs: A Latent Partial Causal Model for Multimodal Learning
Directed Acyclic Graphs (DAGs) are a standard tool in causal modeling, but their suitability for capturing the complexity of large-scale multimodal data is questionable. In practice, real-world multimodal datasets are often collected from heterogeneous generative processes that do not conform to a single DAG. Instead, they may involve multiple, and even opposing, DAG structures with inverse causal directions. To address this gap, in this work, we first propose a novel latent partial causal model tailored for multimodal data representation learning, featuring two latent coupled variables parts connected by an undirected edge, to represent the transfer of knowledge across modalities. Under specific statistical assumptions, we establish an identifiability result, demonstrating that representations learned by MultiModal Contrastive Learning (MMCL) correspond to the latent coupled variables up to a trivial transformation. This result deepens our understanding of the why MMCL works, highlights its potential for representation disentanglement, and expands the utility of pre-trained models like CLIP. Synthetic experiments confirm the robustness of our findings, even when the assumptions are partially violated. Most importantly, experiments on a pre-trained CLIP model embodies disentangled representations, enabling few-shot learning and improving domain generalization across diverse real-world datasets. Together, these contributions push the boundaries of MMCL, both in theory and in practical applications.
cs.LG↗