We propose a video editing framework, NaRCan, which integrates a hybrid deformation field and diffusion prior to generate high-quality natural canonical images to represent the input video. Our approach utilizes homography to model global motion and employs multi-layer perceptrons (MLPs) to capture local residual deformations, enhancing the model's ability to handle complex video dynamics. By introducing a diffusion prior from the early stages of training, our model ensures that the generated images retain a high-quality natural appearance, making the produced canonical images suitable for various downstream tasks in video editing, a capability not achieved by current canonical-based methods. Furthermore, we incorporate low-rank adaptation (LoRA) fine-tuning and introduce a noise and diffusion prior update scheduling technique that accelerates the training process by 14 times. Extensive experimental results show that our method outperforms existing approaches in various video editing tasks and produces coherent and high-quality edited video sequences.

In this section, we apply Theorem 12 and the approach of Foster and Rakhlin [2020] to the setting of contextual bandits with contexts drawn from a smooth distribution, considered in Block et al. [2022]. Unlike in that work, however, we will realize regret bounds achievable by an oracle-efficient algorithm that are polynomially improved both in the horizon and the number of actions in the particular case of noiseless rewards that are piecewise linear.

Vision Transformers (ViTs) are widely used in a variety of applications, while they usually have a fixed architecture that may not match the varying computational resources of different deployment environments. Thus, it is necessary to adapt ViT architectures to devices with diverse computational overheads to achieve an accuracy-efficient trade-off. This concept is consistent with the motivation behind Learngene. To achieve this, inspired by polynomial decomposition in calculus, where a function can be approximated by linearly combining several basic components, we propose to linearly decompose the ViT model into a set of components called learngenes during element-wise training. These learngenes can then be recomposed into differently scaled, pre-initialized models to satisfy different computational resource constraints. Such a decomposition-recomposition strategy provides an economical and flexible approach to generating different scales of ViT models for different deployment scenarios. Compared to model compression or training from scratch, which require to repeatedly train on large datasets for diverse-scale models, such strategy reduces computational costs since it only requires to train on large datasets once. Extensive experiments are used to validate the effectiveness of our method: ViTs can be decomposed and the decomposed learngenes can be recomposed into diverse-scale ViTs, which can achieve comparable or better performance compared to traditional model compression and pre-training methods. The code for our experiments is available in the supplemental material.

We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer neural network with random i.i.d inputs. We study the generalization performances of standard classifiers in the high-dimensional regime where α = n/d is kept finite in the limit of a high dimension d and number of samples n.

We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in lowdimensional problem domains. These results shed light on recent advances in computer vision and graphics that achieve state-of-the-art results by using MLPs to represent complex 3D objects and scenes. Using tools from the neural tangent kernel (NTK) literature, we show that a standard MLP has impractically slow convergence to high frequency signal components. To overcome this spectral bias, we use a Fourier feature mapping to transform the effective NTK into a stationary kernel with a tunable bandwidth. We suggest an approach for selecting problem-specific Fourier features that greatly improves the performance of MLPs for low-dimensional regression tasks relevant to the computer vision and graphics communities.

--Ensemble learning plays a crucial role in practical applications of online learning due to its enhanced classification performance and adaptable adjustment mechanisms. However, most weight allocation strategies in ensemble learning are heuristic, making it challenging to theoretically guarantee that the ensemble classifier outperforms its base classifiers. T o address this issue, a performance-bounded online ensemble learning method based on multi-armed bandits, named PB-OEL, is proposed in this paper . Specifically, multi-armed bandit with expert advice is incorporated into online ensemble learning, aiming to update the weights of base classifiers and make predictions. A theoretical framework is established to bound the performance of the ensemble classifier relative to base classifiers. By setting expert advice of bandits, the bound exceeds the performance of any base classifier when the length of data stream is sufficiently large. Additionally, performance bounds for scenarios with limited annotations are also derived. Numerous experiments on benchmark datasets and a dataset of real-time safety assessment tasks are conducted. The experimental results validate the theoretical bound to a certain extent and demonstrate that the proposed method outperforms existing state-of-the-art methods. Index T erms --Online ensemble learning, performance bound, multi-armed bandits, concept drift, real-time safety assessment. NLINE learning (OL) holds significant potential for handling continuous data and is widely applied across various domains, including industry, recommendation systems, finance, and control systems [1]-[5]. The objective of OL is to continuously learn and update models from new data, enabling adaptation to non-stationary environments for optimized predictions or decisions. One mainstream idea in OL relies on maintaining a set of vectors for decision, as exemplified by the perceptron algorithm [6], passive-aggressive algorithm [7], confidence weighted-based algorithm [8] and imbalanced class weighted-based algorithm [9].

Reinforcement Learning (RL) encompasses diverse paradigms, including modelbased RL, policy-based RL, and value-based RL, each tailored to approximate the model, optimal policy, and optimal value function, respectively. This work investigates the potential hierarchy of representation complexity among these RL paradigms. By utilizing computational complexity measures, including time complexity and circuit complexity, we theoretically unveil a potential representation complexity hierarchy within RL. We find that representing the model emerges as the easiest task, followed by the optimal policy, while representing the optimal value function presents the most intricate challenge. Additionally, we reaffirm this hierarchy from the perspective of the expressiveness of Multi-Layer Perceptrons (MLPs), which align more closely with practical deep RL and contribute to a completely new perspective in theoretical studying representation complexity in RL. Finally, we conduct deep RL experiments to validate our theoretical findings.

The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule.Previous works have analyzed the dynamical equations describing learning in the relatively simplified context of the perceptron under assumptions of a student-teacher framework or a linearized output. While these assumptions have facilitated theoretical understanding, they have precluded a detailed understanding of the roles of the nonlinearity and input-data distribution in determining the learning dynamics, limiting the applicability of the theories to real biological or artificial neural networks.Here, we use a stochastic-process approach to derive flow equations describing learning, applying this framework to the case of a nonlinear perceptron performing binary classification. We characterize the effects of the learning rule (supervised or reinforcement learning, SL/RL) and input-data distribution on the perceptron's learning curve and the forgetting curve as subsequent tasks are learned.In particular, we find that the input-data noise differently affects the learning speed under SL vs. RL, as well as determines how quickly learning of a task is overwritten by subsequent learning. Additionally, we verify our approach with real data using the MNIST dataset.This approach points a way toward analyzing learning dynamics for more-complex circuit architectures.

We introduce KANITE, a framework leveraging Kolmogorov-Arnold Networks (KANs) for Individual Treatment Effect (ITE) estimation under multiple treatments setting in causal inference. By utilizing KAN's unique abilities to learn univariate activation functions as opposed to learning linear weights by Multi-Layer Perceptrons (MLPs), we improve the estimates of ITEs. The KANITE framework comprises two key architectures: 1.Integral Probability Metric (IPM) architecture: This employs an IPM loss in a specialized manner to effectively align towards ITE estimation across multiple treatments. 2. Entropy Balancing (EB) architecture: This uses weights for samples that are learned by optimizing entropy subject to balancing the covariates across treatment groups. Extensive evaluations on benchmark datasets demonstrate that KANITE outperforms state-of-the-art algorithms in both $\epsilon_{\text{PEHE}}$ and $\epsilon_{\text{ATE}}$ metrics. Our experiments highlight the advantages of KANITE in achieving improved causal estimates, emphasizing the potential of KANs to advance causal inference methodologies across diverse application areas.