This work focuses on the analysis of fully connected feed forward ReLU neural networks as they approximate a given, smooth function. In contrast to conventionally studied universal approximation properties under increasing architectures, e.g., in terms of width or depth of the networks, we are concerned with the asymptotic growth of the parameters of approximating networks. Such results are of interest, e.g., for error analysis or consistency results for neural network training. The main result of our work is that, for a ReLU architecture with state of the art approximation error, the realizing parameters grow at most polynomially. The obtained rate with respect to a normalized network size is compared to existing results and is shown to be superior in most cases, in particular for high dimensional input.
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Different approaches have been adopted in addressing the challenges of Artificial Intelligence (AI), some centred on personal data and others on ethics, respectively narrowing and broadening the scope of AI regulation. This contribution aims to demonstrate that a third way is possible, starting from the acknowledgement of the role that human rights can play in regulating the impact of data-intensive systems. The focus on human rights is neither a paradigm shift nor a mere theoretical exercise. Through the analysis of more than 700 decisions and documents of the data protection authorities of six countries, we show that human rights already underpin the decisions in the field of data use. Based on empirical analysis of this evidence, this work presents a methodology and a model for a Human Rights Impact Assessment (HRIA). The methodology and related assessment model are focused on AI applications, whose nature and scale require a proper contextualisation of HRIA methodology. Moreover, the proposed models provide a more measurable approach to risk assessment which is consistent with the regulatory proposals centred on risk thresholds. The proposed methodology is tested in concrete case-studies to prove its feasibility and effectiveness. The overall goal is to respond to the growing interest in HRIA, moving from a mere theoretical debate to a concrete and context-specific implementation in the field of data-intensive applications based on AI.
In the field of architecture, the conversion of single images into 2 and 1/2D and 3D meshes is a promising technology that enhances design visualization and efficiency. This paper evaluates four innovative methods: "One-2-3-45," "CRM: Single Image to 3D Textured Mesh with Convolutional Reconstruction Model," "Instant Mesh," and "Image-to-Mesh." These methods are at the forefront of this technology, focusing on their applicability in architectural design and visualization. They streamline the creation of 3D architectural models, enabling rapid prototyping and detailed visualization from minimal initial inputs, such as photographs or simple sketches.One-2-3-45 leverages a diffusion-based approach to generate multi-view reconstructions, ensuring high geometric fidelity and texture quality. CRM utilizes a convolutional network to integrate geometric priors into its architecture, producing detailed and textured meshes quickly and efficiently. Instant Mesh combines the strengths of multi-view diffusion and sparse-view models to offer speed and scalability, suitable for diverse architectural projects. Image-to-Mesh leverages a generative adversarial network (GAN) to produce 3D meshes from single images, focusing on maintaining high texture fidelity and geometric accuracy by incorporating image and depth map data into its training process. It uses a hybrid approach that combines voxel-based representations with surface reconstruction techniques to ensure detailed and realistic 3D models.This comparative study highlights each method's contribution to reducing design cycle times, improving accuracy, and enabling flexible adaptations to various architectural styles and requirements. By providing architects with powerful tools for rapid visualization and iteration, these advancements in 3D mesh generation are set to revolutionize architectural practices.
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional approximations in polynomials are computed as in stochastic Galerkin finite element methods. This work investigates a residual based adaptive algorithm, akin to classical adaptive FEM, used to approximate the solution of the stationary diffusion equation with lognormal coefficients, i.e. with a non-affine parameter dependence of the data. It is known that the refinement procedure is reliable but the theoretical convergence of the scheme for this class of unbounded coefficients remains a challenging open question. This paper advances the theoretical state-of-the-art by providing a quasi-error reduction result for the adaptive solution of the lognormal stationary diffusion problem. The presented analysis generalizes previous results in that guaranteed convergence for uniformly bounded coefficients follows directly as a corollary. Moreover, it highlights the fundamental challenges with unbounded coefficients that cannot be overcome with common techniques. A computational benchmark example illustrates the main theoretical statement.
Humans are capable of solving complex abstract reasoning tests. Whether this ability reflects a learning-independent inference mechanism applicable to any novel unlearned problem or whether it is a manifestation of extensive training throughout life is an open question. Addressing this question in humans is challenging because it is impossible to control their prior training. However, assuming a similarity between the cognitive processing of Artificial Neural Networks (ANNs) and humans, the extent to which training is required for ANNs' abstract reasoning is informative about this question in humans. Previous studies demonstrated that ANNs can solve abstract reasoning tests. However, this success required extensive training. In this study, we examined the learning-independent abstract reasoning of ANNs. Specifically, we evaluated their performance without any pretraining, with the ANNs' weights being randomly-initialized, and only change in the process of problem solving. We found that naive ANN models can solve non-trivial visual reasoning tests, similar to those used to evaluate human learning-independent reasoning. We further studied the mechanisms that support this ability. Our results suggest the possibility of learning-independent abstract reasoning that does not require extensive training.
We investigate how elimination of variables can affect the asymptotic dynamics and phenotype control of Boolean networks. In particular, we look at the impact on minimal trap spaces, and identify a structural condition that guarantees their preservation. We examine the possible effects of variable elimination under three of the most popular approaches to control (attractor-based control, value propagation and control of minimal trap spaces), and under different update schemes (synchronous, asynchronous, generalized asynchronous). We provide some insights on the application of reduction, and an ample inventory of examples and counterexamples.
Neural networks based on convolutional operations have achieved remarkable results in the field of deep learning, but there are two inherent flaws in standard convolutional operations. On the one hand, the convolution operation is confined to a local window, so it cannot capture information from other locations, and its sampled shapes is fixed. On the other hand, the size of the convolutional kernel are fixed to k $\times$ k, which is a fixed square shape, and the number of parameters tends to grow squarely with size. Although Deformable Convolution (Deformable Conv) address the problem of fixed sampling of standard convolutions, the number of parameters also tends to grow in a squared manner. In response to the above questions, the Linear Deformable Convolution (LDConv) is explored in this work, which gives the convolution kernel an arbitrary number of parameters and arbitrary sampled shapes to provide richer options for the trade-off between network overhead and performance. In LDConv, a novel coordinate generation algorithm is defined to generate different initial sampled positions for convolutional kernels of arbitrary size. To adapt to changing targets, offsets are introduced to adjust the shape of the samples at each position. LDConv corrects the growth trend of the number of parameters for standard convolution and Deformable Conv to a linear growth. Moreover, it completes the process of efficient feature extraction by irregular convolutional operations and brings more exploration options for convolutional sampled shapes. Object detection experiments on representative datasets COCO2017, VOC 7+12, and VisDrone-DET2021 fully demonstrate the advantages of LDConv. LDConv is a plug-and-play convolutional operation that can replace the convolutional operation to improve network performance. The code for the relevant tasks can be found at //github.com/CV-ZhangXin/LDConv.
Bayesian neural networks (BNN) promise to combine the predictive performance of neural networks with principled uncertainty modeling important for safety-critical systems and decision making. However, posterior uncertainty estimates depend on the choice of prior, and finding informative priors in weight-space has proven difficult. This has motivated variational inference (VI) methods that pose priors directly on the function generated by the BNN rather than on weights. In this paper, we address a fundamental issue with such function-space VI approaches pointed out by Burt et al. (2020), who showed that the objective function (ELBO) is negative infinite for most priors of interest. Our solution builds on generalized VI (Knoblauch et al., 2019) with the regularized KL divergence (Quang, 2019) and is, to the best of our knowledge, the first well-defined variational objective for function-space inference in BNNs with Gaussian process (GP) priors. Experiments show that our method incorporates the properties specified by the GP prior on synthetic and small real-world data sets, and provides competitive uncertainty estimates for regression, classification and out-of-distribution detection compared to BNN baselines with both function and weight-space priors.
A lot of effort is currently invested in safeguarding autonomous driving systems, which heavily rely on deep neural networks for computer vision. We investigate the coupling of different neural network calibration measures with a special focus on the Area Under the Sparsification Error curve (AUSE) metric. We elaborate on the well-known inconsistency in determining optimal calibration using the Expected Calibration Error (ECE) and we demonstrate similar issues for the AUSE, the Uncertainty Calibration Score (UCS), as well as the Uncertainty Calibration Error (UCE). We conclude that the current methodologies leave a degree of freedom, which prevents a unique model calibration for the homologation of safety-critical functionalities. Furthermore, we propose the AUSE as an indirect measure for the residual uncertainty, which is irreducible for a fixed network architecture and is driven by the stochasticity in the underlying data generation process (aleatoric contribution) as well as the limitation in the hypothesis space (epistemic contribution).
Nowadays, the Convolutional Neural Networks (CNNs) have achieved impressive performance on many computer vision related tasks, such as object detection, image recognition, image retrieval, etc. These achievements benefit from the CNNs outstanding capability to learn the input features with deep layers of neuron structures and iterative training process. However, these learned features are hard to identify and interpret from a human vision perspective, causing a lack of understanding of the CNNs internal working mechanism. To improve the CNN interpretability, the CNN visualization is well utilized as a qualitative analysis method, which translates the internal features into visually perceptible patterns. And many CNN visualization works have been proposed in the literature to interpret the CNN in perspectives of network structure, operation, and semantic concept. In this paper, we expect to provide a comprehensive survey of several representative CNN visualization methods, including Activation Maximization, Network Inversion, Deconvolutional Neural Networks (DeconvNet), and Network Dissection based visualization. These methods are presented in terms of motivations, algorithms, and experiment results. Based on these visualization methods, we also discuss their practical applications to demonstrate the significance of the CNN interpretability in areas of network design, optimization, security enhancement, etc.
Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.
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