Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for PDEs. An abstract formalism is introduced and stability properties of the underlying PDE are leveraged to derive an estimate for the generalization error in terms of the training error and number of training samples. This abstract framework is illustrated with several examples of nonlinear PDEs. Numerical experiments, validating the proposed theory, are also presented.
Faithfully summarizing the knowledge encoded by a deep neural network (DNN) into a few symbolic primitive patterns without losing much information represents a core challenge in explainable AI. To this end, Ren et al. (2023c) have derived a series of theorems to prove that the inference score of a DNN can be explained as a small set of interactions between input variables. However, the lack of generalization power makes it still hard to consider such interactions as faithful primitive patterns encoded by the DNN. Therefore, given different DNNs trained for the same task, we develop a new method to extract interactions that are shared by these DNNs. Experiments show that the extracted interactions can better reflect common knowledge shared by different DNNs.
Multi-modal Large Language Models (MLLMs) have shown impressive abilities in generating reasonable responses with respect to multi-modal contents. However, there is still a wide gap between the performance of recent MLLM-based applications and the expectation of the broad public, even though the most powerful OpenAI's GPT-4 and Google's Gemini have been deployed. This paper strives to enhance understanding of the gap through the lens of a qualitative study on the generalizability, trustworthiness, and causal reasoning capabilities of recent proprietary and open-source MLLMs across four modalities: ie, text, code, image, and video, ultimately aiming to improve the transparency of MLLMs. We believe these properties are several representative factors that define the reliability of MLLMs, in supporting various downstream applications. To be specific, we evaluate the closed-source GPT-4 and Gemini and 6 open-source LLMs and MLLMs. Overall we evaluate 230 manually designed cases, where the qualitative results are then summarized into 12 scores (ie, 4 modalities times 3 properties). In total, we uncover 14 empirical findings that are useful to understand the capabilities and limitations of both proprietary and open-source MLLMs, towards more reliable downstream multi-modal applications.
Few-Shot Class-Incremental Learning (FSCIL) aims to enable deep neural networks to learn new tasks incrementally from a small number of labeled samples without forgetting previously learned tasks, closely mimicking human learning patterns. In this paper, we propose a novel approach called Prompt Learning for FSCIL (PL-FSCIL), which harnesses the power of prompts in conjunction with a pre-trained Vision Transformer (ViT) model to address the challenges of FSCIL effectively. Our work pioneers the use of visual prompts in FSCIL, which is characterized by its notable simplicity. PL-FSCIL consists of two distinct prompts: the Domain Prompt and the FSCIL Prompt. Both are vectors that augment the model by embedding themselves into the attention layer of the ViT model. Specifically, the Domain Prompt assists the ViT model in adapting to new data domains. The task-specific FSCIL Prompt, coupled with a prototype classifier, amplifies the model's ability to effectively handle FSCIL tasks. We validate the efficacy of PL-FSCIL on widely used benchmark datasets such as CIFAR-100 and CUB-200. The results showcase competitive performance, underscoring its promising potential for real-world applications where high-quality data is often scarce. The source code is available at: //github.com/TianSongS/PL-FSCIL.
Motivation: Electronic Health Records (EHR) represent a comprehensive resource of a patient's medical history. EHR are essential for utilizing advanced technologies such as deep learning (DL), enabling healthcare providers to analyze extensive data, extract valuable insights, and make precise and data-driven clinical decisions. DL methods such as Recurrent Neural Networks (RNN) have been utilized to analyze EHR to model disease progression and predict diagnosis. However, these methods do not address some inherent irregularities in EHR data such as irregular time intervals between clinical visits. Furthermore, most DL models are not interpretable. In this study, we propose two interpretable DL architectures based on RNN, namely Time-Aware RNN (TA-RNN) and TA-RNN-Autoencoder (TA-RNN-AE) to predict patient's clinical outcome in EHR at next visit and multiple visits ahead, respectively. To mitigate the impact of irregular time intervals, we propose incorporating time embedding of the elapsed times between visits. For interpretability, we propose employing a dual-level attention mechanism that operates between visits and features within each visit. Results: The results of the experiments conducted on Alzheimer's Disease Neuroimaging Initiative (ADNI) and National Alzheimer's Coordinating Center (NACC) datasets indicated superior performance of proposed models for predicting Alzheimer's Disease (AD) compared to state-of-the-art and baseline approaches based on F2 and sensitivity. Additionally, TA-RNN showed superior performance on Medical Information Mart for Intensive Care (MIMIC-III) dataset for mortality prediction. In our ablation study, we observed enhanced predictive performance by incorporating time embedding and attention mechanisms. Finally, investigating attention weights helped identify influential visits and features in predictions. Availability: //github.com/bozdaglab/TA-RNN
This study addresses the challenge of extending Large Language Models (LLMs) to non-English languages, specifically those using non-Latin scripts. We propose an innovative approach that utilizes the romanized form of text as an interface for LLMs, hypothesizing that its frequent informal use and shared tokens with English enhance cross-lingual alignment. Focusing on Hindi, we demonstrate through Hindi-to-English translation and sentiment analysis tasks that romanized text not only significantly improves inference efficiency due to its lower fertility compared to native text but also achieves competitive performance with limited pre-training. Additionally, our novel multi-script prompting approach, which combines romanized and native texts, shows promise in further enhancing task performance. These findings suggest the potential of romanization in bridging the language gap for LLM applications, with future work aimed at expanding this approach to more languages and tasks.
The capabilities of transformer networks such as ChatGPT and other Large Language Models (LLMs) have captured the world's attention. The crucial computational mechanism underlying their performance relies on transforming a complete input sequence - for example, all the words in a sentence into a long "encoding vector" - that allows transformers to learn long-range temporal dependencies in naturalistic sequences. Specifically, "self-attention" applied to this encoding vector enhances temporal context in transformers by computing associations between pairs of words in the input sequence. We suggest that waves of neural activity, traveling across single cortical regions or across multiple regions at the whole-brain scale, could implement a similar encoding principle. By encapsulating recent input history into a single spatial pattern at each moment in time, cortical waves may enable temporal context to be extracted from sequences of sensory inputs, the same computational principle used in transformers.
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.
Deep neural networks (DNNs) are successful in many computer vision tasks. However, the most accurate DNNs require millions of parameters and operations, making them energy, computation and memory intensive. This impedes the deployment of large DNNs in low-power devices with limited compute resources. Recent research improves DNN models by reducing the memory requirement, energy consumption, and number of operations without significantly decreasing the accuracy. This paper surveys the progress of low-power deep learning and computer vision, specifically in regards to inference, and discusses the methods for compacting and accelerating DNN models. The techniques can be divided into four major categories: (1) parameter quantization and pruning, (2) compressed convolutional filters and matrix factorization, (3) network architecture search, and (4) knowledge distillation. We analyze the accuracy, advantages, disadvantages, and potential solutions to the problems with the techniques in each category. We also discuss new evaluation metrics as a guideline for future research.
Deep convolutional neural networks (CNNs) have recently achieved great success in many visual recognition tasks. However, existing deep neural network models are computationally expensive and memory intensive, hindering their deployment in devices with low memory resources or in applications with strict latency requirements. Therefore, a natural thought is to perform model compression and acceleration in deep networks without significantly decreasing the model performance. During the past few years, tremendous progress has been made in this area. In this paper, we survey the recent advanced techniques for compacting and accelerating CNNs model developed. These techniques are roughly categorized into four schemes: parameter pruning and sharing, low-rank factorization, transferred/compact convolutional filters, and knowledge distillation. Methods of parameter pruning and sharing will be described at the beginning, after that the other techniques will be introduced. For each scheme, we provide insightful analysis regarding the performance, related applications, advantages, and drawbacks etc. Then we will go through a few very recent additional successful methods, for example, dynamic capacity networks and stochastic depths networks. After that, we survey the evaluation matrix, the main datasets used for evaluating the model performance and recent benchmarking efforts. Finally, we conclude this paper, discuss remaining challenges and possible directions on this topic.
Within the rapidly developing Internet of Things (IoT), numerous and diverse physical devices, Edge devices, Cloud infrastructure, and their quality of service requirements (QoS), need to be represented within a unified specification in order to enable rapid IoT application development, monitoring, and dynamic reconfiguration. But heterogeneities among different configuration knowledge representation models pose limitations for acquisition, discovery and curation of configuration knowledge for coordinated IoT applications. This paper proposes a unified data model to represent IoT resource configuration knowledge artifacts. It also proposes IoT-CANE (Context-Aware recommendatioN systEm) to facilitate incremental knowledge acquisition and declarative context driven knowledge recommendation.