Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph structure, this is an important yet analytically intractable question in general. In this work, we take an alternative approach to the synchronization prediction problem by viewing it as a classification problem based on the fact that any given system will eventually synchronize or converge to a non-synchronizing limit cycle. By only using some basic statistics of the underlying graphs such as edge density and diameter, our method can achieve perfect accuracy when there is a significant difference in the topology of the underlying graphs between the synchronizing and the non-synchronizing examples. However, in the problem setting where these graph statistics cannot distinguish the two classes very well (e.g., when the graphs are generated from the same random graph model), we find that pairing a few iterations of the initial dynamics along with the graph statistics as the input to our classification algorithms can lead to significant improvement in accuracy; far exceeding what is known by the classical oscillator theory. More surprisingly, we find that in almost all such settings, dropping out the basic graph statistics and training our algorithms with only initial dynamics achieves nearly the same accuracy. We demonstrate our method on three models of continuous and discrete coupled oscillators -- the Kuramoto model, Firefly Cellular Automata, and Greenberg-Hastings model. Finally, we also propose an "ensemble prediction" algorithm that successfully scales our method to large graphs by training on dynamics observed from multiple random subgraphs.

Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive function to the output of Mixture Density Networks (MDNs). While MDNs produce flexible real-valued distributions, the invertible positive function maps the model into the time-domain while preserving a tractable density. Using four datasets, we show that Survival MDN performs better than, or similarly to continuous and discrete time baselines on concordance, integrated Brier score and integrated binomial log-likelihood. Meanwhile, Survival MDNs are also faster than ODE-based models and circumvent binning issues in discrete models.

In order to identify a system (module) embedded in a dynamic network, one has to formulate a multiple-input estimation problem that necessitates certain nodes to be measured and included as predictor inputs. However, some of these nodes may not be measurable in many practical cases due to sensor selection and placement issues. This may result in biased estimates of the target module. Furthermore, the identification problem associated with the multiple-input structure may require determining a large number of parameters that are not of particular interest to the experimenter, with increased computational complexity in large-sized networks. In this paper, we tackle these problems by using a data augmentation strategy that allows us to reconstruct the missing node measurements and increase the accuracy of the estimated target module. To this end, we develop a system identification method using regularized kernel-based methods coupled with approximate inference methods. Keeping a parametric model for the module of interest, we model the other modules as Gaussian Processes (GP) with a kernel given by the so-called stable spline kernel. An Empirical Bayes (EB) approach is used to estimate the parameters of the target module. The related optimization problem is solved using an Expectation-Maximization (EM) method, where we employ a Markov-chain Monte Carlo (MCMC) technique to reconstruct the unknown missing node information and the network dynamics. Numerical simulations on dynamic network examples illustrate the potentials of the developed method.

In this paper, we consider to improve the stochastic variance reduce gradient (SVRG) method via incorporating the curvature information of the objective function. We propose to reduce the variance of stochastic gradients using the computationally efficient Barzilai-Borwein (BB) method by incorporating it into the SVRG. We also incorporate a BB-step size as its variant. We prove its linear convergence theorem that works not only for the proposed method but also for the other existing variants of SVRG with second-order information. We conduct the numerical experiments on the benchmark datasets and show that the proposed method with constant step size performs better than the existing variance reduced methods for some test problems.

Relying on the fact that not all inputs require the same amount of computation to yield a confident prediction, multi-exit networks are gaining attention as a prominent approach for pushing the limits of efficient deployment. Multi-exit networks endow a backbone model with early exits, allowing to obtain predictions at intermediate layers of the model and thus save computation time and/or energy. However, current various designs of multi-exit networks are only considered to achieve the best trade-off between resource usage efficiency and prediction accuracy, the privacy risks stemming from them have never been explored. This prompts the need for a comprehensive investigation of privacy risks in multi-exit networks. In this paper, we perform the first privacy analysis of multi-exit networks through the lens of membership leakages. In particular, we first leverage the existing attack methodologies to quantify the multi-exit networks' vulnerability to membership leakages. Our experimental results show that multi-exit networks are less vulnerable to membership leakages and the exit (number and depth) attached to the backbone model is highly correlated with the attack performance. Furthermore, we propose a hybrid attack that exploits the exit information to improve the performance of existing attacks. We evaluate membership leakage threat caused by our hybrid attack under three different adversarial setups, ultimately arriving at a model-free and data-free adversary. These results clearly demonstrate that our hybrid attacks are very broadly applicable, thereby the corresponding risks are much more severe than shown by existing membership inference attacks. We further present a defense mechanism called TimeGuard specifically for multi-exit networks and show that TimeGuard mitigates the newly proposed attacks perfectly.

The standard FL follows three steps: (i) at each iteration, the server distributes the global model to clients; (ii) the client trains the local model on its local private data based on the global model; (iii) the server aggregates local models updated by clients to achieve a new global model, repeated until convergence [1, 4]. FL can ensure effective collaboration between different clients when the data distributions are independent and identically distributed (IID), i.e., private data distributions of clients are similar to each other. However, in many application scenarios, private data of clients may be different in size and class distribution, that is, the data distributions are not independent and identically distributed (Non-IID). In this case, FL may not achieve effective collaboration on different clients due to difference of individual private data [5]. Various algorithms have been proposed to handle the Non-IID data in FL, which can be divided into two categories: average aggregation methods and model-based aggregation methods. As shown in Figure 1(a), average aggregation methods average all local models to generate a global model and distribute it to all clients, where an additional fine-tuning step is performed to train the personalized model in the clients [6, 7, 8, 9].

Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks remains mostly unanswered despite their strong ability for sample generation and density estimation. This paper investigates this problem for such a family of generative models that admits exact invertibility. We propose Neural Principal Component Analysis (Neural-PCA) that operates in full dimensionality while capturing principal components in \emph{descending} order. Without exploiting any label information, the principal components recovered store the most informative elements in their \emph{leading} dimensions and leave the negligible in the \emph{trailing} ones, allowing for clear performance improvements of $5\%$-$10\%$ in downstream tasks. Such improvements are empirically found consistent irrespective of the number of latent trailing dimensions dropped. Our work suggests that necessary inductive bias be introduced into generative modelling when representation quality is of interest.

Equal contribution *To whom correspondence should be addressed. Abstract Recent development in angle-resolved photoemission spectroscopy (ARPES) technique involves spatially resolving samples while maintaining the high-resolution feature of momentum space. This development easily expands the data size and its complexity for data analysis, where one of it is to label similar dispersion cuts and map them spatially. In this work, we demonstrate that the recent development in representational learning (self-supervised learning) model combined with k-means clustering can help automate that part of data analysis and save precious time, albeit with low performance. Finally, we introduce a few-shot learning (k-nearest neighbour or kNN) in representational space where we selectively choose one (k=1) image reference for each known label and subsequently label the rest of the data with respect to the nearest reference image. This last approach demonstrates the strength of the selfsupervised learning to automate the image analysis in ARPES in particular and can be generalized into any science data analysis that heavily involves image data.

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model's parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from a quantum hardware. In this work we study the trainability of quantum kernels from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value, leading to an exponential scaling of the number of measurements required for successful training. We identify four sources that can lead to concentration including: the expressibility of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation and the trainability of quantum kernel methods.

Starting from version 1.6, XGBoost has experimental support for multi-output regression and multi-label classification with Python package. Multi-label classification usually refers to targets that have multiple non-exclusive class labels. For instance, a movie can be simultaneously classified as both sci-fi and comedy. For detailed explanation of terminologies related to different multi-output models please refer to the scikit-learn user guide. Internally, XGBoost builds one model for each target similar to sklearn meta estimators, with the added benefit of reusing data and other integrated features like SHAP.