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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.

As large language models (LLMs) permeate more and more applications, an assessment of their associated security risks becomes increasingly necessary. The potential for exploitation by malicious actors, ranging from disinformation to data breaches and reputation damage, is substantial. This paper addresses a gap in current research by specifically focusing on security risks posed by LLMs within the prompt-based interaction scheme, which extends beyond the widely covered ethical and societal implications. Our work proposes a taxonomy of security risks along the user-model communication pipeline and categorizes the attacks by target and attack type alongside the commonly used confidentiality, integrity, and availability (CIA) triad. The taxonomy is reinforced with specific attack examples to showcase the real-world impact of these risks. Through this taxonomy, we aim to inform the development of robust and secure LLM applications, enhancing their safety and trustworthiness.

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.

Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value function and policy mappings. Commonly used numerical approximators, such as neural networks or basis function expansions, have two main drawbacks: they are black-box models offering little insight into the mappings learned, and they require extensive trial and error tuning of their hyper-parameters. In this paper, we propose a new approach to constructing smooth value functions in the form of analytic expressions by using symbolic regression. We introduce three off-line methods for finding value functions based on a state-transition model: symbolic value iteration, symbolic policy iteration, and a direct solution of the Bellman equation. The methods are illustrated on four nonlinear control problems: velocity control under friction, one-link and two-link pendulum swing-up, and magnetic manipulation. The results show that the value functions yield well-performing policies and are compact, mathematically tractable, and easy to plug into other algorithms. This makes them potentially suitable for further analysis of the closed-loop system. A comparison with an alternative approach using neural networks shows that our method outperforms the neural network-based one.

Continual model learning for nonlinear dynamic systems, such as autonomous robots, presents several challenges. First, it tends to be computationally expensive as the amount of data collected by the robot quickly grows in time. Second, the model accuracy is impaired when data from repetitive motions prevail in the training set and outweigh scarcer samples that also capture interesting properties of the system. It is not known in advance which samples will be useful for model learning. Therefore, effective methods need to be employed to select informative training samples from the continuous data stream collected by the robot. Existing literature does not give any guidelines as to which of the available sample-selection methods are suitable for such a task. In this paper, we compare five sample-selection methods, including a novel method using the model prediction error. We integrate these methods into a model learning framework based on symbolic regression, which allows for learning accurate models in the form of analytic equations. Unlike the currently popular data-hungry deep learning methods, symbolic regression is able to build models even from very small training data sets. We demonstrate the approach on two real robots: the TurtleBot mobile robot and the Parrot Bebop drone. The results show that an accurate model can be constructed even from training sets as small as 24 samples. Informed sample-selection techniques based on prediction error and model variance clearly outperform uninformed methods, such as sequential or random selection.