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Theory · Learning Theory

Milad Sefidgaran, Kimia Nadjahi, Abdellatif Zaidi

In this paper, we leverage stochastic projection and lossy compression to establish new conditional mutual information (CMI) bounds on the generalization error of statistical learning algorithms. It is shown that these bounds are generally tighter than the existing ones. In particular, we prove that for certain problem instances for which existing MI and CMI bounds were recently shown in Attias et al. [2024] and Livni [2023] to become vacuous or fail to describe the right generalization behavior, our bounds yield suitable generalization guarantees of the order of $\mathcal{O}(1/\sqrt{n})$, where $n$ is the size of the training dataset. Furthermore, we use our bounds to investigate the problem of data "memorization" raised in those works, and which asserts that there are learning problem instances for which any learning algorithm that has good prediction there exist distributions under which the algorithm must "memorize'' a big fraction of the training dataset. We show that for every learning algorithm, there exists an auxiliary algorithm that does not memorize and which yields comparable generalization error for any data distribution. In part, this shows that memorization is not necessary for good generalization.

Andrea Montanari, Pierfrancesco Urbani

Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural networks via dynamical mean field theory, a well established technique of non-equilibrium statistical physics. We show that, for large network width $m$, and large number of samples per input dimension $n/d$, the training dynamics exhibits a separation of timescales which implies: $(i)$ The emergence of a slow time scale associated with the growth in Gaussian/Rademacher complexity of the network; $(ii)$ Inductive bias towards small complexity if the initialization has small enough complexity; $(iii)$ A dynamical decoupling between feature learning and overfitting regimes; $(iv)$ A non-monotone behavior of the test error, associated `feature unlearning' regime at large times.

Xiangyu Zhao, Peiyuan Zhang, Kexian Tang, Xiaorong Zhu, Hao Li, Wenhao Chai, Zicheng Zhang, Renqiu Xia, Guangtao Zhai, Junchi Yan 等

Large Multi-modality Models (LMMs) have made significant progress in visual understanding and generation, but they still face challenges in General Visual Editing, particularly in following complex instructions, preserving appearance consistency, and supporting flexible input formats. To study this gap, we introduce RISEBench, the first benchmark for evaluating Reasoning-Informed viSual Editing (RISE). RISEBench focuses on four key reasoning categories: Temporal, Causal, Spatial, and Logical Reasoning. We curate high-quality test cases for each category and propose an robust evaluation framework that assesses Instruction Reasoning, Appearance Consistency, and Visual Plausibility with both human judges and the LMM-as-a-judge approach. We conducted experiments evaluating nine prominent visual editing models, comprising both open-source and proprietary models. The evaluation results demonstrate that current models face significant challenges in reasoning-based editing tasks. Even the most powerful model evaluated, GPT-image-1, achieves an accuracy of merely 28.8%. RISEBench effectively highlights the limitations of contemporary editing models, provides valuable insights, and indicates potential future directions for the field of reasoning-aware visual editing. Our code and data have been released at https://github.com/PhoenixZ810/RISEBench.

Liwei Jiang, Yuanjun Chai, Margaret Li, Mickel Liu, Raymond Fok, Nouha Dziri, Yulia Tsvetkov, Maarten Sap, Yejin Choi

Large language models (LMs) often struggle to generate diverse, human-like creative content, raising concerns about the long-term homogenization of human thought through repeated exposure to similar outputs. Yet scalable methods for evaluating LM output diversity remain limited, especially beyond narrow tasks such as random number or name generation, or beyond repeated sampling from a single model. To address this gap, we introduce Infinity-Chat, a large-scale dataset of 26K diverse, real-world, open-ended user queries that admit a wide range of plausible answers with no single ground truth. We introduce the first comprehensive taxonomy for characterizing the full spectrum of open-ended prompts posed to LMs, comprising 6 top-level categories (e.g., creative content generation, brainstorm & ideation) that further breaks down to 17 subcategories. Using Infinity-Chat, we present a large-scale study of mode collapse in LMs, revealing a pronounced Artificial Hivemind effect in open-ended generation of LMs, characterized by (1) intra-model repetition, where a single model consistently generates similar responses, and more so (2) inter-model homogeneity, where different models produce strikingly similar outputs. Infinity-Chat also includes 31,250 human annotations, across absolute ratings and pairwise preferences, with 25 independent human annotations per example. This enables studying collective and individual-specific human preferences in response to open-ended queries. Our findings show that state-of-the-art LMs, reward models, and LM judges are less well calibrated to human ratings on model generations that elicit differing idiosyncratic annotator preferences, despite maintaining comparable overall quality. Overall, INFINITY-CHAT presents the first large-scale resource for systematically studying real-world open-ended queries to LMs, revealing critical insights to guide future research for mitigating long-term AI safety risks posed by the Artificial Hivemind.

Computer Vision · Everything Else

Zhenhao Zhang, Ye Shi, Lingxiao Yang, Suting Ni, Qi Ye, Jingya Wang

Understanding and synthesizing realistic 3D hand-object interactions (HOI) is critical for applications ranging from immersive AR/VR to dexterous robotics. Existing methods struggle with generalization, performing well on closed-set objects and predefined tasks but failing to handle unseen objects or open-vocabulary instructions. We introduce OpenHOI, the first framework for open-world HOI synthesis, capable of generating long-horizon manipulation sequences for novel objects guided by free-form language commands. Our approach integrates a 3D Multimodal Large Language Model (MLLM) fine-tuned for joint affordance grounding and semantic task decomposition, enabling precise localization of interaction regions (e.g., handles, buttons) and breakdown of complex instructions (e.g., “Find a water bottle and take a sip”) into executable sub-tasks. To synthesize physically plausible interactions, we propose an affordance-driven diffusion model paired with a training-free physics refinement stage that minimizes penetration and optimizes affordance alignment. Evaluations across diverse scenarios demonstrate OpenHOI’s superiority over state-of-the-art methods in generalizing to novel object categories, multi-stage tasks, and complex language instructions.

Applications · Language, Speech and Dialog

Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Yang Yue, Shiji Song, Gao Huang

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning performance of large language models (LLMs), particularly in mathematics and programming tasks. It is widely believed that, similar to how traditional RL helps agents to explore and learn new strategies, RLVR enables LLMs to continuously self-improve, thus acquiring novel reasoning abilities that exceed the capacity of the corresponding base models. In this study, we take a critical look at \textit{the current state of RLVR} by systematically probing the reasoning capability boundaries of RLVR-trained LLMs across diverse model families, RL algorithms, and math/coding/visual reasoning benchmarks, using pass@\textit{k} at large \textit{k} values as the evaluation metric. While RLVR improves sampling efficiency towards the correct path, we surprisingly find that current training does \emph{not} elicit fundamentally new reasoning patterns. We observe that while RLVR-trained models outperform their base models at smaller values of $k$ (\eg, $k$=1), base models achieve higher pass@$k$ score when $k$ is large. Moreover, we observe that the reasoning capability boundary of LLMs often narrows as RLVR training progresses. Further coverage and perplexity analysis shows that the reasoning paths generated by RLVR models are already included in the base models' sampling distribution, suggesting that their reasoning abilities originate from and are \textit{bounded} by the base model. From this perspective, treating the base model as an upper bound, our quantitative analysis shows that six popular RLVR algorithms perform similarly and remain far from optimal in fully leveraging the potential of the base model. In contrast, we find that distillation can introduce new reasoning patterns from the teacher and genuinely expand the model’s reasoning capabilities. Taken together, our findings suggest that current RLVR methods have not fully realized the potential of RL to elicit genuinely novel reasoning abilities in LLMs. This underscores the need for improved RL paradigms—such as continual scaling and multi-turn agent-environment interaction—to unlock this potential.

Matthew T Jackson, Uljad Berdica, Jarek Liesen, Shimon Whiteson, Jakob Foerster

Progress in offline reinforcement learning (RL) has been impeded by ambiguous problem definitions and entangled algorithmic designs, resulting in inconsistent implementations, insufficient ablations, and unfair evaluations. Although offline RL explicitly avoids environment interaction, prior methods frequently employ extensive, undocumented online evaluation for hyperparameter tuning, complicating method comparisons. Moreover, existing reference implementations differ significantly in boilerplate code, obscuring their core algorithmic contributions. We address these challenges by first introducing a rigorous taxonomy and a transparent evaluation protocol that explicitly quantifies online tuning budgets. To resolve opaque algorithmic design, we provide clean, minimalistic, single-file implementations of various model-free and model-based offline RL methods, significantly enhancing clarity and achieving substantial speed-ups. Leveraging these streamlined implementations, we propose Unifloral, a unified algorithm that encapsulates diverse prior approaches and enables development within a single, comprehensive hyperparameter space. Using Unifloral with our rigorous evaluation protocol, we develop two novel algorithms - TD3-AWR (model-free) and MoBRAC (model-based) - which substantially outperform established baselines. Our implementation is publicly available at https://github.com/EmptyJackson/unifloral.

Zhenting Qi, Fan Nie, Alexandre Alahi, James Zou, Himabindu Lakkaraju, Yilun Du, Eric Xing, Sham Kakade, Hanlin Zhang

Modern language model (LM) training has been divided into multiple stages, making it difficult for downstream developers to evaluate the impact of design choices made at each stage. We present EvoLM, a model suite that enables systematic and transparent analysis of LMs' training dynamics across pre-training, continued pre-training, supervised fine-tuning, and reinforcement learning. By training over 100 LMs with 1B and 4B parameters from scratch, we rigorously evaluate both upstream (language modeling) and downstream (problem-solving) reasoning capabilities, including considerations of both in-domain and out-of-domain generalization. Key insights highlight the diminishing returns from excessive pre-training and post-training, the importance and practices of mitigating forgetting during domain-specific continued pre-training, the crucial role of continued pre-training in bridging pre-training and post-training phases, and various intricate trade-offs when configuring supervised fine-tuning and reinforcement learning. To facilitate open research and reproducibility, we release all pre-trained and post-trained models, training datasets for all stages, and our entire training and evaluation pipeline.

Tony Bonnaire, Raphaël Urfin, Giulio Biroli, Marc Mezard

Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we investigate the role of the training dynamics in the transition from generalization to memorization. Through extensive experiments and theoretical analysis, we identify two distinct timescales: an early time $\tau_\mathrm{gen}$ at which models begin to generate high-quality samples, and a later time $\tau_\mathrm{mem}$ beyond which memorization emerges. Crucially, we find that $\tau_\mathrm{mem}$ increases linearly with the training set size $n$, while $\tau_\mathrm{gen}$ remains constant. This creates a growing window of training times with $n$ where models generalize effectively, despite showing strong memorization if training continues beyond it. It is only when $n$ becomes larger than a model-dependent threshold that overfitting disappears at infinite training times. These findings reveal a form of implicit dynamical regularization in the training dynamics, which allow to avoid memorization even in highly overparameterized settings. Our results are supported by numerical experiments with standard U-Net architectures on realistic and synthetic datasets, and by a theoretical analysis using a tractable random features model studied in the high-dimensional limit.

Keshigeyan Chandrasegaran, Michael Poli, Dan Fu, Dongjun Kim, Lea M. Hadzic, Manling Li, Agrim Gupta, Stefano Massaroli, Azalia Mirhoseini, Juan Carlos Niebles 等

Designing model architectures requires decisions such as selecting operators (e.g., attention, convolution) and configurations (e.g., depth, width). However, evaluating the impact of these decisions on model quality requires costly pretraining, limiting architectural investigation. Inspired by how new software is built on existing code, we ask: can new architecture designs be studied using pretrained models? To this end, we present *grafting*, a simple approach for editing pretrained diffusion transformers (DiTs) to materialize new architectures under small compute budgets. Informed by our analysis of activation behavior and attention locality, we construct a testbed based on the DiT-XL/2 design to study the impact of grafting on model quality. Using this testbed, we develop a family of hybrid designs via grafting: replacing softmax attention with gated convolution, local attention, and linear attention, and replacing MLPs with variable expansion ratio and convolutional variants. Notably, many hybrid designs achieve good quality (FID: 2.38–2.64 vs. 2.27 for DiT-XL/2) using $<2$% pretraining compute. We then graft a text-to-image model (PixArt-$\Sigma$), achieving a 1.43$\times$ speedup with less than a 2% drop in GenEval score. Finally, we present a case study that restructures DiT-XL/2 by converting every pair of sequential transformer blocks into parallel blocks via grafting. This reduces model depth by 2$\times$ and yields better quality (FID: 2.77) than other models of comparable depth. Together, we show that new diffusion model designs can be explored by grafting pretrained DiTs, with edits ranging from operator replacement to architecture restructuring. Code and grafted models: https://grafting.stanford.edu.

Zachary Chase, Steve Hanneke, Shay Moran, Jonathan Shafer

We resolve a 30-year-old open problem concerning the power of unlabeled data in online learning by tightly quantifying the gap between transductive and standard online learning. We prove that for every concept class $\mathcal{H}$ with Littlestone dimension $d$, the transductive mistake bound is at least $\Omega(\sqrt{d})$. This establishes an exponential improvement over previous lower bounds of $\Omega(\log \log d)$, $\Omega(\sqrt{\log d})$, and $\Omega(\log d)$, respectively due to Ben-David, Kushilevitz, and Mansour (1995, 1997) and Hanneke, Moran, and Shafer (2023). We also show that our bound is tight: for every $d$, there exists a class of Littlestone dimension $d$ with transductive mistake bound $O(\sqrt{d})$. Our upper bound also improves the previous best known upper bound of $(2/3) \cdot d$ from Ben-David et al. (1997). These results demonstrate a quadratic gap between transductive and standard online learning, thereby highlighting the benefit of advanced access to the unlabeled instance sequence. This stands in stark contrast to the PAC setting, where transductive and standard learning exhibit similar sample complexities.

Zelin Peng, Zhengqin Xu, Qingyang Liu, Xiaokang Yang, Wei Shen

Multi-modal large language models (MLLMs) have emerged as a transformative approach for aligning visual and textual understanding. They typically require extremely high computational resources (e.g., thousands of GPUs) for training to achieve cross-modal alignment at multi-granularity levels. We argue that a key source of this inefficiency lies in the vision encoders they widely equip with, e.g., CLIP and SAM, which lack the alignment with language at multi-granularity levels. To address this issue, in this paper, we leverage hyperbolic space, which inherently models hierarchical levels and thus provides a principled framework for bridging the granularity gap between visual and textual modalities at an arbitrary granularity level. Concretely, we propose an efficient training paradigm for MLLMs, dubbed as \blg, which can optimize visual representations to align with their textual counterparts at an arbitrary granularity level through dynamic hyperbolic radius adjustment in hyperbolic space. \alg employs learnable matrices with M\"{o}bius multiplication operations, implemented via three effective configurations: diagonal scaling matrices, block-diagonal matrices, and banded matrices, providing a flexible yet efficient parametrization strategy. Comprehensive experiments across multiple MLLM benchmarks demonstrate that \alg consistently improves both existing pre-training and fine-tuning MLLMs clearly with less than 1\% additional parameters.

Zhongnan Cai, Yingying Wang, Hui Zheng, Panwang Pan, Zixu Lin, Ge Meng, Chenxin Li, Chunming He, Jiaxin Xie, Yunlong Lin 等

Recently, deep learning-based pan-sharpening algorithms have achieved notable advancements over traditional methods. However, deep learning-based methods incur substantial computational overhead during inference, especially with large images. This excessive computational demand limits the applicability of these methods in real-world scenarios, particularly in the absence of dedicated computing devices such as GPUs and TPUs. To address these challenges, we propose Pan-LUT, a novel learnable look-up table (LUT) framework for pan-sharpening that strikes a balance between performance and computational efficiency for large remote sensing images. Our method makes it possible to process 15K$\times$15K remote sensing images on a 24GB GPU. To finely control the spectral transformation, we devise the PAN-guided look-up table (PGLUT) for channel-wise spectral mapping. To effectively capture fine-grained spatial details, we introduce the spatial details look-up table (SDLUT). Furthermore, to adaptively aggregate channel information for generating high-resolution multispectral images, we design an adaptive output look-up table (AOLUT). Our model contains fewer than 700K parameters and processes a 9K$\times$9K image in under 1 ms using one RTX 2080 Ti GPU, demonstrating significantly faster performance compared to other methods. Experiments reveal that Pan-LUT efficiently processes large remote sensing images in a lightweight manner, bridging the gap to real-world applications. Furthermore, our model surpasses SOTA methods in full-resolution scenes under real-world conditions, highlighting its effectiveness and efficiency.

Jiayi Yuan, Hao Li, Xinheng Ding, Wenya Xie, Yu-Jhe Li, Wentian Zhao, Kun Wan, Jing Shi, Xia Hu, Zirui Liu

Large Language Models (LLMs) are now integral across various domains and have demonstrated impressive performance. Progress, however, rests on the premise that benchmark scores are both accurate and reproducible. We demonstrate that the reproducibility of LLM performance is fragile: changing system configuration, such as evaluation batch size, GPU count, and GPU version, can introduce significant differences in the generated responses. This issue is especially pronounced in reasoning models, where minor rounding differences in early tokens can cascade into divergent chains of thought, ultimately affecting accuracy. For instance, under bfloat16 precision with greedy decoding, a reasoning model like DeepSeek-R1-Distill-Qwen-7B can exhibit up to 9\% variation in accuracy and 9,000 tokens difference in response length due to differences in GPU count, type, and evaluation batch size. We trace the root cause of this variability to the non-associative nature of floating-point arithmetic under limited numerical precision. This work presents the first systematic investigation into how numerical precision affects reproducibility in LLM inference. Through carefully controlled experiments across various hardware, software, and precision settings, we quantify when and how model outputs diverge. Our analysis reveals that floating-point precision—while critical for reproducibility—is often neglected in evaluation practices. Inspired by this, we develop a lightweight inference pipeline, dubbed LayerCast, that stores weights in 16-bit precision but performs all computations in FP32, balancing memory efficiency with numerical stability. Code is available at https://github.com/nanomaoli/llm_reproducibility.

David Chanin, James Wilken-Smith, Tomáš Dulka, Hardik Bhatnagar, Satvik Golechha, Joseph Bloom

Sparse Autoencoders (SAEs) aim to decompose the activation space of large language models (LLMs) into human-interpretable latent directions or features. As we increase the number of features in the SAE, hierarchical features tend to split into finer features (“math” may split into “algebra”, “geometry”, etc.), a phenomenon referred to as feature splitting. However, we show that sparse decomposition and splitting of hierarchical features is not robust. Specifically, we show that seemingly monosemantic features fail to fire where they should, and instead get “absorbed” into their children features. We coin this phenomenon feature absorption, and show that it is caused by optimizing for sparsity in SAEs whenever the underlying features form a hierarchy. We introduce a metric to detect absorption in SAEs, and validate our findings empirically on hundreds of LLM SAEs. Our investigation suggests that varying SAE sizes or sparsity is insufficient to solve this issue. We discuss the implications of feature absorption in SAEs and some potential approaches to solve the fundamental theoretical issues before SAEs can be used for interpreting LLMs robustly and at scale.

Reinforcement Learning · Deep RL

Felix Chalumeau, Daniel Rajaonarivonivelomanantsoa, Ruan John de Kock, Juan Formanek, Sasha Abramowitz, Omayma Mahjoub, Wiem Khlifi, Simon Du Toit, Louay Nessir, Refiloe Shabe 等

Reinforcement learning (RL) systems have countless applications, from energy-grid management to protein design. However, such real-world scenarios are often extremely difficult, combinatorial in nature, and require complex coordination between multiple agents. This level of complexity can cause even state-of-the-art RL systems, trained until convergence, to hit a performance ceiling which they are unable to break out of with zero-shot inference. Meanwhile, many digital or simulation-based applications allow for an inference phase that utilises a specific time and compute budget to explore multiple attempts before outputting a final solution. In this work, we show that such an inference phase employed at execution time, and the choice of a corresponding inference strategy, are key to breaking the performance ceiling observed in complex multi-agent RL problems. Our main result is striking: we can obtain up to a 126% and, on average, a 45% improvement over the previous state-of-the-art across 17 tasks, using only a couple seconds of extra wall-clock time during execution. We also demonstrate promising compute scaling properties, supported by over 60k experiments, making it the largest study on inference strategies for complex RL to date. We make all of our experimental data and code available.

Deep Learning · Attention Mechanisms

Giuseppe Bruno, Federico Pasqualotto, Andrea Agazzi

In this paper, we study the evolution of tokens through the depth of encoder-only transformer models at inference time by modeling them as a system of particles interacting in a mean-field way and studying the corresponding dynamics. More specifically, we consider this problem in the moderate interaction regime, where the number $N$ of tokens is large and the inverse temperature parameter $\beta$ of the model scales together with $N$. In this regime, the dynamics of the system displays a multiscale behavior: a fast phase, where the token empirical measure collapses on a low-dimensional space, an intermediate phase, where the measure further collapses into clusters, and a slow one, where such clusters sequentially merge into a single one. We provide a rigorous characterization of the limiting dynamics in each of these phases and prove convergence in the above mentioned limit, exemplifying our results with some simulations.

Qiusheng Huang, Yuan Niu, Xiaohui Zhong, AnboyuGuo, Lei Chen, dianjun zhang, Xuefeng Zhang, Hao Li

Accurate, high-resolution ocean forecasting is crucial for maritime operations and environmental monitoring. While traditional numerical models are capable of producing sub-daily, eddy-resolving forecasts, they are computationally intensive and face challenges in maintaining accuracy at fine spatial and temporal scales. In contrast, recent data-driven approaches offer improved computational efficiency and emerging potential, yet typically operate at daily resolution and struggle with sub-daily predictions due to error accumulation over time. We introduce FuXi-Ocean, the first data-driven global ocean forecasting model achieving six-hourly predictions at eddy-resolving 1/12° spatial resolution, reaching depths of up to 1500 meters. The model architecture integrates a context-aware feature extraction module with a predictive network employing stacked attention blocks. The core innovation is the Mixture-of-Time (MoT) module, which adaptively integrates predictions from multiple temporal contexts by learning variable-specific reliability , mitigating cumulative errors in sequential forecasting. Through comprehensive experimental evaluation, FuXi-Ocean demonstrates superior skill in predicting key variables, including temperature, salinity, and currents, across multiple depths.

Zhaoxian Wu, Quan Xiao, Tayfun Gokmen, Omobayode Fagbohungbe, Tianyi Chen

As the economic and environmental costs of training and deploying large vision or language models increase dramatically, analog in-memory computing (AIMC) emerges as a promising energy-efficient solution. However, the training perspective, especially its training dynamic, is underexplored. In AIMC hardware, the trainable weights are represented by the conductance of resistive elements and updated using consecutive electrical pulses. While the conductance changes by a constant in response to each pulse, in reality, the change is scaled by asymmetric and non-linear response functions, leading to a non-ideal training dynamic. This paper provides a theoretical foundation for gradient-based training on AIMC hardware with non-ideal response functions. We demonstrate that asymmetric response functions negatively impact Analog SGD by imposing an implicit penalty on the objective. To overcome the issue, we propose residual learning algorithm, which provably converges exactly to a critical point by solving a bilevel optimization problem. We show that the proposed method can be extended to deal with other hardware imperfections like limited response granularity. As far as we know, it is the first paper to investigate the impact of a class of generic non-ideal response functions. The conclusion is supported by simulations validating our theoretical insights.

Computer Vision · Vision Models & Multimodal

Linfeng Tang, Yeda Wang, Zhanchuan Cai, Junjun Jiang, Jiayi Ma

Current image fusion methods struggle with real-world composite degradations and lack the flexibility to accommodate user-specific needs. To address this, we propose ControlFusion, a controllable fusion network guided by language-vision prompts that adaptively mitigates composite degradations. On the one hand, we construct a degraded imaging model based on physical mechanisms, such as the Retinex theory and atmospheric scattering principle, to simulate composite degradations and provide a data foundation for addressing realistic degradations. On the other hand, we devise a prompt-modulated restoration and fusion network that dynamically enhances features according to degradation prompts, enabling adaptability to varying degradation levels. To support user-specific preferences in visual quality, a text encoder is incorporated to embed user-defined degradation types and levels as degradation prompts. Moreover, a spatial-frequency collaborative visual adapter is designed to autonomously perceive degradations from source images, thereby reducing complete reliance on user instructions. Extensive experiments demonstrate that ControlFusion outperforms SOTA fusion methods in fusion quality and degradation handling, particularly under real-world and compound degradations.