Implicit neural representation (INR) models signals as continuous functions using neural networks, offering efficient and differentiable optimization for inverse problems across diverse disciplines. However, the representational capacity of INR—defined by the range of functions the neural network can characterize—is inherently limited by the low-dimensional feature space in conventional multilayer perceptron (MLP) architectures. While widening the MLP can linearly increase feature space dimensionality, it also leads to a quadratic growth in computational and memory costs. To address this limitation, we propose the split-layer, a novel reformulation of MLP construction. The split-layer divides each layer into multiple parallel branches and integrates their outputs via Hadamard product, effectively constructing a high-degree polynomial space. This approach significantly enhances INR’s representational capacity by expanding the feature space dimensionality without incurring prohibitive computational overhead. Extensive experiments demonstrate that the split-layer substantially improves INR performance, surpassing existing methods across multiple tasks, including 2D image fitting, 2D CT reconstruction, 3D shape representation, and 5D novel view synthesis.

Representing signals using coordinate networks dominates the area of inverse problems recently, and is widely applied in various scientific computing tasks. Still, there exists an issue of spectral bias in coordinate networks, limiting the capacity to learn high-frequency components. This problem is caused by the pathological distribution of the neural tangent kernel's (NTK's) eigenvalues of coordinate networks. We find that, this pathological distribution could be improved using classical normalization techniques (batch normalization and layer normalization), which are commonly used in convolutional neural networks but rarely used in coordinate networks. We prove that normalization techniques greatly reduces the maximum and variance of NTK's eigenvalues while slightly modifies the mean value, considering the max eigenvalue is much larger than the most, this variance change results in a shift of eigenvalues' distribution from a lower one to a higher one, therefore the spectral bias could be alleviated (see Fig. 1). Furthermore, we propose two new normalization techniques by combining these two techniques in different ways. The efficacy of these normalization techniques is substantiated by the significant improvements and new state-of-the-arts achieved by applying normalization-based coordinate networks to various tasks, including the image compression, computed tomography reconstruction, shape representation, magnetic resonance imaging, novel view synthesis and multi-view stereo reconstruction.

Large Language Models (LLMs), such as OpenAI’s o1 and DeepSeek’s R1, excel at advanced reasoning tasks like math and coding via Reinforcement Learning with Verifiable Rewards (RLVR), but still struggle with puzzles solvable by humans without domain knowledge. We introduce ENIGMATA, the first comprehensive suite tailored for improving LLMs with puzzle reasoning skills. It includes 36 tasks across 7 categories, each with: 1) a generator that produces unlimited examples with controllable difficulty, and 2) a rule-based verifier for automatic evaluation. This generator-verifier design supports scalable, multi-task RL training, fine-grained analysis, and seamless RLVR integration. We further propose ENIGMATA-Eval, a rigorous benchmark, and develop optimized multi-task RLVR strategies. Our trained model, Qwen2.5-32B-ENIGMATA, consistently surpasses o3-mini-high and o1 on the puzzle reasoning benchmarks like ENIGMATA-Eval, ARC-AGI (32.8%), and ARC-AGI 2 (0.6%). It also generalizes well to out-of-domain puzzle benchmarks and mathematical reasoning, with little multi-tasking trade-off. When trained on larger models like Seed1.5-Thinking (20B activated parameters and 200B total parameters), puzzle data from ENIGMATA further boosts SoTA performance on advanced math and STEM reasoning tasks such as AIME (2024-2025), BeyondAIME and GPQA (Diamond), showing nice generalization benefits of ENIGMATA. This work offers a unified, controllable framework for advancing logical reasoning in LLMs. Project page: https://seed-enigmata.github.io.

We propose reparameterized refocusing convolution (RefConv) as a replacement for regular convolutional layers, which is a plug-and-play module to improve the performance without any inference costs. Specifically, given a pretrained model, RefConv applies a trainable Refocusing Transformation to the basis kernels inherited from the pretrained model to establish connections among the parameters. For example, a depthwise RefConv can relate the parameters of a specific channel of convolution kernel to the parameters of the other kernel, i.e., make them refocus on the other parts of the model they have never attended to, rather than focus on the input features only. From another perspective, RefConv augments the priors of existing model structures by utilizing the representations encoded in the pretrained parameters as the priors and refocusing on them to learn novel representations, thus further enhancing the representational capacity of the pretrained model. The experimental results validated that RefConv can improve multiple convolutional neural network (CNN)-based models by a clear margin on image classification (up to 1.47% higher top-1 accuracy on ImageNet), object detection, semantic segmentation, and adversarial attacks without introducing any extra inference costs or altering the original model structure. Further studies demonstrated that RefConv can strengthen the spatial skeletons of kernels, reduce the redundancy of channels, and smooth the loss landscape, which explains its effectiveness.

In Kubernetes-based Cloud Native platforms, allocating containers to micro-services elastically according to workload changes is benefical to minimizing resource cost while stabling response times. However, inaccurate performance models for multi-container systems, along with coarse-grained container-based allocation, cause performance fluctuations. In this paper, deep learning, traditional Jackson Queuing Network (JQN) and feedback control are integrated to devise a container provisioning algorithm which leverages the neural networks’ ability to fit nonlinear performance models, the real-time responsiveness of feedback control, and the precise prediction of micro-service interactions offered by the JQN. The proposal is evaluated on a real Kubernetes based Cloud Native cluster. Experimental results illustrate that the container cost is decreased by 10.94%$\sim$11.36% while satifisfying Service Level Agreements (SLA) in terms of 95thaccessing-path response times.

Representing signals using coordinate networks domi-nates the area of inverse problems recently, and is widely applied in various scientific computing tasks. Still, there exists an issue of spectral bias in coordinate networks, lim-iting the capacity to learn high-frequency components. This problem is caused by the pathological distribution of the neural tangent kernel's (NTK's) eigenvalues of coordinate networks. We find that, this pathological distribution could be improved using the classical batch normalization (BN), which is a common deep learning technique but rarely used in coordinate networks. BN greatly reduces the maximum and variance of NTK's eigenvalues while slightly modifies the mean value, considering the max eigenvalue is much larger than the most, this variance change results in a shift of eigenvalues' distribution from a lower one to a higher one, therefore the spectral bias could be alleviated (see Fig. 1). This observation is substantiated by the significant improvements of applying BN-based coordinate networks to various tasks, including the image compression, computed tomography reconstruction, shape representation, magnetic resonance imaging and novel view synthesis.

Implicit neural representation (INR) has recently emerged as a promising paradigm for signal representations, which takes coordinates as inputs and generates corresponding signal values. Since these coordinates contain no semantic features, INR fails to take any semantic information into consideration. However, semantic information has been proven critical in many vision tasks, especially for visual signal representation. This paper proposes a reparameterization method termed as SPW, which encodes the semantic priors to the weights of INR, thus making INR contain semantic information implicitly and enhancing its representational capacity. Specifically, SPW uses the Semantic Neural Network (SNN) to extract both low- and high-level semantic information of the target visual signal and generates the semantic vector, which is input into the Weight Generation Network (WGN) to generate the weights of INR model. Finally, INR uses the generated weights with semantic priors to map the coordinates to the signal values. After training, we only retain the generated weights while abandoning both SNN and WGN, thus SPW introduces no extra costs in inference. Experimental results show that SPW can improve the performance of various INR models significantly on various tasks, including image fitting, CT reconstruction, MRI reconstruction, and novel view synthesis. Further experiments illustrate that model with SPW has lower weight redundancy and learns more novel representations, validating the effectiveness of SPW.

Convolutional neural networks (CNNs) and vision transformers (ViT) have obtained great achievements in computer vision. Recently, the research of multi-layer perceptron (MLP) architectures for vision have been popular again. Vision MLPs are designed to be independent from convolutions and self-attention operations. However, existing vision MLP architectures always depend on convolution for patch embedding. Thus we propose X-MLP, an architecture constructed absolutely upon fully connected layers and free from patch embedding. It decouples the features extremely and utilizes MLPs to interact the information across the dimension of width, height and channel independently and alternately. X-MLP is tested on ten benchmark datasets, all obtaining better performance than other vision MLP models. It even surpasses CNNs by a clear margin on various dataset. Furthermore, through mathematically restoring the spatial weights, we visualize the information communication between any couples of pixels in the feature map and observe the phenomenon of capturing long-range dependency.

Container orchestration platforms such as Kubernetes and Kubernetes-derived KubeEdge (called Kubernetes-based systems collectively) have been gradually used to conduct unified management of Cloud, Fog, and Edge resources. Container provisioning algorithms are crucial to guaranteeing quality of services (QoS) of such Kubernetes-based systems. However, most existing algorithms focus on placement and migration of fixed number of containers without considering elastic provisioning of containers. Meanwhile, widely used linear-performance-model-based feedback control or fixed-processing-rate-based queuing model on diverse platforms cannot describe the performance of containerized Web systems accurately. Furthermore, a fixed reference point used by existing methods is likely to generate inaccurate output errors incurring great fluctuations encountered with large arrival-rate changes. In this article, a feedback control method is designed based on a combination of varying-processing-rate queuing model and linear-model to provision containers elastically which improves the accuracy of output errors by learning reference models for different arrival rates automatically and mapping output errors from reference models to the queuing model. Our approach is compared with several state-of-art algorithms on a real Kubernetes cluster. Experimental results illustrate that our approach obtains the lowest percentage of service level agreement (SLA) violation (decreasing no less than 8.44 percent) and the second lowest cost.

Non-orthogonal multiple access (NOMA)-based cognitive heterogeneous multi-homing networks is a very important scenario in the future wireless networks. In this work, we formulate a joint video packet assignment, power control and user scheduling problem as a mixed integer non-linear programming (MINLP) to maximize the total video transmission quality for cognitive multi-homing heterogeneous NOMA networks, which is subject to the maximum accessed number of secondary users at each subchannel, video encoding characteristics, maximum interference power constraint and total available power constraint. For the joint video packet assignment, power control and user scheduling problem, we divide it into a video packet assignment subproblem, a power control subproblem and a secondary user scheduling subproblem for cognitive multi-homing heterogeneous NOMA networks. Firstly, the secondary user scheduling algorithm is proposed using the greedy method. Then, we utilize successive convex approximation (SCA) method to transform the power control subproblem into a convex programming problem, and an approximated optimal power control algorithm is proposed with the dual decomposition method. Finally, a heuristic video packet assignment algorithm is designed, which utilizes the auction theory. Numerical simulation results demonstrate that the proposed algorithms not only improve the video transmission quality, but also enhance the total throughput of cognitive multi-homing heterogeneous NOMA networks.

Functions provided by Web applications are increasingly diverse which make their structures complicated and meshed. Cloud computing platforms provide elastic computing capacities for these meshed Web systems to guarantee Service Level Agreement (SLA). Though workloads of meshed Web systems usually change steadily and periodically in total, sometimes there are sudden fluctuations. In this paper, a hybrid State-space-model-and-Queuing-network based Feedback control method (SQF) is developed for auto-scaling Virtual Machines (VMs) allocated to each tier of meshed Web systems. For the case with workloads changing steadily, a State-space-model based static Feedback Control method (SFC) is proposed in SQF to stabilize request response times near the reference time. For unsteadily changing workloads, a Queuing-network based multi-tier collaborative Feedback Control method (QFC) is proposed for effectively eliminating bottlenecks. QFC builds a control system for each tier individually and uses the queuing network to measure the interaction relationships among different tiers. Experimental results show that QFC is able to improve the efficiency of eliminating bottlenecks (decreasing upper-limit SLA violation ratios by 31.99%$\sim$56.52%) with similar or a little bit high VM rental costs compared to existing methods while SFC obtains more stable response times for requests with reasonable additional costs.

Regularization plays a vital role in machine learning optimization. One novel regularization method called flooding makes the training loss fluctuate around the flooding level. It intends to make the model continue to “random walk” until it comes to a flat loss landscape to enhance generalization. However, the hyper-parameter flooding level of the flooding method fails to be selected properly and uniformly. We propose a novel method called Jitter to improve it. Jitter is essentially a kind of random loss function. Before training, we randomly sample the “Jitter Point” from a specific probability distribution. The flooding level should be replaced by Jitter point to obtain a new target function and train the model accordingly. As Jitter point acting as a random factor, we actually add some randomness to the loss function, which is consistent with the fact that there exists innumerable random behaviors in the learning process of the machine learning model and is supposed to make the model more robust. In addition, Jitter performs “random walk” randomly which divides the loss curve into small intervals and then flipping them over, ideally making the loss curve much flatter and enhancing generalization ability. Moreover, Jitter can be a domain-, task-, and model-independent regularization method and train the model effectively after the training error reduces to zero. Our experimental results show that Jitter method can improve model performance more significantly than the previous flooding method and make the test loss curve descend twice.

Most of existing resource provisioning methods are designed for traditional Web applications with linear structures. However, Web systems with the meshed topology are becoming widespread. Meshed connections among different tiers make Virtual Machine (VM) provisioning and bottleneck elimination complex. In this paper, a Jackson network based Proactive and Reactive VM auto-scaling Method (JPRM) is proposed. In JPRM, request transition behaviors among tiers are modeled as a finite-state Markov stochastic process. A transition probability matrix is studied on-line to predict resource requirements based on M/M/N queuing models as proactive control. For reactive provisioning, the final increased request rate of each tier is determined based on stable state checking and Jackson equilibrium equation solving to eliminate bottleneck tiers and avoid bottleneck shifting. The JPRM is evaluated in a simulation environment established using CloudSim. Experimental results show that JPRM avoids bottleneck shifting with reasonable additional VM rental costs compared with existing methods.

Summary Most existing quality of service (QoS) control algorithms of Web applications take into account Web Server or database connections which can be released immediately. However, many applications are deployed on virtual machines (VMs) or even Spot VMs elastically rented from public Clouds. To save costs, interval‐priced VMs are not released until the ends of rented intervals. Such delays of control effects make existing methods rent or release excess VMs leading to overcontrol. Fluctuated prices make Spot VMs unreliable due to unexpected termination which makes fault‐tolerant strategies crucial. In this article, an unequal‐interval‐based loosely coupled control method is proposed to improve the quality of service (QoS) control ability of fault‐tolerant strategies. A queuing model with arrival‐rate‐adjustment coefficient is used to predict required capacity as a feedforward controller. Another two‐threshold and queuing‐model‐based method is applied to update the coefficient as a loosely coupled feedback controller. Meanwhile, unequal‐interval controller collaborating method is proposed to avoid overcontrol and react quickly to workload changes. Our approach is evaluated on both a simulation platform and a real Kubernetes Cluster. Experimental results illustrate that our approach decreases the percentage of waiting times larger than service level agreements with similar or lower rental costs compared with existing algorithms.

To meet the dynamic workload requirements in widespread task-batch based workflow applications, it is important to design algorithms for DAG-based platforms (such as Dryad, Spark and Pegasus) to rent virtual machines from public clouds dynamically. In terms of depths and functionalities, tasks of different task-batches are merged into task-units. A unit-aware deadline division method is investigated for properly dividing workflow deadlines to task deadlines so as to minimize the utilization of rented intervals. A rule-based task scheduling method is presented for allocating tasks to time slots of rented Virtual Machines (VMs) with a task right shifting operation and a weighted priority composite rule. A Unit-aware Rule-based Heuristic (URH) is proposed for elastically provisioning VMs to task-batch based workflows to minimize the rental cost in DAG-based cloud platforms. Effectiveness of the proposed URH methods is verified by comparing them against two adapted existing algorithms for similar problems on some realistic workflows.

Many workflow applications are moved to clouds for elastic capacities. Elastic resource provisioning is one of the most important problems. Realistic factors are involved, including an interval-based charging model, data transfer time, VM loading time, software setup time, resource utilization, and the workflow deadline. A multirule-based heuristic is proposed for the problem under study which contains two components: a deadline division and task scheduling. Taking into account the gaps between tasks, the impact of different critical paths and the precedence constraints, the workflow deadline is properly divided into task deadlines based on the solution of a relaxed problem. The relaxed problem is modeled by integer programming and solved by CPLEX. All tasks are sorted in terms of the developed depth-based rule. For different realistic factors, three priority rules are developed to allocate tasks to appropriate available time slots, from which a weighted rule is constructed for task scheduling. The weights are calibrated by random instances. Experiments are conducted using a benchmark realistic workflow. Experimental results show that the proposal is effective and efficient for realistic workflows.

In XaaS clouds, resources as services (e.g., infrastructure, platform and software as a service) are sold to applications such as scientific and big data analysis workflows. Candidate services with various configurations (CPU type, memory size, number of machines and so on) for the same task may have different execution time and cost. Further, some services are priced rented by intervals that be shared among tasks of the same workflow to save service rental cost. Establishing a task-mode (service) mapping (to get a balance between time and cost) and tabling tasks on rented service instances are crucial for minimizing the client-oriented cost to rent services for the whole workflow. In this paper, a multiple complete critical-path based heuristic (CPIS) is developed for the task-mode mapping problem. A list based heuristic (LHCM) concerning the task processing cost and task-slot matching is developed for tabling tasks on service instances based on the result of task-mode mapping. Then, the effectiveness of the proposed CPIS is compared with that of the previously proposed CPIL, the existing state-of-the-art heuristics including PCP, SC-PCP ( an extension to PCP), DET, and CPLEX. The effectiveness of the proposed LHCM is evaluated with its use with different task-mode mapping algorithms. Experimental results show that the proposed heuristics can reduce 24 percent of the service renting cost than the compared algorithms on the test benchmarks at most for non-shareable services. In addition, half of the service renting cost could be saved when LHCM is applied to consolidate tasks on rented service instances.

This paper considers the workflow scheduling problem in Clouds with the hourly charging model and data transfer times. It deals with the allocation of tasks to suitable VM instances while maintaining the precedence constraints on one hand and meeting the workflow deadline on the other. A bi-direction adjust heuristic (BDA) is proposed for the considered problem. Matching of tasks and the VM types is modeled as Mixed Integer Linear programming (MILP) problem and solved using CPLEX at the first stage of BDA. In the second stage, forward and backward scheduling procedures are applied to allocate tasks to VM instances according to the result of the first stage. In the backward scheduling procedure, a priority rule considering the finish time, wasted time fractions and added hours is developed to make appropriate matches of tasks and free time slots. Extensive experimental results show that the proposed BDA heuristic outperforms the existing state-of-the-art heuristic ICPCP in all cases. Further, compared with ICPCP, about 80% percentage of VM renting cost is saved for instances with 900 tasks at most.

In this paper, the service scheduling problem with start time constraints is considered for distributed collaborative manufacturing systems, which is different from the discrete time-cost tradeoff problem (DTCTP), well studied during the past decades. The assumption that the ability of services is unlimited in DTCTP is seldom true for practical settings. The fact that most services have limited capabilities, especially for manufacturing services results in constraint start times for requirements. Such a DTCTP is modeled as the DTCTP-STC (discrete time-cost tradeoff problem with start time constraints), also proved to be NP-hard. A service is just available at some time point, which can be assigned as the start time negotiated between a broker and a provider. An effective dynamic programming algorithm is proposed with the time complexity O(N2Mv+1) for the DTCTP-STC. The impact of the number of nodes, the number of modes, and the complexity of the network on the computation time is analyzed by experiments. Simulated experiments are performs on randomly generated instances. The results illustrated that the proposal is very effective for small size instances. As well, the proposal is more suitable for the DTCTP-STC than the DTCTP with faster convergent speed for those general instances with fixed fewer modes.

In this paper, a multi-mode project scheduling problem with deadline constraints is considered to minimize the resource availability cost. Modes of each activity are associated with different durations and renewable resources. Three kinds of rules are developed for activity selection, mode assignment, and time decision, respectively. A lot of combinations of the three kind rules are compared and the choosing probabilities are determined, based on which a regret probability based stochastic (RPBS) method is proposed for the considered problem. Computational results demonstrate that the RPBS method outperforms the existing one and the rule combinations in effectiveness but with a little more computation time.