We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval's identity and introduce a new training strategy through a \textit{spectral loss}. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems. When compared to numerical solvers of the same accuracy, our method demonstrates a $10\times$ increase in performance speed.
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Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANN) and the Yang-Baxter equation (YBE). Unlike traditional error correction methods, which are computationally intensive, we investigate artificial error mitigation. The manuscript introduces the basics of quantum error sources and explores the potential of using classical computation for error mitigation. The Yang-Baxter equation plays a crucial role, allowing us to compress time dynamics simulations into constant-depth circuits. By introducing controlled noise through the YBE, we enhance the dataset for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in correcting errors in time-evolving quantum states.
Adversarial generative models, such as Generative Adversarial Networks (GANs), are widely applied for generating various types of data, i.e., images, text, and audio. Accordingly, its promising performance has led to the GAN-based adversarial attack methods in the white-box and black-box attack scenarios. The importance of transferable black-box attacks lies in their ability to be effective across different models and settings, more closely aligning with real-world applications. However, it remains challenging to retain the performance in terms of transferable adversarial examples for such methods. Meanwhile, we observe that some enhanced gradient-based transferable adversarial attack algorithms require prolonged time for adversarial sample generation. Thus, in this work, we propose a novel algorithm named GE-AdvGAN to enhance the transferability of adversarial samples whilst improving the algorithm's efficiency. The main approach is via optimising the training process of the generator parameters. With the functional and characteristic similarity analysis, we introduce a novel gradient editing (GE) mechanism and verify its feasibility in generating transferable samples on various models. Moreover, by exploring the frequency domain information to determine the gradient editing direction, GE-AdvGAN can generate highly transferable adversarial samples while minimizing the execution time in comparison to the state-of-the-art transferable adversarial attack algorithms. The performance of GE-AdvGAN is comprehensively evaluated by large-scale experiments on different datasets, which results demonstrate the superiority of our algorithm. The code for our algorithm is available at: //github.com/LMBTough/GE-advGAN
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent data resolution and introduce a suitable likelihood scaling to enable consistent cross-level comparisons. We theoretically show that this approach attains the same convergence rates as when using level-independent treatment of data, but at significantly reduced computational cost. Additionally, we show that assumptions of exponential covariance and log-normality of random fields, widely held in multilevel Monte Carlo literature, can be extended to a wide range of covariance structures and random fields. These results are illustrated using numerical experiments for a 2D plane stress problem, where the Young's modulus is estimated from discretisations of the displacement field.
This position paper presents a theoretical framework for enhancing explainable artificial intelligence (xAI) through emergent communication (EmCom), focusing on creating a causal understanding of AI model outputs. We explore the novel integration of EmCom into AI systems, offering a paradigm shift from conventional associative relationships between inputs and outputs to a more nuanced, causal interpretation. The framework aims to revolutionize how AI processes are understood, making them more transparent and interpretable. While the initial application of this model is demonstrated on synthetic data, the implications of this research extend beyond these simple applications. This general approach has the potential to redefine interactions with AI across multiple domains, fostering trust and informed decision-making in healthcare and in various sectors where AI's decision-making processes are critical. The paper discusses the theoretical underpinnings of this approach, its potential broad applications, and its alignment with the growing need for responsible and transparent AI systems in an increasingly digital world.
This paper explores a specific sub-task of cross-modal music retrieval. We consider the delicate task of retrieving a performance or rendition of a musical piece based on a description of its style, expressive character, or emotion from a set of different performances of the same piece. We observe that a general purpose cross-modal system trained to learn a common text-audio embedding space does not yield optimal results for this task. By introducing two changes -- one each to the text encoder and the audio encoder -- we demonstrate improved performance on a dataset of piano performances and associated free-text descriptions. On the text side, we use emotion-enriched word embeddings (EWE) and on the audio side, we extract mid-level perceptual features instead of generic audio embeddings. Our results highlight the effectiveness of mid-level perceptual features learnt from music and emotion enriched word embeddings learnt from emotion-labelled text in capturing musical expression in a cross-modal setting. Additionally, our interpretable mid-level features provide a route for introducing explainability in the retrieval and downstream recommendation processes.
We introduced SSR, which utilizes SAM (segment-anything) as a strong regularizer during training, to greatly enhance the robustness of the image encoder for handling various domains. Specifically, given the fact that SAM is pre-trained with a large number of images over the internet, which cover a diverse variety of domains, the feature encoding extracted by the SAM is obviously less dependent on specific domains when compared to the traditional ImageNet pre-trained image encoder. Meanwhile, the ImageNet pre-trained image encoder is still a mature choice of backbone for the semantic segmentation task, especially when the SAM is category-irrelevant. As a result, our SSR provides a simple yet highly effective design. It uses the ImageNet pre-trained image encoder as the backbone, and the intermediate feature of each stage (ie there are 4 stages in MiT-B5) is regularized by SAM during training. After extensive experimentation on GTA5$\rightarrow$Cityscapes, our SSR significantly improved performance over the baseline without introducing any extra inference overhead.
We propose a new method for learning videos by aggregating multiple models by sequentially extracting video clips from untrimmed video. The proposed method reduces the correlation between clips by feeding clips to multiple models in turn and synchronizes these models through federated learning. Experimental results show that the proposed method improves the performance compared to the no synchronization.
We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We will share our code based on the Timm library and pre-trained models.
Recent work pre-training Transformers with self-supervised objectives on large text corpora has shown great success when fine-tuned on downstream NLP tasks including text summarization. However, pre-training objectives tailored for abstractive text summarization have not been explored. Furthermore there is a lack of systematic evaluation across diverse domains. In this work, we propose pre-training large Transformer-based encoder-decoder models on massive text corpora with a new self-supervised objective. In PEGASUS, important sentences are removed/masked from an input document and are generated together as one output sequence from the remaining sentences, similar to an extractive summary. We evaluated our best PEGASUS model on 12 downstream summarization tasks spanning news, science, stories, instructions, emails, patents, and legislative bills. Experiments demonstrate it achieves state-of-the-art performance on all 12 downstream datasets measured by ROUGE scores. Our model also shows surprising performance on low-resource summarization, surpassing previous state-of-the-art results on 6 datasets with only 1000 examples. Finally we validated our results using human evaluation and show that our model summaries achieve human performance on multiple datasets.
*《Connections between Support Vector Machines, Wasserstein distance and gradient-penalty GANs》A Jolicoeur-Martineau, I Mitliagkas [Mila] (2019)
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