We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is available. Thanks to the maximum a posteriori Bayesian framework, such regularizer can be systematically linked with the distribution of the data. With deep neural networks (DNN), complex distributions can be recovered from a large training database.To reduce the computational burden of this task, we adapt the compressive learning framework to the learning of regularizers parametrized by DNN. We propose two variants of stochastic gradient descent (SGD) for the recovery of deep regularization parameters from a heavily compressed database. These algorithms outperform the initially proposed method that was limited to low-dimensional signals, each iteration using information from the whole database. They also benefit from classical SGD convergence guarantees. Thanks to these improvements we show that this method can be applied for patch based image denoising.}
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Given a local Hamiltonian, how difficult is it to determine the entanglement structure of its ground state? We show that this problem is computationally intractable even if one is only trying to decide if the ground state is volume-law vs near area-law entangled. We prove this by constructing strong forms of pseudoentanglement in a public-key setting, where the circuits used to prepare the states are public knowledge. In particular, we construct two families of quantum circuits which produce volume-law vs near area-law entangled states, but nonetheless the classical descriptions of the circuits are indistinguishable under the Learning with Errors (LWE) assumption. Indistinguishability of the circuits then allows us to translate our construction to Hamiltonians. Our work opens new directions in Hamiltonian complexity, for example whether it is difficult to learn certain phases of matter.
In domains where sample sizes are limited, efficient learning algorithms are critical. Learning using privileged information (LuPI) offers increased sample efficiency by allowing prediction models access to auxiliary information at training time which is unavailable when the models are used. In recent work, it was shown that for prediction in linear-Gaussian dynamical systems, a LuPI learner with access to intermediate time series data is never worse and often better in expectation than any unbiased classical learner. We provide new insights into this analysis and generalize it to nonlinear prediction tasks in latent dynamical systems, extending theoretical guarantees to the case where the map connecting latent variables and observations is known up to a linear transform. In addition, we propose algorithms based on random features and representation learning for the case when this map is unknown. A suite of empirical results confirm theoretical findings and show the potential of using privileged time-series information in nonlinear prediction.
This work proposes to measure the scope of a patent claim as the reciprocal of the self-information contained in this claim. A probability of occurrence of the claim is obtained from a language model and this probability is used to compute the self-information. Grounded in information theory, this approach is based on the assumption that an unlikely concept is more informative than a usual concept, insofar as it is more surprising. In turn, the more surprising the information required to defined the claim, the narrower its scope. Five language models are considered, ranging from simplest models (each word or character is assigned an identical probability) to intermediate models (using average word or character frequencies), to a large language model (GPT2). Interestingly, the scope resulting from the simplest language models is proportional to the reciprocal of the number of words or characters involved in the claim, a metric already used in previous works. Application is made to multiple series of patent claims directed to distinct inventions, where each series consists of claims devised to have a gradually decreasing scope. The performance of the language models is assessed with respect to several ad hoc tests. The more sophisticated the model, the better the results. I.e., the GPT2 probability model outperforms models based on word and character frequencies, which themselves outdo the simplest models based on word or character counts. Still, the character count appears to be a more reliable indicator than the word count.
We observe a large variety of robots in terms of their bodies, sensors, and actuators. Given the commonalities in the skill sets, teaching each skill to each different robot independently is inefficient and not scalable when the large variety in the robotic landscape is considered. If we can learn the correspondences between the sensorimotor spaces of different robots, we can expect a skill that is learned in one robot can be more directly and easily transferred to other robots. In this paper, we propose a method to learn correspondences among two or more robots that may have different morphologies. To be specific, besides robots with similar morphologies with different degrees of freedom, we show that a fixed-based manipulator robot with joint control and a differential drive mobile robot can be addressed within the proposed framework. To set up the correspondence among the robots considered, an initial base task is demonstrated to the robots to achieve the same goal. Then, a common latent representation is learned along with the individual robot policies for achieving the goal. After the initial learning stage, the observation of a new task execution by one robot becomes sufficient to generate a latent space representation pertaining to the other robots to achieve the same task. We verified our system in a set of experiments where the correspondence between robots is learned (1) when the robots need to follow the same paths to achieve the same task, (2) when the robots need to follow different trajectories to achieve the same task, and (3) when complexities of the required sensorimotor trajectories are different for the robots. We also provide a proof-of-the-concept realization of correspondence learning between a real manipulator robot and a simulated mobile robot.
Purpose: To develop biophysics-based method for estimating perfusion Q from arterial spin labeling (ASL) images using deep learning. Methods: A 3D U-Net (QTMnet) was trained to estimate perfusion from 4D tracer propagation images. The network was trained and tested on simulated 4D tracer concentration data based on artificial vasculature structure generated by constrained constructive optimization (CCO) method. The trained network was further tested in a synthetic brain ASL image based on vasculature network extracted from magnetic resonance (MR) angiography. The estimations from both trained network and a conventional kinetic model were compared in ASL images acquired from eight healthy volunteers. Results: QTMnet accurately reconstructed perfusion Q from concentration data. Relative error of the synthetic brain ASL image was 7.04% for perfusion Q, lower than the error using single-delay ASL model: 25.15% for Q, and multi-delay ASL model: 12.62% for perfusion Q. Conclusion: QTMnet provides accurate estimation on perfusion parameters and is a promising approach as a clinical ASL MRI image processing pipeline.
Deep neural networks (DNNs) have become ubiquitous in addressing a number of problems, particularly in computer vision. However, DNN inference is computationally intensive, which can be prohibitive e.g. when considering edge devices. To solve this problem, a popular solution is DNN pruning, and more so structured pruning, where coherent computational blocks (e.g. channels for convolutional networks) are removed: as an exhaustive search of the space of pruned sub-models is intractable in practice, channels are typically removed iteratively based on an importance estimation heuristic. Recently, promising latency-aware pruning methods were proposed, where channels are removed until the network reaches a target budget of wall-clock latency pre-emptively estimated on specific hardware. In this paper, we present Archtree, a novel method for latency-driven structured pruning of DNNs. Archtree explores multiple candidate pruned sub-models in parallel in a tree-like fashion, allowing for a better exploration of the search space. Furthermore, it involves on-the-fly latency estimation on the target hardware, accounting for closer latencies as compared to the specified budget. Empirical results on several DNN architectures and target hardware show that Archtree better preserves the original model accuracy while better fitting the latency budget as compared to existing state-of-the-art methods.
This study examines clusterability testing for a signed graph in the bounded-degree model. Our contributions are two-fold. First, we provide a quantum algorithm with query complexity $\tilde{O}(N^{1/3})$ for testing clusterability, which yields a polynomial speedup over the best classical clusterability tester known [arXiv:2102.07587]. Second, we prove an $\tilde{\Omega}(\sqrt{N})$ classical query lower bound for testing clusterability, which nearly matches the upper bound from [arXiv:2102.07587]. This settles the classical query complexity of clusterability testing, and it shows that our quantum algorithm has an advantage over any classical algorithm.
Despite the increasing use of deep learning in medical image segmentation, acquiring sufficient training data remains a challenge in the medical field. In response, data augmentation techniques have been proposed; however, the generation of diverse and realistic medical images and their corresponding masks remains a difficult task, especially when working with insufficient training sets. To address these limitations, we present an end-to-end architecture based on the Hamiltonian Variational Autoencoder (HVAE). This approach yields an improved posterior distribution approximation compared to traditional Variational Autoencoders (VAE), resulting in higher image generation quality. Our method outperforms generative adversarial architectures under data-scarce conditions, showcasing enhancements in image quality and precise tumor mask synthesis. We conduct experiments on two publicly available datasets, MICCAI's Brain Tumor Segmentation Challenge (BRATS), and Head and Neck Tumor Segmentation Challenge (HECKTOR), demonstrating the effectiveness of our method on different medical imaging modalities.
Data collected by different modalities can provide a wealth of complementary information, such as hyperspectral image (HSI) to offer rich spectral-spatial properties, synthetic aperture radar (SAR) to provide structural information about the Earth's surface, and light detection and ranging (LiDAR) to cover altitude information about ground elevation. Therefore, a natural idea is to combine multimodal images for refined and accurate land-cover interpretation. Although many efforts have been attempted to achieve multi-source remote sensing image classification, there are still three issues as follows: 1) indiscriminate feature representation without sufficiently considering modal heterogeneity, 2) abundant features and complex computations associated with modeling long-range dependencies, and 3) overfitting phenomenon caused by sparsely labeled samples. To overcome the above barriers, a transformer-based heterogeneously salient graph representation (THSGR) approach is proposed in this paper. First, a multimodal heterogeneous graph encoder is presented to encode distinctively non-Euclidean structural features from heterogeneous data. Then, a self-attention-free multi-convolutional modulator is designed for effective and efficient long-term dependency modeling. Finally, a mean forward is put forward in order to avoid overfitting. Based on the above structures, the proposed model is able to break through modal gaps to obtain differentiated graph representation with competitive time cost, even for a small fraction of training samples. Experiments and analyses on three benchmark datasets with various state-of-the-art (SOTA) methods show the performance of the proposed approach.
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
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