Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2606.31990

Evaluation of Population Initialization Methods for Genetic Programming-based Symbolic Regression

Lukas Kammerer·Gabriel Kronberger·Deaglan J. Bartlett·Harry Desmond·Pedro G. Ferreira·Stephan Winkler
View original source ↗Read source document ↗Export metadata ↓

Abstract

We analyze the effect of optimizing the initial population of genetic programming (GP) for symbolic regression (SR) on the accuracy and complexity of solutions. We compare three well-established random initialization methods as well as initialization with small optimized solutions from exhaustive symbolic regression (ESR) using a GP/SR implementation which is based on the multi-objective evolutionary algorithm NSGA-II. We compare the final Pareto fronts found with each initialization method on twelve synthetic problems of varying complexity and one real-world dataset. We find no significant differences in accuracy or model complexity among the initialization methods. The initial advantage of initialization with ESR disappears after only a few generations. Our results show that, given similar diversity in the initial population, the effect of the initialization method in GP-based symbolic regression on the final Pareto front is negligible.

Explore related subjects

cs.NEcs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lukas Kammerer, Gabriel Kronberger, Deaglan J. Bartlett, Harry Desmond, Pedro G. Ferreira, Stephan Winkler. 2026-06-30. Evaluation of Population Initialization Methods for Genetic Programming-based Symbolic Regression. https://arxiv.org/abs/2606.31990

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Rethinking Pairwise Token Interaction in Spiking Transformers

Spiking Transformers inherit token interaction mechanisms from conventional Transformers, yet their sparse binary representations fundamentally alter how token-to-token communication is established. In particular, spike-based query-key matching produces highly sparse and input-dependent interaction patterns, coupling information propagation to the instantaneous availability of matching spike events. This motivates a different interaction paradigm in which long-range communication does not rely solely on pairwise spike coincidence. We therefore propose Gated Spike Axial Propagation (GSAP), a spike-native token interaction mechanism that decouples information propagation from context selection. Instead of directly determining communication through query-key matching, GSAP first propagates spike-based context along the horizontal and vertical axes, allowing information to reach distant tokens through structured sequential propagation. A receiver-conditioned gate then determines how much of the propagated context is incorporated at each token, while a lightweight local pathway preserves fine-grained neighborhood information. In this way, GSAP reformulates token interaction as a propagate-then-select process, enabling structured long-range communication while retaining the sparse event-driven nature of spiking representations. Code is available at https://github.com/Fancyssc/GSAP.

cs.NE↗
arXiv2026

NeuroRule: Making Black-Box Neural Networks Explainable through Rule-set Evolution

High-capacity neural network models have achieved state-of-the-art performance across diverse classification tasks, yet they frequently operate as black-box models, lacking the transparency necessary for critical decision-making. Such opacity creates a persistent trade-off between performance and explainability. This paper proposes a solution to address this gap: the NeuroRule knowledge distillation framework that results in explainable rule-sets from neural network models. NeuroRule adapts the EVOTER rule-set evolution infrastructure to treat neural networks as targets for the evolution process, distilling their performance into concise sets of propositional logic expressions. There are three primary contributions: (1) an evolutionary method for distilling black-box neural network models into explicit rule-set models; (2) a method for making rule sets more explainable by including a conciseness objective to evolution; and (3) a demonstration that the distillation is viable even without access to the original neural network training data. The paper thus establishes that black-box neural network models can be made explainable and therefore useful in real-world applications where trustworthiness is paramount.

cs.NE↗
arXiv2026

The Computational Value of Sensory-Aligned Receptive Fields Depends on Neuronal Expressivity

Biological sensory neurons have selective receptive fields organized along meaningful stimulus coordinates, such as frequency, motion direction, or retinotopic position. Such structure may arise from efficient coding and biological constraints on activity, connectivity, and wiring, as computational studies of simple neurons have shown across modalities. This raises a question: do structured receptive fields confer a computational advantage beyond resource efficiency itself, and does this advantage persist when individual neurons are highly expressive? We address this question in recurrent networks of Expressive Leaky Memory neurons, where we can independently vary neuronal complexity and the organization of feed-forward receptive fields. Across auditory and event-based visual classification tasks, receptive fields aligned with a task-relevant sensory coordinate improve test accuracy relative to budget-matched random receptive fields. This advantage disappears when sensory coordinates are scrambled, or when receptive fields follow task-irrelevant coordinates, showing that the benefit comes from alignment with task geometry rather than restricted connectivity alone. Increasing neuronal complexity reduces the performance advantage of structured receptive fields. Finally, generic synaptic sparsity regularization induces input selectivity and partially recovers performance, but remains substantially below explicitly structured receptive fields, suggesting that sparsity alone is insufficient to recover the full computational benefit of task-aligned receptive fields. Together, our results show that appropriate receptive fields can serve as a computational prior beyond sparsity itself, and that their value depends on the computational expressivity of individual neurons.

cs.NE↗