Many real-world systems can be naturally described by mathematical formulas. The task of automatically constructing formulas to fit observed data is called symbolic regression. Evolutionary methods such as genetic programming have been commonly used to solve symbolic regression tasks, but they have significant drawbacks, such as high computational complexity. Recently, neural networks have been applied to symbolic regression, among which the transformer-based methods seem to be most promising. After training a transformer on a large number of formulas, the actual inference, i.e., finding a formula for new, unseen data, is very fast (in the order of seconds). This is considerably faster than state-of-the-art evolutionary methods. The main drawback of transformers is that they generate formulas without numerical constants, which have to be optimized separately, yielding suboptimal results. We propose a transformer-based approach called SymFormer, which predicts the formula by outputting the symbols and the constants simultaneously. This helps to generate formulas that fit the data more accurately. In addition, the constants provided by SymFormer serve as a good starting point for subsequent tuning via gradient descent to further improve the model accuracy. We show on several benchmarks that SymFormer outperforms state-of-the-art methods while having faster inference.

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data. Historically, symbolic regression has been predominantly realized by genetic programming, a method that evolves populations of candidate solutions that are subsequently modified by genetic operators crossover and mutation. However, this approach suffers from several deficiencies: it does not scale well with the number of variables and samples in the training data-models tend to grow in size and complexity without an adequate accuracy gain, and it is hard to fine-tune the model coefficients using just genetic operators. Recently, neural networks have been applied to learn the whole analytic model, i.e., its structure and the coefficients, using gradient-based optimization algorithms. This paper proposes a novel neural network-based symbolic regression method that constructs physically plausible models based on even very small training data sets and prior knowledge about the system. The method employs an adaptive weighting scheme to effectively deal with multiple loss function terms and an epoch-wise learning process to reduce the chance of getting stuck in poor local optima. Furthermore, we propose a parameter-free method for choosing the model with the best interpolation and extrapolation performance out of all the models generated throughout the whole learning process. We experimentally evaluate the approach on four test systems: the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the longitudinal force of the anti-lock braking system. The results clearly show the potential of the method to find parsimonious models that comply with the prior knowledge provided.

This letter introduces a dataset for training and evaluating methods for 6D pose estimation of hand-held tools in task demonstrations captured by a standard RGB camera. Despite the significant progress of 6D pose estimation methods, their performance is usually limited for heavily occluded objects, which is a common case in imitation learning, where the object is typically partially occluded by the manipulating hand. Currently, there is a lack of datasets that would enable the development of robust 6D pose estimation methods for these conditions. To overcome this problem, we collect a new dataset (Imitrob) aimed at 6D pose estimation in imitation learning and other applications where a human holds a tool and performs a task. The dataset contains image sequences of nine different tools and twelve manipulation tasks with two camera viewpoints, four human subjects, and left/right hand. Each image is accompanied by an accurate ground truth measurement of the 6D object pose obtained by the HTC Vive motion tracking device. The use of the dataset is demonstrated by training and evaluating a recent 6D object pose estimation method (DOPE) in various setups.

Novel view synthesis is a long-standing problem. In this work, we consider a variant of the problem where we are given only a few context views sparsely covering a scene or an object. The goal is to predict novel viewpoints in the scene, which requires learning priors. The current state of the art is based on Neural Radiance Field (NeRF), and while achieving impressive results, the methods suffer from long training times as they require evaluating millions of 3D point samples via a neural network for each image. We propose a 2D-only method that maps multiple context views and a query pose to a new image in a single pass of a neural network. Our model uses a two-stage architecture consisting of a codebook and a transformer model. The codebook is used to embed individual images into a smaller latent space, and the transformer solves the view synthesis task in this more compact space. To train our model efficiently, we introduce a novel branching attention mechanism that allows us to use the same model not only for neural rendering but also for camera pose estimation. Experimental results on real-world scenes show that our approach is competitive compared to NeRF-based methods while not reasoning explicitly in 3D, and it is faster to train.

Deep neural networks designed for vision tasks are often prone to failure when they encounter environmental conditions not covered by the training data. Single-modal strategies are insufficient when the sensor fails to acquire information due to malfunction or its design limitations. Multi-sensor configurations are known to provide redundancy, increase reliability, and are crucial in achieving robustness against asymmetric sensor failures. To address the issue of changing lighting conditions and asymmetric sensor degradation in object detection, we develop a multi-modal 2D object detector, and propose deterministic and stochastic sensor-aware feature fusion strategies. The proposed fusion mechanisms are driven by the estimated sensor measurement reliability values/weights. Reliable object detection in harsh lighting conditions is essential for applications such as self-driving vehicles and human-robot interaction. We also propose a new 'r-blended' hybrid depth modality for RGB-D sensors. Through extensive experimentation, we show that the proposed strategies outperform the existing state-of-the-art methods on the FLIR-Thermal dataset, and obtain promising results on the SUNRGB-D dataset. We additionally record a new RGB-Infra indoor dataset, namely L515-Indoors, and demonstrate that the proposed object detection methodologies are highly effective for a variety of lighting conditions.

Even though various frameworks exist for reasoning under uncertainty, a realistic fault diagnosis task does not fit into any of them in a straightforward way. For each framework, only part of the available data and knowledge is in the desired format. Moreover, additional criteria, like clarity of inference and computational efficiency, require trade-offs to be made. Finally, fault diagnosis is usually just a subpart of a larger process, e.g. condition-based maintenance. Consequently, the final goal of fault diagnosis is not (just) decision making, and the outcome of the diagnosis process should be a suitable input for the subsequent reasoning process. In this paper, we analyze how a knowledge-based diagnosis task is influenced by uncertainty, investigate which additional objectives are of relevance, and compare how these characteristics and objectives are handled in two well-known frameworks, namely the Bayesian and the Dempster-Shafer reasoning framework. In contrast to previous works, which take the reasoning method as the starting point, we start from the application, knowledge-based fault diagnosis, and examine the effectiveness of different reasoning methods for this specific application. It is concluded that the suitability of each reasoning method highly depends on the problem under consideration and on the requirements of the user. The best framework can only be assigned given that the problem (including uncertainty characteristics) and the user requirements are completely known.