Subspace learning is a critical endeavor in contemporary machine learning, particularly given the vast dimensions of modern datasets.

We would like to thank all reviewers for their time and consideration in reviewing our paper. R1: "This work is perhaps the most effective in achieving [training "This paper will spark discussion... and the discussion it sparks will have value". R2: "This work will no doubt be of substantial interest to the image generation community". "It is impressive that a very simple preprocessing strategy can result in substantial improvements "Very handy and simple, which is a virtue". Score), while P, R, C and D stand for Precision, Recall, Density and Coverage metrics.

We thank the reviewers for the positive assessment of our work, useful comments, and proposed improvements. It would be helpful to also provide the derivation for Equation 3. The derivation is straightforward and will be included in the Appendix of the revised version. It would be nice to have some additional discussions in general. We will add a discussion to this effect to the Summary. We will include this missing definition in the revised version.

Finetuning large language models (LLMs) in federated learning (FL) settings has become increasingly important as it allows resource-constrained devices to finetune a model using private data. However, finetuning LLMs using backpropagation requires excessive memory (especially from intermediate activations) for resource-constrained devices. While Forward-mode Auto-Differentiation (AD) can significantly reduce memory footprint from activations, we observe that directly applying it to LLM finetuning results in slow convergence and poor accuracy.

The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained model. In this paper, we introduce a new class of structured matrices, which unifies and generalizes structured classes from previous works. We examine properties of this class and build a structured orthogonal parametrization upon it. We then use this parametrization to modify the orthogonal fine-tuning framework, improving parameter and computational efficiency.

We develop a neural network architecture which, trained in an unsupervised manner as a denoising diffusion model, simultaneously learns to both generate and segment images. Learning is driven entirely by the denoising diffusion objective, without any annotation or prior knowledge about regions during training. A computational bottleneck, built into the neural architecture, encourages the denoising network to partition an input into regions, denoise them in parallel, and combine the results. Our trained model generates both synthetic images and, by simple examination of its internal predicted partitions, semantic segmentations of those images. Without fine-tuning, we directly apply our unsupervised model to the downstream task of segmenting real images via noising and subsequently denoising them. Experiments demonstrate that our model achieves accurate unsupervised image segmentation and high-quality synthetic image generation across multiple datasets.

High dynamic range (HDR) novel view synthesis (NVS) aims to create photorealistic images from novel viewpoints using HDR imaging techniques. The rendered HDR images capture a wider range of brightness levels containing more details of the scene than normal low dynamic range (LDR) images. Existing HDR NVS methods are mainly based on NeRF. They suffer from long training time and slow inference speed. In this paper, we propose a new framework, High Dynamic Range Gaussian Splatting (HDR-GS), which can efficiently render novel HDR views and reconstruct LDR images with a user input exposure time. Specifically, we design a Dual Dynamic Range (DDR) Gaussian point cloud model that uses spherical harmonics to fit HDR color and employs an MLP-based tone-mapper to render LDR color. The HDR and LDR colors are then fed into two Parallel Differentiable Rasterization (PDR) processes to reconstruct HDR and LDR views. To establish the data foundation for the research of 3D Gaussian splatting-based methods in HDR NVS, we recalibrate the camera parameters and compute the initial positions for Gaussian point clouds. Comprehensive experiments show that HDR-GS surpasses the state-of-the-art NeRF-based method by 3.84 and 1.91 dB on LDR and HDR NVS while enjoying 1000 inference speed and only costing 6.3% training time.

We explore the phase diagram of approximation rates for deep neural networks and prove several new theoretical results. In particular, we generalize the existing result on the existence of deep discontinuous phase in ReLU networks to functional classes of arbitrary positive smoothness, and identify the boundary between the feasible and infeasible rates. Moreover, we show that all networks with a piecewise polynomial activation function have the same phase diagram. Next, we demonstrate that standard fully-connected architectures with a fixed width independent of smoothness can adapt to smoothness and achieve almost optimal rates. Finally, we consider deep networks with periodic activations ("deep Fourier expansion") and prove that they have very fast, nearly exponential approximation rates, thanks to the emerging capability of the network to implement efficient lookup operations.

We thank the reviewers for the helpful feedback and the positive assessment of our submission. Reviewer #1, "It is interesting to see if further increase the width of the network (from linear in d to polynomial in d and In the setting of our paper (minimization of the total network size) a large depth is in some sense unavoidable (as e.g. However, in general there is of course some trade-off between width and depth. Assuming a sufficiently constrained family (e.g. a ball in the Barron space Reviewer #4, "Theorem 5.1 extends the approximation results to all piece-wise linear activation functions and not just So in theory, this should also apply to max-outs and other variants of ReLUs such as Leaky ReLUs?" That's right, all these functions are easily expressible one via another using just linear operations (ReLU(x) = Reviewer #4, "I fail to see some intuitions regarding the typical values of r, d, and H for the networks used in practice. T. Poggio et al., Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review.

The ability of Language Models (LMs) to understand natural language makes them a powerful tool for parsing human instructions into task plans for autonomous robots. Unlike traditional planning methods that rely on domain-specific knowledge and handcrafted rules, LMs generalize from diverse data and adapt to various tasks with minimal tuning, acting as a compressed knowledge base.