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Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light curve simulations. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, $H_0$, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and $\Lambda$CDM-dependent baryon acoustic oscillation observations. The inferred $H_0$ values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are $H_0= 66 \pm 6\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$, $H_0= 67 \pm 10\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ and $H_0= 69 \pm 6\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with $\ln R=12.17\pm 0.02$.

Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differential equation that quantifies the physical inconsistency. We prove that for linear differential priors, the problem can be formulated as a kernel regression task. Taking advantage of kernel theory, we derive convergence rates for the minimizer of the regularized risk and show that it converges at least at the Sobolev minimax rate. However, faster rates can be achieved, depending on the physical error. This principle is illustrated with a one-dimensional example, supporting the claim that regularizing the empirical risk with physical information can be beneficial to the statistical performance of estimators.

We introduce a higher-dimensional "cubical" chain complex and apply it to the design of quantum locally testable codes. Our cubical chain complex can be constructed for any dimension $t$, and in a precise sense generalizes the Sipser-Spielman construction of expander codes (case $t=1$) and the constructions by Dinur et. al and Panteleev and Kalachev of a square complex (case $t$=2), which have been applied to the design of classical locally testable and quantum low-density parity check codes respectively. For $t=4$ our construction gives a family of quantum locally testable codes conditional on a conjecture about robustness of four-tuples of random linear maps. These codes have linear dimension, inverse poly-logarithmic relative distance and soundness, and polylogarithmic-size parity checks. Our complex can be built in a modular way from two ingredients. Firstly, the geometry (edges, faces, cubes, etc.) is provided by a set $G$ of size $N$, together with pairwise commuting sets of actions $A_1,\ldots,A_t$ on it. Secondly, the chain complex itself is obtained by associating local coefficient spaces based on codes, with each geometric object, and introducing local maps on those coefficient spaces. We bound the cycle and co-cycle expansion of the chain complex. The assumptions we need are two-fold: firstly, each Cayley graph $Cay(G,A_j)$ needs to be a good (spectral) expander, and secondly, the families of codes and their duals both need to satisfy a form of robustness (that generalizes the condition of agreement testability for pairs of codes). While the first assumption is easy to satisfy, it is currently not known if the second can be achieved.

The dynamic mode decomposition (DMD) is a simple and powerful data-driven modeling technique that is capable of revealing coherent spatiotemporal patterns from data. The method's linear algebra-based formulation additionally allows for a variety of optimizations and extensions that make the algorithm practical and viable for real-world data analysis. As a result, DMD has grown to become a leading method for dynamical system analysis across multiple scientific disciplines. PyDMD is a Python package that implements DMD and several of its major variants. In this work, we expand the PyDMD package to include a number of cutting-edge DMD methods and tools specifically designed to handle dynamics that are noisy, multiscale, parameterized, prohibitively high-dimensional, or even strongly nonlinear. We provide a complete overview of the features available in PyDMD as of version 1.0, along with a brief overview of the theory behind the DMD algorithm, information for developers, tips regarding practical DMD usage, and introductory coding examples. All code is available at //github.com/PyDMD/PyDMD .

Multi-sequence magnetic resonance imaging (MRI) has found wide applications in both modern clinical studies and deep learning research. However, in clinical practice, it frequently occurs that one or more of the MRI sequences are missing due to different image acquisition protocols or contrast agent contraindications of patients, limiting the utilization of deep learning models trained on multi-sequence data. One promising approach is to leverage generative models to synthesize the missing sequences, which can serve as a surrogate acquisition. State-of-the-art methods tackling this problem are based on convolutional neural networks (CNN) which usually suffer from spectral biases, resulting in poor reconstruction of high-frequency fine details. In this paper, we propose Conditional Neural fields with Shift modulation (CoNeS), a model that takes voxel coordinates as input and learns a representation of the target images for multi-sequence MRI translation. The proposed model uses a multi-layer perceptron (MLP) instead of a CNN as the decoder for pixel-to-pixel mapping. Hence, each target image is represented as a neural field that is conditioned on the source image via shift modulation with a learned latent code. Experiments on BraTS 2018 and an in-house clinical dataset of vestibular schwannoma patients showed that the proposed method outperformed state-of-the-art methods for multi-sequence MRI translation both visually and quantitatively. Moreover, we conducted spectral analysis, showing that CoNeS was able to overcome the spectral bias issue common in conventional CNN models. To further evaluate the usage of synthesized images in clinical downstream tasks, we tested a segmentation network using the synthesized images at inference.

The availability of data is limited in some fields, especially for object detection tasks, where it is necessary to have correctly labeled bounding boxes around each object. A notable example of such data scarcity is found in the domain of marine biology, where it is useful to develop methods to automatically detect submarine species for environmental monitoring. To address this data limitation, the state-of-the-art machine learning strategies employ two main approaches. The first involves pretraining models on existing datasets before generalizing to the specific domain of interest. The second strategy is to create synthetic datasets specifically tailored to the target domain using methods like copy-paste techniques or ad-hoc simulators. The first strategy often faces a significant domain shift, while the second demands custom solutions crafted for the specific task. In response to these challenges, here we propose a transfer learning framework that is valid for a generic scenario. In this framework, generated images help to improve the performances of an object detector in a few-real data regime. This is achieved through a diffusion-based generative model that was pretrained on large generic datasets, and is not trained on the task-specific domain. We validate our approach on object detection tasks, specifically focusing on fishes in an underwater environment, and on the more common domain of cars in an urban setting. Our method achieves detection performance comparable to models trained on thousands of images, using only a few hundreds of input data. Our results pave the way for new generative AI-based protocols for machine learning applications in various domains, for instance ranging from geophysics to biology and medicine.

We propose a novel neural network architecture based on conformer transducer that adds contextual information flow to the ASR systems. Our method improves the accuracy of recognizing uncommon words while not harming the word error rate of regular words. We explore the uncommon words accuracy improvement when we use the new model and/or shallow fusion with context language model. We found that combination of both provides cumulative gain in uncommon words recognition accuracy.

We introduce a random recursive tree model with two communities, called balanced community modulated random recursive tree, or BCMRT in short. In this setting, pairs of nodes of different type appear sequentially. Each node of the pair decides independently to attach to their own type with probability 1-q, or to the other type with probability q, and then chooses its parent uniformly within the set of existing nodes with the selected type. We find that the limiting degree distributions coincide for different q. Therefore, as far as inference is concerned, other statistics have to be studied. We first consider the setting where the time-labels of the nodes, i.e., their time of arrival, are observed but their type is not. In this setting, we design a consistent estimator for q and provide bounds for the feasibility of testing between two different values of q. Moreover, we show that if q is small enough, then it is possible to cluster the nodes in a way correlated with the true partition, even though the algorithm is exponential in time (in passing, we show that our clustering procedure is intimately connected to the NP-hard problem of minimum fair bisection). In the unlabelled setting, i.e., when only the tree structure is observed, we show that it is possible to test between different values of q in a strictly better way than by random guessing. This follows from a delicate analysis of the sum-of-distances statistic.

We study the notion of $k$-stabilizer universal quantum state, that is, an $n$-qubit quantum state, such that it is possible to induce any stabilizer state on any $k$ qubits, by using only local operations and classical communications. These states generalize the notion of $k$-pairable states introduced by Bravyi et al., and can be studied from a combinatorial perspective using graph states and $k$-vertex-minor universal graphs. First, we demonstrate the existence of $k$-stabilizer universal graph states that are optimal in size with $n=\Theta(k^2)$ qubits. We also provide parameters for which a random graph state on $\Theta(k^2)$ qubits is $k$-stabilizer universal with high probability. Our second contribution consists of two explicit constructions of $k$-stabilizer universal graph states on $n = O(k^4)$ qubits. Both rely upon the incidence graph of the projective plane over a finite field $\mathbb{F}_q$. This provides a major improvement over the previously known explicit construction of $k$-pairable graph states with $n = O(2^{3k})$, bringing forth a new and potentially powerful family of multipartite quantum resources.

Hashing has been widely used in approximate nearest search for large-scale database retrieval for its computation and storage efficiency. Deep hashing, which devises convolutional neural network architecture to exploit and extract the semantic information or feature of images, has received increasing attention recently. In this survey, several deep supervised hashing methods for image retrieval are evaluated and I conclude three main different directions for deep supervised hashing methods. Several comments are made at the end. Moreover, to break through the bottleneck of the existing hashing methods, I propose a Shadow Recurrent Hashing(SRH) method as a try. Specifically, I devise a CNN architecture to extract the semantic features of images and design a loss function to encourage similar images projected close. To this end, I propose a concept: shadow of the CNN output. During optimization process, the CNN output and its shadow are guiding each other so as to achieve the optimal solution as much as possible. Several experiments on dataset CIFAR-10 show the satisfying performance of SRH.