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Implicit networks are a class of neural networks whose outputs are defined by the fixed point of a parameterized operator. They have enjoyed success in many applications including natural language processing, image processing, and numerous other applications. While they have found abundant empirical success, theoretical work on its generalization is still under-explored. In this work, we consider a large family of implicit networks defined parameterized contractive fixed point operators. We show a generalization bound for this class based on a covering number argument for the Rademacher complexity of these architectures.

Intracranial Hemorrhage is a potentially lethal condition whose manifestation is vastly diverse and shifts across clinical centers worldwide. Deep-learning-based solutions are starting to model complex relations between brain structures, but still struggle to generalize. While gathering more diverse data is the most natural approach, privacy regulations often limit the sharing of medical data. We propose the first application of Federated Scene Graph Generation. We show that our models can leverage the increased training data diversity. For Scene Graph Generation, they can recall up to 20% more clinically relevant relations across datasets compared to models trained on a single centralized dataset. Learning structured data representation in a federated setting can open the way to the development of new methods that can leverage this finer information to regularize across clients more effectively.

Adaptive Mixed-Criticality (AMC) is a fixed-priority preemptive scheduling algorithm for mixed-criticality hard real-time systems. It dominates many other scheduling algorithms for mixed-criticality systems, but does so at the cost of occasionally dropping jobs of less important/critical tasks, when low-priority jobs overrun their time budgets. In this paper we enhance AMC with a deep reinforcement learning (DRL) approach based on a Deep-Q Network. The DRL agent is trained off-line, and at run-time adjusts the low-criticality budgets of tasks to avoid budget overruns, while ensuring that no job misses its deadline if it does not overrun its budget. We have implemented and evaluated this approach by simulating realistic workloads from the automotive domain. The results show that the agent is able to reduce budget overruns by at least up to 50%, even when the budget of each task is chosen based on sampling the distribution of its execution time. To the best of our knowledge, this is the first use of DRL in AMC reported in the literature., Comment: Version submitted to RTNS 2024, on 17/08/2024 (with some typos fixed)

We consider the inverse problem consisting of the reconstruction of an inclusion $B$ contained in a bounded domain $\Omega\subset\mathbb{R}^d$ from a single pair of Cauchy data $(u|_{\partial\Omega},\partial_\nu u|_{\partial\Omega})$, where $\Delta u=0$ in $\Omega\setminus\overline B$ and $u=0$ on $\partial B$. We show that the reconstruction algorithm based on the range test, a domain sampling method, can be written as a neural network with a specific architecture. We propose to learn the weights of this network in the framework of supervised learning, and to combine it with a pre-trained classifier, with the purpose of distinguishing the inclusions based on their distance from the boundary. The numerical simulations show that this learned range test method provides accurate and stable reconstructions of polygonal inclusions. Furthermore, the results are superior to those obtained with the standard range test method (without learning) and with an end-to-end fully connected deep neural network, a purely data-driven method., Comment: 25 pages, 12 figures

Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techniques have proven effective in unconstrained systems as well as those with holonomic constraints. In this work, we adapt LNN techniques to mechanical systems with nonholonomic constraints. We test our approach on some well-known examples with nonholonomic constraints, showing that incorporating these restrictions into the neural network's learning improves not only trajectory estimation accuracy but also ensures adherence to constraints and exhibits better energy behavior compared to the unconstrained counterpart.

Deep learning has been proven to be a powerful tool for addressing the most significant issues in cognitive radio networks, such as spectrum sensing, spectrum sharing, resource allocation, and security attacks. The utilization of deep learning techniques in cognitive radio networks can significantly enhance the network's capability to adapt to changing environments and improve the overall system's efficiency and reliability. As the demand for higher data rates and connectivity increases, B5G/6G wireless networks are expected to enable new services and applications significantly. Therefore, the significance of deep learning in addressing cognitive radio network challenges cannot be overstated. This review article provides valuable insights into potential solutions that can serve as a foundation for the development of future B5G/6G services. By leveraging the power of deep learning, cognitive radio networks can pave the way for the next generation of wireless networks capable of meeting the ever-increasing demands for higher data rates, improved reliability, and security., Comment: The article has been accepted for publication in "Journal of Network and Computer Applications" during October 2024

In many modern computer application problems, the classification of image data plays an important role. Among many different supervised machine learning models, convolutional neural networks (CNNs) and linear discriminant analysis (LDA) as well as sophisticated variants thereof are popular techniques. In this work, two different domain decomposed CNN models are experimentally compared for different image classification problems. Both models are loosely inspired by domain decomposition methods and in addition, combined with a transfer learning strategy. The resulting models show improved classification accuracies compared to the corresponding, composed global CNN model without transfer learning and besides, also help to speed up the training process. Moreover, a novel decomposed LDA strategy is proposed which also relies on a localization approach and which is combined with a small neural network model. In comparison with a global LDA applied to the entire input data, the presented decomposed LDA approach shows increased classification accuracies for the considered test problems.

When solving inverse problems, one has to deal with numerous potential sources of model inexactnesses, like object motion, calibration errors, or simplified data models. Regularized Sequential Subspace Optimization (ReSeSOp) allows to compensate for such inaccuracies within the reconstruction step by employing consecutive projections onto suitably defined subspaces. However, this approach relies on a priori estimates for the model inexactness levels which are typically unknown. In dynamic imaging applications, where inaccuracies arise from the unpredictable dynamics of the object, these estimates are particularly challenging to determine in advance. To overcome this limitation, we propose a learned version of ReSeSOp which allows to approximate inexactness levels on the fly. The proposed framework generalizes established unrolled iterative reconstruction schemes to inexact forward operators and is particularly tailored to the structure of dynamic problems. We also present a comprehensive mathematical analysis regarding the effect of dependencies within the forward problem, clarifying when and why dividing the overall problem into subproblems is essential. The proposed method is evaluated on various examples from dynamic imaging, including datasets from a rheological CT experiment, brain MRI, and real-time cardiac MRI. The respective results emphasize improvements in reconstruction quality while ensuring adequate data consistency., Comment: 21 pages, 7 figures, 4 tables

The increasing capabilities of large generative models and their ever more widespread deployment have raised concerns about their reliability, safety, and potential misuse. To address these issues, recent works have proposed to control model generation by steering model activations in order to effectively induce or prevent the emergence of concepts or behaviors in the generated output. In this paper we introduce Activation Transport (AcT), a general framework to steer activations guided by optimal transport theory that generalizes many previous activation-steering works. AcT is modality-agnostic and provides fine-grained control over the model behavior with negligible computational overhead, while minimally impacting model abilities. We experimentally show the effectiveness and versatility of our approach by addressing key challenges in large language models (LLMs) and text-to-image diffusion models (T2Is). For LLMs, we show that AcT can effectively mitigate toxicity, induce arbitrary concepts, and increase their truthfulness. In T2Is, we show how AcT enables fine-grained style control and concept negation.

Studying protein mutations within amino acid sequences holds tremendous significance in life sciences. Protein language models (PLMs) have demonstrated strong capabilities in broad biological applications. However, due to architectural design and lack of supervision, PLMs model mutations implicitly with evolutionary plausibility, which is not satisfactory to serve as explainable and engineerable tools in real-world studies. To address these issues, we present MutaPLM, a unified framework for interpreting and navigating protein mutations with protein language models. MutaPLM introduces a protein delta network that captures explicit protein mutation representations within a unified feature space, and a transfer learning pipeline with a chain-of-thought (CoT) strategy to harvest protein mutation knowledge from biomedical texts. We also construct MutaDescribe, the first large-scale protein mutation dataset with rich textual annotations, which provides cross-modal supervision signals. Through comprehensive experiments, we demonstrate that MutaPLM excels at providing human-understandable explanations for mutational effects and prioritizing novel mutations with desirable properties. Our code, model, and data are open-sourced at https://github.com/PharMolix/MutaPLM., Comment: NeurIPS 2024 poster

We propose an effective method for inserting adapters into text-to-image foundation models, which enables the execution of complex downstream tasks while preserving the generalization ability of the base model. The core idea of this method is to optimize the attention mechanism related to 2D feature maps, which enhances the performance of the adapter. This approach was validated on the task of meme video generation and achieved significant results. We hope this work can provide insights for post-training tasks of large text-to-image models. Additionally, as this method demonstrates good compatibility with SD1.5 derivative models, it holds certain value for the open-source community. Therefore, we will release the related code (\url{https://songkey.github.io/hellomeme})., Comment: 11 pages, 7 figures, 2 tables

The auto-regressive architecture, like GPTs, is widely used in modern Text-to-Speech (TTS) systems. However, it incurs substantial inference time, particularly due to the challenges in the next-token prediction posed by lengthy sequences of speech tokens. In this work, we introduce VADUSA, one of the first approaches to accelerate auto-regressive TTS through speculative decoding. Our results show that VADUSA not only significantly improves inference speed but also enhances performance by incorporating draft heads to predict future speech content auto-regressively. Furthermore, the inclusion of a tolerance mechanism during sampling accelerates inference without compromising quality. Our approach demonstrates strong generalization across large datasets and various types of speech tokens., Comment: 5 pages, 3 figures, 3 tables. Submitted to ICASSP 2025

Brain tumor detection in multiplane Magnetic Resonance Imaging (MRI) slices is a challenging task due to the various appearances and relationships in the structure of the multiplane images. In this paper, we propose a new You Only Look Once (YOLO)-based detection model that incorporates Pretrained Knowledge (PK), called PK-YOLO, to improve the performance for brain tumor detection in multiplane MRI slices. To our best knowledge, PK-YOLO is the first pretrained knowledge guided YOLO-based object detector. The main components of the new method are a pretrained pure lightweight convolutional neural network-based backbone via sparse masked modeling, a YOLO architecture with the pretrained backbone, and a regression loss function for improving small object detection. The pretrained backbone allows for feature transferability of object queries on individual plane MRI slices into the model encoders, and the learned domain knowledge base can improve in-domain detection. The improved loss function can further boost detection performance on small-size brain tumors in multiplanar two-dimensional MRI slices. Experimental results show that the proposed PK-YOLO achieves competitive performance on the multiplanar MRI brain tumor detection datasets compared to state-of-the-art YOLO-like and DETR-like object detectors. The code is available at https://github.com/mkang315/PK-YOLO., Comment: Accepted by WACV 2025

We present GoRINNs: numerical analysis-informed neural networks for the solution of inverse problems of non-linear systems of conservation laws. GoRINNs are based on high-resolution Godunov schemes for the solution of the Riemann problem in hyperbolic Partial Differential Equations (PDEs). In contrast to other existing machine learning methods that learn the numerical fluxes of conservative Finite Volume methods, GoRINNs learn the physical flux function per se. Due to their structure, GoRINNs provide interpretable, conservative schemes, that learn the solution operator on the basis of approximate Riemann solvers that satisfy the Rankine-Hugoniot condition. The performance of GoRINNs is assessed via four benchmark problems, namely the Burgers', the Shallow Water, the Lighthill-Whitham-Richards and the Payne-Whitham traffic flow models. The solution profiles of these PDEs exhibit shock waves, rarefactions and/or contact discontinuities at finite times. We demonstrate that GoRINNs provide a very high accuracy both in the smooth and discontinuous regions., Comment: 29 pages, 6 figures

This study presents a neural network-enhanced approach to modeling disease spread dynamics over time and space. Neural networks are used to estimate time-varying parameters, with two calibration methods explored: Approximate Bayesian Computation (ABC) with Trust Region Reflective (TRF) optimization, and backpropagation with the Adam optimizer. Simulations show that the second method is faster for larger networks, while the first offers a greater diversity of acceptable solutions. The model is extended spatially by introducing a pathogen compartment, which diffuses through environmental transmission and interpersonal contact. We examine scenarios of exact reporting, overreporting, and underreporting, highlighting their effects on public behavior and infection peaks. Our results demonstrate that neural network-enhanced models more accurately capture dynamic changes in disease spread and illustrate the potential of scientific machine learning (SciML) to improve the predictive power of epidemiological models beyond traditional approaches., Comment: 20 pages

Advanced image segmentation and processing tools present an opportunity to study cell processes and their dynamics. However, image analysis is often routine and time-consuming. Nowadays, alternative data-driven approaches using deep learning are potentially offering automatized, accurate, and fast image analysis. In this paper, we extend the applications of Cellpose, a state-of-the-art cell segmentation framework, with feature extraction capabilities to assess morphological characteristics. We also introduce a dataset of DAPI and FITC stained cells to which our new method is applied.

Traditionally, style has been primarily considered in terms of artistic elements such as colors, brushstrokes, and lighting. However, identical semantic subjects, like people, boats, and houses, can vary significantly across different artistic traditions, indicating that style also encompasses the underlying semantics. Therefore, in this study, we propose a zero-shot scheme for image variation with coordinated semantics. Specifically, our scheme transforms the image-to-image problem into an image-to-text-to-image problem. The image-to-text operation employs vision-language models e.g., BLIP) to generate text describing the content of the input image, including the objects and their positions. Subsequently, the input style keyword is elaborated into a detailed description of this style and then merged with the content text using the reasoning capabilities of ChatGPT. Finally, the text-to-image operation utilizes a Diffusion model to generate images based on the text prompt. To enable the Diffusion model to accommodate more styles, we propose a fine-tuning strategy that injects text and style constraints into cross-attention. This ensures that the output image exhibits similar semantics in the desired style. To validate the performance of the proposed scheme, we constructed a benchmark comprising images of various styles and scenes and introduced two novel metrics. Despite its simplicity, our scheme yields highly plausible results in a zero-shot manner, particularly for generating stylized images with high-fidelity semantics., Comment: 13 pages,6 figures

Neural networks (NNs) have been widely used to solve partial differential equations (PDEs) in the applications of physics, biology, and engineering. One effective approach for solving PDEs with a fixed differential operator is learning Green's functions. However, Green's functions are notoriously difficult to learn due to their poor regularity, which typically requires larger NNs and longer training times. In this paper, we address these challenges by leveraging multiscale NNs to learn Green's functions. Through theoretical analysis using multiscale Barron space methods and experimental validation, we show that the multiscale approach significantly reduces the necessary NN size and accelerates training., Comment: 21 pages, 11 figures

We propose a conjectural counting formula for the coefficients of the chromatic symmetric function of unit interval graphs using reinforcement learning. The formula counts specific disjoint cycle-tuples in the graphs, referred to as Eschers, which satisfy certain concatenation conditions. These conditions are identified by a reinforcement learning model and are independent of the particular unit interval graph, resulting a universal counting expression.

A solar active region can significantly disrupt the Sun Earth space environment, often leading to severe space weather events such as solar flares and coronal mass ejections. As a consequence, the automatic classification of active region groups is the crucial starting point for accurately and promptly predicting solar activity. This study presents our results concerned with the application of deep learning techniques to the classification of active region cutouts based on the Mount Wilson classification scheme. Specifically, we have explored the latest advancements in image classification architectures, from Convolutional Neural Networks to Vision Transformers, and reported on their performances for the active region classification task, showing that the crucial point for their effectiveness consists in a robust training process based on the latest advances in the field.

Representation learning for high-dimensional, complex physical systems aims to identify a low-dimensional intrinsic latent space, which is crucial for reduced-order modeling and modal analysis. To overcome the well-known Kolmogorov barrier, deep autoencoders (AEs) have been introduced in recent years, but they often suffer from poor convergence behavior as the rank of the latent space increases. To address this issue, we propose the learnable weighted hybrid autoencoder, a hybrid approach that combines the strengths of singular value decomposition (SVD) with deep autoencoders through a learnable weighted framework. We find that the introduction of learnable weighting parameters is essential - without them, the resulting model would either collapse into a standard POD or fail to exhibit the desired convergence behavior. Additionally, we empirically find that our trained model has a sharpness thousands of times smaller compared to other models. Our experiments on classical chaotic PDE systems, including the 1D Kuramoto-Sivashinsky and forced isotropic turbulence datasets, demonstrate that our approach significantly improves generalization performance compared to several competing methods, paving the way for robust representation learning of high-dimensional, complex physical systems., Comment: 14 pages

We study a universal approximation property of ODENet and ResNet. The ODENet is a map from an initial value to the final value of an ODE system in a finite interval. It is considered a mathematical model of a ResNet-type deep learning system. We consider dynamical systems with vector fields given by a single composition of the activation function and an affine mapping, which is the most common choice of the ODENet or ResNet vector field in actual machine learning systems. We show that such an ODENet and ResNet with a restricted vector field can uniformly approximate ODENet with a general vector field., Comment: 14 pages

Precise energy load forecasting in residential households is crucial for mitigating carbon emissions and enhancing energy efficiency; indeed, accurate forecasting enables utility companies and policymakers, who advocate sustainable energy practices, to optimize resource utilization. Moreover, smart meters provide valuable information by allowing for granular insights into consumption patterns. Building upon available smart meter data, our study aims to cluster consumers into distinct groups according to their energy usage behaviours, effectively capturing a diverse spectrum of consumption patterns. Next, we design JITtrans (Just In Time transformer), a novel transformer deep learning model that significantly improves energy consumption forecasting accuracy, with respect to traditional forecasting methods. Extensive experimental results validate our claims using proprietary smart meter data. Our findings highlight the potential of advanced predictive technologies to revolutionize energy management and advance sustainable power systems: the development of efficient and eco-friendly energy solutions critically depends on such technologies.

This paper studies the approximation property of ReLU neural networks (NNs) to piecewise constant functions with unknown interfaces in bounded regions in $\mathbb{R}^d$. Under the assumption that the discontinuity interface $\Gamma$ may be approximated by a connected series of hyperplanes with a prescribed accuracy $\varepsilon >0$, we show that a three-layer ReLU NN is sufficient to accurately approximate any piecewise constant function and establish its error bound. Moreover, if the discontinuity interface is convex, an analytical formula of the ReLU NN approximation with exact weights and biases is provided., Comment: 17 pages, 8 figures, submitted to the journal

Chain-of-thought (CoT) reasoning in vision language models (VLMs) is crucial for improving interpretability and trustworthiness. However, current training recipes lack robust CoT reasoning data, relying on datasets dominated by short annotations with minimal rationales. In this work, we show that training VLM on short answers does not generalize well to reasoning tasks that require more detailed responses. To address this, we propose a two-fold approach. First, we distill rationales from GPT-4o model to enrich the training data and fine-tune VLMs, boosting their CoT performance. Second, we apply reinforcement learning to further calibrate reasoning quality. Specifically, we construct positive (correct) and negative (incorrect) pairs of model-generated reasoning chains, by comparing their predictions with annotated short answers. Using this pairwise data, we apply the Direct Preference Optimization algorithm to refine the model's reasoning abilities. Our experiments demonstrate significant improvements in CoT reasoning on benchmark datasets and better generalization to direct answer prediction as well. This work emphasizes the importance of incorporating detailed rationales in training and leveraging reinforcement learning to strengthen the reasoning capabilities of VLMs., Comment: 10 pages + appendix

This paper presents a systematic review of the infrastructure requirements for deploying Large Language Models (LLMs) on-device within the context of small and medium-sized enterprises (SMEs), focusing on both hardware and software perspectives. From the hardware viewpoint, we discuss the utilization of processing units like GPUs and TPUs, efficient memory and storage solutions, and strategies for effective deployment, addressing the challenges of limited computational resources typical in SME settings. From the software perspective, we explore framework compatibility, operating system optimization, and the use of specialized libraries tailored for resource-constrained environments. The review is structured to first identify the unique challenges faced by SMEs in deploying LLMs on-device, followed by an exploration of the opportunities that both hardware innovations and software adaptations offer to overcome these obstacles. Such a structured review provides practical insights, contributing significantly to the community by enhancing the technological resilience of SMEs in integrating LLMs., Comment: 9 pages, 1 figure. The work is supported by the SIT-NVIDIA Joint AI Centre

Simulation plays a crucial role in the rapid development and safe deployment of autonomous vehicles. Realistic traffic agent models are indispensable for bridging the gap between simulation and the real world. Many existing approaches for imitating human behavior are based on learning from demonstration. However, these approaches are often constrained by focusing on individual training strategies. Therefore, to foster a broader understanding of realistic traffic agent modeling, in this paper, we provide an extensive comparative analysis of different training principles, with a focus on closed-loop methods for highway driving simulation. We experimentally compare (i) open-loop vs. closed-loop multi-agent training, (ii) adversarial vs. deterministic supervised training, (iii) the impact of reinforcement losses, and (iv) the impact of training alongside log-replayed agents to identify suitable training techniques for realistic agent modeling. Furthermore, we identify promising combinations of different closed-loop training methods., Comment: 15 pages, 6 figures, 4 tables

Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It utilizes a separated representation form for the parametric PDE solution via a deep neural network and a least-squares solver. In this approach, the output of the deep neural network consists of a vector-valued function, interpreted as basis functions for the parametric solution space, and the least-squares solver determines the optimal solution within the constructed solution space for each given parameter. The LS-Net method requires a quadratic loss function for the least-squares solver to find optimal solutions given the set of basis functions. In this study, we consider loss functions derived from the Deep Fourier Residual and Physics-Informed Neural Networks approaches. We also provide theoretical results similar to the Universal Approximation Theorem, stating that there exists a sufficiently large neural network that can theoretically approximate solutions of parametric PDEs with the desired accuracy. We illustrate the LS-net method by solving one- and two-dimensional problems. Numerical results clearly demonstrate the method's ability to approximate parametric solutions., Comment: 24 pages, 13 figures

Studying the interplay between the geometry of the loss landscape and the optimization trajectories of simple neural networks is a fundamental step for understanding their behavior in more complex settings. This paper reveals the presence of topological obstruction in the loss landscape of shallow ReLU neural networks trained using gradient flow. We discuss how the homogeneous nature of the ReLU activation function constrains the training trajectories to lie on a product of quadric hypersurfaces whose shape depends on the particular initialization of the network's parameters. When the neural network's output is a single scalar, we prove that these quadrics can have multiple connected components, limiting the set of reachable parameters during training. We analytically compute the number of these components and discuss the possibility of mapping one to the other through neuron rescaling and permutation. In this simple setting, we find that the non-connectedness results in a topological obstruction, which, depending on the initialization, can make the global optimum unreachable. We validate this result with numerical experiments., Comment: 23 pages, 5 figures

The pioneering work of Oono and Suzuki [ICLR, 2020] and Cai and Wang [arXiv:2006.13318] initializes the analysis of the smoothness of graph convolutional network (GCN) features. Their results reveal an intricate empirical correlation between node classification accuracy and the ratio of smooth to non-smooth feature components. However, the optimal ratio that favors node classification is unknown, and the non-smooth features of deep GCN with ReLU or leaky ReLU activation function diminish. In this paper, we propose a new strategy to let GCN learn node features with a desired smoothness -- adapting to data and tasks -- to enhance node classification. Our approach has three key steps: (1) We establish a geometric relationship between the input and output of ReLU or leaky ReLU. (2) Building on our geometric insights, we augment the message-passing process of graph convolutional layers (GCLs) with a learnable term to modulate the smoothness of node features with computational efficiency. (3) We investigate the achievable ratio between smooth and non-smooth feature components for GCNs with the augmented message-passing scheme. Our extensive numerical results show that the augmented message-passing schemes significantly improve node classification for GCN and some related models., Comment: 48 pages

We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity and growth of activation functions. This setting directly leads to the use of unbalanced Kantorovich-Rubinstein norms defined by duality with Lipschitz functions, and of spaces of measures dual to those of continuous functions with controlled growth. These allow to make transparent the need for total variation and moment bounds or penalization to obtain existence of minimizers of variational formulations, under which we prove a compactness result in strong Kantorovich-Rubinstein norm, and in the absence of which we show several examples demonstrating undesirable behavior. Further, the Kantorovich-Rubinstein setting enables us to combine the advantages of a completely linear parametrization and ensuing reproducing kernel Banach space framework with optimal transport insights. We showcase this synergy with representer theorems and uniform large data limits for empirical risk minimization, and in proposed formulations for distillation and fusion applications., Comment: 39 pages, 1 table

This study showcases the digitalization of L\"ofstad Castle in Sweden to contribute to preserving its heritage values. The castle and its collections are deteriorating due to an inappropriate indoor climate. To address this, thirteen cloud-connected sensor boxes, equipped with 84 sensors, were installed throughout the main building, from the basement to the attic, to continuously monitor various indoor environmental parameters. The collected extensive multi-parametric data form the basis for creating a parametric digital twin of the building. The digital twin and detailed data analytics offer a deeper understanding of indoor climate and guide the adoption of appropriate heating and ventilation strategies. The results revealed the need to address high humidity problems in the basement and on the ground floor, such as installing vapor barriers. Opportunities for adopting energy-efficient heating and ventilation strategies on the upper floors were also highlighted. The digitalization solution and findings are not only applicable to L\"ofstad Castle but also provide valuable guidance for the conservation of other historic buildings facing similar challenges., Comment: This work has been submitted to the IEEE for possible publication

Deep learning models have made remarkable strides in precipitation prediction, yet they continue to struggle with capturing the spatial details of the features of radar images, particularly over high precipitation intensity areas. This shortcoming is evident in the form of low forecast accuracy in the spatial positioning of radar echo images across varying precipitation intensity regions. To address this challenge, we introduce the multi-task latent diffusion model(MTLDM), a novel approach for precipitation prediction. The basic concept of the MTLDM is based on the understanding that the radar image representing precipitation is the result of multiple factors. Therefore, we adopt a divide-and-conquer approach, that is, we decompose the radar image using decomposition technology and then predict the decomposed sub-images separately. We conceptualize the precipitation image as a composition of various components corresponding to different precipitation intensities. The MTLDM decomposes the precipitation image into these distinct components and employs a dedicated task to predict each one. This method enables spatiotemporally consistent prediction of real-world precipitation areas up to 5-80 min in advance, outperforming existing state-of-the-art techniques across multiple evaluation metrics., Comment: 15 pages, 14figures

With the rapid development of machine learning, numerical discretization methods based on deep neural networks have been widely used in many fields, especially in solving high-dimensional problems where traditional methods face bottlenecks. However, for low-dimensional problems, existing machine learning methods are not as accurate and efficient as traditional methods. In this paper, we propose a subspace method based on neural networks for eigenvalue problems with high accuracy and low cost. Our basic idea is to use neural network based basis functions to span a subspace, then calculate the parameters of the neural network based basis functions through appropriate training, and finally calculate the Galerkin projection of the eigenvalue problem onto the subspace and obtain an approximate solution. In addition, we reduce the dimension of the subspace by applying some dimensionality reduction technique, which can improve the accuracy of the approximate solution in further. Numerical experiments show that we can obtain approximate eigenvalues with accuracy of $10^{-11}$ but with less then 400 epochs, which is significantly superior to other existing neural network based methods., Comment: 29 pages, 3 figures

Labeling datasets is a noteworthy challenge in machine learning, both in terms of cost and time. This research, however, leverages an efficient answer. By exploring label propagation in semi-supervised learning, we can significantly reduce the number of labels required compared to traditional methods. We employ a transductive label propagation method based on the manifold assumption for text classification. Our approach utilizes a graph-based method to generate pseudo-labels for unlabeled data for the text classification task, which are then used to train deep neural networks. By extending labels based on cosine proximity within a nearest neighbor graph from network embeddings, we combine unlabeled data into supervised learning, thereby reducing labeling costs. Based on previous successes in other domains, this study builds and evaluates this approach's effectiveness in sentiment analysis, presenting insights into semi-supervised learning., Comment: 12 pages, 7 figures, accepted at the 2024 8th International Conference on Natural Language Processing and Information Retrieval (NLPIR 2024), Okayama, Japan, 2024

Recent LLM (Large Language Models) advancements benefit many fields such as education and finance, but HR has hundreds of repetitive processes, such as access requests, medical claim filing and time-off submissions, which are unaddressed. We relate these tasks to the LLM agent, which has addressed tasks such as writing assisting and customer support. We present HR-Agent, an efficient, confidential, and HR-specific LLM-based task-oriented dialogue system tailored for automating repetitive HR processes such as medical claims and access requests. Since conversation data is not sent to an LLM during inference, it preserves confidentiality required in HR-related tasks.

This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNNs estimators are given. The first establishes rates for convergence in probability under nonstationary data. The second provides non-asymptotic probability bounds on $\mathcal{L}^{2}$-errors under stationary $\beta$-mixing data. I apply these results to DNN estimators in both regression and classification contexts imposing only a standard H\"older smoothness assumption. These results are then used to demonstrate how asymptotic inference can be conducted on the finite dimensional parameter of a partially linear regression model after first-stage DNN estimation of infinite dimensional parameters. The DNN architectures considered are common in applications, featuring fully connected feedforward networks with any continuous piecewise linear activation function, unbounded weights, and a width and depth that grows with sample size. The framework provided also offers potential for research into other DNN architectures and time-series applications., Comment: 102 pages, 2 figures

Deep learning methods - consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays key tools to solve data driven supervised learning problems. Despite the great success of SGD methods in the training of DNNs, it remains a fundamental open problem of research to explain the success and the limitations of such methods in rigorous theoretical terms. In particular, even in the standard setup of data driven supervised learning problems, it remained an open research problem to prove (or disprove) that SGD methods converge in the training of DNNs with the popular rectified linear unit (ReLU) activation function with high probability to global minimizers in the optimization landscape. In this work we answer this question negatively. Specifically, in this work we prove for a large class of SGD methods that the considered optimizer does with high probability not converge to global minimizers of the optimization problem. It turns out that the probability to not converge to a global minimizer converges at least exponentially quickly to one as the width of the first hidden layer of the ANN and the depth of the ANN, respectively, increase. The general non-convergence results of this work do not only apply to the plain vanilla standard SGD method but also to a large class of accelerated and adaptive SGD methods such as the momentum SGD, the Nesterov accelerated SGD, the Adagrad, the RMSProp, the Adam, the Adamax, the AMSGrad, and the Nadam optimizers., Comment: 91 pages

Knowledge distillation (KD) has been widely used to transfer knowledge from large, accurate models (teachers) to smaller, efficient ones (students). Recent methods have explored enforcing consistency by incorporating causal interpretations to distill invariant representations. In this work, we extend this line of research by introducing a dual augmentation strategy to promote invariant feature learning in both teacher and student models. Our approach leverages different augmentations applied to both models during distillation, pushing the student to capture robust, transferable features. This dual augmentation strategy complements invariant causal distillation by ensuring that the learned representations remain stable across a wider range of data variations and transformations. Extensive experiments on CIFAR-100 demonstrate the effectiveness of this approach, achieving competitive results in same-architecture KD., Comment: 8 pages, 1 figure, 3 tables. This paper presents preliminary results from a project that we have since discontinued, as our research focus has shifted to new directions

Forward-backward stochastic differential equations (FBSDEs) have been generalized by introducing jumps for better capturing random phenomena, while the resulting FBSDEs are far more intricate than the standard one from every perspective. In this work, we establish a forward scheme for potentially high-dimensional FBSDEs with jumps, taking a similar approach to [Bender and Denk, 117 (2007), Stoch. Process. Their Appl., pp.1793-1812], with the aid of machine learning techniques for implementation. The developed forward scheme is built upon a recursive representation that decouples random jumps at every step and converges exponentially fast to the original FBSDE with jumps, often requiring only a few iterations to achieve sufficient accuracy, along with the error bound vanishing for lower jump intensities. The established framework also holds novelty in its neural network-based implementation of a wide class of forward schemes for FBSDEs, notably whether with or without jumps. We provide an extensive collection of numerical results, showcasing the effectiveness of the proposed recursion and its corresponding forward scheme in approximating high-dimensional FBSDEs with jumps (up to 100-dimension) without directly handling the random jumps., Comment: 26 pages, 9 figures, 7 tables

GPR full-waveform inversion optimizes the subsurface property model iteratively to match the entire waveform information. However, the model gradients derived from wavefield continuation often contain errors, such as ghost values and excessively large values at transmitter and receiver points. Furthermore, models updated based on these gradients frequently exhibit unclear characterization of anomalous bodies or false anomalies, making it challenging to obtain accurate inversion results. To address these issues, we introduced a novel full-waveform inversion (FWI) framework that incorporates an embedded convolutional neural network (CNN) to adaptively filter model parameters and gradients. Specifically, we embedded the CNN module before the forward modeling process and ensured the entire FWI process remains differentiable. This design leverages the auto-grad tool of the deep learning library, allowing model values to pass through the CNN module during forward computation and model gradients to pass through the CNN module during backpropagation. Experiments have shown that filtering the model parameters during forward computation and the model gradients during backpropagation can ultimately yield high-quality inversion results., Comment: 16 pages, 6 figures

Multigrid preconditioners are one of the most powerful techniques for solving large sparse linear systems. In this research, we address Darcy flow problems with random permeability using the conjugate gradient method, enhanced by a two-grid preconditioner based on a generalized multiscale prolongation operator, which has been demonstrated to be stable for high contrast profiles. To circumvent the need for repeatedly solving spectral problems with varying coefficients, we harness deep learning techniques to expedite the construction of the generalized multiscale prolongation operator. Considering linear transformations on multiscale basis have no impact on the performance of the preconditioner, we devise a loss function by the coefficient-based distance between subspaces instead of $l^2$-norm of the difference of the corresponding multiscale bases. We discover that leveraging the inherent symmetry in the local spectral problem can effectively accelerate the neural network training process. In scenarios where training data are limited, we utilize the Karhunen-Lo\`eve expansion to augment the dataset. Extensive numerical experiments with various types of random coefficient models are exhibited, showing that the proposed method can significantly reduce the time required to generate the prolongation operator while maintaining the original efficiency of the two-grid preconditioner.

Deep InfoMax (DIM) is a well-established method for self-supervised representation learning (SSRL) based on maximization of the mutual information between the input and the output of a deep neural network encoder. Despite the DIM and contrastive SSRL in general being well-explored, the task of learning representations conforming to a specific distribution (i.e., distribution matching, DM) is still under-addressed. Motivated by the importance of DM to several downstream tasks (including generative modeling, disentanglement, outliers detection and other), we enhance DIM to enable automatic matching of learned representations to a selected prior distribution. To achieve this, we propose injecting an independent noise into the normalized outputs of the encoder, while keeping the same InfoMax training objective. We show that such modification allows for learning uniformly and normally distributed representations, as well as representations of other absolutely continuous distributions. Our approach is tested on various downstream tasks. The results indicate a moderate trade-off between the performance on the downstream tasks and quality of DM., Comment: 22 pages, 3 fugures

We consider a mixed formulation of parametrized elasticity problems in terms of stress, displacement, and rotation. The latter two variables act as Lagrange multipliers to enforce conservation of linear and angular momentum. Due to the saddle-point structure, the resulting system is computationally demanding to solve directly, and we therefore propose an efficient solution strategy based on a decomposition of the stress variable. First, a triangular system is solved to obtain a stress field that balances the body and boundary forces. Second, a trained neural network is employed to provide a correction without affecting the conservation equations. The displacement and rotation can be obtained by post-processing, if necessary. The potential of the approach is highlighted by three numerical test cases, including a non-linear model.

Covering numbers of families of (deep) ReLU networks have been used to characterize their approximation-theoretic performance, upper-bound the prediction error they incur in nonparametric regression, and quantify their classification capacity. These results are based on covering number upper bounds obtained through the explicit construction of coverings. Lower bounds on covering numbers do not seem to be available in the literature. The present paper fills this gap by deriving tight (up to a multiplicative constant) lower and upper bounds on the covering numbers of fully-connected networks with bounded weights, sparse networks with bounded weights, and fully-connected networks with quantized weights. Thanks to the tightness of the bounds, a fundamental understanding of the impact of sparsity, quantization, bounded vs. unbounded weights, and network output truncation can be developed. Furthermore, the bounds allow to characterize the fundamental limits of neural network transformation, including network compression, and lead to sharp upper bounds on the prediction error in nonparametric regression through deep networks. Specifically, we can remove a $\log^6(n)$-factor in the best-known sample complexity rate in the estimation of Lipschitz functions through deep networks thereby establishing optimality. Finally, we identify a systematic relation between optimal nonparametric regression and optimal approximation through deep networks, unifying numerous results in the literature and uncovering general underlying principles.

This paper introduces to a structured application of the One-Class approach and the One-Class-One-Network model for supervised classification tasks, specifically addressing a vowel phonemes classification case study within the Automatic Speech Recognition research field. Through pseudo-Neural Architecture Search and Hyper-Parameters Tuning experiments conducted with an informed grid-search methodology, we achieve classification accuracy comparable to nowadays complex architectures (90.0 - 93.7%). Despite its simplicity, our model prioritizes generalization of language context and distributed applicability, supported by relevant statistical and performance metrics. The experiments code is openly available at our GitHub., Comment: Accepted at "2024 29th IEEE Symposium on Computers and Communications (ISCC): workshop on Next-Generation Multimedia Services at the Edge: Leveraging 5G and Beyond (NGMSE2024)". arXiv admin note: text overlap with arXiv:2410.04098

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to solve two challenging problems in dynamical systems theory: dynamics discovery and parameter estimation. Results demonstrate the effectiveness of the proposed approaches on a suite of test problems exhibiting oscillatory and chaotic dynamics. When comparing the performance of various numerical schemes, such as the Runge-Kutta and linear multistep families of methods, we observe promising results in predicting the system dynamics and estimating physical parameters, given appropriate choices of spatial and temporal discretization schemes and numerical method orders., Comment: 30 pages, 11 figures

This paper explores a structured application of the One-Class approach and the One-Class-One-Network model for supervised classification tasks, focusing on vowel phonemes classification and speakers recognition for the Automatic Speech Recognition (ASR) domain. For our case-study, the ASR model runs on a proprietary sensing and lightning system, exploited to monitor acoustic and air pollution on urban streets. We formalize combinations of pseudo-Neural Architecture Search and Hyper-Parameters Tuning experiments, using an informed grid-search methodology, to achieve classification accuracy comparable to nowadays most complex architectures, delving into the speaker recognition and energy efficiency aspects. Despite its simplicity, our model proposal has a very good chance to generalize the language and speaker genders context for widespread applicability in computational constrained contexts, proved by relevant statistical and performance metrics. Our experiments code is openly accessible on our GitHub., Comment: Accepted at "IEEE 5th International Symposium on the Internet of Sounds, 30 Sep / 2 Oct 2024, Erlangen, Germany"

A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimension. We show that it outperforms multilayer perceptrons in terms of accuracy and converges faster. We also compare it with several proposed KAN networks: the original spline-based KAN network appears to be more effective for smooth functions, while the P1-KAN network is more effective for irregular functions.

The complexity of the cardiovascular system needs to be accurately reproduced in order to promptly acknowledge health conditions; to this aim, advanced multifidelity and multiphysics numerical models are crucial. On one side, Full Order Models (FOMs) deliver accurate hemodynamic assessments, but their high computational demands hinder their real-time clinical application. In contrast, ROMs provide more efficient yet accurate solutions, essential for personalized healthcare and timely clinical decision-making. In this work, we explore the application of computational fluid dynamics (CFD) in cardiovascular medicine by integrating FOMs with ROMs for predicting the risk of aortic aneurysm growth and rupture. Wall Shear Stress (WSS) and the Oscillatory Shear Index (OSI), sampled at different growth stages of the abdominal aortic aneurysm, are predicted by means of Graph Neural Networks (GNNs). GNNs exploit the natural graph structure of the mesh obtained by the Finite Volume (FV) discretization, taking into account the spatial local information, regardless of the dimension of the input graph. Our experimental validation framework yields promising results, confirming our method as a valid alternative that overcomes the curse of dimensionality.