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In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate (q) and momentum (p) variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a generating function. To extend the prediction time period, we develop a new learning scheme by splitting the time series (q_i, p_i) into several partitions. We then train a large-step neural network (LSNN) to approximate the generating function between the first partition (i.e. the initial condition) and each one of the remaining partitions. This partition approach makes our LSNN effectively suppress the accumulative error when predicting the system evolution. Then we train the LSNN to learn the motions of the 2:3 resonant Kuiper belt objects for a long time period of 25000 yr. The results show that there are two significant improvements over the neural network constructed in our previous work (Li et al. 2022): (1) the conservation of the Jacobi integral, and (2) the highly accurate predictions of the orbital evolution. Overall, we propose that the designed LSNN has the potential to considerably improve predictions of the long-term evolution of more general Hamiltonian systems.

Most iterative neural network training methods use estimates of the loss function over small random subsets (or minibatches) of the data to update the parameters, which aid in decoupling the training time from the (often very large) size of the training datasets. Here, we show that a minibatch approach can also be used to train neural network ensembles (NNEs) via trajectory methods in a highly efficent manner. We illustrate this approach by training NNEs to classify images in the MNIST datasets. This method gives an improvement to the training times, allowing it to scale as the ratio of the size of the dataset to that of the average minibatch size which, in the case of MNIST, gives a computational improvement typically of two orders of magnitude. We highlight the advantage of using longer trajectories to represent NNEs, both for improved accuracy in inference and reduced update cost in terms of the samples needed in minibatch updates.

Most recent 6D object pose methods use 2D optical flow to refine their results. However, the general optical flow methods typically do not consider the target's 3D shape information during matching, making them less effective in 6D object pose estimation. In this work, we propose a shape-constraint recurrent matching framework for 6D object pose estimation. We first compute a pose-induced flow based on the displacement of 2D reprojection between the initial pose and the currently estimated pose, which embeds the target's 3D shape implicitly. Then we use this pose-induced flow to construct the correlation map for the following matching iterations, which reduces the matching space significantly and is much easier to learn. Furthermore, we use networks to learn the object pose based on the current estimated flow, which facilitates the computation of the pose-induced flow for the next iteration and yields an end-to-end system for object pose. Finally, we optimize the optical flow and object pose simultaneously in a recurrent manner. We evaluate our method on three challenging 6D object pose datasets and show that it outperforms the state of the art significantly in both accuracy and efficiency.

This paper proposes a novel Self-Supervised Intrusion Detection (SSID) framework, which enables a fully online Machine Learning (ML) based Intrusion Detection System (IDS) that requires no human intervention or prior off-line learning. The proposed framework analyzes and labels incoming traffic packets based only on the decisions of the IDS itself using an Auto-Associative Deep Random Neural Network, and on an online estimate of its statistically measured trustworthiness. The SSID framework enables IDS to adapt rapidly to time-varying characteristics of the network traffic, and eliminates the need for offline data collection. This approach avoids human errors in data labeling, and human labor and computational costs of model training and data collection. The approach is experimentally evaluated on public datasets and compared with well-known ML models, showing that this SSID framework is very useful and advantageous as an accurate and online learning ML-based IDS for IoT systems.

Following the traditional paradigm of convolutional neural networks (CNNs), modern CNNs manage to keep pace with more recent, for example transformer-based, models by not only increasing model depth and width but also the kernel size. This results in large amounts of learnable model parameters that need to be handled during training. While following the convolutional paradigm with the according spatial inductive bias, we question the significance of \emph{learned} convolution filters. In fact, our findings demonstrate that many contemporary CNN architectures can achieve high test accuracies without ever updating randomly initialized (spatial) convolution filters. Instead, simple linear combinations (implemented through efficient $1\times 1$ convolutions) suffice to effectively recombine even random filters into expressive network operators. Furthermore, these combinations of random filters can implicitly regularize the resulting operations, mitigating overfitting and enhancing overall performance and robustness. Conversely, retaining the ability to learn filter updates can impair network performance. Lastly, although we only observe relatively small gains from learning $3\times 3$ convolutions, the learning gains increase proportionally with kernel size, owing to the non-idealities of the independent and identically distributed (\textit{i.i.d.}) nature of default initialization techniques.

We present a novel technique to estimate the 6D pose of objects from single images where the 3D geometry of the object is only given approximately and not as a precise 3D model. To achieve this, we employ a dense 2D-to-3D correspondence predictor that regresses 3D model coordinates for every pixel. In addition to the 3D coordinates, our model also estimates the pixel-wise coordinate error to discard correspondences that are likely wrong. This allows us to generate multiple 6D pose hypotheses of the object, which we then refine iteratively using a highly efficient region-based approach. We also introduce a novel pixel-wise posterior formulation by which we can estimate the probability for each hypothesis and select the most likely one. As we show in experiments, our approach is capable of dealing with extreme visual conditions including overexposure, high contrast, or low signal-to-noise ratio. This makes it a powerful technique for the particularly challenging task of estimating the pose of tumbling satellites for in-orbit robotic applications. Our method achieves state-of-the-art performance on the SPEED+ dataset and has won the SPEC2021 post-mortem competition.

State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of data points related to the state are obtained. The linear-Gaussian state-space model is widely used, since it allows for exact inference when all model parameters are known, however this is rarely the case. The estimation of these parameters is a very challenging but essential task to perform inference and prediction. In the linear-Gaussian model, the state dynamics are described via a state transition matrix. This model parameter is known to behard to estimate, since it encodes the relationships between the state elements, which are never observed. In many applications, this transition matrix is sparse since not all state components directly affect all other state components. However, most parameter estimation methods do not exploit this feature. In this work we propose SpaRJ, a fully probabilistic Bayesian approach that obtains sparse samples from the posterior distribution of the transition matrix. Our method explores sparsity by traversing a set of models that exhibit differing sparsity patterns in the transition matrix. Moreover, we also design new effective rules to explore transition matrices within the same level of sparsity. This novel methodology has strong theoretical guarantees, and unveils the latent structure of the data generating process, thereby enhancing interpretability. The performance of SpaRJ is showcased in example with dimension 144 in the parameter space, and in a numerical example with real data.

The algebraic degree is an important parameter of Boolean functions used in cryptography. When a function in a large number of variables is not given explicitly in algebraic normal form, it might not be feasible to compute its degree. Instead, one can try to estimate the degree using probabilistic tests. We propose a probabilistic test for deciding whether the algebraic degree of a Boolean function $f$ is below a certain value $k$. The test involves picking an affine space of dimension $k$ and testing whether the values on $f$ on that space sum up to zero. If $deg(f)<k$, then $f$ will always pass the test, otherwise it will sometimes pass and sometimes fail the test, depending on which affine space was chosen. The probability of failing the proposed test is closely related to the number of monomials of degree $k$ in a polynomial $g$, averaged over all the polynomials $g$ which are affine equivalent to $f$. We initiate the study of the probability of failing the proposed ``$deg(f)<k$'' test. We show that in the particular case when the degree of $f$ is actually equal to $k$, the probability will be in the interval $(0.288788, 0.5]$, and therefore a small number of runs of the test is sufficient to give, with very high probability, the correct answer. Exact values of this probability for all the polynomials in 8 variables were computed using the representatives listed by Hou and by Langevin and Leander.

Treatment effect estimation is of high-importance for both researchers and practitioners across many scientific and industrial domains. The abundance of observational data makes them increasingly used by researchers for the estimation of causal effects. However, these data suffer from biases, from several weaknesses, leading to inaccurate causal effect estimations, if not handled properly. Therefore, several machine learning techniques have been proposed, most of them focusing on leveraging the predictive power of neural network models to attain more precise estimation of causal effects. In this work, we propose a new methodology, named Nearest Neighboring Information for Causal Inference (NNCI), for integrating valuable nearest neighboring information on neural network-based models for estimating treatment effects. The proposed NNCI methodology is applied to some of the most well established neural network-based models for treatment effect estimation with the use of observational data. Numerical experiments and analysis provide empirical and statistical evidence that the integration of NNCI with state-of-the-art neural network models leads to considerably improved treatment effect estimations on a variety of well-known challenging benchmarks.

The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a consequence the chain-ladder reserving technique is non-robust. In this paper we investigate the sensitivity of reserves and mean squared errors of prediction under Mack's Model (Mack, 1993). This is done through the derivation of impact functions which are calculated by taking the first derivative of the relevant statistic of interest with respect to an observation. We also provide and discuss the impact functions for quantiles when total reserves are assumed to be lognormally distributed. Additionally, comparisons are made between the impact functions for individual accident year reserves under Mack's Model and the Bornhuetter-Ferguson methodology. It is shown that the impact of incremental claims on these statistics of interest varies widely throughout a loss triangle and is heavily dependent on other cells in the triangle. Results are illustrated using data from a Belgian non-life insurer.