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.

For classification and regression on tabular data, the dominance of gradient-boosted decision trees (GBDTs) has recently been challenged by often much slower deep learning methods with extensive hyperparameter tuning. We address this discrepancy by introducing (a) RealMLP, an improved multilayer perceptron (MLP), and (b) strong meta-tuned default parameters for GBDTs and RealMLP. We tune RealMLP and the default parameters on a meta-train benchmark with 118 datasets and compare them to hyperparameter-optimized versions on a disjoint meta-test benchmark with 90 datasets, as well as the GBDT-friendly benchmark by Grinsztajn et al. (2022). Our benchmark results on medium-to-large tabular datasets (1K--500K samples) show that RealMLP offers a favorable time-accuracy tradeoff compared to other neural baselines and is competitive with GBDTs in terms of benchmark scores. Moreover, a combination of RealMLP and GBDTs with improved default parameters can achieve excellent results without hyperparameter tuning.

Large language models (LLMs) have shown impressive performance on language tasks but face challenges when deployed on resource-constrained devices due to their extensive parameters and reliance on dense multiplications, resulting in high memory demands and latency bottlenecks. Shift-and-add reparameterization offers a promising solution by replacing costly multiplications with hardware-friendly primitives in both the attention and multi-layer perceptron (MLP) layers of an LLM. However, current reparameterization techniques require training from scratch or full parameter fine-tuning to restore accuracy, which is resource-intensive for LLMs. To address this, we propose accelerating pretrained LLMs through post-training shift-and-add reparameterization, creating efficient multiplication-free models, dubbed ShiftAddLLM. Specifically, we quantize each weight matrix into binary matrices paired with group-wise scaling factors. The associated multiplications are reparameterized into (1) shifts between activations and scaling factors and (2) queries and adds according to the binary matrices.

We study the \emph{in-context learning} (ICL) ability of a \emph{Linear Transformer Block} (LTB) that combines a linear attention component and a linear multi-layer perceptron (MLP) component. For ICL of linear regression with a Gaussian prior and a \emph{non-zero mean}, we show that LTB can achieve nearly Bayes optimal ICL risk. In contrast, using only linear attention must incur an irreducible additive approximation error. Furthermore, we establish a correspondence between LTB and one-step gradient descent estimators with learnable initialization ( \mathsf{GD}-\beta), in the sense that every \mathsf{GD}-\beta estimator can be implemented by an LTB estimator and every optimal LTB estimator that minimizes the in-class ICL risk is effectively a \mathsf{GD}-\beta estimator.Finally, we show that \mathsf{GD}-\beta estimators can be efficiently optimized with gradient flow, despite a non-convex training objective.Our results reveal that LTB achieves ICL by implementing \mathsf{GD}-\beta, and they highlight the role of MLP layers in reducing approximation error.

Reinforcement Learning (RL) encompasses diverse paradigms, including model-based 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.

Multimodal Large Language Models (MLLMs) have demonstrated an excellent understanding of images and 3D data. However, both modalities have shortcomings in holistically capturing the appearance and geometry of objects. Meanwhile, Neural Radiance Fields (NeRFs), which encode information within the weights of a simple Multi-Layer Perceptron (MLP), have emerged as an increasingly widespread modality that simultaneously encodes the geometry and photorealistic appearance of objects. This paper investigates the feasibility and effectiveness of ingesting NeRF into MLLM. We create LLaNA, the first general-purpose NeRF-languageassistant capable of performing new tasks such as NeRF captioning and Q&A.

Probabilities of causation play a crucial role in modern decision-making. This paper addresses the challenge of predicting probabilities of causation for subpopulations with \textbf{insufficient} data using machine learning models. Tian and Pearl first defined and derived tight bounds for three fundamental probabilities of causation: the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN). However, estimating these probabilities requires both experimental and observational distributions specific to each subpopulation, which are often unavailable or impractical to obtain with limited population-level data. Therefore, for most subgroups, the amount of data they have is not enough to guarantee the accuracy of their probabilities. Hence, to estimate these probabilities for subpopulations with \textbf{insufficient} data, we propose using machine learning models that draw insights from subpopulations with sufficient data. Our evaluation of multiple machine learning models indicates that, given the population-level data and an appropriate choice of machine learning model and activation function, PNS can be effectively predicted. Through simulation studies on multiple Structured Causal Models (SCMs), we show that our multilayer perceptron (MLP) model with the Mish activation function achieves a mean absolute error (MAE) of approximately $0.02$ in predicting PNS for $32,768$ subpopulations across most SCMs using data from only $2,000$ subpopulations with known PNS values.

Evaluating the performance of a lecturer has been essential for enhancing teaching quality, improving student learning outcomes, and strengthening the institution's reputation. The absence of such a system brings about lecturer performance evaluation which was neither comprehensive nor holistic. This system was designed using a web-based platform, created a secure database, and by using a custom dataset, captured some performance metrics which included student evaluation scores, Research Publications, Years of Experience, and Administrative Duties. Multilayer Perceptron (MLP) algorithm was utilized due to its ability to process complex data patterns and generates accurate predictions in a lecturer's performance based on historical data. This research focused on designing multiple performance metrics beyond the standard ones, incorporating student participation, and integrating analytical tools to deliver a comprehensive and holistic evaluation of lecturers' performance and was developed using Object-Oriented Analysis and Design (OOAD) methodology. Lecturers' performance is evaluated by the model, and the evaluation accuracy is about 91% compared with actual performance. Finally, by evaluating the performance of the MLP model, it is concluded that MLP enhanced lecturer performance evaluation by providing accurate predictions, reducing bias, and supporting data-driven decisions, ultimately improving the fairness and efficiency of the evaluation process. The MLP model's performance was evaluated using Mean Squared Error (MSE) and Mean Absolute Error (MAE), achieved a test loss (MSE) of 256.99 and a MAE of 13.76, and reflected a high level of prediction accuracy. The model also demonstrated an estimated accuracy rate of approximately 96%, validated its effectiveness in predicting lecturer performance.

Oversmoothing has long been identified as a major limitation of Graph Neural Networks (GNNs): input node features are smoothed at each layer and converge to a non-informative representation, if the weights of the GNN are sufficiently bounded. This assumption is crucial: if, on the contrary, the weights are sufficiently large, then oversmoothing may not happen. Theoretically, GNN could thus learn to not oversmooth. However it does not really happen in practice, which prompts us to examine oversmoothing from an optimization point of view. In this paper, we analyze backward oversmoothing, that is, the notion that backpropagated errors used to compute gradients are also subject to oversmoothing from output to input. With non-linear activation functions, we outline the key role of the interaction between forward and backward smoothing. Moreover, we show that, due to backward oversmoothing, GNNs provably exhibit many spurious stationary points: as soon as the last layer is trained, the whole GNN is at a stationary point. As a result, we can exhibit regions where gradients are near-zero while the loss stays high. The proof relies on the fact that, unlike forward oversmoothing, backward errors are subjected to a linear oversmoothing even in the presence of non-linear activation function, such that the average of the output error plays a key role. Additionally, we show that this phenomenon is specific to deep GNNs, and exhibit counter-example Multi-Layer Perceptron. This paper is a step toward a more complete comprehension of the optimization landscape specific to GNNs.

The empirical emergence of neural collapse -- a surprising symmetry in the feature representations of the training data in the penultimate layer of deep neural networks -- has spurred a line of theoretical research aimed at its understanding. However, existing work focuses on data-agnostic models or, when data structure is taken into account, it remains limited to multi-layer perceptrons. Our paper fills both these gaps by analyzing modern architectures in a data-aware regime: we prove that global optima of deep regularized transformers and residual networks (ResNets) with LayerNorm trained with cross entropy or mean squared error loss are approximately collapsed, and the approximation gets tighter as the depth grows. More generally, we formally reduce any end-to-end large-depth ResNet or transformer training into an equivalent unconstrained features model, thus justifying its wide use in the literature even beyond data-agnostic settings. Our theoretical results are supported by experiments on computer vision and language datasets showing that, as the depth grows, neural collapse indeed becomes more prominent.