Most of the breeds will have the first type of collapse as in Figure 5, 6, and 7. Figure 5, 6 shows the

Tensor decompositions (TDs) serve as a powerful tool for analyzing multiway data.

Breakthroughs, discoveries, and DIY tips sent six days a week. Bison are an enduring and iconic symbol of North America's vast Great Plains. The large mammals have been hunted for thousands of years, and were almost driven into extinction in the late 1800s. Over thousands of years, bison hunters used different sites, but why they abandoned hunting grounds has been an archaeological mystery. For the Bergstrom site in present-day Montana, climate change may have been to blame.

Such models range broadly in both complexity and biological plausibility.

Reinforcement learning presents an attractive paradigm to reason about several distinct aspects of sequential decision making, such as specifying complex goals, planning future observations and actions, and critiquing their utilities. However, the combined integration of these capabilities poses competing algorithmic challenges in retaining maximal expressivity while allowing for flexibility in modeling choices for efficient learning and inference.

A common strategy for Parameter-Efficient Fine-Tuning (PEFT) of pre-trained Vision Transformers (ViTs) involves adapting the model to downstream tasks by learning a low-rank adaptation matrix. This matrix is decomposed into a product of down-projection and up-projection matrices, with the bottleneck dimensionality being crucial for reducing the number of learnable parameters, as exemplified by prevalent methods like LoRA and Adapter. However, these low-rank strategies typically employ a fixed bottleneck dimensionality, which limits their flexibility in handling layer-wise variations. To address this limitation, we propose a novel PEFT approach inspired by Singular Value Decomposition (SVD) for representing the adaptation matrix. SVD decomposes a matrix into the product of a left unitary matrix, a diagonal matrix of scaling values, and a right unitary matrix. We utilize Householder transformations to construct orthogonal matrices that efficiently mimic the unitary matrices, requiring only a vector. The diagonal values are learned in a layer-wise manner, allowing them to flexibly capture the unique properties of each layer. This approach enables the generation of adaptation matrices with varying ranks across different layers, providing greater flexibility in adapting pre-trained models. Experiments on standard downstream vision tasks demonstrate that our method achieves promising fine-tuning performance.

Large Language Models (LLMs) have achieved remarkable success in various natural language processing tasks, including language modeling, understanding, and generation. However, the increased memory and computational costs associated with these models pose significant challenges for deployment on resource-limited devices. Structural pruning has emerged as a promising solution to reduce the costs of LLMs without requiring post-processing steps. Prior structural pruning methods either follow the dependence of structures at the cost of limiting flexibility, or introduce non-trivial additional parameters by incorporating different projection matrices. In this work, we propose a novel approach that relaxes the constraint imposed by regular structural pruning methods and eliminates the structural dependence along the embedding dimension.

Despite advancements in robotic-assisted surgery, automating complex tasks like suturing remains challenging due to the need for adaptability and precision. Learning-based approaches, particularly reinforcement learning (RL) and imitation learning (IL), require realistic simulation environments for efficient data collection. However, current platforms often include only relatively simple, non-dexterous manipulations and lack the flexibility required for effective learning and generalization. We introduce SurgicAI, a novel platform for development and benchmarking that addresses these challenges by providing the flexibility to accommodate both modular subtasks and more importantly task decomposition in RL-based surgical robotics. Compatible with the da Vinci Surgical System, SurgicAI offers a standardized pipeline for collecting and utilizing expert demonstrations. It supports the deployment of multiple RL and IL approaches, and the training of both singular and compositional subtasks in suturing scenarios, featuring high dexterity and modularization. Meanwhile, SurgicAI sets clear metrics and benchmarks for the assessment of learned policies. We implemented and evaluated multiple RL and IL algorithms on SurgicAI. Our detailed benchmark analysis underscores SurgicAI's potential to advance policy learning in surgical robotics.

A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas Bayesian inference requires the assumption of a specific model. A fundamental question is then whether GNN has a high accuracy in addition to this flexibility. Moreover, whether the achieved performance is predominately a result of the backpropagation or the architecture itself is a matter of considerable interest. To gain a better insight into these questions, a mean-field theory of a minimal GNN architecture is developed for the graph partitioning problem. This demonstrates a good agreement with numerical experiments.