However,whenlargeamounts ofannotated dataareavailable, models thatallow end-to-end training such as neural networks are often preferred.

Substring kernels are classical tools for representing biological sequences or text.

--State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these assumptions, prompting the rise of data-driven filtering techniques. This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation with consistent error covariance quantification. Experiments with non-Gaussian measurement white noise demonstrate that our model outperforms both the conventional Kalman filter and an existing state-of-the-art deep learning based estimator . The Kalman Filter (KF) [1] provides an optimal estimation of a state vector that evolves according to a linear differential equation, with measurements modeled as a linear combination of the state vector.

Real-world robotics applications demand object pose estimation methods that work reliably across a variety of scenarios. Modern learning-based approaches require large labeled datasets and tend to perform poorly outside the training domain. Our first contribution is to develop a robust corrector module that corrects pose estimates using depth information, thus enabling existing methods to better generalize to new test domains; the corrector operates on semantic keypoints (but is also applicable to other pose estimators) and is fully differentiable. Our second contribution is an ensemble self-training approach that simultaneously trains multiple pose estimators in a self-supervised manner. Our ensemble self-training architecture uses the robust corrector to refine the output of each pose estimator; then, it evaluates the quality of the outputs using observable correctness certificates; finally, it uses the observably correct outputs for further training, without requiring external supervision. As an additional contribution, we propose small improvements to a regression-based keypoint detection architecture, to enhance its robustness to outliers; these improvements include a robust pooling scheme and a robust centroid computation. Experiments on the YCBV and TLESS datasets show the proposed ensemble self-training outperforms fully supervised baselines while not requiring 3D annotations on real data.

Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data is available, models that allow end-to-end training such as neural networks are often prefered. Links between recurrent neural networks (RNNs) and substring kernels have recently been drawn, by formally showing that RNNs with specific activation functions were points in a reproducing kernel Hilbert space (RKHS). In this paper, we revisit this link by generalizing convolutional kernel networks---originally related to a relaxation of the mismatch kernel---to model gaps in sequences. It results in a new type of recurrent neural network which can be trained end-to-end with backpropagation, or without supervision by using kernel approximation techniques. We experimentally show that our approach is well suited to biological sequences, where it outperforms existing methods for protein classification tasks.

In order to integrate uncertainty estimates into deep time-series modelling, Kalman Filters (KFs) (Kalman et al., 1960) have been integrated with deep learning models, however, such approaches typically rely on approximate inference techniques such as variational inference which makes learning more complex and often less scalable due to approximation errors. We propose a new deep approach to Kalman filtering which can be learned directly in an end-to-end manner using backpropagation without additional approximations. Our approach uses a high-dimensional factorized latent state representation for which the Kalman updates simplify to scalar operations and thus avoids hard to backpropagate, computationally heavy and potentially unstable matrix inversions. Moreover, we use locally linear dynamic models to efficiently propagate the latent state to the next time step. The resulting network architecture, which we call Recurrent Kalman Network (RKN), can be used for any time-series data, similar to a LSTM (Hochreiter & Schmidhuber, 1997) but uses an explicit representation of uncertainty. As shown by our experiments, the RKN obtains much more accurate uncertainty estimates than an LSTM or Gated Recurrent Units (GRUs) (Cho et al., 2014) while also showing a slightly improved prediction performance and outperforms various recent generative models on an image imputation task.