Jonathan Dong

Pakshal Bohra, Thanh-an Pham, Jonathan Dong et al.

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the image. It depends on the model of the imaging system and on prior knowledge on the image of interest. In this work, we present a Bayesian reconstruction framework for nonlinear imaging models where we specify the prior knowledge on the image through a deep generative model. We develop a tractable posterior-sampling scheme based on the Metropolis-adjusted Langevin algorithm for the class of nonlinear inverse problems where the forward model has a neural-network-like structure. This class includes most practical imaging modalities. We introduce the notion of augmented deep generative priors in order to suitably handle the recovery of quantitative images.We illustrate the advantages of our framework by applying it to two nonlinear imaging modalities-phase retrieval and optical diffraction tomography.

Jonathan Dong, Erik Börve, Mushegh Rafayelyan et al.

Reservoir Computing is a class of Recurrent Neural Networks with internal weights fixed at random. Stability relates to the sensitivity of the network state to perturbations. It is an important property in Reservoir Computing as it directly impacts performance. In practice, it is desirable to stay in a stable regime, where the effect of perturbations does not explode exponentially, but also close to the chaotic frontier where reservoir dynamics are rich. Open questions remain today regarding input regularization and discontinuous activation functions. In this work, we use the recurrent kernel limit to draw new insights on stability in reservoir computing. This limit corresponds to large reservoir sizes, and it already becomes relevant for reservoirs with a few hundred neurons. We obtain a quantitative characterization of the frontier between stability and chaos, which can greatly benefit hyperparameter tuning. In a broader sense, our results contribute to understanding the complex dynamics of Recurrent Neural Networks.

Yan Liu, Jonathan Dong, Thanh-An Pham et al.

Optical projection tomography (OPT) is a powerful tool for biomedical studies. It achieves 3D visualization of mesoscopic biological samples with high spatial resolution using conventional tomographic-reconstruction algorithms. However, various artifacts degrade the quality of the reconstructed images due to experimental imperfections in the OPT instruments. While many efforts have been made to characterize and correct for these artifacts, they focus on one specific type of artifacts. This work has two contributions. First, we systematically document a catalog of mechanical artifacts based on a 3D description of the imaging system that uses a set of angular and translational parameters. Then, we introduce a calibration algorithm that recovers the unknown system parameters fed into the final 3D iterative reconstruction algorithm for a distortion-free volumetric image. Simulations with beads data and experimental results on a fluorescent textile fiber confirm that our algorithm successfully removes miscalibration artifacts in the reconstruction.

Shuya Lin, Yuxiong Wang, Jonathan Dong et al.

This research introduces a Positive Reconstruction Framework based on positive psychology theory. Overcoming negative thoughts can be challenging, our objective is to address and reframe them through a positive reinterpretation. To tackle this challenge, a two-fold approach is necessary: identifying cognitive distortions and suggesting a positively reframed alternative while preserving the original thought's meaning. Recent studies have investigated the application of Natural Language Processing (NLP) models in English for each stage of this process. In this study, we emphasize the theoretical foundation for the Positive Reconstruction Framework, grounded in broaden-and-build theory. We provide a shared corpus containing 4001 instances for detecting cognitive distortions and 1900 instances for positive reconstruction in Mandarin. Leveraging recent NLP techniques, including transfer learning, fine-tuning pretrained networks, and prompt engineering, we demonstrate the effectiveness of automated tools for both tasks. In summary, our study contributes to multilingual positive reconstruction, highlighting the effectiveness of NLP in cognitive distortion detection and positive reconstruction.

Stanislas Ducotterd, Zhiyuan Hu, Michael Unser et al.

Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors in the context of severe undersampling with structured random Fourier measurements. Our results show that those priors significantly improve reconstruction, allowing accurate reconstruction even below the weak recovery threshold.

Giuseppe Alessio D'Inverno, Zhiyuan Hu, Leo Davy et al.

Information propagation characterizes how input correlations evolve across layers in deep neural networks. This framework has been well studied using mean-field theory, which assumes infinitely wide networks. However, these assumptions break down for practical, finite-size networks. In this work, we study information propagation in randomly initialized neural networks with finite width and reveal that the boundary between ordered and chaotic regimes exhibits a fractal structure. This shows the fundamental complexity of neural network dynamics, in a setting that is independent of input data and optimization. To extend this analysis beyond multilayer perceptrons, we leverage recently introduced Fourier-based structured transforms, and show that information propagation in convolutional neural networks also follow the same behavior. Our investigation highlights the importance of finite network depth with respect to the tradeoff between separation and robustness.

Giuseppe Alessio D'Inverno, Jonathan Dong

Reservoir Computing (RC) has become popular in recent years thanks to its fast and efficient computational capabilities. Standard RC has been shown to be equivalent in the asymptotic limit to Recurrent Kernels, which helps in analyzing its expressive power. However, many well-established RC paradigms, such as Leaky RC, Sparse RC, and Deep RC, are yet to be systematically analyzed in such a way. We define the Recurrent Kernel limit of all these RC topologies and conduct a convergence study for a wide range of activation functions and hyperparameters. Our findings provide new insights into various aspects of Reservoir Computing. First, we demonstrate that there is an optimal sparsity level which grows with the reservoir size. Furthermore, our analysis suggests that Deep RC should use reservoir layers of decreasing sizes. Finally, we perform a benchmark demonstrating the efficiency of Structured Reservoir Computing compared to vanilla and Sparse Reservoir Computing.

Jonathan Dong, Ruben Ohana, Mushegh Rafayelyan et al.

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep connection with kernel methods. Our contributions are threefold: a) We rigorously establish the recurrent kernel limit of Reservoir Computing and prove its convergence. b) We test our models on chaotic time series prediction, a classic but challenging benchmark in Reservoir Computing, and show how the Recurrent Kernel is competitive and computationally efficient when the number of data points remains moderate. c) When the number of samples is too large, we leverage the success of structured Random Features for kernel approximation by introducing Structured Reservoir Computing. The two proposed methods, Recurrent Kernel and Structured Reservoir Computing, turn out to be much faster and more memory-efficient than conventional Reservoir Computing.

Ruben Ohana, Jonas Wacker, Jonathan Dong et al.

Approximating kernel functions with random features (RFs)has been a successful application of random projections for nonparametric estimation. However, performing random projections presents computational challenges for large-scale problems. Recently, a new optical hardware called Optical Processing Unit (OPU) has been developed for fast and energy-efficient computation of large-scale RFs in the analog domain. More specifically, the OPU performs the multiplication of input vectors by a large random matrix with complex-valued i.i.d. Gaussian entries, followed by the application of an element-wise squared absolute value operation - this last nonlinearity being intrinsic to the sensing process. In this paper, we show that this operation results in a dot-product kernel that has connections to the polynomial kernel, and we extend this computation to arbitrary powers of the feature map. Experiments demonstrate that the OPU kernel and its RF approximation achieve competitive performance in applications using kernel ridge regression and transfer learning for image classification. Crucially, thanks to the use of the OPU, these results are obtained with time and energy savings.

Jonathan Dong, Sylvain Gigan, Florent Krzakala et al.

Echo-State Networks and Reservoir Computing have been studied for more than a decade. They provide a simpler yet powerful alternative to Recurrent Neural Networks, every internal weight is fixed and only the last linear layer is trained. They involve many multiplications by dense random matrices. Very large networks are difficult to obtain, as the complexity scales quadratically both in time and memory. Here, we present a novel optical implementation of Echo-State Networks using light-scattering media and a Digital Micromirror Device. As a proof of concept, binary networks have been successfully trained to predict the chaotic Mackey-Glass time series. This new method is fast, power efficient and easily scalable to very large networks.

Li-Hao Yeh, Jonathan Dong, Jingshan Zhong et al.

Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different illumination angles, a nonlinear inverse algorithm can be used to computationally reconstruct the high-resolution complex field. Here, we compare and classify multiple proposed inverse algorithms in terms of experimental robustness. We find that the main sources of error are noise, aberrations and mis-calibration (i.e. model mis-match). Using simulations and experiments, we demonstrate that the choice of cost function plays a critical role, with amplitude-based cost functions performing better than intensity-based ones. The reason for this is that Fourier ptychography datasets consist of images from both brightfield and darkfield illumination, representing a large range of measured intensities. Both noise (e.g. Poisson noise) and model mis-match errors are shown to scale with intensity. Hence, algorithms that use an appropriate cost function will be more tolerant to both noise and model mis-match. Given these insights, we propose a global Newton's method algorithm which is robust and computationally efficient. Finally, we discuss the impact of procedures for algorithmic correction of aberrations and mis-calibration.