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Deep model merging represents an emerging research direction that combines multiple fine-tuned models to harness their specialized capabilities across different tasks and domains. Current model merging techniques focus on merging all available models simultaneously, with weight interpolation-based methods being the predominant approaches. However, these conventional approaches are not well-suited for scenarios where models become available sequentially, and they often suffer from high memory requirements and potential interference between tasks. In this study, we propose a training-free projection-based continual merging method that processes models sequentially through orthogonal projections of weight matrices and adaptive scaling mechanisms. Our method operates by projecting new parameter updates onto subspaces orthogonal to existing merged parameter updates while using an adaptive scaling mechanism to maintain stable parameter distances, enabling efficient sequential integration of task-specific knowledge. Our approach maintains constant memory complexity to the number of models, minimizes interference between tasks through orthogonal projections, and retains the performance of previously merged models through adaptive task vector scaling. Extensive experiments on CLIP-ViT models demonstrate that our method achieves a 5-8% average accuracy improvement while maintaining robust performance in different task orderings.

Automated code generation using large language models (LLMs) has gained attention due to its efficiency and adaptability. However, real-world coding tasks or benchmarks like HumanEval and StudentEval often lack dedicated training datasets, challenging existing few-shot prompting approaches that rely on reference examples. Inspired by human metamemory-a cognitive process involving recall and evaluation-we present a novel framework (namely M^2WF) for improving LLMs' one-time code generation. This approach enables LLMs to autonomously generate, evaluate, and utilize synthetic examples to enhance reliability and performance. Unlike prior methods, it minimizes dependency on curated data and adapts flexibly to various coding scenarios. Our experiments demonstrate significant improvements in coding benchmarks, offering a scalable and robust solution for data-free environments. The code and framework will be publicly available on GitHub and HuggingFace., Comment: 11 pages,6 figures

Transformer has been extensively explored for hyperspectral image (HSI) classification. However, transformer poses challenges in terms of speed and memory usage because of its quadratic computational complexity. Recently, the Mamba model has emerged as a promising approach, which has strong long-distance modeling capabilities while maintaining a linear computational complexity. However, representing the HSI is challenging for the Mamba due to the requirement for an integrated spatial and spectral understanding. To remedy these drawbacks, we propose a novel HSI classification model based on a Mamba model, named MambaHSI, which can simultaneously model long-range interaction of the whole image and integrate spatial and spectral information in an adaptive manner. Specifically, we design a spatial Mamba block (SpaMB) to model the long-range interaction of the whole image at the pixel-level. Then, we propose a spectral Mamba block (SpeMB) to split the spectral vector into multiple groups, mine the relations across different spectral groups, and extract spectral features. Finally, we propose a spatial-spectral fusion module (SSFM) to adaptively integrate spatial and spectral features of a HSI. To our best knowledge, this is the first image-level HSI classification model based on the Mamba. We conduct extensive experiments on four diverse HSI datasets. The results demonstrate the effectiveness and superiority of the proposed model for HSI classification. This reveals the great potential of Mamba to be the next-generation backbone for HSI models. Codes are available at https://github.com/li-yapeng/MambaHSI ., Comment: accepted by IEEE TGRS

Based on the seminal Simons' formula, Shen \cite{Shen} and Lin-Xia \cite{LX} obtained gap theorems for compact minimal submanifolds in the unit sphere in the late 1980's. Then due to the effect of Xu \cite{Xu}, Ni \cite{Ni}, Yun \cite{Yun} and Xu-Gu \cite{XuG}, we achieved a comprehensive understanding of gap phenomena of complete submanifolds with parallel mean curvature vector field in the sphere or in the Euclidean space. But such kind of results in case of the hyperbolic space were obtained by Wang-Xia \cite{XiaW}, Lin-Wang \cite{LW} and Xu-Xu \cite{XX} until relatively recently and are not quite complete so far. In this paper first we continue to study gap theorems for complete submanifolds with parallel mean curvature vector field in the hyperbolic space, which generalize or extend several results in the literature. Second we prove a gap theorem for complete hypersurfaces with constant scalar curvature $n(1-n)$ in the hyperbolic space, which extends related results due to Bai-Luo \cite{BL2} in cases of the Euclidean space and the unit sphere. Such kind of results in case of the hyperbolic space are more complicated, due to some extra bad terms in the Simons' formula, and one of main ingredients of our proofs is an estimate for the first eigenvalue of complete submanifolds in the hyperbolic space obtained by Lin \cite{Lin}., Comment: All comments are welcome! 17 pages

In this paper we study eigenvalues of the Dirichlet Laplacian on conformally flat Riemannian manifolds. In particular we establish some universal inequality for eigenvalues of the Dirichlet Laplacian on the hyperbolic space $\mathbb{H}^n(-1)$., Comment: Submitted, 21 pages

In this paper we study eigenvalues of Laplacian and biharmonic operators on compact domains in complete manifolds. We establish several new inequalities for eigenvalues of Laplacian and biharmonic operators respectively by using Sobolev type inequalities., Comment: Accepted by Jounral of Mathematical Study, 16 pages

In this paper, we will prove some rigidity theorems for blow up limits to Type II singularities of Lagrangian mean curvature flow with zero Maslov class or almost calibrated Lagrangian mean curvature flows, especially for Lagrangian translating solitons in any dimension. These theorems generalized previous corresponding results from two dimensional case to arbitrarily dimensional case., Comment: All comments are welcome! 16 pages

Aligning diffusion models with downstream objectives is essential for their practical applications. However, standard alignment methods often struggle with step generalization when directly applied to few-step diffusion models, leading to inconsistent performance across different denoising step scenarios. To address this, we introduce Stepwise Diffusion Policy Optimization (SDPO), a novel alignment method tailored for few-step diffusion models. Unlike prior approaches that rely on a single sparse reward from only the final step of each denoising trajectory for trajectory-level optimization, SDPO incorporates dense reward feedback at every intermediate step. By learning the differences in dense rewards between paired samples, SDPO facilitates stepwise optimization of few-step diffusion models, ensuring consistent alignment across all denoising steps. To promote stable and efficient training, SDPO introduces an online reinforcement learning framework featuring several novel strategies designed to effectively exploit the stepwise granularity of dense rewards. Experimental results demonstrate that SDPO consistently outperforms prior methods in reward-based alignment across diverse step configurations, underscoring its robust step generalization capabilities. Code is avaliable at https://github.com/ZiyiZhang27/sdpo.

We study the following one-dimensional cubic nonlinear Schr\"{o}dinger system: \[ u_i''+2\Big(\sum_{k=1}^Nu_k^2\Big)u_i=-\mu_iu_i \ \,\ \mbox{in}\, \ \mathbb{R} , \ \ i=1, 2, \cdots, N, \] where $\mu_1\leq\mu_2\leq\cdots\leq\mu_N<0$ and $N\ge 2$. In this paper, we mainly focus on the case $N=3$ and prove the following results: (i). The solutions of the system can be completely classified; (ii). Depending on the explicit values of $\mu_1\leq\mu_2\leq\mu_3<0$, there exist two different classes of normalized solutions $u=(u_1, u_2, u_3)$ satisfying $\int _{R}u_i^2dx=1$ for all $i=1, 2, 3$, which are completely different from the case $N=2$; (iii). The linearized operator at any nontrivial solution of the system is non-degenerate. The conjectures on the explicit classification and nondegeneracy of solutions for the system are also given for the case $N>3$. These address the questions of [R. Frank, D. Gontier and M. Lewin, CMP, 2021], where the complete classification and uniqueness results for the system were already proved for the case $N=2$., Comment: 40 pages, 1 figure

Multi-task learning (MTL) leverages a shared model to accomplish multiple tasks and facilitate knowledge transfer. Recent research on task arithmetic-based MTL demonstrates that merging the parameters of independently fine-tuned models can effectively achieve MTL. However, existing merging methods primarily seek a static optimal solution within the original model parameter space, which often results in performance degradation due to the inherent diversity among tasks and potential interferences. To address this challenge, in this paper, we propose a Weight-Ensembling Mixture of Experts (WEMoE) method for multi-task model merging. Specifically, we first identify critical (or sensitive) modules by analyzing parameter variations in core modules of Transformer-based models before and after finetuning. Then, our WEMoE statically merges non-critical modules while transforming critical modules into a mixture-of-experts (MoE) structure. During inference, expert modules in the MoE are dynamically merged based on input samples, enabling a more flexible and adaptive merging approach. Building on WEMoE, we further introduce an efficient-and-effective WEMoE (E-WEMoE) method, whose core mechanism involves eliminating non-essential elements in the critical modules of WEMoE and implementing shared routing across multiple MoE modules, thereby significantly reducing both the trainable parameters, the overall parameter count, and computational overhead of the merged model by WEMoE. Experimental results across various architectures and tasks demonstrate that both WEMoE and E-WEMoE outperform state-of-the-art (SOTA) model merging methods in terms of MTL performance, generalization, and robustness.

Recent advancements in multimodal fusion have witnessed the remarkable success of vision-language (VL) models, which excel in various multimodal applications such as image captioning and visual question answering. However, building VL models requires substantial hardware resources, where efficiency is restricted by two key factors: the extended input sequence of the language model with vision features demands more computational operations, and a large number of additional learnable parameters increase memory complexity. These challenges significantly restrict the broader applicability of such models. To bridge this gap, we propose ADEM-VL, an efficient vision-language method that tunes VL models based on pretrained large language models (LLMs) by adopting a parameter-free cross-attention mechanism for similarity measurements in multimodal fusion. This approach only requires embedding vision features into the language space, significantly reducing the number of trainable parameters and accelerating both training and inference speeds. To enhance representation learning in fusion module, we introduce an efficient multiscale feature generation scheme that requires only a single forward pass through the vision encoder. Moreover, we propose an adaptive fusion scheme that dynamically discards less relevant visual information for each text token based on its attention score. This ensures that the fusion process prioritizes the most pertinent visual features. With experiments on various tasks including visual question answering, image captioning, and instruction-following, we demonstrate that our framework outperforms existing approaches. Specifically, our method surpasses existing methods by an average accuracy of 0.77% on ScienceQA dataset, with reduced training and inference latency, demonstrating the superiority of our framework. The code is available at https://github.com/Hao840/ADEM-VL.

Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling combinatorial optimization challenges. However, their practical realization confronts a dilemma: the requisite circuit depth for satisfactory performance is problem-specific and often exceeds the maximum capability of current quantum devices. To address this dilemma, here we first analyze the convergence behavior of QAOA, uncovering the origins of this dilemma and elucidating the intricate relationship between the employed mixer Hamiltonian, the specific problem at hand, and the permissible maximum circuit depth. Harnessing this understanding, we introduce the Mixer Generator Network (MG-Net), a unified deep learning framework adept at dynamically formulating optimal mixer Hamiltonians tailored to distinct tasks and circuit depths. Systematic simulations, encompassing Ising models and weighted Max-Cut instances with up to 64 qubits, substantiate our theoretical findings, highlighting MG-Net's superior performance in terms of both approximation ratio and efficiency., Comment: 29 pages, 16 figures

Incremental learning is nontrivial due to severe catastrophic forgetting. Although storing a small amount of data on old tasks during incremental learning is a feasible solution, current strategies still do not 1) adequately address the class bias problem, and 2) alleviate the mutual interference between new and old tasks, and 3) consider the problem of class bias within tasks. This motivates us to propose a joint input and output coordination (JIOC) mechanism to address these issues. This mechanism assigns different weights to different categories of data according to the gradient of the output score, and uses knowledge distillation (KD) to reduce the mutual interference between the outputs of old and new tasks. The proposed mechanism is general and flexible, and can be incorporated into different incremental learning approaches that use memory storage. Extensive experiments show that our mechanism can significantly improve their performance., Comment: 11 pages, 4 figues. Accepted by IJCAI 2024

Large language models (LLMs) have shown remarkable capabilities in code generation. However, the effects of hallucinations (e.g., output noise) make it particularly challenging for LLMs to generate high-quality code in one pass. In this work, we propose a simple and effective \textbf{u}ncertainty-aware \textbf{s}elective \textbf{c}ontrastive \textbf{d}ecoding ($\mathbb{USCD}$) mechanism to improve the quality of one-pass code generation in LLMs and reduce the impact of output noise. To be specific, we first elaborately designed a negative prompt (namely lame prompt) to output noise by removing input-output examples from the standard few-shot prompt. Our preliminary study shows that the Jensen-Shannon divergence (JS divergence) between token distribution uncertainty and the output noise is relatively low (approximately $0.25$), indicating their high relevance. Then, we selectively eliminate output noise induced by lame prompts based on the uncertainty of the prediction distribution from the standard prompt. Notably, our proposed plug-and-play mechanism is an inference-only method, enjoying appealing flexibility. Extensive experiments on widely used benchmarks, e.g., HumanEval, MBPP, and MultiPL-E, upon several LLMs (i.e., Inocder-6b, CodeLlama-7b, WizardCoder-15b, StarCoder, and Llama2-7b), demonstrate that our proposed USCD significantly improves one-pass code generation, with an average \textit{pass@$1$} scores increase of 16.59\%. We will release code and data on GitHub., Comment: 13pages,8 figures

Multimodal large language models (MLLMs) have experienced significant advancements recently, but still struggle to recognize and interpret intricate details in high-resolution (HR) images effectively. While state-of-the-art (SOTA) MLLMs claim to process images at 4K resolution, existing MLLM benchmarks only support up to 2K, leaving the capabilities of SOTA models on true HR images largely untested. Furthermore, existing methods for enhancing HR image perception in MLLMs rely on computationally expensive visual instruction tuning. To address these limitations, we introduce HR-Bench, the first deliberately designed benchmark to rigorously evaluate MLLM performance on 4K&8K images. Through extensive experiments, we demonstrate that while downsampling HR images leads to vision information loss, leveraging complementary modalities, e.g., text, can effectively compensate for this loss. Building upon this insight, we propose Divide, Conquer and Combine (DC$^2$), a novel training-free framework for enhancing MLLM perception of HR images. DC$^2$ follows a three-staged approach: 1) Divide: recursively partitioning the HR image into patches and merging similar patches to minimize computational overhead, 2) Conquer: leveraging the MLLM to generate accurate textual descriptions for each image patch, and 3) Combine: utilizing the generated text descriptions to enhance the MLLM's understanding of the overall HR image. Extensive experiments show that: 1) the SOTA MLLM achieves 63% accuracy, which is markedly lower than the 87% accuracy achieved by humans on HR-Bench; 2) our DC$^2$ brings consistent and significant improvements (a relative increase of +6% on HR-Bench and +8% on general multimodal benchmarks). The benchmark and code will be released to facilitate the multimodal R&D community.

Deep model training on extensive datasets is increasingly becoming cost-prohibitive, prompting the widespread adoption of deep model fusion techniques to leverage knowledge from pre-existing models. From simple weight averaging to more sophisticated methods like AdaMerging, model fusion effectively improves model performance and accelerates the development of new models. However, potential interference between parameters of individual models and the lack of interpretability in the fusion progress remain significant challenges. Existing methods often try to resolve the parameter interference issue by evaluating attributes of parameters, such as their magnitude or sign, or by parameter pruning. In this study, we begin by examining the fine-tuning of linear layers through the lens of subspace analysis and explicitly define parameter interference as an optimization problem to shed light on this subject. Subsequently, we introduce an innovative approach to model fusion called zero-shot Sparse MIxture of Low-rank Experts (SMILE) construction, which allows for the upscaling of source models into an MoE model without extra data or further training. Our approach relies on the observation that fine-tuning mostly keeps the important parts from the pre-training, but it uses less significant or unused areas to adapt to new tasks. Also, the issue of parameter interference, which is intrinsically intractable in the original parameter space, can be managed by expanding the dimensions. We conduct extensive experiments across diverse scenarios, such as image classification and text generation tasks, using full fine-tuning and LoRA fine-tuning, and we apply our method to large language models (CLIP models, Flan-T5 models, and Mistral-7B models), highlighting the adaptability and scalability of SMILE. Code is available at https://github.com/tanganke/fusion_bench, Comment: Code is available at https://github.com/tanganke/fusion_bench

In a real federated learning (FL) system, communication overhead for passing model parameters between the clients and the parameter server (PS) is often a bottleneck. Hierarchical federated learning (HFL) that poses multiple edge servers (ESs) between clients and the PS can partially alleviate communication pressure but still needs the aggregation of model parameters from multiple ESs at the PS. To further reduce communication overhead, we bring sequential FL (SFL) into HFL for the first time, which removes the central PS and enables the model training to be completed only through passing the global model between two adjacent ESs for each iteration, and propose a novel algorithm adaptive to such a combinational framework, referred to as Fed-CHS. Convergence results are derived for strongly convex and non-convex loss functions under various data heterogeneity setups, which show comparable convergence performance with the algorithms for HFL or SFL solely. Experimental results provide evidence of the superiority of our proposed Fed-CHS on both communication overhead saving and test accuracy over baseline methods.

Solving multi-objective optimization problems for large deep neural networks is a challenging task due to the complexity of the loss landscape and the expensive computational cost of training and evaluating models. Efficient Pareto front approximation of large models enables multi-objective optimization for various tasks such as multi-task learning and trade-off analysis. Existing algorithms for learning Pareto set, including (1) evolutionary, hypernetworks, and hypervolume-maximization methods, are computationally expensive and have restricted scalability to large models; (2) Scalarization algorithms, where a separate model is trained for each objective ray, which is inefficient for learning the entire Pareto set and fails to capture the objective trade-offs effectively. Inspired by the recent success of model merging, we propose a practical and scalable approach to Pareto set learning problem via mixture of experts (MoE) based model fusion. By ensembling the weights of specialized single-task models, the MoE module can effectively capture the trade-offs between multiple objectives and closely approximate the entire Pareto set of large neural networks. Once the routers are learned and a preference vector is set, the MoE module can be unloaded, thus no additional computational cost is introduced during inference. We conduct extensive experiments on vision and language tasks using large-scale models such as CLIP-ViT and GPT-2. The experimental results demonstrate that our method efficiently approximates the entire Pareto front of large models. Using only hundreds of trainable parameters of the MoE routers, our method even has lower memory usage compared to linear scalarization and algorithms that learn a single Pareto optimal solution, and are scalable to both the number of objectives and the size of the model., Comment: code is available at https://github.com/tanganke/pareto_set_learning

Deep model fusion is an emerging technique that unifies the predictions or parameters of several deep neural networks into a single model in a cost-effective and data-efficient manner. This enables the unified model to take advantage of the original models' strengths, potentially exceeding their performance. Although a variety of deep model fusion techniques have been introduced, their evaluations tend to be inconsistent and often inadequate to validate their effectiveness and robustness against distribution shifts. To address this issue, we introduce FusionBench, which is the first comprehensive benchmark dedicated to deep model fusion. FusionBench covers a wide range of tasks, including open-vocabulary image classification, text classification, and text-to-text generation. Each category includes up to eight tasks with corresponding task-specific models, featuring both full fine-tuning and LoRA fine-tuning, as well as models of different sizes, to ensure fair and balanced comparisons of various multi-task model fusion techniques across different tasks, model scales, and fine-tuning strategies. We implement and evaluate a broad spectrum of deep model fusion techniques. These techniques range from model ensemble methods, which combine the predictions to improve the overall performance, to model merging, which integrates different models into a single one, and model mixing methods, which upscale or recombine the components of the original models. FusionBench now contains 26 distinct tasks, 74 fine-tuned models, and 16 fusion techniques, and we are committed to consistently expanding the benchmark with more tasks, models, and fusion techniques. In addition, we offer a well-documented set of resources and guidelines to aid researchers in understanding and replicating the benchmark results. Homepage https://github.com/tanganke/fusion_bench, Comment: Project homepage: https://github.com/tanganke/fusion_bench

The No-Free-Lunch (NFL) theorem, which quantifies problem- and data-independent generalization errors regardless of the optimization process, provides a foundational framework for comprehending diverse learning protocols' potential. Despite its significance, the establishment of the NFL theorem for quantum machine learning models remains largely unexplored, thereby overlooking broader insights into the fundamental relationship between quantum and classical learning protocols. To address this gap, we categorize a diverse array of quantum learning algorithms into three learning protocols designed for learning quantum dynamics under a specified observable and establish their NFL theorem. The exploited protocols, namely Classical Learning Protocols (CLC-LPs), Restricted Quantum Learning Protocols (ReQu-LPs), and Quantum Learning Protocols (Qu-LPs), offer varying levels of access to quantum resources. Our derived NFL theorems demonstrate quadratic reductions in sample complexity across CLC-LPs, ReQu-LPs, and Qu-LPs, contingent upon the orthogonality of quantum states and the diagonality of observables. We attribute this performance discrepancy to the unique capacity of quantum-related learning protocols to indirectly utilize information concerning the global phases of non-orthogonal quantum states, a distinctive physical feature inherent in quantum mechanics. Our findings not only deepen our understanding of quantum learning protocols' capabilities but also provide practical insights for the development of advanced quantum learning algorithms.

Federated learning aims to collaboratively learn a model by using the data from multiple users under privacy constraints. In this paper, we study the multi-label classification problem under the federated learning setting, where trivial solution and extremely poor performance may be obtained, especially when only positive data w.r.t. a single class label are provided for each client. This issue can be addressed by adding a specially designed regularizer on the server-side. Although effective sometimes, the label correlations are simply ignored and thus sub-optimal performance may be obtained. Besides, it is expensive and unsafe to exchange user's private embeddings between server and clients frequently, especially when training model in the contrastive way. To remedy these drawbacks, we propose a novel and generic method termed Federated Averaging by exploring Label Correlations (FedALC). Specifically, FedALC estimates the label correlations in the class embedding learning for different label pairs and utilizes it to improve the model training. To further improve the safety and also reduce the communication overhead, we propose a variant to learn fixed class embedding for each client, so that the server and clients only need to exchange class embeddings once. Extensive experiments on multiple popular datasets demonstrate that our FedALC can significantly outperform existing counterparts., Comment: To be published in IEEE Transactions on Neural Networks and Learning Systems

Lip-reading is to utilize the visual information of the speaker's lip movements to recognize words and sentences. Existing event-based lip-reading solutions integrate different frame rate branches to learn spatio-temporal features of varying granularities. However, aggregating events into event frames inevitably leads to the loss of fine-grained temporal information within frames. To remedy this drawback, we propose a novel framework termed Multi-view Temporal Granularity aligned Aggregation (MTGA). Specifically, we first present a novel event representation method, namely time-segmented voxel graph list, where the most significant local voxels are temporally connected into a graph list. Then we design a spatio-temporal fusion module based on temporal granularity alignment, where the global spatial features extracted from event frames, together with the local relative spatial and temporal features contained in voxel graph list are effectively aligned and integrated. Finally, we design a temporal aggregation module that incorporates positional encoding, which enables the capture of local absolute spatial and global temporal information. Experiments demonstrate that our method outperforms both the event-based and video-based lip-reading counterparts.