Understanding the power of depth in feed-forward neural networks is an ongoing challenge in the field of deep learning theory. While current works account for the importance of depth for the expressive power of neural-networks, it remains an open question whether these benefits are exploited during a gradient-based optimization process. In this work we explore the relation between expressivity properties of deep networks and the ability to train them efficiently using gradient-based algorithms. We give a depth separation argument for distributions with fractal structure, showing that they can be expressed efficiently by deep networks, but not with shallow ones. These distributions have a natural coarse-to-fine structure, and we show that the balance between the coarse and fine details has a crucial effect on whether the optimization process is likely to succeed. We prove that when the distribution is concentrated on the fine details, gradient-based algorithms are likely to fail. Using this result we prove that, at least in some distributions, the success of learning deep networks depends on whether the distribution can be approximated by shallower networks, and we conjecture that this property holds in general.

Our FreGAN improves the overall quality of generated images and raises the model's frequency awareness, encouraging the generator to produce precise

Shaded regions indicate 95% confidence intervals.

Latent Diffusion Models (LDMs) are generally trained at fixed resolutions, limiting their capability when scaling up to high-resolution images. While training-based approaches address this limitation by training on high-resolution datasets, they require large amounts of data and considerable computational resources, making them less practical. Consequently, training-free methods, particularly patch-based approaches, have become a popular alternative. These methods divide an image into patches and fuse the denoising paths of each patch, showing strong performance on high-resolution generation. However, we observe two critical issues for patch-based approaches, which we call "patch-level distribution shift" and "increased patch monotonicity. " T o address these issues, we propose Adaptive Path Tracing (APT), a framework that combines Statistical Matching to ensure patch distributions remain consistent in upsampled latents and Scale-aware Scheduling to deal with the patch monotonicity. As a result, APT produces clearer and more refined details in high-resolution images. In addition, APT enables a shortcut denoising process, resulting in faster sampling with minimal quality degradation. Our experimental results confirm that APT produces more detailed outputs with improved inference speed, providing a practical approach to high-resolution image generation. 1

Diffusion models have emerged as the leading approach for image synthesis, demonstrating exceptional photorealism and diversity. However, training diffusion models at high resolutions remains computationally prohibitive, and existing zero-shot generation techniques for synthesizing images beyond training resolutions often produce artifacts, including object duplication and spatial incoherence. In this paper, we introduce HiWave, a training-free, zero-shot approach that substantially enhances visual fidelity and structural coherence in ultra-high-resolution image synthesis using pretrained diffusion models. Our method employs a two-stage pipeline: generating a base image from the pretrained model followed by a patch-wise DDIM inversion step and a novel wavelet-based detail enhancer module. Specifically, we first utilize inversion methods to derive initial noise vectors that preserve global coherence from the base image. Subsequently, during sampling, our wavelet-domain detail enhancer retains low-frequency components from the base image to ensure structural consistency, while selectively guiding high-frequency components to enrich fine details and textures. Extensive evaluations using Stable Diffusion XL demonstrate that HiWave effectively mitigates common visual artifacts seen in prior methods, achieving superior perceptual quality. A user study confirmed HiWave's performance, where it was preferred over the state-of-the-art alternative in more than 80% of comparisons, highlighting its effectiveness for high-quality, ultra-high-resolution image synthesis without requiring retraining or architectural modifications.

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This paper presents a novel masked attention-based 3D Gaussian Splatting (3DGS) approach to enhance robotic perception and object detection in industrial and smart factory environments. U2-Net is employed for background removal to isolate target objects from raw images, thereby minimizing clutter and ensuring that the model processes only relevant data. Additionally, a Sobel filter-based attention mechanism is integrated into the 3DGS framework to enhance fine details - capturing critical features such as screws, wires, and intricate textures essential for high-precision tasks. We validate our approach using quantitative metrics, including L1 loss, SSIM, PSNR, comparing the performance of the background-removed and attention-incorporated 3DGS model against the ground truth images and the original 3DGS training baseline. The results demonstrate significant improves in visual fidelity and detail preservation, highlighting the effectiveness of our method in enhancing robotic vision for object recognition and manipulation in complex industrial settings.

This study investigates the application of Super-Resolution techniques in holographic microscopy to enhance quantitative phase imaging. An off-axis Mach-Zehnder interferometric setup was employed to capture interferograms. The study evaluates two Super-Resolution models, RCAN and Real-ESRGAN, for their effectiveness in reconstructing high-resolution interferograms from a microparticle-based dataset. The models were assessed using two primary approaches: image-based analysis for structural detail enhancement and morphological evaluation for maintaining sample integrity and phase map accuracy. The results demonstrate that RCAN achieves superior numerical precision, making it ideal for applications requiring highly accurate phase map reconstruction, while Real-ESRGAN enhances visual quality and structural coherence, making it suitable for visualization-focused applications. This study highlights the potential of Super-Resolution models in overcoming diffraction-imposed resolution limitations in holographic microscopy, opening the way for improved imaging techniques in biomedical diagnostics, materials science, and other high-precision fields.

Understanding the power of depth in feed-forward neural networks is an ongoing challenge in the field of deep learning theory. While current works account for the importance of depth for the expressive power of neural-networks, it remains an open question whether these benefits are exploited during a gradient-based optimization process. In this work we explore the relation between expressivity properties of deep networks and the ability to train them efficiently using gradient-based algorithms. We give a depth separation argument for distributions with fractal structure, showing that they can be expressed efficiently by deep networks, but not with shallow ones. These distributions have a natural coarse-to-fine structure, and we show that the balance between the coarse and fine details has a crucial effect on whether the optimization process is likely to succeed.

We present a novel method to provide efficient and highly detailed reconstructions. Inspired by wavelets, we learn a neural field that decompose the signal both spatially and frequency-wise. We follow the recent grid-based paradigm for spatial decomposition, but unlike existing work, encourage specific frequencies to be stored in each grid via Fourier features encodings. We then apply a multi-layer perceptron with sine activations, taking these Fourier encoded features in at appropriate layers so that higher-frequency components are accumulated on top of lower-frequency components sequentially, which we sum up to form the final output. We demonstrate that our method outperforms the state of the art regarding model compactness and convergence speed on multiple tasks: 2D image fitting, 3D shape reconstruction, and neural radiance fields. Our code is available at https://github.com/ubc-vision/NFFB.