Physics-Informed Neural Networks (PINNs) have emerged recently as a promising application of deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, it has been recognized that adaptive procedures are needed to force the neural network to fit accurately the stubborn spots in the solution of "stiff" PDEs. In this paper, we propose a fundamentally new way to train PINNs adaptively, where the adaptation weights are fully trainable and applied to each training point individually, so the neural network learns autonomously which regions of the solution are difficult and is forced to focus on them. The self-adaptation weights specify a soft multiplicative soft attention mask, which is reminiscent of similar mechanisms used in computer vision. The basic idea behind these SA-PINNs is to make the weights increase as the corresponding losses increase, which is accomplished by training the network to simultaneously minimize the losses and maximize the weights. In addition, we show how to build a continuous map of self-adaptive weights using Gaussian Process regression, which allows the use of stochastic gradient descent in problems where conventional gradient descent is not enough to produce accurate solutions. Finally, we derive the Neural Tangent Kernel matrix for SA-PINNs and use it to obtain a heuristic understanding of the effect of the self-adaptive weights on the dynamics of training in the limiting case of infinitely-wide PINNs, which suggests that SA-PINNs work by producing a smooth equalization of the eigenvalues of the NTK matrix corresponding to the different loss terms. In numerical experiments with several linear and nonlinear benchmark problems, the SA-PINN outperformed other state-of-the-art PINN algorithm in L2 error, while using a smaller number of training epochs.
相關內容
Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會(hui)議。
Publisher：IFIP。
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The Path-dependent Neural Jump ODE (PD-NJ-ODE) is a model for online prediction of generic (possibly non-Markovian) stochastic processes with irregular (in time) and potentially incomplete (with respect to coordinates) observations. It is a model for which convergence to the $L^2$-optimal predictor, which is given by the conditional expectation, is established theoretically. Thereby, the training of the model is solely based on a dataset of realizations of the underlying stochastic process, without the need of knowledge of the law of the process. In the case where the underlying process is deterministic, the conditional expectation coincides with the process itself. Therefore, this framework can equivalently be used to learn the dynamics of ODE or PDE systems solely from realizations of the dynamical system with different initial conditions. We showcase the potential of our method by applying it to the chaotic system of a double pendulum. When training the standard PD-NJ-ODE method, we see that the prediction starts to diverge from the true path after about half of the evaluation time. In this work we enhance the model with two novel ideas, which independently of each other improve the performance of our modelling setup. The resulting dynamics match the true dynamics of the chaotic system very closely. The same enhancements can be used to provably enable the PD-NJ-ODE to learn long-term predictions for general stochastic datasets, where the standard model fails. This is verified in several experiments.
Recent advances in molecular and genetic research have identified a diverse range of brain tumor sub-types, shedding light on differences in their molecular mechanisms, heterogeneity, and origins. The present study performs whole-brain connectome analysis using diffusionweighted images. To achieve this, both graph theory and persistent homology - a prominent approach in topological data analysis are employed in order to quantify changes in the structural connectivity of the wholebrain connectome in subjects with brain tumors. Probabilistic tractography is used to map the number of streamlines connecting 84 distinct brain regions, as delineated by the Desikan-Killiany atlas from FreeSurfer. These streamline mappings form the connectome matrix, on which persistent homology based analysis and graph theoretical analysis are executed to evaluate the discriminatory power between tumor sub-types that include meningioma and glioma. A detailed statistical analysis is conducted on persistent homology-derived topological features and graphical features to identify the brain regions where differences between study groups are statistically significant (p < 0.05). For classification purpose, graph-based local features are utilized, achieving a highest accuracy of 88%. In classifying tumor sub-types, an accuracy of 80% is attained. The findings obtained from this study underscore the potential of persistent homology and graph theoretical analysis of the whole-brain connectome in detecting alterations in structural connectivity patterns specific to different types of brain tumors.
Representations from deep neural networks (DNNs) have proven remarkably predictive of neural activity involved in both visual and linguistic processing. Despite these successes, most studies to date concern unimodal DNNs, encoding either visual or textual input but not both. Yet, there is growing evidence that human meaning representations integrate linguistic and sensory-motor information. Here we investigate whether the integration of multimodal information operated by current vision-and-language DNN models (VLMs) leads to representations that are more aligned with human brain activity than those obtained by language-only and vision-only DNNs. We focus on fMRI responses recorded while participants read concept words in the context of either a full sentence or an accompanying picture. Our results reveal that VLM representations correlate more strongly than language- and vision-only DNNs with activations in brain areas functionally related to language processing. A comparison between different types of visuo-linguistic architectures shows that recent generative VLMs tend to be less brain-aligned than previous architectures with lower performance on downstream applications. Moreover, through an additional analysis comparing brain vs. behavioural alignment across multiple VLMs, we show that -- with one remarkable exception -- representations that strongly align with behavioural judgments do not correlate highly with brain responses. This indicates that brain similarity does not go hand in hand with behavioural similarity, and vice versa.
Kolmogorov-Arnold Networks (KANs), a novel type of neural network, have recently gained popularity and attention due to the ability to substitute multi-layer perceptions (MLPs) in artificial intelligence (AI) with higher accuracy and interoperability. However, KAN assessment is still limited and cannot provide an in-depth analysis of a specific domain. Furthermore, no study has been conducted on the implementation of KANs in hardware design, which would directly demonstrate whether KANs are truly superior to MLPs in practical applications. As a result, in this paper, we focus on verifying KANs for classification issues, which are a common but significant topic in AI using four different types of datasets. Furthermore, the corresponding hardware implementation is considered using the Vitis high-level synthesis (HLS) tool. To the best of our knowledge, this is the first article to implement hardware for KAN. The results indicate that KANs cannot achieve more accuracy than MLPs in high complex datasets while utilizing substantially higher hardware resources. Therefore, MLP remains an effective approach for achieving accuracy and efficiency in software and hardware implementation.
In recent years, graph neural networks (GNNs) have become a popular tool to improve the accuracy and performance of recommender systems. Modern recommender systems are not only designed to serve end users, but also to benefit other participants, such as items and items providers. These participants may have different or conflicting goals and interests, which raise the need for fairness and popularity bias considerations. GNN-based recommendation methods also face the challenges of unfairness and popularity bias and their normalization and aggregation processes suffer from these challenges. In this paper, we propose a fair GNN-based recommender system, called HetroFair, to improve items' side fairness. HetroFair uses two separate components to generate fairness-aware embeddings: i) fairnessaware attention which incorporates dot product in the normalization process of GNNs, to decrease the effect of nodes' degrees, and ii) heterophily feature weighting to assign distinct weights to different features during the aggregation process. In order to evaluate the effectiveness of HetroFair, we conduct extensive experiments over six real-world datasets. Our experimental results reveal that HetroFair not only alleviates the unfairness and popularity bias on items' side, but also achieves superior accuracy on users' side. Our implementation is publicly available at //github.com/NematGH/HetroFair.
Concept Bottleneck Models (CBMs) have recently been proposed to address the 'black-box' problem of deep neural networks, by first mapping images to a human-understandable concept space and then linearly combining concepts for classification. Such models typically require first coming up with a set of concepts relevant to the task and then aligning the representations of a feature extractor to map to these concepts. However, even with powerful foundational feature extractors like CLIP, there are no guarantees that the specified concepts are detectable. In this work, we leverage recent advances in mechanistic interpretability and propose a novel CBM approach -- called Discover-then-Name-CBM (DN-CBM) -- that inverts the typical paradigm: instead of pre-selecting concepts based on the downstream classification task, we use sparse autoencoders to first discover concepts learnt by the model, and then name them and train linear probes for classification. Our concept extraction strategy is efficient, since it is agnostic to the downstream task, and uses concepts already known to the model. We perform a comprehensive evaluation across multiple datasets and CLIP architectures and show that our method yields semantically meaningful concepts, assigns appropriate names to them that make them easy to interpret, and yields performant and interpretable CBMs. Code available at //github.com/neuroexplicit-saar/discover-then-name.
Approximate Nearest Neighbour Search (ANNS) is a subroutine in algorithms routinely employed in information retrieval, pattern recognition, data mining, image processing, and beyond. Recent works have established that graph-based ANNS algorithms are practically more efficient than the other methods proposed in the literature. The growing volume and dimensionality of data necessitates designing scalable techniques for ANNS. To this end, the prior art has explored parallelizing graph-based ANNS on GPU leveraging its massive parallelism. The current state-of-the-art GPU-based ANNS algorithms either (i) require both the dataset and the generated graph index to reside entirely in the GPU memory, or (ii) they partition the dataset into small independent shards, each of which can fit in GPU memory, and perform the search on these shards on the GPU. While the first approach fails to handle large datasets due to the limited memory available on the GPU, the latter delivers poor performance on large datasets due to high data traffic over the low-bandwidth PCIe bus. We introduce BANG, a first-of-its-kind technique for graph-based ANNS on GPU for billion-scale datasets that cannot entirely fit in the GPU memory. BANG stands out by harnessing a compressed form of the dataset on a single GPU to perform distance computations while efficiently accessing the graph index kept on the host memory, enabling efficient ANNS on large graphs within the limited GPU memory. BANG incorporates highly optimized GPU kernels and proceeds in phases that run concurrently on the GPU and CPU. Notably, on the billion-size datasets, we achieve throughputs 40x-200x more than the competing methods for a high recall value of 0.9. Additionally, BANG is the best in cost- and power-efficiency among the competing methods from the recent Billion-Scale Approximate Nearest Neighbour Search Challenge.
In practice, domain shifts are likely to occur between training and test data, necessitating domain adaptation (DA) to adjust the pre-trained source model to the target domain. Recently, universal domain adaptation (UniDA) has gained attention for addressing the possibility of an additional category (label) shift between the source and target domain. This means new classes can appear in the target data, some source classes may no longer be present, or both at the same time. For practical applicability, UniDA methods must handle both source-free and online scenarios, enabling adaptation without access to the source data and performing batch-wise updates in parallel with prediction. In an online setting, preserving knowledge across batches is crucial. However, existing methods often require substantial memory, e.g. by using memory queues, which is impractical because memory is limited and valuable, in particular on embedded systems. Therefore, we consider memory-efficiency as an additional constraint in this paper. To achieve memory-efficient online source-free universal domain adaptation (SF-UniDA), we propose a novel method that continuously captures the distribution of known classes in the feature space using a Gaussian mixture model (GMM). This approach, combined with entropy-based out-of-distribution detection, allows for the generation of reliable pseudo-labels. Finally, we combine a contrastive loss with a KL divergence loss to perform the adaptation. Our approach not only achieves state-of-the-art results in all experiments on the DomainNet dataset but also significantly outperforms the existing methods on the challenging VisDA-C dataset, setting a new benchmark for online SF-UniDA. Our code is available at //github.com/pascalschlachter/GMM.
Neural Cellular Automata (NCA) have proven to be effective in a variety of fields, with numerous biologically inspired applications. One of the fields, in which NCAs perform well is the generation of textures, modelling global patterns from local interactions governed by uniform and coherent rules. This paper aims to enhance the usability of NCAs in texture synthesis by addressing a shortcoming of current NCA architectures for texture generation, which requires separately trained NCA for each individual texture. In this work, we train a single NCA for the evolution of multiple textures, based on individual examples. Our solution provides texture information in the state of each cell, in the form of an internally coded genomic signal, which enables the NCA to generate the expected texture. Such a neural cellular automaton not only maintains its regenerative capability but also allows for interpolation between learned textures and supports grafting techniques. This demonstrates the ability to edit generated textures and the potential for them to merge and coexist within the same automaton. We also address questions related to the influence of the genomic information and the cost function on the evolution of the NCA.
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.
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