Neural Persistence is a prominent measure for quantifying neural network complexity, proposed in the emerging field of topological data analysis in deep learning. In this work, however, we find both theoretically and empirically that the variance of network weights and spatial concentration of large weights are the main factors that impact neural persistence. Whilst this captures useful information for linear classifiers, we find that no relevant spatial structure is present in later layers of deep neural networks, making neural persistence roughly equivalent to the variance of weights. Additionally, the proposed averaging procedure across layers for deep neural networks does not consider interaction between layers. Based on our analysis, we propose an extension of the filtration underlying neural persistence to the whole neural network instead of single layers, which is equivalent to calculating neural persistence on one particular matrix. This yields our deep graph persistence measure, which implicitly incorporates persistent paths through the network and alleviates variance-related issues through standardisation. Code is available at //github.com/ExplainableML/Deep-Graph-Persistence .
相關內容
Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會(hui)議。
Publisher：IFIP。
SIT：
There is a constant need for high-performing and computationally efficient neural network models for image super-resolution: computationally efficient models can be used via low-capacity devices and reduce carbon footprints. One way to obtain such models is to compress models, e.g. quantization. Another way is a neural architecture search that automatically discovers new, more efficient solutions. We propose a novel quantization-aware procedure, the QuantNAS that combines pros of these two approaches. To make QuantNAS work, the procedure looks for quantization-friendly super-resolution models. The approach utilizes entropy regularization, quantization noise, and Adaptive Deviation for Quantization (ADQ) module to enhance the search procedure. The entropy regularization technique prioritizes a single operation within each block of the search space. Adding quantization noise to parameters and activations approximates model degradation after quantization, resulting in a more quantization-friendly architectures. ADQ helps to alleviate problems caused by Batch Norm blocks in super-resolution models. Our experimental results show that the proposed approximations are better for search procedure than direct model quantization. QuantNAS discovers architectures with better PSNR/BitOps trade-off than uniform or mixed precision quantization of fixed architectures. We showcase the effectiveness of our method through its application to two search spaces inspired by the state-of-the-art SR models and RFDN. Thus, anyone can design a proper search space based on an existing architecture and apply our method to obtain better quality and efficiency. The proposed procedure is 30\% faster than direct weight quantization and is more stable.
We present a new perspective on bridging the generalization gap between biological and computer vision -- mimicking the human visual diet. While computer vision models rely on internet-scraped datasets, humans learn from limited 3D scenes under diverse real-world transformations with objects in natural context. Our results demonstrate that incorporating variations and contextual cues ubiquitous in the human visual training data (visual diet) significantly improves generalization to real-world transformations such as lighting, viewpoint, and material changes. This improvement also extends to generalizing from synthetic to real-world data -- all models trained with a human-like visual diet outperform specialized architectures by large margins when tested on natural image data. These experiments are enabled by our two key contributions: a novel dataset capturing scene context and diverse real-world transformations to mimic the human visual diet, and a transformer model tailored to leverage these aspects of the human visual diet. All data and source code can be accessed at //github.com/Spandan-Madan/human_visual_diet.
We investigate the problem of producing diverse solutions to an image super-resolution problem. From a probabilistic perspective, this can be done by sampling from the posterior distribution of an inverse problem, which requires the definition of a prior distribution on the high-resolution images. In this work, we propose to use a pretrained hierarchical variational autoencoder (HVAE) as a prior. We train a lightweight stochastic encoder to encode low-resolution images in the latent space of a pretrained HVAE. At inference, we combine the low-resolution encoder and the pretrained generative model to super-resolve an image. We demonstrate on the task of face super-resolution that our method provides an advantageous trade-off between the computational efficiency of conditional normalizing flows techniques and the sample quality of diffusion based methods.
It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility condition (inclusion of kernels) of the mixed scheme and on local constants related to compact embeddings, which are often known explicitly. Applications include scalar second-order elliptic operators, linear elasticity, and the Steklov eigenvalue problem.
Confounding remains one of the major challenges to causal inference with observational data. This problem is paramount in medicine, where we would like to answer causal questions from large observational datasets like electronic health records (EHRs) and administrative claims. Modern medical data typically contain tens of thousands of covariates. Such a large set carries hope that many of the confounders are directly measured, and further hope that others are indirectly measured through their correlation with measured covariates. How can we exploit these large sets of covariates for causal inference? To help answer this question, this paper examines the performance of the large-scale propensity score (LSPS) approach on causal analysis of medical data. We demonstrate that LSPS may adjust for indirectly measured confounders by including tens of thousands of covariates that may be correlated with them. We present conditions under which LSPS removes bias due to indirectly measured confounders, and we show that LSPS may avoid bias when inadvertently adjusting for variables (like colliders) that otherwise can induce bias. We demonstrate the performance of LSPS with both simulated medical data and real medical data.
We introduce a simple initialization of the Maubach bisection routine for adaptive mesh refinement which applies to any conforming initial triangulation. Using Maubach's routine with this initialization generates meshes that preserve shape regularity and satisfy the closure estimate needed for optimal convergence of adaptive schemes. Our ansatz allows for the intrinsic use of existing implementations.
The generalized optimised Schwarz method proposed in [Claeys & Parolin, 2022] is a variant of the Despr\'es algorithm for solving harmonic wave problems where transmission conditions are enforced by means of a non-local exchange operator. We introduce and analyse an acceleration technique that significantly reduces the cost of applying this exchange operator without deteriorating the precision and convergence speed of the overall domain decomposition algorithm.
A new nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an approximate Gaussian regression. The resulting Toeplitz covariance matrix estimator is positive definite by construction, fully data-driven and computationally very fast. Moreover, this estimator is shown to be minimax optimal under the spectral norm for a large class of Toeplitz matrices. These results are readily extended to estimation of inverses of Toeplitz covariance matrices. Also, an alternative version of the Whittle likelihood for the spectral density based on the Discrete Cosine Transform (DCT) is proposed. The method is implemented in the R package vstdct that accompanies the paper.
The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antiderivative of the integrand. It was long believed that this approach suffers from "low-frequency breakdown," meaning that the accuracy of the calculated value of the integral deteriorates when the integrand is only slowly oscillating. Recently presented experimental evidence, however, suggests that if a Chebyshev spectral method is used to discretize the differential equation and the resulting linear system is solved via a truncated singular value decomposition, then no low-frequency breakdown occurs. Here, we provide a proof that this is the case, and our proof applies not only when the integrand is slowly oscillating, but even in the case of stationary points. Our result puts adaptive schemes based on the Levin method on a firm theoretical foundation and accounts for their behavior in the presence of stationary points. We go on to point out that by combining an adaptive Levin scheme with phase function methods for ordinary differential equations, a large class of oscillatory integrals involving special functions, including products of such functions and the compositions of such functions with slowly-varying functions, can be easily evaluated without the need for symbolic computations. Finally, we present the results of numerical experiments which illustrate the consequences of our analysis and demonstrate the properties of the adaptive Levin method.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
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