The last few years have witnessed a surge in methods for symbolic regression, from advances in traditional evolutionary approaches to novel deep learning-based systems. Individual works typically focus on advancing the state-of-the-art for one particular class of solution strategies, and there have been few attempts to investigate the benefits of hybridizing or integrating multiple strategies. In this work, we identify five classes of symbolic regression solution strategies---recursive problem simplification, neural-guided search, large-scale pre-training, genetic programming, and linear models---and propose a strategy to hybridize them into a single modular, unified symbolic regression framework. Based on empirical evaluation using SRBench, a new community tool for benchmarking symbolic regression methods, our unified framework achieves state-of-the-art performance in its ability to (1) symbolically recover analytical expressions, (2) fit datasets with high accuracy, and (3) balance accuracy-complexity trade-offs, across 252 ground-truth and black-box benchmark problems, in both noiseless settings and across various noise levels. Finally, we provide practical use case-based guidance for constructing hybrid symbolic regression algorithms, supported by extensive, combinatorial ablation studies.

We present SymFlux, a novel deep learning framework that performs symbolic regression to identify Hamiltonian functions from their corresponding vector fields on the standard symplectic plane. SymFlux models utilize hybrid CNN-LSTM architectures to learn and output the symbolic mathematical expression of the underlying Hamiltonian. Training and validation are conducted on newly developed datasets of Hamiltonian vector fields, a key contribution of this work. Our results demonstrate the model's effectiveness in accurately recovering these symbolic expressions, advancing automated discovery in Hamiltonian mechanics.

The last few years have witnessed a surge in methods for symbolic regression, from advances in traditional evolutionary approaches to novel deep learning-based systems. Individual works typically focus on advancing the state-of-the-art for one particular class of solution strategies, and there have been few attempts to investigate the benefits of hybridizing or integrating multiple strategies. In this work, we identify five classes of symbolic regression solution strategies---recursive problem simplification, neural-guided search, large-scale pre-training, genetic programming, and linear models---and propose a strategy to hybridize them into a single modular, unified symbolic regression framework. Based on empirical evaluation using SRBench, a new community tool for benchmarking symbolic regression methods, our unified framework achieves state-of-the-art performance in its ability to (1) symbolically recover analytical expressions, (2) fit datasets with high accuracy, and (3) balance accuracy-complexity trade-offs, across 252 ground-truth and black-box benchmark problems, in both noiseless settings and across various noise levels. Finally, we provide practical use case-based guidance for constructing hybrid symbolic regression algorithms, supported by extensive, combinatorial ablation studies.

As mobile networks embrace the 5G era, the interest in adopting Reinforcement Learning (RL) algorithms to handle challenges in ultra-low-latency and high throughput scenarios increases. Simultaneously, the advent of packetized fronthaul networks imposes demanding requirements that traditional congestion control mechanisms cannot accomplish, highlighting the potential of RL-based congestion control algorithms. Although learning RL policies optimized for satisfying the stringent fronthaul requirements is feasible, the adoption of neural network models in real deployments still poses some challenges regarding real-time inference and interpretability. This paper proposes a methodology to deal with such challenges while maintaining the performance and generalization capabilities provided by a baseline RL policy. The method consists of (1) training a congestion control policy specialized in fronthaul-like networks via reinforcement learning, (2) collecting state-action experiences from the baseline, and (3) performing deep symbolic regression on the collected dataset. The proposed process overcomes the challenges related to inference-time limitations through closed-form expressions that approximate the baseline performance (link utilization, delay, and fairness) and which can be directly implemented in any programming language. Finally, we analyze the inner workings of the closed-form expressions.