We introduce an approach for solving PDEs over manifolds using physics informed neural networks whose architecture aligns with spectral methods. The networks are trained to take in as input samples of an initial condition, a time stamp and point(s) on the manifold and then output the solution's value at the given time and point(s). We provide proofs of our method for the heat equation on the interval and examples of unique network architectures that are adapted to nonlinear equations on the sphere and the torus. We also show that our spectral-inspired neural network architectures outperform the standard physics informed architectures. Our extensive experimental results include generalization studies where the testing dataset of initial conditions is randomly sampled from a significantly larger space than the training set.
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The development of deep learning based image representation learning (IRL) methods has attracted great attention for various image understanding problems. Most of these methods require the availability of a high quantity and quality of annotated training images, which can be time-consuming and costly to gather. To reduce labeling costs, crowdsourced data, automatic labeling procedures or citizen science projects can be considered. However, such approaches increase the risk of including label noise in training data. It may result in overfitting on noisy labels when discriminative reasoning is employed. This leads to sub-optimal learning procedures, and thus inaccurate characterization of images. To address this, we introduce a generative reasoning integrated label noise robust deep representation learning (GRID) approach. Our approach aims to model the complementary characteristics of discriminative and generative reasoning for IRL under noisy labels. To this end, we first integrate generative reasoning into discriminative reasoning through a supervised variational autoencoder. This allows GRID to automatically detect training samples with noisy labels. Then, through our label noise robust hybrid representation learning strategy, GRID adjusts the whole learning procedure for IRL of these samples through generative reasoning and that of other samples through discriminative reasoning. Our approach learns discriminative image representations while preventing interference of noisy labels independently from the IRL method being selected. Thus, unlike the existing methods, GRID does not depend on the type of annotation, neural network architecture, loss function or learning task, and thus can be directly utilized for various problems. Experimental results show its effectiveness compared to state-of-the-art methods. The code of GRID is publicly available at //github.com/gencersumbul/GRID.
Obtaining versions of deep neural networks that are both highly-accurate and highly-sparse is one of the main challenges in the area of model compression, and several high-performance pruning techniques have been investigated by the community. Yet, much less is known about the interaction between sparsity and the standard stochastic optimization techniques used for training sparse networks, and most existing work uses standard dense schedules and hyperparameters for training sparse networks. In this work, we examine the impact of high sparsity on model training using the standard computer vision and natural language processing sparsity benchmarks. We begin by showing that using standard dense training recipes for sparse training is suboptimal, and results in under-training. We provide new approaches for mitigating this issue for both sparse pre-training of vision models (e.g. ResNet50/ImageNet) and sparse fine-tuning of language models (e.g. BERT/GLUE), achieving state-of-the-art results in both settings in the high-sparsity regime, and providing detailed analyses for the difficulty of sparse training in both scenarios. Our work sets a new threshold in terms of the accuracies that can be achieved under high sparsity, and should inspire further research into improving sparse model training, to reach higher accuracies under high sparsity, but also to do so efficiently.
An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map on homology from a sub-sample to the full space. We develop a greedy matroid algorithm for finding an optimal basis for the image of the induced map, and investigate the relationship between this algorithm and the probability of sampling vectors in the image of the induced map.
Recent advances in the performance of large language models (LLMs) have sparked debate over whether, given sufficient training, high-level human abilities emerge in such generic forms of artificial intelligence (AI). Despite the exceptional performance of LLMs on a wide range of tasks involving natural language processing and reasoning, there has been sharp disagreement as to whether their abilities extend to more creative human abilities. A core example is the ability to interpret novel metaphors. Given the enormous and non-curated text corpora used to train LLMs, a serious obstacle to designing tests is the requirement of finding novel yet high-quality metaphors that are unlikely to have been included in the training data. Here we assessed the ability of GPT-4, a state-of-the-art large language model, to provide natural-language interpretations of novel literary metaphors drawn from Serbian poetry and translated into English. Despite exhibiting no signs of having been exposed to these metaphors previously, the AI system consistently produced detailed and incisive interpretations. Human judge - blind to the fact that an AI model was involved - rated metaphor interpretations generated by GPT-4 as superior to those provided by a group of college students. In interpreting reversed metaphors, GPT-4, as well as humans, exhibited signs of sensitivity to the Gricean cooperative principle. These results indicate that LLMs such as GPT-4 have acquired an emergent ability to interpret complex novel metaphors.
We equip a smaller Language Model to generalise to answering challenging compositional questions that have not been seen in training. To do so we propose a combination of multitask supervised pretraining on up to 93 tasks designed to instill diverse reasoning abilities, and a dense retrieval system that aims to retrieve a set of evidential paragraph fragments. Recent progress in question-answering has been achieved either through prompting methods against very large pretrained Language Models in zero or few-shot fashion, or by fine-tuning smaller models, sometimes in conjunction with information retrieval. We focus on the less explored question of the extent to which zero-shot generalisation can be enabled in smaller models with retrieval against a corpus within which sufficient information to answer a particular question may not exist. We establish strong baselines in this setting for diverse evaluation datasets (StrategyQA, CommonsenseQA, IIRC, DROP, Musique and ARC-DA), and show that performance can be significantly improved by adding retrieval-augmented training datasets which are designed to expose our models to a variety of heuristic reasoning strategies such as weighing partial evidence or ignoring an irrelevant context.
Energy efficiency and low latency are crucial requirements for designing wearable AI-empowered human activity recognition systems, due to the hard constraints of battery operations and closed-loop feedback. While neural network models have been extensively compressed to match the stringent edge requirements, spiking neural networks and event-based sensing are recently emerging as promising solutions to further improve performance due to their inherent energy efficiency and capacity to process spatiotemporal data in very low latency. This work aims to evaluate the effectiveness of spiking neural networks on neuromorphic processors in human activity recognition for wearable applications. The case of workout recognition with wrist-worn wearable motion sensors is used as a study. A multi-threshold delta modulation approach is utilized for encoding the input sensor data into spike trains to move the pipeline into the event-based approach. The spikes trains are then fed to a spiking neural network with direct-event training, and the trained model is deployed on the research neuromorphic platform from Intel, Loihi, to evaluate energy and latency efficiency. Test results show that the spike-based workouts recognition system can achieve a comparable accuracy (87.5\%) comparable to the popular milliwatt RISC-V bases multi-core processor GAP8 with a traditional neural network ( 88.1\%) while achieving two times better energy-delay product (0.66 \si{\micro\joule\second} vs. 1.32 \si{\micro\joule\second}).
There has been appreciable progress in unsupervised network representation learning (UNRL) approaches over graphs recently with flexible random-walk approaches, new optimization objectives and deep architectures. However, there is no common ground for systematic comparison of embeddings to understand their behavior for different graphs and tasks. In this paper we theoretically group different approaches under a unifying framework and empirically investigate the effectiveness of different network representation methods. In particular, we argue that most of the UNRL approaches either explicitly or implicit model and exploit context information of a node. Consequently, we propose a framework that casts a variety of approaches -- random walk based, matrix factorization and deep learning based -- into a unified context-based optimization function. We systematically group the methods based on their similarities and differences. We study the differences among these methods in detail which we later use to explain their performance differences (on downstream tasks). We conduct a large-scale empirical study considering 9 popular and recent UNRL techniques and 11 real-world datasets with varying structural properties and two common tasks -- node classification and link prediction. We find that there is no single method that is a clear winner and that the choice of a suitable method is dictated by certain properties of the embedding methods, task and structural properties of the underlying graph. In addition we also report the common pitfalls in evaluation of UNRL methods and come up with suggestions for experimental design and interpretation of results.
Deep neural network architectures have traditionally been designed and explored with human expertise in a long-lasting trial-and-error process. This process requires huge amount of time, expertise, and resources. To address this tedious problem, we propose a novel algorithm to optimally find hyperparameters of a deep network architecture automatically. We specifically focus on designing neural architectures for medical image segmentation task. Our proposed method is based on a policy gradient reinforcement learning for which the reward function is assigned a segmentation evaluation utility (i.e., dice index). We show the efficacy of the proposed method with its low computational cost in comparison with the state-of-the-art medical image segmentation networks. We also present a new architecture design, a densely connected encoder-decoder CNN, as a strong baseline architecture to apply the proposed hyperparameter search algorithm. We apply the proposed algorithm to each layer of the baseline architectures. As an application, we train the proposed system on cine cardiac MR images from Automated Cardiac Diagnosis Challenge (ACDC) MICCAI 2017. Starting from a baseline segmentation architecture, the resulting network architecture obtains the state-of-the-art results in accuracy without performing any trial-and-error based architecture design approaches or close supervision of the hyperparameters changes.
We propose a Bayesian convolutional neural network built upon Bayes by Backprop and elaborate how this known method can serve as the fundamental construct of our novel, reliable variational inference method for convolutional neural networks. First, we show how Bayes by Backprop can be applied to convolutional layers where weights in filters have probability distributions instead of point-estimates; and second, how our proposed framework leads with various network architectures to performances comparable to convolutional neural networks with point-estimates weights. In the past, Bayes by Backprop has been successfully utilised in feedforward and recurrent neural networks, but not in convolutional ones. This work symbolises the extension of the group of Bayesian neural networks which encompasses all three aforementioned types of network architectures now.
This paper proposes a method to modify traditional convolutional neural networks (CNNs) into interpretable CNNs, in order to clarify knowledge representations in high conv-layers of CNNs. In an interpretable CNN, each filter in a high conv-layer represents a certain object part. We do not need any annotations of object parts or textures to supervise the learning process. Instead, the interpretable CNN automatically assigns each filter in a high conv-layer with an object part during the learning process. Our method can be applied to different types of CNNs with different structures. The clear knowledge representation in an interpretable CNN can help people understand the logics inside a CNN, i.e., based on which patterns the CNN makes the decision. Experiments showed that filters in an interpretable CNN were more semantically meaningful than those in traditional CNNs.
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