The paper introduces an exhaustive dataset of univariate canonical skeletons for neural symbolic regression, generated deterministically via a constrained context-free grammar. These skeletons serve as generic structural representations that eliminate redundant expressions and provide uniform operator distribution, thereby avoiding simplicity bias. The authors also present a sampling strategy for clean numerical data and benchmark 150 SR problems across three tiers, demonstrating challenges for current state‑of‑the‑art methods.
arXiv:2511. 04124v3 Announce Type: replace Abstract: Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data.
MOSAIC‑SR is a new symbolic regression method that combines a pretrained Transformer with search‑based refinement. The Transformer generates multiple initial sketches, which seed searches that jointly recover equation structure and constants using scale‑aware optimization and symbolic repair. On the SRSD‑Feynman dataset and six other benchmarks, MOSAIC‑SR achieves the highest symbolic solution rate and ranks among the top two in predictive accuracy, even when irrelevant dummy variables are present.
Neural Symbolic Regression (NSR) uses neural networks as functional preconditioners to learn smooth, noise‑robust approximations of target functions in an interaction‑aware nonlinear feature space. A subsequent LASSO step extracts sparse, interpretable closed‑form expressions, while distributed hyperparameter optimization with Ray Tune and ASHA scheduling improves predictive accuracy and symbolic fidelity. Experiments on the Nguyen benchmark demonstrate that NSR outperforms SINDy and untuned neural baselines in RMSE, noise robustness, and out‑of‑distribution generalization, with ablation studies highlighting the importance of feature interactions, neural depth, and tuning strategies.
SMILE (Sine, Multiplication, Identity, Logarithm, Exponential) is a hybrid framework that merges continuous gradient-based optimization with discrete symbolic recovery for symbolic regression. It operates in three stages: structural analysis to uncover the compositional hierarchy of the target expression, continuous optimization to learn parameters of a network using interpretable activations, and symbolic recovery via structured pruning, coefficient optimization, and rounding to produce a compact expression with exact symbolic constants. Evaluated on SRBench, SMILE achieves the highest symbolic solution rate under high noise, remains on the Pareto front of accuracy versus complexity, and recovers simpler expressions much faster than competing methods.
arXiv:2606. 06724v1 Announce Type: new Abstract: Representative data is fundamental in machine learning, as limited data hinders generalisation.
arXiv:2608. 02628v1 Announce Type: cross Abstract: Symbolic regression (SR) is the task of discovering underlying patterns from data and representing them using mathematical expressions.
arXiv:2608. 09617v1 Announce Type: new Abstract: Symbolic regression is the problem of finding an algebraic expression describing a stochastic dependence of a target variable on a set of inputs.
arXiv:2602. 23561v2 Announce Type: replace-cross Abstract: Symbolic regression (SR) has gained recent traction in AI-driven scientific discovery for learning closed-form physical laws.
The paper introduces SAE‑IDF, a data‑driven approach that uses sparse autoencoders to encode symbols into interpretable sparse codes, re‑weights dimensions by rarity, and matches units across heterogeneous symbolic systems. On 12 tasks spanning six symbolic system types, SAE‑IDF outperforms dense LLM baselines (Gemma‑2‑9B and Llama‑3.1‑8B) by up to 45 points, consistently across layers and configurations. Each sparse dimension carries a human‑readable meaning, allowing matches to decompose into named concepts, thereby enabling a scalable, universal symbolic backbone.
arXiv:2609.36187v1 Announce Type: new Abstract: Symbolic Regression (SR) is a data-driven method for scientific discovery which searches for interpretable analytical relationships within data. Recent...
arXiv:2610.01519v1 Announce Type: cross Abstract: Neuro-Symbolic (NeSy) predictors incorporate prior knowledge into the prediction process of neural networks, ensuring that outputs satisfy specified...
arXiv:2608. 04060v1 Announce Type: cross Abstract: Joint-embedding predictive architectures learn abstract states by predicting target embeddings from context embeddings, but their transition models are typically opaque neural maps.